¢±ñ(b!bb1â1ÄãˆRDâ „QŽ¨@Pž|±ñb)bâiÄ3ˆgËÏ!žGT"œ@ï6+$..éwºæªBáùÿ~Ñ‚àøÕ*ø„N‚ëZ†ß•MuÍxSsZ|~W{{µ§Û÷fMç[ÞÏÛÞn°h›}Þn[½w«­±³ÃãßÔ×ÑÖÙŽ‡j:{»|Þ.:M]³Í½­§ËƒÞ¢Ÿ_áXYáj˜M/¶ºþ(ž‡õ<“îÀÂÀ@u+Ö̦úpJ[kBKþîªÅŠ«´ue«;@_—ÉÈЋ‡™0œ yÜG_6h„=öº±‰£V¬¯ÃÍžTkÂV¤Ÿ-ž´‡¼ÌÀiö;ÁÉÁ
GøAÍþ2Á
ߎçß Ôh-±§¥sìçþÎ…3£:ç)Œ²i»@rtÍä’s÷³ú?¡½›üF#m2XÕÓ>w7ŠA#šÿß–ž›Šâ†œ;™tŠ¬‘Â.Öb2Ýf¤c˜IùJEÛ1:QÈ´âڍjŒÃ…Z9+Ú²9ù<#7¬í_L9v‘΄Ã$+uBÆú¢ Sæ&­˜©é,#Ôyz65÷mÆi¼ŠQ/YÔGµ\îö£Øÿ›;uï–0Ú#Lz2f)‚¡:Ï°kð'+œ;}{ë„Íqg«Ï´ñ0qµ3qnXbg‘í}âX©ïb}¼¾çåÖ(÷-Ä/ŒÞgcg˜ g¶Šñ÷O4~Ñ›€Ç¸Eµ©ñ¨ËSÁcwj<<…*x´¤ÆcW± {Rãqd‘ ¯¦ÂcDó†šç±7#šE*x¬K…‡}®m”HkBÁ¥sôœÇÌ  j)År+«Õ°Äpž‰¶*¸¡Ù©Ù ñ1mQ²r8BVôšïÒÅ(ò®•:d—Y%/ÚèK•INЭ£w8ÄÏ>~ƒnÿâð¢Ý³šõù©Ù q‹¼ƒdQ¶r™­‚h+,IvA+ôVà^×üža7ÙjmßÃm·Z؆˜¾œ›ÚBLÁ1ÐìnlZ•] ³”?'†¥è({ý¯ë‰FY›C¶acgÄðÉèlq@Ù†R”•ÙËì‘Q¦×|\9Ž²0¿ý@â¹nPÃÕ´Aï€N»Ó‰pøù^Ý^þ†ÎÏ¥ÝakN¤·•9?š
<­ohRÄË+5k,|æm"ó6‘y›{›[©Óz^Lø eh³}ç…wôÇ’¦¾îo¦˜¥yr>”/ÚÛVˆÎ'J[½«þ¥Ðƒ±qÞ ¾·Dk÷¤ãÈl[Vî°¹·ôzz|~!ó¸W j|°œb|)–ŸÙ¢0‚ðÂÂþ¤œ)“_þý—ø9÷4Õ%Qûé.SÙ¾üÿJúo,]t2õßÉÒe§«þ;iù_aÅ&ëσ舗ïˆús%œ„Ów¦¾þcµø×\n‰cÍ5=Wl 1¤¤ÿ^Âd¨Çƒ§t²þ»š'o¿&MPÿå†s”õß³ˆ~<ÜÃÅÖû!ZÿU¡ÿÖæš*£4¨–¼Gãé¿£ÌWÿý2×pA¹ïøúÖ(;WÿÅñ7O4þx:Ý(ûƪ‚ÇÅTxä26U+ÈwñÒÒ¶ v°€ûŒKÍŠ²B²2Ì%¥žÅ⩆ˆÊُaŠÙp’ZV,Fæ -ZùÈ*V·;B¹Êe×âj=èq-Ç®Ç÷¸(ÕÄ~‹«ä Ï]:¡h%Ä+Rs:-ûù:à)ÿP†b!}fefÛ‡w¶MJ)8J>­Œü’¸RÑÿ¿úoFÿ™Þå_™·‚‚r´

³„¢0¯-²Ê´š»Pèð
¹¿²ö
ÁæªéGì!•$à&Œï(£
- ˆ9
8 : ÿž
> ­§2ªA”C …ÑOÚGp0دãq™g·â b(­/PPö>F
‰C
Ä™
œ
X0\
á¬ó P¤ØÃiÆúÈ؍Ÿ
4¡
L£
d¥
|§
”©
¬«
Ä­
ܯ
ô±
´
$¶
<¸
Tº
l¼
„¾
œÀ
´Â
ÌÄ
äÆ
üÈ
Ë
,Í
DÏ
\Ñ
tÓ
ŒÕ
¤×
¼Ù
ÔÛ
ìÝ
à
â
4ä
Læ
…üdè
O>
|ê
²;
 ì
ì@
Äî
õ&
ÙÉ6
Š
Å1èЇ
é(€àx/ _A

 F ò
ÌžÍ

Ã
n
–ºEquation ºEquation.DSMT40º*MathType 5.0 Equation̨Í

Ã
š
–ºGrafico ºMSGraph.þÿ

à…ŸòùOh«‘+'³Ù0¼T
hpœ¨ ´À àì ø

äPowerPoint Presentation 502Microsoft PowerPoint@ز9Ý@@¼3ÐÝvÇ
V G¨Sÿÿÿÿ‰g
Ì)
¡'
ÑÁ ÷
€€€€€€€€€ÀÀÀÀÜÀ¦Êð""")))UUUMMMBBB999ÿ|€ÿPPÖ“ÌìÿïÖÆççÖ­©3f™Ì333f3™3Ì3ÿ3f3fff™fÌfÿf™3™f™™™Ì™ÿ™Ì3ÌfÌ™ÌÌÌÿÌfÿ™ÿÌÿ333f3™3Ì3ÿ333333f33™33Ì33ÿ33f33f3ff3™f3Ìf3ÿf3™33™3f™3™™3Ì™3ÿ™3Ì33Ì3fÌ3™Ì3ÌÌ3ÿÌ33ÿ3fÿ3™ÿ3Ìÿ3ÿÿ3f3fff™fÌfÿf3f33ff3f™3fÌ3fÿ3fff3fffff™ffÌff™f3™ff™f™™fÌ™fÿ™fÌf3Ìf™ÌfÌÌfÿÌfÿf3ÿf™ÿfÌÿfÿÌÌÿ™™™3™™™Ì™™33™f™Ì3™ÿ™f™3f™f3™™f™Ìf™ÿ3™3™™f™™™™™Ì™™ÿ™™Ì™3Ì™fÌf™Ì™ÌÌ™ÿÌ™ÿ™3ÿ™fÌ™™ÿ™Ìÿ™ÿÿ™Ì3™fÌ™ÌÌÌ3™33Ìf3Ì™3ÌÌ3Ìÿ3ÌfÌ3fÌff™™fÌÌfÌÿf™™Ì3™Ìf™Ì™™ÌÌ™Ìÿ™ÌÌÌ3ÌÌfÌÌ™ÌÌÌÌÌÿÌÌÿÌ3ÿÌfÿ™™ÿÌÌÿÌÿÿÌ3Ìfÿ™ÿ3Ì33ÿf3ÿ™3ÿÌ3ÿÿ3ÿfÿ3fÿffÌ™fÿÌfÿÿfÌ™ÿ3™ÿf™ÿ™™ÿÌ™ÿÿ™ÿÌÿ3ÌÿfÌÿ™ÌÿÌÌÿÿÌÿ3ÿÿfÿÌ™ÿÿÌÿÿÿfffÿfÿÿfffÿÿfÿfÿÿ¥!___www†††–––ËË˲²²×××ÝÝÝãããêêêñññøøøÿûð  ¤€€€ÿÿÿÿÿÿÿÿÿÿÛ4
¡'A Ìx ÐÀ( x
K€€€€€€€€€ÀÀÀÀÜÀðʦ""")))UUUMMMBBB999€|ÿPPÿ“ÖÿìÌÆÖïÖç琩­3f™Ì3333f3™3Ì3ÿff3fff™fÌfÿ™™3™f™™™Ì™ÿÌÌ3ÌfÌ™ÌÌÌÿÿfÿ™ÿÌ3333f3™3Ì3ÿ3333333f33™33Ì33ÿ3f3f33ff3f™3fÌ3fÿ3™3™33™f3™™3™Ì3™ÿ3Ì3Ì33Ìf3Ì™3ÌÌ3Ìÿ3ÿ33ÿf3ÿ™3ÿÌ3ÿÿff3fff™fÌfÿf3f33f3ff3™f3Ìf3ÿffff3fffff™ffÌf™f™3f™ff™™f™Ìf™ÿfÌfÌ3fÌ™fÌÌfÌÿfÿfÿ3fÿ™fÿÌÌÿÿÌ™™™3™™™™Ì™™33™f™3Ì™ÿ™f™f3™3f™f™™fÌ™3ÿ™™3™™f™™™™™Ì™™ÿ™Ì™Ì3fÌf™Ì™™ÌÌ™Ìÿ™ÿ™ÿ3™Ìf™ÿ™™ÿÌ™ÿÿÌ™3ÌfÌ™ÌÌ™3Ì33Ì3fÌ3™Ì3ÌÌ3ÿÌfÌf3™ffÌf™ÌfÌ™fÿ̙̙3Ì™fÌ™™Ì™ÌÌ™ÿÌÌÌÌ3ÌÌfÌÌ™ÌÌÌÌÌÿÌÿÌÿ3™ÿfÌÿ™ÌÿÌÌÿÿÌ3ÿfÿ™Ì3ÿ33ÿ3fÿ3™ÿ3Ìÿ3ÿÿfÿf3Ìffÿf™ÿfÌÌfÿÿ™ÿ™3ÿ™fÿ™™ÿ™Ìÿ™ÿÿÌÿÌ3ÿÌfÿÌ™ÿÌÌÿÌÿÿÿ3Ìÿfÿÿ™ÿÿÌffÿfÿffÿÿÿffÿfÿÿÿf!¥___www†††–––ËË˲²²×××ÝÝÝãããêêêñññøøøðûÿ¤  €€€ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ@F?F?F?F@F?F?F?F@F?F?F?F@F?F?F?F@F?F?F?F@F?F?F?F@F?F?F?F@F?F?F?F@F?F?F?F@F?F?F?F@F?F?F?F@F?F?F?F@F?F?F?F@F?F?F?F@F?F?F?F@F?F?F?ÿÿÿÿÿÿÿÿÿÿÿÿÿÿ¼’’’’’¼¼ÿÿÿÿÿÿÿÿÿÿFFFEFEon¼“oEFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFÿÿÿÿÿÿÿÿÿÿÿÿ¼’’¼’¼’’’’’ÿÿÿÿÿÿÿÿÿFFn¼’¼¼â’¼nEFF?FF?FF?FF?FF?FF?FF?FF?FF?FF?FF?FF?FF?FF?FF?FF?FF?FF?FF?FF?FF?FF?FF?FF?FF?FF?FF?FF?ÿÿÿÿÿÿÿÿÿ¼ÿ’’’’m’’’’’mmm¼ÿÿÿÿÿÿÿF?o’¼¼¼¼¼’¼¼¼’oFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFÿÿÿÿÿÿÿÿÿÿ¼’’’m¼¼¼¼¼’’’’mÿÿÿÿÿÿÿ?E“ÿ¼¼’¼’mm’¼¼’E?F?F@F?F?F?F@F?F?F?F@F?F?F?F@F?F?F?F@F?F?F?F@F?F?F?F@F?F?F?F@F?F?F?F@F?F?F?F@F?F?F?F@F?F?F?F@F?F?F?F@F?F?F?F@F?ÿÿÿÿÿÿÿÿÿÿ’’’m¼’’mmm¼¼’’mmÿÿÿÿÿÿFn¼¼¼Cmmmm¼¼»nFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFÿÿÿÿÿÿÿÿÿÿ’’m¼’m’¼’¼’¼’’mm¼ÿÿÿÿÿE¼’¼CCCCCmmmm’’¼EF?FF?F?F?FF?F?F?FF?F?F?FF?F?F?FF?F?F?FF?F?F?FF?F?F?FF?F?F?FF?F?F?FF?F?F?FF?F?F?FF?F?F?FF?F?F?FF?ÿÿÿÿÿÿÿÿÿ’’m’m’m’¼¼m’mmm’m’ÿÿÿÿÿo¼ÿ’mmmm’Cmmm’ÿ¼ŽFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFÿÿÿÿÿÿÿÿÿ’’’’’mm’¼’’’’m¼’’mÿÿÿÿÿn¼¼mCmCmmmC’Cs¼¼’F?F?F?F@F?F?F?F@F?F?F?F@F?F?F?F@F?F?F?F@F?F?F?F@F?F?F?F@F?F?F?F@F?F?F?F@F?F?F?F@F?F?F?F@F?F?F?F@F?F?F?F@F?F?F?ÿÿÿÿÿÿÿÿÿm’m’’mm’’¼ø’m’’’mmÿÿÿÿÿ“ÿÿmmmmC’CCmmm¼¼¼FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFÿÿÿÿÿÿÿÿÿ’’’’¼m’’’¼’’’m¼’’mÿÿÿÿÿn¼’’CmmmmmCmCm’¼nF?FF?FF?FF?FF?FF?FF?FF?FF?FF?FF?FF?FF?FF?FF?FF?FF?FF?FF?FF?FF?FF?FF?FF?FF?FF?FF?FF?ÿÿÿÿÿÿÿÿÿm’m’’’m’m’m’mm’’’’ÿÿÿÿÿo»¼’mmmCCmmmm’¼¼oFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFÿÿÿÿÿÿÿÿÿ’’’m’¼’’’’¼’m’’ø’ÿÿÿÿÿE“’¼’mCCCmmCm¼’’EF?F@F?F?F?F@F?F?F?F@F?F?F?F@F?F?F?F@F?F?F?F@F?F?F?F@F?F?F?F@F?F?F?F@F?F?F?F@F?F?F?F@F?F?F?F@F?F?F?F@F?F?F?F@F?ÿÿÿÿÿÿÿÿÿ¼’’m’’m’’’’¼’’m’mÿÿÿÿÿÿFn¼¼¼mmCCmmC¼¼¼nFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFÿÿÿÿÿÿÿÿÿÿ’¼m’’’m¼¼’’’m’m’ÿÿÿÿÿÿE’¼’¼mmCm’¼’’’FF?FF?F?F?FF?F?F?FF?F?F?FF?F?F?FF?F?F?FF?F?F?FF?F?F?FF?F?F?FF?F?F?FF?F?F?FF?F?F?FF?F?F?FF?F?F?FF?ÿÿÿÿÿÿÿÿÿÿ¼’¼m’’¼’’’mm’mm¼ÿÿÿÿÿÿFEi’¼’¼’’’¼’¼’oFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFÿÿÿÿÿÿÿÿÿÿÿ¼’¼’’’¼m’’¼’’¼ÿÿÿÿÿÿÿEFFn’’¼ÿ¼’’nFFEF?F?F?F@F?F?F?F@F?F?F?F@F?F?F?F@F?F?F?F@F?F?F?F@F?F?F?F@F?F?F?F@F?F?F?F@F?F?F?F@F?F?F?F@F?F?F?F@F?F?F?F@F?F?F?ÿÿÿÿÿÿÿÿÿÿÿÿÿ’’’¼’¼m’m’¼ÿÿÿÿÿÿÿÿFFFEFEon“noEFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFÿÿÿÿÿÿÿÿÿÿÿÿÿÿ¼¼’’’’’ÿÿÿÿÿÿÿÿÿÿÿ¨¬-oÕ¶k«;Ð{­¡÷È^†w”’ï[û†ÐÑ3ù(0p¥ñYô'/înï8˜^$p%l Ç*:“:•d €N¥o÷
QI}¼ðþÚ†³ /9×àBmcid>o]ûéÊß×Lûúa% W²¼,ù8z·‹X§Š«=÷­¥-8?†Aýi?ê QÐÉš óô¡˜GèU^¹o½}i~ŽÌo­}²´ã@f@dQÅ!ô<Qý:F>VÄ•î¢J&QiÑYÞ©mÂ,ŠF9üØÕv˜²DDC獀¶²Dk»pŁK›+pu» gü^3H_?wº‡”¶Ó¸Ò=T©Ÿ¨T[…˵͝­µËWwÖj›¸§
œŸÅÝ âšC¸ß¬¯øžtD¡¯’nóÝœST“W¸¡ùnúv?E•ˆˆ±KCà¤æ”jg>„žÞŸðÝœS"×÷Þ¡½ï:?K)w~Né#bÞÝ\ßõmGÖ]@ÝxjHÏ°6RÙ)ßµ9%MT"m߆QŽÃÏOk”ÖÚëÞ‹àŽæõ~x``Ï/^˜‡W;¾ÏàÇDÖK¾w4›È™¿zy}m.:CøÓò:Ä|y÷sþÓ5"{¼ô÷kC"¢àÎX€Ç²tGë'ch´ÑªbtÓÕ’Ñý­š¢»ëôžá9ý ÄûÀé­(§Oû~ìýDÖ¡ÓØ?æwÐÓg–DÔ€ó¤§g|O÷Œ£DÍ,ìAíò4ŒÜ=#MÔ#-…‘äøù­¸6-Þ´½i1b°›ò¾µë«Y\qè`ZülKDĘ3äOÛ"xh›ÄgããõÚ®³r\ôûô:<œ:ùYndŸÓ¤¦ŸŒy.&Ë]- “eiVM1Ù½ÞJyßÉÝ¿öu<„›]¯„¯¥%"êKt%ìúø^Ú$Îð|üª¬7‚>AŠŽ1ÏËaYº•JõÄ8,KÑŠ‡Þ~æ_o7ñ@=†ìíœÀËú« ö1OÑqk¿‡6N §àç6ŠçWIá}‡xÞz¿•p½¼"ž7‹Þ?¯$[¬¿ÛZ²õÉÖ{l$[oÄNæ焝l½ÝT²þnò¢vß·%Þî»ß°ÿ8Ü}Ëþ¤Y–é=÷¹bqâùÁßæ´Õ ÷Ü`”Prҏq$‹ØI&ðœÍüJÃ(§32U¿§wËTÕ>?f\•‰½R~’Ìÿ‚ÞóM†©2u‹Ø
ò|Uôža2LÕï¦L\iU£ô52TÕ7¶E\ S|Uÿ¡®¡ª®§eb*NäÈüߨk̍†2¨êhbŽË­}šA5FžŽòØ'¯,Ëdë±32NÞ;h½¢’l=vFÆíÏÕ’­ÇÎȸëýi$[‘qýÌÚÉÖcgdÜþ> ä±»©VpÆá ;ãZ1f\‹qÞ÷¶cƵØ7Eæ33nj4p¢…fœ2ãXMÝŠ#Ô|+Lža&ßT˜VfòQZ™É7æ èäk±“/TUôäk…L>–ŠB2žËå‚„T†\°¿Š"JHEaÉû«(Ñ„T”^„tU1WÁ ¾*>%š…ŠÂg¡¢ˆ²PQø,T”h* Ÿ…f…sAš1Xh²,LòúkÆ`¡Ùƒ…fš,¾*>Í,4c°ÐdY˜æ«â³ÐìÁB3®`a<È‚«òYpU†.ë®ÊgÁU£YpU>®*Ê‚«òYpÕh\•Ï‚«Š²àª|\5šWå³PÒ,äƒ,”4>%M”…’Æg¡¤E³PÒø,”4†…I¾*>%-š…’Æg¡¤‰²PÒø,”´hJŸ…v…‰ í,´…YhÇ`¡Í²0Mæ3,L‡©bXˆ¡Šaa:LÃ¥Ša!T•(m–…PUÑ,´{²Ð‰©ë€ú”ÇQþ1ÿL¨Ä™\®iBê:Ÿº.JH]çR×£ ©ë|Bêº(!uOH]&¤®ó ©ë¢„Ôu>!u=šºÎŸU#0-&ƒÓ¢jðY¨¢,T >Uƒa¡Hæ3,ÃT‰²P5Šaª(U¡ªDY¨¡ª¢Y¨|,3ÀÂTËä³`™¢,X&ŸËŒfÁ2ù,X¦(–ÉgÁ2£Y°L>–)Ê‚eòY°Ìh,“ÏB#ÈÂt…FÂ,4b°Ð`X ûk°,„ªe¡Á²ªŠfVÅ°ªJ”…ËB¨ªh¦ø½wï×ÊYKüÞ»÷{Ó¬%~ïÝû½ ­’­'~ïÝû=mÖ:¯$[OüÞ{§¿ÛZ²õÄï½wÖ{l$[OüÞ{ÇÏ ;Ùzâ÷Þ;ýÝìqï½Ãþ‚uü`z=ôØG߯îÿ$Tð»ÿÖIãðn
–ºEquation ºEquation.DSMT40º*MathType 5.0 Equation̨Í

Ã
š
–ºGrafico ºMSGraph.Chart.80º4Grafico di Microsoft GraphÌžÍ

Ã
¬
!–ºEquation ºEquation.DSMT40º*MathType 5.0 EquationÌžÍ

Ã
}-–ºEquation ºEquation.DSMT40º*MathType 5.0 EquationÌžÍ

Ã
®
8–ºEquation ºEquation.DSMT40º*MathType 5.0 EquationÌžÍ

Ã

K–ºEquation ºEquation.DSMT40º*MathType 5.0 EquationÌžÍ

Ã
¦
L–ºEquation ºEquation.DSMT40º*MathType 5.0 EquationÌžÍ

Ã
©
M–ºEquation ºEquation.DSMT40º*MathType 5.0 Equationò
/È0Ò
ÕL·DTimes New RomanT©T©¬r’Ü–É0Ü–Õ¤€@ÿÿ¥.©  @£nÿý?" dd@ÿÿïÿÿÿÿÿÿ


@@``€€tðlð`(‹½
R
    ‹!¢ % - /3Chart.80º4Grafico di Microsoft GraphÌžÍ

Ã
¬
!–ºEquation ºEquation.DSMT40º*MathType 5.0 EquationÌžÍ

Ã
}-–ºEquation ºEquation.DSMT40º*MathType 5.0 EquationÌžÍ

Ã
®
8–ºEquation ºEquation.DSMT40º*MathType 5.0 EquationÌžÍ

Ã

K–ºEquation ºEquation.DSMT40º*MathType 5.0 EquationÌžÍ

Ã
¦
L–ºEquation ºEquation.DSMT40º*MathType 5.0 EquationÌžÍ

Ã
©
M–ºEquation ºEquation.DSMT40º*MathType 5.0 Equationò
/È0Ò
ÕL·DTimes New RomanT©T©¬r’Ü–É0Ü–Õ¤€@ÿÿ¥.©  @£nÿý?" dd@ÿÿïÿÿÿÿÿÿ


@@``€€tðlð`(‹¼
R
    ‹!¢ % - /3476:;>@BCEF‰
KMNP$QRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~€‚ƒÿ
ð”2ð$ùª•aŸ¨e§7 ;Ú'¿ÿ
2ð$’eªò'— ¤¼KCÚcÿ0
2ð$Ð(†€3jC9ßÌóìX´‚ÿk
N2ð$ã‰ã6˶»<«"C°³Xÿò
¹%bð$ñ½ìo‚ˆ|Ý[7,9<çÿÜ«6bð$J‰3’…†¾çD!5ƒÿÈ
‡C2ð$ʍê>HÎ J‰ÆoÍë…ÿá0
"ð$$×oyòu)H´ÛÍÍÿF
~<2ð$šó›žÂe¢Áz,¶þk.ÿú
ÄH2ð$ WÌìוùdâž« ÞûIÿv
¾L2ð$µÃK l\­7"Iþ“ÔqÿÞ4P2ð$x‰–(öoþ¾°Qȧ+àÿê
T2ð$¸¿ÚkkçSxÖ9€»ÿÆ
üVð$ÿ2ð$©RØýè™Fö ˜ËgÍm¬ÿx
ÂZƒð0
ƒ
†A¿
À

ÅAÿ

@ñÿ3f™ÿÿ™@ñ
÷ðó€Ðì
ÿâžïÊš;Nh8Êš;

úgþ
ý4EdEd\›’ô–É0Ìýÿÿ¦ÿÿÿ
pûppû
@<�ý4dddd —‘w0T©ˆr’
<�ý4BdBd —‘w0T©ˆr’H<�ý4!d!d —‘w0T©ˆr’
ˆiŠaº___PPT10‹A pµpµä. ºCasaå.±6

?ÙÚ %OÙÚ =ðsóI,
Ÿ¨7How Large is the Retirement Consumption Drop in Italy?¡88

(
Ÿ¨>Erich Battistin Agar Brugiavini Enrico Rettore Guglielmo Weber¡?P?
   !"#$%&'()*+,-./0123456789:;<�=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~€‚ƒ„…†‡ˆ‰Š‹ŒŽ‘’“”•–—˜™š›œžŸ ¡¢£¤¥¦§¨©ª«¬­®¯°±²³´µ¶·¸¹º»¼½¾¿ÀÁÂÃÄÅÆÇÈÉÊËÌÍÎÏÐÑÒÓÔÕÖ×ØÙÚÛÜÝÞßàáâãäåæçèéêëìíîïðñòóôõö÷øùúûüýþÿ

































!
"
#
$
%
&
'
(
)
*
+
,
-
.
w0
1
2
3
4
5
6
7
8
9
:
;
<
=
>
?
@
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
[
\
]
^
_
`
a
b
c
d
e
f
g
h
i
j
k
l
m
n
o
p
q
r
s
t
u
v
w
x
y
z
{
|
}
~

€

‚
ƒ
„
…
†
‡
ˆ
‰
Š
‹
Œ

Ž


‘
’
“
”
•
–
—
˜
™
š
›
œ

ž
Ÿ
 
¡
¢
£
¤
¥
¦
§
¨
©
ª
«
¬
­
®
¯
°
±
²
³
´
µ
¶
·
¸
¹
º
»
¼
½
¾
¿
À
Á
Â
Ã
Ä
Å
Æ
Ç
È
É
Ê
Ë
Ì
Í
Î
Ï
Ð
Ñ
Ò
Ó
Ô
Õ
Ö
×
Ø
Ù
Ú
Û
Ü
Ý
Þ
ß
à
á
â
ã
ä
å
æ
ç
è
é
ê
ë
ì
í
î
ï
ð
ñ
ò
ó
ô
õ
ö
÷
ø
ù
ú
û
ü
ý
þ
ÿ
ª4
 0ó

Ÿ¨ Motivation¡

Ÿ¨É
According to the life-cycle permanent income Hp consumers decide how much to consume, keeping in mind their future prospects They form intertemporal plans aimed at smoothing the (discounted) marginal utility of consumption over the life cycle Any period to period change in the actual level of the marginal utility of consumption is uncorrelated with past information available to the household. That is, it should be a result of unpredictable shocks. ¡TÇ

ÿ3þÿ3þ•

óZ5
Ÿ¨ Motivation¡

Ÿ¨¼
This holds true also around retirement age: any change in the marginal utility of consumption should be uncorrelated with planned retirement behaviour. Recent micro evidence has emphasized that there is a one-off drop in consumption at the time of retirement that might be hard to reconcile with life-time optimizing behaviour (see for example Banks et al., 1998, Bernheim et al., 2001). This is known as the retirement consumption puzzle ¡„º

{ÿ3þÆÿ3þª>Ž
§
&
Hó[6
٬ MotivRoot Entry
ÿÿÿÿÿÿÿÿd›Oφꪹ)è Q„ÆnzÇ
“ Pictures
ÿÿÿÿÿÿÿÿúdCurrent Userÿÿÿÿÿÿÿÿÿÿÿÿ)SummaryInformation(

ÿÿÿÿLìT‚ƒ„…†‹ýÿÿÿýÿÿÿýÿÿÿýÿÿÿŒ”Þýÿÿÿýÿÿÿýÿÿÿþÿÿÿà•–—˜™š›œžŸ ¡¢£¤¥¦§¨©ª«¬­®¯°±²³´µ¶·¸¹º»¼½¾¿ÀÁÂÃÄÅÆÇÈÉÊËÌÍ{ÿÿÿÿÿÿÿÿÿÿÿÿÒÓÔÕÖ×ØÙÚÛÜÝÞßàáâãäåæçèéêëìíîïðñòóôõö÷øùúûüþýÿÿÿÿ‚ƒ„…†‡ˆ‰Š‹ŒŽ‘’“”•–—˜™š›œžŸ ¡¢£¤¥¦§¨©ª«¬­®¯°±²³´µ¶·¸¹º»¼½¾¿ÀÁÂÃÄÅÆÇÈÉÊËÌÍÎÏÐÑÒÓÔÕÖ×þÿÿÿÿÿÿÿÿÿÿÿýÿÿÿÿÿÿÿÿÿÿÿþÿÿÿþÿÿÿÿÿÿÿáâÝÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ
    !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvþÿÿÿxyzþÿÿÿ|}~Ñ€þÿÿÿ   !"#þÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿö_À‘ãÑôsemsemþÿ
ÕÍÕœ.“—+,ù®DÕÍÕœ.“—+,ù®Ü˜
ˆ´ÀÈÐØ à èðø



ýéýPresentazione su schermo£Ñd
('æ-Times New RomanArialStruttura predefinitaMathType 5.0 EquationGrafication¡

Ÿ JSome possible reasons mentioned in the literature: changes in preferences due to increased leisure shocks inducing retirement and affecting the level of consumption reduction in work-related expenditures (transport, meals out, clothing) increase in home production of services and/or more efficient purchases unexpectedly low pensions or liquidity problems (not in Italy, though  think of severance pay - liquidazione!) ¡N3
s
~ÿ3þ

ª–

ó>!
Ÿ¨What Others Have Done¡

Ÿ
 àBanks, Blundell and Tanner (1998) use repeated cross section data from the FES  they estimate log-linear Euler equations from cohort data by IV (using lagged interest rates, consumption and income growth as instruments) and find unexplained negative residuals around typical male retirement ages (60-67). The largest residual obtains at age 63 (1.5%). Altogether, cumulated residual are in the 8-10% region. Non-separabilities between leisure and consumption can explain only part of the drop. ¡>ï
P
P&ÿ3þµ
ª
2


  

D

ó?"
Ÿ¨What Others Have Done¡

Ÿ
 ÈBernheim, Skinner and Weinberg (2001) use panel data from the PSID to estimate Euler equations. Retirement status is instrumented by taking age-specific predicted probabilities conditional on demographics (however cannot explain spikes at ages 62 and 65). Median drop is 14%, but higher for low wealth Sample is split in groups: low wealth-to-income households drop their consumption most.  31% of households reduce their consumption by at least 35 percentage points at retirement .¡Hå
Z* ÿ3þäÿ3þ·ª
Ý
óY4
Ÿ¨What Others Have Done¡

Ÿ
¨‚
Possible explanations and related literature: Many workers are surprised by inadequate resources when they retire (not consistent with life-cycle model & rational expectations). Work related expenses. Home production and/or more efficient shopping (Aguiar and Hurst, 2005, Hurd and Rohwedder, 2006). Miniaci et al (2003) estimate by OLS the Italian retirement consumption drop at 5.4%. ¡0.
ZU
Z,

W
ªPù


 
Pó
Ÿ¨ What We Do¡

Ÿ¨º
An alternative identification strategy: we estimate the change in consumption at retirement by exploiting the exogenous variability in the retirement decision induced by the eligibility rules of the Italian pension system. Information on consumption expenditures, eligibility for retirement and retirement status is obtained from the Bank of Italy Survey on Household Income and Wealth (SHIW). No need of panel data to achieve identification.¡J»
Z&ÿ3þˆÿ3þË/™þó
Ÿ¨ Punch-line¡

Ÿ Key result: household non-durable consumption drops by 9.8% because of male retirement. A larger drop estimated for total food (14.1%). Our strategy provides non-parametric identification only for a subpopulation of those who retire (those who retire at the time they become eligible). We estimate smaller drops for  poverty sample . Our estimates can be reconciled with utility optimization - in the cross section, drop in work-related expenses and leisure substitutes is large enough to explain changes in consumption. ¡ZZ

ÿ3þÿ3þ9ÿ3þ…
ó
Ÿ¨The Causal Problem¡

Ÿ ÚLet S* be a variable denoting time to/from eligibility for retirement, negative values indicate that the subject is not yet eligible. Let R be the retirement status, R=1 for the retired and R=0 otherwise. Since retirement is an option available only to the eligible workers, the probability to retire is zero if S*<�0 (and it is thus discontinuous at S*=0 ). Let (Y1,Y0) be the two potential household consumption expenditures corresponding to the head being retired or not retired, respectively, and let ²=Y1-Y0 . Let Y = Y0+R² be observed consumption, where Ya"Y1 for households whose head is retired and Ya"Y0 otherwise.¡ân
ÿ3þ
ÿ3þ

ÿ3þE
ÿ3þÿ3þÿ3þx
%
 ÿ3þ
ÿ3þçÿÿ3þ
ÿ3þçÿ
ÿ3þ ÿ3þ
"O&ÿ3þ
ÿ3þ
ÿ3þçÿÿ3þÿ3þçÿ

ÿ3þçÿÿ3þ
ÿ3þçÿÿ3þ&ÿ3þ"&ÿ3þ
.ÿ3þçÿ&""
"&ÿ3þ
.ÿ3þçÿ"óJ+
Ÿ¨Identification in a nutshell¡

Ÿ ,
Start by comparing expenditures for households marginally close to S*=0; since Y = Y0+R² we have that Consider the difference around eligibility: ¡
f
,

/ÿ3þ
ÿ3þÿ3þÿ3þ
ÿ3þçÿÿ3þ&ÿ3þ 
ÿ3þ
,
"ªB
Tó
Ÿ¨Identification in a nutshell¡

Ÿ ŽKey identifying restriction (the mean consumption profile under the no-retirement alternative is smooth enough at zero): The result rests upon a weak regularity condition: if none of the heads were to retire no discontinuity in household consumption would take place at the time they become eligible (i.e. at S*=0)  see Hahn et al. (2001) and Battistin and Rettore (2006). This amounts to assuming that any idiosyncratic shocks relevant to the retirement choice and correlated with Y0 (e.g. health shocks) do not occur selectively at either side of the eligibility threshold. ¡–H
`
ÿ3þŒ
˜
çÿ_ª,[


Øó
Ÿ¨Identification in a nutshell¡

Ÿ¨¹
By using simple algebra we have: Estimators of the causal effect of retirement on consumption are analogue estimators obtained by replacing the quantities in the last expression by their empirical counterparts. Following Imbens and Angrist (1994) and Hanh et al. (2001), it can be shown that this expression coincides with the IV estimator obtained by instrumenting the endogenous variable R with the eligibility status defined from S*. ¡–%
Z”
Z

Z!A‹¬

ª>á


·ó\7
Ÿ¨Endogeneity of S*¡*







ª.
Ÿ
 ÌThe S* variable may be the outcome of individual choices (time to enter the labour market, temporary exits, etc). This might casts doubts that our identification strategy is marred by an endogeneity problem. Consider the regression we use to get the numerator of the IV estimate (the reduced form): Y= ´0 + ´1 S* + ´2 S*2 + ´3 1(S*>0) +µ The mean of Y conditional on S* is: E{Y|S*} = ´0 + ´1 S* + ´2 S*2 + ´3 1(S*>0) + E{µ|S*} where the last term does not vanish if S* is endogenous. ¡ +
Z'

Z%
Z5

Z;
Z
%
ÿ3þ
&ÿ3þ.ÿ3þçÿ&ÿ3þ.ÿ3þçÿ
&ÿ3þ
.ÿ3þ&ÿ3þ.ÿ3þçÿ
&ÿ3þ.ÿ3þ&ÿ3þ.ÿ3þçÿÿ3þ
ÿ3þÿ3þ&ÿ3þ"
*"ÿ3þ
ÿ3þÿ3þ
&ÿ3þ.ÿ3þçÿ&ÿ3þ.ÿ3þçÿ
&ÿ3þ
.ÿ3þ&ÿ3þ.ÿ3þçÿ
&ÿ3þ.ÿ3þ&ÿ3þ.ÿ3þçÿÿ3þ
ÿ3þÿ3þ&ÿ3þ
.ÿ3þ  ÿ3þ$"$$&$ÿ3þ$"$
$*$$"$
(( ªjL
i
e




  





 
 



 ó]8
Ÿ¨Endogeneity of S*¡ 



ª.
Ÿ
 ¬Nonetheless, the numerator of the IV estimand: E{Y|S* =0+}-E{Y|S* =0-} is not biased for ´3, the drop in consumption at the eligibility cut-off point, provided that: E{µ|S*=0+}=E{µ|S*=0-}. Our identifying restriction is that the dependence between the unobservables µ and S* is not discontinuously changing at the cut-off for eligibility. ¡‚/Z

Z`
Z

Z–Z


Z

Z
Z4"*"
*"*"
*"""
&ÿ3þ
.ÿ3þçÿ
&ÿ3þJ"ÿ3þ&ÿ3þ
.ÿ3þ&ÿ3þ
.ÿ3þÿ3þ&ÿ3þ
.ÿ3þ&ÿ3þ
.ÿ3þÿ3þM"
*"&ÿ3þ8"
" 
$$ªº 




 
 
 
B   
 






 

ó^
9
Ÿ¨Data¡

ó‹>
Ÿ¨The Reform Process¡

ª@

Ÿ
¨
Two major reforms in 1992 (Amato) and 1995 (Dini) Gradually moving from defined benefit to (notionally) defined contribution Lots of additional minor changes have been made nearly every year since 1992 Further changes will take place in 2008 (restrictions on early retirement)ªR
) 


  
x
 óG
)
ٻ

óC
%
Ÿ¨The measurement of eligibility¡

óD
&
Ÿ¨The measurement of eligibility¡

ó$

ٻ

óH*
ó

Ÿ¨ Retirement by Eligibility Status¡!!

ó
Ÿ¨Measurement Error¡

Ÿ¨OWe observe a non-negligible fraction of retired individuals amongst the ineligibles (this regardless of having imputed the eligibility variable for some individuals): this we take as evidence of measurement error in the data. Measurement error bias in the estimation of causal parameters can be severe (see, for example, Battistin and Chesher, 2004). Misclassification of the retirement status R is unlikely to be important, as retired individuals are asked a detailed set of questions on their pension. Measurement error in the eligibility variable S* is most likely to be the explanation. ¡hPö
›

 (ªO

úó
Ÿ¨Measurement Error¡

Ÿ¨º
Based on what we observe in the data, measurement error in S* can not be classical. If S=S*+u, with u a zero-mean error orthogonal to S* we would not observe any discontinuity in the proportion of retired individual s at the cut-off point. A type of measurement error consistent with the discontinuity in the raw probability of R=1 we observe in the data is: where Z is an indicator for having S= S* and U is a classical measurement error.¡J
i
PR
P<�

 

+

 ZY  % 
  
 


 
 # ó&
Ÿ¨Measurement Error¡

Ÿ¨Parameter of interest ¡B
Zÿ3þ

ÿ3þóP
-
Ÿ¨ Estimation¡

óƒ:
Ÿ¨lA key feature of the Italian pension system is that many individuals retire as soon as they become eligible¡mm


ªl 
Ÿ
ª
ó:

Ÿ fFirst StageE{R|S} = ±0 + ±1 S + ±2 S2 + ±3 1(S>0) ¡Ö4

ÿ3þ 
"*çÿ"*çÿ"*çÿ
"*"*çÿ
ª¨



 
ó;

Ÿ hReduced FormE{Y|S} = ´0 + ´1 S + ´2 S2 + ´3 1(S>0) ¡Þ5

ÿ3þ 
"
 çÿ
"
 çÿ
"
 çÿ
 
"
çÿ  ª°



 
ó(

Ÿ¨Estimation results¡

óX
3
Ÿ¨Estimation results¡

ó.
Ÿ¨Specification tests¡

Ÿ¨ŠIdentification strategy requires no change at S* = 0 in variables that affect consumption but are not affected by eligibility status. We show that this condition is met by education, age, size of the main residence and proportion of couples Exclusion restriction: family size. This is negatively affected by retirement induced by eligibility (-0.30). In particular, number of grown children cohabiting with their parents falls (-0.25). Possible explanation: individuals retire as soon as they become eligible as a way to let their children move out (they give them part of their severance pay) Hence actual consumption drop is even smaller than 9.8%!¡‹Z‹ó‡<
Ÿ¨Economic Interpretation¡

Ÿ In the US, consumption drop is largest among the low pre-retirement wealth (BSW). We estimate a pre-eligibility wealth equation, and use it to predict for the whole sample (w_fit). We show this measure does not change at S*=0. We select those households who w_fit is in the bottom third (w_poor). We call this  poverty sample We estimate small and insignificant effects of eligibility-induced retirement for this poverty sample Our estimated consumption drop is unlikely to be due to lack of financial resources!¡bZ­

ÿ3þP

ÿ3þÿ3þܪ>­
P

Üó…;
Ÿ¨Back of the Envelope Stuff¡

Ÿ¨…A causal effect of retirement on consumption expenditures is not surprising per se. The question is whether this is consistent with life-time optimizing behavior. A consumption drop can occur if utility is not additively separable in consumption and leisure: since leisure increases abruptly at retirement, consumption increases or decreases depending on how leisure affects the marginal utility of consumption. For instance, if utility is Cobb-Douglas in male leisure and non-durable consumption, and individuals work full time prior to retirement, our estimated 9.8% consumption drop implies an elasticity of intertemporal substitution of 0.84¡X†Z=y6…
ó‰=
Ÿ¨Work-Related Expenses¡

Ÿ¨¢
One good model is restrictive: Some goods are leisure substitutes (e.g. food out) or work-related (e.g. travel, clothing), other leisure complements (food in, home heating). We explore which components of household expenditure drive the fall that we have documented. We use data from the 2002 Survey of Family Budgets: this contains no information on eligibility, but detailed information on household expenditures.¡£
Z£
óR/
Ÿ¨Work-Related Expenses¡

Ÿ  We compare expenditures for households whose head s age is 50-54 and 65-69. Heads in the latter group are mostly retired, mostly employed in the former group. The comparison is corrected for composition differences with respect to region of residence, number of equivalent adults and size of the main residence. Support issues turn out to be of no concern. The overall drop is 15.6% : 50% larger than the estimated retirement consumption drop (9.8%). A third of the drop is due to age, two thirds to retirement.¡|
<�/


ÿ3þ=

ÿ3þ@óQ
.
ٻ

óS0
Ÿ¨Work-Related Expenses¡

Ÿ  Total difference is - 241 euros (-15.6%). Mostly accounted for by meals out (-36), clothing (-58), transport (-76). Overall 170 out of 241  drop is accounted for by  work-related expenses . Our estimates imply that consumption should fall by 151 Euros because of eligibility-induced retirement. Work-related expenses are less important for manual workers (canteen meals and overalls normally provided by the employer  public transport is heavily subsidized). This may explain why there is no drop for the poverty sample! óT1
Ÿ¨Conclusions¡

٬I
We estimate that non-durable consumption falls by 9.8% in Italy because of retirement. This drop is lower than in the US (14 %) but comparable to the UK (8%-10%, non-durable consumption). Our estimates can be reconciled with utility optimization: in the cross section, drop in work-related expenses is large enough to explain it./ðDó`
óa

ób
óc
ód
óe
óf
óg
óh
ói
ój
ók
ól
óm
ón
óo
óp
óq
ór
ós
ót
óu
óv
ów
óx
óy
óz
ó{
ó|
ó}
ó~
ó
ó€
ó!
ó‚"
ó„#
ó†$
óˆ%
óŠ&
êîÇï
€0Þ
ðÖ
0ð(ðn
ð(
ð ð(ð° ð( “ð6€dkw€

¿
ÿ


ˆS"ñž
ÿÿÿÿŸ
ÿÿÿÿ 
¡Á¦
ÿÿÿÿð¤°
Ðzðà w ðžð~ ð( sð*€p2}¿

ÿ


ˆð°
ÐðÃ
w ðž
ðH ð
(ƒð0
ƒ
“
ŽŸ‹”
Þ½h¿
ÿ
 ?

ð ÿÿÿ€€€»àã33™™™™Ìˆ‘Š‰º___PPT10‹ië.EÄ
 %å8+Dñ='ñ y
ÿÿÿÿ=ñ @
Bñ
+r
©8‹Àõ>
™…8PÃ
‹
Å1èЇ
é(€àx/ _A

 F ò
ÌžÍ

Ã
8 How Large is the Retirement Consumption Drop in Italy?MotivationMotivationMotivationWhat Others Have DoneWhat Others Have DoneWhat Others Have DoneWhat We DoPunch-lineThe Causal ProblemIdentification in a nutshellIdentification in a nutshellIdentification in a nutshellEndogeneity of S*Endogeneity of S*DataThe Reform ProcessDiapositiva 18The measurement of eligibilityThe measurement of eligibilityDiapositiva 21Diapositiva 22!Retirement by Eligibility StatusMeasurement ErrorMeasurement ErrorMeasurement ErrorEstimationmA key feature of the Italian pension system is that many individuals retire as soon as they become eligible 8First Stage E{R|S} = α0 + α1 S + α2 S2 + α3 1(S>0) 9Reduced Form E{Y|S} = δ0 + δ1 S + δ2 S2 + δ3 1(S>0) Estimation resultsEstimation resultsSpecification testsEconomic InterpretationBack of the Envelope StuffWork-Related ExpensesWork-Related ExpensesDiapositiva 38Work-Related ExpensesConclusionsCaratteri utilizzatiModello struttura
Server OLE incorporatiTitoli diapositive(476:;>@BCEF‰
KMNP$QRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~€‚ƒÿ
ð”2ð$ùª•aŸ¨e§7 ;Ú'¿ÿ
2ð$’eªò'— ¤¼KCÚcÿ0
2ð$Ð(†€3jC9ßÌóìX´‚ÿk
N2ð$ã‰ã6˶»<«"C°³Xÿò
¹%bð$ñ½ìo‚ˆ|Ý[7,9<çÿÜ«6bð$J‰3’…†¾çD!5ƒÿÈ
‡C2ð$ʍê>HÎ J‰ÆoÍë…ÿá0
"ð$$×oyòu)H´ÛÍÍÿF
~<2ð$šó›žÂe¢Áz,¶þk.ÿú
ÄH2ð$ WÌìוùdâž« ÞûIÿv
¾L2ð$µÃK l\­7"Iþ“ÔqÿÞ4P2ð$x‰–(öoþ¾°Qȧ+àÿê
T2ð$¸¿ÚkkçSxÖ9€»ÿÆ
üV2ð$.‚M¸D†XnV$‰Ø'¨ÿÀ
:]2ð$©RØýè™Fö ˜ËgÍm¬ÿx
ÂZƒð0
ƒ
†A¿
À

ÅAÿ

@ñÿ3f™ÿÿ™@ñ
÷ðó€Ðì
ÿâžïÊš;Nh8Êš;

úgþ
ý4EdEd\›’ô–É0Ìýÿÿ¦ÿÿÿ
pûppû
@<�ý4dddd —‘w0T©ˆr’
<�ý4BdBd —‘w0T©ˆr’H<�ý4!d!d —‘w0T©ˆr’
ˆiŠaº___PPT10‹A pµpµä. ºCasaå.±6

?ÙÚ %OÙÚ =ðsóI,
Ÿ¨7How Large is the Retirement Consumption Drop in Italy?¡88

(
Ÿ¨>Erich Battistin Agar Brugiavini Enrico Rettore Guglielmo Weber¡?P?ª4
 0ó

Ÿ¨ Motivation¡

Ÿ¨É
According to the life-cycle permanent income Hp consumers decide how much to consume, keeping in mind their future prospects They form intertemporal plans aimed at smoothing the (discounted) marginal utility of consumption over the life cycle Any period to period change in the actual level of the marginal utility of consumption is uncorrelated with past information available to the household. That is, it should be a result of unpredictable shocks. ¡TÇ

ÿ3þÿ3þ•

óZ5
Ÿ¨ Motivation¡

Ÿ¨¼
This holds true also around retirement age: any change in the marginal utility of consumption should be uncorrelated with planned retirement behaviour. Recent micro evidence has emphasized that there is a one-off drop in consumption at the time of retirement that might be hard to reconcile with life-time optimizing behaviour (see for example Banks et al., 1998, Bernheim et al., 2001). This is known as the retirement consumption puzzle ¡„º

{ÿ3þÆÿ3þª>Ž
§
&
Hó[6
Ÿ¨ Motivation¡

Ÿ JSome possible reasons mentioned in the literature: changes in preferences due to increased leisure shocks inducing retirement and affecting the level of consumption reduction in work-related expenditures (transport, meals out, clothing) increase in home production of services and/or more efficient purchases unexpectedly low pensions or liquidity problems (not in Italy, though  think of severance pay - liquidazione!) ¡N3
s
~ÿ3þ

ª–

ó>!
Ÿ¨What Others Have Done¡

Ÿ
 àBanks, Blundell and Tanner (1998) use repeated cross section data from the FES  they estimate log-linear Euler equations from cohort data by IV (using lagged interest rates, consumption and income growth as instruments) and find unexplained negative residuals around typical male retirement ages (60-67). The largest residual obtains at age 63 (1.5%). Altogether, cumulated residual are in the 8-10% region. Non-separabilities between leisure and consumption can explain only part of the drop. ¡>ï
P
P&ÿ3þµ
ª
2


  

D

ó?"
Ÿ¨What Others Have Done¡

Ÿ
 ÈBernheim, Skinner and Weinberg (2001) use panel data from the PSID to estimate Euler equations. Retirement status is instrumented by taking age-specific predicted probabilities conditional on demographics (however cannot explain spikes at ages 62 and 65). Median drop is 14%, but higher for low wealth Sample is split in groups: low wealth-to-income households drop their consumption most.  31% of households reduce their consumption by at least 35 percentage points at retirement .¡Hå
Z* ÿ3þäÿ3þ·ª
Ý
óY4
Ÿ¨What Others Have Done¡

Ÿ
¨‚
Possible explanations and related literature: Many workers are surprised by inadequate resources when they retire (not consistent with life-cycle model & rational expectations). Work related expenses. Home production and/or more efficient shopping (Aguiar and Hurst, 2005, Hurd and Rohwedder, 2006). Miniaci et al (2003) estimate by OLS the Italian retirement consumption drop at 5.4%. ¡0.
ZU
Z,

W
ªPù


 
Pó
Ÿ¨ What We Do¡

Ÿ¨º
An alternative identification strategy: we estimate the change in consumption at retirement by exploiting the exogenous variability in the retirement decision induced by the eligibility rules of the Italian pension system. Information on consumption expenditures, eligibility for retirement and retirement status is obtained from the Bank of Italy Survey on Household Income and Wealth (SHIW). No need of panel data to achieve identification.¡J»
Z&ÿ3þˆÿ3þË/™þó
Ÿ¨ Punch-line¡

Ÿ Key result: household non-durable consumption drops by 9.8% because of male retirement. A larger drop estimated for total food (14.1%). Our strategy provides non-parametric identification only for a subpopulation of those who retire (those who retire at the time they become eligible). We estimate smaller drops for  poverty sample . Our estimates can be reconciled with utility optimization - in the cross section, drop in work-related expenses and leisure substitutes is large enough to explain changes in consumption. ¡ZZ

ÿ3þÿ3þ9ÿ3þ…
ó
Ÿ¨The Causal Problem¡

Ÿ ÚLet S* be a variable denoting time to/from eligibility for retirement, negative values indicate that the subject is not yet eligible. Let R be the retirement status, R=1 for the retired and R=0 otherwise. Since retirement is an option available only to the eligible workers, the probability to retire is zero if S*<�0 (and it is thus discontinuous at S*=0 ). Let (Y1,Y0) be the two potential household consumption expenditures corresponding to the head being retired or not retired, respectively, and let ²=Y1-Y0 . Let Y = Y0+R² be observed consumption, where Ya"Y1 for households whose head is retired and Ya"Y0 otherwise.¡ân
ÿ3þ
ÿ3þ

ÿ3þE
ÿ3þÿ3þÿ3þx
%
 ÿ3þ
ÿ3þçÿÿ3þ
ÿ3þçÿ
ÿ3þ ÿ3þ
"O&ÿ3þ
ÿ3þ
ÿ3þçÿÿ3þÿ3þçÿ

ÿ3þçÿÿ3þ
ÿ3þçÿÿ3þ&ÿ3þ"&ÿ3þ
.ÿ3þçÿ&""
"&ÿ3þ
.ÿ3þçÿ"óJ+
Ÿ¨Identification in a nutshell¡

Ÿ ,
Start by comparing expenditures for households marginally close to S*=0; since Y = Y0+R² we have that Consider the difference around eligibility: ¡
f
,

/ÿ3þ
ÿ3þÿ3þÿ3þ
ÿ3þçÿÿ3þ&ÿ3þ 
ÿ3þ
,
"ªB
Tó
Ÿ¨Identification in a nutshell¡

Ÿ ŽKey identifying restriction (the mean consumption profile under the no-retirement alternative is smooth enough at zero): The result rests upon a weak regularity condition: if none of the heads were to retire no discontinuity in household consumption would take place at the time they become eligible (i.e. at S*=0)  see Hahn et al. (2001) and Battistin and Rettore (2006). This amounts to assuming that any idiosyncratic shocks relevant to the retirement choice and correlated with Y0 (e.g. health shocks) do not occur selectively at either side of the eligibility threshold. ¡–H
`
ÿ3þŒ
˜
çÿ_ª,[


Øó
Ÿ¨Identification in a nutshell¡

Ÿ¨¹
By using simple algebra we have: Estimators of the causal effect of retirement on consumption are analogue estimators obtained by replacing the quantities in the last expression by their empirical counterparts. Following Imbens and Angrist (1994) and Hanh et al. (2001), it can be shown that this expression coincides with the IV estimator obtained by instrumenting the endogenous variable R with the eligibility status defined from S*. ¡–%
Z”
Z

Z!A‹¬

ª>á


·ó\7
Ÿ¨Endogeneity of S*¡*







ª.
Ÿ
 ÌThe S* variable may be the outcome of individual choices (time to enter the labour market, temporary exits, etc). This might casts doubts that our identification strategy is marred by an endogeneity problem. Consider the regression we use to get the numerator of the IV estimate (the reduced form): Y= ´0 + ´1 S* + ´2 S*2 + ´3 1(S*>0) +µ The mean of Y conditional on S* is: E{Y|S*} = ´0 + ´1 S* + ´2 S*2 + ´3 1(S*>0) + E{µ|S*} where the last term does not vanish if S* is endogenous. ¡ +
Z'

Z%
Z5

Z;
Z
%
ÿ3þ
&ÿ3þ.ÿ3þçÿ&ÿ3þ.ÿ3þçÿ
&ÿ3þ
.ÿ3þ&ÿ3þ.ÿ3þçÿ
&ÿ3þ.ÿ3þ&ÿ3þ.ÿ3þçÿÿ3þ
ÿ3þÿ3þ&ÿ3þ"
*"ÿ3þ
ÿ3þÿ3þ
&ÿ3þ.ÿ3þçÿ&ÿ3þ.ÿ3þçÿ
&ÿ3þ
.ÿ3þ&ÿ3þ.ÿ3þçÿ
&ÿ3þ.ÿ3þ&ÿ3þ.ÿ3þçÿÿ3þ
ÿ3þÿ3þ&ÿ3þ
.ÿ3þ  ÿ3þ$"$$&$ÿ3þ$"$
$*$$"$
(( ªjL
i
e




  





 
 



 ó]8
Ÿ¨Endogeneity of S*¡ 



ª.
Ÿ
 ¬Nonetheless, the numerator of the IV estimand: E{Y|S* =0+}-E{Y|S* =0-} is not biased for ´3, the drop in consumption at the eligibility cut-off point, provided that: E{µ|S*=0+}=E{µ|S*=0-}. Our identifying restriction is that the dependence between the unobservables µ and S* is not discontinuously changing at the cut-off for eligibility. ¡‚/Z

Z`
Z

Z–Z


Z

Z
Z4"*"
*"*"
*"""
&ÿ3þ
.ÿ3þçÿ
&ÿ3þJ"ÿ3þ&ÿ3þ
.ÿ3þ&ÿ3þ
.ÿ3þÿ3þ&ÿ3þ
.ÿ3þ&ÿ3þ
.ÿ3þÿ3þM"
*"&ÿ3þ8"
" 
$$ªº 




 
 
 
B   
 






 

ó^
9
Ÿ¨Data¡

ó‹>
Ÿ¨The Reform Process¡

ª@

Ÿ
¨
Two major reforms in 1992 (Amato) and 1995 (Dini) Gradually moving from defined benefit to (notionally) defined contribution Lots of additional minor changes have been made nearly every year since 1992 Further changes will take place in 2008 (restrictions on early retirement)ªR
) 


  
x
 óG
)
ٻ

óC
%
Ÿ¨The measurement of eligibility¡

óD
&
Ÿ¨The measurement of eligibility¡

ó$

ٻ

óH*
ó

Ÿ¨ Retirement by Eligibility Status¡!!

ó
Ÿ¨Measurement Error¡

Ÿ¨OWe observe a non-negligible fraction of retired individuals amongst the ineligibles (this regardless of having imputed the eligibility variable for some individuals): this we take as evidence of measurement error in the data. Measurement error bias in the estimation of causal parameters can be severe (see, for example, Battistin and Chesher, 2004). Misclassification of the retirement status R is unlikely to be important, as retired individuals are asked a detailed set of questions on their pension. Measurement error in the eligibility variable S* is most likely to be the explanation. ¡hPö
›

 (ªO

úó
Ÿ¨Measurement Error¡

Ÿ¨º
Based on what we observe in the data, measurement error in S* can not be classical. If S=S*+u, with u a zero-mean error orthogonal to S* we woul
    !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxzýÿÿÿ{|}~€d not observe any discontinuity in the proportion of retired individual s at the cut-off point. A type of measurement error consistent with the discontinuity in the raw probability of R=1 we observe in the data is: where Z is an indicator for having S= S* and U is a classical measurement error.¡J
i
PR
P<�

 

+

 ZY  % 
  
 


 
 # ó&
Ÿ¨Measurement Error¡

Ÿ¨Parameter of interest ¡B
Zÿ3þ

ÿ3þóP
-
Ÿ¨ Estimation¡

óƒ:
Ÿ¨lA key feature of the Italian pension system is that many individuals retire as soon as they become eligible¡mm


ªl 
Ÿ
ª
ó:

Ÿ fFirst StageE{R|S} = ±0 + ±1 S + ±2 S2 + ±3 1(S>0) ¡Ö4

ÿ3þ 
"*çÿ"*çÿ"*çÿ
"*"*çÿ
ª¨



 
ó;

Ÿ hReduced FormE{Y|S} = ´0 + ´1 S + ´2 S2 + ´3 1(S>0) ¡Þ5

ÿ3þ 
"
 çÿ
"
 çÿ
"
 çÿ
 
"
çÿ  ª°



 
ó(

Ÿ¨Estimation results¡

óX
3
Ÿ¨Estimation results¡

ó.
Ÿ¨Specification tests¡

Ÿ¨ŠIdentification strategy requires no change at S* = 0 in variables that affect consumption but are not affected by eligibility status. We show that this condition is met by education, age, size of the main residence and proportion of couples Exclusion restriction: family size. This is negatively affected by retirement induced by eligibility (-0.30). In particular, number of grown children cohabiting with their parents falls (-0.25). Possible explanation: individuals retire as soon as they become eligible as a way to let their children move out (they give them part of their severance pay) Hence actual consumption drop is even smaller than 9.8%!¡‹Z‹ó‡<
Ÿ¨Economic Interpretation¡

Ÿ In the US, consumption drop is largest among the low pre-retirement wealth (BSW). We estimate a pre-eligibility wealth equation, and use it to predict for the whole sample (w_fit). We show this measure does not change at S*=0. We select those households who w_fit is in the bottom third (w_poor). We call this  poverty sample We estimate small and insignificant effects of eligibility-induced retirement for this poverty sample Our estimated consumption drop is unlikely to be due to lack of financial resources!¡bZ­

ÿ3þP

ÿ3þÿ3þܪ>­
P

Üó…;
Ÿ¨Back of the Envelope Stuff¡

Ÿ¨…A causal effect of retirement on consumption expenditures is not surprising per se. The question is whether this is consistent with life-time optimizing behavior. A consumption drop can occur if utility is not additively separable in consumption and leisure: since leisure increases abruptly at retirement, consumption increases or decreases depending on how leisure affects the marginal utility of consumption. For instance, if utility is Cobb-Douglas in male leisure and non-durable consumption, and individuals work full time prior to retirement, our estimated 9.8% consumption drop implies an elasticity of intertemporal substitution of 0.84¡X†Z=y6…
ó‰=
Ÿ¨Work-Related Expenses¡

Ÿ¨¢
One good model is restrictive: Some goods are leisure substitutes (e.g. food out) or work-related (e.g. travel, clothing), other leisure complements (food in, home heating). We explore which components of household expenditure drive the fall that we have documented. We use data from the 2002 Survey of Family Budgets: this contains no information on eligibility, but detailed information on household expenditures.¡£
Z£
óR/
Ÿ¨Work-Related Expenses¡

Ÿ  We compare expenditures for households whose head s age is 50-54 and 65-69. Heads in the latter group are mostly retired, mostly employed in the former group. The comparison is corrected for composition differences with respect to region of residence, number of equivalent adults and size of the main residence. Support issues turn out to be of no concern. The overall drop is 15.6% : 50% larger than the estimated retirement consumption drop (9.8%). A third of the drop is due to age, two thirds to retirement.¡|
<�/


ÿ3þ=

ÿ3þ@óQ
.
ٻ

óS0
Ÿ¨Work-Related Expenses¡

Ÿ  Total difference is - 241 euros (-15.6%). Mostly accounted for by meals out (-36), clothing (-58), transport (-76). Overall 170 out of 241  drop is accounted for by  work-related expenses . Our estimates imply that consumption should fall by 151 Euros because of eligibility-induced retirement. Work-related expenses are less important for manual workers (canteen meals and overalls normally provided by the employer  public transport is heavily subsidized). This may explain why there is no drop for the poverty sample! óT1
Ÿ¨Conclusions¡

٬I
We estimate that non-durable consumption falls by 9.8% in Italy because of retirement. This drop is lower than in the US (14 %) but comparable to the UK (8%-10%, non-durable consumption). Our estimates can be reconciled with utility optimization: in the cross section, drop in work-related expenses is large enough to explain it./ðDó`
óa

ób
óc
ód
óe
óf
óg
óh
ói
ój
ók
ól
óm
ón
óo
óp
óq
ór
ós
ót
óu
óv
ów
óx
óy
óz
ó{
ó|
ó}
ó~
ó
ó€
ó!
ó‚"
ó„#
ó†$
óˆ%
óŠ&
êî}ï €
0”
ðŒ
àð
ð$
ð(
ð ð
ð† ð 
Sð€($E¿


ÿ



ðàpÐðÃ
E 𠟪
ð^² ð
“ð6A
ƒ
¿
À

ÿ

?ðâ
ðH ð

ƒð0
ƒ
“
ŽŸ‹”
Þ½h¿
ÿ
 ?

ð ÿÿÿ€€€Ì™33ÌÌÌÿ²²²ˆ‘Š‰º___PPT10‹ië.BÃÅ
¢]+Dñ='ñ }ÿÿÿÿ=ñ @
Bñ
+r
ŒÃGdKõ)
™hÃéM
‹
Å1èЇ
é(€àx/ _A

 F ò
ÌžÍ

Ã
n
–ºEquation ºEquation.DSMT40º*MathType 5.0 Equation̨Í

Ã
š
–ºGrafico ºMSGraph.Chart.80º4Grafico di Microsoft GraphÌžÍ

Ã
¬
!–ºEquation ºEquation.DSMT40º*MathType 5.0 EquationÌžÍ

Ã
}-–ºEquation ºEquation.DSMT40º*MathType 5.0 EquationÌžÍ

Ã
®
8–ºEquation ºEquation.DSMT40º*MathType 5.0 EquationÌžÍ

Ã

K–ºEquation ºEquation.DSMT40º*MathType 5.0 EquationÌžÍ

Ã
¦
L–ºEquation ºEquation.DSMT40º*MathType 5.0 EquationÌžÍ

Ã
©
M–ºEquation ºEquation.DSMT40º*MathType 5.0 Equationò
/È0Ò
ÕL·DTimes New RomanT©T©¬r’Ü–É0Ü–Õ¤€@ÿÿ¥.©  @£nÿý?" dd@ÿÿïÿÿÿÿÿÿ


@@``€€tðlð`(‹¼
R
    ‹!¢ % - /3476:;>@BCEF‰
KMNP$QRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~€‚ƒÿ
ð”2ð$ùª•aŸ¨e§7 ;Ú'¿ÿ
2ð$’eªò'— ¤¼KCÚcÿ0
2ð$Ð(†€3jC9ßÌóìX´‚ÿk
N2ð$ã‰ã6˶»<«"C°³Xÿò
¹%bð$ñ½ìo‚ˆ|Ý[7,9<çÿÜ«6bð$J‰3’…†¾çD!5ƒÿÈ
‡C2ð$ʍê>HÎ J‰ÆoÍë…ÿá0
"ð$$×oyòu)H´ÛÍÍÿF
~<2ð$šó›žÂe¢Áz,¶þk.ÿú
ÄH2ð$ WÌìוùdâž« ÞûIÿv
¾L2ð$µÃK l\­7"Iþ“ÔqÿÞ4P2ð$x‰–(öoþ¾°Qȧ+àÿê
T2ð$¸¿ÚkkçSxÖ9€»ÿÆ
üV2ð$.‚M¸D†XnV$‰Ø'¨ÿÀ
:]2ð$©RØýè™Fö ˜ËgÍm¬ÿx
ÂZƒð0
ƒ
†A¿
À

ÅAÿ

@ñÿ3f™ÿÿ™@ñ
÷ðó€Ðì
ÿâžïÊš;Nh8Êš;

úgþ
ý4EdEd\›’ô–É0Ìýÿÿ¦ÿÿÿ
pûppû
@<�ý4dddd —‘w0T©ˆr’
<�ý4BdBd —‘w0T©ˆr’H<�ý4!d!d —‘w0T©ˆr’
ˆiŠaº___PPT10‹A pµpµä. ºCasaå.±6

?ÙÚ %OÙÚ =ðsóI,
Ÿ¨7How Large is the Retirement Consumption Drop in Italy?¡88

(
Ÿ¨>Erich Battistin Agar Brugiavini Enrico Rettore Guglielmo Weber¡?P?ª4
 0ó

Ÿ¨ Motivation¡

Ÿ¨É
According to the life-cycle permanent income Hp consumers decide how much to consume, keeping in mind their future prospects They form intertemporal plans aimed at smoothing the (discounted) marginal utility of consumption over the life cycle Any period to period change in the actual level of the marginal utility of consumption is uncorrelated with past information available to the household. That is, it should be a result of unpredictable shocks. ¡TÇ

ÿ3þÿ3þ•

óZ5
Ÿ¨ Motivation¡

Ÿ¨¼
This holds true also around retirement age: any change in the marginal utility of consumption should be uncorrelated with planned retirement behaviour. Recent micro evidence has emphasized that there is a one-off drop in consumption at the time of retirement that might be hard to reconcile with life-time optimizing behaviour (see for example Banks et al., 1998, Bernheim et al., 2001). This is known as the retirement consumption puzzle ¡„º

{ÿ3þÆÿ3þª>Ž
§
&
Hó[6
Ÿ¨ Motivation¡

Ÿ JSome possible reasons mentioned in the literature: changes in preferences due to increased leisure shocks inducing retirement and affecting the level of consumption reduction in work-related expenditures (transport, meals out, clothing) increase in home production of services and/or more efficient purchases unexpectedly low pensions or liquidity problems (not in Italy, though  think of severance pay - liquidazione!) ¡N3
s
~ÿ3þ

ª–

ó>!
Ÿ¨What Others Have Done¡

Ÿ
 àBanks, Blundell and Tanner (1998) use repeated cross section data from the FES  they estimate log-linear Euler equations from cohort data by IV (using lagged interest rates, consumption and income growth as instruments) and find unexplained negative residuals around typical male retirement ages (60-67). The largest residual obtains at age 63 (1.5%). Altogether, cumulated residual are in the 8-10% region. Non-separabilities between leisure and consumption can explain only part of the drop. ¡>ï
P
P&ÿ3þµ
ª
2


  

D

ó?"
Ÿ¨What Others Have Done¡

Ÿ
 ÈBernheim, Skinner and Weinberg (2001) use panel data from the PSID to estimate Euler equations. Retirement status is instrumented by taking age-specific predicted probabilities conditional on demographics (however cannot explain spikes at ages 62 and 65). Median drop is 14%, but higher for low wealth Sample is split in groups: low wealth-to-income households drop their consumption most.  31% of households reduce their consumption by at least 35 percentage points at retirement .¡Hå
Z* ÿ3þäÿ3þ·ª
Ý
óY4
Ÿ¨What Others Have Done¡

Ÿ
¨‚
Possible explanations and related literature: Many workers are surprised by inadequate resources when they retire (not consistent with life-cycle model & rational expectations). Work related expenses. Home production and/or more efficient shopping (Aguiar and Hurst, 2005, Hurd and Rohwedder, 2006). Miniaci et al (2003) estimate by OLS the Italian retirement consumption drop at 5.4%. ¡0.
ZU
Z,

W
ªPù


 
Pó
Ÿ¨ What We Do¡

Ÿ¨º
An alternative identification strategy: we estimate the change in consumption at retirement by exploiting the exogenous variability in the retirement decision induced by the eligibility rules of the Italian pension system. Information on consumption expenditures, eligibility for retirement and retirement status is obtained from the Bank of Italy Survey on Household Income and Wealth (SHIW). No need of panel data to achieve identification.¡J»
Z&ÿ3þˆÿ3þË/™þó
Ÿ¨ Punch-line¡

Ÿ Key result: household non-durable consumption drops by 9.8% because of male retirement. A larger drop estimated for total food (14.1%). Our strategy provides non-parametric identification only for a subpopulation of those who retire (those who retire at the time they become eligible). We estimate smaller drops for  poverty sample . Our estimates can be reconciled with utility optimization - in the cross section, drop in work-related expenses and leisure substitutes is large enough to explain changes in consumption. ¡ZZ

ÿ3þÿ3þ9ÿ3þ…
ó
Ÿ¨The Causal Problem¡

Ÿ ÚLet S* be a variable denoting time to/from eligibility for retirement, negative values indicate that the subject is not yet eligible. Let R be the retirement status, R=1 for the retired and R=0 otherwise. Since retirement is an option available only to the eligible workers, the probability to retire is zero if S*<�0 (and it is thus discontinuous at S*=0 ). Let (Y1,Y0) be the two potential household consumption expenditures corresponding to the head being retired or not retired, respectively, and let ²=Y1-Y0 . Let Y = Y0+R² be observed consumption, where Ya"Y1 for households whose head is retired and Ya"Y0 otherwise.¡ân
ÿ3þ
ÿ3þ

ÿ3þE
ÿ3þÿ3þÿ3þx
%
 ÿ3þ
ÿ3þçÿÿ3þ
ÿ3þçÿ
ÿ3þ ÿ3þ
"O&ÿ3þ
ÿ3þ
ÿ3þçÿÿ3þÿ3þçÿ

ÿ3þçÿÿ3þ
ÿ3þçÿÿ3þ&ÿ3þ"&ÿ3þ
.ÿ3þçÿ&""
"&ÿ3þ
.ÿ3þçÿ"óJ+
Ÿ¨Identification in a nutshell¡

Ÿ ,
Start by comparing expenditures for households marginally close to S*=0; since Y = Y0+R² we have that Consider the difference around eligibility: ¡
f
,

/ÿ3þ
ÿ3þÿ3þÿ3þ
ÿ3þçÿÿ3þ&ÿ3þ 
ÿ3þ
,
"ªB
Tó
Ÿ¨Identification in a nutshell¡

Ÿ ŽKey identifying restriction (the mean consumption profile under the no-retirement alternative is smooth enough at zero): The result rests upon a weak regularity condition: if none of the heads were to retire no discontinuity in household consumption would take place at the time they become eligible (i.e. at S*=0)  see Hahn et al. (2001) and Battistin and Rettore (2006). This amounts to assuming that any idiosyncratic shocks relevant to the retirement choice and correlated with Y0 (e.g. health shocks) do not occur selectively at either side of the eligibility threshold. ¡–H
`
ÿ3þŒ
˜
çÿ_ª,[


Øó
Ÿ¨Identification in a nutshell¡

Ÿ¨¹
By using simple algebra we have: Estimators of the causal effect of retirement on consumption are analogue estimators obtained by replacing the quantities in the last expression by their empirical counterparts. Following Imbens and Angrist (1994) and Hanh et al. (2001), it can be shown that this expression coincides with the IV estimator obtained by instrumenting the endogenous variable R with the eligibility status defined from S*. ¡–%
Z”
Z

Z!A‹¬

ª>á


·ó\7
Ÿ¨Endogeneity of S*¡*







ª.
Ÿ
 ÌThe S* variable may be the outcome of individual choices (time to enter the labour market, temporary exits, etc). This might casts doubts that our identification strategy is marred by an endogeneity problem. Consider the regression we use to get the numerator of the IV estimate (the reduced form): Y= ´0 + ´1 S* + ´2 S*2 + ´3 1(S*>0) +µ The mean of Y conditional on S* is: E{Y|S*} = ´0 + ´1 S* + ´2 S*2 + ´3 1(S*>0) + E{µ|S*} where the last term does not vanish if S* is endogenous. ¡ +
Z'

Z%
Z5

Z;
Z
%
ÿ3þ
&ÿ3þ.ÿ3þçÿ&ÿ3þ.ÿ3þçÿ
&ÿ3þ
.ÿ3þ&ÿ3þ.ÿ3þçÿ
&ÿ3þ.ÿ3þ&ÿ3þ.ÿ3þçÿÿ3þ
ÿ3þÿ3þ&ÿ3þ"
*"ÿ3þ
ÿ3þÿ3þ
&ÿ3þ.ÿ3þçÿ&ÿ3þ.ÿ3þçÿ
&ÿ3þ
.ÿ3þ&ÿ3þ.ÿ3þçÿ
&ÿ3þ.ÿ3þ&ÿ3þ.ÿ3þçÿÿ3þ
ÿ3þÿ3þ&ÿ3þ
.ÿ3þ  ÿ3þ$"$$&$ÿ3þ$"$
$*$$"$
(( ªjL
i
e




  





 
 



 ó]8
Ÿ¨Endogeneity of S*¡ 



ª.
Ÿ
 ¬Nonetheless, the numerator of the IV estimand: E{Y|S* =0+}-E{Y|S* =0-} is not biased for ´3, the drop in consumption at the eligibility cut-off point, provided that: E{µ|S*=0+}=E{µ|S*=0-}. Our identifying restriction is that the dependence between the unobservables µ and S* is not discontinuously changing at the cut-off for eligibility. ¡‚/Z

Z`
Z

Z–Z


Z

Z
Z4"*"
*"*"
*"""
&ÿ3þ
.ÿ3þçÿ
&ÿ3þJ"ÿ3þ&ÿ3þ
.ÿ3þ&ÿ3þ
.ÿ3þÿ3þ&ÿ3þ
.ÿ3þ&ÿ3þ
.ÿ3þÿ3þM"
*"&ÿ3þ8"
" 
$$ªº 




 
 
 
B   
 






 

ó^
9
Ÿ¨Data¡

ó‹>
Ÿ¨The Reform Process¡

ª@

Ÿ
¨
Two major reforms in 1992 (Amato) and 1995 (Dini) Gradually moving from defined benefit to (notionally) defined contribution Lots of additional minor changes have been made nearly every year since 1992 Further changes will take place in 2008 (restrictions on early retirement)ªR
) 


  
x
 óG
)
ٻ

óC
%
Ÿ¨The measurement of eligibility¡

óD
&
Ÿ¨The measurement of eligibility¡

ó$

ٻ

óH*
ó

Ÿ¨ Retirement by Eligibility Status¡!!

ó
Ÿ¨Measurement Error¡

Ÿ¨OWe observe a non-negligible fraction of retired individuals amongst the ineligibles (this regardless of having imputed the eligibility variable for some individuals): this we take as evidence of measurement error in the data. Measurement error bias in the estimation of causal parameters can be severe (see, for example, Battistin and Chesher, 2004). Misclassification of the retirement status R is unlikely to be important, as retired individuals are asked a detailed set of questions on their pension. Measurement error in the eligibility variable S* is most likely to be the explanation. ¡hPö
›

 (ªO

úó
Ÿ¨Measurement Error¡

Ÿ¨º
Based on what we observe in the data, measurement error in S* can not be classical. If S=S*+u, with u a zero-mean error orthogonal to S* we would not observe any discontinuity in the proportion of retired individual s at the cut-off point. A type of measurement error consistent with the discontinuity in the raw probability of R=1 we observe in the data is: where Z is an indicator for having S= S* and U is a classical measurement error.¡J
i
PR
P<�

 

+

 ZY  % 
  
 


 
 # ó&
Ÿ¨Measurement Error¡

Ÿ¨Parameter of interest ¡B
Zÿ3þ

ÿ3þóP
-
Ÿ¨ Estimation¡

óƒ:
Ÿ¨lA key feature of the Italian pension system is that many individuals retire as soon as they become eligible¡mm


ªl 
Ÿ
ª
ó:

Ÿ fFirst StageE{R|S} = ±0 + ±1 S + ±2 S2 + ±3 1(S>0) ¡Ö4

ÿ3þ 
"*çÿ"*çÿ"*çÿ
"*"*çÿ
ª¨



 
ó;

Ÿ hReduced FormE{Y|S} = ´0 + ´1 S + ´2 S2 + ´3 1(S>0) ¡Þ5

ÿ3þ 
"
 çÿ
"
 çÿ
"
 çÿ
 
"
çÿ  ª°



 
ó(

Ÿ¨Estimation results¡

óX
3
Ÿ¨Estimation results¡

ó.
Ÿ¨Specification tests¡

Ÿ¨ŠIdentification strategy requires no change at S* = 0 in variables that affect consumption but are not affected by eligibility status. We show that this condition is met by education, age, size of the main residence and proportion of couples Exclusion restriction: family size. This is negatively affected by retirement induced by eligibility (-0.30). In particular, number of grown children cohabiting with their parents falls (-0.25). Possible explanation: individuals retire as soon as they become eligible as a way to let their children move out (they give them part of their severance pay) Hence actual consumption drop is even smaller than 9.8%!¡‹Z‹ó‡<
Ÿ¨Economic Interpretation¡

Ÿ In the US, consumption drop is largest among the low pre-retirement wealth (BSW). We estimate a pre-eligibility wealth equation, and use it to predict for the whole sample (w_fit). We show this measure does not change at S*=0. We select those households who w_fit is in the bottom third (w_poor). We call this  poverty sample We estimate small and insignificant effects of eligibility-induced retirement for this poverty sample Our estimated consumption drop is unlikely to be due to lack of financial resources!¡bZ­

ÿ3þP

ÿ3þÿ3þܪ>­
P

Üó…;
Ÿ¨Back of the Envelope Stuff¡

Ÿ¨…A causal effect of retirement on consumption expenditures is not surprising per se. The question is whether this is consistent with life-time optimizing behavior. A consumption drop can occur if utility is not additively separable in consumption and leisure: since leisure increases abruptly at retirement, consumption increases or decreases depending on how leisure affects the marginal utility of consumption. For instance, if utility is Cobb-Douglas in male leisure and non-durable consumption, and individuals work full time prior to retirement, our estimated 9.8% consumption drop implies an elasticity of intertemporal substitution of 0.84¡X†Z=y6…
ó‰=
Ÿ¨Work-Related Expenses¡

Ÿ¨¢
One good model is restrictive: Some goods are leisure substitutes (e.g. food out) or work-related (e.g. travel, clothing), other leisure complements (food in, home heating). We explore which components of household expenditure drive the fall that we have documented. We use data from the 2002 Survey of Family Budgets: this contains no information on eligibility, but detailed information on household expenditures.¡£
Z£
óR/
Ÿ¨Work-Related Expenses¡

Ÿ  We compare expenditures for households whose head s age is 50-54 and 65-69. Heads in the latter group are mostly retired, mostly employed in the former group. The comparison is corrected for composition differences with respect to region of residence, number of equivalent adults and size of the main residence. Support issues turn out to be of no concern. The overall drop is 15.6% : 50% larger than the estimated retirement consumption drop (9.8%). A third of the drop is due to age, two thirds to retirement.¡|
<�/


ÿ3þ=

ÿ3þ@óQ
.
ٻ

óS0
Ÿ¨Work-Related Expenses¡

Ÿ  Total difference is - 241 euros (-15.6%). Mostly accounted for by meals out (-36), clothing (-58), transport (-76). Overall 170 out of 241  drop is accounted for by  work-related expenses . Our estimates imply that consumption should fall by 151 Euros because of eligibility-induced retirement. Work-related expenses are less important for manual workers (canteen meals and overalls normally provided by the employer  public transport is heavily subsidized). This may explain why there is no drop for the poverty sample! óT1
Ÿ¨Conclusions¡

٬I
We estimate that non-durable consumption falls by 9.8% in Italy because of retirement. This drop is lower than in the US (14 %) but comparable to the UK (8%-10%, non-durable consumption). Our estimates can be reconciled with utility optimization: in the cross section, drop in work-related expenses is large enough to explain it./ðDó`
óa

ób
óc
ód
óe
óf
óg
óh
ói
ój
ók
ól
óm
ón
óo
óp
óq
ór
ós
ót
óu
óv
ów
óx
óy
óz
ó{
ó|
ó}
ó~
ó
ó€
ó!
ó‚"
ó„#
ó†$
óˆ%
óŠ&
êîï
ï €
0
ðþàð
ð–ð(
ð ð
ð^² ð
“ð6A
ƒ
¿
À

ÿ

?ð
ù´1ðH ð

ƒð0
ƒ
“
ŽŸ‹”
Þ½h¿
ÿ
 ?

ð ÿÿÿ€€€Ì™33ÌÌÌÿ²²²ˆ‘Š‰º___PPT10‹ië.BÃÅ
¢]+Dñ='ñ }ÿÿÿÿ=ñ @
Bñ
+r
%NGýÕõ)
™
Nô×
‹
Å1èЇ
é(€àx/ _A

 F ò
ÌžÍ

Ã
n
–ºEquation ºEquation.DSMT40º*MathType 5.0 Equation̨Í

Ã
š
–ºGrafico ºMSGraph.Chart.80º4Grafico di Microsoft GraphÌžÍ

Ã
¬
!–ºEquation ºEquation.DSMT40º*MathType 5.0 EquationÌžÍ

Ã
}-–ºEquation ºEquation.DSMT40º*MathType 5.0 EquationÌžÍ

Ã
®
8–ºEquation ºEquation.DSMT40º*MathType 5.0 EquationÌžÍ

Ã

K–ºEquation ºEquation.DSMT40º*MathType 5.0 EquationÌžÍ

Ã
¦
L–ºEquation ºEquation.DSMT40º*MathType 5.0 EquationÌžÍ

Ã
©
M–ºEquation ºEquation.DSMT40º*MathType 5.0 Equationò
/È0Ò
ÕL·DTimes New RomanT©T©¬r’Ü–É0Ü–Õ¤€@ÿÿ¥.©  @£nÿý?" dd@ÿÿïÿÿÿÿÿÿ


@@``€€tðlð`(‹¼
R
    ‹!¢ % - /3476:;>@BCEF‰
KMNP$QRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~€‚ƒÿ
ð”2ð$ùª•aŸ¨e§7 ;Ú'¿ÿ
2ð$’eªò'— ¤¼KCÚcÿ0
2ð$Ð(†€3jC9ßÌóìX´‚ÿk
N2ð$ã‰ã6˶»<«"C°³Xÿò
¹%bð$ñ½ìo‚ˆ|Ý[7,9<çÿÜ«6bð$J‰3’…†¾çD!5ƒÿÈ
‡C2ð$ʍê>HÎ J‰ÆoÍë…ÿá0
"ð$$×oyòu)H´ÛÍÍÿF
~<2ð$šó›žÂe¢Áz,¶þk.ÿú
ÄH2ð$ WÌìוùdâž« ÞûIÿv
¾L2ð$µÃK l\­7"Iþ“ÔqÿÞ4P2ð$x‰–(öoþ¾°Qȧ+àÿê
T2ð$¸¿ÚkkçSxÖ9€»ÿÆ
üV2ð$.‚M¸D†XnV$‰Ø'¨ÿÀ
:]2ð$©RØýè™Fö ˜ËgÍm¬ÿx
ÂZƒð0
ƒ
†A¿
À

ÅAÿ

@ñÿ3f™ÿÿ™@ñ
÷ðó€Ðì
ÿâžïÊš;Nh8Êš;

úgþ
ý4EdEd\›’ô–É0Ìýÿÿ¦ÿÿÿ
pûppû
@<�ý4dddd —‘w0T©ˆr’
<�ý4BdBd —‘w0T©ˆr’H<�ý4!d!d —‘w0T©ˆr’
ˆiŠaº___PPT10‹A pµpµä. ºCasaå.±6

?ÙÚ %OÙÚ =ðsóI,
Ÿ¨7How Large is the Retirement Consumption Drop in Italy?¡88

(
Ÿ¨>Erich Battistin Agar Brugiavini Enrico Rettore Guglielmo Weber¡?P?ª4
 0ó

Ÿ¨ Motivation¡

Ÿ¨É
According to the life-cycle permanent income Hp consumers decide how much to consume, keeping in mind their future prospects They form intertemporal plans aimed at smoothing the (discounted) marginal utility of consumption over the life cycle Any period to period change in the actual level of the marginal utility of consumption is uncorrelated with past information available to the household. That is, it should be a result of unpredictable shocks. ¡TÇ

ÿ3þÿ3þ•

óZ5
Ÿ¨ Motivation¡

Ÿ¨¼
This holds true also around retirement age: any change in the marginal utility of consumption should be uncorrelated with planned retirement behaviour. Recent micro evidence has emphasized that there is a one-off drop in consumption at the time of retirement that might be hard to reconcile with life-time optimizing behaviour (see for example Banks et al., 1998, Bernheim et al., 2001). This is known as the retirement consumption puzzle ¡„º

{ÿ3þÆÿ3þª>Ž
§
&
Hó[6
Ÿ¨ Motivation¡

Ÿ JSome possible reasons mentioned in the literature: changes in preferences due to increased leisure shocks inducing retirement and affecting the level of consumption reduction in work-related expenditures (transport, meals out, clothing) increase in home production of services and/or more efficient purchases unexpectedly low pensions or liquidity problems (not in Italy, though  think of severance pay - liquidazione!) ¡N3
s
~ÿ3þ

ª–

ó>!
Ÿ¨What Others Have Done¡

Ÿ
 àBanks, Blundell and Tanner (1998) use repeated cross section data from the FES  they estimate log-linear Euler equations from cohort data by IV (using lagged interest rates, consumption and income growth as instruments) and find unexplained negative residuals around typical male retirement ages (60-67). The largest residual obtains at age 63 (1.5%). Altogether, cumulated residual are in the 8-10% region. Non-separabilities between leisure and consumption can explain only part of the drop. ¡>ï
P
P&ÿ3þµ
ª
2


  

D

ó?"
Ÿ¨What Others Have Done¡

Ÿ
 ÈBernheim, Skinner and Weinberg (2001) use panel data from the PSID to estimate Euler equations. Retirement status is instrumented by taking age-specific predicted probabilities conditional on demographics (however cannot explain spikes at ages 62 and 65). Median drop is 14%, but higher for low wealth Sample is split in groups: low wealth-to-income households drop their consumption most.  31% of households reduce their consumption by at least 35 percentage points at retirement .¡Hå
Z* ÿ3þäÿ3þ·ª
Ý
óY4
Ÿ¨What Others Have Done¡

Ÿ
¨‚
Possible explanations and related literature: Many workers are surprised by inadequate resources when they retire (not consistent with life-cycle model & rational expectations). Work related expenses. Home production and/or more efficient shopping (Aguiar and Hurst, 2005, Hurd and Rohwedder, 2006). Miniaci et al (2003) estimate by OLS the Italian retirement consumption drop at 5.4%. ¡0.
ZU
Z,

W
ªPù


 
Pó
Ÿ¨ What We Do¡

Ÿ¨º
An alternative identification strategy: we estimate the change in consumption at retirement by exploiting the exogenous variability in the retirement decision induced by the eligibility rules of the Italian pension system. Information on consumption expenditures, eligibility for retirement and retirement status is obtained from the Bank of Italy Survey on Household Income and Wealth (SHIW). No need of panel data to achieve identification.¡J»
Z&ÿ3þˆÿ3þË/™þó
Ÿ¨ Punch-line¡

Ÿ Key result: household non-durable consumption drops by 9.8% because of male retirement. A larger drop estimated for total food (14.1%). Our strategy provides non-parametric identification only for a subpopulation of those who retire (those who retire at the time they become eligible). We estimate smaller drops for  poverty sample . Our estimates can be reconciled with utility optimization - in the cross section, drop in work-related expenses and leisure substitutes is large enough to explain changes in consumption. ¡ZZ

ÿ3þÿ3þ9ÿ3þ…
ó
Ÿ¨The Causal Problem¡

Ÿ ÚLet S* be a variable denoting time to/from eligibility for retirement, negative values indicate that the subject is not yet eligible. Let R be the retirement status, R=1 for the retired and R=0 otherwise. Since retirement is an option available only to the eligible workers, the probability to retire is zero if S*<�0 (and it is thus discontinuous at S*=0 ). Let (Y1,Y0) be the two potential household consumption expenditures corresponding to the head being retired or not retired, respectively, and let ²=Y1-Y0 . Let Y = Y0+R² be observed consumption, where Ya"Y1 for households whose head is retired and Ya"Y0 otherwise.¡ân
ÿ3þ
ÿ3þ

ÿ3þE
ÿ3þÿ3þÿ3þx
%
 ÿ3þ
ÿ3þçÿÿ3þ
ÿ3þçÿ
ÿ3þ ÿ3þ
"O&ÿ3þ
ÿ3þ
ÿ3þçÿÿ3þÿ3þçÿ

ÿ3þçÿÿ3þ
ÿ3þçÿÿ3þ&ÿ3þ"&ÿ3þ
.ÿ3þçÿ&""
"&ÿ3þ
.ÿ3þçÿ"óJ+
Ÿ¨Identification in a nutshell¡

Ÿ ,
Start by comparing expenditures for households marginally close to S*=0; since Y = Y0+R² we have that Consider the difference around eligibility: ¡
f
,

/ÿ3þ
ÿ3þÿ3þÿ3þ
ÿ3þçÿÿ3þ&ÿ3þ 
ÿ3þ
,
"ªB
Tó
Ÿ¨Identification in a nutshell¡

Ÿ ŽKey identifying restriction (the mean consumption profile under the no-retirement alternative is smooth enough at zero): The result rests upon a weak regularity condition: if none of the heads were to retire no discontinuity in household consumption would take place at the time they become eligible (i.e. at S*=0)  see Hahn et al. (2001) and Battistin and Rettore (2006). This amounts to assuming that any idiosyncratic shocks relevant to the retirement choice and correlated with Y0 (e.g. health shocks) do not occur selectively at either side of the eligibility threshold. ¡–H
`
ÿ3þŒ
˜
çÿ_ª,[


Øó
Ÿ¨Identification in a nutshell¡

Ÿ¨¹
By using simple algebra we have: Estimators of the causal effect of retirement on consumption are analogue estimators obtained by replacing the quantities in the last expression by their empirical counterparts. Following Im‚ƒ„…†‡ˆ‰Š‹ŒŽ‘’“”•–—˜™š›œžŸ ¡¢£¤¥¦§¨©ª«¬­®¯°±²³´µ¶·¸¹º»¼½¾¿ÀÁÂÃÄÅÆÇÈÉÊËÌÍÎÏÐÑÒÓÔÕÖ×ØÙÚÛÜÝÞßàáâãäåæçèéêëìíîïðñòóôõö÷øùúûüýþÿ
bens and Angrist (1994) and Hanh et al. (2001), it can be shown that this expression coincides with the IV estimator obtained by instrumenting the endogenous variable R with the eligibility status defined from S*. ¡–%
Z”
Z

Z!A‹¬

ª>á


·ó\7
Ÿ¨Endogeneity of S*¡*







ª.
Ÿ
 ÌThe S* variable may be the outcome of individual choices (time to enter the labour market, temporary exits, etc). This might casts doubts that our identification strategy is marred by an endogeneity problem. Consider the regression we use to get the numerator of the IV estimate (the reduced form): Y= ´0 + ´1 S* + ´2 S*2 + ´3 1(S*>0) +µ The mean of Y conditional on S* is: E{Y|S*} = ´0 + ´1 S* + ´2 S*2 + ´3 1(S*>0) + E{µ|S*} where the last term does not vanish if S* is endogenous. ¡ +
Z'

Z%
Z5

Z;
Z
%
ÿ3þ
&ÿ3þ.ÿ3þçÿ&ÿ3þ.ÿ3þçÿ
&ÿ3þ
.ÿ3þ&ÿ3þ.ÿ3þçÿ
&ÿ3þ.ÿ3þ&ÿ3þ.ÿ3þçÿÿ3þ
ÿ3þÿ3þ&ÿ3þ"
*"ÿ3þ
ÿ3þÿ3þ
&ÿ3þ.ÿ3þçÿ&ÿ3þ.ÿ3þçÿ
&ÿ3þ
.ÿ3þ&ÿ3þ.ÿ3þçÿ
&ÿ3þ.ÿ3þ&ÿ3þ.ÿ3þçÿÿ3þ
ÿ3þÿ3þ&ÿ3þ
.ÿ3þ  ÿ3þ$"$$&$ÿ3þ$"$
$*$$"$
(( ªjL
i
e




  





 
 



 ó]8
Ÿ¨Endogeneity of S*¡ 



ª.
Ÿ
 ¬Nonetheless, the numerator of the IV estimand: E{Y|S* =0+}-E{Y|S* =0-} is not biased for ´3, the drop in consumption at the eligibility cut-off point, provided that: E{µ|S*=0+}=E{µ|S*=0-}. Our identifying restriction is that the dependence between the unobservables µ and S* is not discontinuously changing at the cut-off for eligibility. ¡‚/Z

Z`
Z

Z–Z


Z

Z
Z4"*"
*"*"
*"""
&ÿ3þ
.ÿ3þçÿ
&ÿ3þJ"ÿ3þ&ÿ3þ
.ÿ3þ&ÿ3þ
.ÿ3þÿ3þ&ÿ3þ
.ÿ3þ&ÿ3þ
.ÿ3þÿ3þM"
*"&ÿ3þ8"
" 
$$ªº 




 
 
 
B   
 






 

ó^
9
Ÿ¨Data¡

ó‹>
Ÿ¨The Reform Process¡

ª@

Ÿ
¨
Two major reforms in 1992 (Amato) and 1995 (Dini) Gradually moving from defined benefit to (notionally) defined contribution Lots of additional minor changes have been made nearly every year since 1992 Further changes will take place in 2008 (restrictions on early retirement)ªR
) 


  
x
 óG
)
ٻ

óC
%
Ÿ¨The measurement of eligibility¡

óD
&
Ÿ¨The measurement of eligibility¡

ó$

ٻ

óH*
ó

Ÿ¨ Retirement by Eligibility Status¡!!

ó
Ÿ¨Measurement Error¡

Ÿ¨OWe observe a non-negligible fraction of retired individuals amongst the ineligibles (this regardless of having imputed the eligibility variable for some individuals): this we take as evidence of measurement error in the data. Measurement error bias in the estimation of causal parameters can be severe (see, for example, Battistin and Chesher, 2004). Misclassification of the retirement status R is unlikely to be important, as retired individuals are asked a detailed set of questions on their pension. Measurement error in the eligibility variable S* is most likely to be the explanation. ¡hPö
›

 (ªO

úó
Ÿ¨Measurement Error¡

Ÿ¨º
Based on what we observe in the data, measurement error in S* can not be classical. If S=S*+u, with u a zero-mean error orthogonal to S* we would not observe any discontinuity in the proportion of retired individual s at the cut-off point. A type of measurement error consistent with the discontinuity in the raw probability of R=1 we observe in the data is: where Z is an indicator for having S= S* and U is a classical measurement error.¡J
i
PR
P<�

 

+

 ZY  % 
  
 


 
 # ó&
Ÿ¨Measurement Error¡

Ÿ¨Parameter of interest ¡B
Zÿ3þ

ÿ3þóP
-
Ÿ¨ Estimation¡

óƒ:
Ÿ¨lA key feature of the Italian pension system is that many individuals retire as soon as they become eligible¡mm


ªl 
Ÿ
ª
ó:

Ÿ fFirst StageE{R|S} = ±0 + ±1 S + ±2 S2 + ±3 1(S>0) ¡Ö4

ÿ3þ 
"*çÿ"*çÿ"*çÿ
"*"*çÿ
ª¨



 
ó;

Ÿ hReduced FormE{Y|S} = ´0 + ´1 S + ´2 S2 + ´3 1(S>0) ¡Þ5

ÿ3þ 
"
 çÿ
"
 çÿ
"
 çÿ
 
"
çÿ  ª°



 
ó(

Ÿ¨Estimation results¡

óX
3
Ÿ¨Estimation results¡

ó.
Ÿ¨Specification tests¡

Ÿ¨ŠIdentification strategy requires no change at S* = 0 in variables that affect consumption but are not affected by eligibility status. We show that this condition is met by education, age, size of the main residence and proportion of couples Exclusion restriction: family size. This is negatively affected by retirement induced by eligibility (-0.30). In particular, number of grown children cohabiting with their parents falls (-0.25). Possible explanation: individuals retire as soon as they become eligible as a way to let their children move out (they give them part of their severance pay) Hence actual consumption drop is even smaller than 9.8%!¡‹Z‹ó‡<
Ÿ¨Economic Interpretation¡

Ÿ In the US, consumption drop is largest among the low pre-retirement wealth (BSW). We estimate a pre-eligibility wealth equation, and use it to predict for the whole sample (w_fit). We show this measure does not change at S*=0. We select those households who w_fit is in the bottom third (w_poor). We call this  poverty sample We estimate small and insignificant effects of eligibility-induced retirement for this poverty sample Our estimated consumption drop is unlikely to be due to lack of financial resources!¡bZ­

ÿ3þP

ÿ3þÿ3þܪ>­
P

Üó…;
Ÿ¨Back of the Envelope Stuff¡

Ÿ¨…A causal effect of retirement on consumption expenditures is not surprising per se. The question is whether this is consistent with life-time optimizing behavior. A consumption drop can occur if utility is not additively separable in consumption and leisure: since leisure increases abruptly at retirement, consumption increases or decreases depending on how leisure affects the marginal utility of consumption. For instance, if utility is Cobb-Douglas in male leisure and non-durable consumption, and individuals work full time prior to retirement, our estimated 9.8% consumption drop implies an elasticity of intertemporal substitution of 0.84¡X†Z=y6…
ó‰=
Ÿ¨Work-Related Expenses¡

Ÿ¨¢
One good model is restrictive: Some goods are leisure substitutes (e.g. food out) or work-related (e.g. travel, clothing), other leisure complements (food in, home heating). We explore which components of household expenditure drive the fall that we have documented. We use data from the 2002 Survey of Family Budgets: this contains no information on eligibility, but detailed information on household expenditures.¡£
Z£
óR/
Ÿ¨Work-Related Expenses¡

Ÿ  We compare expenditures for households whose head s age is 50-54 and 65-69. Heads in the latter group are mostly retired, mostly employed in the former group. The comparison is corrected for composition differences with respect to region of residence, number of equivalent adults and size of the main residence. Support issues turn out to be of no concern. The overall drop is 15.6% : 50% larger than the estimated retirement consumption drop (9.8%). A third of the drop is due to age, two thirds to retirement.¡|
<�/


ÿ3þ=

ÿ3þ@óQ
.
ٻ

óS0
Ÿ¨Work-Related Expenses¡

Ÿ  Total difference is - 241 euros (-15.6%). Mostly accounted for by meals out (-36), clothing (-58), transport (-76). Overall 170 out of 241  drop is accounted for by  work-related expenses . Our estimates imply that consumption should fall by 151 Euros because of eligibility-induced retirement. Work-related expenses are less important for manual workers (canteen meals and overalls normally provided by the employer  public transport is heavily subsidized). This may explain why there is no drop for the poverty sample! óT1
Ÿ¨Conclusions¡

٬I
We estimate that non-durable consumption falls by 9.8% in Italy because of retirement. This drop is lower than in the US (14 %) but comparable to the UK (8%-10%, non-durable consumption). Our estimates can be reconciled with utility optimization: in the cross section, drop in work-related expenses is large enough to explain it./ðDó`
óa

ób
óc
ód
óe
óf
óg
óh
ói
ój
ók
ól
óm
ón
óo
óp
óq
ór
ós
ót
óu
óv
ów
óx
óy
óz
ó{
ó|
ó}
ó~
ó
ó€
ó!
ó‚"
ó„#
ó†$
óˆ%
óŠ&
êr
0Øõ)
™Ø`
‹
Å1èˆ
é(€àx/ _A

 F ò
ÌžÍ

Ã
n
–ºEquation ºEquation.DSMT40º*MathType 5.0 Equation̨Í

Ã
š
–ºGrafico ºMSGraph.Chart.80º4Grafico di Microsoft GraphÌžÍ

Ã
¬
!–ºEquation ºEquation.DSMT40º*MathType 5.0 EquationÌžÍ

Ã
}-–ºEquation ºEquation.DSMT40º*MathType 5.0 EquationÌžÍ

Ã
®
8–ºEquation ºEquation.DSMT40º*MathType 5.0 EquationÌžÍ

Ã

K–ºEquation ºEquation.DSMT40º*MathType 5.0 EquationÌžÍ

Ã
¦
L–ºEquation ºEquation.DSMT40º*MathType 5.0 EquationÌžÍ

Ã
©
M–ºEquation ºEquation.DSMT40º*MathType 5.0 Equationò`
/È0Ò
Õ˜·DTimes New RomanT©T©¬r’Ü–É0Ü–Õ·DArialNew RomanT©T©¬r’Ü–É0Ü–Õ"¤€@ÿÿ¥.©  @£nÿý?" dd@ÿÿïÿÿÿÿÿÿ


@@``€€„ð|ðp0R
    ‹!¢ % - /3476:;>•
@BCEF‰
KMNP$QRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~€‚ƒÿ
ð”2ð$ùª•aŸ¨e§7 ;Ú'¿ÿ
2ð$’eªò'— ¤¼KCÚcÿ0
2ð$Ð(†€3jC9ßÌóìX´‚ÿk
N2ð$ã‰ã6˶»<«"C°³Xÿò
¹%bð$ñ½ìo‚ˆ|Ý[7,9<çÿÜ«6bð$J‰3’…†¾çD!5ƒÿÈ
‡C2ð$ʍê>HÎ J‰ÆoÍë…ÿá0
"ð$$×oyòu)H´ÛÍÍÿF
~<2ð$šó›žÂe¢Áz,¶þk.ÿú
ÄH2ð$ WÌìוùdâž« ÞûIÿv
¾L2ð$µÃK l\­7"Iþ“ÔqÿÞ4P2ð$x‰–(öoþ¾°Qȧ+àÿê
T2ð$¸¿ÚkkçSxÖ9€»ÿÆ
üVð$ÿ2ð$©RØýè™Fö ˜ËgÍm¬ÿx
ÂZƒð0
ƒ
†A¿
À

ÅAÿ

@ñÿ3f™ÿÿ™@ñ
÷ðó€Ðì
ÿâžïÊš;Nh8Êš;

úgþ
ý4EdEd\›’ô–É0Ìýÿÿ¦ÿÿÿ
pûppû
@<�ý4dddd —‘w0T©ˆr’
<�ý4BdBd —‘w0T©ˆr’H<�ý4!d!d —‘w0T©ˆr’
ˆiŠaº___PPT10‹A pµpµä. ºCasaå.±6

?ÙÚ %OÙÚ =ðsóI,
Ÿ¨7How Large is the Retirement Consumption Drop in Italy?¡88

(
Ÿ¨>Erich Battistin Agar Brugiavini Enrico Rettore Guglielmo Weber¡?P?ª4
 0ó

Ÿ¨ Motivation¡

Ÿ¨É
According to the life-cycle permanent income Hp consumers decide how much to consume, keeping in mind their future prospects They form intertemporal plans aimed at smoothing the (discounted) marginal utility of consumption over the life cycle Any period to period change in the actual level of the marginal utility of consumption is uncorrelated with past information available to the household. That is, it should be a result of unpredictable shocks. ¡TÇ

ÿ3þÿ3þ•

óZ5
Ÿ¨ Motivation¡

Ÿ¨¼
This holds true also around retirement age: any change in the marginal utility of consumption should be uncorrelated with planned retirement behaviour. Recent micro evidence has emphasized that there is a one-off drop in consumption at the time of retirement that might be hard to reconcile with life-time optimizing behaviour (see for example Banks et al., 1998, Bernheim et al., 2001). This is known as the retirement consumption puzzle ¡„º

{ÿ3þÆÿ3þª>Ž
§
&
Hó[6
Ÿ¨ Motivation¡

Ÿ JSome possible reasons mentioned in the literature: changes in preferences due to increased leisure shocks inducing retirement and affecting the level of consumption reduction in work-related expenditures (transport, meals out, clothing) increase in home production of services and/or more efficient purchases unexpectedly low pensions or liquidity problems (not in Italy, though  think of severance pay - liquidazione!) ¡N3
s
~ÿ3þ

ª–

ó>!
Ÿ¨What Others Have Done¡

Ÿ
 àBanks, Blundell and Tanner (1998) use repeated cross section data from the FES  they estimate log-linear Euler equations from cohort data by IV (using lagged interest rates, consumption and income growth as instruments) and find unexplained negative residuals around typical male retirement ages (60-67). The largest residual obtains at age 63 (1.5%). Altogether, cumulated residual are in the 8-10% region. Non-separabilities between leisure and consumption can explain only part of the drop. ¡>ï
P
P&ÿ3þµ
ª
2


  

D

ó?"
Ÿ¨What Others Have Done¡

Ÿ
 ÈBernheim, Skinner and Weinberg (2001) use panel data from the PSID to estimate Euler equations. Retirement status is instrumented by taking age-specific predicted probabilities conditional on demographics (however cannot explain spikes at ages 62 and 65). Median drop is 14%, but higher for low wealth Sample is split in groups: low wealth-to-income households drop their consumption most.  31% of households reduce their consumption by at least 35 percentage points at retirement .¡Hå
Z* ÿ3þäÿ3þ·ª
Ý
óY4
Ÿ¨What Others Have Done¡

Ÿ
¨‚
Possible explanations and related literature: Many workers are surprised by inadequate resources when they retire (not consistent with life-cycle model & rational expectations). Work related expenses. Home production and/or more efficient shopping (Aguiar and Hurst, 2005, Hurd and Rohwedder, 2006). Miniaci et al (2003) estimate by OLS the Italian retirement consumption drop at 5.4%. ¡0.
ZU
Z,

W
ªPù


 
Pó
Ÿ¨ What We Do¡

Ÿ¨º
An alternative identification strategy: we estimate the change in consumption at retirement by exploiting the exogenous variability in the retirement decision induced by the eligibility rules of the Italian pension system. Information on consumption expenditures, eligibility for retirement and retirement status is obtained from the Bank of Italy Survey on Household Income and Wealth (SHIW). No need of panel data to achieve identification.¡J»
Z&ÿ3þˆÿ3þË/™þó
Ÿ¨ Punch-line¡

Ÿ Key result: household non-durable consumption drops by 9.8% because of male retirement. A larger drop estimated for total food (14.1%). Our strategy provides non-parametric identification only for a subpopulation of those who retire (those who retire at the time they become eligible). We estimate smaller drops for  poverty sample . Our estimates can be reconciled with utility optimization - in the cross section, drop in work-related expenses and leisure substitutes is large enough to explain changes in consumption. ¡ZZ

ÿ3þÿ3þ9ÿ3þ…
ó
Ÿ¨The Causal Problem¡

Ÿ ÚLet S* be a variable denoting time to/from eligibility for retirement, negative values indicate that the subject is not yet eligible. Let R be the retirement status, R=1 for the retired and R=0 otherwise. Since retirement is an option available only to the eligible workers, the probability to retire is zero if S*<�0 (and it is thus discontinuous at S*=0 ). Let (Y1,Y0) be the two potential household consumption expenditures corresponding to the head being retired or not retired, respectively, and let ²=Y1-Y0 . Let Y = Y0+R² be observed consumption, where Ya"Y1 for households whose head is retired and Ya"Y0 otherwise.¡ân
ÿ3þ
ÿ3þ

ÿ3þE
ÿ3þÿ3þÿ3þx
%
 ÿ3þ
ÿ3þçÿÿ3þ
ÿ3þçÿ
ÿ3þ ÿ3þ
"O&ÿ3þ
ÿ3þ
ÿ3þçÿÿ3þÿ3þçÿ

ÿ3þçÿÿ3þ
ÿ3þçÿÿ3þ&ÿ3þ"&ÿ3þ
.ÿ3þçÿ&""
"&ÿ3þ
.ÿ3þçÿ"óJ+
Ÿ¨Identification in a nutshell¡

Ÿ ,
Start by comparing expenditures for households marginally close to S*=0; since Y = Y0+R² we have that Consider the difference around eligibility: ¡
f
,

/ÿ3þ
ÿ3þÿ3þÿ3þ
ÿ3þçÿÿ3þ&ÿ3þ 
ÿ3þ
,
"ªB
Tó
Ÿ¨Identification in a nutshell¡

Ÿ ŽKey identifying restriction (the mean consumption profile under the no-retirement alternative is smooth enough at zero): The result rests upon a weak regularity condition: if none of the heads were to retire no discontinuity in household consumption would take place at the time they become eligible (i.e. at S*=0)  see Hahn et al. (2001) and Battistin and Rettore (2006). This amounts to assuming that any idiosyncratic shocks relevant to the retirement choice and correlated with Y0 (e.g. health shocks) do not occur selectively at either side of the eligibility threshold. ¡–H
`
ÿ3þŒ
˜
çÿ_ª,[


Øó
Ÿ¨Identification in a nutshell¡

Ÿ¨¹
By using simple algebra we have: Estimators of the causal effect of retirement on consumption are analogue estimators obtained by replacing the quantities in the last expression by their empirical counterparts. Following Imbens and Angrist (1994) and Hanh et al. (2001), it can be shown that this expression coincides with the IV estimator obtained by instrumenting the endogenous variable R with the eligibility status defined from S*. ¡–%
Z”
Z

Z!A‹¬

ª>á


·ó\7
Ÿ¨Endogeneity of S*¡*







ª.
Ÿ
 ÌThe S* variable may be the outcome of individual choices (time to enter the labour market, temporary exits, etc). This might casts doubts that our identification strategy is marred by an endogeneity problem. Consider the regression we use to get the numerator of the IV estimate (the reduced form): Y= ´0 + ´1 S* + ´2 S*2 + ´3 1(S*>0) +µ The mean of Y conditional on S* is: E{Y|S*} = ´0 + ´1 S* + ´2 S*2 + ´3 1(S*>0) + E{µ|S*} where the last term does not vanish if S* is endogenous. ¡ +
Z'

Z%
Z5

Z;
Z
%
ÿ3þ
&ÿ3þ.ÿ3þçÿ&ÿ3þ.ÿ3þçÿ
&ÿ3þ
.ÿ3þ&ÿ3þ.ÿ3þçÿ
&ÿ3þ.ÿ3þ&ÿ3þ.ÿ3þçÿÿ3þ
ÿ3þÿ3þ&ÿ3þ"
*"ÿ3þ
ÿ3þÿ3þ
&ÿ3þ.ÿ3þçÿ&ÿ3þ.ÿ3þçÿ
&ÿ3þ
.ÿ3þ&ÿ3þ.ÿ3þçÿ
&ÿ3þ.ÿ3þ&ÿ3þ.ÿ3þçÿÿ3þ
ÿ3þÿ3þ&ÿ3þ
.ÿ3þ  ÿ3þ$"$$&$ÿ3þ$"$
$*$$"$
(( ªjL
i
e




  





 
 



 ó]8
Ÿ¨Endogeneity of S*¡ 



ª.
Ÿ
 ¬Nonetheless, the numerator of the IV estimand: E{Y|S* =0+}-E{Y|S* =0-} is not biased for ´3, the drop in consumption at the eligibility cut-off point, provided that: E{µ|S*=0+}=E{µ|S*=0-}. Our identifying restriction is that the dependence between the unobservables µ and S* is not discontinuously changing at the cut-off for eligibility. ¡‚/Z

Z`
Z

Z–Z


Z

Z
Z4"*"
*"*"
*"""
&ÿ3þ
.ÿ3þçÿ
&ÿ3þJ"ÿ3þ&ÿ3þ
.ÿ3þ&ÿ3þ
.ÿ3þÿ3þ&ÿ3þ
.ÿ3þ&ÿ3þ
.ÿ3þÿ3þM"
*"&ÿ3þ8"
" 
$$ªº 




 
 
 
B   
 






 

ó^
9
Ÿ¨Data¡

ó‹>
Ÿ¨The Reform Process¡

ª@

Ÿ
¨
Two major reforms in 1992 (Amato) and 1995 (Dini) Gradually moving from defined benefit to (notionally) defined contribution Lots of additional minor changes have been made nearly every year since 1992 Further changes will take place in 2008 (restrictions on early retirement)ªR
) 


  
x
 óG)
óC
%
Ÿ¨The measurement of eligibility¡

óD
&
Ÿ¨The measurement of eligibility¡

ó$

ٻ

óH*
ó

Ÿ¨ Retirement by Eligibility Status¡!!

ó
Ÿ¨Measurement Error¡

Ÿ¨OWe observe a non-negligible fraction of retired individuals amongst the ineligibles (this regardless of having imputed the eligibility variable for some individuals): this we take as evidence of measurement error in the data. Measurement error bias in the estimation of causal parameters can be severe (see, for example, Battistin and Chesher, 2004). Misclassification of the retirement status R is unlikely to be important, as retired individuals are asked a detailed set of questions on their pension. Measurement error in the eligibility variable S* is most likely to be the explanation. ¡hPö
›

 (ªO

úó
Ÿ¨Measurement Error¡

Ÿ¨º
Based on what we observe in the data, measurement error in S* can not be classical. If S=S*+u, with u a zero-mean error orthogonal to S* we would not observe any discontinuity in the proportion of retired individual s at the cut-off point. A type of measurement error consistent with the discontinuity in the raw probability of R=1 we observe in the data is: where Z is an indicator for having S= S* and U is a classical measurement error.¡J
i
PR
P<�

 

+

 ZY  % 
  
 


 
 # ó&
Ÿ¨Measurement Error¡

Ÿ¨Parameter of interest ¡B
Zÿ3þ

ÿ3þóP
-
Ÿ¨ Estimation¡

óƒ:
Ÿ¨lA key feature of the Italian pension system is that many individuals retire as soon as they become eligible¡mm


ªl 
Ÿ
ª
ó:

Ÿ fFirst StageE{R|S} = ±0 + ±1 S + ±2 S2 + ±3 1(S>0) ¡Ö4

ÿ3þ 
"*çÿ"*çÿ"*çÿ
"*"*çÿ
ª¨



 
ó;

Ÿ hReduced FormE{Y|S} = ´0 + ´1 S + ´2 S2 + ´3 1(S>0) ¡Þ5

ÿ3þ 
"
 çÿ
"
 çÿ
"
 çÿ
 
"
çÿ  ª°



 
ó(

Ÿ¨Estimation results¡

óX
3
Ÿ¨Estimation results¡

ó.
Ÿ¨Specification tests¡

Ÿ¨ŠIdentification strategy requires no change at S* = 0 in variables that affect consumption but are not affected by eligibility status. We show that this condition is met by education, age, size of the main residence and proportion of couples Exclusion restriction: family size. This is negatively affected by retirement induced by eligibility (-0.30). In particular, number of grown children cohabiting with their parents falls (-0.25). Possible explanation: individuals retire as soon as they become eligible as a way to let their children move out (they give them part of their severance pay) Hence actual consumption drop is even smaller than 9.8%!¡‹Z‹ó‡<
Ÿ¨Economic Interpretation¡

Ÿ In the US, consumption drop is largest among the low pre-retirement wealth (BSW). We estimate a pre-eligibility wealth equation, and use it to predict for the whole sample (w_fit). We show this measure does not change at S*=0. We select those households who w_fit is in the bottom third (w_poor). We call this  poverty sample We estimate small and insignificant effects of eligibility-induced retirement for this poverty sample Our estimated consumption drop is unlikely to be due to lack of financial resources!¡bZ­

ÿ3þP

ÿ3þÿ3þܪ>­
P

Üó…;
Ÿ¨Back of the Envelope Stuff¡

Ÿ¨…A causal effect of retirement on consumption expenditures is not surprising per se. The question is whether this is consistent with life-time optimizing behavior. A consumption drop can occur if utility is not additively separable in consumption and leisure: since leisure increases abruptly at retirement, consumption increases or decreases depending on how leisure affects the marginal utility of consumption. For instance, if utility is Cobb-Douglas in male leisure and non-durable consumption, and individuals work full time prior to retirement, our estimated 9.8% consumption drop implies an elasticity of intertemporal substitution of 0.84¡X†Z=y6…
ó‰=
Ÿ¨Work-Related Expenses¡

Ÿ¨¢
One good model is restrictive: Some goods are leisure substitutes (e.g. food out) or work-related (e.g. travel, clothing), other leisure complements (food in, home heating). We explore which components of household expenditure drive the fall that we have documented. We use data from the 2002 Survey of Family Budgets: this contains no information on eligibility, but detailed information on household expenditures.¡£
Z£
óR/
Ÿ¨Work-Related Expenses¡

Ÿ  We compare expenditures for households whose head s age is 50-54 and 65-69. Heads in the latter group are mostly retired, mostly employed in the former group. The comparison is corrected for composition differences with respect to region of residence, number of equivalent adults and size of the main residence. Support issues turn out to be of no concern. The overall drop is 15.6% : 50% larger than the estimated retirement consumption drop (9.8%). A third of the drop is due to age, two thirds to retirement.¡|
<�/


ÿ3þ=

ÿ3þ@óQ
.
ٻ

óS0
Ÿ¨Work-Related Expenses¡

Ÿ  Total difference is - 241 euros (-15.6%). Mostly accounted for by meals out (-36), clothing (-58), transport (-76). Overall 170 out of 241  drop is accounted for by  work-related expenses . Our estimates imply that consumption should fall by 151 Euros because of eligibility-induced retirement. Work-related expenses are less important for manual workers (canteen meals and overalls normally provided by the employer  public transport is heavily subsidized). This may explain why there is no drop for the poverty sample! óT1
Ÿ¨Conclusions¡

٬I
We estimate that non-durable consumption falls by 9.8% in Italy because of retirement. This drop is lower than in the US (14 %) but comparable to the UK (8%-10%, non-durable consumption). Our estimates can be reconciled with utility optimization: in the cross section, drop in work-related expenses is large enough to explain it./ðDó`
óa

ób
óc
ód
óe
óf
óg
óh
ói
ój
ók
ól
óm
ón
óo
óp
óq
ór
ós
ót
óu
óv
ów
óx
óy
óz
ó{
ó|
ó}
ó~
ó
ó€
ó!
ó‚"
ó„#
ó†$
óˆ%
óŠ&
êî°;ï€
0Ç:ð¿:àðK”
ðW:ð(
ð ð
ð:ð˜
ðùZ
´ ð”

ð

#"ñ2Ÿ Ã&0´
éè´
´
´
´
ðZ
ù´ðÃ'
ðÐ ð€
 £ð<�€T¿
ƒ
¿

À

ÿ

?ðVL ´ ð\Ÿ¨40¡*
(

"

ª ð× ð
 £ð<�€ˆ¿
ƒ
¿

À

ÿ

?ð&L V ðcŸ¨ 58 and 35¡*
(

"

ª  ðÐ ð~
 £ð<�€Üò¿
ƒ
¿

À

ÿ

?ðAL & ð\Ÿ¨38¡*
(

"

ª ð× ð}
 £ð<�€0á¿
ƒ
¿

À

ÿ

?ð L A ðcŸ¨ 57 and 35¡*
(

"

ª  ðÐ ð|
 £ð<�€Ð¿
ƒ
¿

À

ÿ

?ðL  ð\Ÿ¨38¡*
(

"

ª ð× ð{
 £ð<�€H¾¿
ƒ
¿

À

ÿ

?ðìL  ðcŸ¨ 57 and 35¡*
(

"

ª  ðÑ ðz
 £ð<�€ø¬¿
ƒ
¿

À

ÿ

?ðùL ì ð]Ÿ¨2004 ¡(

"

ª ðÐ ðy
 £ð<�€$ž¿
ƒ
¿

À

ÿ

?ðV˜´L  ð\Ÿ¨40¡*
(

"

ª ð× ðx
 £ð<�€Ž¿
ƒ
¿

À

ÿ

?ð&˜VL  ðcŸ¨ 58 and 35¡*
(

"

ª  ðÐ ðw
 £ð<�€}¿
ƒ
¿

À

ÿ

?ðA˜&L  ð\Ÿ¨37¡*
(

"

ª ð× ðv
 £ð<�€ìk¿
ƒ
¿

À

ÿ

?ð ˜AL  ðcŸ¨ 56 and 35¡*
(

"

ª  ðÐ ðu
 £ð<�€[¿
ƒ
¿

À

ÿ

?ð˜ L  ð\Ÿ¨37¡*
(

"

ª ð× ðt
 £ð<�€èI¿
ƒ
¿

À

ÿ

?ðì˜L  ðcŸ¨ 57 and 35¡*
(

"

ª  ðÑ ðs
 £ð<�€ü8¿
ƒ
¿

À

ÿ

?ðù˜ìL  ð]Ÿ¨2003 ¡(

"

ª ðÐ ðr
 £ð<�€”)¿
ƒ
¿

À

ÿ

?ðVä ´˜ ð\Ÿ¨40¡*
(

"

ª ð× ðq
 £ð<�€p¿
ƒ
¿

À

ÿ

?ð&ä V˜ ðcŸ¨ 58 and 35¡*
(

"

ª  ðÐ ðp
 £ð<�€d¿
ƒ
¿

À

ÿ

?ðAä &˜ ð\Ÿ¨37¡*
(

"

ª ð× ðo
 £ð<�€<õ¿
ƒ
¿

À

ÿ

?ð ä A˜ ðcŸ¨ 55 and 35¡*
(

"

ª  ðÐ ðn
 £ð<�€Pä¿
ƒ
¿

À

ÿ

?ðä ˜ ð\Ÿ¨37¡*
(

"

ª ð× ðm
 £ð<�€8Ó¿
ƒ
¿

À

ÿ

?ðìä ˜ ðcŸ¨ 57 and 35¡*
(

"

ª  ðÑ ðl
 £ð<�€LÂ¿
ƒ
¿

À

ÿ

?ðùä ì˜ ð]Ÿ¨2002 ¡(

"

ª ðÐ ðk
 £ð<�€€²¿
ƒ
¿

À

ÿ

?ðV0´ä  ð\Ÿ¨40¡*
(

"

ª ð× ðj
 £ð<�€\¢¿
ƒ
¿

À

ÿ

?ð&0Vä  ðcŸ¨ 58 and 35¡*
(

"

ª  ðÐ ði
 £ð<�€ ‘¿
ƒ
¿

À

ÿ

?ðA0&ä  ð\Ÿ¨37¡*
(

"

ª ð× ðh
 £ð<�€ˆ€¿
ƒ
¿

À

ÿ

?ð 0Aä  ðcŸ¨ 55 and 35¡*
(

"

ª  ðÐ ðg
 £ð<�€øo¿
ƒ
¿

À

ÿ

?ð0 ä  ð\Ÿ¨37¡*
(

"

ª ð× ðf
 £ð<�€ä_¿
ƒ
¿

À

ÿ

?ðì0ä  ðcŸ¨ 56 and 35¡*
(

"

ª  ðÑ ðe
 £ð<�€¨O¿
ƒ
¿

À

ÿ

?ðù0ìä  ð]Ÿ¨2001 ¡(

"

ª ðÐ ðd
 £ð<�€ˆ?¿
ƒ
¿

À

ÿ

?ðV7´0 ð\Ÿ¨40¡*
(

"

ª ð× ðc
 £ð<�€Ø/¿
ƒ
¿

À

ÿ

?ð&7V0 ðcŸ¨ 57 and 35¡*
(

"

ª  ðÐ ðb
 £ð<�€p ¿
ƒ
¿

À

ÿ

?ðA7&0 ð\Ÿ¨37¡*
(

"

ª ð× ða
 £ð<�€à¿
ƒ
¿

À

ÿ

?ð 7A0 ðcŸ¨ 54 and 35¡*
(

"

ª  ðÐ ð`
 £ð<�€¿
ƒ
¿

À

ÿ

?ð7 0 ð\Ÿ¨37¡*
(

"

ª ð× ð_
 £ð<�€Èéþ¿
ƒ
¿

À

ÿ

?ðì70 ðcŸ¨ 55 and 35¡*
(

"

ª  ðÓ ð^
 £ð<�€ÜØþ¿
ƒ
¿

À

ÿ

?ðù7ì0 ð_Ÿ¨2000 ¡*
(
"

ª ðÐ ð]
 £ð<�€tÉþ¿
ƒ
¿

À

ÿ

?ðV>´7 ð\Ÿ¨40¡*
(

"

ª ð× ð\
 £ð<�€P¹þ¿
ƒ
¿

À

ÿ

?ð&>V7 ðcŸ¨ 57 and 35¡*
(

"

ª  ðÐ ð[
 £ð<�€¨þ¿
ƒ
¿

À

ÿ

?ðA>&7 ð\Ÿ¨37¡*
(

"

ª ð× ðZ
 £ð<�€ü–þ¿
ƒ
¿

À

ÿ

?ð >A7 ðcŸ¨ 53 and 35¡*
(

"

ª  ðÐ ðY
 £ð<�€†þ¿
ƒ
¿

À

ÿ

?ð> 7 ð\Ÿ¨37¡*
(

"

ª ð× ðX
 £ð<�€øtþ¿
ƒ
¿

À

ÿ

?ðì>7 ðcŸ¨ 55 and 35¡*
(

"

ª  ðÓ ðW
 £ð<�€dþ¿
ƒ
¿

À

ÿ

?ðù>ì7 ð_Ÿ¨1999 ¡*
(
"

ª ðÐ ðV
 £ð<�€PTþ¿
ƒ
¿

À

ÿ

?ðVŠ´> ð\Ÿ¨40¡*
(

"

ª ð× ðU
 £ð<�€,Dþ¿
ƒ
¿

À

ÿ

?ð&ŠV> ðcŸ¨ 57 and 35¡*
(

"

ª  ðÐ ðT
 £ð<�€3þ¿
ƒ
¿

À

ÿ

?ðAŠ&> ð\Ÿ¨36¡*
(

"

ª ð× ðS
 £ð<�€à!þ¿
ƒ
¿

À

ÿ

?ð ŠA> ðcŸ¨ 53 and 35¡*
(

"

ª  ðÐ ðR
 £ð<�€Ðþ¿
ƒ
¿

À

ÿ

?ðŠ > ð\Ÿ¨36¡*
(

"

ª ð× ðQ
 £ð<�€þ¿
ƒ
¿

À

ÿ

?ðìŠ> ðcŸ¨ 54 and 35¡*
(

"

ª  ðÑ ðP
 £ð<�€Xîû¿
ƒ
¿

À

ÿ

?ðùŠì> ð]Ÿ¨1998 ¡(

"

ª ð
 ðO
 óðZ€<Üû‚ƒ„‡¿
ƒ
¿

À

ÿ

?ðVZ
´Š ð|Ÿ 0Self  Employed Seniority¡

"
ª ðD
 ðN
 óðZ€Ëû‚ƒ„‡¿
ƒ
¿

À

ÿ

?ð&Z
VŠ 𲟨Self-employed Age & Seniority¡L
1
ÿ
"

"
"
ª$  
 ð=
 ðM
 óðZ€¸¹û‚ƒ„‡¿
ƒ
¿

À

ÿ

?ðAZ
&Š 𫟨Public Sector Seniority¡L
1
ÿ
"

"
"
ª$  
  ðD
 ðL
 óðZ€X¨û‚ƒ„‡¿
ƒ
¿

À

ÿ

?ð Z
AŠ 𲟨Public Sector Age & Seniority¡L
1
ÿ
"

"
"
ª$  
 ð¢
 ðK
 óðZ€ä–û‚ƒ„‡¿
ƒ
¿

À

ÿ

?ðZ
ŠðPˆHŠ@º___PPT9‹"¬€ÿÿ 𸟨Private Sector Seniority¡X
1
ÿ
"

"
"

ª$ 
  ð­
 ðJ
 óðZ€X…û‚ƒ„‡¿
ƒ
¿

À

ÿ

?ðìZ
ŠðRˆJŠBº___PPT9‹$¬€ÿÿ ðÁŸ¨Private Sector Age & Seniority¡Z
³ "
ÿ
"

"
"

ª$ 
 ðï ðI
 óðZ€Dwû‚ƒ„‡¿
ƒ
¿

À

ÿ

?ðùZ
ìŠ ð]Ÿ¨Year ¡(

"

ª ð`B
ð
 ƒð0¿
À
€Ë
8c×
ÿ

?¿ðùZ
´Z
ð`B
ð‚
 ƒð0¿
À
€Ë
8c×
ÿ

?¿ðù´ðTB
ðƒ
 cð$¿
×
ÿ

?¿ðùZ
ùðTB
ð„
 cð$¿
×
ÿ

?¿ð´Z
´ð`B
ð‡
 ƒð0¿
À
€Ë
œ1×
ÿ

?¿ðùŠ´ŠðTB
ð‰
 cð$¿
×
ÿ

?¿ðìZ
ìðTB
ðŒ
 cð$¿
×
ÿ

?¿ðZ
ðTB
ð
 cð$¿
×
ÿ

?¿ð Z
ðTB
ð’
 cð$¿
×
ÿ

?¿ðAZ
AðTB
ð•
 cð$¿
×
ÿ

?¿ð&Z
&ðTB
ð˜
 cð$¿
×
ÿ

?¿ðVZ
VðTB
ðœ
 cð$¿
×
ÿ

?¿ðù>´>ðTB
ð½
 cð$¿
×
ÿ

?¿ðù7´7ðTB
ðÞ
 cð$¿
×
ÿ

?¿ðù0´0ðTB
ðÿ
 cð$¿
×
ÿ

?¿ðùä ´ä ðTB
ð
 cð$¿
×
ÿ

?¿ðù˜´˜ðTB
ðA
 cð$¿
×
ÿ

?¿ðùL ´L ðH ð

ƒð0
ƒ
“
ŽŸ‹”
Þ½h¿
ÿ
 ?

ð ÿÿÿ€€€Ì™33ÌÌÌÿ²²²ˆ‘Š‰º___PPT10‹ië.BÃÅ
¢]+Dñ='ñ '
ÿÿÿÿ=ñ @
Bñ
+r
<`GRèõ)
™` $
‹
Å1èˆ
é(€àx/ _A

 F ò
ÌžÍ

Ã
n
–ºEquation ºEquation.DSMT40º*MathType 5.0 Equation̨Í

Ã
š
–ºGrafico ºMSGraph.Chart.80º4Grafico di Microsoft GraphÌžÍ
ýÿÿÿ    !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz|ýÿÿÿ}~€
Ã
¬
!–ºEquation ºEquation.DSMT40º*MathType 5.0 EquationÌžÍ

Ã
}-–ºEquation ºEquation.DSMT40º*MathType 5.0 EquationÌžÍ

Ã
®
8–ºEquation ºEquation.DSMT40º*MathType 5.0 EquationÌžÍ

Ã

K–ºEquation ºEquation.DSMT40º*MathType 5.0 EquationÌžÍ

Ã
¦
L–ºEquation ºEquation.DSMT40º*MathType 5.0 EquationÌžÍ

Ã
©
M–ºEquation ºEquation.DSMT40º*MathType 5.0 Equationò`
/È0Ò
Õ˜·DTimes New RomanT©T©¬r’Ü–É0Ü–Õ·DArialNew RomanT©T©¬r’Ü–É0Ü–Õ"¤€@ÿÿ¥.©  @£nÿý?" dd@ÿÿïÿÿÿÿÿÿ


@@``€€„ð|ðp0R
    ‹!¢ % - /3476:;>š
@BCEF‰
KMNP$QRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~€‚ƒÿ
ð”2ð$ùª•aŸ¨e§7 ;Ú'¿ÿ
2ð$’eªò'— ¤¼KCÚcÿ0
2ð$Ð(†€3jC9ßÌóìX´‚ÿk
N2ð$ã‰ã6˶»<«"C°³Xÿò
¹%bð$ñ½ìo‚ˆ|Ý[7,9<çÿÜ«6bð$J‰3’…†¾çD!5ƒÿÈ
‡C2ð$ʍê>HÎ J‰ÆoÍë…ÿá0
"ð$$×oyòu)H´ÛÍÍÿF
~<2ð$šó›žÂe¢Áz,¶þk.ÿú
ÄH2ð$ WÌìוùdâž« ÞûIÿv
¾L2ð$µÃK l\­7"Iþ“ÔqÿÞ4P2ð$x‰–(öoþ¾°Qȧ+àÿê
T2ð$¸¿ÚkkçSxÖ9€»ÿÆ
üVð$ÿ2ð$©RØýè™Fö ˜ËgÍm¬ÿx
ÂZƒð0
ƒ
†A¿
À

ÅAÿ

@ñÿ3f™ÿÿ™@ñ
÷ðó€Ðì
ÿâžïÊš;Nh8Êš;

úgþ
ý4EdEd\›’ô–É0Ìýÿÿ¦ÿÿÿ
pûppû
@<�ý4dddd —‘w0T©ˆr’
<�ý4BdBd —‘w0T©ˆr’H<�ý4!d!d —‘w0T©ˆr’
ˆiŠaº___PPT10‹A pµpµä. ºCasaå.±6

?ÙÚ %OÙÚ =ðsóI,
Ÿ¨7How Large is the Retirement Consumption Drop in Italy?¡88

(
Ÿ¨>Erich Battistin Agar Brugiavini Enrico Rettore Guglielmo Weber¡?P?ª4
 0ó

Ÿ¨ Motivation¡

Ÿ¨É
According to the life-cycle permanent income Hp consumers decide how much to consume, keeping in mind their future prospects They form intertemporal plans aimed at smoothing the (discounted) marginal utility of consumption over the life cycle Any period to period change in the actual level of the marginal utility of consumption is uncorrelated with past information available to the household. That is, it should be a result of unpredictable shocks. ¡TÇ

ÿ3þÿ3þ•

óZ5
Ÿ¨ Motivation¡

Ÿ¨¼
This holds true also around retirement age: any change in the marginal utility of consumption should be uncorrelated with planned retirement behaviour. Recent micro evidence has emphasized that there is a one-off drop in consumption at the time of retirement that might be hard to reconcile with life-time optimizing behaviour (see for example Banks et al., 1998, Bernheim et al., 2001). This is known as the retirement consumption puzzle ¡„º

{ÿ3þÆÿ3þª>Ž
§
&
Hó[6
Ÿ¨ Motivation¡

Ÿ JSome possible reasons mentioned in the literature: changes in preferences due to increased leisure shocks inducing retirement and affecting the level of consumption reduction in work-related expenditures (transport, meals out, clothing) increase in home production of services and/or more efficient purchases unexpectedly low pensions or liquidity problems (not in Italy, though  think of severance pay - liquidazione!) ¡N3
s
~ÿ3þ

ª–

ó>!
Ÿ¨What Others Have Done¡

Ÿ
 àBanks, Blundell and Tanner (1998) use repeated cross section data from the FES  they estimate log-linear Euler equations from cohort data by IV (using lagged interest rates, consumption and income growth as instruments) and find unexplained negative residuals around typical male retirement ages (60-67). The largest residual obtains at age 63 (1.5%). Altogether, cumulated residual are in the 8-10% region. Non-separabilities between leisure and consumption can explain only part of the drop. ¡>ï
P
P&ÿ3þµ
ª
2


  

D

ó?"
Ÿ¨What Others Have Done¡

Ÿ
 ÈBernheim, Skinner and Weinberg (2001) use panel data from the PSID to estimate Euler equations. Retirement status is instrumented by taking age-specific predicted probabilities conditional on demographics (however cannot explain spikes at ages 62 and 65). Median drop is 14%, but higher for low wealth Sample is split in groups: low wealth-to-income households drop their consumption most.  31% of households reduce their consumption by at least 35 percentage points at retirement .¡Hå
Z* ÿ3þäÿ3þ·ª
Ý
óY4
Ÿ¨What Others Have Done¡

Ÿ
¨‚
Possible explanations and related literature: Many workers are surprised by inadequate resources when they retire (not consistent with life-cycle model & rational expectations). Work related expenses. Home production and/or more efficient shopping (Aguiar and Hurst, 2005, Hurd and Rohwedder, 2006). Miniaci et al (2003) estimate by OLS the Italian retirement consumption drop at 5.4%. ¡0.
ZU
Z,

W
ªPù


 
Pó
Ÿ¨ What We Do¡

Ÿ¨º
An alternative identification strategy: we estimate the change in consumption at retirement by exploiting the exogenous variability in the retirement decision induced by the eligibility rules of the Italian pension system. Information on consumption expenditures, eligibility for retirement and retirement status is obtained from the Bank of Italy Survey on Household Income and Wealth (SHIW). No need of panel data to achieve identification.¡J»
Z&ÿ3þˆÿ3þË/™þó
Ÿ¨ Punch-line¡

Ÿ Key result: household non-durable consumption drops by 9.8% because of male retirement. A larger drop estimated for total food (14.1%). Our strategy provides non-parametric identification only for a subpopulation of those who retire (those who retire at the time they become eligible). We estimate smaller drops for  poverty sample . Our estimates can be reconciled with utility optimization - in the cross section, drop in work-related expenses and leisure substitutes is large enough to explain changes in consumption. ¡ZZ

ÿ3þÿ3þ9ÿ3þ…
ó
Ÿ¨The Causal Problem¡

Ÿ ÚLet S* be a variable denoting time to/from eligibility for retirement, negative values indicate that the subject is not yet eligible. Let R be the retirement status, R=1 for the retired and R=0 otherwise. Since retirement is an option available only to the eligible workers, the probability to retire is zero if S*<�0 (and it is thus discontinuous at S*=0 ). Let (Y1,Y0) be the two potential household consumption expenditures corresponding to the head being retired or not retired, respectively, and let ²=Y1-Y0 . Let Y = Y0+R² be observed consumption, where Ya"Y1 for households whose head is retired and Ya"Y0 otherwise.¡ân
ÿ3þ
ÿ3þ

ÿ3þE
ÿ3þÿ3þÿ3þx
%
 ÿ3þ
ÿ3þçÿÿ3þ
ÿ3þçÿ
ÿ3þ ÿ3þ
"O&ÿ3þ
ÿ3þ
ÿ3þçÿÿ3þÿ3þçÿ

ÿ3þçÿÿ3þ
ÿ3þçÿÿ3þ&ÿ3þ"&ÿ3þ
.ÿ3þçÿ&""
"&ÿ3þ
.ÿ3þçÿ"óJ+
Ÿ¨Identification in a nutshell¡

Ÿ ,
Start by comparing expenditures for households marginally close to S*=0; since Y = Y0+R² we have that Consider the difference around eligibility: ¡
f
,

/ÿ3þ
ÿ3þÿ3þÿ3þ
ÿ3þçÿÿ3þ&ÿ3þ 
ÿ3þ
,
"ªB
Tó
Ÿ¨Identification in a nutshell¡

Ÿ ŽKey identifying restriction (the mean consumption profile under the no-retirement alternative is smooth enough at zero): The result rests upon a weak regularity condition: if none of the heads were to retire no discontinuity in household consumption would take place at the time they become eligible (i.e. at S*=0)  see Hahn et al. (2001) and Battistin and Rettore (2006). This amounts to assuming that any idiosyncratic shocks relevant to the retirement choice and correlated with Y0 (e.g. health shocks) do not occur selectively at either side of the eligibility threshold. ¡–H
`
ÿ3þŒ
˜
çÿ_ª,[


Øó
Ÿ¨Identification in a nutshell¡

Ÿ¨¹
By using simple algebra we have: Estimators of the causal effect of retirement on consumption are analogue estimators obtained by replacing the quantities in the last expression by their empirical counterparts. Following Imbens and Angrist (1994) and Hanh et al. (2001), it can be shown that this expression coincides with the IV estimator obtained by instrumenting the endogenous variable R with the eligibility status defined from S*. ¡–%
Z”
Z

Z!A‹¬

ª>á


·ó\7
Ÿ¨Endogeneity of S*¡*







ª.
Ÿ
 ÌThe S* variable may be the outcome of individual choices (time to enter the labour market, temporary exits, etc). This might casts doubts that our identification strategy is marred by an endogeneity problem. Consider the regression we use to get the numerator of the IV estimate (the reduced form): Y= ´0 + ´1 S* + ´2 S*2 + ´3 1(S*>0) +µ The mean of Y conditional on S* is: E{Y|S*} = ´0 + ´1 S* + ´2 S*2 + ´3 1(S*>0) + E{µ|S*} where the last term does not vanish if S* is endogenous. ¡ +
Z'

Z%
Z5

Z;
Z
%
ÿ3þ
&ÿ3þ.ÿ3þçÿ&ÿ3þ.ÿ3þçÿ
&ÿ3þ
.ÿ3þ&ÿ3þ.ÿ3þçÿ
&ÿ3þ.ÿ3þ&ÿ3þ.ÿ3þçÿÿ3þ
ÿ3þÿ3þ&ÿ3þ"
*"ÿ3þ
ÿ3þÿ3þ
&ÿ3þ.ÿ3þçÿ&ÿ3þ.ÿ3þçÿ
&ÿ3þ
.ÿ3þ&ÿ3þ.ÿ3þçÿ
&ÿ3þ.ÿ3þ&ÿ3þ.ÿ3þçÿÿ3þ
ÿ3þÿ3þ&ÿ3þ
.ÿ3þ  ÿ3þ$"$$&$ÿ3þ$"$
$*$$"$
(( ªjL
i
e




  





 
 



 ó]8
Ÿ¨Endogeneity of S*¡ 



ª.
Ÿ
 ¬Nonetheless, the numerator of the IV estimand: E{Y|S* =0+}-E{Y|S* =0-} is not biased for ´3, the drop in consumption at the eligibility cut-off point, provided that: E{µ|S*=0+}=E{µ|S*=0-}. Our identifying restriction is that the dependence between the unobservables µ and S* is not discontinuously changing at the cut-off for eligibility. ¡‚/Z

Z`
Z

Z–Z


Z

Z
Z4"*"
*"*"
*"""
&ÿ3þ
.ÿ3þçÿ
&ÿ3þJ"ÿ3þ&ÿ3þ
.ÿ3þ&ÿ3þ
.ÿ3þÿ3þ&ÿ3þ
.ÿ3þ&ÿ3þ
.ÿ3þÿ3þM"
*"&ÿ3þ8"
" 
$$ªº 




 
 
 
B   
 






 

ó^
9
Ÿ¨Data¡

ó‹>
Ÿ¨The Reform Process¡

ª@

Ÿ
¨
Two major reforms in 1992 (Amato) and 1995 (Dini) Gradually moving from defined benefit to (notionally) defined contribution Lots of additional minor changes have been made nearly every year since 1992 Further changes will take place in 2008 (restrictions on early retirement)ªR
) 


  
x
 óG)
óC
%
Ÿ¨The measurement of eligibility¡

óD
&
Ÿ¨The measurement of eligibility¡

ó$

ٻ

óH*
ó

Ÿ¨ Retirement by Eligibility Status¡!!

ó
Ÿ¨Measurement Error¡

Ÿ¨OWe observe a non-negligible fraction of retired individuals amongst the ineligibles (this regardless of having imputed the eligibility variable for some individuals): this we take as evidence of measurement error in the data. Measurement error bias in the estimation of causal parameters can be severe (see, for example, Battistin and Chesher, 2004). Misclassification of the retirement status R is unlikely to be important, as retired individuals are asked a detailed set of questions on their pension. Measurement error in the eligibility variable S* is most likely to be the explanation. ¡hPö
›

 (ªO

úó
Ÿ¨Measurement Error¡

Ÿ¨º
Based on what we observe in the data, measurement error in S* can not be classical. If S=S*+u, with u a zero-mean error orthogonal to S* we would not observe any discontinuity in the proportion of retired individual s at the cut-off point. A type of measurement error consistent with the discontinuity in the raw probability of R=1 we observe in the data is: where Z is an indicator for having S= S* and U is a classical measurement error.¡J
i
PR
P<�

 

+

 ZY  % 
  
 


 
 # ó&
Ÿ¨Measurement Error¡

Ÿ¨Parameter of interest ¡B
Zÿ3þ

ÿ3þóP
-
Ÿ¨ Estimation¡

óƒ:
Ÿ¨lA key feature of the Italian pension system is that many individuals retire as soon as they become eligible¡mm


ªl 
Ÿ
ª
ó:

Ÿ fFirst StageE{R|S} = ±0 + ±1 S + ±2 S2 + ±3 1(S>0) ¡Ö4

ÿ3þ 
"*çÿ"*çÿ"*çÿ
"*"*çÿ
ª¨



 
ó;

Ÿ hReduced FormE{Y|S} = ´0 + ´1 S + ´2 S2 + ´3 1(S>0) ¡Þ5

ÿ3þ 
"
 çÿ
"
 çÿ
"
 çÿ
 
"
çÿ  ª°



 
ó(

Ÿ¨Estimation results¡

óX
3
Ÿ¨Estimation results¡

ó.
Ÿ¨Specification tests¡

Ÿ¨ŠIdentification strategy requires no change at S* = 0 in variables that affect consumption but are not affected by eligibility status. We show that this condition is met by education, age, size of the main residence and proportion of couples Exclusion restriction: family size. This is negatively affected by retirement induced by eligibility (-0.30). In particular, number of grown children cohabiting with their parents falls (-0.25). Possible explanation: individuals retire as soon as they become eligible as a way to let their children move out (they give them part of their severance pay) Hence actual consumption drop is even smaller than 9.8%!¡‹Z‹ó‡<
Ÿ¨Economic Interpretation¡

Ÿ In the US, consumption drop is largest among the low pre-retirement wealth (BSW). We estimate a pre-eligibility wealth equation, and use it to predict for the whole sample (w_fit). We show this measure does not change at S*=0. We select those households who w_fit is in the bottom third (w_poor). We call this  poverty sample We estimate small and insignificant effects of eligibility-induced retirement for this poverty sample Our estimated consumption drop is unlikely to be due to lack of financial resources!¡bZ­

ÿ3þP

ÿ3þÿ3þܪ>­
P

Üó…;
Ÿ¨Back of the Envelope Stuff¡

Ÿ¨…A causal effect of retirement on consumption expenditures is not surprising per se. The question is whether this is consistent with life-time optimizing behavior. A consumption drop can occur if utility is not additively separable in consumption and leisure: since leisure increases abruptly at retirement, consumption increases or decreases depending on how leisure affects the marginal utility of consumption. For instance, if utility is Cobb-Douglas in male leisure and non-durable consumption, and individuals work full time prior to retirement, our estimated 9.8% consumption drop implies an elasticity of intertemporal substitution of 0.84¡X†Z=y6…
ó‰=
Ÿ¨Work-Related Expenses¡

Ÿ¨¢
One good model is restrictive: Some goods are leisure substitutes (e.g. food out) or work-related (e.g. travel, clothing), other leisure complements (food in, home heating). We explore which components of household expenditure drive the fall that we have documented. We use data from the 2002 Survey of Family Budgets: this contains no information on eligibility, but detailed information on household expenditures.¡£
Z£
óR/
Ÿ¨Work-Related Expenses¡

Ÿ  We compare expenditures for households whose head s age is 50-54 and 65-69. Heads in the latter group are mostly retired, mostly employed in the former group. The comparison is corrected for composition differences with respect to region of residence, number of equivalent adults and size of the main residence. Support issues turn out to be of no concern. The overall drop is 15.6% : 50% larger than the estimated retirement consumption drop (9.8%). A third of the drop is due to age, two thirds to retirement.¡|
<�/


ÿ3þ=

ÿ3þ@óQ
.
ٻ

óS0
Ÿ¨Work-Related Expenses¡

Ÿ  Total difference is - 241 euros (-15.6%). Mostly accounted for by meals out (-36), clothing (-58), transport (-76). Overall 170 out of 241  drop is accounted for by  work-related expenses . Our estimates imply that consumption should fall by 151 Euros because of eligibility-induced retirement. Work-related expenses are less important for manual workers (canteen meals and overalls normally provided by the employer  public transport is heavily subsidized). This may explain why there is no drop for the poverty sample! óT1
Ÿ¨Conclusions¡

٬I
We estimate that non-durable consumption falls by 9.8% in Italy because of retirement. This drop is lower than in the US (14 %) but comparable to the UK (8%-10%, non-durable consumption). Our estimates can be reconciled with utility optimization: in the cross section, drop in work-related expenses is large enough to explain it./ðDó`
óa

ób
óc
ód
óe
óf
óg
óh
ói
ój
ók
ól
óm
ón
óo
óp
óq
ór
ós
ót
óu
óv
ów
óx
óy
óz
ó{
ó|
ó}
ó~
ó
ó€
ó!
ó‚"
ó„#
ó†$
óˆ%
óŠ&
êî¾;ï€
0Õ:ðÍ:àðK™
ðe:ð(
ð ð
ð-:ð˜
ðùZ
´  ð™

ð

#"ñ2Ÿ Ã&SÆ


]
M
J
K
ðZ
qÁ ðÃ'
ðÐ ð€
 £ð<�€T¿
ƒ
¿

À

ÿ

?ðVÙ´  ð\Ÿ¨40¡*
(

"

ª ð× ð
 £ð<�€ˆ¿
ƒ
¿

À

ÿ

?ð&ÙV  ðcŸ¨ 58 and 35¡*
(

"

ª  ðÐ ð~
 £ð<�€Üò¿
ƒ
¿

À

ÿ

?ðAÙ&  ð\Ÿ¨38¡*
(

"

ª ð× ð}
 £ð<�€0á¿
ƒ
¿

À

ÿ

?ð ÙA  ðcŸ¨ 57 and 35¡*
(

"

ª  ðÐ ð|
 £ð<�€Ð¿
ƒ
¿

À

ÿ

?ðÙ   ð\Ÿ¨38¡*
(

"

ª ð× ð{
 £ð<�€H¾¿
ƒ
¿

À

ÿ

?ðìÙ  ðcŸ¨ 57 and 35¡*
(

"

ª  ðÑ ðz
 £ð<�€ø¬¿
ƒ
¿

À

ÿ

?ðùÙì  ð]Ÿ¨2004 ¡(

"

ª ðÐ ðy
 £ð<�€$ž¿
ƒ
¿

À

ÿ

?ðV¡ ´Ù ð\Ÿ¨40¡*
(

"

ª ð× ðx
 £ð<�€Ž¿
ƒ
¿

À

ÿ

?ð&¡ VÙ ðcŸ¨ 58 and 35¡*
(

"

ª  ðÐ ðw
 £ð<�€}¿
ƒ
¿

À

ÿ

?ðA¡ &Ù ð\Ÿ¨37¡*
(

"

ª ð× ðv
 £ð<�€ìk¿
ƒ
¿

À

ÿ

?ð ¡ AÙ ðcŸ¨ 56 and 35¡*
(

"

ª  ðÐ ðu
 £ð<�€[¿
ƒ
¿

À

ÿ

?ð¡ Ù ð\Ÿ¨37¡*
(

"

ª ð× ðt
 £ð<�€èI¿
ƒ
¿

À

ÿ

?ðì¡ Ù ðcŸ¨ 57 and 35¡*
(

"

ª  ðÑ ðs
 £ð<�€ü8¿
ƒ
¿

À

ÿ

?ðù¡ ìÙ ð]Ÿ¨2003 ¡(

"

ª ðÐ ðr
 £ð<�€”)¿
ƒ
¿

À

ÿ

?ðVg ´¡  ð\Ÿ¨40¡*
(

"

ª ð× ðq
 £ð<�€p¿
ƒ
¿

À

ÿ

?ð&g V¡  ðcŸ¨ 58 and 35¡*
(

"

ª  ðÐ ðp
 £ð<�€d¿
ƒ
¿

À

ÿ

?ðAg &¡  ð\Ÿ¨37¡*
(

"

ª ð× ðo
 £ð<�€<õ¿
ƒ
¿

À

ÿ

?ð g A¡  ðcŸ¨ 55 and 35¡*
(

"

ª  ðÐ ðn
 £ð<�€Pä¿
ƒ
¿

À

ÿ

?ðg ¡  ð\Ÿ¨37¡*
(

"

ª ð× ðm
 £ð<�€8Ó¿
ƒ
¿

À

ÿ

?ðìg ¡  ðcŸ¨ 57 and 35¡*
(

"

ª  ðÑ ðl
 £ð<�€LÂ¿
ƒ
¿

À

ÿ

?ðùg ì¡  ð]Ÿ¨2002 ¡(

"

ª ðÐ ðk
 £ð<�€€²¿
ƒ
¿

À

ÿ

?ðV´g  ð\Ÿ¨40¡*
(

"

ª ð× ðj
 £ð<�€\¢¿
ƒ
¿

À

ÿ

?ð&Vg  ðcŸ¨ 58 and 35¡*
(

"

ª  ðÐ ði
 £ð<�€ ‘¿
ƒ
¿

À

ÿ

?ðA&g  ð\Ÿ¨37¡*
(

"

ª ð× ðh
 £ð<�€ˆ€¿
ƒ
¿

À

ÿ

?ð Ag  ðcŸ¨ 55 and 35¡*
(

"

ª  ðÐ ðg
 £ð<�€øo¿
ƒ
¿

À

ÿ

?ð g  ð\Ÿ¨37¡*
(

"

ª ð× ðf
 £ð<�€ä_¿
ƒ
¿

À

ÿ

?ðìg  ðcŸ¨ 56 and 35¡*
(

"

ª  ðÑ ðe
 £ð<�€¨O¿
ƒ
¿

À

ÿ

?ðùìg  ð]Ÿ¨2001 ¡(

"

ª ðÐ ðd
 £ð<�€ˆ?¿
ƒ
¿

À

ÿ

?ðV$´ ð\Ÿ¨40¡*
(

"

ª ð× ðc
 £ð<�€Ø/¿
ƒ
¿

À

ÿ

?ð&$V ðcŸ¨ 57 and 35¡*
(

"

ª  ðÐ ðb
 £ð<�€p ¿
ƒ
¿

À

ÿ

?ðA$& ð\Ÿ¨37¡*
(

"

ª ð× ða
 £ð<�€à¿
ƒ
¿

À

ÿ

?ð $A ðcŸ¨ 54 and 35¡*
(

"

ª  ðÐ ð`
 £ð<�€¿
ƒ
¿

À

ÿ

?ð$  ð\Ÿ¨37¡*
(

"

ª ð× ð_
 £ð<�€Èéþ¿
ƒ
¿

À

ÿ

?ðì$ ðcŸ¨ 55 and 35¡*
(

"

ª  ðÓ ð^
 £ð<�€ÜØþ¿
ƒ
¿

À

ÿ

?ðù$ì ð_Ÿ¨2000 ¡*
(
"

ª ðÐ ð]
 £ð<�€tÉþ¿
ƒ
¿

À

ÿ

?ðV+´$ ð\Ÿ¨40¡*
(

"

ª ð× ð\
 £ð<�€P¹þ¿
ƒ
¿

À

ÿ

?ð&+V$ ðcŸ¨ 57 and 35¡*
(

"

ª  ðÐ ð[
 £ð<�€¨þ¿
ƒ
¿

À

ÿ

?ðA+&$ ð\Ÿ¨37¡*
(

"

ª ð× ðZ
 £ð<�€ü–þ¿
ƒ
¿

À

ÿ

?ð +A$ ðcŸ¨ 53 and 35¡*
(

"

ª  ðÐ ðY
 £ð<�€†þ¿
ƒ
¿

À

ÿ

?ð+ $ ð\Ÿ¨37¡*
(

"

ª ð× ðX
 £ð<�€øtþ¿
ƒ
¿

À

ÿ

?ðì+$ ðcŸ¨ 55 and 35¡*
(

"

ª  ðÓ ðW
 £ð<�€dþ¿
ƒ
¿

À

ÿ

?ðù+ì$ ð_Ÿ¨1999 ¡*
(
"

ª ðÐ ðV
 £ð<�€PTþ¿
ƒ
¿

À

ÿ

?ðV~´+ ð\Ÿ¨40¡*
(

"

ª ð× ðU
 £ð<�€,Dþ¿
ƒ
¿

À

ÿ

?ð&~V+ ðcŸ¨ 57 and 35¡*
(

"

ª  ðÐ ðT
 £ð<�€3þ¿
ƒ
¿

À

ÿ

?ðA~&+ ð\Ÿ¨36¡*
(

"

ª ð× ðS
 £ð<�€à!þ¿
ƒ
¿

À

ÿ

?ð ~A+ ðcŸ¨ 53 and 35¡*
(

"

ª  ðÐ ðR
 £ð<�€Ðþ¿
ƒ
¿

À

ÿ

?ð~ + ð\Ÿ¨36¡*
(

"

ª ð× ðQ
 £ð<�€þ¿
ƒ
¿

À

ÿ

?ðì~+ ðcŸ¨ 54 and 35¡*
(

"

ª  ðÑ ðP
 £ð<�€Xîû¿
ƒ
¿

À

ÿ

?ðù~ì+ ð]Ÿ¨1998 ¡(

"

ª ð
 ðO
 óðZ€<Üû‚ƒ„‡¿
ƒ
¿

À

ÿ

?ðVZ
´~ ð|Ÿ 0Self  Employed Seniority¡

"
ª ðD
 ðN
 óðZ€Ëû‚ƒ„‡¿
ƒ
¿

À

ÿ

?ð&Z
V~ 𲟨Self-employed Age & Seniority¡L
1
ÿ
"

"
"
ª$  
 ð=
 ðM
 óðZ€¸¹û‚ƒ„‡¿
ƒ
¿

À

ÿ

?ðAZ
&~ 𫟨Public Sector Seniority¡L
1
ÿ
"

"
"
ª$  
  ðD
 ðL
 óðZ€X¨û‚ƒ„‡¿
ƒ
¿

À

ÿ

?ð Z
A~ 𲟨Public Sector Age & Seniority¡L
1
ÿ
"

"
"
ª$  
 ð¢
 ðK
 óðZ€ä–û‚ƒ„‡¿
ƒ
¿

À

ÿ

?ðZ
~ðPˆHŠ@º___PPT9‹"¬€ÿÿ 𸟨Private Sector Seniority¡X
1
ÿ
"

"
"

ª$ 
  ð­
 ðJ
 óðZ€X…û‚ƒ„‡¿
ƒ
¿

À

ÿ

?ðìZ
~ðRˆJŠBº___PPT9‹$¬€ÿÿ ðÁŸ¨Private Sector Age & Seniority¡Z
³ "
ÿ
"

"
"

ª$ 
 ðý ðI
 óðZ€Dwû‚ƒ„‡¿
ƒ
¿

À

ÿ

?ðùZ
ì~ ðkŸ¨Year ¡6

"


"

ª ð`B
ð
 ƒð0¿
À
€Ë
8c×
ÿ

?¿ðùZ
´Z
ð`B
ð‚
 ƒð0¿
À
€Ë
8c×
ÿ

?¿ðù ´ ðTB
ðƒ
 cð$¿
×
ÿ

?¿ðùZ
ù ðTB
ð„
 cð$¿
×
ÿ

?¿ð´Z
´ ð`B
ð‡
 ƒð0¿
À
€Ë
œ1×
ÿ

?¿ðù~´~ðTB
ð‰
 cð$¿
×
ÿ

?¿ðìZ
ì ðTB
ðŒ
 cð$¿
×
ÿ

?¿ðZ
 ðTB
ð
 cð$¿
×
ÿ

?¿ð Z
 ðTB
ð’
 cð$¿
×
ÿ

?¿ðAZ
A ðTB
ð•
 cð$¿
×
ÿ

?¿ð&Z
& ðTB
ð˜
 cð$¿
×
ÿ

?¿ðVZ
V ðTB
ðœ
 cð$¿
×
ÿ

?¿ðù+´+ðTB
ð½
 cð$¿
×
ÿ

?¿ðù$´$ðTB
ðÞ
 cð$¿
×
ÿ

?¿ðù´ðTB
ðÿ
 cð$¿
×
ÿ

?¿ðùg ´g ðTB
ð
 cð$¿
×
ÿ

?¿ðù¡ ´¡ ðTB
ðA
 cð$¿
×
ÿ

?¿ðùÙ´ÙðH ð

ƒð0
ƒ
“
ŽŸ‹”
Þ½h¿
ÿ
 ?

ð ÿÿÿ€€€Ì™33ÌÌÌÿ²²²ˆ‘Š‰º___PPT10‹ië.BÃÅ
¢]+Dñ='ñ '
ÿÿÿÿ=ñ @
Bñ
+r
F$G\¬õ)
™"$"è
‹
Å1è.ˆ
é(€àm° _A

 F ò
ÌžÍ

Ã
n
–ºEquation ºEquation.DSMT40º*MathType 5.0 Equation̨Í

Ã
š
–ºGrafico ºMSGraph.Chart.80º4Grafico di Microsoft GraphÌžÍ

Ã
¬
!–ºEquation ºEquation.DSMT40º*MathType 5.0 EquationÌžÍ

Ã
}-–ºEquation ºEquation.DSMT40º*MathType 5.0 EquationÌžÍ

Ã
®
8–ºEquation ºEquation.DSMT40º*MathType 5.0 EquationÌžÍ

Ã

K–ºEquation ºEquation.DSMT40º*MathType 5.0 EquationÌžÍ

Ã
¦
L–ºEquation ºEquation.DSMT40º*MathType 5.0 EquationÌžÍ

Ã
©
M–ºEquation ºEquation.DSMT40º*MathType 5.0 Equationò`
/È0Ò
Õ˜·DTimes New RomanT©T©¬r’Ü–É0Ü–Õ·DArialNew RomanT©T©¬r’Ü–É0Ü–Õ"¤€@ÿÿ¥.©  @£nÿý?" dd@ÿÿïÿÿÿÿÿÿ


@@``€€¤ðœð@‘ S
    ‹!¢ % - /3476:;>š
@BCEF‰
KMNP$QRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~€‚ƒ†ÿ
ð”2ð$ùª•aŸ¨e§7 ;Ú'¿ÿ
2ð$’eªò'— ¤¼KCÚcÿ0
2ð$Ð(†€3jC9ßÌóìX´‚ÿk
N2ð$ã‰ã6˶»<«"C°³Xÿò
¹%bð$ñ½ìo‚ˆ|Ý[7,9<çÿÜ«6bð$J‰3’…†¾çD!5ƒÿÈ
‡C2ð$ʍê>HÎ J‰ÆoÍë…ÿá0
"ð$$×oyòu)H´ÛÍÍÿF
~<2ð$šó›žÂe¢Áz,¶þk.ÿú
ÄH2ð$ WÌìוùdâž« ÞûIÿv
¾L2ð$µÃK l\­7"Iþ“ÔqÿÞ4P2ð$x‰–(öoþ¾°Qȧ+àÿê
T2ð$¸¿ÚkkçSxÖ9€»ÿÆ
üVð$ÿ2ð$©RØýè™Fö ˜ËgÍm¬ÿx
ÂZƒð0
ƒ
†A¿
À

ÅAÿ

@ñÿ3f™ÿÿ™@ñ
÷ðó€Ðì
ÿâžïÊš;Nh8Êš;

úgþ
ý4EdEd\›’ô–É0Ìýÿÿ¦ÿÿÿ
pûppû
@<�ý4dddd —‘w0T©ˆr’
<�ý4BdBd —‘w0T©ˆr’H<�ý4!d!d —‘w0T©ˆr’
ˆiŠaº___PPT10‹A pµpµä. ºCasaå.±6

?ÙÚ %OÙÚ =ðsóI,
Ÿ¨7How Large is the Retirement Consumption Drop in Italy?¡88

(
Ÿ¨>Erich Battistin Agar Brugiavini Enrico Rettore Guglielmo Weber¡?P?ª4
 0ó

Ÿ¨ Motivation¡

Ÿ¨É
According to the life-cycle permanent income Hp consumers decide how much to consume, keeping in mind their future prospects They form intertemporal plans aimed at smoothing the (discounted) marginal utility of consumption over the life cycle Any period to period change in the actual level of the marginal utility of consumption is uncorrelated with past information available to the household. That is, it should be a result of unpredictable shocks. ¡TÇ

ÿ3þÿ3þ•

óZ5
Ÿ¨ Motivation¡

Ÿ¨¼
This holds true also around retirement age: any change in the marginal utility of consumption should be uncorrelated with planned retirement behaviour. Recent micro evidence has emphasized that there is a one-off drop in consumption at the time of retirement that might be hard to reconcile with life-time optimizing behaviour (see for example Banks et al., 1998, Bernheim et al., 2001). This is known as the retirement consumption puzzle ¡„º

{ÿ3þÆÿ3þª>Ž
§
&
Hó[6
Ÿ¨ Motivation¡

Ÿ JSome possible reasons mentioned in the literature: changes in preferences due to increased leisure shocks inducing retirement and affecting the level of consumption reduction in work-related expenditures (transport, meals out, clothing) increase in home production of services and/or more efficient purchases unexpectedly low pensions or liquidity problems (not in Italy, though  think of severance pay - liquidazione!) ¡N3
s
~ÿ3þ

ª–

ó>!
Ÿ¨What Others Have Done¡

Ÿ
 àBanks, Blundell and Tanner (1998) use repeated cross section data from the FES  they estimate log-linear Euler equations from cohort data by IV (using lagged interest rates, consumption and income growth as instruments) and find unexplained negative residuals around typical male retirement ages (60-67). The largest residual obtains at age 63 (1.5%). Altogether, cumulated residual are in the 8-10% region. Non-separabilities between leisure and consumption can explain only part of the drop. ¡>ï
P
P&ÿ3þµ
ª
2


  

D

ó?"
Ÿ¨What Others Have Done¡

Ÿ
 ÈBernheim, Skinner and Weinberg (2001) use panel data from the PSID to estimate Euler equations. Retirement status is instrumented by taking age-specific predicted probabilities conditional on demographics (however cannot explain spikes at ages 62 and 65). Median drop is 14%, but higher for low wealth Sample is split in groups: low wealth-to-income households drop their consumption most.  31% of households reduce their consumption by at least 35 percentage points at retirement .¡Hå
Z* ÿ3þäÿ3þ·ª
Ý
óY4
Ÿ¨What Others Have Done¡

Ÿ
¨‚
Possible explanations and related literature: Many workers are surprised by inadequate resources when they retire (not consistent with life-cycle model & rational expectations). Work related expenses. Home production and/or more efficient shopping (Aguiar and Hurst, 2005, Hurd and Rohwedder, 2006). Miniaci et al (2003) estimate by OLS the Italian retirement consumption drop at 5.4%. ¡0.
ZU
Z,

W
ªPù


 
Pó
Ÿ¨ What We Do¡

Ÿ¨º
An alternative identification strategy: we estimate the change in consumption at retirement by exploiting the exogenous variability in the retirement decision induced by the eligibility rules of the Italian pension system. Information on consumption expenditures, eligibility for retirement and retirement status is obtained from the Bank of Italy Survey on Household Income and Wealth (SHIW). No need of panel data to achieve identification.¡J»
Z&ÿ3þˆÿ3þË/™þó
Ÿ¨ Punch-line¡

Ÿ Key result: household non-durable consumption drops by 9.8% because of male retirement. A larger drop estimated for total food (14.1%). Our strategy provides non-parametric identification only for a subpopulation of those who retire (those who retire at the time they become eligible). We estimate smaller drops for  poverty sample . Our estimates can be reconciled with utility optimization - in the cross section, drop in work-related expenses and leisure substitutes is large enough to explain changes in consumption. ¡ZZ

ÿ3þÿ3þ9ÿ3þ…
ó
Ÿ¨The Causal Problem¡

Ÿ ÚLet S* be a variable denoting time to/from eligibility for retirement, negative values indicate that the subject is not yet eligible. Let R be the ret‚ƒ„…†‡ˆ‰Š‹ŒŽ‘’“”•–—˜™š›œžŸ ¡¢£¤¥¦§¨©ª«¬­®¯°±²³´µ¶·¸¹º»¼½¾¿ÀÁÂÃÄÅÆÇÈÉÊËÌÍÎÏÐÑÒÓÔÕÖ×þÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿirement status, R=1 for the retired and R=0 otherwise. Since retirement is an option available only to the eligible workers, the probability to retire is zero if S*<�0 (and it is thus discontinuous at S*=0 ). Let (Y1,Y0) be the two potential household consumption expenditures corresponding to the head being retired or not retired, respectively, and let ²=Y1-Y0 . Let Y = Y0+R² be observed consumption, where Ya"Y1 for households whose head is retired and Ya"Y0 otherwise.¡ân
ÿ3þ
ÿ3þ

ÿ3þE
ÿ3þÿ3þÿ3þx
%
 ÿ3þ
ÿ3þçÿÿ3þ
ÿ3þçÿ
ÿ3þ ÿ3þ
"O&ÿ3þ
ÿ3þ
ÿ3þçÿÿ3þÿ3þçÿ

ÿ3þçÿÿ3þ
ÿ3þçÿÿ3þ&ÿ3þ"&ÿ3þ
.ÿ3þçÿ&""
"&ÿ3þ
.ÿ3þçÿ"óJ+
Ÿ¨Identification in a nutshell¡

Ÿ ,
Start by comparing expenditures for households marginally close to S*=0; since Y = Y0+R² we have that Consider the difference around eligibility: ¡
f
,

/ÿ3þ
ÿ3þÿ3þÿ3þ
ÿ3þçÿÿ3þ&ÿ3þ 
ÿ3þ
,
"ªB
Tó
Ÿ¨Identification in a nutshell¡

Ÿ ŽKey identifying restriction (the mean consumption profile under the no-retirement alternative is smooth enough at zero): The result rests upon a weak regularity condition: if none of the heads were to retire no discontinuity in household consumption would take place at the time they become eligible (i.e. at S*=0)  see Hahn et al. (2001) and Battistin and Rettore (2006). This amounts to assuming that any idiosyncratic shocks relevant to the retirement choice and correlated with Y0 (e.g. health shocks) do not occur selectively at either side of the eligibility threshold. ¡–H
`
ÿ3þŒ
˜
çÿ_ª,[


Øó
Ÿ¨Identification in a nutshell¡

Ÿ¨¹
By using simple algebra we have: Estimators of the causal effect of retirement on consumption are analogue estimators obtained by replacing the quantities in the last expression by their empirical counterparts. Following Imbens and Angrist (1994) and Hanh et al. (2001), it can be shown that this expression coincides with the IV estimator obtained by instrumenting the endogenous variable R with the eligibility status defined from S*. ¡–%
Z”
Z

Z!A‹¬

ª>á


·ó\7
Ÿ¨Endogeneity of S*¡*







ª.
Ÿ
 ÌThe S* variable may be the outcome of individual choices (time to enter the labour market, temporary exits, etc). This might casts doubts that our identification strategy is marred by an endogeneity problem. Consider the regression we use to get the numerator of the IV estimate (the reduced form): Y= ´0 + ´1 S* + ´2 S*2 + ´3 1(S*>0) +µ The mean of Y conditional on S* is: E{Y|S*} = ´0 + ´1 S* + ´2 S*2 + ´3 1(S*>0) + E{µ|S*} where the last term does not vanish if S* is endogenous. ¡ +
Z'

Z%
Z5

Z;
Z
%
ÿ3þ
&ÿ3þ.ÿ3þçÿ&ÿ3þ.ÿ3þçÿ
&ÿ3þ
.ÿ3þ&ÿ3þ.ÿ3þçÿ
&ÿ3þ.ÿ3þ&ÿ3þ.ÿ3þçÿÿ3þ
ÿ3þÿ3þ&ÿ3þ"
*"ÿ3þ
ÿ3þÿ3þ
&ÿ3þ.ÿ3þçÿ&ÿ3þ.ÿ3þçÿ
&ÿ3þ
.ÿ3þ&ÿ3þ.ÿ3þçÿ
&ÿ3þ.ÿ3þ&ÿ3þ.ÿ3þçÿÿ3þ
ÿ3þÿ3þ&ÿ3þ
.ÿ3þ  ÿ3þ$"$$&$ÿ3þ$"$
$*$$"$
(( ªjL
i
e




  





 
 



 ó]8
Ÿ¨Endogeneity of S*¡ 



ª.
Ÿ
 ¬Nonetheless, the numerator of the IV estimand: E{Y|S* =0+}-E{Y|S* =0-} is not biased for ´3, the drop in consumption at the eligibility cut-off point, provided that: E{µ|S*=0+}=E{µ|S*=0-}. Our identifying restriction is that the dependence between the unobservables µ and S* is not discontinuously changing at the cut-off for eligibility. ¡‚/Z

Z`
Z

Z–Z


Z

Z
Z4"*"
*"*"
*"""
&ÿ3þ
.ÿ3þçÿ
&ÿ3þJ"ÿ3þ&ÿ3þ
.ÿ3þ&ÿ3þ
.ÿ3þÿ3þ&ÿ3þ
.ÿ3þ&ÿ3þ
.ÿ3þÿ3þM"
*"&ÿ3þ8"
" 
$$ªº 




 
 
 
B   
 






 

ó^
9
Ÿ¨Data¡

ó‹>
Ÿ¨The Reform Process¡

ª@

Ÿ
¨
Two major reforms in 1992 (Amato) and 1995 (Dini) Gradually moving from defined benefit to (notionally) defined contribution Lots of additional minor changes have been made nearly every year since 1992 Further changes will take place in 2008 (restrictions on early retirement)ªR
) 


  
x
 óG)
óC
%
Ÿ¨The measurement of eligibility¡

óD
&
Ÿ¨The measurement of eligibility¡

ó$

ٻ

óH*
ó

Ÿ¨ Retirement by Eligibility Status¡!!

ó
Ÿ¨Measurement Error¡

Ÿ¨OWe observe a non-negligible fraction of retired individuals amongst the ineligibles (this regardless of having imputed the eligibility variable for some individuals): this we take as evidence of measurement error in the data. Measurement error bias in the estimation of causal parameters can be severe (see, for example, Battistin and Chesher, 2004). Misclassification of the retirement status R is unlikely to be important, as retired individuals are asked a detailed set of questions on their pension. Measurement error in the eligibility variable S* is most likely to be the explanation. ¡hPö
›

 (ªO

úó
Ÿ¨Measurement Error¡

Ÿ¨º
Based on what we observe in the data, measurement error in S* can not be classical. If S=S*+u, with u a zero-mean error orthogonal to S* we would not observe any discontinuity in the proportion of retired individual s at the cut-off point. A type of measurement error consistent with the discontinuity in the raw probability of R=1 we observe in the data is: where Z is an indicator for having S= S* and U is a classical measurement error.¡J
i
PR
P<�

 

+

 ZY  % 
  
 


 
 # ó&
Ÿ¨Measurement Error¡

Ÿ¨Parameter of interest ¡B
Zÿ3þ

ÿ3þóP
-
Ÿ¨ Estimation¡

óƒ:
Ÿ¨lA key feature of the Italian pension system is that many individuals retire as soon as they become eligible¡mm


ªl 
Ÿ
ª
ó:

Ÿ fFirst StageE{R|S} = ±0 + ±1 S + ±2 S2 + ±3 1(S>0) ¡Ö4

ÿ3þ 
"*çÿ"*çÿ"*çÿ
"*"*çÿ
ª¨



 
ó;

Ÿ hReduced FormE{Y|S} = ´0 + ´1 S + ´2 S2 + ´3 1(S>0) ¡Þ5

ÿ3þ 
"
 çÿ
"
 çÿ
"
 çÿ
 
"
çÿ  ª°



 
ó(

Ÿ¨Estimation results¡

óX
3
Ÿ¨Estimation results¡

ó.
Ÿ¨Specification tests¡

Ÿ¨ŠIdentification strategy requires no change at S* = 0 in variables that affect consumption but are not affected by eligibility status. We show that this condition is met by education, age, size of the main residence and proportion of couples Exclusion restriction: family size. This is negatively affected by retirement induced by eligibility (-0.30). In particular, number of grown children cohabiting with their parents falls (-0.25). Possible explanation: individuals retire as soon as they become eligible as a way to let their children move out (they give them part of their severance pay) Hence actual consumption drop is even smaller than 9.8%!¡‹Z‹ó‡<
Ÿ¨Economic Interpretation¡

Ÿ In the US, consumption drop is largest among the low pre-retirement wealth (BSW). We estimate a pre-eligibility wealth equation, and use it to predict for the whole sample (w_fit). We show this measure does not change at S*=0. We select those households who w_fit is in the bottom third (w_poor). We call this  poverty sample We estimate small and insignificant effects of eligibility-induced retirement for this poverty sample Our estimated consumption drop is unlikely to be due to lack of financial resources!¡bZ­

ÿ3þP

ÿ3þÿ3þܪ>­
P

Üó…;
Ÿ¨Back of the Envelope Stuff¡

Ÿ¨…A causal effect of retirement on consumption expenditures is not surprising per se. The question is whether this is consistent with life-time optimizing behavior. A consumption drop can occur if utility is not additively separable in consumption and leisure: since leisure increases abruptly at retirement, consumption increases or decreases depending on how leisure affects the marginal utility of consumption. For instance, if utility is Cobb-Douglas in male leisure and non-durable consumption, and individuals work full time prior to retirement, our estimated 9.8% consumption drop implies an elasticity of intertemporal substitution of 0.84¡X†Z=y6…
ó‰=
Ÿ¨Work-Related Expenses¡

Ÿ¨¢
One good model is restrictive: Some goods are leisure substitutes (e.g. food out) or work-related (e.g. travel, clothing), other leisure complements (food in, home heating). We explore which components of household expenditure drive the fall that we have documented. We use data from the 2002 Survey of Family Budgets: this contains no information on eligibility, but detailed information on household expenditures.¡£
Z£
óR/
Ÿ¨Work-Related Expenses¡

Ÿ  We compare expenditures for households whose head s age is 50-54 and 65-69. Heads in the latter group are mostly retired, mostly employed in the former group. The comparison is corrected for composition differences with respect to region of residence, number of equivalent adults and size of the main residence. Support issues turn out to be of no concern. The overall drop is 15.6% : 50% larger than the estimated retirement consumption drop (9.8%). A third of the drop is due to age, two thirds to retirement.¡|
<�/


ÿ3þ=

ÿ3þ@óQ
.
ٻ

óS0
Ÿ¨Work-Related Expenses¡

Ÿ  Total difference is - 241 euros (-15.6%). Mostly accounted for by meals out (-36), clothing (-58), transport (-76). Overall 170 out of 241  drop is accounted for by  work-related expenses . Our estimates imply that consumption should fall by 151 Euros because of eligibility-induced retirement. Work-related expenses are less important for manual workers (canteen meals and overalls normally provided by the employer  public transport is heavily subsidized). This may explain why there is no drop for the poverty sample! óT1
Ÿ¨Conclusions¡

٬I
We estimate that non-durable consumption falls by 9.8% in Italy because of retirement. This drop is lower than in the US (14 %) but comparable to the UK (8%-10%, non-durable consumption). Our estimates can be reconciled with utility optimization: in the cross section, drop in work-related expenses is large enough to explain it./ðDó`
óa

ób
óc
ód
óe
óf
óg
óh
ói
ój
ók
ól
óm
ón
óo
óp
óq
ór
ós
ót
óu
óv
ów
óx
óy
óz
ó{
ó|
ó}
ó~
ó
ó€
ó!
ó‚"
ó„#
ó†$
óˆ%
óŠ&
êð?
ñ€ 0¿ð·pðx
ðOð(
ð ðx
ð
 ðx
ÓðN
€$z
KX
‚&¬ƒKX
„&¬¿
ƒ
¿

À

ÿ


ð– Õðà z
 ðrŸ *¡ùª¦ñ+

++AAVVð
 ðx
ÓðN
€ˆ’z
KX
‚&¬ƒKX
„&¬¿
ƒ
¿

À

ÿ


ðÖ lÕðÃ
z
 ðtŸ *¡øª¦ñ+

++AAVVðd ðx
cð$

‡


¿
ÿ
 ?

ðA
b‚ðÃz
ð[
 ðx
ÓðN
€Ü•z
KX
‚&¬ƒKX
„&¬¿
ƒ
¿

À

ÿ


ðíqüoðÃz
 ðÅŸ¨uFare clic per modificare gli stili del testo dello schema Secondo livello Terzo livello Quarto livello Quinto livello¢:
ªvð
 ðx
ãðT
€Ä›z
KX
‚&¬ƒKX
„&¬‡¿
ƒ
¿

À

ÿ


ðÚ– ¯ðà z
 ðrŸ *¡úª¦ñ+

++AAVVð
 ðx
ãðT
€˜šz
KX
‚&¬ƒKX
„&¬‡¿
ƒ
¿

À

ÿ


ðÚÖ l¯ðÃz
 ðtŸ *¡ت¦ñ+

++AAVVðH ð
x
ƒð0
ƒ
“
¼—”
6”g¿
ÿ
 ?

ð ÿÿÿ€€€»àã33™™™™Ìˆ8Š0º___PPT10‹ë.§vÇ
Ð0¤FÉ0Àð¸pðäðPð(
ð ðäðü ðä ÓðN
€È|"Xe
‚¬²ƒXe
„¬²¿
ƒ
¿

À

ÿ


ð– Õðà " ðfŸ *¡ùª¦Àaaðþ ðä ÓðN
€€"Xe
‚¬²ƒXe
„¬²¿
ƒ
¿

À

ÿ


ðÖ lÕðÃ
" ðhŸ *¡øª¦Àaað
 ðä ãðT
€p’"Xe
‚¬²ƒXe
„¬²‡¿
ƒ
¿

À

ÿ


ðÚ– ¯ðà " ðfŸ *¡úª¦Àaað
 ðä ãðT
€tœ"Xe
‚¬²ƒXe
„¬²‡¿
ƒ
¿

À

ÿ


ðÚÖ l¯ðÃ" ðhŸ *¡ت¦ÀaaðH ð
äƒð0
ƒ
“
¼—”
6”g¿
ÿ
 ?

ð ÿÿÿ€€€»àã33™™™™Ìˆ8Š0º___PPT10‹ë.0•Æ
@ît=ð
ñ,
 0œ
ð”
€ð|
ð,
ð(
ð ð|
ð^ ð|
Sð¿


ÿ



x
ðA
b‚ðÃz
ðŽ ð|
cð$€`®z
¿


ÿ



x
ðíqüoðÃ
z
 ð"Ÿª
ðH ð
|
ƒð0
ƒ
“
¼—”
6”g¿
ÿ
 ?

ð ÿÿÿ€€€»àã33™™™™Ìˆ8Š0º___PPT10‹ë.§vÇ
X­Fð
ñ

 0œ
ð”
ð€
ð,
ð(
ð ð€
ð^ ð€
Sð¿


ÿ



x
ðA
b‚ðÃXðŽ ð€
cð$€ü¨X¿


ÿ



x
ðíqüoðÃ
X ð"Ÿª
ðH ð
€
ƒð0
ƒ
“
¼—”
6”g¿
ÿ
 ?

ð ÿÿÿ€€€»àã33™™™™Ìˆ8Š0º___PPT10‹ë.§vÇ
0ß®Fð
ñ5
 0œ
ð”
 ð„
ð,
ð(
ð ð„
ð^ ð„
Sð¿


ÿ



x
ðA
b‚ðÃXðŽ ð„
cð$€ä˜X¿


ÿ



x
ðíqüoðÃ
X ð"Ÿª
ðH ð
„
ƒð0
ƒ
“
¼—”
6”g¿
ÿ
 ?

ð ÿÿÿ€€€»àã33™™™™Ìˆ8Š0º___PPT10‹ë.§vÇ
0ß®Fð
ñ6
 0œ
ð”
°ðˆ
ð,
ð(
ð ðˆ
ð^ ðˆ
Sð¿


ÿ



x
ðA
b‚ðÃXðŽ ðˆ
cð$€¸qX¿


ÿ



x
ðíqüoðÃ
X ð"Ÿª
ðH ð
ˆ
ƒð0
ƒ
“
¼—”
6”g¿
ÿ
 ?

ð ÿÿÿ€€€»àã33™™™™Ìˆ8Š0º___PPT10‹ë.§vÇ
Ðe°Fð
ñ!
 0œ
ð”
ÀðŒ
ð,
ð(
ð ðŒ
ð^ ðŒ
Sð¿


ÿ



x
ðA
b‚ðÃXðŽ ðŒ
cð$€”.¿


ÿ



x
ðíqüoðÃ
X ð"Ÿª
ðH ð
Œ
ƒð0
ƒ
“
¼—”
6”g¿
ÿ
 ?

ð ÿÿÿ€€€»àã33™™™™Ìˆ8Š0º___PPT10‹ë.§vÇ
pì±Fð
ñ"
 0œ
ð”
Ðð
ð,
ð(
ð ð
ð^ ð
Sð¿


ÿ



x
ðA
b‚ðÃXðŽ ð
cð$€”´X¿


ÿ



x
ðíqüoðÃ
X ð"Ÿª
ðH ð

ƒð0
ƒ
“
¼—”
6”g¿
ÿ
 ?

ð ÿÿÿ€€€»àã33™™™™Ìˆ8Š0º___PPT10‹ë.§vÇ
s³Fð
ñ4
 0œ
ð”
àð”
ð,
ð(
ð ð”
ð^ ð”
Sð¿


ÿ



x
ðA
b‚ðÃXðŽ ð”
cð$€\ºX¿


ÿ



x
ðíqüoðÃ
X ð"Ÿª
ðH ð
”
ƒð0
ƒ
“
¼—”
6”g¿
ÿ
 ?

ð ÿÿÿ€€€»àã33™™™™Ìˆ8Š0º___PPT10‹ë.§vÇ
°ù´Fð
ñ
 0œ
ð”
ðð˜
ð,
ð(
ð ð˜
ð^ ð˜
Sð¿


ÿ



x
ðA
b‚ðÃXðŽ ð˜
cð$€¤ÀX¿


ÿ



x
ðíqüoðÃ
X ð"Ÿª
ðH ð
˜
ƒð0
ƒ
“
¼—”
6”g¿
ÿ
 ?

ð ÿÿÿ€€€»àã33™™™™Ìˆ8Š0º___PPT10‹ë.§vÇ
°ù´Fð
ñ
 0œ
ð”
ðœ
ð,
ð(
ð ðœ
ð^ ðœ
Sð¿


ÿ



x
ðA
b‚ðÃXðŽ ðœ
cð$€tÆX¿


ÿ



x
ðíqüoðÃ
X ð"Ÿª
ðH ð
œ
ƒð0
ƒ
“
¼—”
6”g¿
ÿ
 ?

ð ÿÿÿ€€€»àã33™™™™Ìˆ8Š0º___PPT10‹ë.§vÇ
P€¶Fð
ñ
 0œ
ð”
ð 
ð,
ð(
ð ð 
ð^ ð 
Sð¿


ÿ



x
ðA
b‚ðÃXðŽ ð 
cð$€ØÎX¿


ÿ



x
ðíqüoðÃ
X ð"Ÿª
ðH ð
 
ƒð0
ƒ
“
¼—”
6”g¿
ÿ
 ?

ð ÿÿÿ€€€»àã33™™™™Ìˆ8Š0º___PPT10‹ë.§vÇ
К¼Fð
ñ+
 0œ
ð”
ð¤
ð,
ð(
ð ð¤
ð^ ð¤
Sð¿


ÿ



x
ðA
b‚ðÃXðŽ ð¤
cð$€ìÓX¿


ÿ



x
ðíqüoðÃ
X ð"Ÿª
ðH ð
¤
ƒð0
ƒ
“
¼—”
6”g¿
ÿ
 ?

ð ÿÿÿ€€€»àã33™™™™Ìˆ8Š0º___PPT10‹ë.§vÇ
PµÂFð
ñ
 0œ
ð”
0ð¨
ð,
ð(
ð ð¨
ð^ ð¨
Sð¿


ÿ



x
ðA
b‚ðÃXðŽ ð¨
cð$€8ãX¿


ÿ



x
ðíqüoðÃ
X ð"Ÿª
ðH ð
¨
ƒð0
ƒ
“
¼—”
6”g¿
ÿ
 ?

ð ÿÿÿ€€€»àã33™™™™Ìˆ8Š0º___PPT10‹ë.§vÇ
ÂÅFð
ñ
 0œ
ð”
@ð¬
ð,
ð(
ð ð¬
ð^ ð¬
Sð¿


ÿ



x
ðA
b‚ðÃXðŽ ð¬
cð$€éX¿


ÿ



x
ðíqüoðÃ
X ð"Ÿª
ðH ð
¬
ƒð0
ƒ
“
¼—”
6”g¿
ÿ
 ?

ð ÿÿÿ€€€»àã33™™™™Ìˆ8Š0º___PPT10‹ë.§vÇ
ÐÏÈFð
ñ7
 0œ
ð”
Pð°
ð,
ð(
ð ð°
ð^ ð°
Sð¿


ÿ



x
ðA
b‚ðÃXðŽ ð°
cð$€ØîX¿


ÿ



x
ðíqüoðÃ
X ð"Ÿª
ðH ð
°
ƒð0
ƒ
“
¼—”
6”g¿
ÿ
 ?

ð ÿÿÿ€€€»àã33™™™™Ìˆ8Š0º___PPT10‹ë.§vÇ
pVÊFð
ñ8
 0œ
ð”
`ð´
ð,
ð(
ð ð´
ð^ ð´
Sð¿


ÿ



x
ðA
b‚ðÃXðŽ ð´
cð$€¿z
¿


ÿ



x
ðíqüoðÃ
X ð"Ÿª
ðH ð
´
ƒð0
ƒ
“
¼—”
6”g¿
ÿ
 ?

ð ÿÿÿ€€€»àã33™™™™Ìˆ8Š0º___PPT10‹ë.§vÇ
ÝËFð
ñ9
 0œ
ð”
pð¸
ð,
ð(
ð ð¸
ð^ ð¸
Sð¿


ÿ



x
ðA
b‚ðÃXðŽ ð¸
cð$€HÈz
¿


ÿ



x
ðíqüoðÃ
z
 ð"Ÿª
ðH ð
¸
ƒð0
ƒ
“
¼—”
6”g¿
ÿ
 ?

ð ÿÿÿ€€€»àã33™™™™Ìˆ8Š0º___PPT10‹ë.§vÇ
ÝËFð
ñ%
 0œ
ð”
€ð¼
ð,
ð(
ð ð¼
ð^ ð¼
Sð¿


ÿ



x
ðA
b‚ðÃXðŽ ð¼
cð$€¤ôX¿


ÿ



x
ðíqüoðÃ
X ð"Ÿª
ðH ð
¼
ƒð0
ƒ
“
¼—”
6”g¿
ÿ
 ?

ð ÿÿÿ€€€»àã33™™™™Ìˆ8Š0º___PPT10‹ë.§vÇ
°cÍFð
ñ)
 0œ
ð”
ðÀ
ð,
ð(
ð ðÀ
ð^ ðÀ
Sð¿


ÿ



x
ðA
b‚ðÃXðŽ ðÀ
cð$€túX¿


ÿ



x
ðíqüoðÃ
X ð"Ÿª
ðH ð
À
ƒð0
ƒ
“
¼—”
6”g¿
ÿ
 ?

ð ÿÿÿ€€€»àã33™™™™Ìˆ8Š0º___PPT10‹ë.§vÇ
°cÍFð
ñ&
 0œ
ð”
 ðÄ
ð,
ð(
ð ðÄ
ð^ ðÄ
Sð¿


ÿ



x
ðA
b‚ðÃXðŽ ðÄ
cð$€"¿


ÿ



x
ðíqüoðÃ
X ð"Ÿª
ðH ð
Ä
ƒð0
ƒ
“
¼—”
6”g¿
ÿ
 ?

ð ÿÿÿ€€€»àã33™™™™Ìˆ8Š0º___PPT10‹ë.§vÇ
°cÍFð
ñ
 0œ
ð”
°ðÈ
ð,
ð(
ð ðÈ
ð^ ðÈ
Sð¿


ÿ



x
ðA
b‚ðÃ"ðŽ ðÈ
cð$€Ü"¿


ÿ



x
ðíqüoðÃ
" ð"Ÿª
ðH ð
È
ƒð0
ƒ
“
¼—”
6”g¿
ÿ
 ?

ð ÿÿÿ€€€»àã33™™™™Ìˆ8Š0º___PPT10‹ë.§vÇ
˜ÐFð
ñ*
 0œ
ð”
ÀðÌ
ð,
ð(
ð ðÌ
ð^ ðÌ
Sð¿


ÿ



x
ðA
b‚ðÃ"ðŽ ðÌ
cð$€¤"¿


ÿ



x
ðíqüoðÃ
" ð"Ÿª
ðH ð
Ì
ƒð0
ƒ
“
¼—”
6”g¿
ÿ
 ?

ð ÿÿÿ€€€»àã33™™™™Ìˆ8Š0º___PPT10‹ë.§vÇ
@¥ÓFð
ñ
 0œ
ð”
ÐðÐ
ð,
ð(
ð ðÐ
ð^ ðÐ
Sð¿


ÿ



x
ðA
b‚ðÃ"ðŽ ðÐ
cð$€ø"¿


ÿ



x
ðíqüoðÃ
" ð"Ÿª
ðH ð
Ð
ƒð0
ƒ
“
¼—”
6”g¿
ÿ
 ?

ð ÿÿÿ€€€»àã33™™™™Ìˆ8Š0º___PPT10‹ë.§vÇ
à+ÕFð
ñ
 0œ
ð”
àðÔ
ð,
ð(
ð ðÔ
ð^ ðÔ
Sð¿


ÿ



x
ðA
b‚ðÃ"ðŽ ðÔ
cð$€À"¿


ÿ



x
ðíqüoðÃ
" ð"Ÿª
ðH ð
Ô
ƒð0
ƒ
“
¼—”
6”g¿
ÿ
 ?

ð ÿÿÿ€€€»àã33™™™™Ìˆ8Š0º___PPT10‹ë.§vÇ
€²ÖFð
ñ
 0œ
ð”
ððØ
ð,
ð(
ð ðØ
ð^ ðØ
Sð¿


ÿ



x
ðA
b‚ðÃ"ðŽ ðØ
cð$€ˆ"¿


ÿ



x
ðíqüoðÃ
" ð"Ÿª
ðH ð
Ø
ƒð0
ƒ
“
¼—”
6”g¿
ÿ
 ?

ð ÿÿÿ€€€»àã33™™™™Ìˆ8Š0º___PPT10‹ë.§vÇ
9ØFð
ñ
 0œ
ð”
ðÜ
ð,
ð(
ð ðÜ
ð^ ðÜ
Sð¿


ÿ



x
ðA
b‚ðÃ"ðŽ ðÜ
cð$€ô "¿


ÿ



x
ðíqüoðÃ
" ð"Ÿª
ðH ð
Ü
ƒð0
ƒ
“
¼—”
6”g¿
ÿ
 ?

ð ÿÿÿ€€€»àã33™™™™Ìˆ8Š0º___PPT10‹ë.§vÇ
`FÛFð
ñ-
 0œ
ð”
ðà
ð,
ð(
ð ðà
ð^ ðà
Sð¿


ÿ



x
ðA
b‚ðÃ"ðŽ ðà
cð$€Ä&"¿


ÿ



x
ðíqüoðÃ
" ð"Ÿª
ðH ð
à
ƒð0
ƒ
“
¼—”
6”g¿
ÿ
 ?

ð ÿÿÿ€€€»àã33™™™™Ìˆ8Š0º___PPT10‹ë.§vÇ
`FÛFð
ñ
 0œ
ð”
ðä
ð,
ð(
ð ðä
ð^ ðä
Sð¿


ÿ



x
ðA
b‚ðÃ"ðŽ ðä
cð$€Œ,"¿


ÿ



x
ðíqüoðÃ
" ð"Ÿª
ðH ð
ä
ƒð0
ƒ
“
¼—”
6”g¿
ÿ
 ?

ð ÿÿÿ€€€»àã33™™™™Ìˆ8Š0º___PPT10‹ë.§vÇ
ÍÜFð
ñ
 0œ
ð”
0ðè
ð,
ð(
ð ðè
ð^ ðè
Sð¿


ÿ



x
ðA
b‚ðÃ"ðŽ ðè
cð$€ø0"¿


ÿ



x
ðíqüoðÃ
" ð"Ÿª
ðH ð
è
ƒð0
ƒ
“
¼—”
6”g¿
ÿ
 ?

ð ÿÿÿ€€€»àã33™™™™Ìˆ8Š0º___PPT10‹ë.§vÇ
 SÞFð
ñ
 0œ
ð”
@ðì
ð,
ð(
ð ðì
ð^ ðì
Sð¿


ÿ



x
ðA
b‚ðÃ"ðŽ ðì
cð$€À6"¿


ÿ



x
ðíqüoðÃ
" ð"Ÿª
ðH ð
ì
ƒð0
ƒ
“
¼—”
6”g¿
ÿ
 ?

ð ÿÿÿ€€€»àã33™™™™Ìˆ8Š0º___PPT10‹ë.§vÇ
@ÚßFð
ñ3
 0œ
ð”
Pðð
ð,
ð(
ð ðð
ð^ ðð
Sð¿


ÿ



x
ðA
b‚ðÃ"ðŽ ðð
cð$€<"¿


ÿ



x
ðíqüoðÃ
" ð"Ÿª
ðH ð
ð
ƒð0
ƒ
“
¼—”
6”g¿
ÿ
 ?

ð ÿÿÿ€€€»àã33™™™™Ìˆ8Š0º___PPT10‹ë.§vÇ
€çâFð
ñ
 0œ
ð”
`ðô
ð,
ð(
ð ðô
ð^ ðô
Sð¿


ÿ



x
ðA
b‚ðÃ"ðŽ ðô
cð$€A"¿


ÿ



x
ðíqüoðÃ
" ð"Ÿª
ðH ð
ô
ƒð0
ƒ
“
¼—”
6”g¿
ÿ
 ?

ð ÿÿÿ€€€»àã33™™™™Ìˆ8Š0º___PPT10‹ë.§vÇ
näFð
ñ/
 0œ
ð”
pðø
ð,
ð(
ð ðø
ð^ ðø
Sð¿


ÿ



x
ðA
b‚ðÃ"ðŽ ðø
cð$€àF"¿


ÿ



x
ðíqüoðÃ
" ð"Ÿª
ðH ð
ø
ƒð0
ƒ
“
¼—”
6”g¿
ÿ
 ?

ð ÿÿÿ€€€»àã33™™™™Ìˆ8Š0º___PPT10‹ë.§vÇ
näFð
ñ.
 0œ
ð”
€ðü
ð,
ð(
ð ðü
ð^ ðü
Sð¿


ÿ



x
ðA
b‚ðÃ"ðŽ ðü
cð$€¨L"¿


ÿ



x
ðíqüoðÃ
" ð"Ÿª
ðH ð
ü
ƒð0
ƒ
“
¼—”
6”g¿
ÿ
 ?

ð ÿÿÿ€€€»àã33™™™™Ìˆ8Š0º___PPT10‹ë.§vÇ
ÀôåFð
ñ0
 0œ
ð”
ðð,
ð(
ð ðð^ ð Sð¿


ÿ



x
ðA
b‚ðÃ"ðŽ ð cð$€xR"¿


ÿ



x
ðíqüoðÃ
" ð"Ÿª
ðH ð
ƒð0
ƒ
“
¼—”
6”g¿
ÿ
 ?

ð ÿÿÿ€€€»àã33™™™™Ìˆ8Š0º___PPT10‹ë.§vÇ
ÀôåFð
ñ1
 0œ
ð”
 ðð,
ð(
ð ðð^ ð Sð¿


ÿ



x
ðA
b‚ðÃ"ðŽ ð cð$€@X"¿


ÿ



x
ðíqüoðÃ
" ð"Ÿª
ðH ð
ƒð0
ƒ
“
¼—”
6”g¿
ÿ
 ?

ð ÿÿÿ€€€»àã33™™™™Ìˆ8Š0º___PPT10‹ë.§vÇ
ÀôåFð
ñ:
 0œ
ð”
Àðð,
ð(
ð ðð^ ð Sð¿


ÿ



x
ðA
b‚ðÃ"ðŽ ð cð$€^"¿


ÿ



x
ðíqüoðÃ
" ð"Ÿª
ðH ð
ƒð0
ƒ
“
¼—”
6”g¿
ÿ
 ?

ð ÿÿÿ€€€»àã33™™™™Ìˆ8Š0º___PPT10‹ë.ªvÇ
@ø%äð(
ñ;
 0¨
ð 
àðð8
ð(
ð ððd ð cð$¿


ÿ



x
ˆðA
b‚ðÃ"ð” ð sð*€Ðc"¿


ÿ



x
ˆðíqüoðÃ
" ð"Ÿª
ðH ð
ƒð0
ƒ
“
¼—”
6”g¿
ÿ
 ?

ð ÿÿÿ€€€»àã33™™™™Ìˆ8Š0º___PPT10‹ë.§vÇ
näFð(
ñ<
 0¨
ð 
ðð8
ð(
ð ððd ð cð$¿


ÿ



x
ˆðA
b‚ðÃ"ð” ð sð*€ i"¿


ÿ



x
ˆðíqüoðÃ
" ð"Ÿª
ðH ð
ƒð0
ƒ
“
¼—”
6”g¿
ÿ
 ?

ð ÿÿÿ€€€»àã33™™™™Ìˆ8Š0º___PPT10‹ë.§vÇ
näFð(
ñ=
 0¨
ð 
ð$ð8
ð(
ð ð$ðd ð$ cð$¿


ÿ



x
ˆðA
b‚ðÃ"ð” ð$ sð*€Hj"¿


ÿ



x
ˆðíqüoðÃ
" ð"Ÿª
ðH ð
$ƒð0
ƒ
“
¼—”
6”g¿
ÿ
 ?

ð ÿÿÿ€€€»àã33™™™™Ìˆ8Š0º___PPT10‹ë.§vÇ
näFrÄ
^èAÛw_@”p}7[ƒ£…LJ뉌3ŽW{’Ÿ”Ö瘛/SŸw¡›£¿¥ã§ª+¬O®s°—²»´߶¹'»K½o¿“Á·ÃÛÅ„ÿdž#ʈSÌŠƒÎõ
™:è³Ð
‹
Å1Root Entry
ÿÿÿÿÿÿÿÿd›Oφꪹ)èPvŒ-wÇ
ß Pictures
ÿÿÿÿÿÿÿÿúdCurrent Userÿÿÿÿÿÿÿÿÿÿÿÿ#SummaryInformation(

ÿÿÿÿLìT‚ƒ„…†‡ˆ‰Š‹ŒŽ‘’“”•–—˜™š›œžŸ ¡¢£¤¥¦§¨©ª«¬­®¯°±²³´µ¶·¸¹º»¼½¾¿ÀÁÂÃÄÅÆÇÈÉÊËÌÍÎÏÐÑÒÓÔÕÖ×þÿÿÿÞýÿÿÿýÿÿÿýÿÿÿþÿÿÿþÿÿÿþÿÿÿàáâÝÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ    !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz|ÿÿÿÿ}~€‚ƒ„…†‹ýÿÿÿýÿÿÿýÿÿÿýÿÿÿŒ”ÿÿÿÿÿÿÿÿÿÿÿÿýÿÿÿÿÿÿÿÿÿÿÿ•–—˜™š›œžŸ ¡¢£¤¥¦§¨©ª«¬­®¯°±²³´µ¶·¸¹º»¼½¾¿ÀÁÂÃÄÅÆÇÈÉÊËÌÍ{ÿÿÿÿÿÿÿÿÿÿÿÿÒÓÔÕÖ×ØÙÚÛÜÝÞßàáâãäåæçèéêëìíîïðñòóôõö÷øùúûüþýÿÿÿÿþÿÿÿ   !"#þÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿlayName°3M–•4g12åeo²‹ºN‡eàzŒTpptjjxb@sem.tsinghua.edu.cnChina Journal of EconomicsPowerPoint Document(
ÿÿÿÿÿÿÿÿÿÿÿÿ/
£ÑDocumentSummaryInformation8
ÿÿÿÿÿÿÿÿ
Œÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿö_À‘ãÑ
ôÚ0  þÿ
ÕÍÕœ.“—+,ù®DÕÍÕœ.“—+,ù®Ü˜
ˆ´ÀÈÐØ à èðø



ýéýPresentazione su schermo£Ñd
('æ-Times New RomanArialStruttura predefinitaMathType 5.0 EquationGrafico di Microsoft Graph8 How Large is the Retirement Consumption Drop in Italy?MotivationMotivationMotivationWhat Others Have DoneWhat Others Have DoneWhat Others Have DoneWhat We DoPunch-lineThe Causal ProblemIdentification in a nutshellIdentification in a nutshellIdentification in a nutshellEndogeneity of S*Endogeneity of S*DataThe Reform ProcessDiapositiva 18The measurement of eligibilityThe measurement of eligibilityDiapositiva 21Diapositiva 22!Retirement by Eligibility StatusMeasurement ErrorMeasurement ErrorMeasurement ErrorEstimationmA key feature of the Italian pension system is that many individuals retire as soon as they become eligible 8First Stage E{R|S} = α0 + α1 S + α2 S2 + α3 1(S>0) 9Reduced Form E{Y|S} = δ0 + δ1 S + δ2 S2 + δ3 1(S>0) Estimation resultsEstimation resultsSpecification testsEconomic InterpretationBack of the Envelope StuffWork-Related ExpensesWork-Related ExpensesDiapositiva 38Work-Related ExpensesConclusionsCaratteri utilizzatiModello struttura
Server OLE incorporatiTitoli diapositive(°
@
ô€ü

4
p
_AdHocReviewCycleID_EmailSubject _AuthorEmail_AuthorEmailDisp