The Social Discount Rate

Discussion Paper 137

Institute for Empirical Macroeconomics Federal Reserve Bank of Minneapolis 90 Hennepin Avenue Minneapolis, Minnesota 55480-0291

January 2001

Andrew Caplin* New York University

John Leahy* Boston University

ABSTRACT ______

In welfare theory it is standard to pick the consumption stream that maximizes the welfare of the representative agent. We argue against this position, and show that a benevolent social planner will generally place a greater weight on future consumption than does the representative agent. ______

*We thank Andy Abel, Marco Basseto, Susanto Basu, Gary Becker, Ed Glaeser, Jeffrey Campbell, Jean-Jacques Laf- font, David Laibson, Robert Lucas Jr., Casey Mulligan, Barry Nalebuff, Mario Rizzo, Nancy Stokey, Robert Solow, and Lars Svensson for helpful comments and discussions. Caplin thanks the C. V. Starr Center at NYU and Leahy thanks the National Science Foundation for financial support. The views expressed herein are those of the authors and not necessarily those of the Federal Reserve Bank of Minneapolis or the Federal Reserve System. ïUU@tðL?@**) |üihi ü@ñi Mii? |üLti êüL ü@ñi ñLðUi_ _ðtUL4uLh| êð|ü |üðt ThitUhðT|ðL?c itTiUð@**) |üLti tii!ð?} |L Lhði?| TýM*ðU TL*ðU) 4Lhi |Lê@h_t |üi uý|ýhië +@4ti) d•b2Hoc êüð*i @U!?Lê*i_}ð?} |ü@| Thðñ@|i @}i?|t _ðtULý?| |üi uý|ýhic @h}ýi_ |ü@| ð| ê@t Ri|üðU@**) ð?_iui?tðM*iâ uLh |üi }Lñih?4i?| |L _L tLë èð}Lý d•bD2oc ú**@ðt d•be.oc @?_ 5L*Lê d•b.eo ü@ñi i Thitti_ tð4ð*@h ñðiêtë 6Lh |üi 4Lt| T@h|c üLêiñihc |üiti ñðiêt ü@ñi ið|üih Mii? ð}?Lhi_ Lh _ðt4ðtti_ @t T@|ih?@*ðt|ðU M) |üi 4@éLhð|) Lu iUL?L4ðt|të úhhLê @?_ kýh3 d•b.fo U@T|ýhi |üi uii*ð?}t Lu |üi ThLuittðL? êüi? |üi) êhð|iG

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•e eë• èL*ðU) W4T*ðU@|ðL?t ïýh @?@*)tðt ü@t ð44i_ð@|i ð4T*ðU@|ðL?t uLh TýM*ðU TL*ðU)G @}i?|t _ðtULý?| |üi uý|ýhi |LL 4ýUü @?_ |üihiuLhi }Lñih?4i?|t tüLý*_ ThL4L|i uý|ýhi Lhðí i?|i_ TL*ðUðitë AüiLhi|ðU@**)c Lýh @?@*)tðt ThLñð_it @ uLý?_@|ðL? uLh êü@| •@*ð?ñ@ý_ d•bHDo U@**t @? ú**@ðt i^ýð*ðMhðý4 E5ii @*tL ú**@ðt d•be.oäë ú? ú*í *@ðt i^ýð*ðMhðý4 ðt @ tð|ý@|ðL? ð? êüðUü ð?_ðñð_ý@* Thiuihi?Uit @hi hi|@ð?i_ uLh |üiUüLðUiMi|êii?UL?tý4T|ðL?}LL_t@||üit@4i_@|icMý|?L|?iUitt@hð*) Mi|êii? UL?tý4T|ðL? }LL_t @| _ðgihi?| _@|itë +i*@|ðñi |L |üi 4@h!i| iñ@*ý@|ðL?c Lýh @?@*)tðt |ðTt |üi tU@*it ð? u@ñLh Lu TL*ðUðit êð|ü tüLh| hý? ULt|t @?_ *L?} hý? Mi?i€|të W? |üi @hi@ Lu €tU@* TL*ðU)c ð| u@ñLht týMtð_ðit |L U@Tð|@* @UUý4ý*@|ðL?ë W? |üi @hi@ Lu 4L?i|@h) TL*ðU)c ð| u@ñLht *Lê ð?ã@|ðL?ë W? |üi @hi@ Lu ?@|ýh@* hitLýhUi i |h@U|ðL?c ð| u@ñLht UL?tihñ@|ðL?ë W? }i?ih@*c ð| u@ñLht ð?ñit|4i?| @?_ t@ñð?} @| |üi i Ti?ti Lu UL?tý4T|ðL?ë eë2 èhLUh@t|ð?@|ðL? ï<#L?L}üýi @?_ +@Mð? d•bbb@o 4L_i* ThLUh@t|ð?@|ðL? ýtð?} |ð4i ð?UL?tðtí |i?| Thiuihi?Uit |ü@| i üðMð| @ Mð@t |Lê@h_t Uýhhi?| ui*ðUð|)ë Aüi) @h}ýi |ü@| ThLUh@t|ð?@|ðL? LUUýht êüi? @ |ð4i ð?UL?tðt|i?| ð?_ðñð_ý@* @U|t *@|ih |ü@? @ |ð4i UL?tðt|i?| ð?_ðñð_ý@* êLý*_ @U|c @?_ |ü@| ThiTL?@|ðL? LUUýht êüi? @ |ð4i ð?UL?tðt|i?| ð?_ðñð_ý@* @U|t hi*@|ðñi*) tLL?ihë Aüi) @h}ýi |ü@| ThLUh@tí |ð?@|ðL? ðt 4Lhi *ð!i*) êüi? @? @}i?| ð?Uýht |üi ULt|t Lu @? @U|ðL? ThðLh |L |üi hiê@h_ @?_ |ü@| ThiTL?@|ðL? ðt 4Lhi *ð!i*) êüi? hiê@h_t ThiUi_i ULt|të #ðtULý?|ð?} T@t| ui*ðUð|) ThLñð_it @? @*|ih?@|ðñi Uü@h@U|ihð3@|ðL? Lu ThLí Uh@t|ð?@|ðL? @?_ ThiTL?@|ðL?ë W? |üðt Uü@h@U|ihð3@|ðL?c @}i?|t @hi |ð4i UL?í tðt|i?|c Mý| |üi) hi}hi| |üiðh T@t| @U|ðL?të èhLUh@t|ð?@|ðL? ðt @ttLUð@|i_ êð|ü @ êðtü |ü@| @? @U|ðL? ü@_ Mii? |@!i? @| @? i@h*ðih _@|ië èhiTL?@|ðL? ðt @ttLUð@|i_ êð|ü @ êðtü |ü@| @? @U|ðL? ü@_ ?L| Mii? |@!i? @| @? i@h*ðih _@|ië út ð? ï<#L?L}üýi @?_ +@Mð?c ThLUh@t|ð?@|ðL? êð** |i?_ |L LUUýh êüi? ULt|t ThiUi_i hiê@h_të ú| |üi |ð4i |ü@| @? @U| ðt TLt|TL?i_c |üiti ULt|t @TTi@h t@*ði?| @?_ |üi uý|ýhi hiê@h_t @hi _ðtULý?|i_ë W? |üi uý|ýhic |üi @}i?| UL4it |L hi}hi| |üðt _i*@)c MiU@ýtic ðu |üi @U|ðL? ü@_ Mii? |@!i?c |üi hiê@h_t êüðUü êLý*_ ?Lê Mi hiUiðñi_ êLý*_ Mi t@*ði?|c @?_ |üi ULt|t êüðUü êLý*_ ü@ñi Mii? ð?Uýhhi_ ð? |üi T@t| êLý*_ Mi _ðtULý?|i_ë W? @ tð4ð*@h 4@??ihc ThiTL?@|ðL? ðt @ttLUð@|i_ êð|ü hiê@h_t |ü@| ThiUi_i ULt|të

•D eëô ú__ðU|ðL? îiU!ih @?_ 5|ð}*ih d•b..o @?_ îiU!ih @?_ •ýhTü) d•bHHo 4L_i* @__ðU|ðL? @t h@|ðL?@*ë ú}i?|t @hi |ð4i UL?tðt|i?| @?_ ü@ñi t|@M*i ui*ðUð|) uý?U|ðL?të Aüi) UL?tUðLýt*) UüLLti |L MiUL4i @__ðU|tc @| i@Uü TLð?| ð? |ð4i êið}üð?} |üi Thiti?| ñ@*ýi Lu ULt|t @?_ Mi?i€|t Lu UL?tý4ð?} |üi @__ðU|ðñi týMt|@?Uië Aüihi ðt @ Mi*ðiu |ü@|c MiU@ýti @__ðU|ðL? ðt |üi hitý*| Lu @ h@|ðL?@* UüLðUi ð? |üðt uh@4iêLh!c @__ðU|t @hi Rü@TT)â Lh @| *i@t| Mi||ih Lg |ü@? |üi) êLý*_ ü@ñi Mii? ðu |üi LT|ðL? |L MiUL4i @__ðU|i_ ü@_ ?iñih i ðt|i_ë Aüðt ñðtðL? Lu |üi Rü@TT) @__ðU|â ü@t U@ýti_ tL4i iUL?L4ðt|t |L ^ýit|ðL? |üi ýtiuý*?itt Lu |üi uh@4iêLh!ë Eï<#L?L}üýi @?_ +@Mð? d•bbbMoä Aüðt êi*u@hi U@*Uý*@|ðL?c üLêiñihc @ttý4it |ü@| @}i?|t @hi hi|hLtTiU|ðñi*) |ð4i UL?tðt|i?|ë O@h4uý* @__ðU|ðL? ðt @ U@ti ð? êüðUü hiê@h_t ThiUi_i ULt|të Aüi @__ðU| _iUð_it |ü@| |üi Mi?i€|t |L Uýhhi?| UL?tý4T|ðL? Lu |üi @__ðU|ðñi týMt|@?Ui Lý|êið}ü |üi uý|ýhi ULt|t Lu ð?Uhi@ti_ @__ðU|ðL?ë út ð? |üi U@ti Lu ThLUh@t|ð?@|ðL?c @}i?|t êüL _ðtULý?| |üi T@t| 4@) UL4i |L hi}hi| |üiðh T@t| Miü@ñðLh @t |üiti uý|ýhi ULt|t MiUL4i t@*ði?|ë +@|ðL?@* UüLðUi 4@) 4@ ð4ð3i ý|ð*ð|) uhL4 |üi Uýhhi?| TihtTiU|ðñic Mý| |üðt _Lit ?L| ð4T*) |ü@| uý|ýhi ý|ð*ð|) ðt @*tL 4@ ð4ð3i_ë +@|ðL?@* @__ðU|t ?ii_ ?L| Mi ü@TT) @__ðU|të eëe Að4i çL?tðt|i?U) Lu 5LUð@* è*@?t W| êLý*_ Mi üLTi_ |ü@| |üi tLUð@* T*@??ih

•S _ðtULý?|ð?}c ð?_ðñð_ý@*t ñ@*ýi |üi Thiti?| @?_ |üi u@h uý|ýhi 4Lhi üð}ü*) |ü@? |üi) _L ð? |üi i TL?i?|ð@* 4L_i*ë ïýh T*@??ih ñ@*ýit |üiti TihðL_t *ittë Wu êi @TT*ði_ Lýh êi*u@hi @?@*)tðt |L |üi ü)TihML*ðU 4L_i*c |üiti |êL uLhUit êLý*_ |i?_ |L M@*@?Ui L?i @?L|üih Lý|c @*|üLý}ü ?L| UL4T*i|i*)ë Aüi hitý*| 4ð}ü| @TThL ð4@|i Thiuihi?Uit êð|ü i TL?i?|ð@* _ðtULý?|ð?}ë eëD èL*ð|ðU@* 6i@tðMð*ð|) èLttðM*) |üi 4Lt| TLêihuý* @h}ý4i?| uLh |üi _ðU|@|LhtüðT Lu |üi Thiti?| ðt TLtð|ðñi h@|üih |ü@? ?Lh4@|ðñië Wu |üi tLUð@* _iUðtðL? hitý*|t uhL4 @ _i4Lí Uh@|ðU ThLUittc |üi? |üi Uýhhi?| ti*u êLý*_ ð?_ii_ @TTi@h |L Mi @ _ðU|@|Lhc tð?Ui L?*) |üi Uýhhi?| ti*u U@? ñL|ië Aüi _ðU|@|LhtüðT Lu |üi Thiti?| 4@) |üihiuLhi @hðti @t @ |)Ti Lu UL?t|h@ð?i_ LT|ð4ý4ë W| 4@) Mi |üi L?*) Uhð|ií hðL? |ü@| ðt Th@U|ðU@**) ð4T*i4i?|@M*ië Aüi ThLTih ê@) |L ý?_iht|@?_ UL?t|h@ð?i_ LT|ð4@c üLêiñihc ðt |L €ht| ý?_iht|@?_ |üi ý?UL?t|h@ð?i_ ThLM*i4c |üi? |L tTiUðu) |üi ?@|ýhi Lu |üi UL?t|h@ð?|tc @?_ €?@**) tL*ñi |üi UL?t|h@ð?i_ ThLM*i4ë ïýh UL?|i?|ðL? ð? |üðt T@Tih ðt |ü@| |üi ý?UL?t|h@ð?i_ ThLM*i4 ðt ?L| êi** ý?_iht|LL_ë OLê |üi? U@? êi Mi tL týhi Lu |üi tL*ý|ðL? |L |üi UL?t|h@ð?i_ ThLM*i4q ï?i 4ð}ü| t@) |ü@| ð| tð4T*) ð4TLttðM*i uLh TiLT*i |L |LL! Mi)L?_ |üiðh Lê? Thiti?| Thiuihi?Uitë úu|ih @**c M) hiñi@*i_ Thiuihi?Uic Thiuihi?Uit @?_ UüLðUi @hi L?i @?_ |üi t@4i |üð?}ë Aüðt UL?U*ýtðL?c üLêiñihc _Lit ?L| ð4í T*) |ü@| |üi _ðU|@|LhtüðT Lu |üi Thiti?| ðt |üi L?*) ui@tðM*i tLUð@* êi*u@hi uý?U|ðL?ë 6ðht|c @}i?|t 4@) Mi @*|hýðt|ðUë Bðñi? @?) ð?_ðñð_ý@* ñL|ihc |üihi @hi 4@?) ð4TLh|@?| TL*ð|ðU@* ðttýit |ü@| 4@ð?*) @giU| |üi êi*u@hi Lu L|üihtë W? iñ@*ý@|ð?} U@?_ð_@|it L? |üiti ðttýit |üi ñL|ih ðt ð? ñih) 4ýUü |üi t@4i TLtð|ðL? @t |üi tLUð@* T*@??ihë AL |üi i |i?| |ü@| ñL|iht *ð!i U@?_ð_@|it |ü@| týTTLh| }LL_ TL*ðUðit iñi? ðu |üiti TL*ðUðit L?*) @giU| L|üihtc |üi _i4LUh@|ðU ThLUitt 4@) ThL_ýUi |üi tLUð@* LT|ð4ý4ë •LhiLñihc L?Ui ð? LæUic U@?_ð_@|it êLý*_ _L êi** |L ?L|i |ü@| |@t|it Uü@?}i Lñih |ð4ië Wu |üi) êðtü |L hi4@ð? ð? LæUic |üi) 4@) ?L| ê@?| |L 4@ ð4ð3i UL?t|ð|ýi?|t< Uýhhi?| ý|ð*ð|)c Mý| |üiðh ý|ð*ð|) @| |üi |ð4i Lu |üi ?i | i*iU|ðL?ë Aüðt 4@) *i@_ |L @ t*ð}ü| uLhê@h_ Mð@t ð? TL*ðU)ë•f 6ð?@**)c |üihi @hi 4@?) tLUð@* _iUðtðL?t |ü@| *ði Lý|tð_i Lu |üi _i4LUh@|ðU

43Lw pd| eh srvvleoh wr hvwlpdwh wkh h{whqw wr zklfk djhqwv glvfrxqw wkh sdvw e| re0 vhuylqj krz srolwlfldqv yrwlqj sdwwhuqv ydu| zlwk wkhlu uhpdlqlqj whup lq rïfh1

•. ThLUittë BLñih?Lht Lu |üi 6i_ih@* +itihñi 5)t|i4 @?_ 6i_ih@* éý_}it @hi @TTLð?|i_ uLh *L?} |ih4t T@h|*) |L @**Lê |üiti _iUðtðL? 4@!iht |L |@!i @ *L?}ih |ih4 TihtTiU|ðñië îi)L?_ }Lñih?4i?|c 4@?) ð?_ðñð_ý@*tc týUü @t T@hi?|t @?_ |i@Uüihtc Lu|i? €?_ |üi4ti*ñit T*@Ui_ ð? tð|ý@|ðL?t êüihi |üiðh _iUðtðL?t @giU| |üi êi*u@hi Lu L|üiht @| ñ@hðLýt TLð?|t ð? |ð4ië Aüiti ð?_ðñð_ý@*t |LL 4@) Miü@ñi *ð!i Lýh tLUð@* T*@??ihë eëS ï? |üi W?|ihThi|@|ðL? Lu |üi N|ð*ð|) 6ý?U|ðL?

N?|ð* |üðt TLð?| êi ü@ñi |hi@|i_ |üi ý|ð*ð|) uý?U|ðL? L| @t |üi êi*u@hi Lu |üi @}i?| ð? TihðL_ |c Mý| êi ü@ñi Mii? _i*ðMih@|i*) ñ@}ýi @t |L êü@| êi 4i@?| M) |üðtë 6Lh 4Lt| Lu |üi @h}ý4i?| @** êi ?ii_ ðt |ü@| L| hiThiti?|t |üi @}i?|

44Vhh Fdsolq dqg Ohdk| ^5333` iru d pruh ghwdlohg glvfxvvlrq ri wkhvh ylhzv dqg wkhlu uhodwlrqvkls wr zhoiduh wkhru|1

•H Aüi êið}ü|t L? ui*ðUð|) ð? ESä hiãiU| |üiti 4ý*|ðT*i TihtTiU|ðñitc @t êi** @t |üi êið}ü|t |ü@| |üi tLUð@* T*@??ih @ttð}?t |L |üiti TihtTiU|ðñitë úUULh_ð?} |L |üi aiñL?ð@? TihtTiU|ðñic |üi _ðU|@|LhtüðT Lu |üi Thiti?| ðt i |hi4i*) 4)LTðUë W| uLUýtit tL*i*) L? Uýhhi?| T*i@týhi @?_ UL4T*i|i*) ð}?Lhit @** uý|ýhi T*i@týhië ú*|ih?@|ðñi*)c |üi 5@4ýi*tL?ð@? TihtTiU|ðñi t|@|it |ü@| |üi T*i@týhi |ü@| @? @}i?| i Tihði?Uit ð? TihðL_ | ðt @ttLUð@|i_ êð|ü |üi TihðL_ | ui*ðUð|) üES|äë ï?*) Uýhhi?| UL?tý4T|ðL? 4@!it |üi @}i?| ü@TT)ë W? Lh_ih |L UL4i |L }hðTt êð|ü |üi u@U| |ü@| @}i?|t U@hi @MLý| uý|ýhi UL?tý4T|ðL? Mý| hiUiðñi ý|ð*ð|) L?*) uhL4 Uýhhi?| UL?tý4T|ðL?c |üi 5@4ýi*tL?ð@? TihtTiU|ðñi _ðñð_it |üi TihðL_ | ti*u ð?|L |êL UL4TL?i?|tG @ _iUðtðL? 4@!ih @?_ @ UL?tý4ihë Aüi UL?tý4ð?} ti*u i Tihði?Uit TihðL_ | ui*ðUð|)ë Aüi _iUðtðL? 4@!ð?} ti*u itti?|ð@**) @U|t @t @? ð?|ih?@* tLUð@* T*@??ih êüL @}}hi}@|it |üi Thiuihi?Uit Lu |üi UL?tý4ð?} ti*ñit Lu ñ@hðLýt TihðL_të W? |üðt ñðiêc L| hiThiti?|t |üi Thiuihi?Uit Lu |üi ð?|ih?@* tLUð@* T*@??ih @| _@|i |ë•2 • úUULh_ð?} |L |üi 5@4ýi*tL?ð@? TihtTiU|ðñic êüi? B ' q3 |üi tLUð@* T*@?í ?ih

45Ndkqhpdq/ Zdnnhu dqg Vdulq ^4<<:` dujxh wkdw wkh h{whuqdo vrfldo sodqqhu vkrxog ljruh wkh shuvshfwlyh ri wkh lqwhuqdo vrfldo sodqqhu dqg irfxv vroho| rq wkh ydulrxv frq0 vxplqj vhoyhv1 Wkh sureohp zlwk wklv dssudrfk lv wkdw lw hqwluho| glyrufhv lqwhuwhpsrudo vrfldo fkrlfh iurp lqwhuwhpsrudo sulydwh fkrlfh1

•b |üi Thiti?Ui Lu ü)TihML*ðU _ðtULý?|ð?}ë ,@Uü UL?tð_iht |üi igiU| Lu |üiti Uü@?}it L? |üi ý|ð*ð|) Lu |üi ñ@hðLýt |i4TLh@* ti*ñitë W? i@Uü U@tic uý|ýhi ti*ñit @hi @ttý4i_ |L T*@Ui ?L êið}ü| L? T@t| UL?tý4T|ðL?ë ûið|üih ?L|i |ü@| |üðt @ttý4T|ðL? ð4T*ðit |ü@| |@t|it Uü@?}i iñi? ðu Thiuihi?Uit @hi |ð4i UL?tðt|i?|ë W? @? ð?|ih}i?ih@|ðL?@* UL?|i | ð| ðt UL44L? |L UL?tð_ih |üi êið}ü| |ü@| T@hi?|t T*@Ui L? |üiðh Uüð*_hi?

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2• D 5LUð@**) ïT|ð4@* BhLê|ü

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