500:. Insurance allows people to translate consumption from periods where their consumption is high (having a low marginal utility) to periods when their consumption is low (having a high marginal utility). Due to many possible states of the world, people want to decrease the amount of uncertain outcomes of the future. Basic insurance theory states that individuals will demand full insurance to fully smooth consumption across difference states of the world. This explains why people purchase insurance, whether in healthcare, unemployment, and social security. To help illustrate this, think of a simplified hypothetical scenario with Person A, who can exist in one of two states of the world. Assume Person A who is healthy and can work; this will be State X of the world. One day, an unfortunate accident occurs, person A no longer can work. Therefore, he cannot obtain income from work and is in State Y of the world. In State X, Person A enjoys a good income from his work place and is able to spend money on necessities, such as paying rent and buying groceries, and luxuries, such as traveling to Europe. In State Y, Person A no longer obtains an income, due to injury, and struggles to pay for necessities. In a perfect world, Person A would have known to save for this future accident and would have more savings to compensate for the lack of income post-injury. Rather than spend money on the trip to Europe in State X, Person A could have saved that money to use for necessities in State Y. However, people tend to be poor predictors of the future, especially ones that are myopic. Therefore, insurance can "smooth" between these two states and provide more certainty for the future.
472:
37:
want to maximize their expected utility, as defined as the weighted sum of utilities across states of the world. The weights in this model are the probabilities of each state of the world happening. According to the "more is better" principle, the first order condition will be positive; however, the second order condition will be negative, due to the principle of diminishing
45:
1619:. The data used are US National Income and Product Accounts (NIPA) quarterly from 1948 to 1977. For the analysis the author does not consider the consumption of durable goods. Although Hall argues that he finds some evidence of consumption smoothing, he does so using a modified version. There are also some econometric concerns about his findings.
509:
suffering in extremely low income states of the world want to prepare for the next time they experience an adverse state of the world. This leads to the support of microfinance as a tool to consumption smooth, stating that those in poverty value microloans tremendously due to its extremely high marginal utility.
27:
Since income tends to be hump-shaped across an individual's life, economic theory suggests that individuals should on average have low or negative savings rate at early stages in their life, high in middle age, and negative during retirement. Although many popular books on personal finance advocate
1622:
Wilcox (1989) argue that liquidity constraint is the reason why consumption smoothing does not show up in the data. Zeldes (1989) follows the same argument and finds that a poor household's consumption is correlated with contemporaneous income, while a rich household's consumption is not. A recent
23:
concept for the practice of optimizing a person's standard of living through an appropriate balance between savings and consumption over time. An optimal consumption rate should be relatively similar at each stage of a person's life rather than fluctuate wildly. Luxurious consumption at an old age
36:
The graph below illustrates the expected utility model, in which U(c) is increasing in and concave in c. This shows that there are diminishing marginal returns associated with consumption, as each additional unit of consumption adds less utility. The expected utility model states that individuals
540:
Friedman's theory argues that consumption is linked to the permanent income of agents. Thus, when income is affected by transitory shocks, for example, agents' consumption should not change, since they can use savings or borrowing to adjust. This theory assumes that agents are able to finance
508:
Though there are arguments stating that microcredit does not effectively lift people from poverty, some note that offering a way to consumption smooth during tough periods has shown to be effective. This supports the principle of diminishing marginal utility, where those who have a history of
427:
An actuarially fair premium to pay for insurance would be the insurance premium that is set equal to the insurer's expected payout, so that the insurer will expect to earn zero profit. Some individuals are risk-averse, as shown by the graph above. The blue line,
467:
is curved upwards, revealing that this particular individual is risk-averse. If the blue line was curved downwards, this would reveal the preference for a risk-seeking individual. Additionally, a straight line would reveal a risk-neutral individual.
1217:
553:
formalized
Friedman's idea. By taking into account the diminishing returns to consumption, and therefore, assuming a concave utility function, he showed that agents optimally would choose to keep a stable path of consumption.
241:
The model shows expected utility as the sum of the probability of being in a bad state multiplied by utility of being in a bad state and the probability of being in a good state multiplied by utility of being in a good state.
41:. Due to the concave actual utility, marginal utility decreases as consumption increase; as a result, it is favorable to reduce consumption in states of high income to increase consumption in low income states.
1366:
993:
190:
1093:
354:
700:
1275:
646:
1602:
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1434:
831:
879:
770:
585:
1657:
899:
851:
790:
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720:
605:
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400:
378:
236:
214:
28:
that individuals should at all stages of their life set aside money in savings, economist James Choi states that this deviates from the advice of economists.
1104:
1869:
Modigliani, F.; Brumberg, R. (1954). "Utility analysis and the consumption function: An interpretation of cross-section data". In
Kurihara, K. K. (ed.).
487:: With fixed probabilities of two alternative states 1 and 2, risk averse indifference curves over pairs of state-contingent outcomes are convex.
533:, the idea that agents prefer a stable path of consumption has been widely accepted. This idea came to replace the perception that people had a
48:
The graph shows expected utility, E, after consumption smoothing (e.g. insurance), and actual utility, U(E), without consumption smoothing.
1607:
This expression shows that agents choose to consume a fraction of their present discounted value of their human and financial wealth.
1283:
1616:
911:
534:
57:
1886:
1004:
522:
250:
1884:
Hall, Robert (1978). "Stochastic
Implications of the Life Cycle-Permanent Income Hypothesis: Theory and Evidence".
530:
2000:
653:
1921:
Wilcox, James A. (1989). "Liquidity
Constraints on Consumption: The Real Effects of Real Lending Policies".
550:
1225:
475:
Risk aversion (red) contrasted to risk neutrality (yellow) and risk loving (orange) in different settings.
1972:"Do consumers really follow a rule of thumb? Three thousand estimates from 144 studies say "probably not""
479:: A risk averse utility function is concave (from below), while a risk loving utility function is convex.
1623:
meta-analysis of 3000 estimates reported in 144 studies finds strong evidence for consumption smoothing.
611:
1971:
1693:
1448:
549:
is one of the main reasons why it is difficult to observe consumption smoothing in the data. In 1978,
431:
1995:
546:
1769:
1953:
1903:
1377:
796:
542:
483:: In standard deviation-expected value space, risk averse indifference curves are upward sloped.
1936:
Zeldes, Stephen P. (1989). "Consumption and
Liquidity Constraints: An Empirical Investigation".
541:
consumption with earnings that are not yet generated, and thus assumes perfect capital markets.
1751:
1701:
1665:
1637:
526:
1442:
Hall also showed that for a quadratic utility function, the optimal consumption is equal to:
1945:
1895:
1741:
38:
857:
748:
563:
1632:
518:
517:
Another model to look at for consumption smoothing is Hall's model, which is inspired by
1852:
884:
836:
775:
726:
705:
590:
407:
385:
363:
221:
199:
1212:{\displaystyle \beta E_{t}R_{t+1}{\frac {u^{\prime }(c_{t+1})}{u^{\prime }(c_{t})}}=1}
1989:
1957:
1907:
1658:"Analysis | Shoplifting in Chicago dropped after a change in the food stamp program"
1439:
Thus, rational agents would expect to achieve the same consumption in every period.
24:
does not compensate for an impoverished existence at other stages in one's life.
471:
1615:
Robert Hall (1978) estimated the Euler equation in order to find evidence of a
587:
being the mathematical expectation conditional on all information available in
1755:
1705:
1669:
497:
44:
1746:
1729:
20:
1821:
Collins, D., Jonathan
Morduch, Stuart Rutherford, and Orlanda Ruthven.
1949:
1899:
470:
43:
1823:
Portfolios of the Poor: How the World's Poor Live on $ 2 a Day
1371:
Which, due to the concavity of the utility function, implies:
537:
and therefore current consumption was tied to current income.
1694:"Opinion | In Retirement, You May Not Need to Spend So Much"
1361:{\displaystyle E_{t}u^{\prime }(c_{t+1})=u^{\prime }(c_{t})}
1337:
1302:
1179:
1145:
245:
Similarly, actuarially fair insurance can also be modeled:
1098:
The first order necessary condition in this case will be:
1730:"Popular Personal Financial Advice versus the Professors"
988:{\displaystyle E_{0}\sum _{t=0}^{\infty }\beta ^{t}\left}
380:= probability you will lose all your wealth/consumption
216:= probability you will lose all your wealth/consumption
185:{\displaystyle EU=q*U(W|badstate)+(1-q)*U(W|goodstate)}
743:
being the strictly concave one-period utility function
1923:
Federal
Reserve Bank of San Francisco Economic Review
1451:
1380:
1286:
1228:
1107:
1007:
914:
887:
860:
839:
799:
778:
751:
729:
708:
656:
614:
593:
566:
434:
410:
388:
366:
253:
224:
202:
60:
905:agents choose the consumption path that maximizes:
1851:
1596:
1428:
1360:
1269:
1211:
1088:{\displaystyle A_{t+1}=R_{t+1}(A_{t}+y_{t}-c_{t})}
1087:
987:
893:
873:
845:
825:
784:
764:
735:
714:
694:
640:
599:
579:
459:
416:
394:
372:
348:
230:
208:
184:
1611:Empirical evidence for Hall and Friedman's model
881:being the assets, apart from human capital, in
349:{\displaystyle EU=(1-q)*U(W-p)+q*U(W-p-d+p/q)}
1835:"Does Microcredit Really Help Poor People?".
998:Subject to a sequence of budget constraints:
8:
1858:. Princeton, NJ: Princeton University Press.
1797:. New York, NY: Worth, 2013. Print. 304-305.
1745:
1583:
1564:
1554:
1532:
1521:
1510:
1500:
1469:
1456:
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1420:
1398:
1385:
1379:
1349:
1336:
1314:
1301:
1291:
1285:
1258:
1233:
1227:
1191:
1178:
1157:
1144:
1137:
1125:
1115:
1106:
1076:
1063:
1050:
1031:
1012:
1006:
971:
950:
940:
929:
919:
913:
886:
865:
859:
838:
817:
804:
798:
777:
756:
750:
728:
707:
695:{\displaystyle r_{t}=R_{t}-1\geq \delta }
674:
661:
655:
648:being the agent's rate of time preference
624:
613:
592:
571:
565:
496:One method used to smooth consumption is
450:
433:
409:
387:
365:
335:
252:
223:
201:
147:
85:
59:
1976:Review of Economic Dynamics, forthcoming
1825:. Princeton: Princeton UP, 2015. Print.
1649:
1723:
1721:
1277:we obtain, for the previous equation:
1270:{\displaystyle R_{t+1}=R=\beta ^{-1}}
504:Microcredit and consumption smoothing
7:
1854:A Theory of the Consumption Function
1789:
1787:
1785:
1783:
1687:
1685:
52:Expected utility can be modeled as:
702:being the real rate of interest in
492:Insurance and consumption smoothing
1522:
941:
641:{\displaystyle \delta =1/\beta -1}
14:
1795:Public Finance and Public Policy
1734:Journal of Economic Perspectives
1597:{\displaystyle c_{t}=\left\left}
460:{\displaystyle U(c)={\sqrt {c}}}
1811:. Pearson. pp. Chapter 4.
1410:
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1355:
1342:
1326:
1307:
1197:
1184:
1169:
1150:
1082:
1043:
977:
964:
535:marginal propensity to consume
444:
438:
343:
311:
296:
284:
275:
263:
179:
148:
141:
132:
120:
114:
86:
79:
1:
1770:"On the demonisation of debt"
1938:Journal of Political Economy
1887:Journal of Political Economy
1807:Perloff, Jeffrey M. (2004).
1429:{\displaystyle E_{t}=c_{t}}
826:{\displaystyle y_{t}=w_{t}}
2017:
1617:random walk in consumption
1850:Friedman, Milton (1956).
1692:Coy, Peter (2022-09-28).
772:being the consumption in
513:Hall and Friedman's model
1871:Post-Keynesian Economics
557:With (cf. Hall's paper)
521:. Since Friedman's 1956
1728:Choi, James J. (2022).
523:permanent income theory
1598:
1526:
1430:
1362:
1271:
1213:
1089:
989:
945:
895:
875:
847:
833:being the earnings in
827:
786:
766:
737:
716:
696:
642:
601:
581:
488:
461:
418:
396:
374:
350:
232:
210:
186:
49:
32:Expected utility model
1610:
1599:
1506:
1431:
1363:
1272:
1214:
1090:
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925:
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876:
874:{\displaystyle A_{t}}
848:
828:
787:
767:
765:{\displaystyle c_{t}}
738:
717:
697:
643:
602:
582:
580:{\displaystyle E_{t}}
512:
474:
462:
419:
397:
375:
351:
233:
211:
187:
47:
17:Consumption smoothing
1747:10.1257/jep.36.4.167
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547:liquidity constraint
529:and Brumberg's 1954
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1793:Gruber, Jonathan.
1698:The New York Times
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543:Empirical evidence
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228:
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182:
50:
1638:Risk compensation
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1485:
1222:By assuming that
1201:
894:{\displaystyle t}
846:{\displaystyle t}
785:{\displaystyle t}
736:{\displaystyle u}
715:{\displaystyle t}
600:{\displaystyle t}
455:
417:{\displaystyle d}
395:{\displaystyle W}
373:{\displaystyle q}
231:{\displaystyle W}
209:{\displaystyle q}
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531:life-cycle model
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39:marginal utility
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2001:Consumer theory
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704:
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670:
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610:
609:
589:
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519:Milton Friedman
515:
506:
494:
430:
429:
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384:
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198:
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56:
55:
34:
12:
11:
5:
2014:
2012:
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2003:
1998:
1988:
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1982:
1981:
1963:
1950:10.1086/261605
1928:
1913:
1900:10.1086/260724
1894:(6): 971–988.
1876:
1861:
1842:
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1809:Microeconomics
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1779:
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1740:(4): 167–192.
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33:
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13:
10:
9:
6:
4:
3:
2:
2013:
2002:
1999:
1997:
1994:
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1991:
1977:
1973:
1967:
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1944:(2): 305–46.
1943:
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1932:
1929:
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1839:. 2009-10-05.
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1099:
1077:
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1038:
1035:
1032:
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1024:
1019:
1016:
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1009:
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1000:
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981:
972:
968:
961:
957:
951:
947:
936:
933:
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926:
920:
916:
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906:
888:
866:
862:
854:
840:
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793:
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757:
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730:
723:
709:
689:
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629:
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536:
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486:
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452:
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411:
403:
389:
381:
367:
359:
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340:
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293:
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90:
82:
76:
73:
70:
67:
64:
61:
53:
46:
42:
40:
31:
29:
25:
22:
18:
1975:
1966:
1941:
1937:
1931:
1922:
1916:
1891:
1885:
1879:
1870:
1864:
1853:
1845:
1836:
1830:
1822:
1817:
1808:
1802:
1794:
1773:
1764:
1737:
1733:
1709:. Retrieved
1697:
1673:. Retrieved
1661:
1652:
1621:
1614:
1606:
1441:
1438:
1370:
1221:
1097:
997:
904:
556:
539:
516:
507:
495:
484:
481:Middle graph
480:
476:
426:
404:
382:
360:
357:
247:
244:
240:
218:
196:
193:
54:
51:
35:
26:
16:
15:
1996:Consumption
551:Robert Hall
545:shows that
485:Right graph
1990:Categories
1774:www.ft.com
1711:2022-11-07
1675:2022-11-07
1644:References
527:Modigliani
477:Left graph
424:= damages
1958:153924721
1756:0895-3309
1706:0362-4331
1670:0190-8286
1523:∞
1508:∑
1338:′
1303:′
1260:−
1256:β
1180:′
1146:′
1109:β
1070:−
948:β
942:∞
927:∑
690:δ
687:≥
681:−
633:−
630:β
616:δ
498:insurance
402:= wealth
324:−
318:−
306:∗
291:−
279:∗
270:−
238:= wealth
136:∗
127:−
74:∗
1925:: 39–52.
1908:54528038
1627:See also
21:economic
1776:. 2011.
358:where:
194:where:
1956:
1906:
1754:
1704:
1668:
19:is an
1954:S2CID
1904:S2CID
1837:CGAP
1752:ISSN
1702:ISSN
1666:ISSN
525:and
1946:doi
1896:doi
1742:doi
1992::
1974:.
1952:.
1942:97
1940:.
1902:.
1892:86
1890:.
1782:^
1772:.
1750:.
1738:36
1736:.
1732:.
1720:^
1700:.
1696:.
1684:^
1664:.
1660:.
1978:.
1960:.
1948::
1910:.
1898::
1873:.
1758:.
1744::
1714:.
1678:.
1591:]
1585:t
1581:A
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87:|
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80:(
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68:=
65:U
62:E
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