Journal of Economic Literature 48 (September 2010): 693–751 http:www.aeaweb.org/articles.php?doi=10.1257/jel.48.3.693

Consumption and Saving: Models of Intertemporal Allocation and Their Implications for Public Policy

Orazio P. Attanasio and Guglielmo Weber*

This paper provides a critical survey of the large literature on the life cycle model of consumption, both from an empirical and a theoretical point of view. It discusses several approaches that have been taken in the literature to bring the model to the data, their empirical successes, and their failures. Finally, the paper reviews a number of changes to the standard life cycle model that could help solve the remaining empirical puzzles.

1. Introduction perspective, it is difficult to construct coher- ent models based on intertemporal opti- n the early 1950s, the prevailing model mizing behavior that are consistent with Iof consumption behavior used by mac- Keynes’s description of the “fundamental roeconomists was inspired by the “funda- ­psychological law.” From an empirical point mental psychological law” mentioned by of view, it seemed that Keynes’s view was John Maynard Keynes (1936) in the General ­inconsistent with a number of facts, both at Theory. At that time, the theoretical and the macro and the micro level. At the aggre- empirical limitations of that model became gate level, for instance, it was observed that increasingly clear. From a theoretical the marginal propensity to consume out of disposable income was lower in the short run * Attanasio: UCL, IFS, NBER, and CEPR. Weber: than in the long run. In cross sections, on the Università di Padova, IFS, and CEPR. We are grateful other hand, saving rates seemed to change to a very large number of people for a number of differ- systematically with the level of income. ent reasons. Our thinking about the issues discussed in this paper has been particularly influenced by a set of people, Moreover, it was observed that groups of several of whom have been coauthors in several projects. individuals with, on average, lower levels They include: Rob Alessie, James Banks, Richard Blundell, of income (such as blacks) had higher sav- ­Martin Browning, Angus Deaton, Hamish Low, Tom MaC- urdy, Costas Meghir, and Luigi Pistaferri. We have discussed ing rates than other groups with higher lev- many of the issues covered in this paper (and sometimes dis- els of average income (such as whites) at agreed) with them. We certainly learned a lot from them. any income level. Finally, it was observed We are very grateful to three referees and Erik Hurst for useful comments and suggestions, and to the Editor for that saving rates are systematically related comments, suggestions, and incredible patience! Attanasio’s to changes in income, being higher for indi- research was partially financed by ESRC grant RES-051- viduals experiencing income increases and 27-0125. Weber’s research was partially financed by MIUR grant 2007AC54X5. Weber is also grateful to ESRI, Cabinet lower for individuals experiencing income Office, Tokyo, for hospitality and many useful discussions. decreases (see George Katona 1949).

693 694 Journal of Economic Literature, Vol. XLVIII (September 2010)

All these observations clearly contra- After its initial development, the other dicted the implications of the Keynesian important step in the development of the model and led to the formulation of the life cycle/permanent income model, which life cycle and permanent income models is currently used as the standard workhorse (Franco Modigliani and Richard Brumberg of modern macroeconomics, was a rigorous 1954, 1980; Milton Friedman 1957). These treatment of uncertainty. In the late 1970s, models combined theoretical consistency the contributions of Robert E. Hall (1978) in that intertemporal consumption and sav- (and Thomas E. MaCurdy 1981, 1999 in the ing choices were set within a coherent opti- context of labor supply) exploited the idea of mization problem with the ability of fitting using the first-order conditions of the inter- most of the facts mentioned in the previous temporal optimization problem faced by the ­paragraph. The saving rates of blacks was consumer to derive testable implications (and is) higher than that of whites at any of the model. This approach, known as the income level because the permanent income Euler equation approach, makes possible of blacks is lower and, therefore, condition- the empirical analysis of a problem that is ing on a common income level, one selects analytically intractable by circumventing the the blacks with a higher level of temporary need to derive closed-form solutions. This shocks that should, according to the model, is achieved by focusing on the economic be saved. Similarly, individuals with income essence of the model: consumers, at the opti- increases are more likely to be affected by mum, will act to keep the marginal utility of positive transitory shocks. At the macro level, wealth constant over time. The marginal util- short-run fluctuations in disposable income ity of wealth is at the same time a sufficient are more likely to be dominated by the vari- statistic for consumer choices and, given its ance of temporary shocks that would be dynamic properties, can be “differenced out” averaged out in the long run. Some of these in a way which is analogous to the treatment facts still hold in modern data, as we docu- of fixed effects in econometrics. ment in section 2. The Euler equation approach became the The development of the ideas in the standard approach as it allowed to both test seminal contributions of Modigliani and the validity of the model and to estimate Brumberg and Friedman also led to the some of the structural parameters of the util- realization of other implications. In a simple ity function. A hypothesis that received much version of the life cycle model, if income is attention, since Hall (1978), is that lagged hump shaped and declines at retirement, values of income, or predictable changes in consumers will save when they are young to income, do not predict future consumption support consumption in the last part of life once current consumption is accounted for. and dissave when they are old. Modigliani Perhaps as a consequence of this focus on and Brumberg then showed that this fact can testing, when it came to policy analysis and explain the correlation between aggregate debates, the model and in particular the growth and aggregate saving: growth implies empirical evidence that has been accumu- that, in a given year, younger cohorts, who lated on it have been rarely used. One of the are saving, are “richer” in lifetime terms reasons for this divorce between the litera- than older ones, who are dissaving. The ture on the life cycle model and what should higher the rate of growth is, the larger the have been its practical use in the design and difference in resources between savers and evaluation of public policy stems from the dissavers and, therefore, the higher the fact that the Euler equation does not deliver aggregate rate of saving. a consumption function. While it can be used Attanasio and Weber: Consumption and Saving 695 to test the model and estimate some of its sion of the model that is flexible enough to be parameters, it cannot be used to determine brought in a serious way to the data and that the effects of specific policy changes on con- allows us to derive specific implications on a sumption or saving. number of policy-relevant questions. At the same time, much of the evidence We start our approach by discussing a num- that came to be perceived as the accepted ber of empirical findings in section 2. We refer view pointed to rejections of the life cycle to both time series and cross sectional findings model that took the form of “excess sensitiv- and we focus especially on results that might ity” of consumption to income. Indeed, in point to empirical rejections of the model. We the next section, we take this evidence as one organize our ­discussion of the empirical evi- of the starting points of our discussion of the dence in two parts. We first discuss evidence life cycle model, of its empirical plausibility, that refers to individual consumption behav- and of its utility for policy analysis. We have ior. We then move on to look at evidence two main goals: to take a stand on where the derived from movements in the distribution literature is and what the main issues are and of consumption, which allows researchers to to discuss the public policy implications of look at the functioning of markets and the the life cycle/permanent income models. smoothing of various types of shocks. The life cycle model can be loosely defined After reviewing this empirical evidence, as a framework where individuals maximize we discuss how a relatively standard but suf- utility over time given a set of intertempo- ficiently rich version of the life cycle model ral trading opportunities. Even at this level can be made consistent with it in section 3. of generality, the model is of some useful- Moreover, we discuss the evidence on the size ness. It establishes a conceptual framework of the relevant structural parameters. Having that treats the intertemporal allocation of established that the model is not wildly at resources in a way which is similar to the variance with the data and some of the evi- allocation of resources among different com- dence that was presented as a rejection of the modities. Decisions will then depend on the life cycle model can be reconciled with it if total amount of resources (in the intertem- one specifies a version that is flexible enough, poral context: current and future income as we go ahead and use the model to quantify, by well as current wealth), on preferences over using simulations, its main properties. In par- the different commodities (in the intertem- ticular, we show how consumption changes poral context: present and future consump- with changes in income and interest rates tion, and possibly bequests), and on relative for different values of the structural param- prices (interest rates and intertemporal trade eters. The use of simulations is necessary in opportunities). this context because it is not possible to obtain Without being more specific, however, it is closed form solutions. not possible to say much more than what is Simulations are also useful to study aspects stated in the previous paragraph. Or, saying of life cycle behavior that cannot be studied it differently, this level of generality encom- with the Euler equation approach (such as passes many different types of behavior and durables, housing, etc.) because transaction has almost no testable implications. In what costs lead to infrequent adjustments. follows, therefore, we construct a specific Besides preferences and income pro- model and analyze its components. This exer- cesses, the other important component of the cise forces us to make a number of strong life cycle model is the intertemporal budget assumptions and modeling choices that we constraint. A specific hypothesis about the discuss below. We choose to work with a ver- nature of the intertemporal budget constraint 696 Journal of Economic Literature, Vol. XLVIII (September 2010) implicitly assumes a certain market structure move on to facts about the cross-sectional and the instruments consumers have to move dispersion of consumption and interpret resources over time (and across states of the movements in time of these moments as world). Section 4, therefore, is devoted to the informative about risk sharing and insurance discussion of alternative market structures, markets available to individuals. starting from the benchmark of complete markets to move on to various models of 2.1 Average Individual Behavior incomplete markets. One of the themes of the paper, and in par- As was mentioned in the introduction, ticular of section 3, is that one can construct the life cycle/permanent income model was rich versions of the life cycle of the model that developed to explain some facts about con- are not inconsistent with some aspects of the sumption. Some of these facts were noticed micro data and can be useful in the conduct of in aggregate statistics: (nondurable) con- policy analysis. Having said that, it is clear that sumption expenditure is less volatile than the simplest versions of the model are incon- income and the marginal propensity to con- sistent with various aspects of the data and sume seems to be smaller in the short run that the empirical literature on consumption than in the long run. These “macro facts” has accumulated a number of puzzles. In sec- still hold and some can also be found in tion 5, we discuss some of these puzzles and micro data (such as the relative variability possible extensions and modifications of the of nondurable consumption and income— basic model. Section 6 concludes the paper. see Orazio P. Attanasio 2000 and Attanasio and Margherita Borella 2006). Other facts 2. Facts explicitly mentioned by the seminal contribu- tions that originated the life cycle/permanent In this section, we present some well income model emerged from cross-sectional known facts about consumption behavior studies and, in particular, from observations both at the aggregate and at the micro level. of how saving rates vary in the cross section Our aim is to present empirical evidence that with income. As with the “macro” facts, these is or might be relevant to judge the valid- empirical regularities still hold in recent data. ity of the life cycle model. Indeed, many of If one looks at U.S. Consumer Expenditure the facts that we list below were presented Survey (CEX) data, one finds that the saving as explicit tests of the life cycle/permanent rate of blacks is higher than that of whites income model and sometimes interpreted as at any income level, as noted by Friedman rejections of the model. In addition to these (1957). Similar evidence can be obtained in facts, however, we will also report some new the United States and the United Kingdom evidence on old findings that motivated the if one looks at the saving rates by current development of the life cycle model. income level of other groups that differ by the We divide the empirical evidence we level of “permanent” income, such as house- present in two parts. We first discuss find- holds headed by individuals with different ings that refer to individual behavior. In this levels of education. Analogously, if one con- first subsection, we consider how individual siders separately individuals whose income consumption moves, on average.1 We then has increased and individuals whose income has decreased, the saving rate of the latter is smaller than that of the former, as noted 1 Which moment is considered to represent the ­measure of location of the distribution of individual consumption is fifty years ago by Modigliani and Brumberg an interesting issue which we discuss in what follows. (1954), citing work by Margaret G. Reid. Attanasio and Weber: Consumption and Saving 697

Levels, by education Levels, by education Compulsory Postcompulsory

800

Income Consumption

600

400 Income and consumption 200

25 35 45 55 65 75 25 35 45 55 65 75 Age of head

Figure 1. Average Income and (Nondurable) Consumption by Education Source: U.K. Family Expenditure Survey, 1978–2007.

The fact that these empirical regularities will find that, for each current income level, still hold is important and we come back to individuals from the group with a lower level them when discussing the empirical valid- of permanent income will have a higher level ity of the life cycle model. At this stage, we of temporary income, which, the model sug- simply stress that the life cycle/permanent gests, should be saved. income model offers a coherent explana- Interestingly, the empirical criticisms of tion for them. The main ideas behind the the life cycle model that have been accumu- use of the life cycle model to explain these lating since have mainly pointed out devia- facts is that consumers have concave util- tions from the prediction that expected ity functions and, therefore, prefer smooth changes in income should not be incorpo- paths of consumption (over time and across rated into consumption. These deviations states of the world) over variable ones. can be classified into three groups: those Therefore, only unanticipated changes in that identify correlations between expected income that are perceived as permanent will changes in income and consumption at low induce substantive changes in consumption. frequencies, those that consider short-run Expected and temporary changes to income fluctuations linked to changes in earnings should not induce a strong change in con- and income, and those that refer to short- sumption. The explanation of the facts men- run fluctuations that are linked to ad hoc tioned above boils down to the observation payments not necessarily related to labor that a large fraction of the changes in income supply behavior. considered in these stylized facts are tem- 2.1.1 Low Frequency, Life Cycle Patterns porary. For instance, if one classifies indi- viduals with different levels of permanent Christopher D. Carroll and Lawrence H. income by the level of current income, one Summers (1991), in an influential paper, 698 Journal of Economic Literature, Vol. XLVIII (September 2010)

Cohort proles Cohort proles 1000 Compulsory Postcompulsory

Income Consumption

500

0

20 40 60 80 20 40 60 80 Age of head

Figure 2. Average Income and Consumption by Cohort and Education Source: U.K. Family Expenditure Survey, 1978–2007. show that life cycle profiles of income and these pictures is very similar to theirs—at consumption track each other. For many life cycle frequencies, consumption pro- countries both income and consumption files do follow income profiles. (This is even life cycle profiles are hump shaped, in that more strikingly true if total expenditure they increase during the first part of the replaces nondurable consumption). life cycle to reach a peak a few years before A drawback with this type of graph is retirement and decline afterwards. Groups that they average over individuals by age, and countries that exhibit relatively “steep” irrespective of their year of birth. If differ- income profiles also exhibit relatively “steep” ent generations have access to different life consumption profiles. Carroll and Summers, cycle resources (as assumed in the life cycle therefore, conclude that income and con- model) this is not the right thing to do. In fig- sumption track each other over the life cycle, ure 2, we show what happens when the data therefore contradicting one of the main pre- are grouped in year of birth cohorts—and dictions of the life cycle model. averages are then taken by age. (In the fig- We reproduce this type of graph in fig- ure, cohorts are ten-year wide). There is still ure 1 where we report life cycle profiles evidence of income tracking, even though for disposable income and nondurable con- this is now less clear cut. sumption for two education groups in the Do these pictures constitute a fundamen- United Kingdom (the Family Expenditure tal rejection of the life cycle model? In the Survey data used here cover the 1978–2007 next section, we will be arguing formally that sample period). We thus adopt the same the answer is no, both in theory and in prac- methodology as Carroll and Summers tice. Here we simply point out that, if one (1991). The message that comes out of wants to be serious about bringing the life Attanasio and Weber: Consumption and Saving 699

Per capita, by cohort Per capita, by cohort Compulsory Postcompulsory 500 Income Consumption

400

300

200

100

20 40 60 80 20 40 60 80 Age of head

Figure 3. Average Per Capita Income and Consumption by Cohort and Education Source: U.K. Family Expenditure Survey, 1978–2007. cycle model to the data, one cannot take the Arguably the largest predictable change simplest version, which is used for pedagogi- in income is the one that occurs at retire- cal reasons, but has to take into account that, ment: earnings decline considerably as in all likelihood, consumption needs evolve individuals exit the labor force and such over time as family composition changes. decline should be anticipated. An obvi- This argument is made by Attanasio and ous prediction of the life cycle model of Martin Browning (1995). Modigliani and Brumberg (1954) is that The simplest way to start considering this individuals, who should have accumulated type of issues is to look at life cycle pro- wealth (either in private assets or in enti- files for consumption that take into account tlements to pension benefits), should start changes in needs, by considering consump- decumulating it to keep a level of consump- tion per capita or consumption per adult tion consistent to the one afforded before equivalent, rather than total household con- retirement. Daniel S. Hamermesh (1984) sumption. Figure 3 reproduces figure 2 but was the first to argue that consumers appar- using consumption per adult equivalent.2 As ently do not save enough to achieve this can be noticed, the profiles for consumption aim. If households enter retirement with are now much flatter. We come back to these inadequate savings, they must cut their pictures and to the interpretation of this evi- consumption level, contrary to the life cycle dence in what follows. model predictions. The recent literature has focused on esti- 2 We are grateful to Cormac O’Dea for his help with the mating how consumption levels change Family Expenditure Survey data. around retirement. The existence of a 700 Journal of Economic Literature, Vol. XLVIII (September 2010)

­consumption fall around retirement is doc- 1980s, instead, found strong rejections of this umented for the United Kingdom (James prediction. John Y. Campbell and N. Gregory Banks, Richard Blundell, and Sarah Tanner Mankiw (1990a), in one of the best known and 1998), for the United States (B. Douglas cited papers, found that regressing changes in Bernheim, Jonathan Skinner, and Steven aggregate U.S. log consumption on interest Weinberg 2001), and for Italy (Erich Battistin rates and changes in log disposable income, et al. 2009) and has come to be known as the the latter variable attracted a coefficient of retirement consumption puzzle (or retire- 0.4, statistically different from zero, even ment savings puzzle). Banks, Blundell, and after instrumenting current variables with Tanner (1998) find that, for ages between lagged ones to avoid picking up the effects of 60 and 67, the level of consumption is lower innovations to the level of permanent income. than that predicted by a version of the life Campbell and Mankiw (1991) replicate the cycle model by as much as 1.5 percent on evidence for the United States for a variety of an annual basis. The cumulated consump- other countries and attribute such a result to tion shortfall over this age band, where most the presence of a large number of consum- people retire, is around 10 percent. For ers who follow a “rule of thumb” and set their the United States, Bernheim, Skinner, and consumption equal or proportional to their Weinberg (2001) estimate a median drop of income. 14 percent but higher drops for low wealth, Hall and Frederic S. Mishkin (1982) low income replacement households. They perform a similar exercise but using micro conclude that “31 percent of the sample data from the United States. Using data on reduce their consumption by at least 35 per- food consumption from the Panel Study of centage points.” Battistin et al. (2009), who Income Dynamics (PSID), they find a sig- use Italian data, estimate at 9.8 percent the nificant correlation between changes in food part of the nondurable consumption drop consumption and lagged changes in income. that is associated with retirement (food They interpret this evidence as indicat- expenditure falls instead by 14 percent). ing that about 20 percent of households set consumption on the basis of current income 2.1.2 Business Cycle Frequency rather than following the life cycle model. The evidence mentioned so far refers to a Another study that uses micro data is by relationship between predictable changes in Stephen P. Zeldes (1989). He uses the same income and consumption at the life cycle fre- data as Hall and Mishkin (1982) but distin- quency. Many papers have also looked at the guishes between consumers with a low level relationship at higher frequencies. This work of assets and a high level of assets and finds is typically based on the Euler equations that that the consumption for the former group is we will be discussing in the next section, but more linked to income than the consumption basically tests the hypothesis that, conditional of the latter. Zeldes (1989) explicitly refers on current consumption, future consumption to the possibility that some consumers are is not affected by predicted changes in income, affected by liquidity constraints and restric- or current level of income. This prediction is tions to borrowing that do not allow them to obviously related to the observations made by set current consumption at the desired level. the early proponents of the life cycle/perma- We come back to the issue of liquidity con- nent income hypothesis between the lack of straints in the next section. strong correlation between changes in con- The evidence mentioned so far is relevant sumption and income both in cross sections for the life cycle model as it exploits the and in the time series. Many studies in the implications of the theoretical framework Attanasio and Weber: Consumption and Saving 701 for changes in consumption. In the next ­varies in relation to changes in income that are section, we map directly this evidence on not only predictable, but also driven by events the theoretical framework of the life cycle that do not have any implications for hours model. However, it is also possible, albeit worked or labour force participation. In par- more complicated, to derive implications ticular, a large number of papers have looked of some version of the model for the level at the effects of tax refunds or other changes of consumption. Intuitively, the theoreti- linked to administrative issues. Papers in cal framework implies that innovations to this literature include Nicholas S. Souleles permanent income should be fully incorpo- (1999), Jonathan A. Parker (1999), Chang- rated in consumption, while innovations to Tai Hsieh (2003), Browning and M. Dolores transitory consumption of income should Collado (2001), and Melvin Stephens (2008). not.3 Therefore, if one specifies a time series Souleles, Parker, Stephens and, in part, Hsieh model of consumption and income and iden- find that consumption reacts to changes in tifies the permanent innovations to the lat- the level of resources available to consum- ter variable, the model predicts that these ers that are fully predictable. Browning and innovations should be translated one to one Collado, on the other hand, as well as the sec- into consumption. This implies cross equa- ond part of Hsieh’s paper, find that consumers tion parametric restrictions on the VAR rep- do not respond to such predictable changes resentation that can be estimated. Campbell in resources. We come back to the interpreta- and Angus Deaton (1989) pointed out these tion of these results later. restrictions and, using aggregate time series 2.2 The Evolution of the Cross-Sectional data, found that consumption seems to Evolution of Consumption be too smooth in that it does not react suf- ficiently to innovations to the permanent In the previous subsection, we have component of income. Similar findings were listed a number of “facts” that have been obtained by Kenneth D. West (1988), Jordi discussed in the literature on the empirical Galí (1991) and Lars Peter Hansen, William implications of the life cycle model. All of T. Roberds, and Thomas J. Sargent (1991). the evidence there referred to the proper- Perhaps surprisingly, no similar test on micro ties of consumption levels and consumption data was performed until the recent paper by changes, on average (either by looking at Attanasio and Nicola Pavoni (2007), who also aggregate data or, in the case of individual find “excess smoothness.”4 data, to regressions aimed at identifying the behavior of the average consumer). The evo- 2.1.3 Predicted Changes in Income lution of the cross-sectional distribution of The changes in income that we have con- consumption—and income—however, can sidered so far are large predictable changes also be very informative about the relevant that occur over the life cycle and/or changes model that describes the data. that are likely to be related to changes in labor One of the first papers to notice the supply. In recent years, a small literature has implications of a simple version of the life developed that studies how consumption cycle model for the evolution of consump- tion inequality was Deaton and Christina Paxson (1994). These authors notice that, if 3 We are abstracting here from the possibility of insur- income has a unit root, in a basic life cycle ing permanent shocks and implicitly considering a con- model, the cross-sectional section of con- sumer who has access to a fairly limited portfolio of assets to move resources over time and across states of the world. sumption increases over time. One can then 4 An exception is Deaton (1992a). consider how the cross-sectional variance of 702 Journal of Economic Literature, Vol. XLVIII (September 2010)

­consumption for a cohort of individuals born will induce an equal increase in the cross- in the same year should increase over time sectional variance of consumption. Therefore, as these individuals age. Testing this forecast the difference between the increase in the for the United Kingdom, the United States, cross-sectional variance of income and that of and Taiwan, Deaton and Paxson (1994) show consumption will identify the changes in the that this is effectively the case. As innova- cross-sectional variance of transitory income. tions accumulate, the cross-sectional distri- The caveat about the market structure in bution of consumption fans out with age.5 the last paragraph makes it clear that there is Battistin, Blundell, and Arthur Lewbel a stringent relationship between the type of (2009) use a similar argument to explain a insurance markets agents have access to and remarkable empirical regularity—the cross- the evolution of consumption inequality. Given sectional distribution of consumption seems an initial distribution of consumption (however to be extremely well approximated by a log determined) in the presence of perfect risk normal. This is true across a wide variety of sharing, that distribution should stay constant countries. Under a standard version of the (with some technical caveats we will discuss in life cycle model, at any age, (log) consump- section 4). Deaton and Paxson (1994) noticed tion is given by past (log) consumption plus a that in a footnote and presented evidence on term that reflects an innovation to permanent the evolution of the cross-sectional variance income. Therefore, by recursive substitution, of consumption as a rejection of the complete one gets that log consumption is given by the market model. In an ingenious paper, Tullio sum of innovations from the beginning of life Jappelli and Luigi Pistaferri (2006) exploit that to the current age. By the central limit theo- idea by looking explicitly at movements in the rem, the sum of independent innovations con- relative ranking in the consumption distribu- verges to a normal distribution under some tion in an Italian survey. As with other papers, regularity assumptions, even if the individual they reject strongly the assumption of perfect innovations are not normally distributed. risk sharing. The facts about the evolution of the cross- Similarly, Attanasio and Steven J. Davis sectional inequality of consumption and (1996), by looking at the evolution of rela- income are also used in another study by tive consumption across different education Blundell and Ian Preston (1998). Under a spe- groups and relating that to changes in rela- cific market assumption, they show that the tive wage changes, interpret the evidence of a relative evolution of consumption and income strong correlation at low frequencies between inequality can be used to identify permanent these two variables as evidence against the and transitory income variances. The idea is complete market hypothesis. Interestingly, relatively simple: if consumers face a simple Attanasio and Davis (1996) cannot reject the asset market structure, changes in the vari- hypothesis that, at relatively high frequen- ance of the permanent component of income cies (like one year), there is no relationship

5 Using repeated cross-sectional data or longitudinal effects. Deaton and Paxson (1994) assume some restric- data, one can follow the evolution of consumption inequal- tions on time effects. A forthcoming issue of the Review of ity for any given cohort and estimate how it evolves with Economic Dynamics contains a collection of papers from age and time. The identification of an average “age pro- different countries (including the United States and the file” for the variance of consumption that is common for United Kingdom) that undertake similar exercises. The different time periods and different cohorts, is compli- shape of the age profile in the United States seems to cated by the fact that age, time, and cohort are obviously depend crucially on whether one considers total household linked and, without additional restrictions or structure, it consumption or consumption per adult equivalent and is not possible to identify separately age, cohort, and time which adult equivalence schemes are used. Attanasio and Weber: Consumption and Saving 703 between consumption and relative wage understated. Reliable information on con- changes. This seems to indicate that, some- sumption is key for a host of issues, ranging how, at high frequencies wage shocks are from the construction of price indexes, which absorbed and not reflected in consumption. are used to index a variety of payments, to Until the early 1990s, as reported also the assessment of living conditions and the by Blundell, Pistaferri, and Preston (2008), measurement of poverty, to the estimation of consumption inequality has increased sub- different models of individual behavior and, stantially, mirroring the increases in inequal- ultimately, to the design of public policy. And ity in wages and earnings. After the early yet, the resources spent in the collection of 1990s, however, the picture is less clear. Dirk reliable consumption data are remarkably Krueger and Fabrizio Perri (2009) report small. The CEX is a relatively small survey that the overall cross-sectional variance of whose quality is perceived to have been dete- consumption in the United States has not riorating over the years.6 While there are signs increased much. Attanasio, Battistin, and that data collection in developed countries Hidehiko Ichimura (2007), instead, find that has become harder as people seem less will- the cross-sectional inequality of consump- ing to respond to survey questions, a redesign tion does increase even in the more recent and improvement of consumption surveys is, period. Even though both papers use the in our opinion, very important. CEX, it turns out that the main difference in the results of these two papers stems from 3. The Life Cycle Model the data used. The CEX is made of two inde- pendent samples: one, called the interview In the first part of the previous section, survey, in which households are asked retro- we mentioned a number of “facts,” relating spective questions about their consumption to both individual and aggregate consump- in the quarter preceding the interview, while tion. After a brief mention of the facts that the other, the diary survey, in which house- motivated the development of the life cycle holds are asked to keep a diary for two weeks. model (and that still hold in recent datasets), It turns out that, in fact, Krueger and Perri we discussed several facts that could be cast use data from the interview survey while as criticisms of the model, in that they con- Attanasio, Battistin, and Ichimura integrate tradict some simple implications of the the- data from the two surveys, following the ory. To summarize, some of these facts are: practice of the Bureau of Labor Statistics, which uses the diary survey for some com- 1. The age profile of consumption is hump modities and the interview survey for others. shaped, apparently tracking the age The different evidence about the evolution ­profile of income for each education of consumption inequality in the United States group; moreover, groups of individuals emerging from two different components of that have “steep” income age profiles, the same survey, which is also the main source seem to have steep consumption age of information on consumption at the micro profiles; level in the largest industrialized country in 2. Consumption drops at retirement; the world, justifies a small digression about the quality of consumption data. Information about expenditure and even more so about 6 If one aggregates the CEX using the appropriate consumption is notoriously difficult to col- weights, one obtains only a fraction of aggregate Personal Consumption expenditure as measured in the National lect in developed countries. At the same time, Accounts. Moreover, this fraction has been declining the importance of this information cannot be considerably. 704 Journal of Economic Literature, Vol. XLVIII (September 2010)

3. The growth rate of consumption seems 3.1 Preferences “too” sensitive to predictable changes in income; The version of the model we consider is 4. Consumption seems to react to changes one in which a consumer unit maximizes in available resources that are fully expected utility over a finite interval subject predictable and transitory, such as tax to a set of constraints refunds. T t − In this section, we present the life cycle (1) max Et ​ ​​ t​ jU(Ct j, zt j, vt j), ∑j 0 β + + + + model in its modern form and discuss to what = extent it provides an explanation for the facts such that listed above. Facts that go under the first three headings will be explained by the con- * sideration that the model does not predict (2) Wt j 1 Wt j(1 R​ t j​ ) + + = + + + that individuals smooth their consumption but their marginal utility from consump- yt j Ct j , + + − + tion. We leave to the end of this section our interpretation of the facts under the fourth N i heading. (3) Wt j ​ ​ ​A​ t j​ ​​ , + = i∑1 + The main idea of the life cycle model is = a very general one: it can be stated by say- N ing that consumers are supposed to allocate * i i (4) R​ t j​ ​ ​ ​ ​ t j​ ​​ ​R​ t j​ ​ , resources over time in order to maximize + = i∑ 1 ω + + = life time utility subject to a resource con- straint. At this level of generality, the model and does not have much empirical content and is not particularly useful. To bring it to bear (5) W 0, on data and make it potentially falsifiable, T ≥ we need to put a bit more structure on its various components. In particular, we where C stands for “consumption,” z for a have to specify the individual preferences potentially large vector of observable vari- that inform the maximization problem, ables that affect utility (that may be chosen the nature of the processes generating the by the consumer, or given to her—this will resources available to consumers, and the normally include household composition type of markets they have access to. In this variables), and v for unobservable factors section, we specify a basic life cycle model also affecting utility. As we shall see, demo- with an eye to the features that would help graphics play a key role in explaining the way us to explain some of the facts we mention consumption varies with age, particularly above. In addition, we also discuss how a in preretirement years. We let the discount version of the model that does fit the avail- factor be time varying to take into account β able data can be characterized and used in a mortality risk (that helps explain why con- variety of contexts. In section 4, we discuss sumption falls in old age—the survival the implications for the model and its appli- probability falls with age, and this makes cations of the facts about the distribution of the consumer progressively more impa- consumption discussed in the second part tient). Throughout the paper, we neglect the of section 2. issue of how decisions are taken within the Attanasio and Weber: Consumption and Saving 705

­household, and simply assume the house- income takes the value of zero would imply hold behaves as a unit.7 assigning positive probability to zero or even The first constraint is a generic budget negative consumption, which the consumer constraint where net worth appears together deeply dislikes. The consumer will then with its return, income, and consumption. never want to borrow even small amounts. Some or all components of income can be One can generalize this to situations where simultaneously determined with consump- the income process is bounded away from tion. For instance, it is possible that income zero. In this case, the consumer will not want is given by the wage rate times the number to borrow more than the present value of the of hours worked, where the number of hours lowest level of income. Similar consider- is one of the components of z. Equations (3) ations apply whenever the survival probabil- and (4) define net worth, W, and its return ​ ity is less than one if longevity risks cannot be i − ​ t j​ are the portfolio shares (or weights). The fully insured. ω + return on net worth is given by the weighted A number of important restrictions are i average of the individual returns, R​ t j​ ​ . We assumed in this formulation. First, the con- + assume these returns do not depend on the sumer is assumed to maximize expected net position taken by the consumer on each utility. This is a strong assumption that is i of these assets, ​A​ t j​ ​ . often used in the literature. Sometimes the + Equation (5) gives the limit for total net Von Neumann–Morgenstern framework is worth at period T. The consumer has to die replaced with different axiomatic structures, without debt, that is, she has to pay back such as the Kreps–Porteus axiomatization her debt with probability one. This simple as parametrized by Larry G. Epstein and restriction imposes quantitatively important Stanley E. Zin (1989, 1991).8 Second, we limitations to the ability to smooth consump- are assuming that preferences are additively tion. Suppose, for instance, that the income separable over time. This precludes the process is not bounded away from zero and consideration of various types of nonsepara- can actually take the value zero with some bility, ranging from durables to habit forma- positive (small) probability. If we further tion. We return to this issue below. Third, we assume that the marginal utility of consump- are implicitly assuming that it is possible to tion tends to infinity at very low levels of con- write down utility as a function of a single sumption, then the consumer will never want commodity. This practice presupposes an to borrow in such a situation. This is because aggregation theorem of the type studied by the presence of debt together with the non- William M. Gorman (1959). bankruptcy constraint and the ­possibility that

7 In the collective model of decision making, house- 8 Expected utility forces a negative relation between risk holds are normally assumed to select efficient allocations aversion and intertemporal substitution, but these are two as suggested in Pierre-Andre Chiappori (1988)—see distinct concepts. This prompted Epstein and Zin (1989) Frederic Vermeulen (2002) for a survey of this in a static to propose an alternative model that is based on Kreps and setting. Browning (2000) is the first paper to look at the Porteus (1978) preferences. Unlike expected utility opti- implications of relaxing the unitary model assumptions on mizers, Kreps and Porteus consumers care about the time intertemporal decisions. Maurizio Mazzocco (2007) tackles when uncertainty is resolved, even if they cannot take any the more general problem of household decision making action as a result. Epstein and Zin (1989) derive a full set in a T-period uncertain world, by deriving the Euler equa- of first order conditions—and show that the Euler equa- tions for individual and household consumption. He looks tion involves not only consumption growth and the interest at the case where individuals can commit to future alloca- rate but also the return on the market portfolio. Epstein tions of resources, and where commitment is instead not and Zin (1991) and Attanasio and Guglielmo Weber (1989) possible—because separation and divorce are a possible present estimates of the Euler equation for this type of way out. preferences. 706 Journal of Economic Literature, Vol. XLVIII (September 2010)

The problem formulated above is able to where It denotes information available at encompass different versions of the model time t (Hall 1978). If consumers have ratio- that have been considered in the literature. nal expectations, then: In particular, we treat as special cases the standard permanent income/life cycle model (7) Ct 1 Ct t 1 E( t 1 Wt) 0 + = + ε + ε + | = with quadratic preferences, the so-called buffer stock saving as well as flexible ver- for all variables W known at time t. Equation sions of the model (with an important role (7) can be used to derive a consumption for demographics and labor supply) that function in the case where no other asset is have been fitted to the data. available to the consumer (as in Truman F. We shall show that the flexible versions Bewley 1977) and the only stochastic vari- of the model can indeed explain the first able is labor income. Substituting (7) into three stylized facts presented at the begin- the budget constraints, Marjorie Flavin ning of the section. In particular, we shall (1981) shows that consumption is set equal show that the hump in the age profile of to permanent income, defined as the interest consumption is due to the interplay of rate times the present value of current and demographics and prudence, the excess expected future incomes: sensitivity of consumption growth to income growth is due to the dependence (8) C r ​ A t = _1 r t of the marginal utility of consumption on + leisure, while the retirement consumption r ∞ ​ ​ ​ E​(yt k It). _ + drop is due partly to adverse shocks induc- + 1 r k∑0​ | ing retirement and partly to more efficient + = shopping that is made convenient by the Equation (8) is derived for the special case increased leisure time. of infinite life but an extension to finite life In order to prove all this, we need to can be derived. work out the solution to the optimization In this model, the first difference in con- problem. Some features of the solution sumption, or the error term in (7), equals the can be understood by looking at the first present value of income revisions due to the order conditions, others require the accrual of new information between periods derivation of the consumption function, t and (t 1): + either analytically (in some special cases) or r ∞ 1 numerically. (9) Ct 1 ​ ​ ​ ​ ​​ ​ + _ _k Δ = 1 r k∑0 (1 r) Let us start with a case where the con- + = + sumption function can be derived analyti- [E(yt k 1 It 1) E(yt k 1 It)]. cally. Let utility be quadratic in consumption × + + | + − + + | (and additively separable in its other argu- ments z) and assume that at least one finan- Equation (7) highlights the consumption cial asset is freely traded and yields a fixed smoothing properties of the solution empha- real return equal to the constant time pref- sized in the seminal paper by Modigliani and erence parameter (1 )/ . The first order Brumberg (1954). Equation (8) makes clear − β β condition with respect to consumption, or the other main implication of the model that Euler equation, implies that consumption is was first stressed in Friedman (1957): con- a random walk: sumption depends on the present discounted value of future expected income. The inter- (6) E(Ct 1 It) Ct, est rate plays the important role of ­converting + | = Attanasio and Weber: Consumption and Saving 707 future resources to present ones and there- have focused on the Euler equations derived fore constitutes an important determinant from the maximization problem faced by the of consumption. Equation (8) imposes cross consumer. The basic first order conditions equation restrictions on the joint time series used in this literature are: process for income and consumption as noted in Sargent (1978). Equation (9) implies that, (10) U c t = λ t in appraising the effects of a given policy, for instance a tax reform that affects disposable and income, a ­distinction must be drawn between k permanent and temporary changes (Alan S. (11) t E[ t 1 (1 r​ t 1​ ) It], λ = λ + β + + | Blinder and Deaton 1985; James M. Poterba 1988). Another implication of (9) is that sav- where equation (11) is valid as long as the ing predicts future changes in income—the kth asset can be freely traded by consumers. so-called “saving for a rainy day” motive Equation (10) says that, at each point in (Campbell 1987). time, the marginal utility of consumption Quadratic utility implies certainty equiva- equals the Lagrange multiplier associated lence: the consumption function (8) is the with the budget constraint relevant for that same as under certainty once expectations period, which is sometimes referred to as the are replaced by realizations. This is conve- marginal utility of wealth. The second condi- nient for analytical purposes, but clearly tion, equation (11), that is derived from inter- restrictive, for instance in its treatment of temporal optimality, dictates the evolution of financial decisions: quadratic preferences the marginal utility of wealth. An equation imply increasing absolute risk aversion in of this type has to hold for each asset k for consumption (or wealth), something that which the consumer is not at a corner. This is is unappealing on theoretical grounds and because the consumer is exploiting that par- strongly counterfactual (riskier portfolios ticular intertemporal margin. are normally held by wealthier households). The attractiveness of Euler equations is Quadratic preferences also imply that the that one can be agnostic about the stochas- willingness to substitute over time is a tic environment faced by the consumer, the decreasing function of consumption—poor time horizon, the possible presence of a consumers should react much more to inter- bequest motive, the presence of imperfec- est rate changes than rich consumers after tions in financial markets (as long as there allowance has been made for the wealth/ is at least one asset that the consumer can income effect. freely trade), and the presence of frictions The alternative adopted in much of the lit- in other variables affecting utility, z. All erature has been to assume power utility and relevant information is summarized in the to allow for the existence of a number of risky level of the marginal utility of wealth. The financial assets. Power utility, also known as approach is conceptually similar to the use of isoelastic, or constant relative risk aversion an (unobservable) fixed effect in economet- 1 utility, is defined as U(c) (C −γ 1)/ rics. By taking first differences, one elimi- = − (1 ); it converges to ln(C) for 1. nates the unobservable marginal utility of − γ γ = Once one deviates from quadratic utility, wealth and is left only with the innovations however, and/or allows for stochastic interest to equation (11). This approach has played rates, one loses the ability to obtain a closed an important role in the empirical analysis of form solution for consumption. Many of the the life cycle model and we will come back studies that made this choice, therefore, to it. 708 Journal of Economic Literature, Vol. XLVIII (September 2010)

The derivation of a closed-form solution 3.2 Estimating Preference Parameters for consumption when certainty equivalence does not hold is possible in the case where the The Euler equation is particularly useful utility function exhibits constant absolute risk from an empirical point of view because it aversion. Ricardo J. Caballero (1991) shows can be cast as a set of orthogonality condi- that, in a modified Flavin model (with certain tions that should hold in a variety of situ- finite life and constant absolute risk aversion ations and allows estimating preference preferences), the optimal consumption–age parameters and testing the validity of the profile is flat with no uncertainty but increas- model without being explicit about all the ing with income uncertainty. This change in details of the stochastic environment faced the slope of the consumption profile is labeled by the consumer and without having to solve as precautionary saving because, early in life, explicitly the dynamic optimization problem consumers save more if labor income is more for consumption or other variables jointly uncertain. Later work by Christian Gollier determined with consumption. As stressed (1995) and Carroll and Miles S. Kimball (1996) by Gary Chamberlain (1984), estimation of established that a similar result holds when- the Euler equation requires observations ever the third derivative of the utility function covering a long period of time, as the orthog- is positive, and this feature of preferences is onality conditions hold in expectation, and labeled prudence. Both constant absolute risk (but for the special case of complete mar- aversion and power utility exhibit prudence. kets) sample expectations converge to popu- The presence and size of precautionary sav- lation expectations only over time (see also ings is a matter of great relevance for public Fumio Hayashi 1987). policy in so far as public insurance schemes A version of the Euler equation holds even covering such risks as unemployment, health, if the consumer chooses labor supply, dura- and longevity should reduce the need for con- ble consumption, and many other variables sumers to accumulate assets. that are subject to different types of adjust- The great merit of even this simple model ment costs and frictions. It holds under a with prudence is that it highlights the need wide variety of assumptions about the infor- to save for rainy days even if sunny days are mation set used by the consumer and, by the equally important. An increased variance in law of iterated expectations, it holds when- the shocks to income reduces consumption ever the information set used by the econo- even if expected income does not change. In metrician is no larger than that available to the case of discrete variables, such as unem- the consumer. To use it, one does not need to ployment or illness, changes in first and sec- specify assumptions about pension systems, ond moments occur simultaneously, but this future wage processes, bequests motives, is not the case for continuous variables. The and so on and so forth. Moreover, it reflects ability to distinguish between first and second the main essence of the life cycle model: the moments effects is of crucial importance in the fact that consumption is chosen so to keep analysis of public policy because public policy (discounted, expected) marginal utility con- can be used to provide social insurance, by stant over time. reducing the variance while keeping the mean The Euler equation can be used for two constant. For instance, a revenue-neutral tax purposes: testing for the validity of some of reform that cuts taxes for the rich may depress the model assumptions, notably the ability of consumption because it induces more precau- consumers to save in response to changes in tionary saving (Hal R. Varian 1980 stresses the intertemporal prices, and estimating prefer- insurance role of a progressive income tax). ence parameters. The first paper to estimate Attanasio and Weber: Consumption and Saving 709 a consumption Euler equation (Hall 1978) and the degree of risk aversion. This is the was entirely devoted to testing the model consequence of the assumption of intertem- but much of the literature since has done poral separability and separability across both. states of the world. Hall took the case of quadratic utility and Substituting equation (10) into (11) and a fixed interest rate such that (1 r) 1. using the properties of the power utility + β = Under these conditions, equation (6) obtains function the Euler equations for consump- and preference parameters are not ­identified. tion corresponding to each asset (k) are: Another notable feature of Hall’s version of the Euler equation for consumption is that −γ Ct 1 k it aggregates perfectly because it involves (12) Et + ​ (1 r​ t 1​ ) 1, _ ​ β + + = linear transformations of the data and can, Ct therefore, be empirically implemented in ca​ b d micro and aggregate data alike. The Euler where is a curvature parameter (equal γ equation (6) implies that no variable known to the relative risk aversion parameter and to the consumer at time t should help pre- to the reciprocal of the elasticity of inter- dict the change in consumption between t temporal substitution) and , the subjec- β and (t 1)—an important and easy to test tive discount factor, measures patience. + implication of the intertemporal optimiza- Equation (12) is an orthogonality condition tion model that has been rejected a number stating that a particular transformation of of times on aggregate and micro data alike the data is orthogonal to the information set (Jappelli and Marco Pagano 1989; Hall and used by the agent. Such a condition suggests Mishkin 1982). naturally the use of some GMM method to The special features of Hall’s model may estimate the unknown parameters and, to explain these rejections—for this reason, in the extent one considers a vector of vari- the literature, Euler equations have been ables whose dimension is greater than that estimated and tested for more general of the parameter to be estimated, to test the preference specifications. As mentioned validity of the model. In essence, Hall (1978) earlier, a popular preference specifica- was the first test, in a specific context, of this tion is the power utility function, given by orthogonality condition. 1 U(c) (C −γ 1)/(1 ), which has been An equation such as (12) can be log­ = − − γ used in the consumption literature since the linearized to obtain (see Hansen and papers by Hansen and Kenneth J. Singleton Singleton 1983): (1982 and 1983). Its main advantage is ana- lytic convenience, as it yields first order con- (13) ln Ct 1 t 1 Δ + = α + ditions that are log-linear in consumption. 1 k k However, such a specification also imposes ​ ln (1 r​ t 1​ ) t 1​ , + _ + + + ε​ + strong restrictions on preferences. The elas- γ ticity of intertemporal substitution of con- where t 1 is a time-varying term that α + sumption is, in this context, constant and depends on the preference parameters γ equal to 1/ . This implies that the degree of and as well as on the conditional second γ β intertemporal substitutability of consump- moment of the argument of the expected tion is independent of the level of consump- utility operator in equation (12). tion, even at very low levels of consumption. Estimating equation (12) seems prefer- Moreover, the same parameter governs both able because no assumption has to be made the elasticity of intertemporal substitution about the conditional variance term but will 710 Journal of Economic Literature, Vol. XLVIII (September 2010) produce inconsistent estimates whenever dominates depends on preference param- there is measurement error in consumption. eters and is, therefore, an empirical issue, Equation (13), instead, can be consistently that depends on the size of the elasticity of estimated if there is serially uncorrelated intertemporal substitution. measurement error as long as one can find An influential paper by Hall (1988) instruments that are orthogonal to both the claimed that this parameter is close to zero. error term and the time varying intercept. This finding has been challenged on various Attanasio and Hamish Low (2004) discuss grounds. A low response of consumption conditions under which equation (13), esti- growth to the real interest rate could obtain mated under the assumption of a constant if some consumers are liquidity constrained t 1, yields consistent estimates for the or if the error term correlates with that part α + ­curvature parameter, . Notice that the other of the real interest rate that is explained by γ preference parameter, the discount factor, is the instruments. Attanasio and Weber (1993, not identified in this framework, as it gets 1995) point out that aggregation bias could buried into the constant.9 be responsible for such a low estimate: the Of particular importance for policy analy- aggregate consumption growth rate is com- sis is 1/ , or elasticity of intertemporal substi- puted by taking logs of the mean of individual γ tution, that tells us how the marginal rate of consumption, whereas equation (13) implies substitution between today and tomorrow’s that means of the logs should be taken consumption reacts to changes in the inter- instead. Attanasio and Weber (1993) provide est rate, keeping lifetime utility constant. evidence that the difference between these The increase in the interest rate represents two terms is highly serially correlated, thus a decrease in the price of future consump- invalidating lagged consumption growth as an tion relative to current consumption and this instrument. When they correct for this, they induces a “substitution effect” of a decrease find higher estimates of the elasticity of inter- in current consumption and a commensu- temporal substitution. Attanasio and Weber rate increase in current saving. This would use cohort data (that is: data from repeated be counteracted by an “income effect” since, cross sections that is consistently aggregated with a higher interest rate, a given target over individuals born in the same years): level of future consumption is achieved with when they focus on cohorts of individuals less saving. As noted by Summers (1981), who are least likely to be liquidity constrained wealth effects, concerning the amount that and control for changes in taste shifters, they expected future incomes are discounted, estimate a much higher elasticity (around 0.8) reinforce substitution effects and also lead using U.K. (1993) and also U.S. cohort data to a decrease in consumption or increase in (1995). Recently, John Karl Scholz, Ananth saving when the interest rate goes up. These Seshadri, and Surachai Khitartrakun (2006) wealth effects tend to be stronger when the address the issue of how well the life cycle time period that the individual cares about model predicts wealth holdings, and take as is longer. Ultimately, which of these forces benchmark case 1/ 0.33, but they also γ = show that the model fits best when they take 1/ 0.67. In a recent, very ingenious paper, 9 Equations (12) and its log-linearized version (13) refer γ = to an individual asset. If the consumer has access to several Gary V. Engelhardt and Anil Kumar (2007) assets for which she is not at a corner, one can consider an use differences in employer’s matching rates Euler equation for each of these assets. These equations in 401(k)s and its effect on participation to have been used extensively to study the implications of the model we are considering for asset pricing since Robert E. identify the elasticity of intertemporal substi- Lucas (1978) and Douglas T. Breeden (1979). tution and obtain a point estimate of 0.74. Attanasio and Weber: Consumption and Saving 711

In much of the macro literature, the 3.3 Liquidity Constraints as an Explanation iso-elastic specification has played a of Excess Sensitivity ­predominant role. Little attention has been paid to the possibility that the elasticity of The Euler equations (12) and (13) have intertemporal substitution may differ across been estimated mostly on aggregate data. consumers, particularly as a function of their In several cases, some of the model impli- consumption. A simple way to capture the cations have been rejected—generally notion that poor consumers may be less able speaking, the error term has been found to to smooth consumption across periods and correlate with information available at time states of nature is to assume that the utility t (rejection of the overidentifying restric- function does not depend on total (nondura- tions) and, in particular, with that part of ble) consumption, rather on the difference income growth that could be explained by between consumption and needs. Thus we such information (excess sensitivity). A good could have retained the analytical attrac- example of this type of results are those in tion of power utility, but have (C C*) as the influential Campbell and Mankiw (1990b − its argument, where C* is an absolute mini- and 1991) papers, which report results mum that the consumer must reach in each from a regression like (13) where changes and every period. This functional form is in aggregate consumption were related to known as Stone–Geary utility in demand changes in (expected—as instrumented) analysis (see Deaton and John Muellbauer disposable income. The significance of the 1980, chapter 3, for example), and is the expected income coefficient is interpreted simplest way to introduce nonhomothetic- in that paper as a fundamental violation of ity in a demand system.10 Attanasio and the basic model, caused either by “rule of Browning (1995) take a different route and thumb” consumers, consuming a fixed pro- extend the isoelastic specification by model- portion of their disposable income, or by ing marginal utility as a quadratic function binding liquidity constraints. In fact, a rea- in the logarithm of consumption. Blundell, son why excess sensitivity or violations of the Browning, and Costas Meghir (1991), overidentifying restrictions may be detected Atkeson and Masao Ogaki (1996), and Fatih is because some consumers are not able to Guvenen (2006) are among the few other borrow and lend at the same interest rate. examples of papers that explicitly allow for Binding liquidity constraints may cause wealth-dependent elasticity of intertempo- excess sensitivity if constrained individuals ral substitution (see also Thomas F. Crossley experience temporary income changes: they and Low 2005). will change consumption by more than the However, a recent paper by Battistin, intertemporal optimization problem implies. Blundell, and Lewbel (2009) suggests that However, excess sensitivity may also have nondurable consumption is log-normally dis- other explanations, as we shall see later. tributed, and this is consistent with the stan- Liquidity constraints can take several dard isoelastic utility specification. forms—in the next section we shall consider market structures in which such constraints are the optimal response to information asymmetries or enforceability problems. However, much of the literature imposes 10 One could interpret “external habits” (Andrew B. such constraints exogenously. If, in addition Abel 1990; Campbell and John H. Cochrane 1999) as a special way to parameterize C * (by making it a fraction of to the nonbankruptcy constraint considered past consumption). in the previous section, one imposes some 712 Journal of Economic Literature, Vol. XLVIII (September 2010) exogenous and more stringent limits on the periods holds as if the liquidity constraint amount people can borrow, it is possible that is not operative. The liquidity constraint consumers will be constrained in a given has an effect on the level of consumption period and the Euler equation (12) will not even when it is not binding. In addition to hold. In this case, assuming a variable rate of the extreme case of an exogenously given interest Rt one would have: borrowing limit, one can consider alterna- tive borrowing restrictions. For instance, (14) Et[ (1 R t 1)u (ct 1)/u (ct)] 1. it is possible to consider the case of a dif- β + + ′ + ′ < ference between borrowing and lending The consumer would like to increase cur- interest rates, or more generally, the case in rent consumption and, therefore, her cur- which the interest rate varies with the posi- rent marginal utility is higher than in the tion of the consumer in a given asset, typi- case in which the borrowing restriction is not cally increasing with higher levels of debts. binding. The presence of a binding liquidity These cases have been studied, for instance, constraint means that the consumer is at a by Christopher A. Pissarides (1978) and F. kink of the intertemporal budget constraint, Thomas Juster and Robert P. Shay (1964). so that the tangency requirement between A direct way to detect binding constraints the ratio of marginal utilities and intertem- is to ask consumers whether they applied poral prices holds as a slack condition. for and were denied credit. Jappelli, (1990) The presence of a binding liquidity con- reports that 12.5 percent of the 1982 wave straint represents an important issue for the of the SCF respondents answered they were empirical application of the Euler equa- denied credit, and models the probability tion. Of course, the borrowing restriction of credit denial as a function of observable will not be binding in every period and, characteristics. The problem with this type when not ­binding, the Euler equation will of question is that consumers may have been hold. However, even in periods in which denied credit for good reasons (likely viola- the liquidity constraint does not bind and tion of the no-bankruptcy condition), or may the Euler equation holds, the level of con- have decided not to apply for credit on the sumption will be affected as the consumer assumption that this would be refused to takes into account the possibility that the them (a discouraged borrower effect). constraint will bind in future periods. Less direct tests for liquidity constraints As pointed out, for instance, by Hayashi that meet these criticisms are based on (1987), the presence of a borrowing restric- the idea that the Euler equation should be tion is equivalent to a shortening of the violated for groups of consumers who are time horizon—a consumer who expects to likely to be constrained, such as the young face a binding liquidity constraint n peri- and those whose liquid assets are particu- ods ahead will plan to have zero wealth in larly low. This strategy was implemented that period, therefore behaving as if the by Zeldes (1989) using the ratio of liquid planning horizon was n periods.11 Notice, assets to income at time t as an indica- however, that the relationship between con- tor of potential constraints. Zeldes reports sumption at n 1 and n 2 is not affected evidence for liquidity constraints among − − and the Euler equation between those two households with very low liquid assets—for this group, consumption growth would rise by 4 percent if the constraint were relaxed. 11 Deaton (1991), simulating a stationary economy with impatient consumers and precautionary saving, shows that However, any sample split based on choice liquidity constraints are rarely binding. variables may induce endogenous selection, Attanasio and Weber: Consumption and Saving 713

­particularly if the error term reflects prefer- Despite all these different approaches, the ence heterogeneity. most widely cited piece of evidence for the For this reason, other papers have fol- operation of liquidity constraints is “excess lowed a different route that works when- sensitivity.” But excess sensitivity of con- ever the amount borrowed depends on sumption to income (both at low and high other variables, such as earnings (see Rob frequency) may be due to incorrect prefer- Alessie, Bertrand Melenberg, and Weber ence specification, as we argue in the next 1988 and Weber 1993) or collateral (such as section. in the case of durables, Agar Brugiavini and Weber 1994, Alessie, Michael P. Devereux, 3.4 Explaining Income Tracking and the and Weber 1997, and Eun Young Chah, Retirement Consumption Drop Valerie A. Ramey, and Ross M. Starr 1995). In this case, the presence of a binding bor- An influential paper by Carroll and rowing restriction distorts not only the Summers (1991) uses micro data to docu- ­intertemporal margin but also the allocation ment “excess sensitivity” of consumption to of resources between different commodi- income. The authors notice not only that the ties (or leisure and consumption) within a life cycle profiles of income and consumption period. Alessie, Devereux, and Weber note track each other but that the shape of the that identification of liquidity constraints is two profiles covary across different groups greatly enhanced if the relationship between in the population. For instance, households the borrowing limit and the choice variable headed by an individual with low education is exogenously changed within the sample have a relatively flat profile for both income period (this is true in their analysis of cars and consumption, while households headed and nondurable expenditure, because the by better educated individuals present more hire-purchase terms were heavily regulated of a hump shape. This evidence has been by the U.K. government over the first part used to argue that consumers are impatient of the sample period, completely unregu- but prudent to the point of holding liquid lated later). They do find evidence of bind- assets to buffer shocks—this has come to be ing liquidity constraints in some of the years known as the buffer-stock model of savings. prior to financial liberalization but only for The different results mentioned above young consumers. Finally, a test for liquidity are reminiscent of the early debate between constraints that compares the first order con- Lester C. Thurow (1969) and James J. ditions across periods to the first order con- Heckman (1974). The former pointed to ditions across goods is proposed by Meghir the covariance over the life cycle between and Weber (1996)—their results suggest income and consumption as a rejection of liquidity constraints may be binding only for the life cycle model, while the latter replied young consumers.12 that a version of the life cycle model where consumption and leisure were not separable 12 A problem with all Euler-equations-based tests, as well as with the direct question, is that, as Hayashi (1987) explains, the presence of an operative, albeit not binding to changes in the slope of such an intertemporal budget liquidity constraint is equivalent to a shortening of the constraint: the interest rate. This approach has been fol- planning horizon. This may be the relevant information lowed by Juster and Shay (1964) and Attanasio, Pinelopi that is needed for policy purposes. Evidence on this can be Koujianou Goldberg, and Ekaterini Kyriazidou (2008). obtained by noting that consumers that are liquidity con- Interest rate elasticities of credit demand have been esti- straints will not be sensitive to changes in the level of the mated by David B. Gross and Souleles (2002) using U.S. interest rate. As they will be at a kink of an intertemporal credit card data and by Alessie, Stefan Hochguertel, and budget constraint, the demand for loans will be inelastic Weber (2005) using Italian installment credit data. 714 Journal of Economic Literature, Vol. XLVIII (September 2010) could well explain such a covariance. The peak in household size and can generate con- micro papers cited above show that con- sumption–income tracking for four differ- sistent with Heckman’s (1974) argument, ent education groups when labor income is excess sensitivity can be reconciled with the uncertain as shown in Attanasio et al. (1999). intertemporal optimization model if more More general preference structures that general, and sensible, utility functions are allow the elasticity of intertemporal substitu- used. In particular, if one assumes that lei- tion to depend also on current consumption sure affects utility in a nonadditive way, con- have been considered in the empirical litera- sumption changes respond to predictable ture (Attanasio and Browning 1995; Blundell, labor income changes, whether or not leisure Browning, and Meghir 1994; Attanasio and is a freely chosen variable. Weber 1995; Meghir and Weber 1996). As Micro data equations typically show the in the standard case, the parameters of these need to take account of the effects of some specifications can be estimated using the time-varying characteristics on prefer- Euler equations and other first order condi- ences—demographics and leisure. A way tions of the optimization problem faced by to introduce this dependence is to specify the consumer. period t utility as: The results obtained in the papers that Z​​ 1 use the Euler equation to estimate prefer- (​eδ​​ t​ C ) −γ (15) u t ​, ence parameters and test the model could be t = _1 − γ summarized by saying that a flexible version where Z contains hours of work and other of the life cycle model is not rejected by indi- taste shifters (Attanasio and Weber 1993, vidual level data, especially if one focuses on 1995), some of which might be unobserv- households headed by prime aged individu- able.13 If one takes the model to micro data, als, that is, excluding very young households one has to allow for the effect that demo- and households on the verge of or passed the graphic variables have on utility. The fact that retirement age. Typically, there is no excess “when you have a wife and a baby a one penny sensitivity of consumption growth to income bun costs three pence” (Gorman) has to be growth once changes in leisure and demo- taken into account if one estimates the model graphics are taken into account. on micro data. Demographics might explain These results show that it is possible to consumption changes as well as the shape find a specification of preferences that is of the consumption–age profile, as argued not inconsistent with the available micro by Browning and Mette Ejrnæs (2002). The data. However, leisure and demograph- increase in household size early in life, and ics variables could capture the essence of decrease past age fifty, can explain why con- the predictability of income and make the sumption age profiles are hump-shaped in estimates of the “excess sensitivity” param- apparent contradiction of the consumption eter imprecise. Such variables, according to smoothing implications of the life cycle the- this interpretation, therefore should not be ory. The interaction between demographics interpreted as “taste shifters.” There are two and prudence explains instead why the peak possible answers to this objection. First, a in consumption occurs later in life than the “horse race” between expected income and these other variables seems to indicate that the introduction of the latter does not just 13 Leisure has also been introduced in the utility inflate the standard error but also reduces function in some papers that use aggregate data, such as Mankiw, Julio J. Rotemberg, and Summers (1985) and the size of the income coefficient. Second, Charles R. Bean (1986). once one has estimated the life cycle model Attanasio and Weber: Consumption and Saving 715 augmented with these additional variables, The evidence of these “natural experi- one should ask whether the implied prefer- ment” papers suggests that consumption ences are sensible and predict features of the reacts to predicted changes in disposable data that were not used to estimate them. income only to the extent that these changes We will come back to this issue below. are relatively small, as noted by Browning Finally, aggregation issues have been and Crossley (2009), because small optimi- proven to be important. As pointed out in zation errors might have trivial utility costs Attanasio and Weber (1993), the difference (Cochrane 1989). between the consistently aggregated equa- A number of recent papers report evidence tion (based on the means of the logarithm of in favor of a liquidity constraints interpreta- consumption) and what is available in macro tion. Stephens (2008) shows that consump- data (the logarithm of the mean) is a highly tion reacts to the repayment of vehicle loans, persistent process that correlates with lagged and this is particularly true for young indi- information. Attanasio and Weber (1993) viduals, who are more likely in principle to also show that results obtained with improp- be liquidity constrained. Sumit Agarwal, erly aggregated micro data are consistent Chunlin Liu, and Souleles (2007) investi- with results obtained with aggregate data gate credit cardholders’ response to the 2001 and indicate rejections of the model that tax rebates and find that most people first instead disappear with properly aggregated increased repayments but then the young data and rich enough preference structures. and those who were initially close to their In models where utility depends on the credit card limit started spending more (and consumption of several goods and leisure, building up debt faster). The eventual rise one can explicitly allow for home production in spending could then be attributed to the of goods and services (Gary S. Becker 1965, operation of liquidity constraints. Similarly, 1981; Gilbert R. Ghez and Becker 1975). Hsieh, Shimizutani, and Hori (2010) find This has been recently emphasized in con- that Japanese consumers’ response to a nection with changes in spending behavior spending coupon program tailored to fami- around retirement (Mark Aguiar and Erik lies with children and the elderly was highest Hurst 2005). The availability of time-use among those with low wealth. data allows testing for the implications of Another piece of evidence that apparently the model in terms of changes of the com- contradicts the life cycle model is the retire- position of consumption over the life cycle ment consumption puzzle. The simple life (Aguiar and Hurst 2007, 2009). cycle model of Modigliani and Brumberg A number of recent papers have estimated (1954) predicts that individuals save during the effects on changes in consumption of their working lives to keep their consumption well-defined predictable tax changes (such level constant once they retire. Hamermesh as tax rebates, social security withholding (1984) was the first paper to argue that con- tax), often finding these effects to be differ- sumers apparently do not save enough to ent from zero (Parker 1999; Souleles 1999; achieve this aim. If households enter retire- Matthew D. Shapiro and Joel Slemrod 2003; ment with inadequate savings, they must cut David S. Johnson, Parker, and Souleles their consumption level, contrary to the life 2006). This violation of the model predic- cycle model predictions. tions is surprising because consumption The recent literature has focused on esti- does not appear to react to other anticipated mating how consumption levels change income changes (Browning and Collado around retirement. The existence of a 2001; Hsieh 2003). consumption fall around retirement is 716 Journal of Economic Literature, Vol. XLVIII (September 2010)

­documented for the United Kingdom (Banks, reduce their consumption by at least 35 per- Blundell, and Tanner 1998), for the United centage points.” The evidence they provide States (Bernheim, Skinner, and Weinberg is consistent with the notion that consumers 2001), and for Italy (Battistin et al. 2009) do indeed enter retirement with inadequate and is known as the retirement consumption savings. A number of papers have further puzzle (or retirement savings puzzle). investigated the issue on U.S. data—Steven Banks, Blundell, and Tanner use British J. Haider and Stephens (2007), who estimate cohort data and show that the standard Euler a smaller consumption drop for those who equation, in which consumption growth is a retire at the expected time; Jonathan Fisher function of intertemporal prices and changes et al. (2005), who use CEX data, deflate in demographics, overpredicts the level of expenditure by the squared root of household consumption by as much as 1.5 percent on size and estimate a smaller drop (around 2.5 an annual basis for ages between 60 and 67. percent) for total expenditure than for food The cumulated consumption shortfall over consumption (around 5.7 percent). this age band, where most people retire, is Recent papers by Aguiar and Hurst around 10 percent. They argue that only (2005 and 2007) and Michael D. Hurd and a fraction of this drop can be attributed to Susann Rohwedder (2006) stress that the the increased leisure time that accompa- drop in expenditure at retirement does not nies retirement. Later work by Sarah Smith necessarily imply an increase in the mar- (2006) uses information on food for U.K. ginal utility of consumption. For instance, households who retired over the sample worker-related expenditure (transport to period and stresses the importance of dis- and from work, canteen meals, and business tinguishing between voluntary and involun- clothing) is no longer needed—whether tary retirement—a significant drop for food they account for a large enough part of pre- consumption is observed only for those who retirement consumption is an open issue. retire early because of poor health or job loss. Also, home production of services (laundry, Indeed, David M. Blau (2008) stresses that gardening, housecleaning, cooking) may consumption drops at retirement can be rec- become advantageous, and the extra leisure onciled with life time optimization if there time may allow consumers to shop more is uncertainty over layoffs, job offers, health, efficiently. This last channel has recently and mortality and retirement is a discrete been stressed by Aguiar and Hurst (2005 event that is freely chosen by the household. and 2007) in their careful analysis of food However, in Blau’s model, the causal effect consumption around retirement, while the of retirement on consumption is zero. increase in home production of services by Bernheim, Skinner, and Weinberg use recent retirees has been documented by PSID data to estimate Euler equations for Hurd and Rohwedder (2006), who exploit food consumption. The retirement status time-use data. The literature has investi- is instrumented by taking age-specific pre- gated as further reasons for this drop unex- dicted probabilities conditional on demo- pectedly low pensions or liquidity problems graphics. The sample is split in groups: low as well as time-inconsistent behavior wealth-to-income households drop their (George-Marios Angeletos et al. 2001). consumption most. Bernheim, Skinner, and Another recent paper by Emma Aguila, Weinberg estimate a median drop of 14 per- Attanasio, and Meghir (2010), which looks cent, but higher drops for low wealth ratio, at changes in consumption around retire- low income replacement households. They ment (using the longitudinal dimension of conclude that “31 percent of the sample the CEX in the United States), finds that Attanasio and Weber: Consumption and Saving 717 the decline in food expenditure is compen- 3.5 Evidence from the Levels of sated by increases in nonfood items, so that Consumption the total is roughly constant. Battistin et al. (2009) use Italian data and Although consumption (growth) appears instrument retirement with public pension on the left hand side of equation (13), that eligibility. To be more precise, they take a is not a consumption function but an equi- regression discontinuity approach and make librium condition. It cannot explain/predict the identifying assumption that spend- consumption levels, even conditional on cur- ing behavior would be smooth around the rent consumption: consumption is crucially k threshold for pension eligibility if individu- determined by the residual term ​ ​ t 1​ ​ and ε + als did not retire. They estimate at 9.8 per- there is nothing in equation (13) that tells cent the part of the nondurable consumption us what determines such a term or how it drop that is associated with retirement changes with news about income, interest induced by eligibility (food expenditure rates, or any other relevant variable, includ- falls instead by 14 percent). They show that ing future ones. This inability to predict how this fall is not driven by liquidity problems consumption moves in response to changes for the less well off in the population and in the economic environment is the price can be accounted for by drops in expenses one pays if one stays within the remit of the that are work related or leisure substitutes. Euler equation. What is bought in terms of However, they also show that retirement robustness is paid in terms of the nonavail- induces a significant drop in the number of ability of a consumption function. grown children living with their parents and As stressed above, the Euler equation this can account for most of the retirement imposes some restrictions on the dynam- consumption drop.14 ics of consumption but, on its own, does As Hurst (2008) recently put it, we should not determine the level of consumption. no longer talk about the retirement consump- Neglecting numerical complications, a solu- tion puzzle, rather about “the retirement of tion for consumption can be obtained con- a consumption puzzle.” Once preferences sidering jointly the Euler equation and the are correctly modeled, home production is sequence of budget constraints faced by the taken into account, and attention is focused consumer as well as her initial wealth and on those who retire at the expected age, then a terminal condition. As noted by Sargent the drop in food spending and total spending (1978), Flavin (1981), and later by Campbell around retirement does not imply a viola- (1987), the Euler equation and the inter- tion of the model prediction that consumers temporal budget constraint imply a number smooth marginal utility over time. of cross-equation restrictions for the joint time series processes of consumption and income. When one is able to obtain a closed form solution for consumption, as is the case 14 A few recent papers study how different expendi- with quadratic utility, these restrictions can ture items vary over the life cycle and in relation to lei- be easily expressed in terms of a linear time sure. Raffaele Miniaci, Chiara Monfardini, and Weber series model and tested. (2002, 2010) focus on changes around retirement age, while Aguiar and Hurst (2009) look at the evolution of To be more specific, given an intertem- work-related expenses over the whole life cycle. This last poral budget constraint that assumes a fixed paper claims that, once allowance is made for the effect of interest rate and a relatively general process changes in family size and composition, all the decline in consumption can indeed be attributed to the fall in work- for labor earnings, with quadratic utility, the related expenses. level of consumption is given by equation (8). 718 Journal of Economic Literature, Vol. XLVIII (September 2010)

Given an assumption on the time series pro- If we follow Campbell (1987) and define cess for income, this equation will imply saving as: cross equation restrictions on the bivariate rA time series model for consumption and earn- (17) s t ​ y C , ings. Some of these restrictions are implied t = _1 r + t − t + by the Euler equation, while others are not. In particular, the restrictions on the contem- we can rewrite (16) as: poraneous correlation between income and consumption are not—as we stressed above, ∞ k the Euler equation is silent about how news (18) st ​ ​ (​1 r)− E( yt k It). + = − ​k∑1 + Δ | about income are translated into news about = consumption. To consider a specific example, let us Equation (18) shows that individuals assume a simple AR representation for should “save for rainy days” (future income labor income: A(L)y a , where A(L) falls) and holds (by the law of iterated pro- t = + ζ t denotes a polynomial in the lag operator. In jections) even if we take expectations condi- this case, equation (8) implies (Flavin 1981) tional on a subset of the information used by that economic agents, such as past income and saving. While Flavin (1981) and Campbell (1987) 1 r (16) A ​ Ct 1 ​ t 1. test the cross equation restriction that arises _1 r Δ + = _1 r ζ + + + in the quadratic utility case in the VAR rep- a​ b resentation of income and consumption, This relation provides a link between the Campbell and Deaton (1989) and West variance of the income shock, t 1, and the (1988) use the same structure to propose a ζ + variance in the error term of the Euler equa- test that links the innovation to permanent tion, t 1. If there is enough persistence in income to consumption. These authors ε + income growth (positive serial correlation ­present evidence that aggregate consump- in the first differenced process), then (16) tion is “excessively smooth” in that it does not implies that Ct 1 t 1 with 1, and react enough to news about income. In par- Δ + = ψ ζ + ψ > consumption growth should vary more than ticular, because the model for earnings seems income growth over time. to be characterized by a unit root and some Notice that the conditioning set for the additional persistence in the first changes, expectations about future earnings in equa- the model would imply that consump- tion (8) is left unspecified. An advantage tion changes should reflect the permanent of the approach pursued here is that one income innovation more than one-to-one. can then condition equation (8) (and the Not only is the income shock permanent corresponding equation for earnings) on a but it also predicts future, smaller shocks smaller information set and obtain a similar of the same sign. This implies that over the expression. This implies that the approach business cycle consumption should be more is robust to the presence of an informa- volatile than income. But, in actual aggregate tional advantage of the consumer over the data, consumption is smoother than income. econometrician. The reason is that, by look- By taking the intertemporal budget con- ing at consumption, we are implicitly using straint as a given, Campbell and Deaton the information the consumer has at her (1989) make a connection between excess disposal. sensitivity and excess smoothness. Hansen, Attanasio and Weber: Consumption and Saving 719

Roberds, and Sargent (1991) propose a test 3.6 Simulation Results of the intertemporal budget constraint (given the martingale behavior of consumption A small literature has developed that implied by the Euler equation) that is shown numerically solves and simulates the to be similar to the Campbell and Deaton intertemporal consumer problem under (1989) and West (1988) tests. Hansen, uncertainty, starting with an influential con- Roberds, and Sargent (1991) clarify what tribution by Deaton (1991), who studied a the restrictions implied by the intertemporal model with power utility and infinite life. budget constraint are and what restrictions Deaton considers the existence of liquidity can be tested with time series data. They also constraints and shows that impatient con- consider a number of generalizations, such sumers hold limited assets to insure against as habits and other forms of nonseparabili- low income draws. Carroll (1992) instead ties. When discussing endogenous liquidity covers the case of finite lives and shows that, constraints below, we argue that the test of if consumers are sufficiently impatient and the intertemporal budget constraint that their labor income is subject to both per- Hansen, Roberds, and Sargent propose can manent and temporary shocks, they set con- be interpreted as a test of market structure. sumption close to income at least until they In situations where preferences are not are in their forties. The model with impatient restricted to functional forms that admit a consumers under labor income uncertainty closed form solution and one considers more has been labeled “the buffer stock model” realistic environments, one has to rely on because saving is kept to the lowest level numerical methods to get the consumption compatible with the need to buffer negative function as shown in the seminal paper by income shocks. Carroll’s buffer stock model Deaton (1991). We discuss the literature on can provide a rationale for the income track- numerical solutions and simulations of the ing of consumption that was highlighted by life cycle model in the next subsection. Carroll and Summers (1991). A less ambitious but potentially profit- Later work by Attanasio et al. (1999)— able approach that does not require numeri- refined by Pierre-Olivier Gourinchas and cal methods or incredibly rich data sets is Parker (2002)—clarifies the role played by the estimation of reduced form equations, age-related changes in demographics and whose specification is informed by the life the hump-shaped age profile of labor income cycle model. These are particularly useful in in generating income tracking for relatively situations in which one analyzes large (and young consumers (as mentioned above, possibly exogenous) changes to some of the micro data show that financial asset accumu- likely determinants of consumption or sav- lation starts in mid-life). R. Glenn Hubbard, ing. Such studies can address substantive Skinner, and Zeldes (1994, 1995) show issues and even test some aspects of the life instead how precautionary motives interact cycle model. Examples of studies of this kind with the insurance properties of social secu- include the reaction of consumption (and rity in the United States. saving) to changes in pension entitlements Attanasio et al. (1999) is the only paper (Attanasio and Brugiavini 2003; Attanasio that thoroughly investigates the interaction and Rohwedder 2003; Miniaci and Weber between demographics and precautionary 1999), to swings in the value of impor- savings. It does it for four different educa- tant wealth components (such as housing, tion groups—in the analysis, education mat- Attanasio and Weber 1994), and to changes ters because income and demographics age in specific taxes as discussed above. profiles are education specific and because 720 Journal of Economic Literature, Vol. XLVIII (September 2010)

Baseline No demographics 1.4 1.4

1.2 1.2 c2 c1 1 1

0.8 0.8

0.6 0.6 20 30 40 50 60 70 20 30 40 50 60 70 Age Age

No uncertainty Comparison 1.4 1.4

1.2 1.2

c3 1 1

0.8 0.8

0.6 0.6 20 30 40 50 60 70 20 30 40 50 60 70 Age Age

Figure 4. Simulated Mean Consumption Age Profiles for High-School Graduates

education can affect patience. Note that case where there is income uncertainty and it imposes that life ends with certainty at demographics evolve with age (“baseline”). age 70—it does not let the discount factor Counterfactual simulations shed light on the change with survival probabilities. Survival role of demographics and uncertainty: in the probabilities can play an important role in NE panel, there is income uncertainty but determining the shape of the consumption demographics do not change with age; in the profile at older ages. SW panel, there is no income uncertainty To illustrate the interplay of demographics and demographics evolve with age. Finally, and uncertainty in shaping the consumption the SE panel presents the previous three age profile, let us consider one of the fig- curves together. ures in Attanasio et al. (1999) that presents The key conclusion drawn from this and the average of a large number of simulated similar pictures for other education groups consumption profiles for a specific educa- is that precautionary savings alone would tion group in the United States (high school imply a peak in consumption quite late in graduates). In figure 4, NW panel, we plot life, while demographic needs would make average consumption age profile simula- consumption peak relatively early. It is the tions corresponding to the solution for the interplay of these two opposing forces that Attanasio and Weber: Consumption and Saving 721

2.5

2

1.5

1 Assets

0.5

0

–0.5 21 24 27 30 33 36 39 42 45 48 51 54 57 60 63 66 69 72 75 78 Age

Baseline EIS 1/2 EIS 1/4 = =

Figure 5. Average Change in Asset Holdings by Age when r Changes

generates a peak in the early to mid-forties When 1, instead, the substitution effect γ < as observed in the data. prevails and current consumption decreases. Simulation results are also useful to study While these effects are quite clear in a simple how consumption reacts to changes in the model, their quantification in a multiperiod interest rate, an important topic for both framework in which preferences are affected monetary and fiscal policies. It is well known by a variety of factors which are possibly that changes in the interest rate have both changing over time is not simple. The effect substitution and income effects on con- of changes in the interest rate will depend sumption, going in opposite directions for a not only on standard preferences param- net saver. Summers (1981) stresses the role eters, such as the elasticity of intertemporal played by the wealth effect that is induced by substitution and the discount rate, but also applying different discount factors to future on their interaction with the evolution of flows of labor income. Which of these effects needs, on the shape of the income profile, on prevails depends on the elasticity of inter- the institutional arrangements for pensions, temporal substitution as well as on other fac- and so on and so forth. tors affecting preferences.15 To gain a better understanding of how With the isoelastic preferences discussed these various factors interact and determine above, in a two period model, if 1, the the final effect, there is little alternative to γ > income effect prevails on the substitution using numerical methods that solve the effects so that an increase in the interest model and simulate life cycle trajectories for rate causes current consumption to increase. a large number of hypothetical consumers to obtain average life cycle profiles for differ- ent sets of parameters and different interest 15 Summers (1981) claims that both for the wealth effect rates. These types of exercises are certainly and for general equilibrium effects the interest rate elastic- ity of saving is bound to be high. Owen J. Evans (1983) not novel. Summers (1981) and Evans provides several counterexamples to this claim. (1983), for instance, present simulation 722 Journal of Economic Literature, Vol. XLVIII (September 2010)

2.5

2

1.5

Assets 1

0.5

0 21 24 27 30 33 36 39 42 45 48 51 54 57 60 63 66 69 72 75 78 –0.5 Age

Baseline Family

Figure 6. Average Change in Assets by Age when r Changes, With and Without Family

results to characterize the interest rate elas- in the life cycle asset profile induced by a ticity of savings. Over the last fifteen years, change in the interest rate from 2 percent however, the literature on the solution of a to 2.5 percent under different elasticities of life cycle model under uncertainty has made intertemporal substitution. great progress so that we are now able to First of all, notice how, in all cases, the solve and simulate realistic and much more effect of the interest rate on savings depends sophisticated models under uncertainty. on age. One of the implications for the aggre- These models normally use parameter val- gate effects of certain policy changes will ues from the empirical studies that have esti- depend on the demographic composition mated preferences from micro data, possibly of the population. Second, notice that the using Euler equations that are robust to the increase induced by interest rate changes is exact specification of the stochastic environ- considerably larger in the baseline case when ment faced by consumers. the elasticity of intertemporal substitution is Attanasio and Matthew Wakefield (2010) 1 (and the discount rate is 0.025). When the simulate a life cycle model to understand the elasticity of substitution is low, the effect up importance of the elasticity of intertempo- to age 45 is basically zero. ral substitution to determine the size of the Figure 6 introduces changing needs over reaction of savings to changes in the interest the life cycle (for the baseline case where rate. They first simulate a model of a single the EIS is unity). These are calibrated using consumer with an isoelastic utility function standard adult equivalent schemes and (they take the elasticity of intertemporal actual U.K. data. Utility depends not on substitution (EIS), 1/ 1 as baseline), no total consumption but on consumption per γ = bequest motive, and a stochastic income pro- adult equivalent. Notice how the effect of a cess calibrated on U.K. data. Figure 5, which change in interest rate on saving is reduced, is taken from their paper, plots the changes even with an elasticity of intertemporal Attanasio and Weber: Consumption and Saving 723

­substitution left at the relatively high level What is often considered the standard of one. Other papers, such as Attanasio and version of the life cycle/permanent income Weber (1993) and Attanasio and Browning model, such as the one we used above to (1995), stressed the importance of demo- derive Euler equations, makes some stark graphics to explain observed patterns of assumptions about the nature of intertempo- consumption life cycle profiles and to fit the ral trades available to agents. Typically, state life cycle model to the data. Figure 6 makes contingent trades are ignored (hence ruling the additional point that the evolution of out insurance) and often the consumer con- consumption needs also affects the way con- sidered in the model is only endowed with a sumers respond to changes in intertemporal single asset that pays a known and fixed inter- prices.16 est rate. On the other hand, this consumer As the age of household members and might be allowed to borrow or save with- family composition evolves, the effect that out limits (except for a nonbankruptcy con- a given level of consumption has on utility straint). Obviously, all of these assumptions obviously changes. In a sense, family com- are very extreme and unrealistic. It is there- position variables play a role in the dynamic fore important to consider explicitly several allocation of resources that is analogous to the alternative market structures. In what fol- discount factor and, as they vary dramatically lows, we stress how different markets struc- over time, can have quantitatively important tures might have only limited implications implications for the level and shape of asset for some of the results typically used in the life cycle profiles.17 Moreover, as we men- literature (in particular Euler equations) and tioned above, their evolution interacts with how they have important implications for the preferences to determine the response to level of consumption and for its relationship specific changes in the environment. to current income. We do not discuss the portfolio problems implied by the consideration of several assets 4. Budget Constraints and Markets: simultaneously or the implications that can Theory and Evidence be derived from the theory for asset pric- The implications of any model of inter- ing. Instead, we focus on the implications of temporal consumption behavior depend ­different market structures for the intertem- heavily on the nature of market arrange- poral allocation of consumption.18 In par- ments through which the agents consid- ticular, we consider four different structures. ered in the model interact and on the type The first, which constitutes a useful, albeit of intertemporal trades agents have access unrealistic, benchmark, is the case in which to. This is especially true for the life cycle the consumer is assumed to have access to model. As the focus of the life cycle model is a full set of state-contingent Arrow–Debreu the intertemporal allocation of resources (in securities. The second is the standard case, an uncertain environment), insurance and credit markets are particularly important. 18 From a theoretical point of view, the consideration of several assets, some of which might have state contingent returns, and others for which several restrictions are rel- 16 In both figures 5 and 6, the change in assets is nor- evant, can be easily added to the model. A useful result in malized by dividing through by expected income at age 21. this respect is the fact that, as long as the consumer is not 17 Evans (1983) stresses that differences in discount fac- at a corner for a given asset, one can write down an Euler tors can alter both the shape of asset life cycle profiles and equation for that particular asset, linking consumption at the way in which they respond to changes in the interest two points in time. This is true regardless of the presence rate. This is also discussed by Jonathan Gruber (2006). of imperfections and frictions in other markets. 724 Journal of Economic Literature, Vol. XLVIII (September 2010) considered above, in which the consumer is where p( t ) is the price of consumption at θ endowed with an exogenously given tech- time t at history t. To compute the equilib- θ nology to move resources into and from the rium that would prevail in such a situation, future at a given rate. We then move on to one has to consider the problem (19) for introduce some specific limits to the inter- each consumer in the economy. The specific temporal trades available to consumers, not type of competitive equilibrium that would only in terms of the type of securities avail- prevail will depend on the specifics of indi- able to them but also, more specifically, in vidual preferences, income processes, and, terms of the amount of resources that can be possibly, initial endowments. The computa- moved from the future. This is what is nor- tion of this type of equilibrium is, in prin- mally referred to as “liquidity constraints.” ciple, very complex. However, the literature Finally, we consider situations where, rather provides some important results that allow than being imposed exogenously, specific lim- one to characterize some key features of the its to intertemporal trades arise endogenously intertemporal allocation of consumption in from the presence of specific imperfections. such a situation. In particular, one can exploit the fact 4.1 Complete Markets that, in the absence of externalities and In this benchmark case, it is assumed that other distortions, competitive equilibrium consumers have access to state contingent allocations are Pareto efficient and invoke securities that pay a certain amount of con- the first Welfare theorem to describe them sumption, which depends on the particular as the result of the optimization problem state of the world that is realized at a given faced by a fictitious social planner that max- time. The implicit assumption behind this imizes the weighted average of individual framework is that very complex contracts can utilities. While the theory is silent about be written and supported by a completely the weights used in this problem (that is on symmetric information structure among the particular competitive equilibrium that consumers and then enforced perfectly. is realized), the study of this problem is use- The stochastic environment in which ful in characterizing the intertemporal con- agents live can be summarized by a vector sumption allocations. If we assume that the of state variables . We will denote with social ­planner has a technology to transfer θt t , , … , } the history of the state aggregate resources to and from the future θ = {θ1 θ2 θ t variables up to time t. We also assume that at a rate r, we can then rewrite equation the sets t of all possible histories up to time (19) as: Θ t are endowed with a certain probability measure. We write as ( t ) the probability of t π θ (20) ​ max ​ j history . The consumer receives resources {​A​ ​, ​c ​ ​​}​ ​ 0, j 1, … N​ θ τ τ τ > = yt that depend on the history of the state variables at time t. The consumer problem t t i t can be written as: ​ ​ i​ ​ ​ ​ ​ ​( )U(​C​ t ​ ​( )) ∑i ϕ ∑t β ∑ t π θ θ θ t t ​ (19) max E ​ ​ U(Ct( )) , ∑t β θ S T such that such that S​ T

t t t t i t i t ​ ​ pt​( )(Ct( ) yt( )) 0, , A t 1 (1 r)A t ​ (​​C​ t ​ ​( ) y​ t ​ ​ ( )), ∑t θ θ − θ ≤ ∀θ + ≤ + + ∑​i θ − ​ θ Attanasio and Weber: Consumption and Saving 725 where index i refers to individuals, is Individuals can have different consumption ϕi the Pareto weight given to individual i, and levels if Pareto weights are different but, A t 1 is the asset available to society to move over time, the cross section of consumption + resources over time. The social planner moves to guarantee that (21) holds for each achieves a given intrapersonal and inter- individual. temporal consumption allocation by a set An important possible implication of the of transfers among the agents. Notice that, complete markets, full insurance model is in this formulation, the presence of indi- that it allows the construction of a “rep- vidual savings is not necessary. The social resentative” consumer. That is, an impor- planner could achieve any given allocation tant aggregation theorem holds under implied by a certain amount of individual the hypothesis that markets are complete savings without them and via different sets and idiosyncratic risk is fully diversified. of interpersonal transfers. The problem in Aggregate consumption moves as if it was (20) assumes the possibility of aggregate determined by a representative consumer borrowing and the existence of a fixed rate who acts according to the life cycle model at which resources can be moved over time. subject to an intertemporal budget con- Moreover, it also assumes that individuals straint similar to that in equation (20). have homogeneous preferences and dis- This result holds, as shown, for instance, count factors. These assumptions can be by Robert M. Townsend (1994), even in relaxed. It is also possible to use more gen- the presence of heterogeneous prefer- eral forms of preferences incorporating, for ences (see also Andrew Atkeson and Ogaki instance, leisure. 1996). The preferences of the representa- From the first order conditions of problem tive consumer will aggregate individual (20), one can derive some interesting rela- preferences. tionships. In particular, one set of first order Equation (21) has constituted the basis conditions will be: for much of the empirical tests of perfect insurance. Log linearizing (21) and tak- t t t t (21) i ​U​C​ ​ i ​ ​ (​ ​ t​)​ ( )/ ( ). ing first differences one obtains the simple ϕ β t θ = μ θ π θ proposition that changes in marginal util- Equation (21) states that the marginal util- ity of consumption should be the same in a ity of consumption for individual i, at a given cross section of consumers who share risk state of the world at time t, multiplied by efficiently her Pareto weight, is equal to the aggregate constraint multiplier relevant in that state of the world (divided by the probability of that (22) ln ( ) ln(​U​C​ ​ i ​ ​(​ ​ t​))​ β + Δ t θ particular history). Notice that the right-hand side of equation ln( ( t)/ t( t)) . = Δ μ θ π θ ≡ νt (21) does not depend on the index i. This implies that consumption for each individual With a specific assumption about the util- has to be such that the (discounted) marginal ity function, it is easy to derive from equa- utility multiplied by that person’s Pareto tion (22) an expression that can be brought weight has to be equal to the right-hand side to data. For instance, with CRRA utility, one of equation (21). This implication of per- gets: fect risk-sharing means that idiosyncratic risk is diversified and only aggregate fluc- i tuations determine individual ­consumption. (23) ln(​C ​ ​) ln( ) . γΔ ​ t = − β + νt 726 Journal of Economic Literature, Vol. XLVIII (September 2010)

Notice that the left-hand side is individual of view, the strategy proposed by Townsend consumption growth, while on the right- (1994) is appealing because it allows one to hand side we only have aggregate variables, test efficient risk sharing without specifying that is quantities that do not vary in the cross the entire budget constraint relevant for the section.19 A possible test of perfect risk shar- individual agents. Agents may use a host of ing, therefore, is to add to equation (23) a different instruments to achieve efficient variable related to the change in resources intertemporal allocations, including a variety accruing to household i in period t and test of privately held assets, informal interper- the significance of such a coefficient. sonal transfers, implicit contracts, and so on. The Townsend (1994) test looks at the actual i i i (24) ln(​C​ ​ ​) k y​ ​ ​ ​ ​ ​, allocation of resources regardless of how it Δ t = + νt + φΔ ​ t + εt was achieved. where y could be household income, or Townsend (1994) applies his test to three wages, the term , the multiplier on the Indian villages and finds some important νt aggregate resources constraint, can be cap- rejections of full risk sharing. Cochrane i tured by time dummies and ​ ​ ​ ​ represents a (1991) and Mace (1991), instead, use U.S. εt regression residual. The test of perfect risk data and test the implications of equation sharing, therefore, will be that the coeffi- (23) using different specifications for the cient 0. It is worth noting that equation utility function. Cochrane (1991) shows that φ = (22), and therefore (23), holds without error the growth rates of food consumption do not as perfect insurance assumes the possibility respond to some shocks (such as strikes or of writing contracts that determine the allo- involuntary moves) but are affected by invol- cation of resources under any possible state untary job loss and long illness. Perhaps sur- of the world. The presence of a residual in prisingly, Mace (1991) does not reject the equation (24), therefore, has to be justified hypothesis of full risk sharing. It has been by measurement error in either consump- pointed out, however, that her results could tion or y. In the latter case, however, one be due to measurement error (see Julie A. has to take into account the fact that esti- Nelson 1994). mates of will be affected by attenuation Strong rejections of the perfect insurance φ bias. hypothesis, instead, are reported by both This implication of perfect risk sharing, Hayashi, Joseph G. Altonji, and Laurence first noticed by Townsend (1994) and tested J. Kotlikoff (1996) and Attanasio and Davis for the United States by Cochrane (1991) (1996). Attanasio and Davis (1996), in par- and Barbara J. Mace (1991), is very powerful ticular, show that, while short run changes and the empirical tests that can be derived in relative male wages (across education and from it very appealing.20 From a theoreti- cohort groups) do not seem to be related to cal point of view, it captures the fundamen- changes in relative consumption, when one tal idea of risk sharing—that risk is pooled considers lower frequencies, one finds sig- efficiently among the participants in a risk nificant effects.21 sharing agreement. From an empirical point

19 In this example, we do not consider preference het- erogeneity (for example in discount factors). Townsend 21 Hayashi, Altonji, and Kotlikoff (1996) use food con- (1994) discusses cases with heterogeneity in risk attitudes. sumption data from PSID to test for complete risk-sharing 20 Sumru Altug and Robert A. Miller (1990) estimate across all households and across households that belong to and test a model of household consumption and labor sup- the same family (dynasty): in both cases they reject the null ply choices with complete markets. of complete risk-sharing. Attanasio and Weber: Consumption and Saving 727

An alternative test of perfect insurance the hypothesis of perfect insurance. This can be obtained by looking at the evolu- is true both in developed and developing tion of cross sectional second moments. countries. In developed countries, it seems Considering again the log-linearization of that low frequency, persistent shocks are equation (21), one can easily obtain the not completely insured. However, one can result that the cross sectional variance of often also reject the hypothesis that these the log of ­marginal ­utilities should be con- shocks are completely uninsured and, stant over time, under perfect risk sharing, therefore, fully reflected in consumption. a fact first noted by Deaton and Paxson This is not inconsistent with the evidence (1994). Deaton and Paxson (1994) stress the on “the excess smoothness of consumption” fact that, in many countries, the life cycle we mentioned in section 3.5. On the other profile of consumption inequality seems hand, it seems that transitory shocks are, to to be increasing with age—a fact that is a large extent, insured. Given this evidence, consistent with simple versions of the life therefore, the focus of much of the current cycle model with a single asset but not with research is on models without perfect risk complete markets. Since that contribution, sharing and incomplete markets. other papers have tested this implication 4.2 Exogenously Incomplete Markets (see, for instance, Attanasio and Jappelli 2001 and Attanasio and Miguel Székely Much of the literature on consump- 2004). Further research that tries to relate tion assumes that individuals have a cer- consumption inequality to income inequal- tain number of exogenously given assets ity includes papers by Blundell, Pistaferri, that they use to move resources over time. and Preston (2008), Attanasio, Battistin, What is common to the set of studies we and Ichimura (2007), Krueger and Perri consider here is that the financial market (2006), and Guvenen (2007). structure and, therefore, the type of assets The paper by Blundell, Pistaferri, and individuals have access to is exogenously Preston (2008) is particularly interest- given as in the discussion in section 3. ing because it decomposes innovations to Some of these papers consider explicitly household income into “temporary” and the asset prices that clear these markets. “permanent” components. These authors However, the type of assets considered is consider how changes in the variance of exogenously given. permanent and transitory income com- Many studies have considered a situa- ponents are translated into changes in tion in which consumers borrow and lend the variance of consumption and estimate in an asset whose net supply is zero: in such the fraction of permanent and transitory a situation, individuals with (temporary) income shocks that are effectively insured. positive shocks will lend to individuals with They find that a large fraction of temporary (temporary) negative shocks. Models of this shocks are indeed insured, especially in the type are often referred to as “Bewley” mod- case of “better off” households, while most els, from Bewley (1977), who was among (but not all) ­permanent shocks seem to be the first to study the competitive equi- uninsured. We will come back to a possible librium in a model where individuals try interpretation of these results below. to smooth income fluctuations over time. One can summarize the evidence on the Other versions of the model also consider implications of complete markets saying the presence of aggregate saving, which can that the large majority of empirical work play a role in production, as, for instance, in in this area points to a sound rejection of S. Rao Aiyagari (1994). Finally, while some 728 Journal of Economic Literature, Vol. XLVIII (September 2010) versions of the model allow for both borrow- imperfections. Unlike the economies we ing and saving, others prohibit borrowing. have considered so far, the market structure The equilibrium conditions that are rele- and the assets available to an individual con- vant in the presence of exogenously missing sumer are not given but are determined as markets are effectively those we discussed an equilibrium outcome. in the first part of section 3 and that have 4.3 Endogenously Incomplete Markets been used for the empirical work on the life cycle model. The Euler equation (12) As we mentioned above, there is strong in section 3.2 is the relevant equilibrium evidence that rejects the hypothesis of condition when individuals can borrow complete contingent markets that provide and lend at the interest rate r k in asset k. full insurance against idiosyncratic risk. An If consumers are prevented from borrowing important theoretical and empirical chal- and are at the corner in terms of their asset lenge, therefore, is to construct models position, the relevant condition becomes in which full risk sharing is not achieved the inequality in equation (14). It is worth in equilibrium because of the presence of stressing that, even in the presence of bor- specific imperfections. From a theoretical rowing restrictions, the expression in (14) viewpoint, it is certainly preferable to map can hold as equality if the liquidity con- the nature of imperfections one considers straint is not binding between two given into particular market structures rather than time periods.22 making more or less ad hoc assumptions Notice the difference between the Euler about the nature of markets. From a policy equation implied by the Bewley model and point of view, the fact that the market struc- the first order condition of the social planner ture is an equilibrium outcome allows one problem. First, the first order condition (12) to take into account the possible effects that holds in expectations, while equation (21) given policy interventions have on the nature holds state by state. Second, there is no indi- and extent of private insurance markets. This vidual Euler equation in the full insurance might be fundamental to evaluate the effects case but something similar to it. To see this, of a given policy. one can appeal to the aggregation theorem The literature on endogenously incom- referred to in the last paragraph and derive plete markets has mainly focused on two the Euler equation for the representative types of imperfections—imperfect infor- consumer. In this sense, as is obvious, the mation and imperfect enforceability of model with complete markets is much more contracts. We discuss these two classes of restrictive. models in turn. We have already discussed the evidence 4.3.1 Imperfect Information Models on Euler equations and liquidity constraints in section 3. We now move on to the discus- In imperfect information models, indi- sion of economies where markets are not viduals are assumed to have private informa- complete because of the presence of specific tion either about their income or about the effort they put in producing income (moral hazard). It is therefore necessary when 22 Indeed, if one considers the so called “natural” liquidity constraints that is the present discounted value of ­looking at an insurance market to guarantee the lowest income realization with a positive probability of that, in equilibrium, individuals are induced occurring, under some regularity conditions on the utility to reveal their private information. The con- function, the constraint will never be binding. But even for lower bounds, such as zero, the liquidity constraint might strained efficient allocation of resources can be binding only occasionally. be studied in a way similar to the case of Attanasio and Weber: Consumption and Saving 729 perfect insurance by looking at the problem This is consistent with the fact that, in this solved by a social planner. A problem like world, all aggregate saving is done through (20) has to be supplemented with the incen- the social planner. Like in the full informa- tive compatibility constraints that guarantee tion case we discuss above, as the social the revelation of private information. From planner observes private savings, she can a methodological point of view, the char- use aggregate wealth to maximize aggregate acterization of these contracts can become utility and adjust transfers to replicate any extremely complex as the transfers through allocation achieved without private assets in which the social planner redistributes a situation in which these assets are held by income among private agents can be a func- the ­individual ­consumers. As agents do not tion of the entire history of individual past hold assets, there is no necessity for the stan- income. A big methodological breakthrough dard Euler equation to hold. Equation (25), in this literature came with the Jonathan instead, holds as part of the dynamic incen- P. Thomas and Tim Worrall (1990) and tive compatibility constraint. Atkeson and Lucas (1992) papers in which In this world, if consumers were left to these authors rewrote the problem in terms their own devices, they would save too much of “promised utilities.”23 This technical trick compared to the social optimum correspond- allows a relatively simple characterization of ing to equation (25). This has important pol- the equilibrium. icy implications for optimal capital income A result that is particularly important in taxation.24 this literature, first derived by William P. Not many empirical papers have stud- Rogerson (1985), can be useful to study the ied asymmetric information models of the empirical implications of these models (see type described here. An exception is Ligon Ethan Ligon 1998). In contrast to the per- (1998), one of the first papers that tries to manent income model where the marginal discriminate between the self insurance utility of consumption follows a martingale, (permanent income hypothesis) and the here it is the reciprocal of the marginal util- imperfect information partial insurance ity of consumption that has this property. In models. Ligon fits three different models particular, it can be proven that: by maximum likelihood using per capita consumption data for households living in the three Southern Indian villages stud- 1 1 (25) Et _ ​ _ ​. ied by Townsend (1994). Ligon points out U (Ct 1) = U (Ct) ′ + ′ that the only difference between the per- c​ d manent income hypothesis Euler equa- The intuition behind this result follows from tion and the imperfect information inverse the fact that the problem, in the Atkeson Euler equation (25) lies in the expected and Lucas (1992) approach, is formulated in sign of the b0 coefficient in the equation ​b0​ ​ terms of promised utilities that are obtained Et(Ct 1,h /Ct,h​)​ ​ 1: in the former case, + = as a function of consumption by inverting the this is minus the coefficient of relative risk utility function. From (25), it follows that, given Jensen’s inequality, the standard Euler 24 An interesting result in this literature is the so called equation for consumption will not hold. “immiserization”—because of the trade-off between incentives and insurance faced in each period by the plan- ner, the efficient allocation equilibrium implies “an ever- 23 Other important papers in this literature include increasing fraction of resources to an ever-diminishing Edward J. Green (1987) and Christopher Phelan and fraction of society’s population” (Atkeson and Lucas 1992; Townsend (1991). see also Green 1987 as well as Thomas and Worrall 1990). 730 Journal of Economic Literature, Vol. XLVIII (September 2010)

­aversion, in the latter case it is plus the coef- prefer, ceteris paribus, transfers that are ficient of relative risk aversion. In the case front loaded. Finally, the relative prefer- of full insurance, this coefficient cannot be ence for front loading will be stronger for estimated because there is no variability agents with a low income realization than across households in consumption growth. for agents with a high income realization. The exercise can be carried out for a num- The implication of this will be that incen- ber of different instrument sets and is con- tive compatible transfers cannot deliver less sistent with permanent income behavior in net present value to high income agents. one village and with imperfect information But risk sharing would imply giving more behavior in the other two. Full information net present value to low income agents. cannot be rejected in some cases. Therefore, incentive compatibility works In the standard asymmetric informa- exactly in the opposite direction than insur- tion model, it is often assumed that income ance. It turns out that, in the constrained or effort are not observable and contrac- efficient allocation, all agents will receive table upon. At the same time, however, it the same net present value that they will is assumed that individual assets are fully smooth using the hidden technology. observable. This assumption implies that, This result has been considered particu- when considering the social planner prob- larly important because it constitutes a micro lem that is often used to characterize the foundation for a specific market structure equilibrium in this class of models, one can (a single bond with a fixed interest rate) dispose of individual assets altogether and that has been widely used in the literature assume that all assets are held by the social and that we have been discussing above. It planner. Any equilibrium with private asset would, therefore, seem that imperfect infor- ownership can be replicated by an appropri- mation about income and assets could pro- ate set of transfers. The situation becomes vide a justification for a market structure very different when not only individual where the only type of insurance agents can income but also assets are not publicly get is self-insurance through savings. The observable. This problem has been analyzed Cole and Kocherlakota (2001) result, which in an important recent paper by Harold L. is reminiscent of the results in Franklin Allen Cole and Narayana R. Kocherlakota (2001). (1985), is an important one even though These authors show that, in their model, the some recent papers have claimed that it is constrained efficient allocation coincides not very robust. Árpád Ábrahám and Pavoni with the one that would occur when agents (2004), for example, have shown that, in a are allowed to save with a single asset paying model with pure moral hazard (rather than a fixed interest rate. adverse selection of the type considered in When agents have the possibility of saving Cole and Kocherlakota), one obtains their on their own, they will use this intertempo- results only under very strong assumptions ral margin. This implies two things. First, on the nature of the income process and of from a technical point of view, the Euler the moral hazard. equation for consumption will have to hold In a recent paper, Attanasio and Pavoni (and indeed it becomes part of the incen- (2007) have shown that, in a relatively tive compatibility constraints). Second, general moral hazard model with hidden agents, because of their ability to transfer assets, the social planner can provide more resources over time, will have a strong pref- insurance to the agents than in the bond erence for strategies that lead to high net economy mentioned above. In particular, present value transfers. Moreover, they will the amount of risk sharing that can occur Attanasio and Weber: Consumption and Saving 731 in equilibrium depends on the severity of ­taxation survives. The positive taxation of the moral hazard problem. Attanasio and capital follows from the fact that the stan- Pavoni (2007) write examples for which a dard Euler equation does not hold and, closed form solution can be derived and instead, the “inverse Euler equation” does. in which the amount of risk sharing over The intuition behind this result is that, in and above that obtained by self-insurance these models, an increase in capital has two can be related to the degree of excess effects on welfare in the following period. smoothness discussed in section 3 and On one hand, as in the standard model, it estimated on aggregate data by Campbell increases the resources available to the indi- and Deaton (1989). In particular, these vidual in the second period. On the other, it authors can interpret the degree of excess has a negative effect on incentives. In other smoothness as reflecting the severity of the words, it is optimal for the government to moral hazard problem. The larger the out- introduce a wedge between the interest rate put loss involved with shirking, the easier paid to and the interest rate received by the it is to provide incentives and, therefore, ­consumer—by taxing interest rates the gov- insurance, and the larger is the degree of ernment reduces private savings.25 “excess smoothness,” i.e., the lesser is the The exploration of models with asymmet- response of consumption to innovations ric information and their implications for to permanent income. In their empirical risk sharing and consumption behavior is work, Attanasio and Pavoni (2007) frame only beginning. There are very few empiri- their test as a test of the intertemporal bud- cal studies of this type of model that con- get constraint along the lines proposed by stitute an exciting and important research Hansen, Roberds, and Sargent (1991). Risk agenda. Kocherlakota and Pistaferri (2009), sharing over and above the self-insurance whose paper we discuss in section 5, is an provided by saving results in a violation of example. the intertemporal budget constraint with 4.3.2 Imperfect Enforceability of Contracts a single asset because it ignores the trans- fers connected with this insurance arrange- The other imperfection that the literature ment. Attanasio and Pavoni (2009) show has explored as a possible reason for the evidence from U.K. micro data that is con- lack of complete markets is the imperfect sistent with excess smoothness and inter- enforceability of contracts. There might be pret it within their theoretical framework. situations in which institutions that guar- Some important implications of incom- antee the execution of contracts are not plete and asymmetric information models developed enough and, as a consequence, are those about the optimal taxation of capi- individuals only enter contracts that are tal. In particular, some recent contributions have shown how imperfect information can provide a rationale for capital taxation, 25 The paper by Golosov, Kocherlakota, and Tsyvinski which contradicts the standard Ramsey (2003) has been followed by other contributions that have result on optimal dynamic fiscal policy. looked at different aspects of this type of model. In particu- Mikhail Golosov, Kocherlakota, and Aleh lar, while this paper does not provide results on the decen- tralization of the constrained efficient allocations they Tsyvinski (2003) show that, in a model with study, Stefania Albanesi and Christopher Sleet (2006) and unobserved and evolving skills, it is indeed Kocherlakota (2006) study tax systems that could decen- optimal to have a positive rate of taxation tralize those allocations. More recently, Emmanuel Farhi and Iván Werning (2006) have considered the quantitative of capital income, although the Atkinson– implications of models in which the inverse Euler equa- Stiglitz result of uniform commodity tion holds. 732 Journal of Economic Literature, Vol. XLVIII (September 2010)

­self-enforceable. These models have been moving some resources from one consumer studied in a variety of contexts. 26 to the other. Clearly, only the participation Self-enforceable contracts can generate constraint for one of the two individuals can very rich dynamics and dynamic allocations be binding. This implies that only one of the that resemble some of the features seen in two Kuhn Tucker multipliers associated to reality. In particular, one can generate inter- the participation constraints is positive, while personal transfers of resources that are mid- the other is zero. Thomas and Worrall (1988) way between insurance and loans. This type and Ligon, Thomas, and Worrall (2002) show of allocations has been observed in several that the behavior of the two consumer econ- developing countries: Christopher Udry omy can be summarized by a single state vari- (1994), for instance, describes loan contracts able, which is the ratio of marginal utilities of in Northern Nigeria where the terms of the the two consumers. Notice that, under per- contract (interest rate and maturity) vary ex fect risk sharing, this ratio is a constant and post with the shocks received both by bor- equal to the ratio of Pareto weights. In this rowers and lenders. Jean-Philippe Platteau, context, however, this is not any longer true. Jose Murickan, and Etienne Delbar (1985), Instead, when the participation constraint instead, describing fisheries in Kerala, India, of one of the two consumers is binding, the refer to quasi credit arrangements. In both ratio of marginal utilities will move. It is as cases, a distinctive feature of the observed if the social planner changes the consump- contracts and implied transfers is that they tion allocation relative to the one that would are state contingent, like insurance ­contracts. be observed under perfect risk sharing to On the other hand, they seem to have a guarantee that the constrained consumer is memory, like debt contracts. indifferent between staying in the contract To understand how limited enforceability and leaving. This implies rewarding the con- contracts may induce this type of transfers, strained consumer with a shift in promised it is useful to consider a simple example in utility. Effectively the Pareto weights that are which there are only two individuals, A and an exogenous constant (which pick a specific B. In such a situation, one can consider a competitive equilibrium) under perfect risk social planner problem (like 16) and augment sharing become endogenous and move to it with two participation constraints. These guarantee enforceability. imply that each of the two consumers, in each In such a situation, it can happen that, history, prefers being in the contract to reneg- if consumer A receives a sequence of con- ing and consuming its current income. With secutive positive shocks and is “constrained” two consumers, a given transfer will imply by the risk sharing agreement, the ratio of

26 Thomas and Worrall (1988) introduced some of the and characterize contracts that, in some sense, are self- concepts used in this literature in the context of wage enforceable. It is, therefore, necessary to establish what contracts. Timothy J. Kehoe and David K. Levine (1993) happens out of equilibrium when somebody does not ­introduced a framework in which, in a deterministic respect the terms of a contract. Most of the papers in this world, simple idiosyncratic income fluctuations cannot literature have resorted to the equilibrium concept pro- be smoothed because of these enforceability problems. posed by Dilip Abreu, David Pearce, and Ennio Stacchetti Kocherlakota (1996) analyzes a consumption problem, (1990): when somebody deviates from the contract, the while Kehoe and Levine (2001) extend their 1993 model economy reverts to the worst sub-game perfect equilib- to consider stochastic environments. Stephen Coate and rium, which turns out to be autarky. The punishment, on Martin Ravallion (1993) look at the consequences of lack of the basis of which some risk sharing is implemented, there- enforceability for consumption allocations. The contracts fore consists in denying the benefits from future risk shar- considered in that paper, however, are not fully efficient, as ing. The amount of utility an individual can derive in the they are restricted to be stationary. An important issue is the absence of risk sharing determines crucially the amount of concept of equilibrium one uses. One wants to construct risk sharing that can be sustained in equilibrium. Attanasio and Weber: Consumption and Saving 733

­marginal utilities shifts progressively in her applied widely: Fernando Alvarez and favor. It can, therefore, also happen that, in Urban J. Jermann (2000) have studied the some situations, consumer B, after receiv- asset pricing implications of these models ing an income below her long-term average, and stressed how the price of risk is deter- actually transfers resources to consumer A mined by a subset of agents, while Patrick who has experienced a positive shock.27 This J. Kehoe and Perri (2002) have looked at type of behavior makes the optimal contract, the implications for international financial in this situation, resemble a debt contract: markets. In an interesting paper, Costas having borrowed from A, B is repaying some Azariadis and Luisa Lambertini (2003) have of her debt. However, the analogy only lasts introduced imperfectly enforceable con- until B is constrained by her participation tracts in an overlapping generations model. constraint. When that happens, all past his- There, to get some risk sharing, punishment tory is erased and the transfer of resources must imply a prohibition on saving, as well will be determined only by the necessity of as participation in insurance markets. keeping consumer B in the contract. When There is not much empirical work on neither participation constraint binds, the models with imperfectly enforceable con- efficient equilibrium will dictate that the tracts. One of the earliest contributions can ratio of marginal utility is kept constant and be found in Andrew D. Foster and Mark R. transfers of resources between the two con- Rosenzweig (2001), who extend the dynamic sumers will guarantee that. limited commitment model to the case where Clearly the nature of preferences and the consumers have altruistic preferences. They properties of income processes will deter- stress that altruism within extended fami- mine the amount of risk sharing that can lies has an ambiguous effect on risk-sharing be sustained in equilibrium. For instance, arrangements: there are greater utility gains it can be proven that, if the discount fac- from insurance but scope for insurance is tor is high enough, perfect risk sharing will more limited if incomes of family members be sustainable, while, if it is low enough, are highly correlated. Also, if altruism is very autarky is the only equilibrium. In general strong, the threat of autarky is no longer cred- (but not always), an increase in the vari- ible and the mutual insurance scheme loses ance of income will lead to an increase in some of its appeal. Foster and Rosenzweig risk sharing, as it makes the value of autarky use transfer information data for the same lower, while an increase in the persistence three Indian villages analyzed by Townsend of idiosyncratic income will reduce risk and show that imperfect commitment effects sharing.28 This class of models has been (generating history dependence) are gener- ally important but transfers are more respon- 27 It turns out that this type of situation can only occur sive to shocks and less history dependent if there are aggregate shocks. when income correlation is lower and altru- 28 Whether an increase in the variance of income causes ism is moderate—as is the case of transfers a decrease or an increase in the amount of risk sharing depends on a variety of factors but, in particular, on how to family members who live outside the vil- one increases the variance. If it is increased by expanding lage—in line with model predictions. the range of income values it is possible to have a decrease Ligon, Thomas, and Worrall (2002) in risk sharing. This is because the value of autarky for indi- viduals at the right tail of the income distribution might go develop, solve, and estimate a model with up if the discount factor is low enough. On the other hand, imperfect enforceability in a context where when the variance is increased by keeping the support of saving/borrowing is not allowed. They use the income process unchanged and increasing the weights on the tails, one gets an increase in the amount of risk shar- the same Indian village data of Townsend ing as the value of autarky declines. (1994) and Ligon (1998), and carry out 734 Journal of Economic Literature, Vol. XLVIII (September 2010) a fully structural estimation of the three estimation that is highly computer inten- deep parameters that characterize the solu- sive (to the point that Ligon, Thomas, and tion (subjective discount factor, relative risk Worrall do not even report standard errors aversion, and a state-independent punish- of their estimated deep parameters!). They ment for reneging on the dynamic insur- show that the model is not rejected by the ance arrangement), conditional upon the data and that their estimated parameters estimated income process. Two estimation imply that the probability of a self-enforcing procedures are carried out—one where the contract binds is 10 percent if the relative criterion function is in terms of the differ- risk aversion parameter is assumed to be ence between observed and predicted indi- equal to 1.5.29 vidual log consumption, another one where Most if not all of the papers we have cited the criterion function is instead the differ- so far assume complete information. This ence between changes of individual con- implies the possibility of complete contin- sumption shares over time. Even though gent markets: (self) enforceability is the only estimated parameters take sensible values, constraint that is imposed on the contracts they can either explain the distribution or available to an individual. These assump- the dynamics of consumption—not both. tions do not seem too strong for simple vil- Pierre Dubois, Bruno Jullien, and Thierry lage economies of the type studied by Udry Magnac (2008) add formal, incomplete con- (1994)30 and Platteau, Murickan, and Delbar tracts to a model of dynamic, limited com- (1985). Whether they make these models mitment with storage. These contracts are relevant for developed economies is an inter- meant to capture such arrangements as land- esting question. However, much has been renting and sharecropping. They derive the learned from them and interesting directions efficient equilibrium allocation that is char- of research can be taken up. First, one can, acterized by two equations—an Euler equa- in principle, try to introduce simultaneously tion linking consumption growth to lagged information and enforceability problems. consumption and current income because of Atkeson (1991) considers one such model the limited commitment insurance scheme in the context of international financial mar- (that introduces a borrowing restriction term kets. Phelan (1998) considers one-sided lack in an otherwise standard equation), and an of commitment and asymmetric informa- income equation, where current income is tion in a banking model. Alternatively, one affected by lagged consumption because of can also introduce punishments that differ the formal contracts. from the permanent exclusion from finan- Dubois, Jullien, and Magnac (2008) stress cial markets. Hanno Lustig and Stijn G. van that the existence of formal contracts may Nieuwerburgh (2005), for instance, have either help or hinder informal transfers as it considered collateral constraints, in that indi- affects both incentives and the possibilities vidual consumers can only borrow against without an agreement, a point also made by their housing wealth. This induces interest- Attanasio and Jose-Victor Rios-Rull (2000) ing effects of house prices on consumption and further developed in Pedro Albarran and, more generally, on asset pricing. and Attanasio (2003). An important contri- bution of the paper by Dubois, Jullien, and Magnac is the derivation of (nonlinear) esti- mable equations for income and consump- 29 Other papers that have studied this class of models are Kehoe and Perri (2002) and Kehoe and Levine (2001). tion—in their application to Pakistani village 30 Udry (1994), however, stresses the importance of pri- data they can, thus, avoid fully structural vate information in the region of Nigeria he studies. Attanasio and Weber: Consumption and Saving 735

5. Alternative Models We start this section by listing some of the puzzles that have been identified in the The standard model we have considered literature. We then discuss some extensions so far assumes that individuals solve a well and modifications of the standard model that specified optimization problem and the have been proposed in the literature. observed outcomes reflect, by and large, this 5.1 Some Puzzles type of behavior. This approach might find it hard to explain some facts that have attracted The literature has identified a number of attention in recent years with the increased facts that seem to be inconsistent with the interest in the so-called behavioral econom- standard versions of the life cycle model ics. These facts generally refer to deviations that we have discussed so far. Here we dis- from optimal behavior. It has become fash- cuss some of those that have received the ionable to report anecdotes about apparently most attention. irrational or suboptimal behavior that “leaves 5.1.1 Inertial Behavior money on the table.” In this section, we dis- cuss some of these puzzles and the evidence A series of recent papers (Brigitte C. that generates them and try to put the issues Madrian and Dennis F. Shea 2001; James in perspective. J. Choi et al. 2002, 2004, 2006) have docu- Our general take is that a model of indi- mented that default options have important vidual behavior cannot fit the data perfectly and surprising effects on the structure and and there will always be room for unex- level of saving of individual households. In plained behavior, which for lack of a bet- particular, these papers have shown that, ter word, we define as “taste shocks.” Of if newly hired individuals are enrolled by course, if one were to find out that there are default into a 401(k) retirement plan (rather systematic deviations of observed behavior than having to enroll), they are much more from what is predicted by the model and likely to participate even though they have that most observations need a “taste shock,” the possibility of opting out of the plan. In it would be an indication that the model is other words, the evidence seems to indicate not a good representation of reality. The that individuals with the same opportunity model would lose its predictive power and set make different choices depending on its usefulness. The issue is whether the the default option they are (exogenously) model is able to capture some key features assigned to. As the authors of these papers of individual behavior and, in particular, the note, this fact contradicts the standard response to economic incentives. This is, in model where, in the absence of large adjust- the end, what matters not only from a theo- ment costs, the default option should not retical point of view, but also from a policy matter. The authors of these papers propose perspective. a number of different explanations, ranging We argue that, in the case of life cycle con- from the importance of “inertial behav- sumption and saving decisions, it is impor- ior” and procrastination (possibly induced tant to build models that are flexible enough by the difficulty of the problem relative to to reflect the complexity of the environment individual ability to solve it) to the possibil- and incentives that individuals face. It is also ity that defaults are somehow perceived as a important to take into account the constraints form of endorsement or advice, to “present (in terms of information as well as resources) bias.” that individuals are subject to. We will come More recent papers, such as Gabriel D. back to these issues in the conclusions. Carroll et al. (2009) and Choi et al. (2009), 736 Journal of Economic Literature, Vol. XLVIII (September 2010) show that inertial behavior might extend saving decisions but that they save more as to other related phenomena. The former a result.31 paper, for instance, shows that, in addition 5.1.3 Credit Card Debt with Low Interest to default, even forcing individuals to make Asset Holdings an explicit choice (without giving them a default option) has an important effect on Gross and Souleles (2002) were the first to the decision to enroll in retirement plans. point out that many households who borrow The latter, instead, show that the portfolio at high interest on credit cards have nonneg- allocation of individuals with (exogenously) ligible investments in low-yield liquid assets. different allocations of the employer’s David Laibson, Andrea Repetto, and Jeremy matched contributions is not systematically Tobacman (2003) report that among house- different, while it should be under a stan- holds with a head between ages 20–29 that dard model. are in the top wealth quartile, three-fourths did not repay their credit card bills in full. For 5.1.2 Demand for Commitment Devices households whose head is in their thirties, There is evidence that individuals are over 80 percent of median wealth-holders interested in devices that tie their hands had credit card debt. Even among the house- in some relevant economic domain. For holds with a head between ages 50–59 that instance, Stefano DellaVigna and Ulrike were between the fiftieth and seventy-fifth Malmendier (2006) discuss the choice of wealth percentiles, 56 percent borrowed and contracts offered by three health clubs and paid interest on credit card debt in the past taken up by their members: surprisingly month. Laibson, Repetto, and Tobacman large fractions of individuals choose to pay (2009) conclude that “The typical American a flat monthly fee but then rarely show up at household accumulates wealth in the years the gym. For these individuals, the option of leading up to retirement and simultaneously a ten-visit pass would work out to be much borrows on their credit cards.” cheaper. An explanation is that consumers 5.1.4 High Saving Rates in Developing are willing to pay more for contracts that Countries force them to do what is right for them in the long run but is hard in the short run. Richard The life cycle model explains cross-coun- H. Thaler and Shlomo Benartzi (2004) report try differences in saving rates as follows: evidence on the first three implementations in high growth countries the young—who of a program whereby people commit in save—are life-time richer than the old—who advance to allocating a portion of their future dissave. This explains why high growth coun- salary increases toward retirement savings. tries save more. The very high saving rates This program has had a very high take up in China have been explained by Modigliani rate (almost 80 percent) and has led par- and Shi Larry Cao (2004), who point to the ticipants to save much more than they used effects of the one-child policy on middle-­ to before enrollment. Finally, Nava Ashraf, aged families in a country where most Dean Karlan, and Wesley Yin (2006) report people cannot expect to receive a pension evidence from the sale of a commitment sav- when they retire. The demographic imbal- ings product for a Philippine bank that led ance implies that the traditional mechanism to significant and lasting increases in savings of intergenerational risk-sharing cannot be by those customers who were offered it and purchased it. Thus, there is evidence that 31 DellaVigna (2009) reviews a number of other papers consumers not only like to tie their hands in in this area. Attanasio and Weber: Consumption and Saving 737 expected to provide adequate coverage for presence of a small long run predictable com- risks related to longevity and old age health ponent in consumption growth and show that problems. Private savings are then the only their model, with Epstein–Zin preferences, way to ensure an acceptable standard of liv- can explain several features of observed asset ing in old age. Recently, Marcos D. Chamon prices. More recently, some papers, includ- and Eswar S. Prasad (2010) have used micro ing Lustig and van Nieuwerburgh (2005), data to analyze household saving rates by Yi-Li Chien, Cole and Lustig (2009), Chien urban Chinese and found that the age profile and Lustig (2010), and Kocherlakota and of savings displays a U-shape. This is hard to Pistaferri (2009), have considered the asset explain in a standard life cycle model, where pricing implications of models with asym- nonpension wealth should be decumulated metric information and suggested that this in old age. The evidence that at least in some class of models could be part of the solution high-growth countries (China, Taiwan) the to the equity premium puzzle. older generations save could be due to some An issue conceptually related to the equity form of habits (Paxson 1996). premium puzzle is the limited participa- tion into financial markets—in most coun- 5.1.5 The Equity Premium Puzzle (and Low tries, relatively few households actively hold Stock Market Participation) shares and equities. This has been labeled The equity premium puzzle (Rajnish the stockholding puzzle by Michael Haliassos Mehra and Edward C. Prescott 1985) has and Carol C. Bertaut (1995)—given the rela- attracted much attention in the macro- tively high returns on equities that have pre- finance literature. Given the historically high vailed in many countries, households should equity premium (the difference in expected invest at least some of their wealth in stocks. return between stocks and bonds), asset Even though this issue relates to the equity markets equilibrium requires consumers to premium, it has not been addressed in the have very high risk aversion. This, in models context of habits or imperfect information with expected utility maximization and inter- models, rather in models where consum- temporally separable preferences, in turn ers are affected by transaction costs or have would imply a very low elasticity of intertem- access to limited financial information.32 poral substitution, contrary to the empirical 5.2 Modifying the Basic Model evidence and inconsistent with equilibrium conditions for the risk-free interest rate. 5.2.1 Relaxing Geometric Discounting A number of possible solutions for this puzzle have been presented in the literature. There is evidence, briefly reviewed earlier One prominent hypothesis is the presence of on, that individuals are interested in devices habits in the utility function as in Campbell that tie their hands in saving decisions and and Cochrane (1999). We discuss habits, dif- that they save more as a result. The standard ferent ways in which they can be modeled, model of intertemporal decisions is at pains and the evidence on their presence below. to explain this type of behavior—where con- However, Ravi Bansal and Amir Yaron (2004) sumers apparently fear their lack of control claim that habits are not required to explain the key patterns of financial returns and con- 32 Studies that have looked at this issue include Erzo G. sumption data as long as one recognizes the J. Luttmer (1999), Mankiw and Zeldes (1991), Suleyman existence of time-varying risk premia that Basak and Domenico Cuoco (1998), Attanasio, Banks, and Tanner (2002), Annette Vissing-Jorgensen (2002), Monica generate consumption growth predictability. Paiella (2004), Attanasio and Paiella (forthcoming), and Bansal and Yaron, in particular,­ allow for the Guvenen (2009). 738 Journal of Economic Literature, Vol. XLVIII (September 2010) and their inability to stick to their chosen period that crucially affects the properties of optimal plan. Time inconsistent or temp- the solution but the length of which is arbi- tation preferences have been proposed to trarily set by the researcher. rationalize some of the facts. A more tractable and elegant specifica- An elegant way to introduce time-incon- tion of preferences that may be used to sistent preferences is provided by the quasi model quasi-rational impatience has been hyperbolic discounting framework proposed put forward by Faruk Gul and Wolfgang by Laibson (1997) who developed ideas Pesendorfer (2001, 2004), who stress the previously introduced by Robert H. Strotz importance of self-control problems leading (1956) and Edmund S. Phelps and Robert to the postponement of saving. Their model A. Pollak (1968). Consumers are assumed to can be characterized by a period t util- maximize the expected value of the following ity function as follows (Alessandro Bucciol lifetime utility index: 2009):

T t − t (27) Ut U Ct U CHt U Ct , (26) u(Ct) ​ ​ ​u(Ct ). = ( ) − τ ( ( ) − ( )) + β ​t∑1 δ +τ = where CH denotes cash on hand (the sum of This implies that a different, lower discount income and wealth), and is a ­nonnegative τ factor is used to choose between this period constant. The larger is, the stronger the τ and the next (the product of and ) and role played by temptation, inducing consum- β δ between any two other periods ( ), in agree- ers to try and equalize consumption and cash δ ment with experimental evidence provided in hand. (In this version of the model, con- by Thaler (1981) and Uri Benzion, Amnon sumption cannot exceed cash on hand). Rappoport, and Joseph Yagil (1989). This Manuel Amador, Werning, and Angeletos discounting mechanism generates time (2006) consider the issue of optimal trade- inconsistent plans with too little saving for off between commitment and flexibility in a retirement. Naive consumers can do little model where individuals expect to receive about this but sophisticated consumers relevant information regarding tastes and, recognize the problem and tie their hands thus, they value the flexibility provided by to prevent their current self from leaving larger choice sets, but also expect to suffer their future selves in financial distress. This from temptation, with or without self-con- explains why consumers may choose to enter trol, and value the commitment afforded long-term saving commitment plans, such by smaller choice sets. Their key finding is as 401(k)s in the United States (Choi et al. that imposing a minimum level of savings 2006) or other committed saving products is always a feature of the solution. This has (Asharf, Karlan, and Yin 2006). important implications for public policy— The quasi hyperbolic discounting model compulsory contributions to social security lends itself to estimation and testing but or other retirement saving schemes may be requires solving for the consumption func- justified on welfare grounds even if actuari- tion numerically. Even though an Euler ally fair annuities are available to consum- equation for this model has been derived, its ers. The optimal size of these contributions empirical use is limited because it involves will depend not only on the preference the marginal propensity to consume out of parameters discussed above (the elasticity wealth (Christopher Harris and Laibson of intertemporal substitution and the rate 2001). It also suffers from some potential dif- of time preference) but also on the impa- ficulties related to the definition of the time tience parameter in (26) or the self-control Attanasio and Weber: Consumption and Saving 739

­parameter in (27). In economies character- account, risk aversion is found to be less (and ized by dynamic inefficiency, the presence of statistically different from) one.33 impatient or tempted consumers may help 5.2.2 Relaxing Intertemporal Separability reduce the (excessive) amount of capital. The hyperbolic discounting model finds The standard model presented in section 2 its justification mostly in experiments. Shane assumes preferences to be additive over time Frederick, George Loewenstein, and Ted and over states of nature—this implies that O’Donoghue (2002) provide an overview of risk aversion and intertemporal substitu- experiments that support that notion that tion are functionally related. In the special individuals discount the near and the distant case of the isoelastic function, the relative future at different rates. Ariel Rubinstein risk aversion coefficient is the reciprocal of (2003) casts doubts on the interpretation the elasticity of intertemporal substitution. given to the experimental evidence by show- The assumption of intertemporal separabil- ing that differently designed experiments still ity, however, might be too strong as it can- suggest a marked preference for today versus not capture phenomena such as habits and tomorrow but not in a way that is compatible durability. with hyperbolic discounting. Recently, Jesus The simplest way to introduce habits/ Fernandez-Villaverde and Arijit Mukherji durability of consumption is to write the util- (2006) claim that the role played by uncer- ity function as follows: tainty biases results against exponential util- ity. To counter this criticism, John Ameriks (28) ​ u​(xt xt 1; zt), − ϑ′ − et al. (2007) devise a set of questions aimed ∑t at eliciting self-control problems directly where x is a vector of goods or services and z and claim most people are affected by such is any other variable that affects marginal util- problems (less so as they age). Fernandez- ity (demographics, leisure, other goods that Villaverde and Mukherji (2006) devise a are not explicitly modeled). The param- ϑ different experiment where sophisticated eters are positive for goods that provide ser- hyperbolic discounters should take a com- vices across periods (durability), negative for mitment device, while exponential discount- goods that are addictive (habit formation) ers and naïve hyperbolic discounters should or zero for goods that are fully nondurable, not. They report that only 13 percent choose non-habit-forming (Hayashi 1985). the commitment device in their experiment. Martin Eichenbaum and Hansen (1990) In recent years, an increasing body of evi- and Ogaki and Carmen M. Reinhart (1998) dence comes also from estimation. Laibson, test and reject the separability of durables Repetto, and Tobacman (2009) follow a fully and nondurables within the context of an structural approach and show that the sophis- Euler equation estimated on aggregate data. ticated hyperbolic discounting model can Alessie, Devereux, and Weber (1997) and reconcile credit card debt with illiquid asset Mario Padula (1999) test and reject separa- holdings over the life cycle. Bucciol (2009) bility between nondurable consumption and follows a similar approach but estimates the the stock of cars using micro data from the temptation model instead. To identify the parameters, he uses liquid and quasi-liquid 33 Giovanni Mastrobuoni and Matthew Weinberg (retirement) wealth holdings at different (2009) report that Social Security benefit recipients with- ages as target moments. He finds evidence out savings (about a fourth of the sample) consume 25 per- cent fewer calories the week before they receive checks of a small but significantly positive degree of relative to the week afterwards. They show that their find- temptation—when temptation is taken into ings are consistent with hyperbolic discounting. 740 Journal of Economic Literature, Vol. XLVIII (September 2010)

Family Expenditure Survey and the CEX, aggregation (John Heaton 1993), aggrega- respectively.34 tion over consumers, and by data construc- Habits have attracted much attention in tion methods (particularly for the services the macro-finance literature. In the presence from durable goods). For this reason, micro of habits, the functional restriction between data seem preferable. intertemporal substitution and risk aversion The Euler equations corresponding to (28) is relaxed. Campbell and Cochrane (1999) involve x at four different periods of time make the distinction between the overall and their estimation typically requires panel curvature ( in the isoelastic case), which is data. High quality consumption panel data γ relevant for intertemporal allocations of con- are rare and this has limited the scope for sumption, and the local curvature of the util- empirical analysis. Meghir and Weber (1996) ity function, ( over the surplus consumption have used CEX quarterly data on food, trans- γ ratio, which is the share of consumption net port, and services (and a more flexible speci- of habits over consumption), which is instead fication of intertemporal nonseparabilities relevant for portfolio decisions. Habits can than is implied by equation 28), and found take various forms—today’s marginal util- no evidence of either durability or habits ity may depend on the consumer’s own past once leisure, stock of durables, and cars as consumption level (internal habits) or the well as other conditioning variables are taken past consumption level of other consumers into consideration. 35 (external habits). Campbell and Cochrane Similarly, negative evidence on habits has consider the case of external habits, where been reported by Dynan (2000) using PSID consumers are influenced by other house- annual food at home data. On the other hand, holds’ lagged consumption, not their own, Raquel Carrasco, Jose M. Labeaga, and J. and show that their model can solve the David López-Salido (2005) use Spanish equity premium puzzle for plausible param- panel data that follow households over eight eter values. The external habits model seems consecutive quarters and find evidence for to work better than the internal habits model habits once they control for fixed effects. on aggregate data even though Xiaohong Habits are more likely to explain the high Chen and Sydney C. Ludvigson (2009) chal- saving in developing countries puzzle if they lenge this conclusion. persist over a long period. Viola Angelini Empirical macro-evidence on the pres- (2009) has worked out the analytical solution ence of habits is quite mixed and this may of the dynamic optimization problem when be due to the very nature of aggregate con- preferences are CARA and there are habits sumption data as stressed in Karen E. Dynan in the utility function. An interesting feature (2000). The serial correlation of aggregate of the solution is the interplay of habits and consumption growth is affected by time the precautionary saving motive—another is the dependence of beginning of life con- sumption on “inherited habits”—a feature 34 A special feature of durable goods is that they might be subject to adjustment costs. The case of convex adjust- ment costs is a relatively simple extension and captures well repairs and maintenance activity (see Ben Bernanke 1985). 35 Indeed, Flavin and Shinobu Nakagawa (2008) argue To model replacement decisions, nonconvex adjustment that the presence of nonseparable, illiquid durable goods, costs are more plausible as they lead to infrequent adjust- such as housing, in a standard utility function explains the ment and explain why durable goods are not replaced all smoothness of aggregate nondurable consumption the the time—the seminal paper is Sanford J. Grossman and same way as the external habits model. This could recon- Guy Laroque (1990) and applications are Janice C. Eberly cile the failure to find micro-evidence on habits with the (1994), Attanasio (2000), and Giuseppe Bertola, Luigi success of the external habits model to fit the aggregate Guiso, and Pistaferri (2005). consumption and financial returns data. Attanasio and Weber: Consumption and Saving 741 that could be exploited in empirical work 6. Conclusions in data sets that contain information on the standard of living enjoyed early in life before The aim of this paper was to survey the leaving the parental home. theoretical and empirical literature on the The few studies that have used micro data life cycle model to draw the implications on nondurable consumption items to inves- that plausible versions of the model have for tigate the issue find little or no evidence of public policy and, in particular, for policies habits, at least once preferences capture the that influence the intertemporal allocation presence of nonseparabilities between goods of resources. Rather than summarizing what and leisure. we have discussed above, we conclude this paper by taking a stand on what we think are 5.2.3 Financial Literacy and Information profitable directions for future research. A standard assumption in the life cycle One possible reading of the empirical lit- literature, made mainly for analytical and erature on the life cycle model is that it is empirical convenience, is that of rational possible to construct rich versions of the expectations. This assumption states that model that are not inconsistent with available individuals know the stochastic environment micro data, especially for households headed in which they live, have at least as much by prime aged individuals. Much of this evi- information as the econometrician in making dence comes from the estimation of Euler their consumption and saving decision, and equations. Euler equations are remarkably use it optimally. Recently, much evidence has useful because they let researchers estimate been gathered that sheds important doubts important preference parameters in a rela- on this assumption. A number of papers tively robust way, allowing for—but without (see, for instance, Annamaria Lusardi and the need to explicitly model—important Olivia S. Mitchell 2007, 2009 and Lusardi phenomena such as labor supply, housing, and Peter Tufano 2009) have used explicit durables, and so on. and quantitative measures of financial liter- However, to conduct a useful policy acy and related them to individual financial debate, it is necessary to be able to say decisions. Lusardi and Mitchell (2007, 2009) something about the level of consumption. show that more “financially literate” indi- A reduced form approach that exploits key viduals are more “retirement ready,” while theoretical insights can shed light on some Lusardi and Tufano (2009) show that more issues—for instance on the nature of par- “financially literate” youths are less likely ticular business cycle episodes or whether to hold unsustainable debt. It has also been consumers perceive specific shocks to be shown that stock holdings are much less permanent or temporary. A structural form common among the less financially literate. approach is more generally informative but Perhaps it is not surprising that financial requires, except for special cases, numeri- sophistication affects individual behavior. It cal methods and simulations. Moreover, it could also be that financial literacy is corre- requires specifying completely the environ- lated with other individual attributes (such ment in which economic agents operate, as total human capital) that are linked to the including their perceptions and information amount of resources an individual controls (a sets, institutional factors such as pensions, fact recognized by some of the papers in the and intertemporal trades available to them. literature). However, the evidence that has The necessity to provide so much detail been gathered so far is reasonably convinc- makes this approach inherently not robust. ing and should be taken seriously. This is not to deny its usefulness but to make 742 Journal of Economic Literature, Vol. XLVIII (September 2010) it clear that the general validity of results smooth shocks, how they react to policy obtained using simulated life cycle models is innovations these policy functions become not to be taken for granted. essential. Studies that do this in a system- Many of the features to be included in atic fashion are few and far between. In our the model to make it realistic involve impor- opinion, an important paper is Browning tant nonconvexities that make the optimiza- and Crossley (2009), which looks at how tion problem difficult to solve numerically. individuals use the timing of the purchase Much progress has been made since the first of durables to smooth out specific transitory numerical simulations of life cycle models shocks. Much more work is necessary in this with uncertainty were developed by Deaton direction. The recent recession and some (1991). Current models are able to con- of the policy measures taken in the United sider, in very sophisticated fashion, housing Kingdom can supply important examples choices, labor supply, liquidity constraints, of questions to which policymakers would and a number of other factors. Much work, like to have answers that economists are still however, remains to be done to develop unable to provide. For instance, if one low- these models. Moreover, while some of the ers temporarily the rate of indirect taxation, parameters of these models can be estimated what is the effect on consumption and, in by Euler equations, many of them cannot particular, on durable purchases? And how and one has to obtain sensible estimates of does the answer change when the decrease crucial parameters from alternative sources. happens in response to an increase in the There is still work to be done in terms of level of uncertainty in the economy? understanding intertemporal preferences. Another important potential use of this The work on the Euler equation has made it class of models is to study aggregate con- clear that one needs to take into account the sumption and saving and, possibly, to con- evolution of individual needs and the non- struct realistic equilibrium models. The work separability between consumption and labor on this is still in its infancy and faces some supply. Another aspect that has received less severe problems. The life cycle model is an attention, but could turn out to be important, intrinsically dynamic model in which choices is the role played by durable and semidu- depend on future variables. The equilib- rable commodities. There is some evidence rium values of these variables depend, in of nonseparabilities that could be important turn, on the behavior of all consumers in the in assessing individual responses to different economy. It is therefore difficult to establish shocks and innovations. what determines equilibrium values. Other The Euler equation approach is use- equilibrium phenomena that are important ful because it can allow for the presence of and interesting are the determination of the these nonseparabilities even when some of type of assets that are available to individuals the choice variables are affected by noncon- both to smooth income shocks and to finance vexities and other imperfections. The Euler investments (such as human capital accumu- equation provides equilibrium conditions lation) when information problems (adverse that the policy functions that determine con- selection and moral hazard) are important. sumption and other choice variables have The explicit modeling of imperfections to satisfy and that can be used to estimate and frictions that cause markets to be incom- structural parameters even if we cannot plete is highly promising and potentially very characterize these policy functions explicitly. useful in characterizing the implications that However, to understand the intertempo- a structure, such as the life cycle model, has ral allocation of resources, how individuals for policy. The recent exciting development Attanasio and Weber: Consumption and Saving 743 of the new dynamic public economics is a empirical work requires measures of beliefs good example of that. and expectations. Progress has been made in In section 5, we have mentioned a number this direction (especially in measuring expec- of directions in which some strong assump- tations). But much more work is necessary. tions routinely made in the literature on the In our opinion, measuring financial literacy life cycle model can be relaxed. The list con- (and its determinants) is an important direc- tained in section 5 is not exhaustive. However, tion of research. The same applies to individ- we chose those topics that we think are more ual beliefs, attitudes, and preferences. In the promising in terms of future research. The same way in which the development of survey analysis of alternative preference structures, methods has allowed in recent years a much such as the analysis of temptation in Gul and more precise measurement of household Pesendorfer (2004), is very important and so financial wealth and (more recently) subjec- is the consideration of habit formation. tive expectations, we need to develop similar As for the model that relaxes geometric methods for the measurement of these other discounting, systematic empirical studies are objects that are obviously key determinants still rare. The situation is slightly better in of individual choices. Integrating these mea- terms of habits, although the evidence based sures within rigorous but flexible structural on micro data still comes from a handful of models can yield high returns in terms of studies. The biggest limitation so far comes academic research and information useful from the fact that many of these studies for the design of effective policies. only consider habits with a very short dura- tion, not necessarily because this is the most References appealing model of habits but because of Abel, Andrew B. 1990. “Asset Prices under Habit For- data limitations. The study with longer last- mation and Catching Up with the Joneses.” American ing habit stocks should be a high priority. Economic Review, 80(2): 38–42. 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