Consumption smoothing and the welfare consequences of social insurance in developing economies

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1 Journal of Publi Eonomis 90 (2006) Consumption smoothing and the welfare onsequenes of soial insurane in developing eonomies Raj Chetty a,, Adam Looney b a UC-Berkeley and NBER, USA b Federal Reserve Board, USA Reeived 4 February 2006; reeived in revised form 4 July 2006; aepted 7 July 2006 Available online 17 August 2006 Abstrat Studies of risk in developing eonomies have foused on onsumption flutuations as a measure of the value of insurane. A ommon view in the literature is that the welfare osts of risk and benefits of soial insurane are small if inome shoks do not ause large onsumption flutuations. We present a simple model showing that this onlusion is inorret if the onsumption path is smooth beause individuals are highly risk averse. Hene, soial safety nets ould be valuable in low-inome eonomies even when onsumption is not very sensitive to shoks Elsevier B.V. All rights reserved. Keywords: Risk; Unemployment 1. Introdution A signifiant strand of the literature on risk and insurane in developing eonomies has foused on estimating the response of household onsumption to inome flutuations. Many of these studies (e.g. Townsend, 1994) find that household onsumption remains quite stable when shoks our. Based on suh evidene, a ommon view is that, if onsumption does not flutuate very muh to begin with, the welfare gains from smoothing onsumption further through soial insurane must be small. Morduh (1995) remarks that: The emerging onsensus of the empirial literature [on onsumption-smoothing in developing eonomies] is that holes in effetive [onsumption] insurane exist But, in general, the holes are a good deal smaller than many had assumed The results have lear Corresponding author. addresses: hetty@eon.berkeley.edu (R. Chetty), adam.looney@frb.gov (A. Looney) /$ - see front matter 2006 Elsevier B.V. All rights reserved. doi: /j.jpubeo

2 2352 R. Chetty, A. Looney / Journal of Publi Eonomis 90 (2006) poliy impliations. [If] markets and alternative mehanisms do indeed provide reasonably good insurane and redit, publily provided finanial servies and soial seurity ould rowd out private efforts with limited net gain to soiety. The onsensus on the empirial evidene has eroded somewhat sine Morduh's review. More reent empirial studies have pointed out that onsumption drops may be larger, espeially among subgroups suh as the poor (Ravallion and Chaudhuri, 1997; Morduh, 1999). However, the presumption that onsumption flutuations give a measure of the welfare osts of risks, and therefore the value of additional insurane, remains prevalent (see Gertler and Gruber, 2002; Fafhamps, 2003; Cameron and Worswik, 2003 for reent examples). In this paper, we question whether empirial estimates of the effet of inome shoks on onsumption have lear poliy impliations. We show that the welfare gains from inreasing insurane annot be diretly inferred from the size of onsumption drops. Indeed, the value of insurane may be very large even in environments where onsumption does not flutuate muh. To see the basi idea underlying our argument, onsider two eonomies where agents fae inome shoks. In the first ase, agents have aess to redit markets and networks that allow them to smooth onsumption easily when hit by a shok. In the seond eonomy, private market insurane is very limited. However, households are lose to a subsistene level of onsumption and are very relutant to ut onsumption further when their inome falls for fear of starvation. These risk-averse households therefore use whatever methods they an to avoid a substantial onsumption drop (suh as taking hildren out of shool). In both of these ases, an eonometriian would observe a smooth onsumption path in the data. However, in the latter ase where the smoothness of onsumption is the result of high risk aversion and not effiient private insurane markets soial insurane ould yield large welfare gains. Intuitively, these welfare gains arise from redued reliane on ostly onsumption-smoothing mehanisms, leading to improvements suh as greater eduation for hildren. To formalize this idea, we adopt from the publi finane literature a normative model of soial insurane developed in Baily (1978) and Chetty (in press). These studies show that the welfare gain from soial insurane (ignoring effiieny osts aused by distortions to behavior) is determined by the produt of the perentage onsumption drop aused by the shok D with the oeffiient of relative risk aversion (γ). Holding γ fixed, a smoother onsumption path (smaller D ) does in fat imply smaller welfare gains from soial insurane. However, it is important to observe that γ and D are inversely related. Highly risk-averse households will take extremely ostly measures to insure a smooth onsumption path. Therefore, in order to understand whether a soial safety net is valuable, one must determine the reason that D is small. If it is small beause agents have good private insurane, soial insurane may indeed be unneessary. But if D is small beause γ is large, small onsumption flutuations may belie large welfare gains from insurane beause the produt g D ould be quite large. The results of this paper are related to those of Newbery and Stiglitz (1979), who show that the welfare benefits of ommodity prie stabilization shemes are determined by risk aversion and the hange in output. Our ontribution is to develop a welfare measure for soial insurane and analyze its poliy impliations for developing eonomies in the ontext of empirial findings. Our analysis is also related to studies whih have reognized that soial safety nets may generate value by reduing the use of ineffiient smoothing behaviors (e.g. Rosenzweig and Wolpin, 1993; Morduh, 1999). We link these results on ineffiient smoothing to the onsumption-smoothing literature by haraterizing the normative impliations of the risk-sharing models developed by Townsend (1994) and others.

3 R. Chetty, A. Looney / Journal of Publi Eonomis 90 (2006) The remainder of the paper proeeds as follows. The next setion develops a simple model of inome shoks and derives a formula for the welfare gains from soial insurane. Setion 3 shows how small onsumption flutuations an arise from either good private insurane or high risk aversion, with different impliations for optimal poliy. Setion 4 onludes. 2. Normative framework To derive a formula for the marginal welfare gain from insurane, onsider the following stati model of inome shoks. Suppose the agent has utility over onsumption u(). Let the disutility of obtaining $ of onsumption be given by a linear funtion wðþ ¼h A negative shok suh as bad weather, illness, rop damage or unemployment an be modeled in this framework as an inrease in θ, whih makes earning money more diffiult. In the good state, θ aptures the disutility of effort required to generate inome under normal onditions. In the bad state, θ rises beause generating $ of onsumption requires more ostly ativities suh as planting new rops, searhing for another job, or reduing human apital and health investments in hildren. Suppose there are two states (good and bad), with θ b N θ g =1. With this normalization, θ b an be interpreted as how muh more diffiult it is to earn money in the bad state than the good state. For example, θ b =2 implies that the disutility of generating onsumption is doubled in the bad state. Let p denote the probability that the bad state ours. Let b denote onsumption in the bad state and g onsumption in the good state. Consumption will differ in the bad state and the good state if private insurane markets are inomplete. An atuarially fair insurane program that raises b by $1 must lower g by gain from suh a program is given by ew ¼ puvð b Þ ð1 pþ p 1 p uv g ¼ puv ð b Þ uv g p 1 p. The marginal welfare We onvert this expression into a money metri by normalizing this welfare gain measure by the welfare hange from a $1 inrease in onsumption in the good state. The welfare gain from soial insurane relative to an inrease in inome in the good state is proportional to: W uvð bþ uvð g Þ uvð g Þ To simplify this expression, take a Taylor approximation to the utility funtion and write W g uwð gþ g b uvð g Þ ¼ g D ð1þ where D ¼ g b b is the average observed onsumption drop, and g ¼ uw u V g is the oeffiient of relative risk aversion. The intuition for this formula is straightforward: The marginal welfare gain from $1 of insurane (or, onversely, the marginal welfare ost of an inome shok) depends on

4 2354 R. Chetty, A. Looney / Journal of Publi Eonomis 90 (2006) the size of onsumption flutuations D and the utility value of having a smoother onsumption path (γ). Note that this simple formula holds in a more general setting than the one analyzed here. Chetty (in press) shows that (1) applies in a general dynami lifeyle model where agents maximize expeted lifetime utility subjet with an arbitrary set of hoie variables and onstraints under some weak regularity onditions. Hene, (1) provides a robust guide for welfare analysis. 3. Welfare gain from insurane Eq. (1) shows that the welfare gain from insurane depends on the produt of γ and D, and not the onsumption drop alone. To explore the normative onsequenes of this point, onsider a parametri example of the model above. Suppose the agent has CRRA utility over onsumption in eah state: u ðþ¼ 1 g 1 g In this setting, the worker hooses onsumption in eah state by solving 1 g max 1 g h Hene ðhþ ¼h 1=g The onsumption drop from the employed to the unemployed state is therefore D ¼ g b ¼ 1 b ¼ 1 1 1=g g g h b D This expression shows that is dereasing in γ and inreasing in θ b. Intuitively, high γ makes onsumption redutions partiularly ostly, and the agent therefore exerts greater effort in the unemployed state to maintain onsumption lose to the employed level. Similarly, high θ b makes earning inome while unemployed partiularly ostly, making it preferable to tolerate a larger onsumption drop. These omparative statis indiate that the value of D observed in some developing eonomies ould be small for two distint reasons: (1) θ b is low, i.e. agents are able to easily and inexpensively smooth onsumption by borrowing or through informal insurane mehanisms or (2) γ is high, i.e. agents are very risk averse to flutuations and work hard to have a small onsumption dropeven though θ b might be high. In ase 1, the marginal welfare gain from soial insurane g D is likely to be small. In ontrast, in ase 2, the gain from soial insurane ould be quite large even if D D is small beause g may be large. Table 1 illustrates this point quantitatively by showing simulations of the implied onsumption drop and welfare gain for a range of γ and θ b. Part A of the table shows that a relatively small onsumption drop of D 10 15% an be generated by a variety of ombinations of γ and θ b, indiated in bold on the diagonal of the table. Part B shows that the welfare impliations implied by the different ombinations an vary widely. With γ =5 and θ b =2, the marginal inrease in

5 R. Chetty, A. Looney / Journal of Publi Eonomis 90 (2006) Table 1 Calibrations of onsumption drop and welfare gains of soial insurane Disutility of effort in unemp. state (θ b ) Coeffiient of relative risk aversion (γ) A. Consumption drop (Δ/) B. Marginal welfare gain (γδ/) Panel A shows the implied onsumption drop without soial insurane for various ombinations of risk aversion and disutility of effort to earn inome in the bad state for the stylized model in Setion 3. The table shows that many ombinations of risk aversion and disutility of effort an generate onsumption drops similar to those observed in the data (in bold on diagonal). Panel B shows the marginal welfare gains of soial insurane for eah ombination of parameters. Welfare gains are rising on the diagonal even though the onsumption drop is onstant. expeted utility from an extra dollar of insurane is three times as large as the gain with γ=2 and θ b =1.25, even though both sets of parameters generate roughly the same D. To understand this result more onretely, onsider two different desriptions of an eonomy, both of whih ould generate a onsumption drop of 10 perent. In the first senario (low γ, low θ b ), agents have aess to redit markets and finanial networks that allow them to smooth onsumption easily when hit by a shok. In this ase, an inrease in soial insurane would primarily rowd out existing private market arrangements at the margin, with little net welfare gain. In the seond senario (high γ, high θ b ), private market insurane arrangements are very poor, but households are very risk averse. They therefore use ostly, high θ b, methods to avoid a substantial onsumption drop. In this ase, the provision of soial insurane ould yield large welfare gains despite the smoothness of onsumption, beause suh programs redue households' reliane on ostly onsumption-smoothing mehanisms when hit by shoks. It follows that one annot infer the marginal welfare gain of insurane based on the size of the onsumption drop alone. 4. Conlusion This paper has shown that empirial evidene on the response of household onsumption to inome shoks must be interpreted autiously when drawing poliy inferenes. Small onsumption flutuations need not imply that existing insurane is adequate in developing eonomies. In fat, the onverse may be true: onsumption may be smooth preisely beause the welfare osts of onsumption flutuations are very high. To evaluate the welfare onsequenes of insurane poliies, one must determine why and how households smooth onsumption beause of high risk aversion (high γ) or through good insurane arrangements (low θ b )? This question is of pratial relevane beause many

6 2356 R. Chetty, A. Looney / Journal of Publi Eonomis 90 (2006) households in low-inome ountries ould have high γ, e.g. due to subsistene onstraints. Evidene that household resort to ostly onsumption-smoothing mehanisms (e.g. Frankenberg et al., 1999; Deron, 2002; Miguel, 2005; Chetty and Looney, in press) also suggests that γ ould potentially be high for many households. Distinguishing between the two explanations of onsumption smoothness would be a useful diretion for future researh on risk and insurane. Aknowledgement We have benefited from omments by Robin Boadway, Roger Gordon, Ted Miguel, anonymous referees and seminar partiipants at the NBER East Asian Seminar. The analysis and onlusions set forth are those of the authors and do not indiate onurrene by other members of the researh staff or the Board of Governors of the Federal Reserve. Referenes Baily, Martin, Some aspets of optimal unemployment insurane. Journal of Publi Eonomis 10, Cameron, L., Worswik, C., The labor market as a smoothing devie: labor supply responses to rop loss. Review of Development Eonomis 7 (2), Chetty, Raj, in press. A general formula for the optimal level of soial insurane. Journal of Publi Eonomis. Chetty, Raj, and Looney, Adam, in press. Inome risk and the benefits of soial insurane: evidene from Indonesia and the United States. In: Ito, T., and Rose, A. eds., Fisal Poliy and Management: East Asia Seminar on Eonomis 16. Also available as NBER working paper Deron, S., Inome risk, oping strategies, and safety nets. The World Bank Researh Observer 17 (2), (Fall). Fafhamps, Marel, Rural Poverty, Risk and Development. Elgar Publishing, Cheltenham, UK. ISBN pp. Frankenberg, E., Thomas, D., Beegle, K., The Real Costs of Indonesia's Eonomi Crisis: Preliminary Findings from the Indonesia Family Life Surveys. RAND, Santa Monia, CA. DRU-2064-NIA/NICHD. Gertler, P., Gruber, J., Insuring onsumption against illness. The Amerian Eonomi Review 92 (1), (Marh, (20). Miguel, Edward, Poverty and with killing. Review of Eonomi Studies 72 (4), Morduh, Jonathan, Inome smoothing and onsumption smoothing. Journal of Eonomi Perspetives 9 (3), Morduh, Jonathan, Between the state and the market: an informal insurane path the safety net? The World Bank Researh Observer 14 (2), (August). Newbery, D., Stiglitz, J., The theory of ommodity prie stabilization rules: welfare impats and supply responses. The Eonomi Journal 89 (356), (De.). Ravallion, M., Chaudhuri, S., Risk and insurane in village India: omment. Eonometria 65 (1), (Jan.). Rosenzweig, M., Wolpin, K., Credit market onstraints, onsumption smoothing, and the aumulation of durable prodution assets in low-inome ountries: investments in bulloks in India. Journal of Politial Eonomy 101 (2), Townsend, Robert, Risk and insurane in village India. Eonometria 62 (3), (May).