Takeup, Social Multipliers, and Optimal Social Insurance∗ Kory Kroft† THIS DRAFT: October, 2006 FIRST DRAFT: February, 2006 Abstract This paper examines optimal social insurance with endogenous takeup. A simple framework is presented that accounts for behavioral responses along both the intensive and extensive margins. Two formulations of takeup are considered: in the first, individuals face a takeup cost that is exogenous; in the second, the cost depends endogenously on the number of people who take up social benefits. The latter formu- lation captures the intuitive notion that taking up benefits is less costly, possibly due to lower stigma or learning, when others are also taking up benefits. Such endogenous costs to takeup lead to a social mul- tiplier. Formulas for the optimal replacement rate are derived directly using the behavioral elasticities and the social multiplier. These formulas are presented in the tradition of the optimal income taxation literature, facilitating intuition and interpretation, and leading to several novel insights: first, the optimal replacement rate depends on the consumption smoothing benefit- for the segment of the population that receives UI benefits- and the takeup elasticity; second, for a given aggregate takeup elasticity, the precise decomposition into direct effects and multiplier effects matters, implying that knowledge of the social multiplier is important for conducting normative analysis. This paper uses a reform-based strategy to estimate the social multiplier in unemployment insurance takeup. This leads to an estimate of 1.9 for the social multiplier. On the consumption side, a large consumption smoothing role is found when the full takeup assumption is relaxed: consumption for UI recipients, in the absent of unemployment insurance benefits, would fall by 4 times as much as consumption for non-UI recipients. Formulas for the optimal replacement rate are calibrated using the estimated social multiplier, along with the behavioral elasticities and consumption measures. Social multiplier effects significantly increase optimal replacement rates. ∗I would like to thank Alan Auerbach, David Card, Raj Chetty, Bryan Graham, and Emmanuel Saez for many helpful comments, corrections, and suggestions. Useful feedback from Madhav Chandrasekher, Paul Chen, Thomas Davidoff, Zack Grossman, Rafael Lalive, Day Manoli, Yooki Park, Devin Pope, and Justin Sydnor is also gratefully acknowledged. Finally, a special thank you to Raj Chetty and Adam Szeidl for PSID data and to Brian McCall for CPS data. †Department of Economics, University of California - Berkeley, 549 Evans Hall 3880, Berkeley, CA 94720. E-MAIL: [email protected]. WEB: http://korykroft.googlepages.com/ 1 1 Introduction One of the central assumptions in the theory of social insurance provision is that all agents who are eligible for benefits claim them. This assumption originates in the seminal paper by Baily (1978). It is also present in more recent analyses of optimal unemployment insurance (Lentz, 2005; Shimer and Werning, 2005; Chetty, 2006). Empirically, the takeup rate, defined as the fraction of eligible individuals who claim benefits when unemployed, is well below one, with estimates ranging from .4 to .7 (Blank and Card, 1991; Vroman, 1991; McCall, 1995; Anderson and Meyer, 1997). As Currie (2004) remarks, “although people generally have means-tested programs in the United States in mind when they discuss takeup (where entitlement is conditional on income), low takeup is also a problem in many non means-tested social insurance programs and in other countries...takeup of Unemployment Insurance (UI) is generally similar to takeup of programs such as AFDC and Food Stamps.”1 In addition, takeup rates tend to correlate positively with the size of expected benefits.2 This evidence suggests that taking up benefits is costly and calls into question the “full takeup” assumption. Moreover, a recent empirical literature has emerged suggesting the prominence of social interactions in takeup decisions (Borjas and Hilton, 1996; Bertrand et al., 2000; Sorensen, 2001; Duflo and Saez, 2003; Aizer and Currie, 2004). This has motivated some to consider the theoretical implications of social inter- actions in social insurance programs (Lindbeck et al., 1999; Lindbeck and Persson, 2006; Lindbeck, 2006). These studies are purely positive analyses however and as a result, do not cast light on the debate of whether it is important to decompose the general equilibrium effect from a policy change into partial equilibrium and social multiplier effects (Glaeser et al., 2003). The goal of this paper is to derive elasticity-based formulas for the optimal replacement rate in a setting with endogenous takeup and social interactions in takeup. A simple framework is developed that encom- 1Low takeup is also a feature of health insurance programs like Medicaid and CHIP (Remler et al., 2001). 2The consensus elasticity of takeup with respect to benefits is around .4. Blank and Card (1991) find evidence of a takeup response using state-level data but not micro data; McCall (1995) and Anderson and Meyer (1997) estimate elasticities in the range .35-.5. 1 passes behavioral responses along both the intensive and extensive margin. Two formulations of takeup are considered, one where the takeup cost is exogenous and a second where the takeup cost endogenously de- pends on the number people who takeup social benefits.3 The latter formulation captures the intuitive notion that when others are taking up benefits, takeup might be less costly due to a reduction in social stigma or increased learning. Formulas for the optimal replacement rate are derived directly using behavioral elas- ticities. These formulas are presented in the tradition of the optimal income taxation literature, facilitating intuition and interpretation, and leading to several novel insights. First, the optimal replacement rate depends on the sum of the behavioral elasticities and the consump- tion smoothing benefit– for the segment of the population that receives UI benefits. To see the intuition for this, consider the thought experiment of increasing benefits by $1. This change induces behavioral re- sponses along the intensive margin and extensive margin. On the intensive margin, individuals will choose to stay unemployed longer, an effect that is summarized by the duration elasticity. Next, when benefits are increased, costs will become outweighed for some, leading to a higher takeup rate. This latter response– one that has heretofore been ignored in the literature on optimal social insurance– is represented by the elasticity of takeup with respect to benefits. The finding that the formula depends on the consumption smoothing ben- efit for UI recipients is a primae facie one; nevertheless, since the decision to takeup benefits has not been formalized in models of unemployment insurance, the literature has not distinguished between UI recipients and non-UI recipients when estimating the consumption smoothing benefits of unemployment insurance and when calibrating optimal replacement rates. This paper fills this gap. Second, when social interactions are present, the formula depends on the social multiplier. The formula shows that for a given aggregate takeup elasticity, the precise decomposition into direct effects and multiplier effects matters. Intuitively, this follows since agents do not internalize the effect of their takeup decision on others, generating an externality that social welfare policy seeks to correct. This paper shows that this externality is fully summarized by the social multiplier, along with private utility. The implication is that 3Davidson and Woodbury (1997) consider the impact of less than full eligibility on optimal unemployment insurance. They find that accounting properly for UI-ineligibles raises the optimal replacement rate by around 10 percentage points to 70-80%. To focus on the issue of takeup, this paper assumes that all individuals who become unemployed are eligible for benefits. 2 the social multiplier is a sufficient statistic, that can be used with the other reduced-form parameters of the model, to test whether existing unemployment insurance benefit levels are optimal, in the presence of social spillovers. There is currently no evidence on the importance of spillover effects in unemployment insurance takeup. This paper estimates the social multiplier using a reform-based strategy, one that exploits policy variation in benefit levels across states and years. It is shown that by removing a single layer of identification from a quasi-experimental design very standard to the social insurance literature, it is possible to recover an estimate for the social multiplier. The intuition underlying this identification strategy is related to the well-known idea that social interactions cause excess between-group variance, a result that has been formally established for models with continuous action spaces in Glaeser and Scheinkman (2002) and Graham (2005), and for the discrete action model considered in Glaeser et al. (1996). A contribution of this paper is to demonstrate that for a more general interactive process with discrete actions, based on individual optimization, the social multiplier is equal to the ratio of the ‘between-variance’ to the ‘within-variance’.4 Interestingly, this ratio is also the F-statistic for the equality of group means in a standard one-way analysis of variance (ANOVA), making it relatively simple to compute estimates. Importantly however, if there are omitted variable cor-