Sufficient Statistics for Welfare Analysis: A Bridge Between Structural and Reduced-Form Methods

The debate between “structural” and “reduced-form”approaches has generated substantial controversy in applied economics. This article reviews a recent literature in public economics that combines the advantages of reduced-form strategies –transparent and credible identi…cation –with an important advantage of structural models – the ability to make predictions about counterfactual outcomes and welfare. This literature has developed formulas for the welfare consequences of various policies that are functions of reduced-form elasticities rather than structural primitives. I present a general framework that shows how many policy questions can be answered by estimating a small set of su¢ cient statistics using program evaluation methods. I use this framework to synthesize the modern literature on taxation, social insurance, and behavioral welfare economics. Finally, I discuss problems in macroeconomics, labor, development, and industrial organization that could be tackled using the su¢ cient statistic approach. This article has been prepared for the …rst issue of the Annual Review of Economics. E-mail: [email protected]. Thanks to Joshua Angrist, David Card, Gary Chamberlain, Liran Einav, Amy Finkelstein, John Friedman, James Hines, Hilary Hoynes, Lawrence Katz, Patrick Kline, Erzo Luttmer, Justin McCrary, Enrico Moretti, Ariel Pakes, Emmanuel Saez, Juan Carlos Suarez Serrato, Glen Weyl, and numerous seminar participants for helpful comments and discussions. Gregory Bruich provided outstanding research assistance. I am grateful for funding from NSF grant SES 0645396. There are two competing paradigms for policy evaluation and welfare analysis in economics: the “structural” approach and the “reduced-form” approach (also known as the “program evaluation” or “treatment e¤ect” approach). The division between structural and reduced-form methods has split the economics profession into two camps whose research programs have evolved almost independently despite focusing on similar questions. The structural approach speci…es complete models of economic behavior and estimates or calibrates the primitives of such models. Armed with the fully estimated model, these studies then simulate the e¤ects of changes in policies and the economic environment on behavior and welfare. This powerful methodology has been applied to an array of topics, ranging from the design of tax and transfer policies in public …nance to the sources of inequality in labor economics and antitrust policy in industrial organization. Critics of the structural approach argue that it is di¢ cult to identify all primitive parameters in an empirically compelling manner because of selection e¤ects, simultaneity bias, and omitted variables. These researchers instead advocate “reduced-form”strategies that estimate statistical relationships, placing priority on identi…cation of causal e¤ects using research designs that exploit quasi-experimental variation.1 Reduced-form studies have identi…ed a variety of important empirical regularities, especially in labor, public, and development economics. Advocates of the structural paradigm criticize the reduced-form approach for estimating statistics that are not policy invariant parameters of economic models, and therefore have limited relevance for policy and welfare analysis (Rosenzweig and Wolpin 2000, Heckman and Vytlacil 2005, Deaton 2009).2 This paper argues that a set of papers in public economics written over the past decade (see Table 1) provide a middle ground between the two methods. These papers develop “su¢ cient statistic”formulas that combine the advantages of reduced-form empirics –transparent and credible identi…cation –with an important advantage of structural models –the ability to make precise statements about welfare. The central concept of the su¢ cient sta1The term “reduced-form”is a misnomer: the relationships that are estimated are generally not reducedforms of economic models. I use “reduced form” here simply for consistency with standard terminology used to describe design-based studies that identify treatment e¤ects. 2See Section 1 of Rosenzweig and Wolpin (2000) and Table V of Heckman and Vytlacil (2005) for a more detailed comparison of the structural and treatment e¤ect approaches.