Su¢ cient Statistics for Welfare Analysis: A Bridge Between Structural and Reduced-Form Methods

A central methodological divide in economics is between “structural” and “reducedform” approaches. 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 precise statements about welfare. This recent literature has developed formulas that map the high-level elasticities estimated in the program evaluation literature into measures of the welfare consequences of various policies. I present a general framework that explains how many policy questions can be answered by identifying a small set of su¢ cient statistics rather than the full set of structural primitives. I use this framework to synthesize the modern literature on taxation, social insurance, and behavioral welfare economics. Finally, I discuss topics in labor economics, industrial organization, and macroeconomics that can be tackled using the su¢ cient statistic approach. This article has been prepared for the inaugural issue of the Annual Review in Economics. E-mail: [email protected]. Thanks to David Card, John Friedman, Patrick Kline, Justin McCrary, Enrico Moretti, Ariel Pakes, Emmanuel Saez, and numerous seminar participants for helpful comments and discussions. 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 “reduced-form”approach (also known as the “program evaluation” or “treatment e¤ect” approach). The division between structural and reduced-form approaches 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 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 optimal design of tax and transfer policies in public …nance to the sources of inequality in labor economics and optimal competition 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, paying particular attention to identi…cation concerns using research designs that exploit quasi-experimental exogenous variation. Reduced-form studies have identi…ed a variety of important empirical regularities, especially in labor economics, public economics, and development. Advocates of the structural paradigm criticize the reduced-form approach for estimating statistics that are not directly connected to economic models and therefore have limited policy relevance (Heckman and Vytlacil 2005).1 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. The papers develop “su¢ cient statistic”formulas that combine the advantages of reduced-form empirics –transparent and credible identi…cation –with the main advantage of structural models –the ability to make precise statements about welfare. The central concept of the su¢ cient statistic approach –illustrated in Figure 1 –is to derive formulas for the welfare consequences of policies in terms of high-level elasticities estimated in the program evaluation literature. The formulas are derived using envelope conditions and other restrictions implied by a positive 1See Table V of Heckman and Vytlacil (2005) for a more detailed comparison of the structural and treatment e¤ect approaches.