This paper studies the identification and estimation of preferences and technologies in equilibrium hedonic models. In it, we identify nonparametric structural relationships with nonadditive heterogeneity. We determine what features of hedonic models can be identified from equilibrium observations in a single market under weak assumptions about the available information. We then consider use of additional information about structural functions and heterogeneity distributions. Separability conditions facilitate identification of consumer marginal utility and firm marginal product functions. We also consider how identification is facilitated using multimarket data.

“An Empirical Analysis of Racial Differences in Police Use of Force” (Fryer 2019) addresses a fundamental aspect of racial inequality in America. The paper suggests that there is evidence of discrimination against African Americans in police use of force except for officer-involved shootings. Given the importance of the issues involved, clarity is needed in understanding how this or any other piece of research contributes to understanding the nature of contemporary racial inequality and injustice. In this comment, we focus on the paper’s failure to find empirical differences in police shootings by race. This finding has received the most publicity and is the one that the paper most strongly defends: “[T]he data do more to provide a more compelling case that there is no discrimination in officer-involved shootings than they do to illuminate the reasons behind racial differences in nonlethal uses of force” (Fryer 2019, 1216). In our judgment, this paper does not establish credible evidence on the presence or absence of discrimination against African Americans in police shootings. We applaud analyses of data about police use of force of any type. But it is important to state clearly what the available data do and do not prove. The evidence provided in this paper fails to give any reason to conclude that discrimination is absent.

This paper defines and estimates general equilibrium treatment effects. The conventional approach in the literature on treatment effects ignores interactions among individuals induced by the policy interventions being studied. Focusing on the impact of tuition policy, and using estimates from our dynamic overlapping generations general equilibrium model of capital and human capital formation, we find that general equilibrium impacts of tuition on college enrollment are an order of magnitude smaller than those reported in the literature on microeconomic treatment effects. The assumptions used to justify the LATE parameter in a partial equilibrium setting do not hold in a general equilibrium setting. Policy changes induce two way flows. We extend the LATE concept to a general equilibrium setting. We present a more comprehensive evaluation to program evaluation by considering both the tax and benefit consequences of the program being evaluated and placing the analysis in a market setting.

Missing from recent discussions of tax reform is any systematic analysis of the effects of various tax proposals on skill formation. This gap in the literature in empirical public finance is due to the absence of any empirically based general equilibrium models with both human capital formation and physical capital formation that are consistent with observations on modern labor markets. This paper is a progress report on our ongoing research on formulating and estimating dynamic general equilibrium models with endogenous heterogeneous human capital accumulation. Our model explains many features of rising wage inequality in the U.S. economy (James Heckman, Lance Lochner and Christopher Taber, 1998). In this paper, we use our model to study the impacts on skill formation of proposals to switch from progressive taxes to flat income and consumption taxes. For the sake of brevity, we focus on steady states in this paper, although we study both transitions and steady states in our research.

The conventional approach to social programme evaluation focuses on estimating mean impacts of programmes. Yet many interesting questions regarding the political economy of programmes, the distribution of programme benefits and the option values conferred on programme participants require knowledge of the distribution of impacts, or features of it. This paper presents evidence that heterogeneity in response to programmes is empirically important and that classical probability inequalities are not very informative in producing estimates or bounds on the distribution of programme impacts. We explore two methods for supplementing the information in these inequalities based on assumptions about participant decision-making processes and about the strength in dependence between outcomes in the participation and non-participation states. Dependence is produced as a consequence of rational choice by participants. We test for stochastic rationality among programme participants and present and implement methods for estimating the option values of social programmes.

This paper estimates marginal returns to college for individuals induced to enroll in college by different marginal policy changes. The recent instrumental variables literature seeks to estimate this parameter, but in general it does so only under strong assumptions that are tested and found wanting. We show how to utilize economic theory and local instrumental variables estimators to estimate the effect of marginal policy changes. Our empirical analysis shows that returns are higher for individuals with values of unobservables that make them more likely to attend college. We contrast our estimates with IV estimates of the return to schooling.

Economic models for hedonic markets characterize the pricing of bundles of attributes and the demand and supply of these attributes under different assumptions about market structure, preferences and technology. (See Jan Tinbergen, 1956, Sherwin Rosen, 1974 and Dennis Epple, 1987, for contributions to this literature). While the theory is well formulated, and delivers some elegant analytical results, the empirical content of the model is under debate. It is widely believed that hedonic models fit in a single market are fundamentally underidentified and that any empirical content obtained from them is a consequence of arbitrary functional form assumptions. The problem of identification in hedonic models is a prototype for the identification problem in a variety of economic models in which agents sort on unobservable (to the economist) characteristics: models of monopoly pricing (Michael Mussa and Sherwin Rosen, 1978; Robert Wilson, 1993) and models for taxes and labor supply (James Heckman, 1974). Sorting is an essential feature of econometric models of social interactions. (See William Brock and Steven Durlauf, 2001). In this paper we address the sorting problem in hedonic models. Nesheim (2001) extends this analysis to a model with peer effects. In this paper we note that commonly used linearization strategies made to simplify estimation and justify the application of instrumental variables methods, produce identification problems. The hedonic model is generically nonlinear. It is the linearization of a fundamentally nonlinear model that produces the form of the identification problem that dominates discussion in the applied literature. Linearity is an arbitrary and misleading functional form when applied to empirical hedonic models. Our research establishes that even though sorting equilibrium in a single market implies no exclusion restrictions, the hedonic model is generically nonparametrically identified. Instrumental variables and transformation model methods identify economically relevant parameters even 1 without exclusion restrictions. Multimarket data, widely viewed as the most powerful source of identification, achieves this result only under implausible assumptions about why hedonic functions vary across markets.

This paper considers the identification and estimation of hedonic models. We establish that in an additive version of the hedonic model, technology and preferences are generically nonparametrically identified from data on demand and supply in a single hedonic market. The empirical literature that claims that hedonic models estimated on data from a single market are fundamentally underidentified is based on arbitrary linearizations that do not use all the information in the model. The exact economic model that justifies linear approximations is unappealing. Nonlinearities are generic features of equilibrium in hedonic models and a fundamental and economically motivated source of identification.