Four alternative but related approaches to empirical evaluation of policy interventions are studied: social experiments, natural experiments, matching methods, and instrumental variables. In each case the necessary assumptions and the data requirements are considered for estimation of a number of key parameters of interest. These key parameters include the average treatment effect, the treatment of the treated and the local average treatment effect. Some issues of implementation and interpretation are discussed drawing on the labour market programme evaluation literature.

This paper considers the nonparametric and semiparametric methods for estimating regression models with continuous endogenous regressors. We list a number of different generalizations of the linear structural equation model, and discuss how three common estimation approaches for linear equations — the “instrumental variables, ” “fitted value, ” and “control function ” approaches — may or may not be applicable to nonparametric generalizations of the linear model and to their semiparametric variants. The discussion then turns to a particular semiparametric model, the binary response model with linear index function and nonparametric error distribution, and describes in detail how estimation of the parameters of interest can be constructed using the “control function ” approach. This estimator is then applied to an empirical problem of the relation of labor force participation to nonlabor income, viewed as an endogenous regressor.

We analyze a 2 × 2 simultaneous game. We start by showing that a likelihood function defined over the set of four observable outcomes and all possible variations of the game exists only if players have incomplete information. We assume a general incomplete information structure, where players ’ beliefs are conditioned on a vector of signals Z observable by the researcher but whose exact distribution is known only to the players. The resulting Bayesian-Nash equilibrium (BNE) is characterized as a vector of conditional moment restrictions. We show how to exploit the information contained in these equilibrium conditions efficiently. The proposal takes the form of a two-step estimator. The first step estimates the unknown equilibrium beliefs using semiparametric restrictions analog to the population BNE conditions. The second step maximizes a trimmed log-likelihood function using the estimates from the first step as plug-ins for the unknown equilibrium beliefs. The trimming set is an interior subset of the support of Z where the BNE conditions have a unique solution. The resulting estimator of the vector of structural parameters ‘θ ’ is √ N−consistent and exploits all information in the model efficiently. We allow Z to

We conduct an extensive Monte Carlo experiment to examine the finite samples properties of maximum likelihood based inference in the bivariate probit model with endogenous dummy. We analyse the relative performance of alternative exogeneity tests, the impact of distributional mis-specification and the role of exclusion restrictions to achieve parameter identification in practice. The results of our investigation allow us to draw some important guidelines for the applied econo-metric practice.

conference for helpful comments. Milligan thanks the NBER for hosting him while the paper was being written and gratefully acknowledges the support of a SSHRC Standard Research Grant. Stabile gratefully acknowledges support from the Canadian Institutes for Health Research. The views expressed herein are those of the author(s) and do not necessarily reflect the views of the National Bureau of Economic Research.

We consider identification of nonparametric random utility models of multinomial choice using observation of consumer choices. Our model of preferences nests random coefficients discrete choice models widely used in practice with parametric functional form and distributional assumptions. However, our model is nonparametric and distribution free. It incorporates choice-specific unobservables, endogenous choice characteristics, unknown heteroskedasticity, and correlated taste shocks. We consider full identification of the random utility model as well as identification of demand. Under standard orthogonality, “large support,” and instrumental variables assumptions, we show identifiability of choice-specific unobservables and the joint distribution of preferences conditional on any vector of observed and unobserved characteristics. We demonstrate robustness of these results to relaxation of the large support condition and show that when this condition is replaced with a much weaker “common choice probability” condition, the demand structure is still identified. We also show that key maintained hypotheses are testable. We have had helpful conversations on this topic with Hide Ichimura, Rosa Matzkin and Yuichi Kitamura. We

We describe two methods for correcting for omitted variables in discrete choice models: a fixed effects approach and a control function approach. We apply the methods to disaggregate data on customer’s choice among television options including cable, satellite, and antenna. Estimates are similar for the two methods, and the estimated price response rises substantially when the correction is applied with either method. 1

In a sample selection or treatment effects model, common unobservables may affect both the outcome and the probability of selection in unknown ways. This paper shows that the distribution function of potential outcomes, conditional on covariates, can be identifiedgivenanobservedvariableVthat affects the treatment or selection probability in certain ways and is conditionally independent of the potential outcome equation error terms. Selection model estimators based on this identification are provided, which take the form of either simple weighted averages or GMM or two stage least squares. These estimators permit endogenous and mismeasured regressors. Empirical applications are provided to estimation of a firm investment model and a returns to schooling wage model. Portions of this paper were previously circulated under other titles including, ”Two Stage Least Squares Estimation

We consider nonparametric identification in models of differentiated products markets, using only market level observables. On the demand side we consider a nonparametric random utility model nesting random coefficients discrete choice models widely used in applied work. We allow for product/market-specific unobservables, endogenous product characteristics (e.g., prices), and high-dimensional taste shocks with arbitrary correlation and heteroskedasticity. On the supply side we specify marginal costs nonparametrically, allow for unobserved firm heterogeneity, and nest a variety of equilibrium oligopoly models. We pursue two approaches to identification. One relies on instrumental variables conditions used previously to demonstrate identification in a nonparametric regression framework. With this approach we can show identification of the demand side without reference to a particular supply model. Adding the supply side allows identification of firms’ marginal costs as well. Our second approach, more closely linked to classical identification arguments for supply and demand models, employs a change of variables approach. This leads to constructive identification results relying on exclusion and support conditions. Our results lead to a testable restriction that provides the first general formalization of Bresnahan’s (1982) intuition for empirically discriminating between alternative models of oligopoly competition.

We present methods to estimate marginal utility and marginal product functions that are nonadditive in the unobservable random terms, using observations from a single hedonic equilibrium market. We show that nonadditive marginal utility and nonadditive marginal product functions are capable of generating equilibria that exhibit bunching, as well as other types of equilibria. We provide conditions under which these types of utility and production functions are nonparametrically identified, and we propose nonparametric estimators for them. The estimators are shown to be consistent and asymptotically normal.