We reconsider the identification and estimation of Gorman-Lancasterstyle hedonic models of demand for differentiated products in the spirit of Sherwin Rosen. We generalize Rosen’s first stage to account for product characteristics that are not observed and to allow the hedonic pricing function to have a general nonseparable form. We take an alternative semiparametric approach to Rosen’s second stage in which we assume that the parametric form of utility is known, but we place no restrictions on the aggregate distribution of utility parameters. If there are only a small number of products, we show how to construct bounds on individuals’ utility parameters, as well as other economic objects such as aggregate demand and consumer surplus. We apply our methods to estimating the demand for personal computers.

This paper builds on the structural equations, treatment effect, and machine learning literatures to provide a causal framework that permits the identification and estimation of causal effects from observational studies. We begin by providing a causal interpretation for standard exogenous regressors and standard “valid” and “relevant” instrumental variables. We then build on this interpretation to characterize extended instrumental variables (EIV) methods, that is methods that make use of variables that need not be valid instruments in the standard sense, but that are nevertheless instrumental in the recovery of causal effects of interest. After examining special cases of single and double EIV methods, we provide necessary and sufficient conditions for the identification of causal effects by means of EIV and provide consistent and asymptotically normal estimators for the effects of interest.

Causality is a very intuitive notion that is difficult to make precise without lapsing into tautology. Two ingredients are central to any definition: (1) a set of possible outcomes (counterfactuals) generated by a function of a set of ‘‘factors’ ’ or ‘‘determinants’ ’ and (2) a manipulation where one (or more) of the ‘‘factors’ ’ or ‘‘determinants’’ is changed. An effect is realized as a change in the argument of a stable function that produces the same change in the outcome for a class of interventions that change the ‘‘factors’ ’ by the same amount. The outcomes are compared at different levels of the factors or generating variables. Holding all factors save one at a constant level, the change in the outcome associated with manipulation of the varied factor is called a causal effect of the manipulated factor. This definition, or some version of it, goes back to Mill (1848) and Marshall (1890). Haavelmo’s (1943) made it more precise within the context of linear equations models. The phrase ‘ceteris paribus’ (everything else held constant) is a mainstay of economic analysis

We consider the identification of a Markov process {Wt, X ∗ t} when only {Wt}, a subset of the variables, are observed. In structural dynamic models, Wt includes the sequences of choice variables and observed state variables of an optimizing agent, while X ∗ t denotes the sequence of serially correlated unobserved state variables. The to depend Markov setting allows the distribution of the unobserved state variable X ∗ t on Wt−1 and X ∗ t−1. In the non-stationary case, we show that the Markov transition density fWt,X ∗ t |Wt−1,X ∗ is identified from the observation of five periods of data t−1 Wt+1, Wt, Wt−1, Wt−2, Wt−3 under reasonable assumptions. In the stationary case, only four observations Wt+1, Wt, Wt−1, Wt−2 are required. Identification of fWt,X ∗ t |Wt−1,X ∗ t−1 is a crucial input in methodologies for estimating Markovian dynamic models based on the “conditional-choice-probability (CCP)” approach pioneered by Hotz and Miller.

This paper develops a generalization of the widely used Difference-In-Difference (DID) method for evaluating the effects of policy changes. We propose a model that allows the control group and treatment groups to have different average benefits from the treatment. The assumptions of the proposed model are invariant to the scaling of the outcome. We provide conditions under which the model is nonparametrically identified and propose an estimator that can be applied using either repeated cross-section or panel data. Our approach provides an estimate of the entire counterfactual distribution of outcomes that would have been experienced by the treatment group in the absence of the treatment, and likewise for the untreated group in the presence of the treatment. Thus, it enables the evaluation of policy interventions according to criteria such as a mean-variance tradeoff. We also propose methods for inference, showing that our estimator for the average treatment effect is root-N consistent and asymptotically normal. We consider extensions to allow for covariates, discrete dependent variables, and multiple groups and time periods.

When demands for heterogeneous goods in a concentrated market shift over time due to network or contagion effects, forward-looking firms consider the strategic impact of investment, pricing, and other conduct. Network effects may be a substantial barrier to entry, giving both entrants and incumbents powerful strategic incentives to “tip” the market. A Markov perfect equilibrium model captures this strategic behavior, and permits the comparison of “as is ” market trajectories with “but for ” trajectories under counterfactuals where “bad acts ” by some firms are eliminated. Our analysis is applied to a stylized description of the browser war between Netscape and Microsoft. Appendices give conditions for econometric identification and estimation of a Markov perfect equilibrium model from observations on partial trajectories, and discuss estimation of the impacts of

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.

This note revisits the identification theorems of B. Brown (1983) and Roehrig (1988). We describe an error in the proofs of the main identification theorems in these papers, and provide an important counterexample to the theorems on the identification of the reduced form. Specifically, contrary to the theorems, the reduced form of a nonseparable simultaneous equations model is not identified even under the assumptions of those papers. We conclude the note with a conjecture that it may be possible to use classical exclusion restrictions to recover some of the key implications of the theorems. ∗We have had very helpful conversations with Pat Bayer, Don Brown, Yossi Feinberg, Guido Imbens, Yuliy Sannikov, Andy Skrzypacz, and Chris Timmons. Any remaining In this note, we reconsider the nonparametric identification of nonlinear simultaneous equations models, as in B. Brown (1983) and Roehrig (1988). We

For vectors z and w and scalar v, let r(v, z, w) be a function that can be nonparametrically estimated consistently and asymptotically normally, such as a distribution, density, or conditional mean regression function. We provide consistent, asymptotically normal nonparametric estimators for the functions G and H, wherer(v, z, w) = H[vG(z),w], and some related models. This framework encompasses homothetic and homothetically separable functions, and transformed partly additive models r(v, z, w) =h[v + g(z),w] for unknown functions g and h. Such models reduce the curse of dimensionality, provide a natural generalization of linear index models, and are widely used in utility, production, and cost function applications. We also provide an estimator of G that is oracle efficient, achieving the same performance as an estimator based on local least squares knowing H.

This paper unifies three complementary approaches to defining, identifying, and estimating causal effects: the classical structural equations approach of the Cowles Commision; the treatment effects framework of Rubin (1974) and Rosenbaum and Rubin (1983); and the Directed Acyclic Graph (DAG) approach of Pearl. The settable system framework nests these prior approaches, while affording significant improvements to each. For example, the settable system approach permits identification of causal effects without requiring exogenous instruments; instead, a weaker conditional exogeneity condition suffices. It removes the stable unit treatment value assumption of the treatment effect approach and provides significant insight into the selection of covariates. It generalizes the DAG ap-proach by accommodating mutual causality and attributes. We provide a variety of results ensuring structural identification of general covariate-conditioned average causal effects, laying the founda-tion for parametric and nonparametric estimation of effects of interest and new tests for structural identification.