In this paper, we propose a framework to estimate the distribution of marginal effects in a general class of structural models that allow for arbitrary smooth nonlinearities, high dimensional heterogeneity, and unrestricted correlation between the persistent components of this heterogeneity and all covariates. The main idea is to form a derivative dependent variable using two periods of the panel, and use differences in outcome variables of nearby subpopulations to obtain the distribution of marginal effects. We establish constructive nonparametric identification for the population of ``stayers" (Chamberlain (1982)), and show generic non-identification for the ``movers". We propose natural semiparametric sample counterparts estimators, and establish that they achieve the optimal (minimax) rate. Moreover, we analyze their behavior through a Monte-Carlo study, and showcase the importance of allowing for nonlinearities and correlated heterogeneity through an application to demand for junk food. In this application, we establish profound differences in marginal income effects between poor and wealthy households, which may partially explain health issues faced by the less privileged population.

This paper studies the identification of causal effects of a continuous treatment using a new difference-in-difference strategy. Our approach allows for endogeneity of the treatment, and employs repeated cross-sections. It requires an exogenous change over time which affects the treatment in a heterogeneous way, stationarity of the distribution of unobservables and a rank invariance condition on the time trend. On the other hand, we do not impose any functional form restrictions or an additive time trend, and we are invariant to the scaling of the dependent variable. Under our conditions, the time trend can be identified using a control group, as in the binary difference-in-differences literature. In our scenario, however, this control group is defined by the data. We then identify average and quantile treatment effect parameters. We develop corresponding nonparametric estimators and study their asymptotic properties. Finally, we apply our results to the effect of disposable income on consumption.

This paper studies nonparametric identification in market-level demand models for differentiated products with heterogeneous consumers. We consider a general class of models that allows for the individual-specific coefficients to vary continuously across the population and give conditions under which the density of these coefficients, and hence also functionals such as the fractions of individuals who benefit from a counterfactual intervention, is identified.

The control function approach which employs an instrumental variable excluded from the outcome equation is a very common solution to deal with the problem of endogeneity in nonseparable models. Exclusion restrictions, however, are frequently controversial. We first argue that, in a nonparametric triangular structure typical of the control function literature, one can actually test this exclusion restriction provided the instrument satisfies a local irrelevance condition. Second, we investigate identification without such exclusion restrictions, i.e., if the “instrument” that is independent of the unobservables in the outcome equation also directly affects the outcome variable. In particular, we show that identification of average causal effects can be achieved in the two most common special cases of the general nonseparable model: linear random coefficients models and single index models.

We develop a linear regression panel data model allowing random coefficients to be correlated with regressors not only within periods but also across periods. The random coefficients are modeled as sums of independent possibly nonidentically distributed past and current shocks. This structure allows feedback, in the sense that future regressors can be correlated with all past shocks, and also allows all lagged dependent variables to be regressors. For each time period, we identify all marginal first moments of the random coefficients. These moments have causal interpretations. The identification results rest on a novel functional fixed point argument and lead to natural estimators of these moments. We provide simulation evidence of the usefulness of this approach. shows that increasing the sample size by a factor of four does decrease the resulting standard error by roughly a factor of two, as theory suggests.

We consider nonparametric identification and estimation of pricing kernels, or equivalently of marginal utility functions up to scale, in consumption-based asset pricing Euler equations. Ours is the first paper to prove nonparametric identification of Euler equations under low level conditions (without imposing functional restrictions or just assuming completeness). We also propose a novel nonparametric estimator based on our identification analysis, which combines standard kernel estimation with the computation of a matrix eigenvector problem. Our estimator avoids the ill-posed inverse issues associated with nonparametric instrumental variables estimators. We derive limiting distributions for our estimator and for relevant associated functionals. A Monte Carlo experiment shows a satisfactory finite sample performance for our estimators.

We consider nonparametric identi(cid:133)cation and estimation of pricing kernels, or equivalently of marginal utility functions up to scale, in consumption based asset pricing Euler equations. Ours is the (cid:133)rst paper to prove nonparametric identi(cid:133)cation of Euler equations under low level conditions (without imposing functional restrictions or just assuming completeness). We also propose a novel nonparametric estimator based on our identi(cid:133)cation analysis, which combines standard kernel estimation with the computation of a matrix eigenvector problem. Our estimator avoids the ill-posed inverse issues associated with nonparametric instrumental variables estimators. We derive limiting distributions for our estimator and for relevant associated functionals. A Monte Carlo shows a satisfactory (cid:133)nite sample performance for our estimators. JEL C14, investigate nonparametric identi(cid:133)cation and estimation of marginal utilities and asset pricing Euler equations. The main features of our nonparametric identi(cid:133)cation results are: (i) the decomposition of the pricing kernel into its marginal utility and discount factor components, cast in the form equation (1), and (ii) the use of shape restrictions (positive marginal utilities). Together, these allow us to establish nonparametric global point iden-ti(cid:133)cation of the model. Based on our identi(cid:133)cation arguments, we propose a new nonparametric estimator for marginal utilities and the discount factor that combines standard kernel estimation with the computation of a ((cid:133)nite-dimensional) matrix eigenvalue-eigenvector problem. No numerical integration or optimization is involved. The estimator is based on a sample analogue of (1) and is easy to implement, since no numerical searches are required. We establish a useful expansion for the marginal utility (suitably normalized), and limiting distribution theory for the discount factor and associated functionals of the marginal utility like the average level of relative risk aversion. Due to the well-posedness of equation (1), our estimator converges at comparable rates to ordinary nonparametric regression and does not su⁄er from issues associated with nonparametric instrumental variables estimation.

In this paper, we suggest and analyze a new class of specification tests for random coefficient models. These tests allow to assess the validity of central structural features of the model, in particular linearity in coefficients, generalizations of this notion like a known nonlinear functional relationship, or degeneracy of the distribution of a random coefficient, that is, whether a coefficient is fixed or random, including whether an associated variable can be omitted altogether. Our tests are nonparametric in nature, and use sieve estimators of the characteristic function. We provide formal power analysis against global as well as against local alternatives. Moreover, we perform a Monte Carlo simulation study, and apply the tests to analyze the degree of nonlinearity in a heterogeneous random coefficients demand model. While we find some evidence against the popular QUAIDS specification with random coefficients, it is not strong enough to reject the specification at the conventional significance level.

In this paper, we suggest and analyze a new class of specification tests for random coefficient models. These tests allow to assess the validity of central structural features of the model, in particular linearity in coefficients, generalizations of this notion like a known nonlinear functional relationship, or degeneracy of the distribution of a random coefficient, i.e., whether a coefficient is fixed or random, including whether an associated variable can be omitted altogether. Our tests are nonparametric in nature, and use sieve estimators of the characteristic function. We provide formal power analysis against global as well as against local alternatives. Moreover, we perform a Monte Carlo simulation study, and apply the tests to analyze the degree of nonlinearity in a heterogeneous random coefficients demand model. While we find some evidence against the popular QUAIDS specification with random coefficients, it is not strong enough to reject the specification at the conventional significance level.

SummaryThis paper proposes a framework to model welfare effects that are associated with a price change in a population of heterogeneous consumers. The framework is similar to that of Hausman and Newey (Econometrica, 1995, 63, 1445–1476), but allows for more general forms of heterogeneity. Individual demands are characterized by a general model that is nonparametric in the regressors, as well as monotonic in unobserved heterogeneity, allowing us to identify the distribution of welfare effects. We first argue why a decision maker should care about this distribution. Then we establish constructive identification, propose a sample counterparts estimator, and analyze its large‐sample properties. Finally, we apply all concepts to measuring the heterogeneous effect of a change of gasoline price using US consumer data and find very substantial differences in individual effects across quantiles.

It is almost self-evident that social interactions can determine economic behavior and outcomes. Yet, information on social ties does not exist in most publicly available and widely used datasets. We present methods to recover information on the entire structure of social networks from observational panel data that contains no information on social ties between individuals. In the context of a canonical social interactions model, we provide sufficient conditions under which the social interactions matrix, endogenous and exogenous social effect parameters are all globally identified. We describe how high-dimensional estimation techniques can be used to estimate the model based on the Adaptive Elastic Net GMM method. We showcase our method in Monte Carlo simulations using two stylized and two real world network structures. Finally, we employ our method to study tax competition across US states. We find the identified network structure of tax competition differs markedly from the common assumption of tax competition between geographically neighboring states. We analyze the identified social interactions matrix to provide novel insights into the long-standing debate on the relative roles of factor mobility and yardstick competition in driving tax setting behavior across states. Most broadly, our method shows how the analysis of social interactions can be usefully extended to economic realms where no network data exists. JEL Classification: C18, C31, D85, H71.

This paper studies binary response static games of complete information allowing complex heterogeneity through a random coefficients specification. The main result of the paper establishes nonparametric point identification of the joint density of all random coefficients except those on interaction effects. Under additional independence assumptions, we identify the joint density of the interaction coefficients. Moreover, we prove that in the presence of covariates that are common to both players, the player-specific coefficient densities are identified, while the joint density of all random coefficients is not point-identified. However, we do provide bounds on counterfactual probabilities that involve this joint density.

This paper discusses nonparametric estimation of the distribution of random coefficients in a structural model that is nonlinear in the random coefficients. We establish that the problem of recovering the probability density function ( pdf ) of random parameters falls into the class of convexly-constrained inverse problems. The framework offers an estimation method that separates computational solution of the structural model from estimation. We first discuss nonparametric identification. Then, we propose two alternative estimation procedures to estimate the density and derive their asymptotic properties. Our general framework allows us to deal with unobservable nuisance variables, e.g., measurement error, but also covers the case when there are no such nuisance variables. Finally, Monte Carlo experiments for several structural models are provided which illustrate the performance of our estimation procedure.

This paper studies nonparametric identification in market level demand models for differentiated products with heterogeneous consumers. We consider a general class of models that allows for the individual specific coefficients to vary continuously across the population and give conditions under which the density of these coefficients, and hence also functionals such as welfare measures, is identified. A key finding is that two leading models, the BLP-model (Berry, Levinsohn, and Pakes, 1995) and the pure characteristics model (Berry and Pakes, 2007), require considerably different conditions on the support of the product characteristics.

Recall that ̂(| ) = 01β̂ (|) where 1 is defined after (4.3). Noting that uniformly in ( ) ∈ R×U0 S () =  ()S+ ()  and B (;) =  ()BG+1 (|)+  ¡  ¢  with ̄ ≡ +  we have ̂(|)−(|) = +101S−1  BG+1 (|) +  ()−1 01S−1  V (;) + (̄) Proof of Lemma C.2. Noting that  ( ;) − ̄ ( ;) =  () and ̄ ( ;) =  ( + ) by the proof of (b) below, (a) follows from Theorem 2.1 of Su and White (2012). To prove (b), write ̄ ( ;) = 1The compact support of the kernel function in Masry (1996) can be easily relaxed, following the line of proof in Hansen (2008, Theorem 4).

In this paper, we propose and implement an estimator for price elasticities in demand models that makes use of Panel data. Our underlying demand model is nonparametric, and accommodates general distributions of product-specific unobservables which can lead to endogeneity of price. Our approach allows these unobservables to vary over time while, at the same time, not requiring the availability of instruments which are orthogonal to these unobservables. Monte Carlo simulations demonstrate that our estimator works remarkably well, even with modest sample sizes. We provide an illustrative application to estimating the cross-price elasticity matrix for carbonated soft drinks.

Do individuals use all information at their disposal when forming expectations about future events? In this paper we present an econometric framework to answer this question. We show how individual information sets can be characterized by simple nonparametric exclusion restrictions and provide a quantile based test for constrained information processing. In particular, our methodology does not require individuals’ expectations to be rational, and we explicitly allow for individuals to have access to sources of information which the econometrician cannot observe. As an application, we use microdata on individual income expectations to study which information agents employ when forecasting future earnings. Consistent with models where information processing is limited, we nd that individuals’ information sets are coarse in that valuable information is discarded. We then quantify the utility costs of coarse information within a standard consumption life-cycle model. Consumers would be willing to pay 0.04% of their permanent income to incorporate the econometrician’s information set in their forecasts.

In this paper, we suggest and analyze a new class of specification tests for random coefficient models. These tests allow to assess the validity of central structural features of the model, in particular linearity in coefficients and generalizations of this notion like a known nonlinear functional relationship. They also allow to test for degeneracy of the distribution of a random coefficient, i.e., whether a coefficient is fixed or random, including whether an associated variable can be omitted altogether. Our tests are nonparametric in nature, and use sieve estimators of the characteristic function. We analyze their power against both global and local alternatives in large samples and through a Monte Carlo simulation study. Finally, we apply our framework to analyze the specification in a heterogeneous random coefficients consumer demand model.

This paper is concerned with testing a core economic restriction, negative semidefiniteness of the Slutsky matrix. We consider a system of nonseparable structural equations with infinite dimensional unobservables, and employ quantile regression methods because they allow us to utilize the entire distribution of the data. Difficulties arise because the restriction involves several equations, while the quantile is a univariate concept. We establish that we may use quantiles of linear combinations of the dependent variable, develop a new empirical process based test that applies kernel quantile estimators, and investigate its finite and large sample behavior. Finally, we apply all concepts to Canadian microdata.