An important class of structural models studies the determinants of skill formation and the optimal timing of interventions. In this article, I provide new identification results for these models and investigate the effects of seemingly innocuous scale and location restrictions on parameters of interest. To do so, I first characterize the identified set of all parameters without these additional restrictions and show that important policy-relevant parameters are point identified under weaker assumptions than commonly used in the literature. The implications of imposing standard scale and location restrictions depend on how the model is specified, but they generally impact the interpretation of parameters and may affect counterfactuals. Importantly, with the popular constant elasticity of substitution (CES) production function, commonly used scale restrictions fix identified parameters and lead to misspecification. Consequently, simply changing the units of measurements of observed variables might yield ineffective investment strategies and misleading policy recommendations. I show how existing estimators can easily be adapted to solve these issues. As a byproduct, this article also presents a general and formal definition of when restrictions are truly normalizations.

This article studies non-parametric panel data models with multidimensional, unobserved individual effects when the number of time periods is fixed. I focus on models where the unobservables have a factor structure and enter an unknown structural function non-additively. The setup allows the individual effects to impact outcomes differently in different time periods and it allows for heterogeneous marginal effects. I provide sufficient conditions for point identification of all parameters of the model. Furthermore, I present a non-parametric sieve maximum likelihood estimator as well as flexible semiparametric and parametric estimators. Monte Carlo experiments demonstrate that the estimators perform well in finite samples. Finally, in an empirical application, I use these estimators to investigate the relationship between teaching practice and student achievement. The results differ considerably from those obtained with commonly used panel data methods.

This paper provides positive testability results for the identification condition in a nonparametric instrumental variable model, known as completeness, and it links the outcome of the test to properties of an estimator of the structural function. In particular, I show that the data can provide empirical evidence in favor of both an arbitrarily small identified set as well as an arbitrarily small asymptotic bias of the estimator. This is the case for a large class of complete distributions as well as certain incomplete distributions. As a byproduct, the results can be used to estimate an upper bound of the diameter of the identified set and to obtain an easy to report estimator of the identified set itself.

This study provides a structural analysis of detailed, alternating‐offer bargaining data from eBay, deriving bounds on buyers and sellers private value distributions and the gains from trade using a range of assumptions on behavior and the informational environment. These assumptions range from weak (assuming only that acceptance and rejection decisions are rational) to less weak (e.g., assuming that bargaining offers are weakly increasing in players' private values). We estimate the bounds and show what they imply for consumer negotiation behavior and inefficient breakdown. For the median product, bargaining ends in impasse in 37% of negotiations even when the buyer values the good more than the seller.

We propose a nonparametric method to study which characteristics provide incremental information for the cross-section of expected returns. We use the adaptive group LASSO to select characteristics and to estimate how selected characteristics affect expected returns nonparametrically. Our method can handle a large number of characteristics and allows for a flexible functional form. Our implementation is insensitive to outliers. Many of the previously identified return predictors don’t provide incremental information for expected returns, and nonlinearities are important. We study our method’s properties in simulations and find large improvements in both model selection and prediction compared to alternative selection methods.

We propose a simple and computationally attractive method to deal with missing data in in cross-sectional asset pricing using conditional mean imputations and weighted least squares, cast in a generalized method of moments (GMM) framework. This method allows us to use all observations with observed returns; it results in valid inference; and it can be applied in nonlinear and high-dimensional settings. In simulations, we find it performs almost as well as the efficient but computationally costly GMM estimator. We apply our procedure to a large panel of return predictors and find that it leads to improved out-of-sample predictability.