Recent work on nonparametric identification of average partial effects (APEs) from panel data require restrictions on individual or time heterogeneity. Identifying assumptions under the “generalized first-differencing” category, such as time homogeneity (Chernozhukov et al., 2013), have testable equality restrictions on the distribution of the outcome variable. This paper proposes specification tests based on these restrictions. The bootstrap critical values for the resulting Kolmogorov–Smirnov and Cramer–von-Mises statistics are shown to be asymptotically valid and deliver good finite-sample properties in Monte Carlo simulations. An empirical application illustrates the merits of testing nonparametric identification from an empiricist's perspective.

Microeconomic panel data, also known as longitudinal data or repeated measures, allow the researcher to observe the same individual across time. One of the advantages of panel data is that they allow the researcher to control for unobservable individual heterogeneity. The linear fixed effects model is the most commonly used method in empirical work to control for unobservable heterogeneity. Chapter 1 reviews the special features of the linear fixed effects model in detail, giving special attention to the definition of fixed effects and correlated random effects. It discusses the issues that arise when we move from a linear model to fully nonseparable models and reviews the two strands of the literature that are relevant for this dissertation: (1) the literature on nonlinear parametric panel data models with fixed effects, (2) the literature on nonparametric identification in nonseparable panel data models. Chapter 2 falls under the parametric nonlinear panel data models with fixed effects. Nonlinear panel data models with fixed effects are an important example in econometrics where the incidental parameter problem arises and the maximum likelihood estimator (MLE) is asymptotically biased. Bias correction of the MLE achieves consistency without increasing the asymptotic variance. Chapter 2 proposes a shrinkage estimator that combines that is shown to lead to a higher-order mean-square error improvement over the analytical bias-corrected estimator. Chapter 3 falls under the literature on nonparametric identification in nonseparable panel data models. Starting from a general DGP that exhibits nonseparability of the structural function, arbitrary individual and time heterogeneity, I give a necessary and sufficient condition for the point-identification of the APE for a subpopulation. This condition is then used to characterize the trade-off between assumptions on unobservable heterogeneity and the structural function that achieve identification. The identifying assumptions here have clear testable implications on the distribution of observables. I hence propose bootstrap-adjusted Kolmogorv- Smirnov and Cramer-von-Mises statistics to test these implications. Chapter 4 is an empirical paper that studies the issue of manipulation of air pollution data by Chinese cities. It applies tests similar in spirit to the tests proposed in Chapter 3 to test the presence of manipulation

We consider constructing probability forecasts from a parametric binary choice model under a large family of loss functions ("scoring rules"). Scoring rules are weighted averages over the utilities that heterogeneous decision makers derive from a publicly announced forecast (Schervish, 1989). Using analytical and numerical examples, we illustrate howdifferent scoring rules yield asymptotically identical results if the model is correctly specified. Under misspecification, the choice of scoring rule may be inconsequential under restrictive symmetry conditions on the data-generating process. If these conditions are violated, typically the choice of a scoring rule favors some decision makers over others.

We approach attrition in field experiments with baseline data as an identification problem in a panel model. A systematic review of the literature indicates that there is no consensus on how to test for attrition bias. We establish identifying assumptions for treatment effects for both the respondent subpopulation and the study population, and propose procedures to test their sharp implications. We then relate our proposed tests to current empirical practice, and demonstrate that the most commonly used test in the literature is not a test of internal validity in general. We illustrate the relevance of our analysis using several empirical applications.

Attrition is a common and potentially important threat to internal validity in treatment effect studies. We extend the changes-in-changes approach to identify the average treatment effect for respondents and the entire study population in the presence of attrition. Our method, which exploits baseline outcome data, can be applied to randomized experiments as well as quasi-experimental difference-in-difference designs. A formal comparison highlights that while widely used corrections typically impose restrictions on whether or how response depends on treatment, our proposed attrition correction exploits restrictions on the outcome model. We further show that the conditions required for our correction can accommodate a broad class of response models that depend on treatment in an arbitrary way. We illustrate the implementation of the proposed corrections in an application to a large-scale randomized experiment.

The ultimate impact of climate change on human systems will depend on the natural resilience of ecosystems on which societies rely as well as on adaptation measures taken by agents, individually and collectively. No sector of the economy is more reliant on climate than agriculture. Evidence from the American settlement process suggests that societies can successfully adapt to new climatic environments. Whether and how much agriculture will manage to adapt to a changing climate remains an open question in the empirical economics literature, however. This article reviews the existing evidence on weather and/or climate impacts on agricultural outcomes from the economics literature, with a focus on methodological questions. Some key econometric issues associated with climate impact measurement are discussed. We also outline important questions that have not been adequately addressed and suggest directions for future research.

China is one of the most heavily polluted nations and is also the largest agricultural producer. There are relatively few studies measuring the effects of pollution on crop yields in China, and most are based on experiments or simulation methods. We use observational data to study the impact of increased air pollution (surface ozone) on rice yields in Southeast China. We examine nonlinearities in the relationship between rice yields and ozone concentrations and find that an additional day with a maximum ozone concentration greater than 120 ppb is associated with a yield loss of 1.12% ± 0.83% relative to a day with maximum ozone concentration less than 60 ppb. We find that increases in mean ozone concentrations, SUM60, and AOT40 during panicle formation are associated with statistically significant yield losses, whereas such increases before and after panicle formation are not. We conclude that heightened surface ozone levels will potentially lead to reductions in rice yields that are large enough to have implications for the global rice market.