Program Evaluation and Causal Inference With High‐Dimensional Data

In this paper, we provide efficient estimators and honest confidence bands for a variety of treatment effects including local average (LATE) and local quantile treatment effects (LQTE) in data‐rich environments. We can handle very many control variables, endogenous receipt of treatment, heterogeneous treatment effects, and function‐valued outcomes. Our framework covers the special case of exogenous receipt of treatment, either conditional on controls or unconditionally as in randomized control trials. In the latter case, our approach produces efficient estimators and honest bands for (functional) average treatment effects (ATE) and quantile treatment effects (QTE). To make informative inference possible, we assume that key reduced‐form predictive relationships are approximately sparse. This assumption allows the use of regularization and selection methods to estimate those relations, and we provide methods for post‐regularization and post‐selection inference that are uniformly valid (honest) across a wide range of models. We show that a key ingredient enabling honest inference is the use of orthogonal or doubly robust moment conditions in estimating certain reduced‐form functional parameters. We illustrate the use of the proposed methods with an application to estimating the effect of 401(k) eligibility and participation on accumulated assets. The results on program evaluation are obtained as a consequence of more general results on honest inference in a general moment‐condition framework, which arises from structural equation models in econometrics. Here, too, the crucial ingredient is the use of orthogonal moment conditions, which can be constructed from the initial moment conditions. We provide results on honest inference for (function‐valued) parameters within this general framework where any high‐quality, machine learning methods (e.g., boosted trees, deep neural networks, random forest, and their aggregated and hybrid versions) can be used to learn the nonparametric/high‐dimensional components of the model. These include a number of supporting auxiliary results that are of major independent interest: namely, we (1) prove uniform validity of a multiplier bootstrap, (2) offer a uniformly valid functional delta method, and (3) provide results for sparsity‐based estimation of regression functions for function‐valued outcomes.     

Bargaining With Asymmetric Information: An Empirical Study of Plea Negotiations

This paper empirically investigates how sentences to be assigned at trial impact plea bargaining. The analysis is based on the model of bargaining with asymmetric information by Bebchuk, 1984. I provide conditions for the nonparametric identification of the model, propose a consistent nonparametric estimator, and implement it using data on criminal cases from North Carolina. Employing the estimated model, I evaluate how different sentencing reforms affect the outcome of criminal cases. My results indicate that lower mandatory minimum sentences could greatly reduce the total amount of incarceration time assigned by the courts, but may increase conviction rates. In contrast, the broader use of non‐incarceration sentences for less serious crimes reduces the number of incarceration convictions, but has a very small effect over the total assigned incarceration time. I also consider the effects of a ban on plea bargains. Depending on the case characteristics, over 20 percent of the defendants who currently receive incarceration sentences would be acquitted if plea bargains were forbidden.     

Linear Regression for Panel With Unknown Number of Factors as Interactive Fixed Effects

In this paper, we study the least squares (LS) estimator in a linear panel regression model with unknown number of factors appearing as interactive fixed effects. Assuming that the number of factors used in estimation is larger than the true number of factors in the data, we establish the limiting distribution of the LS estimator for the regression coefficients as the number of time periods and the number of cross‐sectional units jointly go to infinity. The main result of the paper is that under certain assumptions, the limiting distribution of the LS estimator is independent of the number of factors used in the estimation as long as this number is not underestimated. The important practical implication of this result is that for inference on the regression coefficients, one does not necessarily need to estimate the number of interactive fixed effects consistently.     

Identification of Nonseparable Models Using Instruments With Small Support

I consider nonparametric identification of nonseparable instrumental variables models with continuous endogenous variables. If both the outcome and first stage equations are strictly increasing in a scalar unobservable, then many kinds of continuous, discrete, and even binary instruments can be used to point‐identify the levels of the outcome equation. This contrasts sharply with related work by Imbens and Newey, 2009 that requires continuous instruments with large support. One implication is that assumptions about the dimension of heterogeneity can provide nonparametric point‐identification of the distribution of treatment response for a continuous treatment in a randomized controlled experiment with partial compliance.     

Spurious Inference in Reduced‐Rank Asset‐Pricing Models

This note studies some seemingly anomalous results that arise in possibly misspecified, reduced‐rank linear asset‐pricing models estimated by the continuously updated generalized method of moments. When a spurious factor (that is, a factor that is uncorrelated with the returns on the test assets) is present, the test for correct model specification has asymptotic power that is equal to the nominal size. In other words, applied researchers will erroneously conclude that the model is correctly specified even when the degree of misspecification is arbitrarily large. The rejection probability of the test for overidentifying restrictions typically decreases further in underidentified models where the dimension of the null space is larger than 1.     

Fixed‐Smoothing Asymptotics in a Two‐Step Generalized Method of Moments Framework

This paper develops the fixed‐smoothing asymptotics in a two‐step generalized method of moments (GMM) framework. Under this type of asymptotics, the weighting matrix in the second‐step GMM criterion function converges weakly to a random matrix and the two‐step GMM estimator is asymptotically mixed normal. Nevertheless, the Wald statistic, the GMM criterion function statistic, and the Lagrange multiplier statistic remain asymptotically pivotal. It is shown that critical values from the fixed‐smoothing asymptotic distribution are high order correct under the conventional increasing‐smoothing asymptotics. When an orthonormal series covariance estimator is used, the critical values can be approximated very well by the quantiles of a noncentral F distribution. A simulation study shows that statistical tests based on the new fixed‐smoothing approximation are much more accurate in size than existing tests.     

On Completeness and Consistency in Nonparametric Instrumental Variable Models

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.     

A Test of Exogeneity Without Instrumental Variables in Models With Bunching

This paper presents a test of the exogeneity of a single explanatory variable in a multivariate model. It does not require the exogeneity of the other regressors or the existence of instrumental variables. The fundamental maintained assumption is that the model must be continuous in the explanatory variable of interest. This test has power when unobservable confounders are discontinuous with respect to the explanatory variable of interest, and it is particularly suitable for applications in which that variable has bunching points. An application of the test to the problem of estimating the effects of maternal smoking in birth weight shows evidence of remaining endogeneity, even after controlling for the most complete covariate specification in the literature.     

Matching on the Estimated Propensity Score

Propensity score matching estimators (Rosenbaum and Rubin (1983)) are widely used in evaluation research to estimate average treatment effects. In this article, we derive the large sample distribution of propensity score matching estimators. Our derivations take into account that the propensity score is itself estimated in a first step, prior to matching. We prove that first step estimation of the propensity score affects the large sample distribution of propensity score matching estimators, and derive adjustments to the large sample variances of propensity score matching estimators of the average treatment effect (ATE) and the average treatment effect on the treated (ATET). The adjustment for the ATE estimator is negative (or zero in some special cases), implying that matching on the estimated propensity score is more efficient than matching on the true propensity score in large samples. However, for the ATET estimator, the sign of the adjustment term depends on the data generating process, and ignoring the estimation error in the propensity score may lead to confidence intervals that are either too large or too small.     

Testing for Causal Effects in a Generalized Regression Model With Endogenous Regressors

A unifying framework to test for causal effects in nonlinear models is proposed. We consider a generalized linear‐index regression model with endogenous regressors and no parametric assumptions on the error disturbances. To test the significance of the effect of an endogenous regressor, we propose a statistic that is a kernel‐weighted version of the rank correlation statistic (tau) of Kendall (1938). The semiparametric model encompasses previous cases considered in the literature (continuous endogenous regressors (Blundell and Powell (2003)) and a single binary endogenous regressor (Vytlacil and Yildiz (2007))), but the testing approach is the first to allow for (i) multiple discrete endogenous regressors, (ii) endogenous regressors that are neither discrete nor continuous (e.g., a censored variable), and (iii) an arbitrary “mix” of endogenous regressors (e.g., one binary regressor and one continuous regressor).     

Uncertainty Shocks in a Model of Effective Demand

Can increased uncertainty about the future cause a contraction in output and its components? An identified uncertainty shock in the data causes significant declines in output, consumption, investment, and hours worked. Standard general‐equilibrium models with flexible prices cannot reproduce this comovement. However, uncertainty shocks can easily generate comovement with countercyclical markups through sticky prices. Monetary policy plays a key role in offsetting the negative impact of uncertainty shocks during normal times. Higher uncertainty has even more negative effects if monetary policy can no longer perform its usual stabilizing function because of the zero lower bound. We calibrate our uncertainty shock process using fluctuations in implied stock market volatility, and show that the model with nominal price rigidity is consistent with empirical evidence from a structural vector autoregression. We argue that increased uncertainty about the future likely played a role in worsening the Great Recession. The economic mechanism we identify applies to a large set of shocks that change expectations of the future without changing current fundamentals.     

The Role of Contracts on Quality and Returns to Quality in Offshore Software Development Outsourcing

In this study, we examine how the different incentive structures inherent in two primary contract types—time and materials (T&M) and fixed price (FP)—influence the quality provided by the vendor in the software development outsourcing industry. We argue that the incentive structure of FP contracts motivates a vendor to be more efficient in the software development process, which results in higher quality as compared to projects executed under a T&M contract. We thus argue that vendors consistently staff FP projects with better trained personnel because they face the most risk on these contracts, resulting in better outcomes on these projects. We extend our analysis to propose that providing higher quality is associated with higher profit margins for the vendor only for FP contracts. We develop and test these hypotheses on data collected from 100 software projects completed by a leading Indian offshore vendor. The results provide strong support for our fundamental thesis that the drivers of and returns to quality vary by contract type. We discuss the implications of our research for both researchers and practitioners.     

Structural Change and the Kaldor Facts in a Growth Model With Relative Price Effects and Non‐Gorman Preferences

U.S. data reveal three facts: (1) the share of goods in total expenditure declines at a constant rate over time, (2) the price of goods relative to services declines at a constant rate over time, and (3) poor households spend a larger fraction of their budget on goods than do rich households. I provide a macroeconomic model with non‐Gorman preferences that rationalizes these facts, along with the aggregate Kaldor facts. The model is parsimonious and admits an analytical solution. Its functional form allows a decomposition of U.S. structural change into an income and substitution effect. Estimates from micro data show each of these effects to be of roughly equal importance.     

Media Effects on Group Collaboration: An Empirical Examination in an Ethical Decision‐Making Context

Even though it is widely acknowledged that collaboration underlies much of the decision‐making efforts in contemporary organizations, and that organizational groups are increasingly making decisions that have ethical implications, few studies have examined group ethical decision‐making processes and outcomes. In addition, while there is increasing evidence that groups often collaborate/communicate using different mediating technologies, few studies have examined the effect of the characteristics of the media in group ethical decision‐making contexts. Finally, there is a clear paucity of studies that have investigated group decision making pertaining to information technology (IT)‐related ethical dilemmas, an area of rising importance for information systems (IS) and decision science researchers. This article seeks to address the gaps described above through an experimental study where groups collaborating either in a face‐to‐face context or in a computer‐mediated context (using NetMeeting or Wiki) were required to make a decision with respect to a scenario with an IT‐related ethical dilemma. Results indicate that media characteristics (e.g., anonymity, immediacy of feedback, parallelism) do not have an effect on whether groups make ethical (or unethical) decisions. However, several media characteristics were found to play a significant role on downstream variables, such as the quality of a follow‐up task (i.e., creation of a decision justification document), and overall process satisfaction of the group members.