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Using Heteroscedasticity to Identify and Estimate Mismeasured and Endogenous Regressor Models
This article proposes a new method of obtaining identification in mismeasured regressor models, triangular systems, and simultaneous equation systems. The method may be used in applications where other sources of identification, such as instrumental variables or repeated measurements, are not available. Associated estimators take the form of two-stage least squares or generalized method of moments. Identification comes from a heteroscedastic covariance restriction that is shown to be a feature of many models of endogeneity or mismeasurement. Identification is also obtained for semiparametric partly linear models, and associated estimators are provided. Set identification bounds are derived for cases where point-identifying assumptions fail to hold. An empirical application estimating Engel curves is provided.
Journal Article
Comparing Cross-Section and Time-Series Factor Models
We use the cross-section regression approach of Fama and MacBeth (1973) to construct cross-section factors corresponding to the time-series factors of Fama and French (2015). Time-series models that use only cross-section factors provide better descriptions of average returns than time-series models that use time-series factors. This is true when we impose constant factor loadings and when we use time-varying loadings that are natural for time-series factors and time-varying loadings that are natural for cross-section factors.
Journal Article
Evaluation of the Azure Kinect and Its Comparison to Kinect V1 and Kinect V2
The Azure Kinect is the successor of Kinect v1 and Kinect v2. In this paper we perform brief data analysis and comparison of all Kinect versions with focus on precision (repeatability) and various aspects of noise of these three sensors. Then we thoroughly evaluate the new Azure Kinect; namely its warm-up time, precision (and sources of its variability), accuracy (thoroughly, using a robotic arm), reflectivity (using 18 different materials), and the multipath and flying pixel phenomenon. Furthermore, we validate its performance in both indoor and outdoor environments, including direct and indirect sun conditions. We conclude with a discussion on its improvements in the context of the evolution of the Kinect sensor. It was shown that it is crucial to choose well designed experiments to measure accuracy, since the RGB and depth camera are not aligned. Our measurements confirm the officially stated values, namely standard deviation ≤17 mm, and distance error <11 mm in up to 3.5 m distance from the sensor in all four supported modes. The device, however, has to be warmed up for at least 40–50 min to give stable results. Due to the time-of-flight technology, the Azure Kinect cannot be reliably used in direct sunlight. Therefore, it is convenient mostly for indoor applications.
Journal Article
Random Coefficients on Endogenous Variables in Simultaneous Equations Models
This article considers a classical linear simultaneous equations model with random coefficients on the endogenous variables. Simultaneous equations models are used to study social interactions, strategic interactions between firms, and market equilibrium. Random coefficient models allow for heterogeneous marginal effects. I show that random coefficient seemingly unrelated regression models with common regressors are not point identified, which implies random coefficient simultaneous equations models are not point identified. Important features of these models, however, can be identified. For two-equation systems, I give two sets of sufficient conditions for point identification of the coefficients’ marginal distributions conditional on exogenous covariates. The first allows for small support continuous instruments under tail restrictions on the distributions of unobservables which are necessary for point identification. The second requires full support instruments, but allows for nearly arbitrary distributions of unobservables. I discuss how to generalize these results to many equation systems, where I focus on linear-in-means models with heterogeneous endogenous social interaction effects. I give sufficient conditions for point identification of the distributions of these endogenous social effects. I propose a consistent nonparametric kernel estimator for these distributions based on the identification arguments. I apply my results to the Add Health data to analyse peer effects in education.
Journal Article
Potential Outcome and Directed Acyclic Graph Approaches to Causality
In this essay I discuss potential outcome and graphical approaches to causality, and their relevance for empirical work in economics. I review some of the work on directed acyclic graphs, including the recent The Book of Why (Pearl and Mackenzie 2018). I also discuss the potential outcome framework developed by Rubin and coauthors (e.g., Rubin 2006), building on work by Neyman (1990 [1923]). I then discuss the relative merits of these approaches for empirical work in economics, focusing on the questions each framework answers well, and why much of the the work in economics is closer in spirit to the potential outcome perspective.
Journal Article
Quantile regression with nonadditive fixed effects
This paper introduces a quantile regression estimator for panel data (QRPD) with nonadditive fixed effects, maintaining the nonseparable disturbance term commonly associated with quantile estimation. QRPD estimates the impact of exogenous or endogenous treatment variables on the outcome distribution using “within” variation in the instruments for identification purposes. Most quantile panel data estimators include additive fixed effects which separates the disturbance term and assumes the parameters vary based only on the time-varying components of the disturbance term. QRPD produces consistent estimates for small T. I estimate the effect of the 2008 tax rebates on the short-term household consumption distribution.
Journal Article
A Practitioner's Guide to Cluster-Robust Inference
We consider statistical inference for regression when data are grouped into clusters, with regression model errors independent across clusters but correlated within clusters. Examples include data on individuals with clustering on village or region or other category such as industry, and state-year differences-in-differences studies with clustering on state. In such settings, default standard errors can greatly overstate estimator precision. Instead, if the number of clusters is large, statistical inference after OLS should be based on cluster-robust standard errors. We outline the basic method as well as many complications that can arise in practice. These include cluster-specific fixed effects, few clusters, multiway clustering, and estimators other than OLS.
Journal Article
Identification and Estimation of Triangular Simultaneous Equations Models Without Additivity
This paper uses control variables to indentify and estimate models with nonseparable, multidimensional disturbances. Triangular simultaneous equations models are considered, with instruments and disturbances that are independent and a reduced form that is strictly monotonic in a scalar disturbance. Here it is shown that the conditional cumulative distribution function of the endogenous variable given the instruments is a control variable. Also, for any control variable, identification results are given for quantile, average, and policy effects. Bounds are given when a common support assumption is not satisfied. Estimators of identified objects and bounds are provided, and a demand analysis empirical example is given.
Journal Article