Search Results
Working Paper
Pre-event Trends in the Panel Event-study Design
We consider a linear panel event-study design in which unobserved confounds may be related both to the outcome and to the policy variable of interest. We provide sufficient conditions to identify the causal effect of the policy by exploiting covariates related to the policy only through the confounds. Our model implies a set of moment equations that are linear in parameters. The effect of the policy can be estimated by 2SLS, and causal inference is valid even when endogeneity leads to pre-event trends (?pre-trends?) in the outcome. Alternative approaches perform poorly in our simulations
Working Paper
Identification Through Sparsity in Factor Models
Factor models are generally subject to a rotational indeterminacy, meaning that individual factors are only identified up to a rotation. In the presence of local factors, which only affect a subset of the outcomes, we show that the implied sparsity of the loading matrix can be used to solve this rotational indeterminacy. We further prove that a rotation criterion based on the 1-norm of the loading matrix can be used to achieve identification even under approximate sparsity in the loading matrix. This enables us to consistently estimate individual factors, and to interpret them as structural ...
Working Paper
xtevent: Estimation and Visualization in the Linear Panel Event-Study Design
Linear panel models and the “event-study plots” that often accompany them are popular tools for learning about policy effects. We introduce the Stata package xtevent, which enables the construction of event-study plots following the suggestions in Freyaldenhoven et al. (Forthcoming). The package implements various procedures to estimate the underlying policy effects and allows for nonbinary policy variables and estimation adjusting for pre-event trends.
Working Paper
Factor Models with Local Factors—Determining the Number of Relevant Factors
We extend the theory on factor models by incorporating “local” factors into the model. Local factors affect only an unknown subset of the observed variables. This implies a continuum of eigenvalues of the covariance matrix, as is commonly observed in applications. We de-rive which factors are pervasive enough to be economically important and which factors are pervasive enough to be estimable using the common principal component estimator. We then introduce a new class of estimators to determine the number of those relevant factors. Un-like existing estimators, our estimators use not only ...
Working Paper
A Generalized Factor Model with Local Factors
I extend the theory on factor models by incorporating local factors into the model. Local factors only affect an unknown subset of the observed variables. This implies a continuum of eigenvalues of the covariance matrix, as is commonly observed in applications. I derive which factors are pervasive enough to be economically important and which factors are pervasive enough to be estimable using the common principal component estimator. I then introduce a new class of estimators to determine the number of those relevant factors. Unlike existing estimators, my estimators use not only the ...
Working Paper
Visualization, Identification, and stimation in the Linear Panel Event-Study Design
Linear panel models, and the “event-study plots” that often accompany them, are popular tools for learning about policy effects. We discuss the construction of event-study plots and suggest ways to make them more informative. We examine the economic content of different possible identifying assumptions. We explore the performance of the corresponding estimators in simulations, highlighting that a given estimator can perform well or poorly depending on the economic environment. An accompanying Stata package, xtevent, facilitates adoption of our suggestions.
Working Paper
Constructing Applicants from Loan-Level Data: A Case Study of Mortgage Applications
We develop a clustering-based algorithm to detect loan applicants who submit multiple applications (“cross-applicants”) in a loan-level dataset without personal identifiers. A key innovation of our approach is a novel evaluation method that does not require labeled training data, allowing us to optimize the tuning parameters of our machine learning algorithm. By applying this methodology to Home Mortgage Disclosure Act (HMDA) data, we create a unique dataset that consolidates mortgage applications to the individual applicant level across the United States. Our preferred specification ...
Working Paper
Measuring Fairness in the U.S. Mortgage Market
Black Americans are both substantially more likely to have their mortgage application rejected and substantially more likely to default on their mortgages than White Americans. We take these stark inequalities as a starting point to ask the question: How fair or unfair is the U.S. mortgage market? We show that the answer to this question crucially depends on the definition of fairness. We consider six competing and widely used definitions of fairness and find that they lead to markedly different conclusions. We then combine these six definitions into a series of stylized facts that offer a ...