ABSTRACT I propose a new imputation estimator for missing covariate values in nonlinear models. The estimator provides efficiency gains relative to just using the complete cases, and is consistent for any model that falls under M‐estimation. This is unlike the commonly used dummy variable method and regression imputation, which I show to be generally inconsistent in nonlinear models. The proposed estimator is straightforward to implement, and relies only on the commonly used assumptions on missingness. To test these assumptions, I provide a novel and simple variable addition test. I show how the framework applies to nonlinear models for fractional and nonnegative responses.
ABSTRACT Wage markup shocks, an important driver of business cycles, are hard to pin down. We quantify the importance of exogenous variation in wage bargaining power, one source of those shocks, from German minimum wage introduction episodes and strikes. This disciplines the impulse responses of unemployment and output, and sharpens inference for other variables, which behave consistently with predictions from search‐and‐matching models. We find that wage bargaining shocks meaningfully contribute to aggregate fluctuations in unemployment and inflation, exhibit substantial pass‐through to prices, and imply plausible dynamics for the vacancy rate, firms' profits, and the labor share.
This paper proposes a simple smooth specification test for the propensity score in the spirit of Neyman (1937). We derive a particular restriction on the propensity score and construct the specification test based on it. Using the density-weighting method, we transform the original specification testing problem into a test of the joint significance of the generalized Fourier coefficients. We propose a novel projection method to eliminate the parameter estimation effect arising from estimating unknown nuisance parameters. The proposed test is shown to follow a standard distribution under the null hypothesis and to possess nontrivial asymptotic power against local alternatives that converge to the null at the parametric rate , where is the sample size. To enhance the practical applicability of the procedure, we further introduce a data-driven selection method for determining the testing order, enabling automatic selection based on the observed data. Compared to existing methods, our test does not suffer from the "curse of dimensionality" faced by Shaikh et al. (2009); at the same time, our test is both asymptotically pivotal and more computationally efficient than that of Sant'Anna and Song (2019). Extensive simulations demonstrate that the proposed test yields satisfactory empirical size and power. Compared with previous tests, our test exhibits comparable overall performance and delivers clear improvements in some cases, especially for high-frequency alternatives. Two empirical applications further illustrate the practical applicability of our proposal, examining propensity score specifications in the Soviet 156 Program and the US Job Corps Program.
ABSTRACT We estimate average equivalised consumption measures across 370 local authority districts in Great Britain, using small‐area estimation methods that combine information from a household budget survey, a much larger survey of local demographics and employment, and area‐level information on bank account outflows and energy consumption. We show that including bank account data substantially improves our estimates, showing that these and other financial footprints data can play an important role in measuring local consumption and hence living standards. We also compare consumption measures that correspond to welfare under different assumptions about mobility and the capitalisation of local amenities into house prices, as well as traditional local income measures, and show that the rankings of local authorities are sensitive to the choice of measure.
This study proposes specification tests for interference structure in causal inference with spillovers. We focus on experimental settings in which the treatment assignment mechanism is known. To test whether a given exposure mapping adequately summarizes the true interference structure, we develop conditional randomization tests by utilizing the hierarchical relationship between the null and alternative exposure mappings. When there are multiple candidate exposure mappings of interest, we propose a sequential specification testing procedure that controls the false discovery rate. Through extensive simulation exercises, we demonstrate that our tests have desirable size properties and satisfactory power. To illustrate the proposed methods, we revisit two existing social network experiments: One on farmers' insurance adoption and another on anti-conflict education programs.
ABSTRACT While existing work shows COVID‐19 stay‐at‐home (SAH) policies decreased mobility on average, we lack evidence regarding heterogeneity in policy effectiveness across US counties. To uncover potential heterogeneity, we implement a novel two‐stage approach. First, we employ recent advances in synthetic control estimation and inference to obtain and bound both time‐average and county‐specific treatment effects. Next, we use a local linear forest to explain observed heterogeneity using county‐level predictors. This procedure reveals substantial variation in policy effectiveness and identifies predictors of policy effectiveness which can be used to target future SAH policies.
This paper studies heterogeneous mixed-frequency panel data models, focusing on linear specifications that allow heterogeneity in both aggregation weights and slope coefficients. To address potential correlations between the heterogeneity and the covariates, we first show that, under additional normalization conditions, the mean-group estimator delivers consistent and asymptotically normal slope estimates but biased weights estimators. As an alternative, we propose a correlated random effects estimator using a generalized Mundlak specification. We further discuss the implementation of these two estimators when covariates are observed at substantially higher sampling frequencies. Monte Carlo simulations are conducted to assess their finite-sample properties. As an empirical illustration, we revisit the impact of temperature fluctuations on economic growth using the proposed framework.
The external validity of regression discontinuity designs is crucial for informing policy but is rarely examined in applied work. To advance empirical practice, we propose a joint inference procedure for the treatment effect and its local external validity, captured by the treatment effect derivative (TED), within a robust bias correction framework. We further introduce a locally linear treatment effects assumption, which extends the scope of the TED and enables identification and the construction of a uniform confidence band for extrapolated effects. These methods apply to most empirical studies. Empirical illustrations demonstrate their practical usefulness.
We examine how parental income and family structure during childhood and adolescence affect adult income, emphasizing the timing of these effects. Using an ordered multinomial probability model with functional covariates, we find that these familial influences are strongest in middle childhood and adolescence. We also uncover a complementary relationship in the effects of income and family structure trajectories during key developmental periods. By flexibly controlling for personal and family characteristics using nonparametric methods, our approach effectively handles high-dimensional covariates. The results advance the understanding of intergenerational income mobility and highlight the long-term importance of early-life familial conditions for adult economic success.
I provide a precision-sampler-based replication of the multivariate unobserved component stochastic volatility outlier-adjusted model of Stock and Watson (2016) applied to inflation in the United States and the Euro Area (EA). I find a substantial post-2020 increase in trend inflation for both the United States and the EA, and estimate end-2024 trend inflation at 2.3 and 2.0 percent, respectively.
We propose a unified framework for interpreting and comparing a broad class of synthetic control (SC) methods. Our framework is built on an analysis of a mean-squared prediction error (MSPE) bound for the counterfactual predicted by a generic SC method, without imposing a specific outcome model. Using this framework, we develop a generalized SC method that provides a more comprehensive regularization of the MSPE bound than several existing SC methods. Through simulation studies and placebo analyses, we demonstrate the effectiveness of the proposed approach in predicting the counterfactual.
We build on Modestino et al., who analysed "opportunistic upskilling" during the 2007 recession in the US, by extending their approach to European labour markets following recent economic shocks. Using a comprehensive dataset of online job postings (2019-2023) and an instrumental variable approach leveraging Ukrainian refugee inflows, we find that increases in labour supply have a significant positive effect on both education and experience requirements. Our findings reinforce the idea that employers opportunistically upskill labour demand in different but challenging macroeconomic contexts. The identification of such patterns, however, depends on the presence of a plausibly exogenous shock to labour markets.
This paper introduces a novel method to adaptively design randomized experiments. For randomized experiments with a pilot stage, or multistage experiments, Hahn et al. (2011) propose an adaptive experimental design that adjusts the next stage's propensity score based on data from the previous stages. This paper discusses how the discretization of covariates affects the precision of the estimation of the average treatment effect (ATE) through the estimated propensity score for the next stage. Also, this paper proposes an algorithm using the bootstrap technique to find the optimal level of discretization of covariates. Monte Carlo simulations and an application with actual data show that the suggested method performs well.
We propose a simple approach to treatment effect estimation in panel data that is valid when the number of time periods is small and the parallel trends condition is violated due to the presence of interactive fixed effects. The procedure allows the covariates to be affected by treatment and enables separation of the part of the estimated treatment effect that is due to the covariates from the part that is not. The asymptotic properties of the new approach are established, and their accuracy in small samples is investigated using Monte Carlo simulations. The procedure is illustrated using as an example the effect of increased trade competition on firm markups in China. We estimate that about half of the impact of China's entrance into the WTO on markup dispersion came from the changes in industry-level productivity.
This paper revisits the empirical analysis of Nakamura and Steinsson (2014). I reconstructed and extended the original dataset to cover the period 1966-2019, harmonizing two major sources of data: the Defense Contract Action Data System (DCADS) and USAspending.gov. I discuss how to aggregate these contract-level data to better capture spending more directly tied to domestic stimulus. Estimated multipliers are slightly lower in narrow replications but increase when incorporating later fiscal episodes. I also assess the validity and stability of cross-sectional estimates. While some heterogeneity exists, dispersion in state-level responses remains within reasonable boundaries, especially when accounting for dynamic persistence.
We introduce a dynamic factor correlation model whose core methodological innovation is a variation-free parametrization of dynamic factor loadings, inspired by the generalized Fisher transformation. The model accommodates time-varying correlations, heterogeneous heavy tails, and dependent idiosyncratic shocks. Applied to a Small Universe of 12 assets and a Large Universe of 323 stocks, the factor structure induces a sparse idiosyncratic correlation matrix with dependencies concentrated within subindustries, enabling scalability to high dimensions under a sparse block structure. Both factor loadings and correlations vary substantially. Allowing for heterogeneous heavy tails via convolution- distributions yields sizable improvements relative to Gaussian and multivariate- benchmarks.
Double/debiased machine learning (DML) uses for estimating an average treatment effect (ATE) a double-robust score function that relies on the prediction of nuisance functions, such as the propensity score, which is the probability of treatment assignment given covariates. Estimators relying on double-robust score functions are highly sensitive to errors in propensity score predictions. Machine learning algorithms have been found to produce models that often overestimate or underestimate these probabilities. Several calibration approaches have been proposed to improve probabilistic forecasts of machine learners. This paper explores their integration into the DML framework, showing via simulations that using calibrated propensity scores significantly reduces the root mean squared error of ATE estimates in finite samples while preserving DML's asymptotic properties.
The effects of monetary policy shocks are regularly estimated using high-frequency surprises in asset prices around central bank meetings as an instrument. These studies, insofar as they explicitly model the relationship between instrument and structural shock, assume a constant relationship between the instrument and the monetary policy shock. By allowing for time variation in this relationship, we show that only a few distinct periods are informative about monetary policy shocks. Therefore, we build a narrative for instrument-based identification. For the instrument in Gertler and Karadi, the effect on the (log) price level is almost 50% larger than the standard specification would suggest.
We present four novel tests of equal predictive accuracy and encompassing & aacute; Pitarakis (2023, 2025) for factor-augmented regressions. Factors are estimated using cross-section averages (CAs) of grouped series and our theoretical findings are empirically relevant: asymptotic normality, robustness to an overspecification of the number of factors, tractability of different degrees of predictor persistence, and invariance to the location of structural breaks in the loadings. Simulations reveal good local power properties of our tests. We apply them to the novel EA-MD-QD dataset by Barigozzi et al. (2024b)-which covers the Euro Area as a whole and its primary member countries-and show that factors offer predictive power.
The rise of machine learning (ML) is one of the most prominent developments in applied econometrics in the past decade. The focus of much economic analysis is causal, rather than prediction, and Belloni et al. (2014) demonstrate how ML methods can be used in causal inference. This paper undertakes a narrow and wide replication of the Monte Carlo and empirical examples presented by Belloni et al. (2014). We discuss practical implications of this replication for the use of double ML methods in applied econometric research.
