Abstract This paper studies identification and doubly robust (DR) estimation of quantile treatment effects (QTEs) in difference-in-discontinuities (diff-in-disc) designs when a new treatment is introduced in the post period and a confounding discontinuous policy is present in both periods. We show that QTEs are point identified under a conditional stable-distributional-effect assumption for the confounding treatment, a restriction that is analogous to the distributional parallel trends assumption in the recent difference-in-differences literature. We then propose a DR estimator and inference procedure that remain valid when either the outcome regression or the propensity score model is correctly specified, while avoiding high-dimensional nonparametric adjustment for covariates in the local estimation setting. We establish asymptotic normality of the proposed estimator, and Monte Carlo simulations illustrate its double-robustness and good finite-sample performance. In an application to Italian municipal fiscal data (Grembi et al. 2016),, the estimates suggest that relaxing fiscal constraints increases deficits primarily over the lower and central portions of the distribution, shifting municipalities from surplus or near balance into moderate deficits—a distributional pattern not captured by mean effects.
Abstract This paper develops numerical and causal interpretations of two-way fixed effects (TWFE) regressions in settings with nonbinary, nonstaggered treatments and time-varying covariates. Using the equivalence between TWFE and pooled first-difference (FD) regressions, I express the TWFE coefficient as a weighted average of FD coefficients across all horizons, clarifying how short- and long-run changes contribute to the estimate. Causal interpretation of the TWFE coefficient relies on common trends assumptions at all horizons simultaneously, whereas each FD coefficient relies on the assumption only at its own horizon. This structure opens the identifying assumptions to empirical scrutiny: I propose diagnostic procedures that assess common trends horizon by horizon, and illustrate them by reexamining TWFE estimates of minimum-wage effects on employment.
Summary Putting a price on carbon emissions helps mitigate climate change but may also raise overall price inflation. Using high-frequency event studies based on regulatory news in the European carbon market, we show that carbon price surprises generate significant increases not only in energy futures prices, but also in inflation swap rates and break-even inflation rates. These measures of inflation compensation respond positively at both short and long horizons, with significant effects up to ten years out. Such persistent effects of climate policy on market-based inflation expectations are relevant for central banks. However, despite the sustained effects on inflation compensation, forward-looking nominal interest rates show no meaningful response to the carbon policy shocks, suggesting that investors do not anticipate that the European Central Bank will lean against the inflationary effects of higher carbon prices.
Many policies are replicated by other policymakers at different times. We introduce a synthetic control methodology to study policies with staggered adoption. Our method estimates the dynamic average treatment effects on the treated using variation introduced by the staggered adoption of policies. Our method gives asymptotically unbiased estimators of many interesting quantities and delivers asymptotically valid inference. Applying the method to intergovernmental coordination reforms that centralize information sharing and enable joint policing across jurisdictions, we find that violent theft and cartel activity fall after adoption. Homicide is largely unchanged for most post-treatment periods, but rises later on.
Summary Insurers adjust premiums for renewing policyholders based on past claims, a practice known as experience rating. This paper examines experience rating in insurance contracts with deductibles, a key instrument for mitigating inefficiencies arising from information asymmetry between policyholders and insurers. We propose a copula-based panel data model that accounts for the endogeneity of deductible choice, particularly when the assumption of contemporaneous exogeneity is violated—consistent with theories of adverse selection and moral hazard. We also introduce a computationally efficient algorithm for inference and prediction. The framework accommodates various types of non-Gaussian outcomes and is well suited for predictive applications. We apply the method to a government property insurance programme, using historical claims data to develop an experience rating scheme. Results reveal a negative relationship between deductible choice and underlying risk, providing empirical support for endogenous selection behaviour. Compared to standard approaches that treat deductibles as exogenous, our model enables more refined risk segmentation and improved identification of profitable business.
We propose a novel econometric methodology for Structural Vector Autoregressions with external instruments (`proxy-SVARs' or `SVAR-IVs') in panel data characterized by strong cross-sectional dependence, dynamic heterogeneity, and limited availability of direct external instruments for the shocks of interest. For each unit, we specify a Factor-Augmented proxy-SVAR (`proxy-FA-SVAR') that incorporates factors summarizing cross-sectional information from the non-policy variables of the system. The effects of the policy shocks are then recovered indirectly by estimating unit-specific policy reaction functions through a Minimum Distance approach. Identification relies on global instruments for the non-policy shocks; that is, proxies common to all units in the panel, internally constructed from a separate SVAR estimated on factors for the policy and non-policy variables. These global instruments can be complemented with local (idiosyncratic) instruments constructed from auxiliary unit-level SVARs. Their joint use renders the proxy-FA-SVARs overidentified and therefore statistically testable. We illustrate the methodology by estimating government spending multipliers for Italian NUTS-2 regions using annual data. The global and local instruments for the regional output shocks are obtained from Blanchard-Perotti-type SVARs.
This paper introduces a robust specification test for linear regression built on a rank-score empirical process. The proposed test is distribution-free, easy to implement, and accommodates a broad class of score functions. We derive the asymptotic properties of the test statistics under the null, fixed alternatives, and a sequence of local alternatives. To implement the test in finite samples, we employ a simple multiplier bootstrap procedure with establishing its asymptotic validity. Simulations and an empirical application indicate reliable size and strong power with notable robustness to heavy-tailed errors and outliers.
Testing for mediation suffers from low power near the origin. This can be addressed by augmenting the likelihood ratio critical region as discussed in previous work within an asymptotic framework. In this paper we consider exact distributions of test statistics and use this to derive optimal augmentation regions for arbitrary sample sizes. The resulting test is very simple and reliable, making it relevant for empirical research, even with a very small number of observations. This new test is $\alpha$-coherent, as required for the p-values, which are easily calculated for the new test. Simulations confirm robust power improvement and size control, even with non-normal errors.
We study inference via heteroskedasticity in linear models commonly used for macroeconomic policy analysis, where covariate endogeneity must often be addressed with limited time and data. Our framework nests standard heteroskedasticity-based approaches, allows for new non-nested restrictions, and does not require ex ante regime labelling. We propose an easily implementable weak identification robust test and derive sufficient conditions for its validity. Simulation results show good size and power properties for a wide range of settings. Empirical applications to the fuel-price passthrough in Sierra Leone, the effect of remittances on consumption in the Philippines, and exchange-rate passthroughs in many countries illustrate the versatility and scalability of our approach.
A novel dynamic model for joint estimation of multiple quantiles of a time series conditionally on a set of covariates is presented. The model preserves quantile monotonicity and allows for a clear interpretation of covariate effects across quantiles. Model parameters are estimated using a two-step M-estimator. The resulting estimator is consistent, and its finite sample properties are analyzed through simulations. The new model is used to study the impact of different levels of stress in the financial system on GDP growth rate. The analysis shows that worsened financial conditions imply a more pessimistic economic outlook when the financial scenario is already severely distressed, and an overall increased macroeconomic uncertainty. Additionally, past information on GDP growth is found to be critical in studying and predicting economic vulnerability. These findings hold true even when alternative measures of real economic activity are considered.
This paper proposes the Regularized Generalized Covariance (RGCov) estimator, a ridge-type extension of the Generalized Covariance (GCov) estimator for high-dimensional stationary time series. By regularizing the GCov objective function, which involves the inverse of the covariance matrix, RGCov improves numerical stability while preserving positive definiteness. Under suitable conditions, the new estimator is consistent, asymptotically normal, and semi-parametrically efficient. We also extend the GCov specification test and the nonlinear serial dependence (NLSD) test to their regularized versions, both of which are asymptotically chi-square distributed. Simulation studies confirm the reliability of the RGCov and associated tests in high-dimensional settings. In the empirical application, RGCov is used to estimate a mixed causal-noncausal Vector Autoregressive (VAR) model for green energy stocks in the RENIXX index and to construct two bubble-based investment strategies: bubble-riding and bubble-hedging, both of which outperform the benchmark index.
This study presents a model that enables automatic trend detection in Bayesian vector autoregressions (BVARs). The proposed model features cyclical components that follow a stationary VAR and trend components that evolve as a random walk. We employ a spike-and-slab prior on the variance of shocks in the trend component, enabling the automatic identification of stochastic trends and, if present, their estimation within the same Gibbs sampling procedure. A marginal likelihood comparison provides evidence in favour of the proposed model over standard BVARs. Furthermore, out-of-sample forecasting exercises demonstrate that our model significantly enhances predictive accuracy, particularly for highly persistent variables and longer-horizon forecasts. These results remain robust across models of different sizes, including small, medium, and large.
We complement previous partial global identification results for the non-Gaussian structural vector autoregressive (SVAR) model by showing that in the absence of co-skewness among the strucural shocks, the skewed shocks are identified and in the absence of excess co-kurtosis, the shocks with non-zero excess kurtosis are identified. The former case has the advantage that dependent conditional heteroskedasticity is allowed for. In each case, the remaining shocks are set identified, and these results can be combined to identify both skewed and non-mesokurtic shocks. To capture the non-Gaussian features of the data, versatile error distributions must be specified. We discuss the Bayesian implementation of an SVAR model with skewed t-distributed errors that exhibit dependent stochastic volatility, including the assessment of identification and checking the validity of exogenous instruments potentially used for identification. The methods are illustrated in an empirical application to US monetary policy.
This paper analyses possibly time-varying shock transmission in structural vector autoregressive (VAR) models when the reduced-form VAR coefficients are time invariant and the shocks are identified through non-Gaussianity. To check for possible time variation in the impulse responses, we propose Wald tests for two situations: (1) homoskedastic and (2) heteroskedastic structural shocks with changes in the unconditional variances. For the latter case, the challenge is to ensure that the test does not indicate time-varying impulse responses if the changes are due only to changes in the variances of the shocks. To illustrate the usefulness of the tests, they are applied to an empirical model of the crude-oil market. They support time-varying shock transmission reflected in impulse response functions that change over time.
This study considers the practically important case of nonparametrically estimating heterogeneous average treatment effects that vary with a limited number of discrete and continuous covariates in a selection-on-observables framework where the number of possible confounders is very large. We propose a two-step estimator for which the first step is estimated by machine learning. We show that this estimator has desirable statistical properties such as consistency, asymptotic normality, and rate double robustness. In particular, we derive the coupled convergence conditions between the nonparametric and the machine-learning steps. We also show that estimating population average treatment effects by averaging the estimated heterogeneous effects is semiparametrically efficient. The resulting estimators are compared to other suggestions in the literature in Monte Carlo experiments that are inspired by real data. They are found to perform relatively better in most settings. The new estimators are applied to the empirical example of the effects of mothers' smoking during pregnancy on the birthweight of their babies.
Impulse responses and forecasts are central concepts for policymakers. They are also sufficient statistics to solve many important macroeconomic problems, from policy counterfactuals to policy evaluation, and offer a promising alternative to the standard structural modelling approach. In this work, we discuss and extend recent progress on the use of these sufficient macro statistics for policy evaluation. We illustrate the methods by evaluating the performance of the European Central Bank over 1999-2023.
Many popular estimation methods in panel data rely on the assumption that the covariates of interest are strictly exogenous. However, this assumption is empirically restrictive in a wide range of settings. In this paper I argue that credible empirical work requires meaningfully relaxing strict exogeneity assumptions. Econometricians have developed methods that allow for sequential exogeneity, which in contrast with strict exogeneity allows for the presence of feedback from past outcomes to future covariates or treatments. I review some of the classic work on linear models with constant coefficients, and then describe some approaches that allow for coefficient heterogeneity in models with feedback. Finally, in the last two parts of the paper I review recent work that allows for sequential exogeneity in nonlinear panel data models, and mention possible extensions to network settings.
In cluster randomized controlled trials (CRCT) with a finite populations, the exact design-based variance of the Horvitz-Thompson (HT) estimator for the average treatment effect (ATE) depends on the joint distribution of unobserved cluster-aggregated potential outcomes and is therefore not point-identifiable. We study a common two-stage sampling design-random sampling of clusters followed by sampling units within sampled clusters-with treatment assigned at the cluster level. First, we derive the exact (infeasible) design-based variance of the HT ATE estimator that accounts jointly for cluster- and unit-level sampling as well as random assignment. Second, extending Aronow et al (2014), we provide a sharp, attanable upper bound on that variance and propose a consistent estimator of the bound using only observed outcomes and known sampling/assignment probabilities. In simulations and an empirical application, confidence intervals based on our bound are valid and typically narrower than those based on cluster standard errors.
This paper proposes a debiased estimator for causal effects in high-dimensional generalized linear models with binary outcomes and general link functions. The estimator augments a regularized regression plug-in with weights computed from a single convex optimization that approximately balances link-derivative-weighted covariates and controls variance; it does not rely on estimated propensity scores. Under standard conditions, the estimator is $\sqrt{n}$-consistent and asymptotically normal for dense linear contrasts and causal parameters. Simulation results show the superior performance of our approach in comparison to alternatives such as inverse propensity score estimators and double machine learning estimators in finite samples. When applied to National Supported Work training data, our estimates and confidence intervals are close to the experimental benchmark.
