arXiv subjects

Alessandro Casini

Publications and source records attributed to Alessandro Casini.

13 recordsLinked to original sources

arXiv2025

Dynamic Local Average Treatment Effects in Time Series

This paper discusses identification, estimation, and inference on dynamic local average treatment effects (LATEs) in instrumental variables (IVs) settings. First, we show that compliers--observations whose treatment status is affected by the instrument--can be identified individually in time series data using smoothness assumptions and local comparisons of treatment assignments. Second, we show that this result enables not only better interpretability of IV estimates but also direct testing of the exclusion restriction by comparing outcomes among identified non-compliers across instrument values. Third, we document pervasive weak identification in applied work using IVs with time series data by surveying recent publications in leading economics journals. However, we find that strong identification often holds in large subsamples for which the instrument induces changes in the treatment. Motivated by this, we introduce a method based on dynamic programming to detect the most strongly-identified subsample and show how to use this subsample to improve estimation and inference. We also develop new identification-robust inference procedures that focus on the most strongly-identified subsample, offering efficiency gains relative to existing full sample identification-robust inference when identification fails over parts of the sample. Finally, we apply our results to heteroskedasticity-based identification of monetary policy effects. We find that about 75% of observations are compliers (i.e., cases where the variance of the policy shifts up on FOMC announcement days), and we fail to reject the exclusion restriction. Estimation using the most strongly-identified subsample helps reconcile conflicting IV and GMM estimates in the literature.

econ.EM↗

arXiv2025

Identification and Estimation of Causal Effects in High-Frequency Event Studies

We provide precise conditions for nonparametric identification of causal effects by high-frequency event study regressions, which have been used widely in the recent macroeconomics, financial economics and political economy literatures. The high-frequency event study method regresses changes in an outcome variable on a measure of unexpected changes in a policy variable in a narrow time window around an event or a policy announcement (e.g., a 30-minute window around an FOMC announcement). We show that, contrary to popular belief, the narrow size of the window is not sufficient for identification. Rather, the population regression coefficient identifies a causal estimand when (i) the effect of the policy shock on the outcome does not depend on the other variables (separability) and (ii) the surprise component of the news or event dominates all other variables that are present in the event window (relative exogeneity). Technically, the latter condition requires the ratio between the variance of the policy shock and that of the other variables to be infinite in the event window. Under these conditions, we establish the causal meaning of the event study estimand corresponding to the regression coefficient and the consistency and asymptotic normality of the event study estimator. Notably, this standard linear regression estimator is robust to general forms of nonlinearity. We apply our results to Nakamura and Steinsson's (2018a) analysis of the real economic effects of monetary policy, providing a simple empirical procedure to analyze the extent to which the standard event study estimator adequately estimates causal effects of interest.

econ.EM↗

arXiv2024

Theory of Low Frequency Contamination from Nonstationarity and Misspecification: Consequences for HAR Inference

We establish theoretical results about the low frequency contamination (i.e., long memory effects) induced by general nonstationarity for estimates such as the sample autocovariance and the periodogram, and deduce consequences for heteroskedasticity and autocorrelation robust (HAR) inference. We present explicit expressions for the asymptotic bias of these estimates. We distinguish cases where this contamination only occurs as a small-sample problem and cases where the contamination continues to hold asymptotically. We show theoretically that nonparametric smoothing over time is robust to low frequency contamination. Our results provide new insights on the debate between consistent versus inconsistent long-run variance (LRV) estimation. Existing LRV estimators tend to be in inflated when the data are nonstationary. This results in HAR tests that can be undersized and exhibit dramatic power losses. Our theory indicates that long bandwidths or fixed-b HAR tests suffer more from low frequency contamination relative to HAR tests based on HAC estimators, whereas recently introduced double kernel HAC estimators do not super from this problem. Finally, we present second-order Edgeworth expansions under nonstationarity about the distribution of HAC and DK-HAC estimators and about the corresponding t-test in the linear regression model.

econ.EM↗

arXiv2024

Prewhitened Long-Run Variance Estimation Robust to Nonstationarity

We introduce a nonparametric nonlinear VAR prewhitened long-run variance (LRV) estimator for the construction of standard errors robust to autocorrelation and heteroskedasticity that can be used for hypothesis testing in a variety of contexts including the linear regression model. Existing methods either are theoretically valid only under stationarity and have poor finite-sample properties under nonstationarity (i.e., fixed-b methods), or are theoretically valid under the null hypothesis but lead to tests that are not consistent under nonstationary alternative hypothesis (i.e., both fixed-b and traditional HAC estimators). The proposed estimator accounts explicitly for nonstationarity, unlike previous prewhitened procedures which are known to be unreliable, and leads to tests with accurate null rejection rates and good monotonic power. We also establish MSE bounds for LRV estimation that are sharper than previously established and use them to determine the data-dependent bandwidths.

econ.EM↗

arXiv2024

Theory of Evolutionary Spectra for Heteroskedasticity and Autocorrelation Robust Inference in Possibly Misspecified and Nonstationary Models

We develop a theory of evolutionary spectra for heteroskedasticity and autocorrelation robust (HAR) inference when the data may not satisfy second-order stationarity. Nonstationarity is a common feature of economic time series which may arise either from parameter variation or model misspecification. In such a context, the theories that support HAR inference are either not applicable or do not provide accurate approximations. HAR tests standardized by existing long-run variance estimators then may display size distortions and little or no power. This issue can be more severe for methods that use long bandwidths (i.e., fixed-b HAR tests). We introduce a class of nonstationary processes that have a time-varying spectral representation which evolves continuously except at a finite number of time points. We present an extension of the classical heteroskedasticity and autocorrelation consistent (HAC) estimators that applies two smoothing procedures. One is over the lagged autocovariances, akin to classical HAC estimators, and the other is over time. The latter element is important to flexibly account for nonstationarity. We name them double kernel HAC (DK-HAC) estimators. We show the consistency of the estimators and obtain an optimal DK-HAC estimator under the mean squared error (MSE) criterion. Overall, HAR tests standardized by the proposed DK-HAC estimators are competitive with fixed-b HAR tests, when the latter work well, with regards to size control even when there is strong dependence. Notably, in those empirically relevant situations in which previous HAR tests are undersized and have little or no power, the DK-HAC estimator leads to tests that have good size and power.

econ.EM↗

arXiv2024

Change-Point Analysis of Time Series with Evolutionary Spectra

This paper develops change-point methods for the spectrum of a locally stationary time series. We focus on series with a bounded spectral density that change smoothly under the null hypothesis but exhibits change-points or becomes less smooth under the alternative. We address two local problems. The first is the detection of discontinuities (or breaks) in the spectrum at unknown dates and frequencies. The second involves abrupt yet continuous changes in the spectrum over a short time period at an unknown frequency without signifying a break. Both problems can be cast into changes in the degree of smoothness of the spectral density over time. We consider estimation and minimax-optimal testing. We determine the optimal rate for the minimax distinguishable boundary, i.e., the minimum break magnitude such that we are able to uniformly control type I and type II errors. We propose a novel procedure for the estimation of the change-points based on a wild sequential top-down algorithm and show its consistency under shrinking shifts and possibly growing number of change-points. Our method can be used across many fields and a companion program is made available in popular software packages.

math.ST↗

arXiv2024

The Fixed-b Limiting Distribution and the ERP of HAR Tests Under Nonstationarity

We show that the nonstandard limiting distribution of HAR test statistics under fixed-b asymptotics is not pivotal (even after studentization) when the data are nonstationarity. It takes the form of a complicated function of Gaussian processes and depends on the integrated local long-run variance and on on the second moments of the relevant series (e.g., of the regressors and errors for the case of the linear regression model). Hence, existing fixed-b inference methods based on stationarity are not theoretically valid in general. The nuisance parameters entering the fixed-b limiting distribution can be consistently estimated under small-b asymptotics but only with nonparametric rate of convergence. Hence, We show that the error in rejection probability (ERP) is an order of magnitude larger than that under stationarity and is also larger than that of HAR tests based on HAC estimators under conventional asymptotics. These theoretical results reconcile with recent finite-sample evidence in Casini (2021) and Casini, Deng and Perron (2021) who showing that fixed-b HAR tests can perform poorly when the data are nonstationary. They can be conservative under the null hypothesis and have non-monotonic power under the alternative hypothesis irrespective of how large the sample size is.

econ.EM↗

arXiv2021

Continuous Record Asymptotics for Change-Points Models

For a partial structural change in a linear regression model with a single break, we develop a continuous record asymptotic framework to build inference methods for the break date. We have T observations with a sampling frequency h over a fixed time horizon [0, N] , and let T with h 0 while keeping the time span N fixed. We impose very mild regularity conditions on an underlying continuous-time model assumed to generate the data. We consider the least-squares estimate of the break date and establish consistency and convergence rate. We provide a limit theory for shrinking magnitudes of shifts and locally increasing variances. The asymptotic distribution corresponds to the location of the extremum of a function of the quadratic variation of the regressors and of a Gaussian centered martingale process over a certain time interval. We can account for the asymmetric informational content provided by the pre- and post-break regimes and show how the location of the break and shift magnitude are key ingredients in shaping the distribution. We consider a feasible version based on plug-in estimates, which provides a very good approximation to the finite sample distribution. We use the concept of Highest Density Region to construct confidence sets. Overall, our method is reliable and delivers accurate coverage probabilities and relatively short average length of the confidence sets. Importantly, it does so irrespective of the size of the break.

math.ST↗

arXiv2021

Simultaneous Bandwidths Determination for DK-HAC Estimators and Long-Run Variance Estimation in Nonparametric Settings

We consider the derivation of data-dependent simultaneous bandwidths for double kernel heteroskedasticity and autocorrelation consistent (DK-HAC) estimators. In addition to the usual smoothing over lagged autocovariances for classical HAC estimators, the DK-HAC estimator also applies smoothing over the time direction. We obtain the optimal bandwidths that jointly minimize the global asymptotic MSE criterion and discuss the trade-off between bias and variance with respect to smoothing over lagged autocovariances and over time. Unlike the MSE results of Andrews (1991), we establish how nonstationarity affects the bias-variance trade-o?. We use the plug-in approach to construct data-dependent bandwidths for the DK-HAC estimators and compare them with the DK-HAC estimators from Casini (2021) that use data-dependent bandwidths obtained from a sequential MSE criterion. The former performs better in terms of size control, especially with stationary and close to stationary data. Finally, we consider long-run variance estimation under the assumption that the series is a function of a nonparametric estimator rather than of a semiparametric estimator that enjoys the usual T^(1/2) rate of convergence. Thus, we also establish the validity of consistent long-run variance estimation in nonparametric parameter estimation settings.

econ.EM↗

arXiv2021

Generalized Laplace Inference in Multiple Change-Points Models

Under the classical long-span asymptotic framework we develop a class of Generalized Laplace (GL) inference methods for the change-point dates in a linear time series regression model with multiple structural changes analyzed in, e.g., Bai and Perron (1998). The GL estimator is defined by an integration rather than optimization-based method and relies on the least-squares criterion function. It is interpreted as a classical (non-Bayesian) estimator and the inference methods proposed retain a frequentist interpretation. This approach provides a better approximation about the uncertainty in the data of the change-points relative to existing methods. On the theoretical side, depending on some input (smoothing) parameter, the class of GL estimators exhibits a dual limiting distribution; namely, the classical shrinkage asymptotic distribution, or a Bayes-type asymptotic distribution. We propose an inference method based on Highest Density Regions using the latter distribution. We show that it has attractive theoretical properties not shared by the other popular alternatives, i.e., it is bet-proof. Simulations confirm that these theoretical properties translate to better finite-sample performance.

math.ST↗

arXiv2020

Continuous Record Laplace-based Inference about the Break Date in Structural Change Models

Building upon the continuous record asymptotic framework recently introduced by Casini and Perron (2018a) for inference in structural change models, we propose a Laplace-based (Quasi-Bayes) procedure for the construction of the estimate and confidence set for the date of a structural change. It is defined by an integration rather than an optimization-based method. A transformation of the least-squares criterion function is evaluated in order to derive a proper distribution, referred to as the Quasi-posterior. For a given choice of a loss function, the Laplace-type estimator is the minimizer of the expected risk with the expectation taken under the Quasi-posterior. Besides providing an alternative estimate that is more precise|lower mean absolute error (MAE) and lower root-mean squared error (RMSE)|than the usual least-squares one, the Quasi-posterior distribution can be used to construct asymptotically valid inference using the concept of Highest Density Region. The resulting Laplace-based inferential procedure is shown to have lower MAE and RMSE, and the confidence sets strike the best balance between empirical coverage rates and average lengths of the confidence sets relative to traditional long-span methods, whether the break size is small or large.

econ.EM↗

arXiv2018

Tests for Forecast Instability and Forecast Failure under a Continuous Record Asymptotic Framework

We develop a novel continuous-time asymptotic framework for inference on whether the predictive ability of a given forecast model remains stable over time. We formally define forecast instability from the economic forecaster's perspective and highlight that the time duration of the instability bears no relationship with stable period. Our approach is applicable in forecasting environment involving low-frequency as well as high-frequency macroeconomic and financial variables. As the sampling interval between observations shrinks to zero the sequence of forecast losses is approximated by a continuous-time stochastic process (i.e., an Ito semimartingale) possessing certain pathwise properties. We build an hypotheses testing problem based on the local properties of the continuous-time limit counterpart of the sequence of losses. The null distribution follows an extreme value distribution. While controlling the statistical size well, our class of test statistics feature uniform power over the location of the forecast failure in the sample. The test statistics are designed to have power against general form of insatiability and are robust to common forms of non-stationarity such as heteroskedasticty and serial correlation. The gains in power are substantial relative to extant methods, especially when the instability is short-lasting and when occurs toward the tail of the sample.

econ.EM↗

arXiv2018

Structural Breaks in Time Series

This chapter covers methodological issues related to estimation, testing and computation for models involving structural changes. Our aim is to review developments as they relate to econometric applications based on linear models. Substantial advances have been made to cover models at a level of generality that allow a host of interesting practical applications. These include models with general stationary regressors and errors that can exhibit temporal dependence and heteroskedasticity, models with trending variables and possible unit roots and cointegrated models, among others. Advances have been made pertaining to computational aspects of constructing estimates, their limit distributions, tests for structural changes, and methods to determine the number of changes present. A variety of topics are covered. The first part summarizes and updates developments described in an earlier review, Perron (2006), with the exposition following heavily that of Perron (2008). Additions are included for recent developments: testing for common breaks, models with endogenous regressors (emphasizing that simply using least-squares is preferable over instrumental variables methods), quantile regressions, methods based on Lasso, panel data models, testing for changes in forecast accuracy, factors models and methods of inference based on a continuous records asymptotic framework. Our focus is on the so-called off-line methods whereby one wants to retrospectively test for breaks in a given sample of data and form confidence intervals about the break dates. The aim is to provide the readers with an overview of methods that are of direct usefulness in practice as opposed to issues that are mostly of theoretical interest.

econ.EM↗