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A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelationconsistent Covariance Matrix
TL;DR: In this article, a simple method of calculating a heteroskedasticity and autocorrelation consistent covariance matrix that is positive semi-definite by construction is described.
Abstract: This paper describes a simple method of calculating a heteroskedasticity and autocorrelation consistent covariance matrix that is positive semi-definite by construction. It also establishes consistency of the estimated covariance matrix under fairly general conditions.
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TL;DR: In this article, the authors proposed new tests for detecting the presence of a unit root in quite general time series models, which accommodate models with a fitted drift and a time trend so that they may be used to discriminate between unit root nonstationarity and stationarity about a deterministic trend.
Abstract: SUMMARY This paper proposes new tests for detecting the presence of a unit root in quite general time series models. Our approach is nonparametric with respect to nuisance parameters and thereby allows for a very wide class of weakly dependent and possibly heterogeneously distributed data. The tests accommodate models with a fitted drift and a time trend so that they may be used to discriminate between unit root nonstationarity and stationarity about a deterministic trend. The limiting distributions of the statistics are obtained under both the unit root null and a sequence of local alternatives. The latter noncentral distribution theory yields local asymptotic power functions for the tests and facilitates comparisons with alternative procedures due to Dickey & Fuller. Simulations are reported on the performance of the new tests in finite samples.
16,874 citations
TL;DR: In this article, the authors show that strategies that buy stocks that have performed well in the past and sell stocks that had performed poorly in past years generate significant positive returns over 3- to 12-month holding periods.
Abstract: This paper documents that strategies which buy stocks that have performed well in the past and sell stocks that have performed poorly in the past generate significant positive returns over 3- to 12-month holding periods. We find that the profitability of these strategies are not due to their systematic risk or to delayed stock price reactions to common factors. However, part of the abnormal returns generated in the first year after portfolio formation dissipates in the following two years. A similar pattern of returns around the earnings announcements of past winners and losers is also documented
10,806 citations
TL;DR: In this article, the authors randomly generate placebo laws in state-level data on female wages from the Current Population Survey and use OLS to compute the DD estimate of its "effect" as well as the standard error of this estimate.
Abstract: Most papers that employ Differences-in-Differences estimation (DD) use many years of data and focus on serially correlated outcomes but ignore that the resulting standard errors are inconsistent. To illustrate the severity of this issue, we randomly generate placebo laws in state-level data on female wages from the Current Population Survey. For each law, we use OLS to compute the DD estimate of its “effect” as well as the standard error of this estimate. These conventional DD standard errors severely understate the standard deviation of the estimators: we find an “effect” significant at the 5 percent level for up to 45 percent of the placebo interventions. We use Monte Carlo simulations to investigate how well existing methods help solve this problem. Econometric corrections that place a specific parametric form on the time-series process do not perform well. Bootstrap (taking into account the autocorrelation of the data) works well when the number of states is large enough. Two corrections based on asymptotic approximation of the variance-covariance matrix work well for moderate numbers of states and one correction that collapses the time series information into a “pre”- and “post”-period and explicitly takes into account the effective sample size works well even for small numbers of states.
9,397 citations
TL;DR: In this article, the authors examine the different methods used in the literature and explain when the different approaches yield the same (and correct) standard errors and when they diverge, and give researchers guidance for their use.
Abstract: In both corporate finance and asset pricing empirical work, researchers are often confronted with panel data. In these data sets, the residuals may be correlated across firms and across time, and OLS standard errors can be biased. Historically, the two literatures have used different solutions to this problem. Corporate finance has relied on clustered standard errors, while asset pricing has used the Fama-MacBeth procedure to estimate standard errors. This paper examines the different methods used in the literature and explains when the different methods yield the same (and correct) standard errors and when they diverge. The intent is to provide intuition as to why the different approaches sometimes give different answers and give researchers guidance for their use.
7,647 citations
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TL;DR: The authors describes the advantages of these studies and suggests how they can be improved and also provides aids in judging the validity of inferences they draw, such as multiple treatment and comparison groups and multiple pre- or post-intervention observations.
Abstract: Using research designs patterned after randomized experiments, many recent economic studies examine outcome measures for treatment groups and comparison groups that are not randomly assigned. By using variation in explanatory variables generated by changes in state laws, government draft mechanisms, or other means, these studies obtain variation that is readily examined and is plausibly exogenous. This paper describes the advantages of these studies and suggests how they can be improved. It also provides aids in judging the validity of inferences they draw. Design complications such as multiple treatment and comparison groups and multiple pre- or post-intervention observations are advocated.
7,222 citations
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TL;DR: In this paper, a limited-information two-step estimator for models with rational expectations and serially correlated disturbances was proposed. But the estimator greatly extends the area of applicability of McCallum's (1976) instrumental variables approach to rational expectations models.
Abstract: This paper introduces a limited-information two-step estimator for models with rational expectations and serially correlated disturbances. The estimator greatly extends the area of applicability of McCallum's (1976) instrumental variables approach to rational expectations models. Section I reviews McCallum's method and discusses in detail the problems surrounding its use in many empirical contexts. Section II presents the two-step two-stage least squares estimator (2S2S1) and demonstrates its efficiency relative to that of McCallum (1979). Section III provides a comparison nf several estimators for a two equation macroeconomic model with rational expectations due to Taylor (1979).Institutional subscribers to the NBER working paper series, and residents of developing countries may download this paper without additional charge at www.nber.org.
248 citations
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TL;DR: In this paper, the authors developed and applied a novel test of the Holt, et al. linear quadratic inventory model for non-durables data aggregated to the two-digit SIC code level.
Abstract: This paper develops and applies a novel test of the Holt, et al(1961) linear quadratic inventory model It is shown that a central property of the model is that a certain weighted sum of variances and covariances of production, sales and inventories must be nonnegative The weights are the basic structural parameters of the model The model may be tested by seeing whether this sum in fact is nonnegative When the test is applied to some non-durables data aggregated to the two-digit SIC code level, it almost always rejects the model, even though the model does well by traditional criteria
171 citations