All Events Induce Variance: Analyzing Abnormal Returns When Effects Vary across Firms

2007 ◽  
Vol 42 (1) ◽  
pp. 229-256 ◽  
Author(s):  
Scott E. Harrington ◽  
David G. Shrider
Keyword(s):  
Least Squares ◽  
Weighted Least Squares ◽  
Abnormal Returns ◽  
Event Studies ◽  
Standard Errors ◽  
Cross Sectional ◽  
Explanatory Variables ◽  
Robust Tests ◽  
Nonzero Mean ◽  
Short Horizon

AbstractWe demonstrate analytically that cross-sectional variation in the effects of events, i.e., in true abnormal returns, necessarily produces event-induced variance increases, biasing popular tests for mean abnormal returns in short-horizon event studies. We show that unexplained cross-sectional variation in true abnormal returns plausibly produces nonproportional heteroskedasticity in cross-sectional regressions, biasing coefficient standard errors for both ordinary and weighted least squares. Simulations highlight the resulting biases, the necessity of using tests robust to cross-sectional variation, and the power of robust tests, including regression-based tests for nonzero mean abnormal returns, which may increase power by conditioning on relevant explanatory variables.

Estimating cross-sectional regressions in event studies with conditional heteroskedasticity and regression designs that have leverage

2014 ◽  
Vol 10 (4) ◽  
pp. 418-431 ◽  
Author(s):  
Imre Karafiath
Keyword(s):  
Least Squares ◽  
Event Studies ◽  
Standard Errors ◽  
Conditional Heteroskedasticity ◽  
Test Statistics ◽  
Finite Sample ◽  
Cross Sectional ◽  
Content Type ◽  
Finite Sample Properties ◽  
Regression Design

Purpose – In the finance literature, fitting a cross-sectional regression with (estimated) abnormal returns as the dependent variable and firm-specific variables (e.g. financial ratios) as independent variables has become de rigueur for a publishable event study. In the absence of skewness and/or kurtosis the explanatory variable, the regression design does not exhibit leverage – an issue that has been addressed in the econometrics literature on the finite sample properties of heteroskedastic-consistent (HC) standard errors, but not in the finance literature on event studies. The paper aims to discuss this issue. Design/methodology/approach – In this paper, simulations are designed to evaluate the potential bias in the standard error of the regression coefficient when the regression design includes “points of high leverage” (Chesher and Jewitt, 1987) and heteroskedasticity. The empirical distributions of test statistics are tabulated from ordinary least squares, weighted least squares, and HC standard errors. Findings – None of the test statistics examined in these simulations are uniformly robust with regard to conditional heteroskedasticity when the regression includes “points of high leverage.” In some cases the bias can be quite large: an empirical rejection rate as high as 25 percent for a 5 percent nominal significance level. Further, the bias in OLS HC standard errors may be attenuated but not fully corrected with a “wild bootstrap.” Research limitations/implications – If the researcher suspects an event-induced increase in return variances, tests for conditional heteroskedasticity should be conducted and the regressor matrix should be evaluated for observations that exhibit a high degree of leverage. Originality/value – This paper is a modest step toward filling a gap on the finite sample properties of HC standard errors in the event methodology literature.

scholarly journals Robust Standard Errors for Panel Regressions with Cross-Sectional Dependence

2007 ◽  
Vol 7 (3) ◽  
pp. 281-312 ◽  
Author(s):  
Daniel Hoechle
Keyword(s):  
Least Squares ◽  
Fixed Effects ◽  
Weighted Least Squares ◽  
Ordinary Least Squares ◽  
Standard Errors ◽  
Least Squares Regression ◽  
Finite Sample ◽  
Cross Sectional ◽  
Finite Sample Properties ◽  
Cross Sectional Dependence

I present a new Stata program, xtscc, that estimates pooled ordinary least-squares/weighted least-squares regression and fixed-effects (within) regression models with Driscoll and Kraay (Review of Economics and Statistics 80: 549–560) standard errors. By running Monte Carlo simulations, I compare the finite-sample properties of the cross-sectional dependence–consistent Driscoll–Kraay estimator with the properties of other, more commonly used covariance matrix estimators that do not account for cross-sectional dependence. The results indicate that Driscoll–Kraay standard errors are well calibrated when cross-sectional dependence is present. However, erroneously ignoring cross-sectional correlation in the estimation of panel models can lead to severely biased statistical results. I illustrate the xtscc program by considering an application from empirical finance. Thereby, I also propose a Hausman-type test for fixed effects that is robust to general forms of cross-sectional and temporal dependence.

Event Studies in Logistics Research

2018 ◽  
pp. 231-259
Author(s):  
Lincoln C. Wood
Keyword(s):  
Supply Chain ◽  
Event Study ◽  
Abnormal Returns ◽  
Event Studies ◽  
Research Articles ◽  
Management Research ◽  
Cross Sectional ◽  
Design Considerations ◽  
Managerial Decisions ◽  
Event Study Method

The event study method allows researchers to examine the importance of an event to firms based on the magnitude and direction of abnormal returns, and then use these results in a cross-sectional regression to understand which managerial decisions may affect these outcomes. While the method has been heavily used in some disciplines, in-management research and logistics research, in particular, the method remains little used and is often used with little thought to key assumptions and design considerations. This chapter aims to provide an overview of the method for logistics and supply chain researchers with a focus on developing the capability to design an effective study and to evaluate research articles to determine possible weaknesses.

scholarly journals Analysis of algebraic weighted least-squares estimators for enzyme parameters

1992 ◽  
Vol 288 (2) ◽  
pp. 533-538 ◽  
Author(s):  
M E Jones
Keyword(s):  
Least Squares ◽  
Coefficient Of Variation ◽  
Constant Coefficient ◽  
Weighted Least Squares ◽  
Simulated Data ◽  
Standard Errors ◽  
Parameter Estimates ◽  
Spreadsheet Program ◽  
Least Squares Estimators ◽  
Constant Coefficient Of Variation

An algorithm for the least-squares estimation of enzyme parameters Km and Vmax. is proposed and its performance analysed. The problem is non-linear, but the algorithm is algebraic and does not require initial parameter estimates. On a spreadsheet program such as MINITAB, it may be coded in as few as ten instructions. The algorithm derives an intermediate estimate of Km and Vmax. appropriate to data with a constant coefficient of variation and then applies a single reweighting. Its performance using simulated data with a variety of error structures is compared with that of the classical reciprocal transforms and to both appropriately and inappropriately weighted direct least-squares estimators. Three approaches to estimating the standard errors of the parameter estimates are discussed, and one suitable for spreadsheet implementation is illustrated.

Multibrand Transition Probabilities as a Function of Explanatory Variables: Estimation by a Least-Squares-Based Approach

1986 ◽  
Vol 23 (2) ◽  
pp. 177-183 ◽  
Author(s):  
Fred S. Zufryden
Keyword(s):  
Least Squares ◽  
Goodness Of Fit ◽  
Transition Probabilities ◽  
Weighted Least Squares ◽  
Estimation Procedure ◽  
Explanatory Variables ◽  
First Order ◽  
Proposed Model ◽  
Markov Transition ◽  
The Relationship

A model is formulated to express the relationship between first-order Markov transition probabilities for a multibrand market and explanatory variables. The author shows that the parameters of the model can be estimated through a proposed restricted weighted least squares procedure. An empirical implementation of the estimation procedure illustrates the structure, goodness of fit, and predictive validity of the proposed model.

scholarly journals Predictors of age-associated decline in maximal aerobic capacity: a comparison of four statistical models

1998 ◽  
Vol 84 (6) ◽  
pp. 2163-2170 ◽  
Author(s):  
Mitchell J. Rosen ◽  
John D. Sorkin ◽  
Andrew P. Goldberg ◽  
James M. Hagberg ◽  
Leslie I. Katzel
Keyword(s):  
Least Squares ◽  
Aerobic Capacity ◽  
Weighted Least Squares ◽  
General Linear Model ◽  
Ordinary Least Squares ◽  
Fat Free Mass ◽  
Maximal Aerobic Capacity ◽  
Cross Sectional ◽  
Indicator Variable ◽  
Log Linear

Studies assessing changes in maximal aerobic capacity (V˙o 2 max) associated with aging have traditionally employed the ratio ofV˙o 2 max to body weight. Log-linear, ordinary least-squares, and weighted least-squares models may avoid some of the inherent weaknesses associated with the use of ratios. In this study we used four different methods to examine the age-associated decline inV˙o 2 max in a cross-sectional sample of 276 healthy men, aged 45–80 yr. Sixty-one of the men were aerobically trained athletes, and the remainder were sedentary. The model that accounted for the largest proportion of variance was a weighted least-squares model that included age, fat-free mass, and an indicator variable denoting exercise training status. The model accounted for 66% of the variance inV˙o 2 max and satisfied all the important general linear model assumptions. The other approaches failed to satisfy one or more of these assumptions. The results indicated thatV˙o 2 max declines at the same rate in athletic and sedentary men (0.24 l/min or 9%/decade) and that 35% of this decline (0.08 l ⋅ min−1 ⋅ decade−1) is due to the age-associated loss of fat-free mass.

THE PERFORMANCE OF LEVERAGE BASED NEAR NEIGHBOUR-ROBUST WEIGHT LEAST SQUARES IN MULTIPLE LINEAR REGRESSION IN THE PRESENCE OF HETEROSCEDASTIC ERRORS AND OUTLIER

2015 ◽  
Vol 76 (13) ◽  
Author(s):  
Khoo Li Peng ◽  
Robiah Adnan ◽  
Maizah Hura Ahmad
Keyword(s):  
Linear Regression ◽  
Multiple Linear Regression ◽  
Least Squares ◽  
Standard Error ◽  
Weighted Least Squares ◽  
Ordinary Least Squares ◽  
Standard Errors ◽  
Data Sets ◽  
Near Neighbour ◽  
Heteroscedastic Errors

In this study, Leverage Based Near Neighbour–Robust Weighted Least Squares (LBNN-RWLS) method is proposed in order to estimate the standard error accurately in the presence of heteroscedastic errors and outliers in multiple linear regression. The data sets used in this study are simulated through monte carlo simulation. The data sets contain heteroscedastic errors and different percentages of outliers with different sample sizes.  The study discovered that LBNN-RWLS is able to produce smaller standard errors compared to Ordinary Least Squares (OLS), Least Trimmed of Squares (LTS) and Weighted Least Squares (WLS). This shows that LBNN-RWLS can estimate the standard error accurately even when heteroscedastic errors and outliers are present in the data sets.

The evaluation of sires from progeny test data

1965 ◽  
Vol 7 (2) ◽  
pp. 221-231 ◽  
Author(s):  
E. P. Cunningham
Keyword(s):  
Least Squares ◽  
Test Data ◽  
Field Data ◽  
Weighted Least Squares ◽  
Standard Errors ◽  
Breeding Values ◽  
Worked Example ◽  
Sire Evaluation ◽  
Orthogonal Field ◽  
Genetic Trends

SUMMARYThe extraction of sire proofs from non-orthogonal field data of the type met with in cattle A.I. populations presents special problems.A weighted least squares procedure for the estimation of sire effects from data of this kind, cross-classified by sire and herd, is described. Expected Breeding Values computed from these estimates have certain optimum properties. The standard errors of the estimates of the Expected Breeding Values are derived. The method makes it possible to classify the sires into groups before the proofs are computed. This sub-division of the stud could be useful in young sire evaluation and in measuring genetic trends in the proven stud. The computations are readily programmed for a computer, and the assumptions involved in the use of the method are particularly well suited to A.I. progeny field data, especially where an annual draft of young sires is being tested. A worked example is given.

Evaluation for estimating of the PDF and the CDF of Generalized Inverted Exponential Distribution with Application in Industry

2020 ◽  
pp. 507-522
Author(s):  
Parisa Torkaman
Keyword(s):  
Least Squares ◽  
Exponential Distribution ◽  
Mean Squared Error ◽  
Weighted Least Squares ◽  
Real Data ◽  
Minimum Variance ◽  
Cumulative Distribution ◽  
Estimation Methods ◽  
Data Set ◽  
Better Than

The generalized inverted exponential distribution is introduced as a lifetime model with good statistical properties. This paper, the estimation of the probability density function and the cumulative distribution function of with five different estimation methods: uniformly minimum variance unbiased(UMVU), maximum likelihood(ML), least squares(LS), weighted least squares (WLS) and percentile(PC) estimators are considered. The performance of these estimation procedures, based on the mean squared error (MSE) by numerical simulations are compared. Simulation studies express that the UMVU estimator performs better than others and when the sample size is large enough the ML and UMVU estimators are almost equivalent and efficient than LS, WLS and PC. Finally, the result using a real data set are analyzed.

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