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## Estimating standard errors in finance panel data sets: comparing approaches. (2009)

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Venue: | Review of Financial Studies |

Citations: | 889 - 7 self |

### Citations

3625 | W.Econometric Analysis - GREENE - 1990 |

3540 | Econometric Analysis of Cross Section and Panel Data - Wooldridge - 2002 |

3209 | A heteroscedasticity-consistent covariance matrix estimator and a direct test of heteroscedasticity - White - 1980 |

1540 | Risk, return and equilibrium: empirical tests
- Fama, MacBeth
- 1973
(Show Context)
Citation Context ...ive way to estimate the regression coefficients and standard errors which has been used in the literature, and one often suggested when the residuals are not independent, is the FamaMacBeth approach (=-=Fama and MacBeth, 1973-=-).10 In this approach, the researcher runs T cross sectional regressions. The average of the T estimates is the coefficient estimate and the estimated variance of the Fama-MacBeth estimate is calculat... |

1187 |
Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation,Econometrica
- Andrews
- 1991
(Show Context)
Citation Context ...cients and the standard errors using the Fama-MacBeth procedure (Fama-MacBeth, 1973). Twenty-nine percent of the papers included dummy variables for each cluster (e.g. fixed effects). The next two most common methods used OLS (or an analogous method) to estimate the coefficients but reported standard errors adjusted for correlation within a cluster. Seven percent of the papers adjusted the standard errors using the 2 Newey-West procedure (Newey and West, 1987) modified for use in a panel data set, while 23 percent of the papers reported clustered standard errors (Williams, 2000, Rogers, 1993, Andrews, 1991, Moulton, 1990, Arellano, 1987, Moulton, 1986) which are White standard errors adjusted to account for possible correlation within a cluster. These are also called Rogers standard errors. Although the literature has used a diversity of methods to estimate standard errors in panel data sets, the chosen method is often incorrect and the literature provides little guidance to researchers as to which method should be used. Since the methods sometimes produce incorrect estimates, it is important to understand how the methods compare and how to select the correct one. That is this paper’s objective... |

1130 |
Asset Pricing.
- Cochrane
- 2001
(Show Context)
Citation Context ...setting. I show that OLS and Fama-MacBeth standard errors are biased and clustered standard errors are unbiased. Simulating the temporary firm effect also allows me to examine the relative accuracy of two additional methods for adjusting standard errors: fixed effects (firm dummies) and an adjusted Fama-MacBeth standard error whose use is becoming more popular. I show that including fixed effects eliminates the bias in OLS standard errors only when the firm effect is fixed. I also show that even after adjusting Fama-MacBeth standard errors, as suggested by some authors, they are still biased (Cochrane, 2001). Most papers do not report standard errors estimated by multiple methods. Thus in Section VI, I apply the various estimation techniques to two real data sets and compare their relative performance. This serves two purposes. First, it demonstrates that the methods used in some published papers produce biases in the standard errors and t-statistics which are significant. This is why using the correct method to estimate standard errors is important. Examining actual data also allows me to show how differences in standard error estimates (e.g. White versus clustered standard error) can provide in... |

828 | How much should we trust differences-indifferences estimates? Quarterly - Bertrand, Duflo, et al. - 2004 |

775 | Estimating long-run relationships from dynamic heterogenous panels - Pesaran, R - 1995 |

692 |
An Illustration of a Pitfall in Estimating the Effects of Aggregate Variables on Micro Units
- Moulton
- 1990
(Show Context)
Citation Context ...andard errors using the Newey-West procedure (Newey and West, 1987) modified for use in a panel data set, while 22 percent of the papers reported Rogers standard errors (Rogers, 1993, Williams, 2000, =-=Moulton, 1990-=-) which are White standard errors adjusted to account for possible correlation within a cluster. These are also called clustered standard errors. 2Although the literature has used a diversity of metho... |

577 |
Random Group Effects and the Precision of Regression Estimates.”
- Moulton
- 1986
(Show Context)
Citation Context ... Xs. We will return to this issue in Section V when we examine non-fixed firm effects. If the panel is unbalanced, the true standard error and the bias in the OLS standard errors will be even larger (=-=Moulton, 1986-=-).s6 Var [ β̂OLS & β ] ' E jN i'1 jT t'1 Xit εit 2 jN i'1 jT t'1 X 2it &2 ' E jN i'1 jT t'1 Xit εit 2 jN i'1 jT t'1 X 2it &2 ' E jN i'1 jT t'1 X 2it ε 2 it % 2jT&1 t'1 jT s't%1 Xit Xis εit εis jN i'1 ... |

427 | 2002), “Market Timing and Capital Structure - Baker, Wurgler |

382 | Disappearing Dividends: Changing Firm Characteristics or Lower Propensity to Pay?
- Fama, French
- 2001
(Show Context)
Citation Context ...firm effect. As part of my literature survey, I looked for papers which regressed a persistent firm characteristics on other persistent firm characteristics. This is the type of data that will likely contain a firm effect. Since I am not able to replicate each of the studies, I will discuss several examples of where Fama-MacBeth standard errors have been used with such data. The first example is a logit estimate of whether a firm pays a dividend (a highly persistent variable) on firm characteristics such as the firm’s market to book ratio, the earnings to assets ratio, and relative firm size (Fama and French, 2001). Another example are the papers which examine how the market values firms by regressing a firm’s market to book ratio on firm characteristics such as the firm’s age, a dummy for whether it pays a dividend, leverage, and firm size (Pastor and Veronesi, 2003, and Kemsley and Nissim, 2002).10 A third example are the papers which run capital structure regressions. In these papers, the authors try to explain a firm’s use of leverage by regressing the firm’s debt to asset ratio on firm characteristics such as the firm’s market to book ratio, the ratio of property, plant, and equipment to total asse... |

367 | Testing Trade-off and Pecking Order Predictions about Dividends and Debt,” Working Paper,
- Fama, French
- 2000
(Show Context)
Citation Context ...ave suggested adjusting the standard errors for the estimated first order auto-correlation of the estimated slope coefficients (Chen, Hong, and Stein, 2001; Cochrane, 2001;sLakonishok, and Lee, 2001; =-=Fama and French, 2002-=-; Bakshi, Kapadia, and Madan, 2003; Chakravarty, Gulen, and Mayhew, 2004). The proposed adjustment is to estimate the correlation between the yearly coefficient estimates (i.e. Corr[βt , βt-1 ] = θ), ... |

362 |
Specification Tests in
- Hausman
- 1978
(Show Context)
Citation Context ... (ρε) and the first order auto correlation (φ), I can alter the pattern of auto correlations in the residual. The correlation of lag length k is: An analogous data structure is specified for the independent variable. The correlation for lags one 16 I assumed the model is correctly specified [i.e. Corr( Xi t , εi t ) = 0 ]. In this case, the only purpose of including firm dummies is to correct the standard errors. In real applications, the model may not be correctly specified [i.e. Corr( Xi t , εi t ) … 0 ], and so including fixed effects may be necessary to test the model’s specification (see Hausman, 1978). Instead of including firm dummies, we could have first differenced the data within firm. However, it would still be necessary to use clustered opposed to OLS standard errors, since the residuals would be correlated. 26 through nine for the four data specifications I examine are graphed in Figure 6. They range from a fixed firm effect (ρ=0.25 and φ=0.00) to a standard AR1 process (ρ=0.00 and φ=0.75). I assume the same process for both the independent variable and the residual, since it is the interaction of the two correlations which cause the bias in the standard error estimates (see Section... |

362 | Robust inference with multiway clustering. - Cameron, Gelbach, et al. - 2010 |

293 | Conjoint Analysis - Srinivasan - 1990 |

278 |
Founding-family ownership and firm performance:
- Anderson, Reeb
- 2004
(Show Context)
Citation Context ...ng on that dimension. Since most panel data sets have more firms than years, the most common approach is to include dummy variables for each year (to absorb the time effect) and then cluster by firm (=-=Anderson and Reeb, 2004-=-, Gross and Souleles, 2004, Petersen and Faulkendar, 2004, Sapienza, 2004, and Lamont and Polk, 2001).sI will use this approach in our simulations.sA) Rogers Standard Error Estimates. To test the rela... |

250 | 2000): “A Note on Robust Variance Estimation for Cluster-Correlated Data - Williams |

243 |
Computing robust standard errors for within-groups estimators
- Arellano
- 1987
(Show Context)
Citation Context ... using the Fama-MacBeth procedure (Fama-MacBeth, 1973). Twenty-nine percent of the papers included dummy variables for each cluster (e.g. fixed effects). The next two most common methods used OLS (or an analogous method) to estimate the coefficients but reported standard errors adjusted for correlation within a cluster. Seven percent of the papers adjusted the standard errors using the 2 Newey-West procedure (Newey and West, 1987) modified for use in a panel data set, while 23 percent of the papers reported clustered standard errors (Williams, 2000, Rogers, 1993, Andrews, 1991, Moulton, 1990, Arellano, 1987, Moulton, 1986) which are White standard errors adjusted to account for possible correlation within a cluster. These are also called Rogers standard errors. Although the literature has used a diversity of methods to estimate standard errors in panel data sets, the chosen method is often incorrect and the literature provides little guidance to researchers as to which method should be used. Since the methods sometimes produce incorrect estimates, it is important to understand how the methods compare and how to select the correct one. That is this paper’s objective. There are two general forms o... |

196 | Does the source of capital affect capital structure? - Faulkender, Petersen - 2006 |

195 | When does the market matter? stock prices and the investment of equity-dependent firms,
- Baker, Stein, et al.
- 2003
(Show Context)
Citation Context ...2004, for similar results). This conclusion, however, is sensitive to the firm effect being fixed. If the firm effect decays over time, the firm dummies no longer completely capture the within cluster dependence and 27 OLS standard errors are still biased (see Table 7 - Panel A, columns II-IV). In these simulations, the firm effect decays over time (in column II, 92 percent of the firm effect dissipates after 9 years). Once the firm effect is temporary, the OLS standard errors again underestimate the true standard errors even when firm dummies are included in the regression (Wooldridge, 2004, Baker, Stein, and Wurgler, 2003). The magnitude of the underestimation depends upon the magnitude of the temporary component of the firm effect (i.e. φ). The bias rises from about 17% when φ is 50 percent (column IV) to about 33 percent when φ is 75% (columns II and III). C) Adjusted Fama-MacBeth Standard Errors. As I showed in Section II, the presence of a firm effect causes the Fama-MacBeth standard error to be biased downward. Several authors have acknowledged the bias and have suggested adjusting the standard errors for the estimated first order auto-correlation of the estimated slope coefficients (Pontiff, 1996; Graham... |

190 | Do Conglomerate Firms Allocate Resources Inefficiently across Industries? Theory and Evidence”, - Maksimovic, Phillips - 2002 |

177 | The effects of government ownership on bank lending.
- Sapienza
- 2004
(Show Context)
Citation Context ...ost common approach is to include dummy variables for each year (to absorb the time effect) and then cluster by firm (Anderson and Reeb, 2004, Gross and Souleles, 2004, Petersen and Faulkendar, 2004, =-=Sapienza, 2004-=-, and Lamont and Polk, 2001).sI will use this approach in our simulations.sA) Rogers Standard Error Estimates. To test the relative performance of the two methods, 5,000 data sets were simulated with ... |

166 | Cluster-sample methods in applied econometrics. - Wooldridge - 2003 |

156 |
Costly arbitrage: Evidence from closed-end funds,
- Pontiff
- 1996
(Show Context)
Citation Context ...in, and Wurgler, 2003). The magnitude of the underestimation depends upon the magnitude of the temporary component of the firm effect (i.e. φ). The bias rises from about 17% when φ is 50 percent (column IV) to about 33 percent when φ is 75% (columns II and III). C) Adjusted Fama-MacBeth Standard Errors. As I showed in Section II, the presence of a firm effect causes the Fama-MacBeth standard error to be biased downward. Several authors have acknowledged the bias and have suggested adjusting the standard errors for the estimated first order auto-correlation of the estimated slope coefficients (Pontiff, 1996; Graham, Lemmon, and Schallheim, 1998; Christopherson, Ferson, and Glassman, 1998; Chen, Hong, and Stein, 2001; Cochrane, 2001; Lakonishok, and Lee, 2001; Fama and French, 2002; Kemsley and Nissim, 2002; Bakshi, Kapadia, and Madan, 2003; Pastor and Veronesi, 2003; Chakravarty, Gulen, and Mayhew, 2004). The proposed adjustment is to estimate the correlation between the yearly coefficient estimates (i.e. Corr[βt , βt-1 ] = θ), and then multiply the estimated variance by (1+ θ)/(1-θ) to account for serial correlation of the βs (see Chakravarty, Gulen, Mayhew, 2004 and Fama and French, 2002, foot... |

149 |
Are insider trades informative.
- LAKONISHOK, LEE
- 2001
(Show Context)
Citation Context ...the auto correlation of the slope coefficients was calculated. I then calculated the original and adjusted Fama-MacBeth standard errors, assuming both an infinite and a finite lag of T-1 periods (see =-=Lakonishok and Lee, 2001-=-).17 The estimated autocorrelation is imprecisely estimated as predicted by Fama and French (2002). The 90th percentile confidence interval ranges from -0.602 to 0.413, but the mean is -0.1134 (see Ta... |

147 | Stock valuation and learning about profitability. - Pastor, Veronesi - 2003 |

142 | Simple formulas for standard errors that cluster by both firm and time. Unpublished working paper. - Thompson - 2006 |

141 | What Drives Firm-Level Stock Returns?”
- Vuolteenaho
- 2002
(Show Context)
Citation Context ...ifferent number of observations per year. Thus in an unbalanced panel data set, Fama-MacBeth and OLS coefficient estimates can differ due to a different weighting of observations (Cohen, Gompers, and =-=Vuolteenaho, 2002-=-, Vuolteenaho, 2002). In addition, since Fama-MacBeth runs cross sectional regressions, any variable which does not vary across firms within a year (e.g. the stock market return, or the growth of GDP)... |

138 | Stock Return Characteristics, Skew Laws,
- Bakshi, Kapadia, et al.
- 2003
(Show Context)
Citation Context ... percent when φ is 75% (columns II and III). C) Adjusted Fama-MacBeth Standard Errors. As I showed in Section II, the presence of a firm effect causes the Fama-MacBeth standard error to be biased downward. Several authors have acknowledged the bias and have suggested adjusting the standard errors for the estimated first order auto-correlation of the estimated slope coefficients (Pontiff, 1996; Graham, Lemmon, and Schallheim, 1998; Christopherson, Ferson, and Glassman, 1998; Chen, Hong, and Stein, 2001; Cochrane, 2001; Lakonishok, and Lee, 2001; Fama and French, 2002; Kemsley and Nissim, 2002; Bakshi, Kapadia, and Madan, 2003; Pastor and Veronesi, 2003; Chakravarty, Gulen, and Mayhew, 2004). The proposed adjustment is to estimate the correlation between the yearly coefficient estimates (i.e. Corr[βt , βt-1 ] = θ), and then multiply the estimated variance by (1+ θ)/(1-θ) to account for serial correlation of the βs (see Chakravarty, Gulen, Mayhew, 2004 and Fama and French, 2002, footnote 1). This would seem to make intuitive sense since the presence of a firm effect causes the yearly coefficient estimates to be serially correlated. To test the merits of this idea, I simulated data sets where the fixed firm effect ac... |

124 |
Market reactions to tangible and intangible information, Working paper,
- Daniel, Titman
- 2001
(Show Context)
Citation Context ...ne to make the R2 comparable between the OLS and the Fama-MacBeth results. Although the Fama-MacBeth procedure estimates a separate intercept for each year, the constant is calculated as the average of the yearly intercepts. Thus the Fama-MacBeth R2 does not include the explanatory power of time dummies. Procedurally, I subtracted the yearly means off of each variable before running the OLS regressions. 31 dummies. This makes the efficiency of the OLS and Fama-MacBeth coefficients similar.20 A) Asset Pricing Application. For the asset pricing example, I used the equity return regressions from Daniel and Titman (2004, “Market Reactions to Tangible and Intangible Information”). To demonstrate the effect of equity issues on future equity returns, they regress monthly returns on annual values of lagged book to market ratios, historic changes in book and market values, and a measure of the firm’s equity issuance. The data is briefly described in the appendix and in detail in their paper. Each observation of the dependent variable is a monthly equity return. However, the independent variables are annual values (based on the prior year). Thus for the twelve observations in a year, the dependent variable (equity... |

117 |
cross-listings and the private benefits of control: Evidence from dualclass firms
- Doidge
(Show Context)
Citation Context ...h was designed to deal with time effects in a panel data set, not firm effects, I turn to this data structure in the next section. E) Newey-West Standard Errors. An alternative approach for addressing the correlation of errors across observation is the Newey-West procedure (Newey and West, 1987). This procedure was initially designed to account for serial correlation of unknown form in the residuals of a single time series. It has been modified for use in a panel data set by estimating only correlations between lagged residuals in the same cluster (see Bertrand, Duflo, and Mullainathan, 2004, Doidge, 2004, MacKay, 2003, Brockman and Chung, 2001). The problem of choosing a lag length is simplified in a panel data set, since the maximum lag length is one less than the maximum number of years per firm.12 To examine the relative performance of the Newey-West, I simulated 5,000 data sets where the fixed firm effect is assumed to account for twenty-five percent of the variability of both the independent variable and the residual. The standard error estimated by the Newey-West is an increasing function of the lag length in the simulation. When the lag length is set to zero, the estimated standard err... |

114 | An empirical analysis of personal bankruptcy and delinquency.
- Gross, Souleles
- 2002
(Show Context)
Citation Context ...ce most panel data sets have more firms than years, the most common approach is to include dummy variables for each year (to absorb the time effect) and then cluster by firm (Anderson and Reeb, 2004, =-=Gross and Souleles, 2004-=-, Petersen and Faulkendar, 2004, Sapienza, 2004, and Lamont and Polk, 2001).sI will use this approach in our simulations.sA) Rogers Standard Error Estimates. To test the relative performance of the tw... |

111 | Conditioning Manager Alphas on Economic Information: Another Look at the Persistence of Performance." - Christopherson, Ferson, et al. - 1998 |

96 | Forecasting crashes: Trading volume, past returns, and conditional skewness in stock prices.
- Chen, Hong, et al.
- 2001
(Show Context)
Citation Context ...used the Fama-MacBeth approach have acknowledged the downward bias and have suggested adjusting the standard errors for the estimated first order auto-correlation of the estimated slope coefficients (=-=Chen, Hong, and Stein, 2001-=-; Cochrane, 2001;sLakonishok, and Lee, 2001; Fama and French, 2002; Bakshi, Kapadia, and Madan, 2003; Chakravarty, Gulen, and Mayhew, 2004). The proposed adjustment is to estimate the correlation betw... |

95 |
Robust Standard Errors Estimation in Fixed-Effects Panel Models
- Kezdi
- 2003
(Show Context)
Citation Context ...s with in a cluster, its consistency depends upon having a sufficient number of clusters to estimate these standard errors. Based on these results, 10 clusters is too small and 500 in sufficient (see =-=Kezdi, 2002-=-, and Bertrand, Duflo, and Mullainathan, 2004 for similar results). To explore this issue further, I simulated data sets of 5,000 observations but with the number of years (or clusters) ranging from 1... |

91 | Why Constrain Your Mutual Fund Manager?" - Almazan, Brown, et al. - 2004 |

90 | Short sales, institutional investors, and the cross-section of stock returns, - Nagel - 2005 |

82 | Debt, Leases, Taxes, and the Endogeneity of Corporate Tax Status. - Graham, Lemmon, et al. - 1998 |

79 |
Regression Standard Errors in
- Rogers
- 1993
(Show Context)
Citation Context ... of the papers adjusted the standard errors using the Newey-West procedure (Newey and West, 1987) modified for use in a panel data set, while 22 percent of the papers reported Rogers standard errors (=-=Rogers, 1993-=-, Williams, 2000, Moulton, 1990) which are White standard errors adjusted to account for possible correlation within a cluster. These are also called clustered standard errors. 2Although the literatur... |

78 | Do domestic investors have an edge? The trading experience of foreign investors in Korea, - Choe, Kho, et al. - 2005 |

68 | Does diversification destroy value? evidence from the industry shocks,
- Lamont, Polk
- 2002
(Show Context)
Citation Context ...is to include dummy variables for each year (to absorb the time effect) and then cluster by firm (Anderson and Reeb, 2004, Gross and Souleles, 2004, Petersen and Faulkendar, 2004, Sapienza, 2004, and =-=Lamont and Polk, 2001-=-).sI will use this approach in our simulations.sA) Rogers Standard Error Estimates. To test the relative performance of the two methods, 5,000 data sets were simulated with 21 both a firm and a time e... |

64 | Informed trading in stock and option markets.
- Chakravarty, Gulen, et al.
- 2004
(Show Context)
Citation Context ...ated first order auto-correlation of the estimated slope coefficients (Chen, Hong, and Stein, 2001; Cochrane, 2001;sLakonishok, and Lee, 2001; Fama and French, 2002; Bakshi, Kapadia, and Madan, 2003; =-=Chakravarty, Gulen, and Mayhew, 2004-=-). The proposed adjustment is to estimate the correlation between the yearly coefficient estimates (i.e. Corr[βt , βt-1 ] = θ), and then multiply the estimated variance by (1+ θ)/(1-θ) to account for ... |

59 |
An Asymptotic Theory for Estimating BetaPricing Models Using Cross-Sectional Regression.”
- Jagannathan, Wang
- 1998
(Show Context)
Citation Context ...imates in a more general context, I simulated a data structure which includes both a permanent component (a fixed firm effect) and a temporary component (non-fixed firm effect) which I assume is a first order auto Var( ηit ) ' σ 2 ς if t ' 1 ' φ2 σ2ς % (1 & φ 2) σ2ς ' σ 2 ς if t > 1 15 I multiply the ς term by %&1&- &φ&2 to make the residuals homoscedastic. From equation (16), where the last step is by recursion (if it is true for t=m, it is true for t=m+1). Assuming homoscedastic residuals is not necessary since the Fama-MacBeth and clustered standard errors are robust to heteroscedasticity (Jagannathan and Wang, 1998, & Rogers, 1993). However, assuming homoscedasticity makes the interpretation of the results simpler. If I assume the residuals are homoscedastic, then any difference in the standard errors I find is due to the dependence of observations within a cluster not heteroscedasticity. 25 ηit ' ςit if t ' 1 ' φ ηit&1 % 1 & φ 2 ςit if t > 1 (16) Corr (εi,t , εi,t&k ) ' Cov( γi % ηi,t ,γi % ηi,t&k ) Var ( γi % ηi,t ) Var ( γi % ηi,t&k ) ' σ2γ % φk σ 2 η σ2γ % σ 2 η ' ρε % (1 & ρε ) φ k (17) regressive process. This allows the firm effect to die away at a rate between a first order autoregressive decay ... |

55 | Do Behavioral Biases Affect Prices? - Coval, Shumway - 2005 |

55 | Asymptotic properties of a robust variance matrix estimator for panel data when T is large. Journal of Econometrics. forthcoming
- Hansen
- 2005
(Show Context)
Citation Context ...he problem arises due to the limited number of clusters (e.g. years). When I estimated the standard errors in the presence of the firm effects, I had 500 firms (clusters). When I estimated the standard errors in the presence of a time effect, I have only 10 years (clusters). Since the clustered standard error places no restriction on the correlation structure of the residuals within a cluster, its consistency depends upon having a sufficient number of clusters. Based on these results, 10 clusters is too small and 500 is sufficient (see Kezdi, 2004, and Bertrand, Duflo, and Mullainathan, 2004, Hansen, 2005). To explore this issue, I simulated data sets of 5,000 observations with the number of years 21 (or clusters) ranging from 10 to 100. In all of the simulations, 25 percent of the variability in both the independent variable and the residual is due to the time effect [i.e. ρX = ρε = 0.25]. The bias in the clustered standard error estimates declines with the number of clusters, dropping from 13 percent when there are 10 years (or clusters) to 4 percent when there are 40 years to under 1 percent when there are 100 years (see Figure 5). The bias in the clustered standard error estimates is a prod... |

41 |
Managerial Timing and Corporate Liquidity: Evidence from Actual Share Repurchases,
- Brockman, Chung
- 2001
(Show Context)
Citation Context .... It can be modified for use in a panel data set by estimating only correlations between lagged residuals in the same cluster (seesBertrand, Duflo, and Mullainathan, 2004, Doidge, 2004, MacKay, 2003, =-=Brockman and Chung, 2001-=-). This also simplifies the problem of choosing a lag length since the maximum lag length is one less than the maximum number of years per firm.11 To examine the relative performance of the and T-t le... |

39 | Vuolteenaho (2002). Who Underreacts to Cash-Flow News? Evidence from Trading Between Individuals and Institutions - Cohen, Gompers, et al. |

32 | t-statistic based correlation and heterogeneity robust inference. - Ibragimov, Muller - 2010 |

31 | Liquidity: Urban versus rural firms - Loughran, Schultz - 2005 |

29 | Longitudinal analysis using generalized linear models. - LIANG, ZEGER - 1986 |

24 | 2006), “Inference with Difference in Differences and Other Panel Data,” forthcoming in The Review of Economics and Statistics - Donald, Lang |

22 | Dividend taxes and share prices: evidence from real estate investment trusts - Gentry, Kemsley, et al. - 2003 |

20 |
Real Flexibility and Financial Structure: An Empirical Analysis”
- MacKay
- 2003
(Show Context)
Citation Context ...le time series. It can be modified for use in a panel data set by estimating only correlations between lagged residuals in the same cluster (seesBertrand, Duflo, and Mullainathan, 2004, Doidge, 2004, =-=MacKay, 2003-=-, Brockman and Chung, 2001). This also simplifies the problem of choosing a lag length since the maximum lag length is one less than the maximum number of years per firm.11 To examine the relative per... |

20 | 2006), “Market Reaction to Tangible and Intangible - Daniel, Titman |

19 |
Bootstrap measures for standard errors, confidence intervals, and other measures of statistical accuracy.
- Efron, Tibshirani
- 1986
(Show Context)
Citation Context ...ustered standard error formula (see footnote 5) except for the weighting function [w(j)]. The clustered standard errors use a weighting function of one for all co-variances. The Newey-West procedure was originally designed for a single time-series and the weighting function was necessary to make the estimate of this matrix positive semi-definite. For fixed j the 13 Although the bootstrap method of estimating standard errors was rarely used in the articles which I surveyed, it is an alternative way to estimate the standard errors in a panel data set (see for example Kayhan and Titman, 2004 and Efron and Tibshirani, 1986). To test its relative performance, I drew 100 samples with replacement and re-estimated the regression for each simulated data set. When I drew observations independently (e.g. I drew 5,000 firm-year), the estimated standard errors are the same as the OLS standard errors reported in Table I (e.g. 0.0282 for the bootstrap versus 0.0283 for OLS when ρX = ρε = 0.50). When I drew observations as a cluster (e.g. I drew 500 firms with replacement and took all 10 years for any firm which was drawn), the estimated standard errors are the same as the clustered standard errors (e.g. 0.0505 for bootstra... |

17 | Robust Standard Error Estimation - Kezdi - 2004 |

10 | The limits of noise trading: An experimental analysis. Discussion paper, - Bloomfeld, O’Hara, et al. - 2005 |

8 | Debt Maturity and the Effects of Growth Opportunities - Johnson - 2003 |

6 | and Doron Nissim, 2002, “Valuation of the Debt Tax Shield - Kemsley |

6 |
An Illustration of a Pitfall in Estimating the Effects of
- Moulton
- 1990
(Show Context)
Citation Context ...standard errors using the Fama-MacBeth procedure (Fama-MacBeth, 1973). Twenty-nine percent of the papers included dummy variables for each cluster (e.g. fixed effects). The next two most common methods used OLS (or an analogous method) to estimate the coefficients but reported standard errors adjusted for correlation within a cluster. Seven percent of the papers adjusted the standard errors using the 2 Newey-West procedure (Newey and West, 1987) modified for use in a panel data set, while 23 percent of the papers reported clustered standard errors (Williams, 2000, Rogers, 1993, Andrews, 1991, Moulton, 1990, Arellano, 1987, Moulton, 1986) which are White standard errors adjusted to account for possible correlation within a cluster. These are also called Rogers standard errors. Although the literature has used a diversity of methods to estimate standard errors in panel data sets, the chosen method is often incorrect and the literature provides little guidance to researchers as to which method should be used. Since the methods sometimes produce incorrect estimates, it is important to understand how the methods compare and how to select the correct one. That is this paper’s objective. There are two... |

4 |
Firms' Histories and Their Capital Structures” University of Texas at Austin working paper.
- Kayhan, Titman
- 2004
(Show Context)
Citation Context ... This is identical to the clustered standard error formula (see footnote 5) except for the weighting function [w(j)]. The clustered standard errors use a weighting function of one for all co-variances. The Newey-West procedure was originally designed for a single time-series and the weighting function was necessary to make the estimate of this matrix positive semi-definite. For fixed j the 13 Although the bootstrap method of estimating standard errors was rarely used in the articles which I surveyed, it is an alternative way to estimate the standard errors in a panel data set (see for example Kayhan and Titman, 2004 and Efron and Tibshirani, 1986). To test its relative performance, I drew 100 samples with replacement and re-estimated the regression for each simulated data set. When I drew observations independently (e.g. I drew 5,000 firm-year), the estimated standard errors are the same as the OLS standard errors reported in Table I (e.g. 0.0282 for the bootstrap versus 0.0283 for OLS when ρX = ρε = 0.50). When I drew observations as a cluster (e.g. I drew 500 firms with replacement and took all 10 years for any firm which was drawn), the estimated standard errors are the same as the clustered standard ... |

4 |
Stock Valuation and Learning about
- Pastor, Veronesi
- 2003
(Show Context)
Citation Context ...ses the true standard error of the estimated coefficients. To make this concrete, take the extreme example where ρXρε is equal to one; the true standard error is (σε/NσX) while the estimated FamaMacBeth standard error is zero. This additional source of bias shrinks as the number of years increases since the estimated slope coefficient will converge to the true coefficient (see Figure 3). Although I have just demonstrated that the Fama-MacBeth standard errors are biased in the 10 Both papers correct the Fama-MacBeth standard errors for the first order auto-correlation of the estimated slopes. Pastor and Veronesi (2003) report that this does not change their answer. I will show in Section V-C that this correction still produces biased standard errors and this may explain Pastor and Veronesi’s finding that the adjustment has little effect on their estimated standard errors. 11 Baker and Wurgler (2002) estimate both White and Fama-MacBeth standard errors but do not report the Fama-MacBeth standard errors since they are the same as the White standard errors. Fama and French (2002) acknowledge that Fama-MacBeth standard errors may understate the true standard errors and so report adjusted FamaMacBeth standard er... |

2 | Panel Data inference in Finance: Least-Squares vs Fama-MacBeth” Northwestern working paper.
- Skoulakis
- 2005
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Citation Context ...ama-MacBeth will effectively under weight the later observations. To correct this, I took a weighted average of the monthly coefficient estimates where the weights were proportional to Nt. When I compare the weighted and un-weighted coefficient estimates and standard errors, they are very close (compare columns IV and V of Table 8). The weights are uncorrelated with the variables and thus do not effect the results, in this case. More sophisticated weighting schemes should be able to improve the efficiency of Fama-MacBeth estimates. However such estimators can be unstable in small samples (see Skoulakis, 2005). B) Corporate Finance Application. For the corporate finance illustration, I used a capital structure regression since this is an example of where the literature uses Fama-MacBeth standard errors. The independent variables are those which are common from the literature (firm size, firm age, asset tangibility, and firm profitability). The sample contains NYSE firms which pay a dividend in the previous year for the years 1965-2003. I lagged the independent variables one year relative to the dependent variable. The 35 results are reported in Table 9. The relative importance of the firm effect an... |

1 | Robust Interfence wiht Multiway Clustering,” University of California-Davis working paper - Cameron, Gelbach, et al. - 2006 |

1 | Firms' Histories and Their Capital Structures” forthcoming - Kayhan, Titman - 2004 |

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Debt Maturity and the Effects of Growth Opportunites and Liquidity Risk on
- Johnson
- 2003
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Citation Context ... age, a dummy for whether it pays a dividend, leverage, and firm size (Pastor and Veronesi, 2003, and Kemsley and Nissim, 2002).10 A third example are the papers which run capital structure regressions. In these papers, the authors try to explain a firm’s use of leverage by regressing the firm’s debt to asset ratio on firm characteristics such as the firm’s market to book ratio, the ratio of property, plant, and equipment to total assets, the earnings to assets, depreciation to asset ratio, R&D to assets ratio, and firm size (see for example Baker and Wurgler, 2002, Fama and French, 2002, and Johnson, 2003).11 Since both the left and right hand side variables in these 16 three regressions are highly persistent, this is the kind of data which likely contains a significant firm effect. In Section VI-B, I will estimate a capital structure regression and show that the magnitude of the bias is indeed large. Despite the presence of a firm effect and the resulting bias of FamaMacBeth standard errors documented above, they are still used in the literature. The literature is a teaching tool. Authors read published papers to learn which econometric methods are appropriate in which situations. Thus when re... |