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Standard Errors in CF

Standard Errors in CF. Robin Greenwood Empirical Topics in Corporate Finance March 2011. Panel regressions. “Clustering is a Cambridge sickness” Tuomo Vuolteenaho. Panel Regressions. Hard to disentangle issues associated with specification design with issues related to standard errors

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Standard Errors in CF

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  1. Standard Errors in CF Robin Greenwood Empirical Topics in Corporate Finance March 2011

  2. Panel regressions • “Clustering is a Cambridge sickness” • TuomoVuolteenaho

  3. Panel Regressions • Hard to disentangle issues associated with specification design with issues related to standard errors • Today all about SEs

  4. Lang, Ofek, Stulz (1995) • Leverage and Investment (panel regression) • OLS, p-values, no firm fixed effects

  5. Opler, Pinkowitz, Stulz, Williamson (1999) • Corporate Cash Holdings • White SE, or Fama Macbeth, plus FE regs

  6. Stulz and Williamson (2003) • Culture, Openness, and Finance • Back to OLS country regressions

  7. Helwege, Pirinsky, and Stulz • Why do firms become widely held? • Pooled OLS: Depvar = 5% drop in ownership

  8. Stulz and Fahlenbrach (2009) • Changes in q and changes in ownership, cluster

  9. Doidge, Karolyi, and Stulz • Why has IPO activity picked up everywhere but for the US?

  10. Fama-Macbeth • Workhorse empirical method in modern finance • Used to deal with panels where there is high degree of cross-sectional correlation, but not much time correlation • Makes sense to use this when describing returns • Mostly random • Correlated across firms • Some time-dependence, however, at least in the expected return component • Vastly overused • Together with “portfolio” approaches

  11. Panel Analysis ←N→ ←N→ Yit 100 Xit 3 4 100 100 ↑ T ↓ 100 100 Fama Macbeth 5 100 100 100 100 1 2

  12. Panel Analysis ←N→ ←N→ Yit 100 Xit 3 4 100 100 ↑ T ↓ 100 100 Fama Macbeth 5 100 100 100 100 1 2

  13. Watch out for persistence • Good scenario for bts: • Bad scenario:

  14. Watch out for persistence • Good scenario for bts: • Bad scenario:

  15. Watch out for persistence • Good scenario for bts: • Bad scenario: Simple fix: Modify using Newey-West In my experience, Approximately doubles The SEs

  16. Fama & Macbeth • Original use in asset pricing • Stage 1: Estimate betas • Stage 2: Estimate cross-sectional relation between returns and betas • Stage 3: Collect your estimates and get t-stat • Benefit: Flexible parameters, not memory intensive • These benefits are less apparent today, yet method still popular because it’s hard to game • Main benefit: Weights PERIODS equally • Can get close to this by running panel and weighting by 1/N(t), but people will be suspicious

  17. Still mostly used in Asset Pricing • Pontiff and Woodgate, Share issuance and cross-sectional returns • Table VI

  18. Gong, Louis, Sun“Earnings management following open-market repurchases”

  19. Examples of FM from Corporate Finance • Fama French 2002– Testing tradeoff vs. pecking order

  20. Main table 1965-1999

  21. Estimating Standard Errors in Finance Panel Data Sets: Comparing Approaches Mitch Petersen RFS 2009

  22. Papers Contribution • Examines a variety of approaches to estimating standard errors and statistical significance in panel data sets • Also looks at a variety of papers published from 2001-2004: • Only 42% of papers adjusted standard errors for possible dependence in residuals. • Many different approaches. • Which are correct under what circumstances. • The bar for you will be much higher

  23. Overview • OLS standard errors are unbiased when residuals are independent and identically distributed. • Residuals in panel data may be correlated by firm-specific effects that are correlated across time. • Firm effect. • Residuals of a given year may be correlated across different firms (cross sectional dependence) • Time effect.

  24. Paper’s Approach • Simulate data that has either firm effect or a time effect. • Test various estimation techniques. • See how they deal with the simulated data. • Then takes regression approaches to actual data and compares them.

  25. Firm Fixed Effects • Assumption of OLS is that cross product matrix has only non-zero numbers on the diagonal. • Figure 1 – Example of a firm effect. • Cluster standard errors by firm.

  26. Time for other firms Time for this firm

  27. Time for this firm Time for other firms Firm 1, date 1 Firm 1, date 2 … Firm 2, date 1 Firm 2, date 2

  28. OLS vs. Clustering by Time vs. FM with Firm Effect • Simulate 5000 samples with 5000 observations. • 500 firms and ten years of observations. • Let the residual and independent variable variance due to the firm effect vary between 0 and 75%. How do you do this? X_g = normrnd(0,1,[NUM_FIRMS 1]); X_i = normrnd(0,1,[NUM_BOTH 1]); E_g = normrnd(0,2,[NUM_FIRMS 1]); E_i = normrnd(0,2,[NUM_BOTH 1]); X(i) = sqrt(variation_X)*X_g(c_f) + sqrt(1-variation_X)*X_i(i); E(i) = sqrt(variation_E)*E_g(c_f) + sqrt(1-variation_E)*E_i(i); • 500 clusters by firm.

  29. OLS vs. Clustering on Firm vs. FM with Firm Effect • Table 1 • Compare average coefficients, st. dev. of coefficient estimates, % significant, average SE clustered and % significant with clustered SE. • Vary how much of the independent variable variation is due to firm effect and how much of the residual variation is due to firm effect. • Figure 2 – Compare OLS, Clustered by firm, and Fama-McBeth. • Table 2- Fama-MacBeth

  30. Table 1

  31. Table 1 • Why is the true standard error increasing as we ramp up the firm effect?

  32. Table 2

  33. OLS vs. Clustering by Time vs. FM with Time Effect • Simulate 5000 samples with 5000 observations. • Let the residual and independent variable variance due to the time effect vary between 0 and 75%. • Not this is the situation that FM developed FM for. • Clustering will be by the 10 years.

  34. OLS vs. Clustering by Time vs. FM with Time Effect • Table 3 – Compare OLS and Clustering by time. • OLS does pretty poor job. • Table 4 – Using FM to estimate.

  35. Table 3

  36. Table 4

  37. Lit Review • Petersen points out many papers which have persistent firm characteristics on other persistent firm characteristics. Both OLS and FM will be biased here • Fama and French 2001 (DivPayer on M/B, size, etc) • M/B on firm chars • Pastor and Veronesi, Kemsley and Nissim • Capital structure regressions • Baker and Wurgler 2002; Fama and French 2002; Johnson 2003

  38. Lit Review • Obnoxious • Wu (2004) “FM method accounts for the lack of independence because of multiple yearly observations per company” • Denis, Denis, Yost (2002” “pooling of cross-sectional and TS data in our tests creates a lack of independence in the regression models…..to address the importance of this bias, we estimate the regression model separately for each of the 14 years…” • Choe, Bong-Chan, and Stulz (2005) “The FM regressions take into account the cross-correlations and the serial correaltion in the error term, so that the t-stats are more conservative”

  39. OLS vs. Clustering by Time vs. FM with Firm and Time Effect • In many typical examples, could have both a firm and time effect. • Figure 6, typical structure with both. • Can cluster by firm and time together. • See Samuel Thompson’s 2006 working paper for math. • We’ll cover this later today

  40. Figure 6

  41. OLS vs. Clustering by Time vs. FM with Firm and Time Effect • Simulate 5000 samples with 5000 observations. • Let the residual and independent variable variance due to firm and time effect vary • Table 5 – Compare OLS, with and without firm dummies, Clustered by firm and time, GLS, and FM.

  42. Real Data • Table 6 – Look at asset pricing application. • Equity returns on asset tangibility. • Different methods matter. • OLS and firm clusters do poorly. • Time and firm clustering and FM work well. • Seems to say that for returns may be more affected by a time effect.

  43. Real Data • Table 7 – Capital structure regressions. • OLS, clustering by time, and FM do poorly. • Clustering by firm and clustering by firm and time do well. • Says that within corporate finance a lot of the effects seem to have firm level persistence.

  44. Table 6

  45. Table 7

  46. Recommendations • Think about the structure of the panel data structure. • What is the likely source of dependence. • Comparing different methods may provide additional information about the research question. • Starting point should probably be double clustering by firm and year

  47. Samuel Thompson • Simple formulas for standard errors that cluster by both firm and time (JFE 2011) • Basic formula: • This means you can do it in STATA • Email Sam Hanson or go to Mitch Petersen’s website, there is pre-packaged code to do this

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