SAFA CONFERENCE 2009 Using panel data regression models in accounting research

1. SAFA CONFERENCE 2009Using panel data regression models in accounting research Phillip de Jager University of Pretoria Contact email: phillip.dejager@up.ac.za or pdjager@gmail.com

2. Value add of paper • SA accounting researchers are not using panel data as they should • Standard tests that should be reported in a panel setting • Illustration of the instability of regression results in a panel setting when different techniques are used

3. Presentation approach • Brief review of selected theory • SA accounting research vs international accounting research when using panel data • Demonstration of the instability of regression coefficients when using accounting data in a panel setting

4. What is panel data? • What is panel data? • Data with movement over time of cross-sectional units • Other names for panel data: • Pooled data • Combination of time-series and • cross-sectional data • Micropanel data • Longitudinal data • Regression models based on such data is called panel data regression models

5. Why use panel data? • Can control for heterogeneity that is typical in panel data • Time series are too short and need more observations • Structural breaks make time series data incomparable • Correctly used panel data controls for cross section specific unobservable effects

6. What is different in panel data regression models? Extreme 1: Pooled OLS (whereby a single regression is estimated for all firms over all time periods Extreme 2: OLS for every cross-section • What about the middle road? • Possibilities: • Fixed effects • Random effects • Allowing for cross-sectional/period variances to differ • Seemingly unrelated regressions (SUR)

7. Choosing between fixed effects and random effects • Fixed effects approach: • an appropriate specification if one is focusing on a specific set of firms and inference is limited to that set of firms • 9/10 accounting panel data studies use fixed effects • Wooldridge demonstrates that fixed effects models can offer robust results even in settings where there is variation in slope and intercept coefficients • Random effects approach: • Only have large sample validity • Any unobserved effects are independent of the explanatory variables in the model • Observations can be considered “random draws” from a larger population

8. Seemingly unrelated regressions - SUR • Tends to the extreme of individual regressions for each cross-section, but use is made of any cross-sectional correlation in the error terms • Can perform a Lagrange multiplier test of Breusch and Pagan for cross-sectional correlation in the residuals. In the case of significant correlation SUR usage can help extract the information. • SUR can only be used if the number of time-series exceeds the number of cross-sectional units

9. Hypothesis testing with panel data • Testing for poolability • Serial correlation • Heteroscedasticity • Misspecification of regressors

10. Poolability • Pooled vs. individual regressions for each cross-section H0: Common intercept and common slope coefficients 2. Pooled vs. cross-sectional fixed effects and time effects H0: Common intercept and common slope coefficients 3. Pooled vs. cross-sectional fixed effects H0: Common intercept and common slope coefficients • Pooled vs period fixed effects H0: Common intercept and common slope coefficients All the tests compare the sum of errors of the least restricted regression with the sum of errors of the more restrictive regression and building an F-statistic

11. Panel data tests (other) • Test for heteroscedasticity between cross-sections H0: The error variances of each cross-section is the same and equal to the error variance across all cross-sections • Test for serial correlation in error terms (given the presence of differences between cross-sections in terms of intercepts) H0: No relation between current error term and past error term

12. Panel data stationarity • Gujarati describes stationarity as the time-series issue and heterogeneity as the cross-sectional issue • When data panels start having longer time-series (>15) they should be tested for stationarity • No finance or accounting papers were found that tested/corrected for non stationarity

13. Theory summary • The precise middle path to follow should be decided by appropriate statistical tests (pooling tests) • In 90% of cases the fixed effects model should be appropriate, corrected for heteroscedasticity and serial correlation where necessarry • Remember why we chose fixed effects over random effects • Always take note of model selection criteria indicators

14. SA vs international research

15. Example of parameter instability in panel data

16. Conclusion • Accountancy research frequently uses data with panel characteristics without compensating for cross-sectional heterogeneity • These results are statistically questionable • Proper use of panel data overcomes cross-sectional heterogeneity & controls for firm-specific unobservable effects