# Fixed Effects Model Interpretation

$$\ln(\text{pay})_{itj}= \alpha_{ij} + \beta\ln(\text{performance})_{jt} + \gamma X_{ijt} + T_t + ε_{ijt}$$

This fixed effects model was used to investigate the link between pay-performance throughout the corporate hierarchy. It controls for employee-firm match fixed effects ($$\alpha_{ij}$$). $$i=$$ employee, $$j=$$ firm, and $$t=$$ time.

How would the coefficients on performance from this table be interpreted.

• Log-log coefficients are typically interpreted in terms of percentages. Further, you'd be looking to assess the statistical significance of the result. In particular, the starting assumption is that there is no causal relationship between X and Y, and we require evidence to the contrary. If your t-stat is above a certain critical value - then there exists statistical evidence. Or in other words, we reject our null hypothesis of no linear/causal relation. Typically this is obtained by a so-called t-stat given: beta/s.e, or 0.208/0.025 = 8.32, which is greater than t-critical (1.645) Nov 20, 2020 at 9:10
• Is it correct that ln(performance) has subscripts i and j only? If it is time-varying, please add a t subscript as well in order to avoid confusion. Nov 22, 2020 at 10:51
• @chan1142 thank you for the catch. It is time varying. Nov 22, 2020 at 17:21

## 1 Answer

You have a log-log model, so the coefficients on performance can be interpreted as the elasticity of your outcome (performnce) with respect to the regressor of interest (level in the corporate heirarchy).

This table only shows the coefficient of interest for four separate regressions. For each of these job levels (CEO, other board, white-collar, all other), a 1% increase in the 'total expected ex ante pay' leads to a x-% increase in 'total shareholder returns'.

For example, based on the results reported in this table, a 1% increase in total ex-ante CEO pay is associated with a 0.22% increase in total shareholder returns, a 1% increase in total ex-ante 'other board executive' pay is associated with a 0.21% increase in total shareholder returns, etc.

All four coeficients are statistically significant at the 1% level (which you can confirm by looking up the values of each coefficient's t-statistic, which is just the coefficient value divided by the standard error).