# 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 '20 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 '20 at 10:51
• @chan1142 thank you for the catch. It is time varying. Nov 22 '20 at 17:21