Plausibly Exogenous Instrument Regressions (Market-Level Data)
| Dependent Variable: Log(Real Wage) | |||
|---|---|---|---|
| (1) | (2) | (3) | |
![]() | -0.141*** | -0.149*** | -0.137*** |
| (0.0186) | (0.0184) | (0.0184) | |
| Log tightness | 0.00387 | 0.00526 | |
| (0.00310) | (0.00344) | ||
| Market (CZ × six-digit SOC) FE | ✓ | ✓ | ✓ |
| year–quarter FE | ✓ | ||
| year–quarter FE × CZ FE | ✓ | ||
| Observations | 59,485 | 58,642 | 56,679 |
| R-squared | 0.674 | 0.671 | 0.715 |
| β (lower bound) | -0.178 | -0.177 | -0.157 |
| β (upper bound) | 0.0362 | 0.0357 | 0.0349 |
| γmax | -0.105 | -0.112 | -0.100 |
Notes: Data are for the period 2010Q1–2013Q4. We consider the following model in which the instrument is not fully exogenous and therefore can enter in the second stage: log(wm,t) = β·logHHIm,t + γ·z + θ·Xm,t + αt + δm + εm,t, where z is our instrumental variable. We implement the plausibly exogenous instrument regression methodology as follows. We start by running reduced form OLS regressions analogous to our IV specifications, but including the instrument directly in the second stage instead of log HHI. The value of γ in the table refers to the coefficient of the instrument in this regression. We take
as the lower bound for the range of γ and zero as the upper bound, and then compute bounds for the coefficient on log HHI (β) using the plausibly exogenous regression methodology of Conley, Hansen, and Rossi (2010). We implement the methodology by (i) within-transforming all the variables (including the dependent variable, the regressors, and the instruments) by running regressions with each variable on the left-hand side and the corresponding set of fixed effects on the right-hand side, and taking the residuals as the transformed variables, and (ii) running the plausibly exogenous instrument regressions on the within-transformed variables using the plausexog command in Stata developed by Clarke (2017). We cluster standard errors at the market level. We also calculate the value of the lower bound for γ that would make the interval for β be fully to the left of zero. We call this value γmax.
* p < 0.1,
** p < 0.05,
↵*** p < 0.01.