Technical Appendix — Productivity Effects of Hiring Foreign Experts

A1: Robustness — Alternative Estimators

Comparing the preferred lpdid estimator with TWFE and Callaway & Sant'Anna (csdid):

Event time	(1) TWFE	(2) csdid	(3) lpdid
$T_0-5$	-0.006 (0.020)	-0.001 (0.020)	0.011 (0.022)
$T_0-4$	0.029 (0.021)	0.012 (0.020)	0.025 (0.021)
$T_0-3$	0.021 (0.021)	0.014 (0.017)	0.004 (0.020)
$T_0-2$	0.023 (0.018)	0.023 (0.017)	0.019 (0.016)
$T_0-1$	reference period
$T_0$	-0.015 (0.018)	-0.004 (0.018)	0.004 (0.016)
$T_0+1$	0.025 (0.020)	0.021 (0.022)	0.038* (0.019)
$T_0+2$	0.045** (0.020)	0.065** (0.021)	0.076* (0.020)**
$T_0+3$	0.078*** (0.020)	0.098*** (0.022)	0.116* (0.021)**
$T_0+4$	0.051** (0.020)	0.086*** (0.025)	0.100* (0.024)**
$T_0+5$	0.010 (0.022)	0.099*** (0.028)	0.108* (0.026)**

Pre-trend Wald tests: The joint hypothesis that all pre-event coefficients equal zero cannot be rejected for csdid ($p=0.33$) or lpdid ($p=0.14$)

A2: Robustness — Alternative TFP Measures

← Back to presentation

Sensitivity of results to the production function estimation method:

Event time	Wooldridge (2009)	ACF (2015)	Translog
$T_0-5$	0.011 (0.022)	0.010 (0.022)	0.055 (0.032)
$T_0-4$	0.025 (0.021)	0.030 (0.022)	0.071* (0.029)
$T_0-3$	0.004 (0.020)	0.003 (0.021)	0.023 (0.032)
$T_0-2$	0.019 (0.016)	0.016 (0.017)	0.028 (0.026)
$T_0-1$	reference period
$T_0$	0.004 (0.016)	-0.005 (0.017)	-0.009 (0.025)
$T_0+1$	0.038* (0.019)	0.028 (0.020)	0.023 (0.029)
$T_0+2$	0.076* (0.020)**	0.071* (0.021)**	0.050 (0.032)
$T_0+3$	0.116* (0.021)**	0.112* (0.022)**	0.102* (0.032)**
$T_0+4$	0.100* (0.024)**	0.101* (0.025)**	0.071 (0.038)
$T_0+5$	0.108* (0.026)**	0.110* (0.028)**	0.068 (0.043)

ACF vs Wooldridge: Very similar point estimates. The translog specification shows a similar peak at $T_0+3$ (+10.2%) but has larger standard errors, likely due to higher parameter demands.

A3: Robustness — Sample Restrictions

← Back to presentation

Testing whether results are driven by repeated hiring or sample composition:

Event time	No compo.	Non-Abs.	Single Exp.
$T_0-5$	0.032 (0.026)	0.008 (0.022)	-0.004 (0.031)
$T_0-4$	0.040 (0.025)	0.016 (0.021)	0.012 (0.028)
$T_0-3$	0.010 (0.024)	0.003 (0.019)	0.023 (0.025)
$T_0-2$	0.014 (0.020)	0.017 (0.017)	-0.011 (0.021)
$T_0-1$	reference period
$T_0$	0.010 (0.020)	0.003 (0.016)	-0.007 (0.018)
$T_0+1$	0.043 (0.022)	0.040* (0.020)	-0.001 (0.022)
$T_0+2$	0.080* (0.022)**	0.074* (0.022)**	0.063** (0.024)
$T_0+3$	0.105* (0.024)**	0.103* (0.025)**	0.088 (0.027)**
$T_0+4$	0.088* (0.025)**	0.062* (0.027)	0.053 (0.032)
$T_0+5$	0.106* (0.026)**	0.080* (0.034)	0.064 (0.033)

No composition: Balanced panel — same firms across all horizons. Rules out that results are driven by changing sample composition across cross-sections.
Non-absorbing: Treatment "switches off" when the expert leaves. Effect remains (+10.5% at $T_0+3$).
Single expert: Only firms hiring exactly one expert. A standalone hire still raises TFP by +8.8%.

A4: Labor and Capital Productivity

← Back to presentation

Labor productivity $\ln(VA/(L+H))$

Mirrors TFP closely: +9.2% by $T_0+5$.

Capital productivity $\ln(VA/K)$

Immediate effect at $T_0$ (+6%), rising to +20% by $T_0+5$.

The instant surge in capital productivity at $T_0$ may reflect internal reallocation: e.g. as firms/expert manager optimize labor deployment.

A5: Lowering the Expert Threshold to 1.5 Price Base Amounts

← Back to presentation

When the income threshold is lowered from 2 to 1.5 price base amounts, the definition broadens to include more generally highly skilled foreign labor.

The positive TFP effect persists but is somewhat attenuated.
Consistent with a "dose-response" pattern: the most highly paid experts drive the strongest effects.

Event study: TFP effect with expert threshold at 1.5 price base amounts.