positive due to nominal sales growth. The first specification in Column (2) is the SDID specification where _τ_ 0<sup>_sales_</sup> = _−_ 0 _._ 025 (0.002), indicating sales are on average declining by 2.5 percent annually in investigated industries relative to the control.<sup>15</sup> This coefficient estimate has a smaller standard error compared to the DID specification in Column (3) and the SC specification in Column (4). This is consistent with evidence in Arkhangelsky et al. (2021) who show the use of the SDID can be more precise.

The contrast, when cases end in sanction Column (2) shows _τ_ 1<sup>_sales_</sup> = 0 _._ 038 (0.004) and implying an increase in sales of 3.8 percent annually relative to cases that are closed without trial. Moreover, this coefficient is larger than the coefficient _τ_ 0<sup>_sales_</sup> indicating that a financial sanction on average completely reverses the decline in sales observed in investigated cases, increasing sales overall.

In Column (5), we return to the SDID outcome change, but include in the meta regression the random effects parameter _uj ∼ N_ (0 _, γj_ ) and weigh the regression instead by the term <u>1</u><sup>This yields coefficients that are larger in</sup> _σj_<sup>2+</sup><sup>_γ_2, distributing weight more equally across cases.</sup> absolute value, though they are estimated less precisely. The random effects model produces _τ_ 0<sup>_sales_</sup> = _−_ 0 _._ 071 (0.011) and _τ_ 1<sup>_sales_</sup> = 0 _._ 058 (0.018), reproducing the qualitative pattern that sales are declining after closed cases, but that this trend is reversed when there is ˆ a sanction. The variance of the random effect term estimated at _γ_<sup>2</sup> = 0 _._ 00625, or 0.625 percent, indicating modest heterogeneity across industries in the effect of antitrust on sales.

**Antitrust and workers** The effects of antitrust on workers’ outcomes are reported in Table 2. Our discussion focuses on the random effects specification using the SDID estimator in Column (5), though results are qualitatively similar in Columns (1) - (4), as in Table 1. Panel A reports results where the outcome is the industry wage bill. In Column (5) _τ_ 1<sup>_wagebill_</sup> = 0 _._ 055 (0 _._ 016) and _τ_ 0<sup>_wagebill_</sup> = _−_ 0 _._ 054 (0 _._ 010). This implies a statistically significant 5.4 percent annual decline in wages relative to the synthetic control when an investigation is closed, but, relative to this counterfactual, a 5.5 percent annual increase in wages when there are sanctions. Panel B reports results when the outcome change is the log of employment, or number of workers, yielding _τ_ 1<sup>_employment_</sup> = 0 _._ 033 (0 _._ 014) and _τ_ 0<sup>_wage_</sup> = _−_ 0 _._ 047 (0 _._ 009). Panel C reports the results when the outcome change is the log of the total wage bill divided by total employment in the industry, yielding _τ_ 1<sup>_wagerate_</sup> = 0 _._ 028 (0 _._ 008) and _τ_ 0<sup>_wage_</sup> = _−_ 0 _._ 014 (0 _._ 005). The results in Panels B and C are quantitatively similar to Panel A. The values in Panel C (wage rate) are not exactly the values in Panel A (wage bill) divided by the values in Panel B

> 15 SDID effects are annualized by dividing the SDID effect and its standard error by the number of years that elapse between the pre-treatment and post-treatment averages. This number varies slightly across cases because the SDID estimator weights pre-treatment periods differently in each case to improve precision (Arkhangelsky et al., 2021).

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