如何量化广义（强度）双重差分估计系数的经济意义

第一种方法：对强度变量进行标准化（Garrett et al.,2020）

【1】Abstract：Since 2002, the US government has encouraged business investment using accelerated depreciation policies that significantly reduce investment costs. We provide the first in-depth analysis of this stimulus on employment and earnings. Our local labor markets approach exploits cross-industry variation in policy generosity interacted with county-level industry location data. This strategy identifies the partial equilibrium effects of accelerated depreciation. Places that experience larger decreases in investment costs see an increase in employment and earnings. In contrast, the policy does not have positive effects on earnings-per-worker. Overall, our findings suggest federal corporate tax policy has large effects on local labor markets.

自2002年以来，美国政府通过实施显著降低投资成本的加速折旧政策刺激企业投资。本文首次深入分析了这一激励政策对就业和收入的影响。本研究采用的地方劳动力市场分析方法巧妙地利用了政策优惠力度在区县-行业层面的差异，这一策略识别了加速折旧政策产生的局部均衡效应。投资成本降幅较大的地区呈现出就业岗位增加和总收入上升的趋势。然而值得注意的是，该政策对人均收入并未产生积极影响。总体而言，研究结果表明加速折旧政策对地方劳动力市场具有重大影响。

【2】模型设定：利用事件研究法分析美国加速折旧政策对就业的累积效应。

最后一句话是进行IQR标准化的意思（IQR是第三四分位数（Q3，75%）与第一四分位数（Q1，25%）的差值，即IQR=Q3−Q1，这里的四分位数计算根据全样本来计算）。

【3】政策强度变量：首先，根据资产使用年限、年度折旧额以及贴现率计算各个行业的折现值，资产使用年限越长，折现值越低，受到加速折旧政策的影响越大；其次，根据净现值定义treat的取值，如果折现值位于分布底端的30%，则该行业属于加速折旧政策的处理组，否则属于加速折旧政策的控制组。最后，利用各区县各行业人数占区县总人数的比重加权计算出各个区县受加速折旧政策影响的程度。

【4】结果解释：Table 1 reports the average eect on employment for years 2003-2012. Our main specication in column (2) shows that increasing the Exposure to bonus depreciation from the 25th to the 75th percentile of the exposure distribution increased employment by 1.9%.

第二种方法：将强度变量定义为二值虚拟变量（Saez et al.,2019）

【1】Abstract:This paper uses administrative data to analyze a large employer-borne payroll tax rate cut for young workers in Sweden. We find no effect on net-of-tax wages of young treated workers relative to slightly older untreated workers, and a 2–3 percentage point increase in youth employment. Firms employing many young workers receive a larger tax windfall and expand right after the reform: employment, capital, sales, and profits increase. These effects appear stronger in credit-constrained firms. Youth-intensive firms also increase the wages of all their workers collectively, young as well as old, consistent with rent sharing of the tax windfall.

本文利用行政数据分析了瑞典一项针对年轻员工、由雇主承担的大规模工资税税率削减政策。研究发现，与未受政策影响的年长员工相比，受政策影响的年轻员工的税后工资未发生显著变化，但其就业率提升了2-3个百分点。雇佣大量年轻员工的企业获得了更大的税收红利，并在政策实施后立即扩张，具体表现为就业规模、资本投入、销售额和利润均有所增长。这一效应在流动性约束强的企业中更为明显。此外，年轻员工占比高的企业提高了所有员工的工资水平，这与减税红利的租金共享理论相一致。

【2】模型设定：利用广义双重差分法识别针对年轻员工的工薪税减税政策对企业生产的影响。

【3】政策强度变量：根据2006年（政策前1年）支付19-25岁年轻员工的工资收入比重，将大于75%分位数的企业定义为处理组，介于25%-75%分位数的企业定义为处理组。

【4】结果解释：将年轻员工占比高的公司与年轻员工占比适中的公司进行比较，工资税削减政策使得就业增加4.6%。

Corresponding regression estimates of the implied treatment effect are provided in Table 5, top row. Comparing high share young vs. medium share young firms, the payroll tax cut boosts employment by 4.6%, a precisely estimated effect with a standard error of .3% (based on an OLS regression with just 18 group-aggregated observations). This employment growth differential is with respect to a 2.4% initial differential in average labor costs that the reform induces between these two firm groups. Splitting the top group into two, we estimate an employment effect for fairly high vs. medium share young at a somewhat smaller 2.8%, and the employment effect for very high vs. medium share young is higher at 6.5%.

Refs:

[1] Garrett D G, Ohrn E, Suárez Serrato J C. Tax policy and local labor market behavior[J]. American Economic Review: Insights, 2020, 2(1): 83-100.

[2] Saez E, Schoefer B, Seim D. Payroll taxes, firm behavior, and rent sharing: Evidence from a young workers’ tax cut in Sweden[J]. American Economic Review, 2019, 109(5): 1717-1763.

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