本文选取相同行业同年度内其他公司的社会责任报告净正面语调的均值TONE_meant 作为工具变量进行2SLS回归，解决内生性处理。回归结果见表5。这个工具变量满足相关性和外生性的要求。从相关性来看，同行业的公司面临相似的外部环境和行业特征，因此，他们的社会责任报告语调具有一定的相关性，并且从表5第（1）列显示，社会责任报告语调的行业均值TONE_meant 的符号在1%的水平上显著为正，故满足相关性原则。且没有证据表明其他行业公司的社会责任报告语调会影响本公司的股价崩盘风险，所以满足外生性的原则。

——摘自《审计与经济研究》某篇论文

处于同一个城市和行业的企业可能在当地的经理人市场上争夺企业家人才, 企业是否为管理层提供薪酬激励计划需参考当地的竞争对手提供的激励薪酬, 而竞争对手提供的激励薪酬不应对本企业的创新产生直接的影响。我们参照Fisman&Svensson(2007) 的方法用CEO 持股(CEO Share) 、激励薪酬(Incentive) 、利润激励(Profit Inc) 和销售量激励(Sales Inc) 的区域-行业平均值作为对应变量的工具变量。——摘自《经济研究》某篇论文

Using independent variable group averages as instrumental variables. Independent variables’ group averages are also sometimes used as instrumental variables. Specifically, the researcher instruments for a potentially endogenous regressor  using the regressor’s group average,  , calculated excluding the observation at hand. The typical justification for such instruments is that the group average of X is correlated with but is not otherwise related to the dependent variable, . For example, a researcher estimating the impact of ROA on leverage but concerned that financial constraints introduce a simultaneity bias might propose using industry ROA to instrument for firm ROA. Using group averages of the independent variables as instrumental variables, however, leads to inconsistent estimates in the presence of unobserved grouplevel heterogeneity, as in Equation (1). The instrument violates the exclusion restriction whenever the unobserved heterogeneity,  , is correlated with the independent variable,  , because  is then necessarily also correlated with  . As noted earlier, such correlations are pervasive in practice. In this example, unobserved industry investment opportunities likely affect both ROA and leverage, making the proposed IV estimator inconsistent. Unlike the other applications discussed in this section, the problem with the IV estimation cannot be solved by adding fixed effects to the estimating equation. Although fixed effects control for the unobserved heterogeneity ,  , in the second stage estimation, the fixed effects reintroduce the endogeneity problem in the first stage estimation. Recall that the instrument,  , is just the group mean excluding the observation at hand. After controlling for industry fixed effects, the instrument becomes  which is perfectly correlated with the endogenous regressor, . Put differently, the instrument exploits strictly industry-level variation, which is not well-identified in the presence of industry fixed effects. For a group average instrument to be valid, the independent variable, , must be correlated with its group mean and the underlying economic source of this correlation must be unrelated to  (the part of the industry variation that affects ). Although it is possible that there exist scenarios where these conditions hold, examples are rare. Researchers should not assume these conditions hold absent a strong economic justification.

——以上摘取自Gormley and Matsa（2014）论文

参考资料

[1]Todd A. Gormley, David A. Matsa. Common Errors: How to (and Not to) Control for Unobserved Heterogeneity[J]. The Review of Financial Studies, 2014, 27(2):617–661.

[2]邱嘉平. 因果推断实用计量方法[M].上海：上海财经大学出版社, 2020