Treatment of Outliers: Firm Heterogeneity in Managerial Incentive and Corporate Innovation

Ordinary least squares (OLS) estimates are frequently used to measure the effects of managerial incentives on corporate innovation. However, these estimates suffer from two data problems. First, corporate innovation data have a discrete spike at zero because many firms never engage in corporate innovation. Second, univariate outliers are common in our data. This paper uses a mixture distribution model which contains a two-stage regression procedure to handle these problems. In the first-stage, a cross-sectional logistic regression is used to objectively distinguish innovative industries from non-innovative ones. In the second-stage, quantile regressions are used to estimate the heterogeneous effects only across firms in the innovative industries. Our out-of-sample tests indicate that the mixture distribution model outperforms the single equation model which uses all the firms in the estimation. Our quantile regression results differ meaningfully between the two models. We find a positive relation between corporate innovation and vega (sensitivity of CEO wealth to stock volatility) only through the mixture distribution model. We also find that OLS coefficient estimates of delta (CEO pay-for-performance sensitivity) are fragile to outliers while quantile regression estimates are not. Dropping only one firm from a sample of 635 firms reduces the OLS estimates of delta by more than 250%, rendering them statistically insignificant.