Moment Estimation with Attrition: An Application to Economic Models
M. Abowd, John, Bruno, Crepon, Francis, Kramarz, Journal of the American Statistical Association
We study the effects of the attrition of firms from longitudinal samples on the estimates of dynamic labor demand models. The reasons for attrition from business-based longitudinal samples are extremely varied and are related to both the economic activity of the business and the methods of acquiring sampling frame information for those businesses. We do an exhaustive study of the available information regarding the attrition of French firms from our analysis sample. We propose flexible attrition models based on a longitudinal generalization of the missing at random assumption. We implement these models with a weighted generalized method of moments estimator that is consistent and efficient (in the class of moment estimators). Our flexible attrition models substantially alter and improve the estimation results for dynamic factor demand models. We attribute the improvement to the ability of our models to handle the very diverse reasons for attrition that our audit uncovered without requiring specific knowledge of which reason applies to a particular exiting firm.
KEY WORDS: Adjustment costs; Attrition audit; Business missing data; Dynamic labor demand; Generalized method of moments; Reweighted estimation.
When statisticians sample fragments of the lives of businesses the effects of deaths, reorganizations, and other movements are often manifested as unexplained attrition from the sample. Model estimation and inference can be very seriously affected - most estimated coefficients are biased and inconsistent even under rather strong ancillary assumptions. The classical solution is to estimate jointly the process of interest and a model based on the economic reasons for exit (see, for example, Heckman 1979, and Olley and Pakes 1996). Current techniques may introduce serious biases and inconsistencies in estimates based on samples of firms or establishments when they make structural assumptions about the exit process, which are at odds with the real reasons for attrition.
The reasons for attrition from business-based longitudinal samples are extremely varied and are related to both the economic activity and the methods used to maintain the sampling frame. To demonstrate this heterogeneity we do an exhaustive study of the reasons for the attrition of French firms from our analysis sample. Attrition from our sample is very rarely associated with the death of the economic assets used by the firm. We next show that the use of more flexible attrition models substantially changes the estimation results for dynamic factor demand models. Finally, we compare estimates with and without our attrition correction to external evidence on adjustment costs in France. Our reweighted estimates, reflecting the attrition correction, are much closer to the external evidence than the uncorrected estimates, which are implausibly low for France. Hence, modeling attrition as if it implied economic death leads to very serious inference errors that are substantially mitigated by the use of the more fle xible models that we propose.
Dynamic factor adjustments are related to a set of costs that measure the firm's difficulty in reallocating its assets and employment. If adjustment costs are minimal, then assets and employment move very freely among firms. In this case, the attrition of a firm from the sample probably means that its assets and employment are zero because they have moved to another economic activity, presumably represented by one of the firms already in the sample or a firm born in a subsequent period. When adjustment costs are substantial, neither assets nor employment are very mobile because the reallocation costs discourage their redeployment. In this case, the disappearance of a firm from the sample must be viewed with caution because it is unlikely that its assets or employment have been completely redeployed and, consequently, it is unlikely that another firm in the sample (or newly born) represents the missing economic activity. …