New Methods of Inference and Software for the Empirical Analysis of Network Generated Data

Statacorp Llc, College Station TX

Investigators

Abstract

This project will (i) develop new statistical methods of estimation and hypothesis testing for network- generated observational data that will significantly expand the range of applications and (ii) make those methods available to empirical researchers by implementing them in user-friendly, computationally efficient, large-data capable commands in the widely used statistical software Stata. Applications of network analysis are of growing importance and range over a wide variety of disciplines, including the social sciences, the behavioral sciences, the humanities, and the health sciences. In these fields, spatial networks and, increasingly, social networks have received special attention, aided by the increasing availability of datasets that provide spatial information or information on social networks. For example, the National Cancer Institute's GIS Portal provides interactive mapping and visualization of cancer-related geo-spatial data, and the National Longitudinal Study of Adolescent to Adult Health (Add Health) and National Social Life, Health, and Aging Project (NSHAP) provide data on peers. Many datasets such as those listed above provide longitudinal information, outcomes on several variables are often determined simultaneously, and networks are often formed endogenously. In the proposal, we illustrate this with two examples in the area of health. The first example relates to peer effects on different exercise activities by individuals. An understanding of such peer effects is important in light of recent research on the connection between exercise and the reduced risk for cognitive impairments. The second example relates to the supply and demand for nursing home beds. Estimation methods developed under the assumption of exogenous network formation are generally inconsistent if the actual network formation is endogenous. Consequently, it is important to develop estimation methodologies for network-generated data that remain consistent under endogenous network formation. Until recently, a crucial obstacle toward developing such methodologies was a lack of appropriate limit theorems. However, Kuersteiner and Prucha (2013, 2015) introduced fairly general limit theorems that can be exploited to develop inference methods for endogenous networks from longitudinal data. The aims of the proposed research are as follows: 1. Define and formally derive the statistical proper- ties of generalized method-of-moments (GMM) estimation methods for simultaneous-equation models for longitudinal data, allowing for endogenous network formation. 2. Define and formally derive the statistical properties of robust tests for network dependence, allowing for endogenous network formation. 3. Define impact measures and derive their statistical properties, to provide a better interpretation of estimation results. 4. Implement and provide access to these methodologies in Stata.