Joint work with Santiago Pereda Fernández. Published in: Econometric Reviews, 44(9), September 2025 (pp. 1321-1360).
Abstract. Conventional methods for the estimation of peer, social or network effects are invalid if individual unobservables and covariates correlate across observations. In this paper we characterize the identification conditions for consistently estimating all the parameters of a spatially autoregressive or linear-in-means model when the structure of social or peer effects is exogenous, but the observed and unobserved characteristics of agents are cross-correlated over some given metric space. We show that identification is possible if the network of social interactions is non-overlapping up to enough degrees of separation, and the spatial matrix that characterizes the co-dependence of individual unobservables and covariates is known up to a multiplicative constant. We propose a GMM approach for the estimation of the model’s parameters, and we evaluate its performance through Monte Carlo simulations. Finally, we revisit an empirical application about classmates in college. Contrasting with conventional methods, our methodology can estimate zero, non-significant peer effects on both academic performance and major choice.
Abstract. This paper introduces an estimator for quadratic forms based on the linear parameters of a semi-parametric model. The leading example is the workhorse model of wage determination by Abowd, Kramarz, and Margolis (1999, AKM): our estimator targets standard variance components while allowing for a nonparametric treatment of both worker- and firm-level observable characteristics. We propose a bias-corrected estimator robust to heteroskedasticity that controls for approximating functions of the covariates. We show that this estimator is asymptotically unbiased and consistent when the number of linear parameters (e.g. the AKM fixed effects) is proportional to the sample size. In particular, consistency hinges on a strengthened smoothness condition (which we discuss for the first time) on the nonparametric component’s functional class. In an empirical application, we show that adding a rich set of controls to the standard AKM model yields implausibly large firm effects. Our method addresses this issue, yielding estimates of variance components that aremore robust relative to conventional approaches. Confounding—not functional-form choice—drives the standard model’s instability.