Semiparametric Estimation of Individual Coefficients in a Dyadic Link Formation Model Lacking Observable Characteristics

TL;DR

This paper introduces a semiparametric method to estimate individual effects in dyadic network formation models using only network data, addressing challenges when entity characteristics are unobserved.

Contribution

It develops a novel estimator that normalizes fixed effects without distributional assumptions, improving convergence and applicability in unobserved characteristic scenarios.

Findings

Estimator converges at the same rate as if the error distribution was known

Normalization method outperforms standardization in many cases

Potential benefits are significant with strongly convex or concave error distributions

Abstract

Dyadic network formation models have wide applicability in economic research, yet are difficult to estimate in the presence of individual specific effects and in the absence of distributional assumptions regarding the model noise component. The availability of (continuously distributed) individual or link characteristics generally facilitates estimation. Yet, while data on social networks has recently become more abundant, the characteristics of the entities involved in the link may not be measured. Adapting the procedure of \citet{KS}, I propose to use network data alone in a semiparametric estimation of the individual fixed effect coefficients, which carry the interpretation of the individual relative popularity. This entails the possibility to anticipate how a new-coming individual will connect in a pre-existing group. The estimator, needed for its fast convergence, fails to implement the monotonicity assumption regarding the model noise component, thereby potentially reversing the order if the fixed effect coefficients. This and other numerical issues can be conveniently tackled by my novel, data-driven way of normalising the fixed effects, which proves to outperform a conventional standardisation in many cases. I demonstrate that the normalised coefficients converge both at the same rate and to the same limiting distribution as if the true error distribution was known. The cost of semiparametric estimation is thus purely computational, while the potential benefits are large whenever the errors have a strongly convex or strongly concave distribution.