Testing for peer effects in short panels without identifying the network structure
We propose an instrument-based test for peer effects in short-T panels when the underlying network is unknown. The test avoids estimating the network by aggregating pairwise comparisons between covariate-projected outcomes of potential peers and residualized own outcomes. The statistic is designed for fixed-T, large-N settings with individual fixed effects, heterogeneous slopes, heteroskedasticity, and serial dependence within units. We also develop a weighted extension that accounts for additive common time effects. The limiting distribution is standard Gaussian when the norm of the projected component of the outcomes is bounded away from zero, but can be nonstandard when it is local to zero. We derive a conditional Gaussian limit experiment and a feasible conditional Monte Carlo procedure to obtain uniformly valid critical values. Monte Carlo evidence shows that the conditional procedure leads to accurate size control while retaining power against latent peer-effect alternatives.