Using Instrumental Variables to Estimate the Share of Backward- Looking Firms

This paper examines the small-sample distribution of the instrumental variables (IV) estimation procedure employed by Gali and Gertler (1999) to assess the empirical fit of the New Keynesian Phillips Curve (NKPC) and the hybrid Phillips Curve (HPC). Their estimation method is now widely used to assess the importance of firms that act in a backward- looking manner. Unfortunately, the IV method is highly sensitive to the way the hybrid model is normalized. Using Monte Carlo simulations, I find that one normalization used by Gali and Gertler (and others) finds evidence of backward-looking firms even when there is none by construction. In addition, the IV estimates are also sensitive to the choice of normalization in a broader range of specifications. Using Monte Carlo experiments, I identify which normalizations work better than others. Finally, I find that the bootstrapped standard errors are, not surprisingly, bigger than the asymptotic ones reported by Gali and Gertler. When using my preferred normalization, I find that the NKPC is rejected at the 5 percent but not at the 1 percent level.