Table 4

State-year panel data with differences-in-differences estimation Monte Carlo Rejection Rates of True Null Hypothesis (Slope = 0) with Different Number of Clusters and Different Rejection Methods

Nominal 5% rejection rates
Numbers of Clusters
Estimation Method610203050
Wald tests
    Default standard errors, T(Nk) for critical value0.5890.5700.5450.5260.556
    Cluster on state, T(Nk) for critical value0.1490.0980.0650.0440.061
    Cluster on state, T(G – 1) for critical value0.0750.0660.0520.0390.058
    Cluster on state, T(G – 2) for critical value0.0590.0630.0520.0380.058
    Pairs cluster bootstrap for standard error, T(G – 1) for critical value0.0560.0600.0500.0360.057
Bootstrap percentile-T methods
    Pairs cluster bootstrap0.0050.0190.0510.0440.069
    Wild cluster bootstrap, Rademacher two-point distribution0.0500.0590.0500.0360.055
    Wild cluster bootstrap, Webb 6 point distribution0.0560.0590.0480.0370.058
  • Notes: March 1997–2012 CPS data, from IPUMS download. Models include state and year fixed effects and a “fake policy” dummy variable that turns on in 1995 for a random subset of half of the states. For six and ten clusters, 4,000 Monte Carlo replications. For 20–50 clusters, 1,000 Monte Carlo replications. The bootstraps use 399 replications.