Model: Estimation Method: | Standard Errors | p-values | ||||
---|---|---|---|---|---|---|

1 OLS-FE | 2 OLS-no FE | 3 FGLS AR(1) | 1 OLS-FE | 2 OLS-no FE | 3 FGLS AR(1) | |

Slope coefficient | 0.0156 | 0.0040 | −0.0042 | |||

Standard errors | ||||||

Default standard errors, T(N − k) for critical value | 0.0037 | 0.0062 | 0.0062 | 0.000 | 0.521 | 0.494 |

White Robust, T(N − k) for critical value | 0.0037 | 0.0055 | na | 0.000 | 0.470 | na |

Cluster on state, T(G − 1) for critical value | 0.0119 | 0.0226 | 0.0084 | 0.195 | 0.861 | 0.617 |

Cluster on state, CR2 bias correction, T(G − 1) for critical value | 0.0118 | 0.0226 | na | 0.195 | 0.861 | na |

Cluster on state, CR2 bias correction, T(IK degrees of freedom) | 0.0118 | 0.0226 | na | 0.195 | 0.861 | na |

Pairs cluster bootstrap for standard error, T(G − 1) for critical value | 0.0118 | 0.0221 | 0.0086 | 0.191 | 0.857 | 0.624 |

Bootstrap percentile-T methods | ||||||

Pairs cluster bootstrap | na | na | 0.162 | 0.878 | ||

Wild cluster bootstrap, Rademacher two-point distribution | na | na | 0.742 | 0.968 | ||

Wild cluster bootstrap, Webb six-point distribution | na | na | 0.722 | 0.942 | ||

Imbens-Kolesar effective DOF | 50 | 50 | ||||

CSS effective number of clusters | 51 | 51 | ||||

Number of observations | 1,836 | 1,836 | 1,836 | |||

Number clusters (states) | 51 | 51 | 51 |

Notes: March 1997–2012 CPS data, from IPUMS download. Models 1 and 3 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. Model 2 includes year fixed effects but not state fixed effects. The bootstraps use 999 replications. Model 3 uses FGLS, assuming an AR(1) error within each state. “IK effective DOF” from Imbens and Kolesar (2013), and “CSS effective number of clusters” from Carter, Schnepel, and Steigerwald (2013), see Section VID.