OLSvsIV_nonsimCI: Coverage and Width of OLS, TSLS and Naive CIs
In fditraglia/fmscr:

Description Usage Arguments Details Value Examples

Coverage and Width of OLS, TSLS and Naive CIs

1	OLSvsIV_nonsimCI(tau, pi_sq, size = 0.05, n_sim = 50000L)

`tau`	Controls degree of endogeneity of OLS.
`pi_sq`	First-stage R-squared (strengh of instruments).
`size`	One minus the norminal coverage probability of the intervals.
`n_sim`	Number of simulation draws from the limit experiment.

This function gives results based on simulations from the limit experiment for the OLS versus TSLS example in Section 5.1 of the paper. The confidence intervals computed here are for the non-simulation based procedures: the OLS estimator, the TSLS estimator and a naive interval for the post-FMSC estimator. This naive interval is constructed from the textbook interval for whichever estimator the FMSC selects: if OLS is selected it uses the standard OLS interval, and if TSLS is selected it uses the TSLS interval. This procedure can perform very badly depending on parameter values. Note that the median widths in this example are not particularly interesting: the width of each OLS and TSLS interval is fixed across all simulations and the median width of the naive interval equals that of OLS when OLS is chosen more than 50 percent of the time and equals that of TSLS otherwise. The median widths are provided merely for consistency with other functions for which this quantity is more interesting, namely the simulation-based intervals that try to correct some of the deficiencies of the naive interval.

List containing empirical coverage probabilities and median width of confidence intervals for the OLS and TSLS estimators and the same for a "naive" confidence interval for the FMSC-selected estimator.