Montiel Olea-Pflueger effective F test for weak instruments — morie_iv_montiel_olea

The weak-instrument test of Montiel Olea and Pflueger (2013) for one endogenous regressor, robust to heteroskedasticity, clustering and serial correlation. After partialling out the included exogenous regressors and the constant, the instruments are orthonormalised ($Z'Z = nI$) and $$F_{eff} = \frac{Y_2' P_Z Y_2}{tr(\hat W_2)},$$ where $\hat W_2$ is the (robust, clustered or HAC) variance of $n^{-1/2}\sum_i Z_i v_{2i}$ from the first stage, with the $n/(n-K-L-1)$ degrees-of-freedom correction. Under homoskedasticity $F_{eff}$ is the ordinary first-stage F.

Usage

morie_iv_montiel_olea_pflueger(
  data,
  outcome,
  endogenous,
  instruments,
  exogenous = NULL,
  vcov = c("robust", "iid", "cluster", "hac"),
  cluster = NULL,
  lag = NULL,
  alpha = 0.05,
  tau = c(0.05, 0.1, 0.2, 0.3)
)

Arguments

data: A data.frame (or tibble) holding the outcome, endogenous regressors, instruments, and any exogenous controls.
outcome: Outcome column (needed for the generalized TSLS/LIML bounds).
endogenous: Character vector; column names of the endogenous regressors.
instruments: Character vector; column names of the instrumental variables.
exogenous: Optional character vector of additional exogenous regressors included in both the structural equation and the first stage. NULL (default) for a just-identified design.
vcov: "robust" (default), "iid", "cluster" or "hac" (Bartlett kernel).
cluster: Cluster column for vcov = "cluster".
lag: HAC truncation lag (default $\lfloor 4(n/100)^{2/9} \rfloor$).
alpha: Test size (default 0.05).
tau: Worst-case bias thresholds (default 5, 10, 20 and 30 percent).

Value

A list with F_eff, critical_values (a data frame: tau, simplified, tsls, liml and the matching effective degrees of freedom), B_tsls, B_liml, reject (logical per tau, generalized TSLS), n, K, vcov and alpha.

Details

The null hypothesis is that the Nagar bias exceeds a fraction $\tau$ of a worst-case benchmark. Critical values come from the Patnaik approximation of the noncentral chi-square: $x = 1/\tau$ for the simplified (conservative) test, $x = B/\tau$ with the estimated worst-case bias bound $B$ for the generalized TSLS and LIML tests. Everything is computed from the data; no table is consulted. Reject weak instruments when $F_{eff}$ exceeds the critical value.

References

Montiel Olea, J. L. and Pflueger, C. (2013). A robust test for weak instruments. Journal of Business and Economic Statistics 31(3), 358-369. Pflueger, C. E. and Wang, S. (2015). A robust test for weak instruments in Stata. Stata Journal 15(1), 216-225.

Examples

set.seed(2)
n <- 500
z1 <- rnorm(n); z2 <- rnorm(n); u <- rnorm(n)
d <- 0.3 * z1 + 0.2 * z2 + u * (1 + abs(z1)) / 2
y <- 0.5 * d + u + rnorm(n)
mop <- morie_iv_montiel_olea_pflueger(data.frame(y, d, z1, z2), "y", "d",
                                      c("z1", "z2"))
mop$F_eff
#> [1] 25.86756
mop$critical_values
#>    tau simplified      tsls      liml K_eff_simplified K_eff_tsls K_eff_liml
#> 1 0.05   34.20340 16.246226 25.480348         1.498554   1.509354   1.501449
#> 2 0.10   20.68086 10.685707 15.871738         1.504430   1.524469   1.509940
#> 3 0.20   13.19218  7.481602 10.472346         1.515506   1.550328   1.525519
#> 4 0.30   10.42457  6.259983  8.451557         1.525762   1.571639   1.539470