Summarizing Multilevel GMM Estimation with Endogenous Regressors Model Fits
summary method for class "rendo.multilevel".
## S3 method for class 'rendo.multilevel' summary(object, model = c("REF", "FE_L2", "FE_L3", "GMM_L2", "GMM_L3"), ...)
object: an object of class "rendo.multilevel", usually, a result of a call to multilevelIV.model: character string to indicate which fitted model should be summarized. Possible values are: "REF", "FE_L2", "FE_L3", "GMM_L2", or "GMM_L3"....: ignored, for consistency with the generic function.For the model specified in argument model, the function summary.rendo.multilevel computes and returns a list of summary statistics and the results of the omitted variable tests for the fitted multilevel object given in object.
An object of class summary.rendo.multilevel is returned that is a list using the component call of argument object, plus,
summary.model: the model parameter with which the summary function was called.
coefficients: a px4 matrix with columns for the estimated coefficients, its standard error, the t-statistic and corresponding (two-sided) p-value.
OVT.table: results of the Hausman omitted variable test for the specified model compared to all other models.
vcov: variance covariance matrix derived from the GMM fit of this model.
The multilevelIV() function estimates three models, namely: the usual random effects model (REF), the fixed effects model (FE) and the hierarchical GMM model (GMM) proposed by Kim and Frees (2007). The fixed effects and the GMM estimators are calculated at each level - so in the case of a three-level model, the function estimates, besides the random effects, fixed effects models at level two (FE_L2) and at level three (FE_L3). The same is true for the GMM estimators, the multilevelIV() function will return a GMM estimator at level-three (GMM_L3) and a GMM estimator at level two (GMM_L2).
In order to facilitate the choice of estimator to be used, the summary() function also returns an omitted variable test (OVT). This test is based on the Hausman test for panel data. The OVT allows the comparison of a robust eastimator and an estimator which is efficient under the null hypothesis of no omitted variables. Moreover, it allows the comparison of two robust estimators at different levels.
For the model specified in argument model, the summary() function returns the summary statistics of the estimated coefficients, together with the results of the omitted variable test between the specified model and each other model.
data("dataMultilevelIV") # Fit two levels model res.ml.L2 <- multilevelIV(y ~ X11 + X12 + X13 + X14 + X15 + X21 + X22 + X23 + X24 + X31 + X32 + X33 + (1|SID) | endo(X15), data = dataMultilevelIV, verbose = FALSE) # Get summary for FE_L2 (does not print) res.sum <- summary(res.ml.L2, model = "FE_L2") # extract table with coefficients summary statistics sum.stat.FE_L2 <- coef(res.sum) # extract vcov of model FE_L2 FE_L2.vcov <- vcov(res.sum) # same as above FE_L2.vcov <- vcov(res.ml.L2, model = "FE_L2")
The model fitting function multilevelIV
Function coef will extract the coefficients matrix and function vcov will extract the component vcov.