Fuller: Fuller-k Estimator In ivmodel: Statistical Inference and Sensitivity Analysis for Instrumental Variables Model

Description

`Fuller` computes the Fuller-k (Fuller 1977) estimate for the `ivmodel` object.

Usage

 ```1 2 3``` ```Fuller(ivmodel, beta0 = 0, alpha = 0.05, b = 1, heteroSE = FALSE,clusterID=NULL) ```

Arguments

 `ivmodel` `ivmodel` object. `beta0` Null value β_0 for testing null hypothesis H_0: β = β_0 in `ivmodel`. Default is 0. `alpha` The significance level for hypothesis testing. Default is 0.05. `b` Positive constant b in Fuller-k estimator. Default is 1. `heteroSE` Should heteroscedastic-robust standard errors be used? Default is FALSE. `clusterID` If cluster-robust standard errors are desired, provide a vector of length that's identical to the sample size. For example, if n = 6 and clusterID = c(1,1,1,2,2,2), there would be two clusters where the first cluster is formed by the first three observations and the second cluster is formed by the last three observations. clusterID can be numeric, character, or factor.

Details

`Fuller` computes the Fuller-k estimate for the instrumental variables model in `ivmodel`, specifically for the parameter beta. The computation uses `KClass` with the value of k = k_{LIML} - b/(n - L - p). It generates a point estimate, a standard error associated with the point estimate, a test statistic and a p value under the null hypothesis H_0: β = β_0 in `ivmodel` along with a 1-α confidence interval.

Value

`Fuller` returns a list containing the following components

 `k` The k value used when computing the Fuller estimate with the k-Class estimator. `point.est` Point estimate of β. `std.err` Standard error of the estimate. `test.stat` The value of the test statistic for testing the null hypothesis H_0: β = β_0 in `ivmodel`. `p.value` The p value of the test under the null hypothesis H_0: β = β_0 in `ivmodel`. `ci` A matrix of one row by two columns specifying the confidence interval associated with the Fuller estimator.

Author(s)

Yang Jiang, Hyunseung Kang, Dylan Small

References

Fuller, W. (1977). Some properties of a modification of the limited information estimator. Econometrica, 45, 939-953.

See also `ivmodel` for details on the instrumental variables model. See also `KClass` for more information about the k-Class estimator.
 ``` 1 2 3 4 5 6 7 8 9 10``` ```data(card.data) Y=card.data[,"lwage"] D=card.data[,"educ"] Z=card.data[,c("nearc4","nearc2")] Xname=c("exper", "expersq", "black", "south", "smsa", "reg661", "reg662", "reg663", "reg664", "reg665", "reg666", "reg667", "reg668", "smsa66") X=card.data[,Xname] card.model2IV = ivmodel(Y=Y,D=D,Z=Z,X=X) Fuller(card.model2IV,alpha=0.01) ```