weakTest: Tests for weak Instruments

In momentfit: Methods of Moments

Tests for weak Instruments

Description

This is a collection of tests for weak instruments. It includes the Cragg and Donald test for the reduced rank hypothesis, the conditional F-test of Sanderson and Windmeijer (2016), the robust effective F test of Montiel Olea and Pflueger (2013) and the Lewis and Mertens (2022) robust test with multiple endogenous variables. The critical values of Stock and Yogo (2005) for the null hypothesis of weak instruments are also provided.

Usage

SWtest(object, j=1, print=TRUE, ...)

CDtest(object, print=TRUE, SWcrit=FALSE, ...)

MOPtest(object, tau=0.10, size=0.05, print=TRUE,
        estMethod = c("TSLS", "LIML"), simplified = TRUE,
        digits = max(3L, getOption("digits") - 3L), ...)

LewMertest(object, tau=0.10, size=0.05, print=TRUE,
           simplified = TRUE, digits = max(3L, getOption("digits") -
           3L), npoints=10, ...)

SYTables(object, print=TRUE, SWcrit=FALSE)

Arguments

object	A model of class linearModel
j	The Sanderson and Windmeijer test is based on the regression of y_j-\delta y_{-j} on the set on instruments, where y_j is the jth included endogenous variable and y_{-j} is the vector of the other included endogenous variables.
tau	The desired bias.
size	The size of the test for the critical value.
estMethod	Which method we want to test the weak instruments for? The method determined the critical value associated with a given relative bias.
simplified	Should we perform the simplified test? The test produce more conservative critical values. The generalized test is computationally more demanding.
print	If TRUE, the result is printed and nothing is returned. See below for details on what the functions return when it is set to FALSE
digits	The number of digits to print when print is set to TRUE.
SWcrit	If true, the critical values and the test are ajusted to Sanderson and Windmeijer (2016). See details.
npoints	The number of minimizations to run in order to find the global minimum, which is used for the Lewis and Mertens critical value. It affects the results only when simplified is set to TRUE.
...	Arguments passed to formatC to print the statistic. For MOPtest, they are passed to momentfit:::getMOPx.

Details

The CDtest function computes the test for the model object and runs SYTables to extract the critical values that are specific to the model.

Let l be the number of included endogenous variables and s be the number of excluded exogenous. The Stock and Yogo (2005) tables are based on these two values and they are only available for l=1,2 and s=1,...,30. For the SW test, which is only defined for $l>1$, we compare the statistic with the critical values associated with l=l-1 and s=s-l+1. These are the critical values that are returned when the argument SWcrit of SYTables is set to TRUE. This allows us to test for weak instruments in models with 2 or 3 included endogenous variable using the same tables of critical values.

Sanderson and Windmeijer (2016) show that we can use the same critical values if we modify the CD test by multiplying it by s/(s-l+1), which is what the function CDtest returns if the argument SWcrit is set to TRUE.

Value

The function CDtest returns the Cragg anb Donald statistic when print is set to FALSE.

The function SYTable returns a list with the following elements when print is set to FALSE:

biasTSLS, biasFuller	Named vectors of critical values for TSLS or Fuller (see kclassfit). These critical values are used to achieve the maximum relative bias given by their names. The values are defined only for models with a number of overidentifying restrictions greater or equal to 2.
sizeTSLS, sizeLIML	A named vector of critical values for TSLS or LIML (see kclassfit). These critical values are used to acheive a size that does not exceed the one given by their names.

Both functions return NULL invisibly when print is set to TRUE

Examples

data(simData)
theta <- c(beta0=1,beta1=2)
model1 <- momentModel(y~x1, ~z1+z2, data=simData)
CDtest(model1)
model2 <- momentModel(y~y1+y2+x1, ~z1+z2+z3+z4+x1, data=simData)
SWtest(model2, 1, FALSE)
SWtest(model2, 2, FALSE)

momentfit documentation built on June 26, 2024, 3 p.m.