[Gmm-commits] r229 - in pkg/momentfit: R vignettes

[noreply at r-forge.r-project.org]

Author: chaussep
Date: 2024-02-26 23:20:06 +0100 (Mon, 26 Feb 2024)
New Revision: 229

Modified:
   pkg/momentfit/R/weak.R
   pkg/momentfit/vignettes/weak.Rmd
   pkg/momentfit/vignettes/weak.pdf
Log:
working on the vignette

Modified: pkg/momentfit/R/weak.R
===================================================================
--- pkg/momentfit/R/weak.R	2024-02-23 22:44:23 UTC (rev 228)
+++ pkg/momentfit/R/weak.R	2024-02-26 22:20:06 UTC (rev 229)
@@ -556,8 +556,7 @@
         " for ", estMethod, "\n", sep="")
     cat("Type of LS covariance matrix: ", vcov, "\n", sep="")
     cat("Number of included Endogenous: ", ncol(X2), "\n", sep="")
-    cat("Effective degrees of freedom: ", Keff, "\n", sep="")
-    cat("x: ", x, "\n", sep="")
+    cat("Effective degrees of freedom: ", Keff, "(with x = ", x, ")\n", sep="")
     cat("Statistics: ", formatC(Feff, ...), "\n", sep="")
     cat(paste("Critical Value (size=",size,"): ", formatC(crit, digits=digits),
               "\n", sep=""))
@@ -662,8 +661,6 @@
     invisible()
 }
 
-
-
 nearestSPD <- function (A) 
 {
     stopifnot(is.numeric(A), is.matrix(A))
@@ -747,7 +744,10 @@
     {
         if (is.null(eA))
             eA <- eigen(A)
-        eA$vec%*%diag(FUN(eA$val))%*%t(eA$vec)
+        if (length(eA$val) == 1)
+            FUN(A)
+        else
+            eA$vec%*%diag(FUN(eA$val))%*%t(eA$vec)
     }
     
     N <- nrow(W)/K-1

Modified: pkg/momentfit/vignettes/weak.Rmd
===================================================================
--- pkg/momentfit/vignettes/weak.Rmd	2024-02-23 22:44:23 UTC (rev 228)
+++ pkg/momentfit/vignettes/weak.Rmd	2024-02-26 22:20:06 UTC (rev 229)
@@ -750,8 +750,10 @@
 
 ## Testing for weak instruments: @lewis-mertens22
 
-The authors generalize the MOP test for models with multiple
-endogenous variables. The statistic proposed by the authors is
+The authors generalize the test by @montiel-olea-pflueger13 for models
+with multiple endogenous variables. The test is therefore robust to
+non-iid errors. The statistic proposed by the authors is a
+generalization of the Cragg and Donald test. It is defined as:
 
 \[ g_{min} =
 \min\eval[n\hat\Phi^{-1/2}\hat{\Pi}_2'\hat{\Pi}_2\hat\Phi^{-1/2}] \,,
@@ -760,15 +762,46 @@
 where $\Phi = (I_{k_2}\otimes \vect(I_{l_2}))'[W_2\otimes
 I_{l_2}](I_{k_2}\otimes \vect(I_{l_2}))$. If we write $W_2$ as a
 $k_2\times k_2$ block matrix, with $A_{ij}$ being the $l_2\times l_2$
-matrix in the ith row and jth column, then $\Phi_{ij}=\tr(A_{ij})$. It
-is clear that this is the MOP effective F test when $k_2=1$, because
-$k_2=1$ implies that $\Phi=\tr(W_2)$.
+matrix in the ith row and jth column, then
+$\Phi_{ij}=\tr(A_{ij})$. The bock matrix $A_{ij}$ is a robust
+estimator of the covariance matrix between $(Z_2'e_i)$ and
+$(Z_2'e_j)$. It is clear that this is the MOP effective F test when
+$k_2=1$, because $k_2=1$ implies $\Phi=\tr(W_2)$. As for the MOP test,
+we have the choice between a less computationally demanding but more
+conservative critical value, called simplified, and the generalized
+one. The function `LewMertest` computes only the simplified version by
+default. To obtain both, we set the argument `simplified` to `FALSE`.
 
 ```{r}
 LewMertest(mod3, simplified=FALSE)
 ```
 
+The function is based on the Matlab code the authors provided with
+their paper. As for the other tests, the instruments are weak under the
+null hypothesis. And by weak, we mean that it is weak enough for the
+bias to exceed the bias of the benchmark by 10% (the selected $\tau$
+by default). Therefore, we fail to reject the hypothesis that the
+instruments are weak in `mod3` using both the simplified and
+generalized critical values.
 
+Note that the critical values for the generalized approach are
+obtained by solving a maximization problem numerically. The function
+seems to have more than one local minimum, so the procedure is to
+solve the problem using random starting values and to keep the largest
+solution. The number of starting values is determined by the argument
+`npoints`. By default, it is equal to 10. The authors suggest 1000 in
+their Matlab code, but it seems that there is very little effect of
+going from 10 to 1000. We can see what happens if we increase the
+number of points.
+
+```{r}
+LewMertest(mod3, simplified=FALSE, print=FALSE, npoints=1)$crit
+LewMertest(mod3, simplified=FALSE, print=FALSE, npoints=20)$crit
+```
+
+Finally, note that the authors do not provide any method to obtain the
+critical values for the LIML estimator. These are only for TSLS.
+
 ## Data Generating Process (for later use)
 
 The following function is used to generate dataset with $k$

Modified: pkg/momentfit/vignettes/weak.pdf
===================================================================
(Binary files differ)