vignettes/Diagnostics-for-2SLS-Regression.Rmd
Diagnostics-for-2SLS-Regression.Rmdivreg() function provides a user-friendly formula-based
-interface to ivreg.fit().
+regressors (see e.g., Greene 2003). The
+ivreg.fit() function in the package computes the 2SLS
+estimator employing a low-level interface not generally intended for
+direct use, and returns a list containing quantities that facilitate the
+computation of various diagnostics. The ivreg() function
+provides a user-friendly formula-based interface to
+ivreg.fit().
ivreg() is derived from and supersedes the
ivreg() function in the AER package (Kleiber and Zeileis 2008), making additional
provision for regression diagnostics. The principal subject of this
@@ -179,9 +180,9 @@
As an alternative, we can obtain exactly the same estimates \(b_{\mathrm{2SLS}}\) of \(\beta\) by performing an OLS regression of -\(y\) on \(\widehat{X}\), producing \(b_{\mathrm{2SLS}} = (\widehat{X}^\top \widehat{X}) -\widehat{X}^\top y\). This is Basmann’s approach and it motivates -the name “2SLS.”
+\(y\) on \(\widehat{X}\), producing \(b_{\mathrm{2SLS}} = (\widehat{X}^\top +\widehat{X})^{-1} \widehat{X}^\top y\). This is Basmann’s +approach and it motivates the name “2SLS.”Whether we think of the second stage as IV estimation or OLS
regression, we can combine the two stages into a single formula: \[
b_{\mathrm{2SLS}} = [X^\top Z(Z^\top Z)^{-1} Z^\top X]^{-1} X^\top Z
@@ -481,10 +482,10 @@ By default, Unusual Data Diagnostics: An Exampl
## Multiple R-Squared: 0.6396, Adjusted R-squared: 0.572
## Wald test: 10.7 on 3 and 16 DF, p-value: 0.0004196
summary() prints the results of three
-“diagnostic” tests for 2SLS regression. These tests (which can be
-suppressed by setting the argument diagnostics=FALSE) are
-not the focus of the vignette and so we’ll comment on them only
-briefly:diagnostics=FALSE) are not the focus of the
+vignette and so we’ll comment on them only briefly:
A good instrumental variable is highly correlated with one or more of the explanatory variables while remaining uncorrelated with the @@ -1394,6 +1395,10 @@
vignettes/ivreg.Rmd
ivreg.RmdThe development version of ivreg is hosted on GitHub
at https://github.com/zeileis/ivreg/. It can be
-conveniently installed installed via the install_github()
-function in the remotes
+conveniently installed via the install_github() function in
+the remotes
package:
remotes::install_github("https://github.com/zeileis/ivreg/")gt rather than the kableExtra package (recently not actively maintained) is used now for the modelsummary table shown in the package vignette (contributed by Vincent Arel-Bundock).The gt rather than the kableExtra package (recently not actively maintained) is used now for the modelsummary table shown in the package vignette (contributed by Vincent Arel-Bundock).
Further small improvements in the package vignettes.
Greene, W.H. (1993) Econometric Analysis, 2nd ed., Macmillan.
+Greene, W.H. (2003) Econometric Analysis, 5th ed., Upper Saddle River: Prentice Hall.