The ivgets package provides general-to-specific modeling functionality for two-stage least squares (2SLS or TSLS) models. There are two main uses. Starting from a generalized unrestricted model (GUM), the algorithm searches over the set of exogenous regressors to find a specification that can explain the data while trying to be as parsimonious as possible. Second, the package can perform indicator saturation methods to detect outliers and structural breaks in the data.
You can install the released version of ivgets from CRAN with:
install.packages("ivgets")And the development version from GitHub with:
# install.packages("devtools")
devtools::install_github("jkurle/ivgets")The ivgets package relies heavily on two packages. The estimation of 2SLS models is based on the ivreg package and model selection uses the gets package.
ivgets avoids specifying minimum or maximum versions of the
dependencies in the DESCRIPTION file if possible. This is
to avoid forcing users to update their packages and potentially break
existing code.
Suppose we want to model the potential effect of some regressors \(x_{1}\) to \(x_{11}\) on a dependent variable \(y\). We are worried that \(x_{11}\) could be endogenous, so we use a 2SLS model to estimate the parameters. For the exogenous regressors \(x_{1}\) to \(x_{10}\) we are unsure whether they are relevant but our theory tells us that they might be relevant. So we want to include all of them in the original model and then use model selection to determine which regressors are actually relevant. Furthermore suppose we are concerned that the sample might contain outlying observations and that these outliers are biasing our results.
Formally, our structural equation is
\[ y_{i} = \beta_{1} x_{1i} + \beta_{2} x_{2i} + ... + \beta_{11} x_{11i} + u_{i} = x_{i}^{\prime} \beta + u_{i} \].
The first stage can be written as
\[x_{i} = \Pi^{\prime} z_{i} + r_{i}\],
where \(z_{i}\) includes all the exogenous regressors \(x_{1}\) to \(x_{10}\) and the excluded instruments \(z_{11}\) and \(z_{12}\).
Since we are concerned about outliers, we first do impulse indicator saturation to detect observations with unusually large errors. We still include all our potentially relevant exogenous regressors in the model.
library(ivgets)
#> Lade nötiges Paket: gets
#> Lade nötiges Paket: zoo
#>
#> Attache Paket: 'zoo'
#> Die folgenden Objekte sind maskiert von 'package:base':
#>
#> as.Date, as.Date.numeric
#> Lade nötiges Paket: parallel
#> Lade nötiges Paket: ivreg
# we specify "-1" in the formula because x1 is already an intercept in our data frame
fml <- y ~ -1+x1+x2+x3+x4+x5+x6+x7+x8+x9+x10+x11 | -1+x1+x2+x3+x4+x5+x6+x7+x8+x9+x10+z11+z12
base <- ivreg(formula = fml, data = artificial2sls_contaminated)
# do impulse indicator saturation
indicators <- isat(base, iis = TRUE, t.pval = 1/100, print.searchinfo = FALSE)
print(indicators$final)
#>
#> Call:
#> ivreg::ivreg(formula = as.formula(fml_sel), data = d)
#>
#> Coefficients:
#> x1 x2 x3 x4 x5 x6 x7 x8
#> 5.26264 -4.89609 0.13239 0.12368 -0.14055 -0.13028 0.68213 0.13232
#> x9 x10 iis9 iis11 iis43 iis73 x11
#> 0.03797 -0.12167 3.09339 3.39235 3.08462 2.91605 3.24507For the selection of indicators, we use a significance level,
t.pval, of 1/100. The data set has 100 observations and we
select over 100 impulse indicators. So we expect to falsely retain one
indicator on average. As the output shows, the algorithm has retained
four indicators: iis9, iis11, iis43, iis73. Since this is artificial
data, we know which observations were outliers. In this case, all of the
retained indicators correspond to actual outlying observations 9, 11,
43, and 73. The algorithm has only missed one additional outlier, which
was observation 78.
The object indicators is a list with two entries. The
first entry, $selection, stores the information related to
the search, such as the number of estimations and all terminal models.
The second entry, $final, is an object of class
"ivreg" and is the model result of the final model.
Now that we have identified (some of the) outliers, we still want to
find out which of our theoretical exogenous regressors are actually
relevant. As before, we can simply pass the final model from the
previous step to the gets() method. Since we do not want to
select over the impulse indicators again, we need to specify this
accordingly in the function call. The names of the indicators are
conveniently saved in the $selection$ISnames entry.
selection <- gets(indicators$final, keep_exog = indicators$selection$ISnames, print.searchinfo = FALSE)
print(selection$final)
#>
#> Call:
#> ivreg::ivreg(formula = as.formula(fml_sel), data = d)
#>
#> Coefficients:
#> x1 x2 iis9 iis11 iis43 iis73 x11
#> 5.864 -4.988 3.072 3.424 3.205 3.087 2.943As before, the returned object is a list with entry
$selection, which stores information about the search, and
$final, which is an "ivreg" model object of
the final model. There is an additional third entry named
$keep that specifies the names of all regressors in the
second stage that were not selected over. This can be used as a check
that the selection was done correctly.
# as specified, the impulse indicators and the endogenous regressor, x11, were not selected over
print(selection$keep)
#> [1] "iis9" "iis11" "iis43" "iis73" "x11"The final model has only retained the exogenous theory variables
\(x_{1}\) and \(x_{2}\), which is the correct selection.
The data generating process only contained the variables \(x_{1}\), \(x_{2}\), and \(x_{11}\). Their true parameters were
c(6, -5, 3), so the estimates are quite close.