README

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.

Installation

install.packages("ivgets")

# install.packages("devtools")
devtools::install_github("jkurle/ivgets")

Dependencies

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.

Versions

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.

Example

Setup

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.

[ y_{i} = \beta_{1} x_{1i} + \beta_{2} x_{2i} + … + \beta_{11} x_{11i} + u_{i} = x_{i}^{\prime} \beta + u_{i}](https://latex.codecogs.com/png.image?%5Cdpi%7B110%7D&space;%5Cbg_white&space;%0Ay_%7Bi%7D%20%3D%20%5Cbeta_%7B1%7D%20x_%7B1i%7D%20%2B%20%5Cbeta_%7B2%7D%0Ax_%7B2i%7D%20%2B%20…%20%2B%20%5Cbeta_%7B11%7D%20x_%7B11i%7D%20%2B%20u_%7Bi%7D%20%3D%20x_%7Bi%7D%5E%7B%5Cprime%7D%20%5Cbeta%20%2B%20u_%7Bi%7D%0A ” y_{i} = {1} x{1i} + {2} x{2i} + … + {11} x{11i} + u_{i} = x_{i}^{} + u_{i} “)

where $z_{i}$ includes all the exogenous regressors $x_{1}$ to $x_{10}$ and the excluded instruments $z_{11}$ and $z_{12}$ .

Indicator Saturation

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   3.24507

For 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.

General-to-Specific Theory Modeling

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   2.943

As 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.