ivr function

Two-Stage Least Squares (2SLS) Instrumental Variable Regression

Performs a two-stage least squares regression on a single equation including endogenous regressors Y and exogenous regressors X on the right hand-side. Note that by specifying the set of endogenous regressors Y by endog the set of remaining regressors X are assumed to be exogenous and therefore automatically considered as part of the instrument in the first stage of the 2SLS. These variables are not to be specified in the iv argument. Here only instrumental variables outside the equation under consideration are specified.

ivr(formula, data = list(), endog, iv, contrasts = NULL, details = FALSE, ...)

Arguments

• formula: model formula.
• data: name of the data frame used. To be specified if variables are not stored in environment.
• endog: character vector of endogenous (to be instrumented) regressors.
• iv: character vector of predetermined/exogenous instrumental variables NOT already included in the model formula.
• contrasts: an optional list. See the contrasts.arg of model.matrix.default.
• details: logical value indicating whether details should be printed out by default.
• ...: further arguments that lm.fit() understands.

Returns

A list object including:

adj.r.squ	adjusted coefficient of determination (adj. R-squared).
coefficients	IV-estimators of model parameters.
data/model	matrix of the variables' data used.
data.name	name of the data frame used.
df	degrees of freedom in the model (number of observations minus rank).
exogenous	exogenous regressors.
f.hausman	exogeneity test: F-value for simultaneous significance of all instrument parameters. If H0: "Instruments are exogenous" is rejected, usage of IV-regression can be justified against OLS.
f.instr	weak instrument test: F-value for significance of instrument parameter in first stage of 2SLS regression. If H0: "Instrument is weak" is rejected, instruments are usually considered sufficiently strong.
fitted.values	fitted values of the IV-regression.
fsd	first stage diagnostics (weakness of instruments).
has.const	logical value indicating whether model has a constant (internal purposes).
instrumented	name of instrumented regressors.
instruments	name of instruments.
model.matrix	the model (design) matrix.
ncoef	integer, giving the rank of the model (number of coefficients estimated).
nobs	number of observations.
p.hausman	according p-value of exogeneity test.
p.instr	according p-value of weak instruments test.
p.values	vector of p-values of single parameter significance tests.
r.squ	coefficient of determination (R-squared).
residuals	residuals in the IV-regression.
response	the endogenous (response) variable.
shea	Shea's partial R-squared quantifying the ability to explain the endogenous regressors.
sig.squ	estimated error variance (sigma-squared).
ssr	sum of squared residuals.
std.err	vector of standard errors of the parameter estimators.
t.values	vector of t-values of single parameter significance tests.
ucov	the (unscaled) variance-covariance matrix of the model's estimators.
vcov	the (scaled) variance-covariance matrix of the model's estimators.
modform	the model's regression R-formula.

Examples

## Numerical Illustration 20.1 in Auer (2023)
ivr(contr ~ score, endog = "score", iv = "contrprev", data = data.insurance, details = TRUE)

## Replicating an example of Ani Katchova (econometric academy)
## (https://www.youtube.com/watch?v=lm3UvcDa2Hc)
## on U.S. Women's Labor-Force Participation (data from Wooldridge 2013)

if (requireNamespace('wooldridge', quietly = TRUE)) {
  library('wooldridge')
  data(mroz)
  # Select only working women
  mroz = mroz[mroz$"inlf" == 1,]
  mroz = mroz[, c("lwage", "educ", "exper", "expersq", "fatheduc", "motheduc")]
  attach(mroz)

  # Regular ols of lwage on educ, where educ is suspected to be endogenous
  # hence estimators are biased
  ols(lwage ~ educ, data = mroz)

  # Manual calculation of ols coeff
  Sxy(educ, lwage)/Sxy(educ)

  # Manual calculation of iv regression coeff
  # with fatheduc as instrument for educ
  Sxy(fatheduc, lwage)/Sxy(fatheduc, educ)

  # Calculation with 2SLS
  educ_hat = ols(educ ~ fatheduc)$fitted
  ols(lwage ~ educ_hat)

  # Verify that educ_hat is completely determined by values of fatheduc
  head(cbind(educ,fatheduc,educ_hat), 10)

  # Calculation with ivr()
  ivr(lwage ~ educ, endog = "educ", iv = "fatheduc", data = mroz, details = TRUE)

  # Multiple regression model with 1 endogenous regressor (educ)
  # and two exogenous regressors (exper, expersq)

  # Biased ols estimation
  ols(lwage ~ educ + exper + expersq, data = mroz)

  # Unbiased 2SLS estimation with fatheduc and motheduc as instruments
  # for the endogenous regressor educ
  ivr(lwage ~ educ + exper + expersq,
    endog = "educ", iv = c("fatheduc", "motheduc"),
    data = mroz)

  # Manual 2SLS
  # First stage: Regress endog. regressor on all exogen. regressors
  # and instruments -> get exogenous part of educ
  stage1.mod = ols(educ ~ exper + expersq + fatheduc + motheduc)
  educ_hat = stage1.mod$fitted

  # Second stage: Replace endog regressor with predicted value educ_hat
  # See the uncorrected standard errors!
  stage2.mod = ols(lwage ~ educ_hat + exper + expersq, data = mroz)

  ## Simple test for endogeneity of educ:
  ## Include endogenous part of educ into model and see if it is signif.
  ## (is signif. at 10% level)
  uhat = ols(educ ~ exper + expersq + fatheduc + motheduc)$resid
  ols(lwage ~ educ + exper + expersq + uhat)
  detach(mroz)

} else {
  message("Package 'wooldridge' not available.")
}

References

Auer, L.v. (2023): Ökonometrie - Eine Einführung, 8th ed., Springer-Gabler (https://www.oekonometrie-lernen.de).

Wooldridge, J.M. (2013): Introductory Econometrics: A Modern Approach, 5th Edition, Cengage Learning, Datasets available for download at Cengage Learning