This formula estimates an instrumental variables regression using two-stage least squares with a variety of options for robust standard errors

iv_robust(formula, data, weights, subset, clusters, se_type = NULL, ci = TRUE, alpha = 0.05, return_vcov = TRUE, try_cholesky = FALSE)

formula | an object of class formula of the regression and the instruments.
For example, the formula |
---|---|

data | A |

weights | the bare (unquoted) names of the weights variable in the supplied data. |

subset | An optional bare (unquoted) expression specifying a subset of observations to be used. |

clusters | An optional bare (unquoted) name of the variable that corresponds to the clusters in the data. |

se_type | The sort of standard error sought. If `clusters` is not specified the options are "HC0", "HC1" (or "stata", the equivalent), "HC2" (default), "HC3", or "classical". If `clusters` is specified the options are "CR0", "CR2" (default), or "stata". Can also specify "none", which may speed up estimation of the coefficients. |

ci | logical. Whether to compute and return p-values and confidence intervals, TRUE by default. |

alpha | The significance level, 0.05 by default. |

return_vcov | logical. Whether to return the variance-covariance matrix for later usage, TRUE by default. |

try_cholesky | logical. Whether to try using a Cholesky decomposition to solve least squares instead of a QR decomposition, FALSE by default. Using a Cholesky decomposition may result in speed gains, but should only be used if users are sure their model is full-rank (i.e., there is no perfect multi-collinearity) |

An object of class `"iv_robust"`

.

The post-estimation commands functions `summary`

and `tidy`

return results in a `data.frame`

. To get useful data out of the return,
you can use these data frames, you can use the resulting list directly, or
you can use the generic accessor functions `coef`

, `vcov`

,
`confint`

, and `predict`

.

An object of class `"iv_robust"`

is a list containing at least the
following components:

the estimated coefficients

the estimated standard errors

the estimated degrees of freedom

the p-values from a two-sided t-test using `coefficients`

, `std.error`

, and `df`

the lower bound of the `1 - alpha`

percent confidence interval

the upper bound of the `1 - alpha`

percent confidence interval

a character vector of coefficient names

the significance level specified by the user

the standard error type specified by the user

the residual variance

the number of observations used

the number of columns in the design matrix (includes linearly dependent columns!)

the rank of the fitted model

the fitted variance covariance matrix

the \(R^2\) of the second stage regrssion

the \(R^2\) of the second stage regression, but penalized for having more parameters, `rank`

a vector with the value of the second stage F-statistic with the numerator and denominator degrees of freedom

whether or not weights were applied

the original function call

This function performs two-stage least squares estimation to fit
instrumental variables regression. The syntax is similar to that in
`ivreg`

from the `AER`

package. Regressors and instruments
should be specified in a two-part formula, such as
`y ~ x1 + x2 | z1 + z2 + z3`

, where `x1`

and `x2`

are
regressors and `z1`

, `z2`

, and `z3`

are instruments. Unlike
`ivreg`

, you must explicitly specify all exogenous regressors on
both sides of the bar.

The default variance estimators are the same as in `lm_robust`

.
Without clusters, we default to `HC2`

standard errors, and with clusters
we default to `CR2`

standard errors. 2SLS variance estimates are
computed using the same estimators as in `lm_robust`

, however the
design matrix used are the second-stage regressors, which includes the estimated
endogenous regressors, and the residuals used are the difference
between the outcome and a fit produced by the second-stage coefficients and the
first-stage (endogenous) regressors. More notes on this can be found at
the mathematical appendix.

library(fabricatr) dat <- fabricate( N = 40, Y = rpois(N, lambda = 4), Z = rbinom(N, 1, prob = 0.4), D = Z * rbinom(N, 1, prob = 0.8), X = rnorm(N) ) # Instrument for treatment `D` with encouragement `Z` tidy(iv_robust(Y ~ D + X | Z + X, data = dat))#> term estimate std.error p.value ci.lower ci.upper df outcome #> 1 (Intercept) 3.7273864 0.4776022 2.471825e-09 2.759673 4.6951003 37 Y #> 2 D -0.7100564 0.7858244 3.720629e-01 -2.302288 0.8821750 37 Y #> 3 X 0.1560677 0.3621421 6.690000e-01 -0.577702 0.8898373 37 Y# Instrument with Stata's `ivregress 2sls , small rob` HC1 variance tidy(iv_robust(Y ~ D | Z, data = dat, se_type = "stata"))#> term estimate std.error p.value ci.lower ci.upper df outcome #> 1 (Intercept) 3.6666667 0.4700241 2.083704e-09 2.715153 4.6181808 38 Y #> 2 D -0.6140351 0.7436379 4.141183e-01 -2.119451 0.8913811 38 Y# With clusters, we use CR2 errors by default dat$cl <- rep(letters[1:5], length.out = nrow(dat)) tidy(iv_robust(Y ~ D | Z, data = dat, clusters = cl))#> term estimate std.error p.value ci.lower ci.upper df #> 1 (Intercept) 3.6666667 0.2317241 0.0001712102 2.997917 4.3354161 3.646251 #> 2 D -0.6140351 0.4874346 0.2764953738 -1.969373 0.7413026 3.985068 #> outcome #> 1 Y #> 2 Y# Again, easy to replicate Stata (again with `small` correction in Stata) tidy(iv_robust(Y ~ D | Z, data = dat, clusters = cl, se_type = "stata"))#> term estimate std.error p.value ci.lower ci.upper df outcome #> 1 (Intercept) 3.6666667 0.2391517 0.0001055703 3.002675 4.3306582 4 Y #> 2 D -0.6140351 0.5047569 0.2906673250 -2.015465 0.7873946 4 Y