Instrumental-Variable Regression by 2SLS Estimation Involving Ranks

Fit instrumental-variable regression involving ranks by two-stage least squares (2SLS). This is equivalent to direct instrumental-variables estimation when the number of instruments is equal to the number of regressors.

Usage

ivregranks(
  formula,
  data,
  subset,
  na.action,
  weights,
  offset,
  contrasts = NULL,
  model = TRUE,
  y = TRUE,
  x = FALSE,
  method = "OLS",
  omega = 1,
  ...
)

# S3 method for class 'ivregranks'
plot(x, which = 1, ...)

# S3 method for class 'ivregranks'
predict(object, newdata, ...)

# S3 method for class 'ivregranks'
summary(object, vcov. = NULL, df = NULL, diagnostics = NULL, ...)

# S3 method for class 'summary.ivregranks'
print(x, ...)

# S3 method for class 'ivregranks'
confint(
  object,
  parm,
  level = 0.95,
  component = c("stage2", "stage1"),
  complete = TRUE,
  vcov. = NULL,
  df = NULL,
  ...
)

# S3 method for class 'ivregranks'
vcov(object, component = c("stage2", "stage1"), complete = TRUE, ...)

Arguments

formula: formula specification(s) of the regression relationship and the instruments. formula has three parts as in r(y) ~ x1 + r(x2) | r(z1) + z2 + z3.
data: an optional data frame containing the variables in the model. By default the variables are taken from the environment of the formula.
subset: currently not supported.
na.action: currently not supported.
weights: currently not supported.
offset: an optional offset that can be used to specify an a priori known component to be included during fitting.
contrasts: an optional list. See the contrasts.arg of model.matrix.default.
model, x, y: logicals. If TRUE the corresponding components of the fit (the model frame, the model matrices, the response) are returned. These components are necessary for computing regression diagnostics.
method: the method used to fit the stage 1 and 2 regression: "OLS" for traditional 2SLS regression (the default and only option).
omega: real number in the interval [0,1] defining how ties are handled (if there are any).
...: further arguments passed to ivreg.fit.
which: As in plot.ivreg. Currently only no. 1 is available.
object: An object of class "ivregranks".
newdata: An optional data frame in which to look for variables with which to predict. If omitted, the fitted values are used.
vcov.: Optionally either a coefficient covariance matrix or a function to compute such a covariance matrix from fitted ivreg model objects. If NULL (the default) the standard covariance matrix (based on the information matrix) is used. Alternatively, covariance matrices (e.g., clustered and/or heteroscedasticity-consistent) can be plugged in to adjust Wald tests or confidence intervals etc. In summary, if diagnostics = TRUE, vcov. must be a function (not a matrix) because the alternative covariances are also needed for certain auxiliary models in the diagnostic tests. If vcov. is a function, the ... argument can be used to pass on further arguments to this function.
df: For summary, optional residual degrees of freedom to use in computing model summary.
diagnostics: currently not supported.
parm: parameters for which confidence intervals are to be computed; a vector or numbers or names; the default is all parameters.
level: confidence level; the default is 0.95.
component: Character indicating "stage2" or "stage1".
complete: logical indicating if the full variance-covariance matrix should be returned also in case of an over-determined system where some coefficients are undefined and coef(.) contains NAs correspondingly. When complete = TRUE, vcov() is compatible with coef() also in this singular case.

Value

ivregranks returns an object of class "ivregranks" that inherits as much as possible from class ivreg, with the following additional components:

rank_terms_indices: an integer vector with indices of entries of terms.labels attribute of terms(formula) for the outcome equation which correspond to ranked regressors.
rank_instruments_indices: an integer vector with indices of entries of the ranked instrumental variables.
ranked_response: a logical entry.
omega: an entry corresponding to the omega argument.

Details

Regressors and instruments for ivregranks are most easily specified in a formula with two parts on the right-hand side, e.g., r(y) ~ x1 + r(x2) | r(z1) + z2 + z3, where x1 and r(x2) are the explanatory variables and r(z1), z2, and z3 are the instrumental variables. Note that exogenous regressors have to be included as instruments for themselves.

For example, if there is one exogenous regressor ex and one endogenous regressor r(en) with instrument r(in), the appropriate formula would be r(y) ~ r(en) + ex | r(in) + ex. Alternatively, a formula with three parts on the right-hand side can also be used: r(y) ~ ex | r(en) | r(in). The latter is typically more convenient, if there is a large number of exogenous regressors.

Moreover, two further equivalent specification strategies are possible that are typically less convenient compared to the strategies above. One option is to use an update formula with a . in the second part of the formula is used: r(y) ~ r(en) + ex | . - r(en) + r(in). Another option is to use a separate formula for the instruments (only for backward compatibility with earlier versions): formula = r(y) ~ r(en) + ex, instruments = ~ r(in) + ex.

Internally, all specifications are converted to the version with two parts on the right-hand side.

Methods (by generic)

plot(ivregranks): Plot diagnostics for an ivregranks object

Displays plots useful for assessing quality of model fit. Currently, only one plot is available, which plots fitted values against residuals (for homoscedacity check).
predict(ivregranks): Predict method for IV Model for Ranks Fits
summary(ivregranks): Summary and Inference Methods for "ivregranks" Objects
vcov(ivregranks): Calculate Variance-Covariance Matrix for a Fitted ivregranks object

Returns the variance-covariance matrix of the regression coefficients (main parameters) of a fitted ivregranks object. Its result is theoretically valid and asymptotically consistent, in contrast to naively running vcov(ivreg(...)).

References

Chetverikov and Wilhelm (2023), "Inference for Rank-Rank Regressions". arXiv preprint arXiv:2310.15512

Examples

# rank-rank regression:
Z <- rnorm(500)
X <- Z + rnorm(500)
Y <- X + rnorm(500)
rrfit <- ivregranks(r(Y) ~ r(X) | r(Z))
summary(rrfit)
#> 
#> Call:
#> ivregranks(formula = r(Y) ~ r(X) | r(Z))
#> 
#> Residuals:
#>       Min        1Q    Median        3Q       Max 
#> -0.535939 -0.124013  0.002403  0.114031  0.556328 
#> 
#> Coefficients:
#>             Estimate Std. Error z value Pr(>|z|)    
#> (Intercept)  0.10579    0.01658   6.379 1.78e-10 ***
#> r(X)         0.78884    0.03310  23.831  < 2e-16 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 

# naive version of the rank-rank regression:
RZ <- frank(Z, increasing = TRUE, omega = 1)
RX <- frank(X, increasing = TRUE, omega = 1)
RY <- frank(Y, increasing = TRUE, omega = 1)
fit <- ivreg::ivreg(RY ~ RX | RZ)
summary(fit)
#> 
#> Call:
#> ivreg::ivreg(formula = RY ~ RX | RZ)
#> 
#> Residuals:
#>       Min        1Q    Median        3Q       Max 
#> -0.535939 -0.124013  0.002403  0.114031  0.556328 
#> 
#> Coefficients:
#>             Estimate Std. Error t value Pr(>|t|)    
#> (Intercept)  0.10579    0.02025   5.225 2.57e-07 ***
#> RX           0.78884    0.03723  21.190  < 2e-16 ***
#> 
#> Diagnostic tests:
#>                  df1 df2 statistic p-value    
#> Weak instruments   1 498   580.619  <2e-16 ***
#> Wu-Hausman         1 497     0.024   0.876    
#> Sargan             0  NA        NA      NA    
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Residual standard error: 0.1763 on 498 degrees of freedom
#> Multiple R-Squared: 0.6285,	Adjusted R-squared: 0.6278 
#> Wald test:   449 on 1 and 498 DF,  p-value: < 2.2e-16 
#> 
# the coefficient estimates are the same as in the ivregranks function, but
# the standard errors, t-values, p-values are incorrect.

# support for `data` argument:
ivr <- ivregranks(r(mpg) ~ r(hp) + cyl | r(disp) + cyl, data = mtcars)
summary(ivr)
#> 
#> Call:
#> ivregranks(formula = r(mpg) ~ r(hp) + cyl | r(disp) + cyl, data = mtcars)
#> 
#> Residuals:
#>      Min       1Q   Median       3Q      Max 
#> -1.49398 -0.41639 -0.06979  0.44197  2.02883 
#> 
#> Coefficients:
#>             Estimate Std. Error z value Pr(>|z|)
#> (Intercept)  -1.4537     9.5927  -0.152    0.880
#> r(hp)        -7.1939    23.4357  -0.307    0.759
#> cyl           0.9336     3.5509   0.263    0.793
#>