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Doubly robust Hausman test of unconfoundedness

Source: R/dr-hausman.R
dr_hausman.Rd

Tests whether the treatment is unconfounded given the covariates, using the comparison proposed by Słoczyński, Uysal, and Wooldridge (2022, Section 5), building on Donald, Hsu, and Lieli (2014). Under one-sided noncompliance (nobody takes the treatment without the instrument: \(\Pr(D = 1 \mid Z = 0) = 0\)), the LATT identified through the instrument equals the ATT identified through unconfoundedness of the treatment — so a significant difference between the doubly robust LATT estimate (which uses the instrument) and the doubly robust ATT estimate (which does not) is evidence against unconfoundedness. Unlike the textbook OLS-vs-IV Hausman test, this comparison is robust to treatment effect heterogeneity.

Usage

dr_hausman(
  outcome,
  treatment,
  instrument,
  data,
  omodel = c("linear", "logit", "poisson"),
  tmodel = c("logit", "linear", "poisson"),
  ivmodel = c("logit", "ipt"),
  weights = NULL,
  cluster = NULL,
  pstolerance = 1e-05,
  subset = NULL
)

Arguments

outcome

A formula y ~ covariates for the outcome model. Use y ~ 1 for no covariates (required when method = "ipw").

treatment

A formula d ~ covariates for the treatment model.

instrument

A formula z ~ covariates for the instrument propensity score model; z must be binary 0/1. Use z ~ 1 when method = "ra".

data

A data frame containing all variables.

omodel

Outcome model family: "linear" (default; continuous), "logit" or "probit" (outcome must be 0/1), "poisson" (outcome must be non-negative), or "flogit" / "fprobit" (fractional outcome in [0, 1], e.g. a proportion). The f-prefixed families share all estimation with "logit" / "probit" and only relax the response to the unit interval, matching the Stata lateffects omodel options.

tmodel

Treatment model family: "logit" (default; treatment must be 0/1), "probit", "linear", or "poisson".

ivmodel

Instrument propensity score model for the LATT half: "logit" (default) or "ipt".

weights

Optional sampling weights (a numeric vector, or a column name in data given as a string).

cluster

Optional cluster identifier for clustered standard errors (a vector, or a column name in data given as a string).

pstolerance

Overlap tolerance: estimation stops with an error if any estimated instrument propensity score is below pstolerance or above 1 - pstolerance. Default 1e-5.

subset

Optional logical or integer vector selecting rows of data.

Value

An object of class "htest" with the z statistic, p-value, and the DR LATT, DR ATT, and difference estimates.

Details

The DR ATT estimator follows the paper's equation (33): a treatment propensity score \(\Pr(D = 1 \mid X)\) is fitted by logit QMLE on the treatment-equation covariates; the outcome model is fitted on the untreated sample weighted by the odds \(\hat p/(1-\hat p)\); and \(\hat\tau_{ATT}\) is the treated-sample mean outcome minus the mean imputed counterfactual. The standard error of the difference comes from stacking the moment conditions of both estimators (and the difference) into one M-estimation system, so the covariance between them is accounted for analytically — the analytic option suggested in the paper.

Note that the two halves adjust on their respective formulas: the LATT half's propensity score uses the instrument-equation covariates, while the ATT half's uses the treatment-equation covariates (both share the outcome model). Supply the same covariate set to all three formulas unless you intend them to differ.

References

Słoczyński, T., S. D. Uysal, and J. M. Wooldridge (2022). "Doubly Robust Estimation of Local Average Treatment Effects Using Inverse Probability Weighted Regression Adjustment." doi:10.48550/arXiv.2208.01300

Donald, S. G., Y.-C. Hsu, and R. P. Lieli (2014). "Testing the Unconfoundedness Assumption via Inverse Probability Weighted Estimators of (L)ATT." Journal of Business & Economic Statistics 32(3), 395-415.

Examples

d <- drlate_sim
d$nvstat[d$rsncode == 0] <- 0L   # impose one-sided noncompliance
dr_hausman(lwage ~ age + educ, nvstat ~ age + educ,
           rsncode ~ age + educ, data = d)
#> 
#> 	Doubly robust Hausman test of unconfoundedness
#> 	(Sloczynski-Uysal-Wooldridge 2022, one-sided noncompliance)
#> 
#> data:  d
#> z = -5.7425, p-value = 9.331e-09
#> alternative hypothesis: two.sided
#> sample estimates:
#>    DR LATT     DR ATT difference 
#>  0.3760331  0.6323210 -0.2562878 
#>