Identification using heteroscedasticity

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Description

This function estimates the model parameters and associated standard errors for a linear regression model with one or more endogenous regressors. Identification is achieved through heteroscedastic covariance restrictions within the triangular system.

Usage

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lewbel(formula, data, clustervar = NULL, robust = TRUE)

Arguments

formula

an object of class “formula” (or one that can be coerced to that class).

data

the data frame containing these data. This argument must be used.

clustervar

a character value naming the cluster on which to adjust the standard errors and test statistics.

robust

if TRUE the function reports standard errors and test statistics that have been corrected for the presence heteroscedasticity using White's method.

Details

The formula follows a four-part specification. Each part is separated by a vertical bar character “|”. The following formula is an example: y2 ~ y1 | x1 + x2 + x3 | x1 + x2 | z1. Here, y2 is the dependent variable and y1 is the endogenous regressor. The code x1 + x2 + x3 represents the exogenous regressors whereas the third part x1 + x2 specifies the exogenous heteroscedastic variables from which the instruments are derived. The final part z1 is optional, allowing the user to include tradtional instrumental variables. If both robust=TRUE and !is.null(clustervar) the function overrides the robust command and computes clustered standard errors and test statistics adjusted to account for clustering. This function computes partial F-statistics that indicate potentially weak identification. In cases where there is more than one endogenous regressor the Angrist-Pischke (2009) method for multivariate first-stage F-statistics is employed.

Value

coef.est

a coefficient matrix with columns containing the estimates, associated standard errors, test statistics and p-values.

call

the matched call.

num.obs

the number of observations.

j.test

J-test for overidentifying restrictions.

f.test.stats

Partial F-test statistics for weak IV detection.

References

Angrist, J. and Pischke, J.S. (2009). Mostly Harmless Econometrics: An Empiricist's Companion, Princeton University Press.

Lewbel, A. (2012). Using heteroscedasticity to identify and estimate mismeasured and endogenous regressor models. Journal of Business & Economic Statistics, 30(1), 67-80.

Examples

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set.seed(1234)
n = 1000
x1 = rnorm(n, 0, 1)
x2 = rnorm(n, 0, 1)
u = rnorm(n, 0, 1)
s1 = rnorm(n, 0, 1)
s2 =  rnorm(n, 0, 1)
ov = rnorm(n, 0, 1)
z1 = rnorm(n, 0 ,1)
e1 = u + exp(x1)*s1 + exp(x2)*s1
e2 = u + exp(-x1)*s2 + exp(-x2)*s2
y1 = 1 + x1 + x2 + ov + e2 + 2*z1
y2 = 1 + x1 + x2 + y1 + 2*ov + e1
data = data.frame(y2, y1, x1, x2, z1)

lewbel(formula = y2 ~ y1 | x1 + x2 | x1 + x2, data = data)
lewbel(formula = y2 ~ y1 | x1 + x2 | x1 + x2 | z1, data = data)

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