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Define GMM Moment Conditions for Lewbel Triangular System

Source: R/lewbel-gmm.R
lewbel_triangular_moments.Rd

Creates the moment function for GMM estimation of a triangular system using Lewbel's heteroskedasticity-based identification.

Usage

lewbel_triangular_moments(
  theta,
  data,
  y1_var,
  y2_var,
  x_vars,
  z_vars,
  add_intercept
)

Arguments

theta

Numeric vector. Parameters to estimate: c(beta1, gamma1, beta2).

data

Data frame containing all required variables. Must include the dependent variables and any exogenous regressors specified in the model.

y1_var

Character. Name of the first dependent variable (default: "Y1").

y2_var

Character. Name of the second dependent variable/endogenous regressor (default: "Y2").

x_vars

Character vector. Names of exogenous variables (default: "Xk").

z_vars

Character vector. Names of heteroskedasticity drivers (default: NULL, uses centered X).

add_intercept

Logical. Whether to add an intercept to the exogenous variables.

Value

Matrix of moment conditions (n x q).

Details

For the triangular system: $$Y_1 = X'\beta_1 + \gamma_1 Y_2 + \epsilon_1$$ $$Y_2 = X'\beta_2 + \epsilon_2$$

The moment conditions are:

  • \(E[X \times \epsilon_1] = 0\)

  • \(E[X \times \epsilon_2] = 0\)

  • \(E[Z \times \epsilon_1 \times \epsilon_2] = 0\)

where Z = g(X) is a mean-zero transformation of X.

References

Lewbel, A. (2012). Using heteroscedasticity to identify and estimate mismeasured and endogenous regressor models. Journal of Business & Economic Statistics, 30(1), 67-80. doi:10.1080/07350015.2012.643126

See also

lewbel_gmm for the main GMM estimation function. lewbel_simultaneous_moments for simultaneous system moments.