Define GMM Moment Conditions for Lewbel Simultaneous System

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

Usage

lewbel_simultaneous_moments(
  theta,
  data,
  y1_var,
  y2_var,
  x_vars,
  z_vars,
  add_intercept,
  z_sq
)

Arguments

theta

Numeric vector. Parameters: c(beta1, gamma1, beta2, gamma2).

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).

add_intercept

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

z_sq

Logical. Whether to include squared terms in the Z matrix for simultaneous equations.

Value

Matrix of moment conditions (n x q).

Details

For the simultaneous system: $$Y_1 = X'\beta_1 + \gamma_1 Y_2 + \epsilon_1$$ $$Y_2 = X'\beta_2 + \gamma_2 Y_1 + \epsilon_2$$

The moment conditions are the same as the triangular system. Note: Requires gamma1 * gamma2 != 1 for identification.

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_triangular_moments for triangular system moments.