generate_param: Parameters of 2SLS model (Monte Carlo)

Description

By default, generate_param creates random parameters of a 2SLS model that satisfy conditions for 2SLS models, such as positive definite variance-covariance matrices. The user can also specify certain parameters directly, which are then checked for their validity.

Usage

generate_param(
  dx1,
  dx2,
  dz2,
  intercept = TRUE,
  beta = NULL,
  sigma = 1,
  mean_z = NULL,
  cov_z = NULL,
  Sigma2_half = NULL,
  Omega2 = NULL,
  Pi = NULL,
  seed = 42
)

Value

generate_param returns a list with the (randomly created or user-specified) parameters that are required for drawing random data that. The parameters are generated to fulfill the 2SLS model assumptions.

$structural: A list with two components storing the mean ($mean) and variance-covariance matrix ($cov) for the structural error (u), the random first stage errors (r2), and all instruments (excluding the intercept since it is not random) (z).

$params

A list storing the parameters of the 2SLS model. $beta is the coefficient vector (including intercept if present) of the structural equation, $Pi the coefficient matrix of the first stage projections, $Omega2 the covariance between the structural error and the endogenous first stage errors, $Sigma2_half the square root of the variance-covariance matrix of the endogenous first stage errors, $mean_z the mean of all instruments (excluding the intercept since it is not random), $cov_z the variance-covariance matrix of the endogenous first-stage errors, $Ezz the expected value of the squared instruments.

$settings

A list storing the function call ($call), whether an intercept is included in the model ($intercept), a regression formula for the model setup ($formula), and the dimensions of the regressors and instruments ($dx1, $dx2, $dz2.

$names

A list storing generic names for the regressors, instruments, and errors as character vectors ($x1, $x2, $x, $z2, $z, $r, and $u).

Arguments

dx1: An integer value specifying the number of exogenous regressors. This should include the intercept if it is present in the model (see argument intercept).
dx2: An integer value specifying the number of endogenous regressors.
dz2: An integer value specifying the number of outside / excluded instruments.
intercept: A logical value (TRUE / FALSE) indicating whether the model should contain an intercept.
beta: A numeric vector of length dx1 + dx2 specifying the parameters of the structural equation.
sigma: A strictly positive numeric value specifying the standard deviation of the error in the structural model.
mean_z: A numeric vector of length dx1 + dz2 specifying the mean of the exogenous variables, x1 and z2.
cov_z: A numeric positive definite matrix specifying the variance-covariance matrix of the exogenous variables, x1 and z2.
Sigma2_half: A numeric positive definite matrix of dimension dx2 by dx2 such that its square is the variance-covariance matrix of the random first stage errors (Sigma2).
Omega2: A numeric vector of length dx1 specifying the correlation between the scaled random first stage error and the structural error.
Pi: A numeric matrix of dimension (dx1 + dz2) by (dx1 + dx2) specifying the first stage parameter matrix.
seed: An integer for setting the seed for the random number generator.