generate_param {robust2sls}

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
)

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.

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).