impacts.bingmm {spldv}

Estimation of the average marginal effects for SARB model estimated using GMM procedures.

Description

Obtain the average marginal effects from bingmm or binlgmm class model.

Usage

## S3 method for class 'bingmm'
impacts(
  object,
  vcov = NULL,
  vce = c("robust", "efficient", "ml"),
  het = TRUE,
  atmeans = FALSE,
  type = c("mc", "delta"),
  R = 100,
  approximation = FALSE,
  pw = 5,
  tol = 1e-06,
  empirical = FALSE,
  ...
)

## S3 method for class 'binlgmm'
impacts(
  object,
  vcov = NULL,
  het = TRUE,
  atmeans = FALSE,
  type = c("mc", "delta"),
  R = 100,
  approximation = FALSE,
  pw = 5,
  tol = 1e-06,
  empirical = FALSE,
  ...
)

## S3 method for class 'impacts.bingmm'
print(x, ...)

## S3 method for class 'impacts.bingmm'
summary(object, ...)

## S3 method for class 'summary.impacts.bingmm'
print(x, digits = max(3, getOption("digits") - 3), ...)

Arguments

object

an object of class bingmm, binlgmm, or impacts.bingmm for summary and print method.

vcov

an estimate of the asymptotic variance-covariance matrix of the parameters for a bingmm or binlgmm object.

vce

string indicating what kind of variance-covariance matrix of the estimate should be computed when using effect.bingmm. For the one-step GMM estimator, the options are "robust" and "ml". For the two-step GMM estimator, the options are "robust", "efficient" and "ml". The option "vce = ml" is an exploratory method that evaluates the VC of the RIS estimator using the GMM estimates.

het

logical. If TRUE (the default), then the heteroskedasticity is taken into account when computing the average marginal effects.

atmeans

logical. If FALSE (the default), then the average marginal effects are computed at the unit level.

type

string indicating which method is used to compute the standard errors of the average marginal effects. If "mc", then the Monte Carlo approximation is used. If "delta", then the Delta Method is used.

R

numerical. Indicates the number of draws used in the Monte Carlo approximation if type = "mc".

approximation

logical. If TRUE then (I - \lambda W)^{-1} is approximated as I + \lambda W + \lambda^2 W^2 + \lambda^3 W^3 + ... +\lambda^q W^q. The default is FALSE.

pw

numeric. The power used for the approximation I + \lambda W + \lambda^2 W^2 + \lambda^3 W^3 + ... +\lambda^q W^q. The default is 5.

tol

Argument passed to mvrnorm: tolerance (relative to largest variance) for numerical lack of positive-definiteness in the coefficient covariance matrix.

empirical

logical. Argument passed to mvrnorm (default FALSE): if TRUE, the coefficients and their covariance matrix specify the empirical not population mean and covariance matrix

...

further arguments. Ignored.

x

an object of class impacts.bingmm.

digits

the number of digits.

Details

Let the model be:

y^*= X\beta + WX\gamma + \lambda W y^* + \epsilon = Z\delta + \lambda Wy^{*} + \epsilon

where y = 1 if y^*>0 and 0 otherwise; \epsilon \sim N(0, 1) if link = "probit" or \epsilon \sim L(0, \pi^2/3) if link = "logit".

The marginal effects respect to variable x_r can be computed as

diag(f(a))D^{-1}_{\lambda}A^{-1}_{\lambda}\left(I_n\beta_r + W\gamma_r\right) = C_r(\theta)

where f() is the pdf, which depends on the assumption of the error terms; diag is the operator that creates a n \times n diagonal matrix; A_{\lambda}= (I -\lambda W); and D_{\lambda} is a diagonal matrix whose elements represent the square root of the diagonal elements of the variance-covariance matrix of u = A_{\lambda}^{-1}\epsilon.

We implement these three summary measures: (1) The average total effects, ATE_r = n^{-1}i_n'C_{r}i_n, (2) The average direct effects, ADE_r = n^{-1}tr(C_{r}), and (3) the average indirect effects, ATE_r - ADE_r.

The standard errors of the average total, direct and indirect effects can be estimated using either Monte Carlo (MC) approximation, which takes into account the sampling distribution of \theta, or Delta Method.

Value

An object of class impacts.bingmm.

Author(s)

Mauricio Sarrias and Gianfranco Piras.

See Also

sbinaryGMM, sbinaryLGMM.

Examples

# Data set
data(oldcol, package = "spdep")

# Create dependent (dummy) variable
COL.OLD$CRIMED <- as.numeric(COL.OLD$CRIME > 35)

# Two-step (Probit) GMM estimator
ts <- sbinaryGMM(CRIMED ~ INC + HOVAL| HOVAL,
                link = "probit", 
                listw = spdep::nb2listw(COL.nb, style = "W"), 
                data = COL.OLD, 
                type = "twostep")
                
# Marginal effects using Delta Method
summary(impacts(ts, type = "delta"))

# Marginal effects using MC with 100 draws
summary(impacts(ts, type = "mc", R = 100))

# Marginal effects using efficient VC matrix
summary(impacts(ts, type = "delta", vce = "efficient"))

# Marginal effects using efficient VC matrix and ignoring the heteroskedasticity
summary(impacts(ts, type = "delta", vce = "efficient", het = FALSE))