sbinaryLGMM {spldv}

Estimation of SAR for binary models using Linearized GMM.

Description

Estimation of SAR model for binary dependent variables (either Probit or Logit), using Linearized GMM estimator suggested by Klier and McMillen (2008). The model is:

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) link = "logit".

Usage

sbinaryLGMM(
  formula,
  data,
  listw = NULL,
  nins = 2,
  link = c("logit", "probit"),
  ...
)

## S3 method for class 'binlgmm'
coef(object, ...)

## S3 method for class 'binlgmm'
vcov(object, ...)

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

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

## S3 method for class 'summary.binlgmm'
print(x, digits = max(3, getOption("digits") - 2), ...)

Arguments

formula

a symbolic description of the model of the form y ~ x | wx where y is the binary dependent variable, x are the independent variables. The variables after | are those variables that enter spatially lagged: WX. The variables in the second part of formula must also appear in the first part.

data

the data of class data.frame.

listw

object. An object of class listw, matrix, or Matrix.

nins

numerical. Order of instrumental-variable approximation; as default nins = 2, such that H = (Z, WZ, W^2Z) are used as instruments.

link

string. The assumption of the distribution of the error term; it can be either link = "probit" (the default) or link = "logit".

...

additional arguments.

x, object

an object of class binlgmm.

digits

the number of digits

Details

The steps for the linearized spatial Probit/Logit model are the following:

1. Estimate the model by standard Probit/Logit model, in which spatial autocorrelation and heteroskedasticity are ignored. The estimated values are \beta_0. Calculate the generalized residuals assuming that \lambda = 0 and the gradient terms G_{\beta} and G_{\lambda}.

2. The second step is a two-stage least squares estimator of the linearized model. Thus regress G_{\beta} and G_{\lambda} on H = (Z, WZ, W^2Z, ...., W^qZ) and obtain the predicted values \hat{G}. Then regress u_0 + G_{\beta}'\hat{\beta}_0 on \hat{G}. The coefficients are the estimated values of \beta and \lambda.

The variance-covariance matrix can be computed using the traditional White-corrected coefficient covariance matrix from the last two-stage least squares estimator of the linearlized model.

Value

An object of class “bingmm”, a list with elements:

coefficients

the estimated coefficients,

call

the matched call,

X

the X matrix, which contains also WX if the second part of the formula is used,

H

the H matrix of instruments used,

y

the dependent variable,

listw

the spatial weight matrix,

link

the string indicating the distribution of the error term,

fit

an object of lm representing the T2SLS,

formula

the formula.

Author(s)

Mauricio Sarrias and Gianfranco Piras.

References

Klier, T., & McMillen, D. P. (2008). Clustering of auto supplier plants in the United States: generalized method of moments spatial logit for large samples. Journal of Business & Economic Statistics, 26(4), 460-471.

Piras, G., & Sarrias, M. (2023). One or Two-Step? Evaluating GMM Efficiency for Spatial Binary Probit Models. Journal of choice modelling, 48, 100432.

Piras, G,. & Sarrias, M. (2023). GMM Estimators for Binary Spatial Models in R. Journal of Statistical Software, 107(8), 1-33.

See Also

sbinaryGMM, impacts.bingmm.

Examples

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

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

# LGMM for probit using q = 3 for instruments
lgmm <- sbinaryLGMM(CRIMED ~ INC + HOVAL | INC,
                link  = "probit", 
                listw = spdep::nb2listw(COL.nb, style = "W"),
                nins  = 3, 
                data  = COL.OLD)
summary(lgmm)