simsart {CDatanet}

Simulating data from Tobit models with social interactions

Description

simsart simulates censored data with social interactions (see Xu and Lee, 2015).

Usage

simsart(formula, Glist, theta, tol = 1e-15, maxit = 500, cinfo = TRUE, data)

Arguments

formula

a class object formula: a symbolic description of the model. formula must be as, for example, y ~ x1 + x2 + gx1 + gx2 where y is the endogenous vector and x1, x2, gx1 and gx2 are control variables, which can include contextual variables, i.e. averages among the peers. Peer averages can be computed using the function peer.avg.

Glist

The network matrix. For networks consisting of multiple subnets, Glist can be a list of subnets with the m-th element being an ns*ns adjacency matrix, where ns is the number of nodes in the m-th subnet.

theta

a vector defining the true value of \theta = (\lambda, \Gamma, \sigma) (see the model specification in details).

tol

the tolerance value used in the fixed point iteration method to compute y. The process stops if the \ell_1-distance between two consecutive values of y is less than tol.

maxit

the maximal number of iterations in the fixed point iteration method.

cinfo

a Boolean indicating whether information is complete (cinfo = TRUE) or incomplete (cinfo = FALSE). In the case of incomplete information, the model is defined under rational expectations.

data

an optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which simsart is called.

Details

For a complete information model, the outcome y_i is defined as:

\begin{cases}y_i^{\ast} = \lambda \bar{y}_i + \mathbf{z}_i'\Gamma + \epsilon_i, \\ y_i = \max(0, y_i^{\ast}),\end{cases}

where \bar{y}_i is the average of y among peers, \mathbf{z}_i is a vector of control variables, and \epsilon_i \sim N(0, \sigma^2). In the case of incomplete information modelswith rational expectations, y_i is defined as:

\begin{cases}y_i^{\ast} = \lambda E(\bar{y}_i) + \mathbf{z}_i'\Gamma + \epsilon_i, \\ y_i = \max(0, y_i^{\ast}).\end{cases}

Value

A list consisting of:

yst

y^{\ast}, the latent variable.

y

the observed censored variable.

Ey

E(y), the expectation of y.

Gy

the average of y among friends.

GEy

the average of E(y) friends.

meff

a list includinh average and individual marginal effects.

iteration

number of iterations performed by sub-network in the Fixed Point Iteration Method.

References

Xu, X., & Lee, L. F. (2015). Maximum likelihood estimation of a spatial autoregressive Tobit model. Journal of Econometrics, 188(1), 264-280, doi:10.1016/j.jeconom.2015.05.004.

See Also

sart, simsar, simcdnet.

Examples

# Groups' size
set.seed(123)
M      <- 5 # Number of sub-groups
nvec   <- round(runif(M, 100, 200))
n      <- sum(nvec)

# Parameters
lambda <- 0.4
Gamma  <- c(2, -1.9, 0.8, 1.5, -1.2)
sigma  <- 1.5
theta  <- c(lambda, Gamma, sigma)

# X
X      <- cbind(rnorm(n, 1, 1), rexp(n, 0.4))

# Network
G      <- list()

for (m in 1:M) {
  nm           <- nvec[m]
  Gm           <- matrix(0, nm, nm)
  max_d        <- 30
  for (i in 1:nm) {
    tmp        <- sample((1:nm)[-i], sample(0:max_d, 1))
    Gm[i, tmp] <- 1
  }
  rs           <- rowSums(Gm); rs[rs == 0] <- 1
  Gm           <- Gm/rs
  G[[m]]       <- Gm
}

# Data
data   <- data.frame(X, peer.avg(G, cbind(x1 = X[,1], x2 =  X[,2])))
colnames(data) <- c("x1", "x2", "gx1", "gx2")

## Complete information game
ytmp    <- simsart(formula = ~ x1 + x2 + gx1 + gx2, Glist = G, theta = theta, 
                   data = data, cinfo = TRUE)
data$yc <- ytmp$y

## Incomplete information game
ytmp    <- simsart(formula = ~ x1 + x2 + gx1 + gx2, Glist = G, theta = theta, 
                   data = data, cinfo = FALSE)
data$yi <- ytmp$y