HMMpanelFE {MCMCpack} | R Documentation |
HMMpanelFE generates a sample from the posterior distribution of the fixed-effects model with varying individual effects model discussed in Park (2011). The code works for both balanced and unbalanced panel data as long as there is no missing data in the middle of each group. This model uses a multivariate Normal prior for the fixed effects parameters and varying individual effects, an Inverse-Gamma prior on the residual error variance, and Beta prior for transition probabilities. The user supplies data and priors, and a sample from the posterior distribution is returned as an mcmc object, which can be subsequently analyzed with functions provided in the coda package.
HMMpanelFE(subject.id, y, X, m, mcmc=1000, burnin=1000, thin=1, verbose=0, b0=0, B0=0.001, c0 = 0.001, d0 = 0.001, delta0=0, Delta0=0.001, a = NULL, b = NULL, seed = NA, ...)
subject.id |
A numeric vector indicating the group number. It should start from 1. |
y |
The response variable. |
X |
The model matrix excluding the constant. |
m |
A vector of break numbers for each subject in the panel. |
mcmc |
The number of MCMC iterations after burn-in. |
burnin |
The number of burn-in iterations for the sampler. |
thin |
The thinning interval used in the simulation. The number of MCMC iterations must be divisible by this value. |
verbose |
A switch which determines whether or not the progress of
the sampler is printed to the screen. If |
b0 |
The prior mean of beta. This can either be a scalar or a column vector with dimension equal to the number of betas. If this takes a scalar value, then that value will serve as the prior mean for all of the betas. |
B0 |
The prior precision of beta. This can either be a scalar or a square matrix with dimensions equal to the number of betas. If this takes a scalar value, then that value times an identity matrix serves as the prior precision of beta. Default value of 0 is equivalent to an improper uniform prior for beta. |
c0 |
c0/2 is the shape parameter for the inverse Gamma prior on sigma^2 (the variance of the disturbances). The amount of information in the inverse Gamma prior is something like that from c0 pseudo-observations. |
d0 |
d0/2 is the scale parameter for the inverse Gamma prior on sigma^2 (the variance of the disturbances). In constructing the inverse Gamma prior, d0 acts like the sum of squared errors from the c0 pseudo-observations. |
delta0 |
The prior mean of alpha. |
Delta0 |
The prior precision of alpha. |
a |
a is the shape1 beta prior for transition probabilities. By default, the expected duration is computed and corresponding a and b values are assigned. The expected duration is the sample period divided by the number of states. |
b |
b is the shape2 beta prior for transition probabilities. By default, the expected duration is computed and corresponding a and b values are assigned. The expected duration is the sample period divided by the number of states. |
seed |
The seed for the random number generator. If NA, current R system seed is used. |
... |
further arguments to be passed |
HMMpanelFE
simulates from the fixed-effect hidden Markov panel model introduced by Park (2011).
The model takes the following form:
y_it = x'_it * beta + epsilon_it, m = 1,...,M.
Unlike conventional fixed-effects models, individual effects and variances are assumed to be time-varying at the subject level:
epsilon_it ~ N(alpha_im, sigma^2_im)
We assume standard, semi-conjugate priors:
beta ~ N(b0,B0^(-1))
And:
sigma^(-2) ~ Gamma(c0/2, d0/2)
And:
alpha ~ N(delta0, Delta0^(-1))
beta, alpha and sigma^(-2) are assumed a priori independent.
And:
p_mm ~ Beta(a, b), m = 1,...,M.
Where M is the number of states.
OLS estimates are used for starting values.
An mcmc object that contains the posterior sample. This
object can be summarized by functions provided by the coda package.
The object contains an attribute sigma
storage matrix that contains time-varying residual variance, an attribute state
storage
matrix that contains posterior samples of hidden states, and an attribute delta
storage matrix containing time-varying intercepts.
Jong Hee Park, jhp@uchicago.edu, http://home.uchicago.edu/~jhp/.
Jong Hee Park, 2011. “A Unified Method for Dynamic and Cross-Sectional Heterogeneity: Introducing Hidden Markov Panel Models." Working Paper.
Siddhartha Chib. 1998. “Estimation and comparison of multiple change-point models.” Journal of Econometrics. 86: 221-241.
## Not run: ## data generating set.seed(1974) N <- 30 T <- 80 NT <- N*T ## true parameter values true.beta <- c(1, 1) true.sigma <- 3 x1 <- rnorm(NT) x2 <- runif(NT, 2, 4) ## group-specific breaks break.point = rep(T/2, N); break.sigma=c(rep(1, N)); break.list <- rep(1, N) X <- as.matrix(cbind(x1, x2), NT, ); y <- rep(NA, NT) id <- rep(1:N, each=NT/N) K <- ncol(X); true.beta <- as.matrix(true.beta, K, 1) ## compute the break probability ruler <- c(1:T) W.mat <- matrix(NA, T, N) for (i in 1:N){ W.mat[, i] <- pnorm((ruler-break.point[i])/break.sigma[i]) } Weight <- as.vector(W.mat) ## draw time-varying individual effects and sample y j = 1 true.sigma.alpha <- 30 true.alpha <- true.alpha1 <- true.alpha2 <- rep(NA, N) for (i in 1:N){ Xi <- X[j:(j+T-1), ] true.mean <- Xi weight <- Weight[j:(j+T-1)] true.alpha1[i] <- rnorm(1, 0, true.sigma.alpha) true.alpha2[i] <- -1*true.alpha1[i] y[j:(j+T-1)] <- ((1-weight)*true.mean + (1-weight)*rnorm(T, 0, true.sigma) + (1-weight)*true.alpha1[i]) + (weight*true.mean + weight*rnorm(T, 0, true.sigma) + weight*true.alpha2[i]) j <- j + T } ## extract the standardized residuals from the OLS with fixed-effects FEols <- lm(y ~ X + as.factor(id) -1 ) resid.all <- rstandard(FEols) time.id <- rep(1:80, N) ## model fitting G <- 100 BF <- testpanelSubjectBreak(subject.id=id, time.id=time.id, resid= resid.all, max.break=3, minimum = 10, mcmc=G, burnin = G, thin=1, verbose=G, b0=0, B0=1/100, c0=2, d0=2, Time = time.id) ## get the estimated break numbers estimated.breaks <- make.breaklist(BF, thresh=3) ## model fitting out <- HMMpanelFE(subject.id = id, y, X=X, m = estimated.breaks, mcmc=G, burnin=G, thin=1, verbose=G, b0=0, B0=1/1000, c0=2, d0=2, delta0=0, Delta0=1/1000) ## print out the slope estimate ## true values are 1 and 1 summary(out) ## compare them with the result from the constant fixed-effects summary(FEols) ## End(Not run)