phtt (version 3.1.2)

Simulated Data for the KSS-Model: DGP2: Simulated Panel-Data Set with Polynomial Factor Structure and endogenous regressors.

Description

A Panel-Data Sets with: time-index : t=1,...,T=30

individual-index : i=1,...,N=60

This panel-data set has a polynomial factor structure (3 common factors) and endogenous regressors.

Usage

data(DGP2)

Format

A data frame containing :

Y

dependent variable as N*T-vector

X1

first regressor as N*T-vector

X2

second regressor as N*T-vector

CF.1

first (unobserved) common factor: $CF.1(t)=1$

CF.2

second (unobserved) common factor: $CF.2(t)=(t/T)$

CF.3

thrid (unobserved) common factor: $CF.3(t)=(t/T)^2$

Remark: The time-index t is running "faster" than the individual-index i such that e.g. Y_it is ordered as: $Y_{11},Y_{12},\ldots,Y_{1T},Y_{21},Y_{22},\ldots$

Details

The panel-data set DPG2 is simulated according to the simulation-study in Kneip, Sickles & Song (2012): $Y_{it}=\beta_{1}X_{it1}+\beta_{2}X_{it2}+v_i(t)+\epsilon_{it}, i=1,\dots,n, t=1,\dots,T$ -Slope parameters: $beta_{1}=beta_{2}=0.5$

-Time varying individual effects being second order polynomials: $v_i(t)=theta_{i0}+theta_{i1}*frac{t}{T}+theta_{i2}*(frac{t}{T})^2$ Where theta_i1, theta_i1, and theta_i1 are iid as N(0,4)

The Regressors X_it=(X_it1,X_it2)' are simulated from a bivariate VAR model: $X_{it}=R X_{i,t-1}+eta_{it} with R=matrix(c(0.4,0.05,0.05,0.4),2,2) and eta_{it}~N(0,I_2)$

After this simulation, the N regressor-series $(X_{1i1},X_{2i1})',\dots,(X_{1iT},X_{2iT})'$ are additionally shifted such that there are three different mean-value-clusters. Such that every third of the N regressor-series fluctuates around on of the following mean-values $mu_1=(5,5)', mu_2=(7.5,7.5)', and mu_3=(10,10)'$ In this Panel-Data Set the regressor X_it2 is made endogenous by the re-definition: $X_{it2}:=X_{it2}+0.5*v_i(t)$

See Kneip, Sickles & Song (2012) for more details.

References

• Kneip, A., Sickles, R. C., Song, W., 2012 “A New Panel Data Treatment for Heterogneity in Time Trends”, Econometric Theory

Examples

data(DGP2)

## Dimensions
N    <- 60
T    <- 30

## Observed Variables
Y    <- matrix(DGP2$Y,  nrow=T,ncol=N)
X1   <- matrix(DGP2$X1, nrow=T,ncol=N)
X2   <- matrix(DGP2$X2, nrow=T,ncol=N)

## Unobserved common factors
CF.1 <- DGP2$CF.1[1:T]
CF.2 <- DGP2$CF.2[1:T]
CF.3 <- DGP2$CF.3[1:T]

## Take a look at the simulated data set DGP2:
par(mfrow=c(2,2))
matplot(Y,  type="l", xlab="Time", ylab="", main="Depend Variable")
matplot(X1, type="l", xlab="Time", ylab="", main="First Regressor")
matplot(X2, type="l", xlab="Time", ylab="", main="Second Regressor")
## Usually unobserved common factors:
matplot(matrix(c(CF.1,
                 CF.2,
                 CF.3), nrow=T,ncol=3),
        type="l", xlab="Time", ylab="", main="Unobserved Common Factors")
par(mfrow=c(1,1))

## Esimation
KSS.fit      <- KSS(Y~-1+X1+X2)
(KSS.fit.sum <- summary(KSS.fit))

plot(KSS.fit.sum)