Simulated Panel-Data Set with Polynomial Factor Structure and exogenous regressors.

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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 exogenous regressors.

Usage

1

Format

A list 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},…,Y_{1T},Y_{21},Y_{22},…

Details

The panel-data set DPG1 is simulated according to the simulation-study in Kneip, Sickles & Song (2012): Y_{it}=β_{1}X_{it1}+β_{2}X_{it2}+v_i(t)+ε_{it}, i=1,…,n, t=1,…,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})',…,(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 regressors are exogenous. See Kneip, Sickles & Song (2012) for more details.

Author(s)

Dominik Liebl

References

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

Examples

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data(DGP1)

## Dimensions
N    <- 60
T    <- 30

## Observed Variables
Y    <- matrix(DGP1$Y,  nrow=T,ncol=N)
X1   <- matrix(DGP1$X1, nrow=T,ncol=N)
X2   <- matrix(DGP1$X2, nrow=T,ncol=N)

## Unobserved common factors
CF.1 <- DGP1$CF.1[1:T]
CF.2 <- DGP1$CF.2[1:T]
CF.3 <- DGP1$CF.3[1:T]

## Take a look at the simulated data set DGP1:
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))

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

plot(KSS.fit.sum)