Description Usage Format Details Author(s) References Examples
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.
1 |
A data frame containing :
dependent variable as N*T-vector
first regressor as N*T-vector
second regressor as N*T-vector
first (unobserved) common factor: CF.1(t)=1
second (unobserved) common factor: CF.2(t)=(t/T)
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},…
The panel-data set DPG2 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 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.
Dominik Liebl
Kneip, A., Sickles, R. C., Song, W., 2012 “A New Panel Data Treatment for Heterogneity in Time Trends”, Econometric Theory
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 | 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)
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