# Simulated_KSS_Data_DGP1: Simulated Panel-Data Set with Polynomial Factor Structure and... In phtt: Panel Data Analysis with Heterogeneous Time Trends

## 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` ```data(DGP1) ```

## 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.

Dominik Liebl

## References

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

## Examples

 ``` 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(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) ```

phtt documentation built on May 30, 2017, 12:30 a.m.