Panel data stationarity tests and estimation procedure

This supplement to the Stata Guide explains how to test for stationarity for a single panel and an entire panel. The data file healthpanel will be used for the examples. You will estimate a healthcare spending model. The dependent variable is spend. The explanatory variables are inc and ins. The commands for doing stationarity tests are dfuller and xtunitroot.

Use a Dickey-Fuller test to test the null hypothesis that spend has a unit root for the state of Michigan. Do the test for three alternative null hypotheses. 1) Spending has a random walk. 2) Spending has a random walk with drift. 3) Spending has a random walk with drift around a stochastic trend.

tsset state year

dfuller spend in 211/220, nocon

dfuller spend in 211/220

dfuller spend in 211/220 , trend

Comments

The tsset command tells Stata the panel variable (state) and the time variable (year). The in 211/220 range after the variable spend tells Stata to perform the tests for observations 211 through 220. These are the spend time series data for Michigan, which is state 22. The option nocon suppresses the constant term in the regression for the test and indicates the null hypothesis is a random walk without drift. The trend option allows for a stochastic trend. To tell Stata to report the test statistic and the regression results, add the option reg.

Use an augmented Dickey-Fuller test to test the null hypothesis that spend has a unit root for the state of Michigan. Do the test for three alternative null hypotheses. 1) Spending has a random walk. 2) Spending has a random walk with drift. 3) Spending has a random walk with drift around a stochastic trend.

dfuller spend in 211/220, nocon lags(2)

dfuller spend in 211/220 , lags(2)

dfuller spend in 211/220 , trend, lags(2)

The commands are the same as the Dickey-Fuller test. But now the Dickey-Fuller regression includes two lagged difference variables to account for possible serial correlation. You may choose any number of lags you desire.

Use the Levin-Lin-Chu (LLC) test to test the null hypothesis that spend has a unit root for all 50 states. Do three versions of the test making the following assumptions. 1) Fixed-effects, no cross-correlation of errors, no state-specific time trends. Use the Akaike information criterion to select the number of lags between one and a maximum of four. 2) Fixed-effects, cross-correlation of errors, no state-specific time trends. Use the Akaike information criterion to select the number of lags between one and a maximum of four. 3) Fixed-effects, cross-correlation of errors, state-specific time trends. Use the Akaike information criterion to select the number of lags between one and a maximum of four.

xtunitroot llc spend, lags(aic 4)

xtunitroot llc spend, demean, lags(aic 4)

xtunitroot llc spend, demean trend, lags(aic 4)

You may choose any maximum lag length you desire. If you want to choose the lag length yourself, omit aic from the lags option. For example, if you want to choose three lags include the option lags(3). The option demean tells Stata to account for possible cross correlation of errors among states. For the LLC test, Stata only reports the p-value for the test statistic, not critic values. To accept or reject the null hypothesis, compare the p-value to the level of significance. If the p-value is less than or equal to the level of significance reject the null. If not accept the null.

Use the Harris-Tzavalis (HT) test to test the null hypothesis that spend has a unit root for all 50 states. Do three versions of the test making the following assumptions. 1) Fixed-effects, no cross-correlation of errors, no state-specific time trends. 2) Fixed-effects, cross-correlation of errors, no state-specific time trends. 2) Fixed-effects, cross-correlation of errors, state-specific time trends.

xtunitroot ht spend

xtunitroot ht spend, demean

xtunitroot ht spend, demean trend

Like the LLC test, Stata only reports the p-value for the test statistic for the HT test. To accept or reject the null hypothesis, compare the p-value to the level of significance.

Use the version of the Im-Pesaran-Shin (IPS) test that is appropriate when the number of states is large relative to the number of years to test the null hypothesis that spend has a unit root for all 50 states. Do three versions of the test making the following assumptions. 1) Fixed-effects, no cross-correlation of errors, no state-specific time trends. 2) Fixed-effects, cross-correlation of errors, no state-specific time trends. 2) Fixed-effects, cross-correlation of errors, state-specific time trends.

xtunitroot ips spend

xtunitroot ips spend, demean

xtunitroot ips spend, demean trend

To use the version of the IPS test that is appropriate when the number states and time period are large, included the lags(#) and choose the number of lags # to include.

Estimate the healthcare spending equation in first-differences.

tsset state year

gen dspend=d.spend

gen dinc=d.inc

gen dins=d.ins

regress dspend dinc dins

You must transform each variable to first-difference. The gen command creates the first-difference variables. The first-difference operator is d. It is prefixed to the variable that is transformed to first-difference. To create the first-difference variable, make sure you have previously used the tsset command.

Estimate the healthcare spending equation in first-differences with time dummy variables.

gen t92=(year==1992)

gen t93=(year==1993)

gen t94=(year==1994)

gen t95=(year==1995)

gen t96=(year==1996)

gen t97=(year==1997)

gen t98=(year==1998)

gen t99=(year==1999)

gen dt92=D.t92

gen dt93=D.t93

gen dt94=D.t94

gen dt95=D.t95

gen dt96=D.t96

gen dt97=D.t97

gen dt98=D.t98

gen dt99=D.t99

gen dt00=D.t00