In this simple tutorial, we demonstrate the basic review of Dickey Fuller Verses Phillips Perron Unit Root Tests. The comparison is based on the null hypothesis formulation, critical values computation and regression specification to test the null of unit root in the series.
We can see from the file file details for Dickey Fuller Unit Root that
it performs the augmented Dickey-Fuller test that a variable follows a unit-root process. The null hypothesis is that the variable contains a unit root, and the alternative is that the variable was generated by a stationary process. You may optionally exclude the constant, include a trend term, and include lagged values of the difference of the variable in the regression (Stata Help File for Dickey Fuller Unit Root test).
while the details in the Stata help file or Phillips-Perron unit root tests are:
Phillips Perron Unit Root Test provided evidence on that a variable has a unit root. The null hypothesis is that the variable contains a unit root, and the alternative is that the variable was generated by a stationary process. Phillips Perron Unit Root Test uses Newey-West standard errors to account for serial correlation, whereas the augmented Dickey-Fuller test implemented in Dickey Fuller Unit Root uses additional lags of the first-difference variable (Stata Help File for Phillips Perron Unit Root Test).
This gives us the basic observation on Dickey Fuller Verses Phillips Perron Unit Root Tests that the null hypothesis of the both is same that the variable is unit root against the alternative of no unit root. Also, we can see that the regression specification is different because Dickey Fuller Unit Root adjusted the regression model through addition of additional lags in the equation and Phillips Perron Unit Root Test uses Newey-White adjustment for the residuals to cover for serial correlation.
The following regression specification is used in Dickey Fuller Unit Root test in Stata:
and the null hypothesis that Y is unit root when β=0 is rejected.
Now, we can see the regression model to test unit root in Phillips Perron unit root test as:
Where the null hypothesis of unit root is tested based on ρ=1 is rejected. Note, the above equation is estimated with the Newey–West (1987) heteroskedasticity- and autocorrelation-consistent covariance matrix estimator. Also, Phillips and Perron (1988) proposed two alternative statistics. Phillips and Perron’s test statistics can be viewed as Dickey–Fuller statistics that have been made robust to serial correlation by using (Stata Help File for Phillips Perron unit root test).
These differences in the regression specification can easily be found in the two regression results from Stata to compare Dickey Fuller Verses Phillips Perron Unit Root Tests. The first image is showing results DFULLER command as:
While the results output from PPERRON command is:
Where we can easily see the difference between the two tests. PPERRON does not add the lags as we see in DFULLER commands output because Dickey Fuller Verses Phillips Perron Unit Root Tests differ in the nature of controlling for Standard Errors and Serial Correlation in the regression model and basic null hypothesis of the two tests remains the same.
Note, Dickey Fuller Verses Phillips Perron Unit Root Tests are actually based on these simple specifications:
I am sure this basic tutorial on Dickey Fuller Verses Phillips Perron Unit Root Tests would help you determine the true nature of the given tests and in selection of unit root nature of the time series data through application of these approaches in Stata.