ADF Test Variable Choice

[John Don]

Dear Users,

I have the following naïve question:

I have a macroeconomic variable for the years 1980 to 2018 which you may find its scatter below:

This variable is not stationary at level. Please find the ADF test results below:

dfuller a, lags(1) trend

Augmented Dickey-Fuller test for unit root Number of obs = 152

---------- Interpolated Dickey-Fuller ---------
Test 1% Critical 5% Critical 10% Critical
Statistic Value Value Value
------------------------------------------------------------------------------
Z(t) 1.632 -4.023 -3.443 -3.143
------------------------------------------------------------------------------
MacKinnon approximate p-value for Z(t) = 1.0000


The lag is chosen according to SBIC criteria.

When I take the first difference of the variable, the ADF test results turn out to be:

dfuller D.a, lags(1) trend

Augmented Dickey-Fuller test for unit root Number of obs = 151

---------- Interpolated Dickey-Fuller ---------
Test 1% Critical 5% Critical 10% Critical
Statistic Value Value Value
------------------------------------------------------------------------------
Z(t) -8.839 -4.023 -3.443 -3.143
------------------------------------------------------------------------------
MacKinnon approximate p-value for Z(t) = 0.0000


That means my variable is stationary at the difference.

I have the following three questions:

1. So, does that mean "I can only use the difference of this variable in my estimation, not the level itself"?
2. If the following code "dfuller a, lags(1) trend" provided a stationary result at level estimation (MacKinnon p value less than 0.05), in that case, should I use the level of the variable in my estimation as the dfuller command includes "trend" option?
3. What would be the answer of the second question with a drift instead of a trend?

[Justin Niakamal]

1. It depends. You'd have to be more specific as to what you're trying to accomplish.
2 & 3. The ADF test can be sensitive to the inclusion of trend and or intercept, but it's clear from the chart that your series is non-stationary.

Hope this helps.

[John Don]

Dear Justin,

Thank you very much for your kind response.

For your answers of 2 & 3, could you please elaborate more? You mean "obtaining the stationary series at the level with ADF test (in the sense that level + drift or trend) does not mean anything unless it is visually approved by graphs"?

[Justin Niakamal]

What I was saying was that it’s clear that you have a non-stationary series without needing a formal test done. There are also sorts of unit root tests and different specifications. Sometimes the results aren’t clear cut: include trend, include a trend and intercept, how many lags to use, etc. In your case, most macroeconomic variables are non-stationary and have a stochastic trend and therefore should be differenced if you want a stationary series.