Solved – How to identify structural change using a Chow test on Eviews

chow-testinterpretation

I have this little problem and I would appreciate some help.

As part of my master thesis, I have to identify a trend in a univariate (GDP) time series for different countries. I have to separate the trend and the stochastic element in it for each country.

I have managed to do so by doing:

variable c @trend // for each country.

And then running a AR(1) on the residuals // for each country.

However, now I need to identify structural breaks in one of these countries. I've been reading and searching all over the internet and books and I've found that the test most people use to identify these structural changes is the Chow Test.

I know how to run the test, but I have't been able to figure out how to interpret the results, and decide whether there is a structural break or not.

Here there is an example of the results:

enter image description here

What puzzles me the most is the fact that, regardless the point I choose to break the series, I always get

Prob. F(2,47) 0.0016 //or any very significant value, with the same degrees of freedom.

Can someone please help me understand how I should interpret these results in order to identify where the breaks lie?

Best Answer

I am assuming that you are treating each country separately, and are attempting to determine if there is a break-point in the level of a series. Here are three (EDIT: four) main points that I hope will help:

  1. The Chow test assumes that there is a known break-point in the series. If this point is not know, the Chow test is not appropriate (there are alternatives, although inference will be difficult in such a small sample).
  2. The degrees of freedom in the F-test will be the same for each test of break-point. That is, it will always be F(2,47). The F-statistic calculated (7.438332 in your example) should be different at each tested point. However, given that you have a relatively small sample, such a test may suggest that there is a structural break at every point in the series.
  3. Have you considered alternatives to the full structural break? For example, including a dummy variable for 1991 that could pick up an exogenous shock (such as a policy implementation that impacted GDP growth only in that period, but the economy returned to trend after). Alternatively, you could consider a broken trend model, if you think that the trend growth in GDP has shifted but not the intercept.
  4. EDIT: Following from another user's point (mpiktas) that GDP may have a unit root. You should probably be looking at GDP as a natural logarithm (as we often see GDP moving with an exponential trend, due to the nature of population growth, etc.). Inference from a trend model on the log of GDP should be fine (log-GDP is probably trend-stationary - although you should do some testing - which implies that once accounting for the trend the residual series is stationary).

From your example: $$ y_t = \beta_0 + \beta_1 t + \epsilon_t \qquad (1)$$ The basic form of the Chow test is:

  1. Construct a dummy variable $D_t$ that is $=0$ before the break and $=1$ after the break.
  2. Run a regression: $$ y_t = \beta_0 + \beta_1 t + \gamma_0 D_t + \gamma_1 t D_t + \nu_t \qquad (2) $$
  3. Test the sum of squared residuals from (1) against (2) where: $$ H_0 : \gamma_0 = \gamma_1 = 0 $$ $$ H_1 \text{: At least one coefficient not equal to zero} $$ And, $ F = \frac{SSR_{(1)} - SSR_{(2)}}{SSR_{(1)}} \frac{N-k}{q} $ Where $q$ is the number of restrictions (the number of equals signs in the null hypothesis $H_0$ above, and $k$ is the number of parameters in the restricted model (after applying the null hypothesis, so just $\beta_0$ and $\beta_1$).

Hope this helps.

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