Question

Explain in full how you will use a dummy variable regression to test for a structural break. Also discuss the advantages of using a dummy variable regression over the Chow test when testing for structural break in data.

Answer 1

I will explain you with a small example , go through the below content carefully.

How do we find out that a structural change has in fact occurred? To answer this question, we consider the GDP of Ethiopia (measured on constant 2010 US$) over the period of 1981 to 2015. Like many other countries in the world, Ethiopia has adopted the policy of regulated globalization during the early nineties of the last century. So, our aim is to whether the GDP of Ethiopia has undergone any structural changes following the major policy shift due to adoption of globalization policy. To answer this question, we have two options in statistical and econometric research. The most important classes of tests on structural change are the tests from the generalized fluctuation test framework on the one hand and tests based on F statistic on the other. The first class includes in particular the CUSUM and MOSUM tests and the fluctuation test, while the Chow and the supF test belong to the latter. A topic that gained more interest rather recently is to monitor structural change, i.e., to start after a history phase (without structural changes) to analyze new observations and to be able to detect a structural change as soon after its occurrence as possible.

Let us divide the whole study period in two sub-periods

1. pre-globalization (1981 – 1991)
2. post-globalization (1992-2015)

Boi + B1ut+ U Pre globalization period (1981 -1991): Post globalization period (1992 2015): Whole period (1981 - 2015) nGDP nGDP B02 B12t + u2 INGDP Bo+Bit u --

The regression for the whole period assumes that there is no difference between the two time periods and, therefore, estimates the GDP growth rate for the entire time period. In other words, this regression assumes that the intercept, as well as the slope coefficient, remains the same over the entire period; that is, there is no structural change. If this is, in fact, the situation, then

Bo1 = Bo2 = Bo and B B12 = B1

The first two regression lines assume that the regression parameters are different in two sub-period periods, that is, there is structural instability either because of changes in slope parameters or intercept parameters.

Solution by Chow:

To apply Chow test to visualize the structural changes empirically, the following assumptions are required:

i. The error terms for the two sub-period regressions are normally distributed with the same variance;
ii. The two error terms are independently distributed.
iii. The break-point at which the structural stability to be examined should be known apriori.

The Chow test examines the following set of hypotheses:

Steps in Chow test

Step 1: Estimate third regression assuming that there is no parameter instability, and obtain the Residual Sum Squares

So, in present case k=2, as there are two parameters (intercept term and slope coefficient).

RSSR with df — (п1 + ng — 2k) where kNo of parameters estimated n1 No of observations in first period No of observations in second sub-periods n2

We call this Restricted Residual Sum Squares as it assumes the restriction of structural stability, that is, β01=β02=β0   and   β11=β12=β1β01=β02=β0   and   β11=β12=β1

Step 2: Estimate the first and second regressions assuming that there is parameter instability and obtain the respective Residual Sum Squares as

RSSI Residual Sum Squares for the first sub-period regression with df n1 RSS2 Residual Sum Squares for the second sub-period regression with df n2 k k

Step 3: As the two sets of samples supposed to be independent, we can add "RSS_1" and "RSS_2" and the resultant Residual Sum Squares may be called the Unrestricted Residual Sum of Squares, that is,

RSSUR df 3 (пл + пэ — 2k) RSS1RSS with The test statistic to be used is given as: (RSSR-RSSUR)/k F (RSSUR)/(n1n2-2k)

Under the assumption of true null hypothesis, this follows F-distribution.

Now if this F-test is significant, we can reject the null hypothesis of no structural instability and conclude that the fluctuations is the GGP is high enough to believe that it leads to structural instability in the GDP growth path.

Advantages of using a dummy variable regression over the Chow test when testing for structural break in data.

The benefit of this approach is that we do not lose any degrees of freedom through a loss of observations.the benefit of this approach is that we do not lose any degrees of freedom through a loss of observations.

If there is evidence of a structural break, it may mean we need to split the data into 2 samples and run separate regressions