Testing the weak form of the Property Market Efficiency

• Testing for a Random Walk

Traditionally, testing a random walk is done by regressing the current changes by the lagged changes, such as using the Dickey Fuller test shown below (Pindyck and Rubinfeld, 1998).


But this regression makes an implicit assumption that there are no serial correlations of any kind in the error term (Pindyck & Rubinfeld, 1998). According to Case and Shiller (1989), they prove that there would be a positive serial correlation in the estimated changes in the log price index for both BNM and the weighted regressions.

So tests of a random walk such as the Dicky Fuller test cannot be used for this regression, according to Case & Shiller (1989) an alternative test of a random walk can be made by randomly dividing the sample into two halves, A and B, then running the WRS (weighted repeat sales) regression on each of the samples. With the estimated log index of each sample, the lagged changes in the log index of one sample are regressed on the current changes of the other and vice versa. If the coefficient of the lagged index is positive and significant, then this regression can show that increases or decreases in the house price index is predictable and that returns do not follow a random walk (Case & Shiller 1989).

Results

The resulting weighted repeat sales index of the two randomly drawn samples is shown below, both samples are trending almost simultaneously as shown in the graph, an indication of a good fit to the data.




According to these results we can conclude that the total weighted index is a good fit to the data. As stated by Case and Shiller (1989), the no lagged regression of a random sample A and B provides a good diagnostic test for the goodness of fit for the model. This is concluded from the fact that the intercept above is insignificant from zero and the coefficient of sample B is significant and close to 1.

As for the test of the weak form efficient hypothesis, according to the summary above, the coefficients for both lagged A on B and lagged B on A have a positive coefficient that are both significant. These results suggest that the quarterly returns in the housing market of Auckland exhibit inertia (Case and Shiller 1989), which means increases in prices in one quarter, means a high probability of an increase of prices in the following quarter.

We can conclude that the real returns in the Auckland residential property market do not follow a random walk, since past returns of property have some explanatory power in the next period’s returns. This result provides some evidence that the weak form efficiency for the real estate market in Auckland does not hold, because prices can be, to some degree predicted based on the index. But despite the rejection of a “random walk” in the index, to fully reject the weak form hypothesis requires abnormal excess returns to be exploitable (Case & Shiller 1989).