The Bai and Perron (1998) Structural Break Tests for Fast-moving Institutional Changes

To empirically assess whether the political reforms caused structural breaks immediately after the 1970s, Table 6.1 presents two forms of the Bai and Perron (1998) structural break tests. The univariate test applies to the changes in house prices only, for the purpose of detecting the structural breaks in housing prices. The multivariate test applies to house price against mortgage outstanding , mortgage rate of Building Societies , house completion , real aggregate household disposable income , foreign portfolio investment and general index of retail price at the first natural log difference scale. The rationale for the multivariate test is detecting the structural breaks in the housing market which contains a group of economic variables.

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Table 6.1 Bai and Perron (1998) Structural Break Tests

Bai and Perron (1998) structural break test for

|

6.149 25.010*** 19.309*** 14.644*** 12.203*** 34.300***

| | | /

1.887 3.139 2.019 25.010*** 32.064*** /

Number of breaks selected Identified break dates

Sequential Procedure LWZ BIC / 85th Observation 112th Observation

0 0 2 / 1989Q3 1996Q2

Bai and Perron (1998) structural break test for against , , , , and

|

1202.66*** 547.291*** 192781.922 *** 6084796.474*** 5267225.103*** 62.386***

| | | /

58.586*** 62.386*** 9.641 6084796.474*** 8061287.479*** /

Number of breaks selected Identified break dates

Sequential Procedure LWZ BIC 22th Observation 78th Observation 116th Observation

2 0 0 1973Q4 1987Q4 1997Q2

Notes: denotes the first difference. is house price, means mortgage outstanding, means mortgage rate

of Building Societies, means house completion, means real aggregate household disposable income,

means foreign portfolio investment, and means the general index of retail price. Throughout the thesis, lower case

letters for time-dependent variables represent the natural logarithm of their capital counterparts. In the Bai and

Perron (1998) tests, the chapter sets the maximum number of break points , minimum length of distance

equals 23, trimming equals 0.10. The sample size ranges from 1968Q2 to 2007Q4. *** denotes statistical

significance at the 1% significance level. The null hypothesis for test is there are statistical structural breaks, where, . The null hypothesis for | test is there are statistical significant

structural breaks conditional on structural breaks. The null hypothesis for the test and the test

are there is no structural break. BIC is Bayesian Information Criteria and LWZ is a modified Schwartz’s Criteria. Sequential Procedure, LWZ and BIC test for the number of breaks selected, respectively.

From Table 6.1, the test and the test consistently reject the null hypotheses that there are no structural breaks. However, there are controversies on the dates of the breaks. In the univariate tests, the test, Sequential Procedure test and LWZ test fail to reject the null hypothesis and suggest that there is no structural break. The tests through

are statistically significant and suggests that there are 2 to 5 structural breaks, respectively. The BIC test suggests there are two structural breaks or fast-moving institutional changes at 1989Q3 and 1996Q2. In the multivariate tests, the tests through suggest there are 5 structural breaks. The tests | through | suggest there are 4 statistical significant structural breaks. The Sequential Procedure test suggests there are 2 statistical significant structural breaks. However, the LWZ and BIC tests suggest there is no statistical significant structural break. For the sake of prudence, this chapter identifies three statistical significant structural breaks at 1973Q4, 1987Q4 and 1997Q2. The first structural break 1973Q4 roughly follows the collapse of the Bretton Woods Agreement in 1971, the 1973 oil crisis, and the Secondary Banking Crisis of 1973-1975. The second structural break, 1987Q4 or

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1989Q3, follows the UK Building Societies Act 1986, the Lawson boom from 1986 to 1988, the ‘Big Bang’ in 1986, the general election in June 1987, and the Black Monday on 19th

October 1987. Finally, 1996Q2 or 1997Q2 follows the UK recession in 1992, the US savings and loan crisis in the early 1990s, the 1994 economic crisis in Mexico, the 1997 Asian financial crisis and/or the UK general election in May 1997. The dates of the structural breaks appear to match the unexpected market shocks rather than political events. However, some of the political events would be the real drivers of the market shocks. It seems the unexpected shocks in particular financial crises often drive people to coordinate their future anticipations around the new rules of the economy, and thereby leads to structural break. Table 6.1 empirically supports that the political and/or legal reform is often a necessary but insufficient condition for fast-moving institutional changes, given people’s shared beliefs can persist even after changing the formal laws (Gérard, 2004; Culpepper, 2005).

Building on a sample from 1971Q4 to 1989Q2, Brown et al. (1997) uses the Chow (1960) structural break test to find that 1983Q2 is a statistically significant structural break in the UK which seems to differ slightly from Table 6.1. Given 1983Q2 is in the middle of the recession of the early 1980s in the UK, the implications of Table 6.1 indeed remain consistent with Brown et al. (1997). Guirguis et al. (2005) empirically support the coefficient instability of the US housing market by using three statistical tests including, the rolling OLS, the Chow (1960) structural break test and the RESET test. Unfortunately, Guirguis et al. (2005) fail to detect the numbers and the possible dates of the structural breaks.

The Chow (1960) test is a linear regression based known break point model, which is essentially a test of parameter constancy or homogeneity. In practice, one has two options: to pick an arbitrary potential break point; or to pick a break point based on some known characteristic of the time series. In the earlier case, the real break point can be missed. In the latter case, the tests can be misleading due to the candidate break points being endogenous. Moreover, people can easily obtain distinctly different results, given the selection of candidate break points are far more art than science. By contrast, the Bai and Perron (1998) test is an unknown break point test. One of the key points of the Bai and Perron (1998) test is how to estimate ‘confident intervals’ for the break point. The Bai and Perron (1998) break test can extend to more than one break point given the maximum number of possible breakpoints are known. For the Chow (1960) test,

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one has to split the sample at the estimated break point and test for further breaks on the two subsamples by repeating the Chow (1960) test until there are no further breaks. In recent

econometric practice, the unknown break test such as the Bai and Perron (1998) test has replaced the more well-known break tests, in particular the Chow (1960) test, see (Hansen, 2001).

6.4 The Time Varying Parameter Models for Slow-moving Institutional Changes