Estimating Break in Mean and Trend

To complement the ocular evidence presented in the plots of the national and regional rent-price ratios (Figure2.1 and Figure 2.B.1) we implement three tests, namely the SupF test of Andrews (1993) and the ExpF and AveF of Andrews

and Ploberger (1994) (refer eq. (2.52), (2.53) and (2.54) from §2.5.1) to test

for possible breaks in the mean and trend of each series. Inference for presence or absence of breaks is based on Hansen (2000)’s bootstrap heteroskedasticity corrected p-values. We limit our analysis to one break considering the relatively short sample size we are estimating on.

Table 2.7. Structural Change Tests on National and Regional δt’s

Housing Market SupF ExpF AveF Breakdate

Test Stat. Bootstrap p Hetero- p Test Stat. Bootstrap p Hetero- p Test Stat. Bootstrap p Hetero- p

FHFA 488.186 0.000*** 0.000*** 239.635 0.000*** 0.000*** 83.092 0.000*** 0.000*** 2004Q4 Case-Shiller 210.574 0.000*** 0.000*** 101.105 0.000*** 0.000*** 64.012 0.000*** 0.000*** 2003Q1 Census 348.712 0.000*** 0.000*** 170.718 0.000*** 0.000*** 60.832 0.000*** 0.000*** 2004Q3 Midwest Chicago 466.886 0.000*** 0.000*** 229.448 0.000*** 0.000*** 117.522 0.000*** 0.000*** 2003Q2 Cleveland 795.594 0.000*** 0.000*** 394.258 0.000*** 0.000*** 350.387 0.000*** 0.000*** 2003Q2 Detroit 1317.230 0.000*** 0.000*** 654.215 0.000*** 0.000*** 515.738 0.000*** 0.000*** 2003Q1 Northeast Boston 65.951 0.000*** 0.001*** 29.831 0.000*** 0.001*** 33.870 0.000*** 0.000*** 1989Q4 New York 90.028 0.000*** 0.000*** 41.159 0.000*** 0.000*** 34.680 0.000*** 0.000*** 2004Q4 Philadelphia 158.642 0.000*** 0.000*** 75.380 0.000*** 0.000*** 40.127 0.000*** 0.000*** 2004Q4 South Atlanta 564.129 0.000*** 0.000*** 277.694 0.000*** 0.000*** 132.966 0.000*** 0.000*** 2003Q4 Dallas 255.068 0.000*** 0.000*** 123.601 0.000*** 0.000*** 152.733 0.000*** 0.000*** 1999Q4 Houston 100.265 0.000*** 0.000*** 46.521 0.000*** 0.000*** 64.974 0.000*** 0.000*** 2004Q1 West Los Angeles 161.429 0.000*** 0.000*** 76.369 0.000*** 0.000*** 37.796 0.000*** 0.000*** 2005Q1 San Francisco 128.458 0.000*** 0.000*** 60.427 0.000*** 0.000*** 41.437 0.000*** 0.000*** 2004Q4 Seattle 302.679 0.000*** 0.000*** 147.719 0.000*** 0.000*** 85.516 0.000*** 0.000*** 2004Q4 Notes: This table reports the test statistics of the SupF test ofAndrews (1993) and the ExpF and AveF ofAndrews and Ploberger (1994) (refer eq. (2.52), (2.53) and (2.54) from §2.5.1) and Hansen(2000) bootstrap p values under homoskedastic (Bootstrap p in the table)and heteroskedastic (Hetero- p in the table) residuals. All the three tests examine the null of no breaks against the alternative of breaks in the mean and trend. The trimming parameter is set at 0.15 which means the starting index for break search is 18.

Table 2.7 reports the test statistics of the three break tests (SupF , AveF and ExpF ) along with Hansen (2000)’s bootstrap p values under homoskedastic and heteroskedastic residual processes. All the three tests examine the null of no change against the alternative of a structural change in the mean (µ) and trend (ψ) of the log rent-price ratio’s. The reported p values uniformly reject the null hypothesis at the 1% level strongly implying the presence of a structural break in the mean and trend of all the log rent-price series. The estimated breakdate for the national series is illustrated in Fig. 2.1.

Figure 2.1. Estimated Breakdates of National Rent-Price Ratio’s

Notes: This figure provides a graphical illustration of the estimated breaks in mean and trend of the log rent-price ratio’s of FHFA, Case-Shiller and Census aggregate series. The break date of each series is given in text in the corresponding plots.

A brief review of the estimated breakdates reveal that in general they are centered around 2003Q1-2004Q4. On visual inspection it is clear that there is a marked change in the trajectory of the log rent-price ratio’s between 1982Q4- 2003Q1 and then on. This is consistent with a sudden upsurge followed by down- turn in housing prices highlighted by a U shape in the δt trajectory from 2004Q4.

Our structural change test revealed one endogenous break in all of the series. The breakdate was found to lie in general in the 2003-04 time period.

This breakdate suggests a shift in household beliefs. For example, Piazzesi

and Schneider (2009) using Michigan Consumer Survey data finds that the U.S.

housing boom had two distinct stages. In the first stage, during 2002-03, about 72% of households cited favourable credit conditions and believed that the time for buying a house was good. From 2004, in the second stage, houses were con- sidered too expensive but the number of agents who were optimistic about future price increased from 10% in 2003Q4 to over 20% by 2005Q2. Our results thus empirically validate these arguments.

From the breakdates for the regional MSA’s, it is apparent that they mirror the national series i.e. the breakdates found are in and around the 2004-05 time period. The exception to this was Boston (1989Q4) and Dallas (1999Q4). This divergent behaviour we believe has more to do with regional rental changes rather than house prices. Severe regulations cap the rent you can charge on residential households in several MSA’s in the United States which includes the Boston and Dallas metropolises.

A recent forecasting paper byBarari et al.(2014) found four structural breaks in the aggregate Case-Shiller Index (1991:1-2009:12) by applying the Bai and

Perron (1998, 2003) procedure. It is well documented that the Bai and Perron

(1998) procedure could overestimate the number of breaks when the regressors are non-stationary. Canarella et al. (2011) applied the Lumsdaine and Papell

(1997) and theLee and Strazicich(2001) tests to the Case-Shiller 10 city regional HPI’s and found two breaks in the intercept and trend for all the 10 metro areas. Specifically the tests indicated that the second breakdate for the most of the metro areas (Chicago, Los Angeles, San Francisco, New York) was found to occur around 2005-2006 time period concurring with our results. Both these papers however do not take into account the effects of the rental series. Nevertheless, Nneji et al.

(2013) use a Markov switching approach to the aggregate FHFA price-rent ratio in the period 1960-2011 and finds that the housing market switched from a low price-rent ratio to a high price-rent ratio around the year 2000.

Now that we have identified breaks we proceed to a robust estimation of long memory on the de-meaned and de-trended series, i.e. δt− ˆµ − ˆψ. The next section