Hemoglobinopatías estructurales

Table 2.1. Unit Root Results

Housing Market Unit Root Tests Conclusion

ADF DF-GLS KPSS FHFA -2.202 -2.350 0.090 I(0)/I(1) Case-Shiller -2.455 -2.333 0.104 I(0)/I(1) Census -2.471 -2.524 0.088 I(0)/I(1) Midwest Chicago -2.398 -2.219 0.114 I(0)/I(1) Cleveland -0.674 -1.499 0.229*** I(1) Detroit -1.622 -1.691 0.213** I(1) Northeast Boston -3.034 -2.965* 0.078 I(0)/I(1)

New York -2.458 -2.341 0.083 I(0)/I(1)

Philadelphia -1.741 -2.116 0.095 I(0)/I(1) South Atlanta -2.288 -2.315 0.120* I(1) Dallas -2.936 -1.813 0.201** I(1) Houston -1.258 -1.618 0.163** I(1) West

Los Angeles -1.710 -2.046 0.072 I(0)/I(1)

San Francisco -0.553 -1.219 0.081 I(0)/I(1)

Seattle 0.288 -1.188 0.115 I(0)/I(1)

Crit. Value

1% -4.042 -3.565 0.216

5% -3.450 -3.018 0.146

10% -3.150 -2.728 0.119

Notes: This table reports the unit root test results for the log rent-price ratios of the three national indexes (i.e. FHFA, Case-Shiller and Census) and the 12 regional MSA’s. The sample spans the time period 1982Q4-2013Q4, except Case-Shiller which is 1987Q1-2013Q4. Critical values (1%, 5% and 10%) for the tests is given in the last three rows. All the unit root test statistics reported assume the presence of an intercept and a trend. p-values/Critical Values for DF-GLS, KPSS is obtained from MacKinnon(1996) and Kwiatoski-Phillips-Schmidt-Shin (1992). The null hypothesis for all the tests except KPSS is that δt

has a unit root. The null hypothesis for KPSS is that the series is stationary. Lags are fixed at 12. For the KPSS test, the Newey West automatic method using Bartlett kernel selects the bandwidth. ”*”,”**” and”***” indicate rejection of the null hypothesis at the 10%, 5% and 1% levels respectively. The last column gives the resultant conclusion of the unit root tests, specifically says whether the series is stationary I(0), a unit root bubble process, I(1) or I(0)/I(1) when the tests contradict each other.

Integer order tests are implemented to examine the stationarity, I(0), or non- stationarity, I(1), of the log rent-price ratio (δt). The presence of a unit root,

I(1), in δt is consistent with the presence of housing price bubbles.

Table 2.1 reports the unit root results for the Housing Market. Column 1 defines the housing series estimated and columns 2-4 report test statistics of all the different tests implemented. We use two tests, namely the Augmented Dicky- Fuller (ADF) and the GLS-detrended Dicky-FullerElliot et al.(1996). Both these

tests have a null hypothesis that the rent to price ratio has a unit root. The way in which classical hypothesis testing is carried out ensures that the null hypothesis is hard to reject. Kwiatkowski et al.(1992) argue that such unit-root tests often fail to reject a unit root because they have low power against relevant alternatives, such as, fractionally integrated series. They propose tests, known as KPSS tests, with the null hypothesis of stationarity against the alternative of a unit root. They argue that such tests should complement unit-root tests and that by testing both the unit-root and the stationarity hypotheses, one can distinguish between series that appear to be integrated, series that appear to be stationary, and series that are not very informative about whether or not they are stationary or have a unit root. The KPSS test statistics are reported in column 4 of Table 2.1. The lags for all these tests are fixed at 12 and the tests employ the presence of an intercept and a trend in the test regression.

The results in Table2.1 aid us in presenting a preliminary empirical evidence on the presence of price bubbles in the U.S. Housing Market. The last column in the Table shows the conclusions we draw from the three tests. There are three cases we have to consider here. First, the case of unit root and bubbles - I(1). This occurs when both the ADF and the DF-GLS test were unable to reject the null of a unit root and the KPSS test rejected the null of stationarity, I(0). We find that 5 out of 15 series showed this behaviour.

Second, the case of no bubbles I(0) when the ADF and the DF-GLS test reject the null of a unit root and the KPSS test do not reject the null of stationarity. We observe that none of the series exhibited this behaviour.

Third, the case of I(0)/I(1) when the tests contradict each other. In this scenario, no conclusion can be drawn about bubbles from the tests. We will explain this with an example. Take the case of the aggregate FHFA series. The ADF and the DF-GLS both were unable to reject the unit root which should mean that the KPSS test will reject the null of stationarity. However, the KPSS test do not reject its null. In this case, we conclude that the series could be either an I(0)/I(1). The majority, 10 out of 15 series, fall in this category. These series which include all the aggregate ones may possess long memory and mean reversion implying no bubbles or unit root or explosive indicating bubbles.

It is this inability of these standard unit root tests that validate our use of the fractional order methods. In the following sections, we make use of both parametric and semi-parametric estimation methods and also consider structural breaks to arrive at an efficient method to analyse housing bubbles.

We discuss the results for the regional series in more detail here. The results for the FHFA Regional MSA’s are mixed. All the West and the Northeast regions as well as Chicago from the Midwest follow the national indexes in that they could be mean-reverting (I(0)/I(1)). However, Cleveland and Detroit from the Midwest; and Atlanta, Dallas and Houston from the South; show unit root tendency.20 Most of the current literature that analyse the time series properties of U.S. Housing Indexes do not consider the ratio of rental to housing price series and tests for rational bubbles. They concentrate on merely the persistence of the house prices. Hence, an effective comparison with our results is not possible. Nevertheless, they uniformly find unit root persistence in the U.S. HPI’s. For instance Canarella

et al. (2011) who uses the DF-GLS test and finds overwhelming evidence to the

presence of a unit root in the Case-Shiller MSA’s for the monthly 23 year time period, January 1987-April 2009. Using quarterly data from 1975 to 1996 from the 50 US states, Mu˜noz(2004) also finds unit roots in house price changes, using the Dickey-Fuller Generalised Least Squares (DF–GLS) test. Meen (2002) compares the time-series behaviour of house prices in the US and the UK. Using quarterly data from 1976 to 1999 for the US and from 1969 to 1999 for the UK, Meen

(2002) conducts both Augmented Dickey–Fuller (ADF) and Phillips–Perron (PP) unit-root tests on the level of house prices. He finds that in both countries house prices follow a difference stationary process. That is, house prices are I(1).

It is clear from the results in Table 2.1 that the standard unit root tests do not provide a clear analysis about the exact persistence of the rent-price ratio’s primarily because these test are too restrictive in that they consider only two possible values of d in the real space d ∈ [0, 1]. A recent unit root test byCavaliere

and Xu (2014) is widely applicable in series which are naturally bounded. THis

test unlike the conventional ADF tests do not over-reject the null hypothesis. Nominal interest rates, unemployment rates and target zone exchange rates are examples of such bounded series. However, the use of this test in a model designed to detect bubbles which are marked by deviations from any bounds based on fundamentals is not appropriates. Nevertheless, this test complements the unit root tests used here. Furthermore, much research argues that the presence of structural breaks distorts the validity of standard unit root tests (Perron (1989,

1997)). This motivates our use of both parametric and semi-parametric methods for estimating the actual persistence or memory parameter (d). Koustas and

Serletis(2005) also finds that unit root tests like ADF have low power in detecting

20_{Firstly, the KPSS test rejects the null of stationarity and secondly, both the ADF and the} DF-GLS do not reject the null of a unit root.

asset price bubbles in the dividend-price ratio and advocates the use of ARF IM A based parametric estimation methods. The following two sections describe their results.