Testing For Asset Price Bubbles In The Philippines Using Right-Tailed Unit Root Tests

A NEW RIGHT-TAILED UNIT ROOT TEST FOR ASSET PRICE BUBBLES DETECTION IN THE PHILIPPINES

Ruben Carlo O. Asuncion De La Salle University – School of Economics ECO718M – Macroeconometrics December 2013

I. Introduction With the Philippine economy surpassing economic growth forecasts recently, one cannot help but question whether the said promising economic expansion prospects are sustainable. A recent Forbes columnist, Jesse Colombo, in an article entitled, Here’s Why The Philippines’ Economic Miracle Is Really A Bubble In Disguise (21 November 2013), pointed out that the Philippines has an “inflating property bubble”. Colombo further said that housing prices have nearly doubled since 2004 and rising by at least 42% in 2012. Lending standards have been relaxed with waivers of income proof for Filipino overseas contract workers (OFW), who continuously buy real estate housing units. Real estate developers might be overbuilding with huge demand from OFWs. Consequently, the Philippine construction sector is expected to expand by double digits in 2014 and will account for half of the country’s economic growth. These are tell-tale signs, according to Colombo, that the Philippines is headed for another inflationary binge hurting economic growth prospects in the long-run. Furthermore, the International Monetary Fund (IMF) has warned the Philippine government of the risks that the economy faces. One of the said risks is a “domestic asset price bubble”. If the said bubble could burst, it will directly weaken the financial sector and eventually slow down economic growth. This assessment by the IMF was contained in its Country Report No. 12/102. Therefore, it is very crucial to detect whether there are domestic asset price bubbles in a certain economy to augment economic policy in order to help sustain economic growth well into the future. However, can asset price bubbles be detected? Gurkaynak (2008) survey econometric tests of asset price bubbles showing that, despite recent advances, econometric detection of asset price bubbles cannot be achieved with a satisfactory degree of certainty. For each paper that finds evidence of bubbles, there is another one that fits the data equally well without allowing for a bubble. We are still unable to distinguish bubbles from time-varying or regime-switching fundamentals, while many small sample econometrics problems of bubble tests remain unresolved. Diba and Grossman (1988) cited the explosive behaviour of bubbles and perhaps introduced the most applied methods for detecting price bubbles in literature, particularly the right-tailed unit root test and the cointegration test. These methods have been widely used to detect stock and housing price bubbles over the last twenty years. The right-tailed unit root tests are applied to asset prices and their respective fundamentals. The null hypothesis for the test describes a unit root (no bubbles), while the alternative hypothesis defines an explosive root for bubbles. Blanchard (1979) refers to periodically collapsing behaviour of bubbles and Evans (1991) documents the incapability of Diba-Grossman test under periodically collapsing characteristics of bubbles. Phillips et al (2011) [or PWY (2011)] proposed the recursive right-tailed unit root test or sup ADF test (SADF) that shows significant power improvement compared to the DibaGrossman test and also recommended a strategy to identify the origination and termination

dates of certain bubbles on a particular sample which can detect exuberance in an asset price during its inflationary phase and can eventually serve as an early warning system for potential bubbles in the economy. Phillips et al (2013) [or PSY (2013)] demonstrated through the S&P 500 price-dividend ratio from January 1871 to December 2010 data that the SADF test of PWY (2011) may fail to reveal the existence of bubbles in the presence of multiple collapses. Thus, a generalized sup ADF (GSADF) test is proposed. The GSADF test improves the power significantly over the SADF. Moreover, PSY (2013) suggested a bubble locating strategy based on GSADF statistic that leads to distinct power gains over the date-stamping strategy of PWY (2011) when there are two bubbles in the sample period. Gonzales et al (2013) and Yui et al (2013) are recent studies in literature that apply SADF and GSADF tests in stock and housing prices in Columbia and Hong Kong, respectively. While, Taipalus (2012) used PSY (2013) data set citing the validity of the new indicator as robust and more powerful than the traditional standard tests. This paper proposes the use of the right-tailed unit root tests introduced by PSY (2013) to detect asset price bubbles for the stock market in the Philippines. This paper is organized as follows: Section 2 discusses the four (4) tests in the EViews add-in package on right-tailed unit root testing namely, the standard ADF, the rolling ADF or RADF, the SADF of PWY (2011) and the GSADF of PSY (2013). Section 3 describes the results of the bubble detection methods. Section 4 concludes with future work and important suggestions for use with actual Philippine data.

II. The Right-Tailed Unit Root Tests Bubble Detection Caspi (2013) describes these tests as largely based on the standard left-tailed unit root DickeyFuller (DF) test. This, however, involves the different variation of a right-tailed unit root DF test where the null hypothesis is of a unit root and the alternative is of a mildly explosive autoregressive coefficient:

where

is the estimated first order regression coefficient from the following empirical equation: ∑

(1)

where is an intercept, is the maximum number of lags, lags coefficients and is the error term.

for

… are the differenced

The first test included in the add-in is a right-tailed version of the standard ADF unit root test. The -statistic from this test matches the one from the ADF unit root test included in the typical EViews software package. However, the critical values for testing the null hypothesis is different from the ones used in the usual ADF unit root test since we now need the right-tail of the statistic’s non-standard distribution. The rolling ADF or simply RADF is a rolling version of the first test wherein the ADF statistic is calculated over a rolling window of a size specified by the user. During this particular procedure, the window’s start and end point are incremented one step at a time and the RADF statistic is the maximal ADF statistic estimated among all possible windows. The sup ADF test or simply SADF test is based on recursive calculations of the ADF statistics with an expanding window. The estimation procedure is described as follows (see Figure 1): First, for a sample interval of [0, 1] (i.e. , the sample size, is normalized to 1) the first observation in our sample is set as the starting point of the estimation window, , i.e., (all given as fractions of the sample). Secondly, the end point of the initial estimation window, , is set according to some choice of minimal window size, such that the initial window size is (again, in fraction terms). Lastly, the model is recursively estimated, while incrementing the window size, , one observation at a time. Each estimation yields an ADF statistic denoted as ADF . Note that the last step, estimation will be based on the whole sample (i.e., and the statistic will be ADF1). The SADF statistic is defined as the supremum value of the ADF sequence for : {

}

(2)

Figure 1. Illustration of the SADF Procedure

PSY (2013) showed that the SADF test suffers from a loss of power in the presence of multiple periodically collapsing bubbles. As an alternative, the authors suggest the GSADF test which is a generalization of the SADF test that allows a more flexible estimation window where the starting point, , is allowed to vary within the range (see Figure 2). Formally, the GSADF statistic is defined as:

{

}

(3)

Figure 2. Illustration of GSADF Procedure

Date-Stamping The recursive right-tailed tests, SADF and GSADF, can also be used as a date-stamping procedure that estimates the origination and termination of bubbles. In other words, if the null hypotheses of these tests are rejected, we can estimate the start and end points of a specific bubble. Caspi (2013) shows the date-stamping procedures: The first date-stamping strategy is based on the SADF test. PWY (2011) propose comparing each of the ADF sequence to the corresponding right-tailed critical values of the standard ADF statistic to identify a bubble initiating at time . The estimated origination point of a bubble is the first chronological observation in which ADF crosses the corresponding critical value (from above) denoted by , and the estimated termination point is the first chronological observation after in which ADF crosses below the critical value, denoted by . Formally, the estimates of the bubble period are given by: ̂ ̂ where

is the

̂

{

}

(4)

{

}

(5)

critical value of the standard ADF statistic based on

observations. Similarly, the estimates of the bubble period based on the GSADF are given by:

̂ ̂ where

̂

is the

{

}

(6)

{

}

(7)

critical value of the sup ADF statistic based on

observations. BSADF( for GSADF statistic by noting that:

, is the backward sup ADF statistic that relates to the

{

}

(8)

Simulating Critical Values This EViews add-in also enables the user to derive finite sample critical values for all four test statistics, based on Monte Carlo simulations using the following random walk process with an asymptotically negligible drift as the null: , where , and are constants, and to unity.

(9)

is the sample size and

is the error term. PSY (2013) set ,

III. Implementation of the Right-tailed ADF Tests Using historical monthly stock market data of the Philippine Stock Exchange Index (PSEi) from July 1997 to November 2013 as the sample to implement the all the right-tailed ADF tests in EViews with add-in for right-tailed tests by Caspi (2013), Figure 3 below describes the PSEi. Figure 3. PSEi, July 1997-November 2013 8,000 7,000 6,000 5,000 4,000 3,000 2,000 1,000 0 97 98

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As mentioned earlier, the EViews add-in package has four (4) right-tailed unit root test. The four are the following: 1) ADF; 2) Rolling ADF (RADF); 3) Sup ADF (SADF) or PWY (2011); and, 4) Generalized sup ADF (GSADF) or PSY (2013). Table 1. ADF Test Result

t-Statistic ADF Test critical values:

99% level 95% level 90% level

-0.150610 0.693352 0.057688 -0.299003

*Right-tailed test

The ADF test result above show that the absolute value of the ADF t-Statistic is more than all the test critical values at all the possible levels suggests the existence of explosive bubbles in the data. However, this ADF test is limited in explanatory power. Table 2. RADF Test Result t-Statistic max RADF Test critical values:

99% level 95% level 90% level

57.29341 6.649007 1.169925 0.356815

*Right-tailed test

The RADF results tell that the PSEi data exhibits explosive bubbles (see Table 2). Figure 4 presents a better picture of how the data behaves. However, it’s date-stamping capability, as PWY (2011) mentions is weak or the identification of the origination and termination of certain bubbles are uncertain. However, it does indicate negative bubbles in the PSEi rendering it further to be ineffective in determining the when and how long did the asset price bubble started and lasted, respectively. Table 3 outlines the SADF test results indicate that only at the 90% level of confidence that it can be said that there is the existence of bubbles. Again, this is consistent with PSY (2013) that formulated the GSADF making it more consistent and reliable in detecting bubbles. Figure 5 confirms the existence of one episode of an asset price bubble in the PSEi beginning mid-2012. This was when the Philippine stock market started to reach new highs amidst the euphoria of the macroeconomic good news such as various investment grade upgrades given by the different credit rating agencies. However, this notes the inability of the SADF test to detect multiple bubbles as noted by PSY (2013).

Figure 4. Rolling ADF Test 60 50 40 30 60

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The Rolling ADF sequence (left axis) The 95% critical value sequence (left axis) PSEICPI (right axis)

Table 3. SADF Test Result (PWY 2011)

t-Statistic SADF Test critical values:

1.223930 1.786929 1.233532 0.947637

99% level 95% level 90% level

*Right-tailed test

Figure 5. SADF Test Results (PWY 2011) 60 50 40 30 2

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The foward ADF sequence (left axis) The 95% critical value sequence (left axis) PSEICPI (right axis)

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Table 4. GSADF Test Result (PSY 2013)

t-Statistic GSADF Test critical values:

57.29341 14.82692 4.244944 2.131062

99% level 95% level 90% level

*Right-tailed test

Table 4 shows the existence of multiple bubbles in all levels of significance tested by the GSADF. Figure 6 shows multiple bubbles in the PSEi. First is in 1999, 2001, 2005, and 2010. Currently, the GSADF test does not detect any asset price bubble in the PSEi. Figure 6. GSADF Test Result (PSY 2013) 60 50 40 30 60

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The bacwards SADF sequence (left axis) The 95% critical value sequence (left axis) PSEICPI (right axis)

IV. Conclusion The SADF and GSADF tests are new tests that can detect bubbles in asset price bubbles in a certain economy. The results do show the possible existence of bubbles in the PSEi. SADF (PWY 2011) consistently was unable to detect possible bubble, while the GSADF (PSY 2013) was able to detect multiple bubbles. However, robustness checks had to be done to determine further the accuracy of the bubbles. It would be good to use housing market prices to detect if indeed asset price bubbles are forming in the Philippines economy.

References: Diba, B.T., and Grossman, H.I., 1988, Explosive rational bubbles in stock prices? The American Economic Review, 78, 520– 530. Evans, G.W., 1991, Pitfalls in testing for explosive bubbles in asset prices. The American Economic Review, 81, 922– 930. Caspi, I., 2013, EViews 8 Add-in Package on Right-Tailed ADF Tests. Accessed on 16 December 2013 (http://davegiles.blogspot.com/2013/08/right-tail-augmented-dickeyfuller.html). Gonzalez, J., Joya, J., Guerra, C., and Sicard, N., 2013, “Testing for Bubbles in Housing Markets: New Results Using a New Method”, Borradores de Economia No. 753, 2013. Gurkaynak, R. S., 2008, Econometric tests of asset price bubbles: taking stock. Journal of Economic Surveys, 22, 166– 186. Phillips, P.C.B., S. Shi, and Yu, J., 2012, “Testing For Multiple Bubbles”. Cowles Foundation Discussion Paper No 1843. Phillips, P., Shi, S., and Yu, J., 2013, Testing for Multiple Bubbles: Historical Episodes of Exuberance and Collapse in the S&P 500”. Phillips, P., Wu, Y., and Yu, J., 2011, “Explosive Behavior in the 1990s Nasdaq: When Did Exuberance Escalate Asset Values?” International economic review, 201(February):201– 226. Taipalus, K., 2012, “Signaling Asset Price Bubbles With Time-Series Methods”, Bank of Finland Research Discussion Papers. Yiu, M., Yu, J. and Jin, L., 2012, “Detecting bubbles in Hong Kong residential property market”. Hong Kong Institute for Monetary Research. Working Paper No. 1/2012.