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 Diba-

Grossman 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 Dickey-

Fuller (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, for … are the differenced

lags coefficients and is the error term.

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:

{

} (4)

{

} (5)

where

is the critical value of the standard ADF statistic based on

observations.

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

{

} (6)

{

} (7)

where

is the critical value of the sup ADF statistic based on

observations. BSADF( for , is the backward sup ADF statistic that relates to the

GSADF statistic by noting that:

{ } (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:

, (9)

where , and are constants, is the sample size and is the error term. PSY (2013) set ,

and to unity.

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

0

1,000

2,000

3,000

4,000

5,000

6,000

7,000

8,000

97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13

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 -0.150610

Test critical values: 99% level 0.693352

95% level 0.057688

90% level -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 57.29341

Test critical values: 99% level 6.649007

95% level 1.169925

90% level 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

-40

-20

0

20

40

60

0

10

20

30

40

50

60

97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13

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 1.223930

Test critical values: 99% level 1.786929

95% level 1.233532

90% level 0.947637

*Right-tailed test

Figure 5. SADF Test Results (PWY 2011)

-6

-4

-2

0

2

0

10

20

30

40

50

60

97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13

The foward ADF sequence (left axis)

The 95% critical value sequence (left axis)

PSEICPI (right axis)

Table 4. GSADF Test Result (PSY 2013)

t-Statistic GSADF 57.29341

Test critical values: 99% level 14.82692

95% level 4.244944

90% level 2.131062

*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)

-20

0

20

40

60

0

10

20

30

40

50

60

97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13

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-dickey-

fuller.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.