An application of non linear co integration test model to gold inflation hedging ability

1 AN APPLICATION OF NON-LINEAR CO-INTEGRATION TEST MODEL TO GOLD INFLATION HEDGING ABILITY HO TRAN THAO NGUYEN International University - Vietnam National University, HCM City, Vietnam

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AN APPLICATION OF NON-LINEAR CO-INTEGRATION TEST

MODEL TO GOLD INFLATION HEDGING ABILITY

HO TRAN THAO NGUYEN International University - Vietnam National University, HCM City, Vietnam

LE HONG NHUNG International University - Vietnam National University, HCM City, Vietnam

VUONG DUC HOANG QUAN

Ho Chi Minh City Institute for Development Studies (HIDS), HCM City, Vietnam

(Contact Person: quan_vdh@yahoo.com)

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ABSTRACT

This study aims to analyze the question of how effective gold is as an inflation hedge in both long-term and short-term in Vietnam from a new perspective – non-linear co-integration The two-stage testing procedure is applied to analyze the inflation hedging ability of gold in Vietnam both in long and short-run with monthly data of gold price from World Gold Council (per ounce denominated in Vietnam Dong) and CPI of Vietnam from International Monetary Fund (IMF) over the period of January 1995 to July 2014 are used for analysis The results figure out the long-term effective hedging ability but unstable relationship between gold and inflation To further explore the inflation hedging ability of Gold in short-run, the study uses the non-linear error-correction model (TC-TVECM) to examine the price rigidity in low regime (when variation margin of gold price is lower than that of CPI) and high regime (when variation margin

of gold price is higher) It is found that in short-run, gold is partially effective in hedging against inflation The protection ability is stronger in low momentum than in high momentum Furthermore, by comparing the results in two countries – Vietnam and Thailand, this research tries to provide a broader view on inflation-hedge of gold across South-east Asian countries

Key words: Non-linear, Co-integration test model, Gold, Inflation hedging, Vietnam

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1 Introduction

The economic role of gold has been recognized since ancient time From a form of currency to the Gold Standard monetary system in late 19th century and the exchange rate mechanism under the Bretton Woods system by the late 20th century, gold demonstrated itself as a centerpiece of international monetary system However, the breakdown of Bretton Woods system in 1973 diminished this role of gold Gold is now considered as an investment instrument that gains a lot

of attentions from international researchers due to its potential effect on inflation

Gold has many unique features that make it looks attractive to investors, monetary authorities and researchers in modern economy Firstly, gold had “a strong historical link to money, which might reinforce the culturally and traditionally embedded image as an immutable store of value”(Baur & Lucey, 2010) Secondly, it is treated as a commodity or physical asset which are typically considered as excellent inflation hedge compared with financial assets like stocks or bonds Furthermore, due to a series of severe financial crises and the incapability of some popular financial assets to reflect inflation’s movement over a longer period of time (Stock and Watson (1999), Cecchetti, Chu, and Steindel (2000), Banerjee and Marcellino (2006)), gold is strongly believed that possess the ability to preserve purchasing power over the long period, therefore, will be an effective tool to hedge against inflation Academic researches on gold have mainly focused on this property

The effectiveness of gold in hedging inflation relies on the existence of a stable long-run relationship between gold price and inflation rate And the theory suggests if gold is an effective long-run inflation hedge, the price of gold and the general price level should move together or there is a co-integration between gold price and inflation (Ghosh, Levin, Macmillan, & Wright, 2004) Moreover, gold not only is an inflation hedge in the long-run but it is also characterized

by significant short-run price volatility(Aggarwal, 1992) Therefore, co-integration techniques is considered by many researchers as a suitable tool to analyze both long-term and short-term relationship between gold price and inflation However, the argument around what co-integration test: linear or non-linear should be chosen is attracting concerns of many literature

The rational for this study is to contribute to the literature by adopting a new model of integration test – threshold model to examine the long-run and short-run relationship between

it is one of the major gold consumer country in the world like Vietnam and has quite similar economic backgrounds with Vietnam as well

2 Literature Review

Apparently, researchers have invested large amount of effort studying about the relationship between gold price and inflation The theoretical literature that sets the foundation for this relationship is the well-known Fisher hypothesis This theory, which can be applied to any investment assets, states that expected nominal return on asset must equal expected inflation rate plus real return (Fisher, 1930) Fama and Schwert (1977) try to estimate the extent to which the Fisher’s effect can be applied to all investment assets by translating Fisher’s theory into a regression model They confirm that only residential real estate among treasury bills, government bonds, labor income and common stocks performs effectively as an inflation hedge This empirical research has opened a new area of study including the relationship between gold and inflation for following researches

Since 1977, several empirical tests concentrated on the correlation between gold and inflation have been conducted by different authors such as Kolluri (1981), J Chua and Woodward (1982), Moore (1990), Chappell and Dowd (1997), Mahdavi and Zhou (1997),Ghosh et al (2004), Capie, Mills, and Wood (2005), Levin, Montagnoli, and Wright (2006), Tkacz (2007), Worthington and Pahlavani (2007), Blose (2010), Wang, Lee, and Thi (2011), Beckmann and Czudaj (2013), Batten, Ciner, and Lucey (2014) These empirical studies in general can be classified into three stages of development

(1)By applying conventional testing method including regression model, linear integration or error-correction models, the earlier researches and studies havefound some initial

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evidence on the ability of gold as inflation-hedging asset, especially in developed countries The first study on the subject taken by J Chua and Woodward (1982) figures out that the effectiveness of gold as an inflationary hedge will vary across country In detail, by employing simple regression model on both expected and unexpected inflation, the research concludes that among six industrialized countries consist of Canada, Germany, Japan, the USA, Switzerland and UK; the U.S is the only country where gold can act as an effective inflation hedge Moore (1990) reports a positive correlation between gold return and inflation and concludes that inflation can be used as a leading indicator to predict the price of gold Mahdavi and Zhou (1997) examines the performance of gold in conducting monetary policy using a technique built on co-integration and error-correction modeling However, they find no significant evidence on gold as

a leading indicator of inflation Contradictory to J Chua and Woodward (1982), Harmston (1998) provide evidence that gold is an effective long-run inflation hedge in the U.S., Britain, France, Germany and Japan due to its ability to maintain real purchasing power over the very long time By adopting the same technique - co-integration regression, the analysis of Ghosh et

al (2004) finds clues on both long-term and short-term movement in the price of gold The results suggest that gold can be regarded as a long-term inflation hedge in the U.S and the movements of nominal gold price are dominated by short-run influences Levin et al (2006) extends the scope of investigation to major gold consuming countries outside of the USA and come to two critical conclusions through estimating a conventional vector error-correction model Firstly, there is a long-term one-for-one relationship between the price of gold and the general price level in the USA Secondly, investors in major gold consuming countries such as Turkey, India, Indonesia, Saudi Arabia, and China also can consider gold as an inflation hedge

In an attempt to achieve more adequate evidence across countries, Tkacz (2007) develops a model that include the rate return of gold and exchange rate as the major determinants of inflation and examine that model on 14 countries over the period of 1994 to 2005 The research discovers that gold price contains significant information for future inflation in several countries, especially in those that have adopted formal inflation targets Nevertheless, the causality relationship between gold and general price level is questioned again by Blose (2010) The study argue that any speculative profit in holding gold will be offset by the higher interest rate costs

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(2) Former researches have shown inconsistent results on the correlation between gold price and CPI While most favor the existence of long-term relationship as well as short-term adjustment rely much on the time or place in which the research is conducted, some have given evidence to confirm that recent judgments on the price of gold and general price level are misplaced The possible reason for the contradicting findings may lie on the employed technique Indeed, it is arguable among researchers whether conventional co-integration techniques are able

to verify the presence of a stable long-run relationship between two time series As a result, at the beginning of the 21th century, researchers apply mix techniques to figure out which one is suitable to describe the connection between gold and inflation For instance, Kyrtsou and Labys (2006) doubts the results generated by traditional statistical tools on time series data like commodity price and inflation Hence, they utilize three steps testing procedure consist of linear co-integration (VAR), non-linear Granger causality and non-linear co-integration (bivariate noisy Mackey-Glass Model) and discover the incapability of linear test to explain fully the relationship Worthington and Pahlavani (2007) notices structural changes followed the transformation of gold from being an everyday currency to an investment asset in post-war period and the early 1970s Thus, in order to present the stable long-run relationship between gold price and inflation in the USA during that period, they take in account endogenously structural breaks to modify the old co-integration approach The outcomes support the widely held view that direct and indirect gold investment can serve as an effective inflation hedge Batten et al (2014) deploy three techniques at the same time (Johansen co-integration, Single equation error-correction model, Co-integration with structural breaks) to examine the long term dynamic relationship between general price level and the price of gold The study comes to conclusion that co-integration analysis might not be helpful to describe the relationship if there are significant structural changes in the series Moreover, the Kalman filter-based approach also helps them conclude that there is no stable connection between gold price and inflation In general, these mix techniques papers prove that rejecting such substantial changes in the relationship between time series variables will lead to the wrong assessment on the inflation hedging effectiveness of gold Consequently, latest articles have established an innovative methodology that accounts for the possibility of existence of asymmetric effect (non-linear co-integration) on the relationship between CPI and the price of gold

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(3) The pioneer study that examine entirely the possibility of non-linear co-integration in the relation between gold and inflation is provided by Wang et al (2011) By arguing that the presence of transaction costs and the business cycle dependence of the gold demand might lead

to a nonlinear relationship between gold price and CPI, they conduct both linear and threshold co-integration framework in the USA and Japan for a sample period covering from January 1971

to January 2010 The findings state that in long-term, the relationship between gold price in Japan is characterized by non-linear (asymmetric) threshold co-integration, while that in the U.S

is presented with the linear (symmetric) co-integration Hence, gold can act as an effective hedging tool in the U.S while only partially effective in Japan For short-term adjustment, the authors employ a complex non-linear threshold error correction model and explore that in low momentum regimes, gold is unable to hedge against inflation in both the U.S and Japan, however, in high regimes, gold investment can effectively hedge against inflation in the U.S and partly hedge in Japan Due to their significant findings and innovative techniques, this research will mainly adopt their procedure to test the long-term and short-term relationship between gold price and inflation in the context of Vietnam and Thailand In addition, adding to the school of thought for non-linear technique, Beckmann and Czudaj (2013) realize that the traditional co-integration and VECM methodology seems to be too restrictive due to major structural changes

in gold price since the early 17th consist of the breakdown of Bretton Woods in 1973, oil price shocks in 1973 and 1979/1980 plus several serious crises comprise the collapse of Soviet Union

in 1991, the burst of the ‘dot-com bubble’ in 2001 and the recent financial and economic crises started in 2007 Therefore, they use Bi-variation co-integration test and Markov switching vector error correction model (MS-VECM) approach to confirm that gold is partially able to hedge future inflation in the long-run and this ability is stronger in the USA and the UK compared to Japan and the Euro Area Additionally, the benefits of adopting the non-linear model is also found in explaining the correlation among other time series variables, for instance, Gold and Dollar (Capie et al., 2005), Purchasing Power Parity (Heimonen, 2006), Stock Price and Dividends (Esteve & Prats, 2010), Gold and The Yen (Wang & Lee, 2011)

In conclusion, the empirical evidence on the inflation hedge of gold is still controversial Theoretically, most of previous studies supported this relationship That is, the price of gold tends to move in the same direction and positive correlation with CPI When inflation occurs,

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gold will become "safe haven" for investors However, recent analysis suggest that this relationship is not clear and sustainable; gold is not completely hedge against inflation This relation depends very much on place and time the study surveyed Thus, the questions here are not only on does gold act as an inflation hedge, but also on how well it is Besides, the previous approaches of authors are varied and different Recent researches have put efforts on discovering new techniques in attempting to reflect more accurately the nature of this relationship For that reason, this paper wants to adopt the new testing method of (Wang et al (2011)) to present further asymmetric impact on the relationship between CPI and gold prices in long term in Vietnam To the best of our knowledge, due to the lack of literature on gold-inflation

relationship, only one research “Gold as a Hedge against Inflation: The Vietnam Case” of Le

Long et al (2013)was found to investigate on the same topic They figure out that gold do provide a good hedge against both the ex post and ex ante inflation in Vietnam, consistent with the conventional belief and supported the Fisher hypothesis (Fisher, 1930) However, by using simple regression model, their research do not account for asymmetric effect that possibly exists

in the Gold price – Inflation relation

3 Data & Methodology

3.1 Data collection

To understand the inflation hedge ability of gold in Vietnam, monthly data of gold price from World Gold Council (per ounce denominated in Vietnam Dong) and CPI from International Monetary Fund (IMF) over the period of January 1995 to July 2014 are used for analysis

3.2 Methodology

The study follows the steps adapted from the research of Wang et al (2011) about the inflation hedging effectiveness of gold in the U.S and Japan The flow of the steps is shown infigure 1

Figure 1

The first section applies linear co

well as threshold co-integration test suggested by

inflation hedging effectiveness of gold in Vietnam

tell us how well gold can act as an inflation hedge in long

the unit root test applied to natural l

qualified to have the same order of integrated,

findings show no significant evidence on linear co

integration test is employed next to figure out what nature of the long

gold price and inflation in Vietnam actually is

Short-run relationship will be analyzed in the second section The research will be based

on the combination of the nature of both long

applicable model for short-run adjustment First of all, the linearity test for short

conducted to determine the nature of short

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Figure 1 Flow chart of testing procedure

applies linear co-integration proposed by Engle and Granger (1987)integration test suggested by Enders and Siklos (2001) to analyzeinflation hedging effectiveness of gold in Vietnam The results from two types of techniques will tell us how well gold can act as an inflation hedge in long-run The testing procedure starts with the unit root test applied to natural logarithm of both price of gold and CPI After

qualified to have the same order of integrated, linear co-integration tests is conducted first, If the findings show no significant evidence on linear co-integration, non-linear threshold integration test is employed next to figure out what nature of the long-term relationship between gold price and inflation in Vietnam actually is

run relationship will be analyzed in the second section The research will be based

on of the nature of both long-run and short-run relationship to find the most

run adjustment First of all, the linearity test for shortconducted to determine the nature of short-run relationship Then, there are two

Engle and Granger (1987) as

o analyze long-run The results from two types of techniques will

run The testing procedure starts with

of both price of gold and CPI After two series are

integration tests is conducted first, If the

linear threshold term relationship between

co-run relationship will be analyzed in the second section The research will be based

run relationship to find the most run adjustment First of all, the linearity test for short-run will be

run relationship Then, there are two cases to be

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considered If short-run relationship is symmetric (linear), Error Correction Model (ECM) is

employed for both symmetric and asymmetric long-run relationship If short-run relationship is

asymmetric (non-linear), long-run relationship is symmetric (linear), threshold vector error

correction model (TVECM) is used as framework to analyze; or if long-run relationship is

asymmetric (non-linear): threshold co-integration – threshold vector error correction model

(TC-TVECM) is applied

Finally, the Granger causality test and Impulse Response analysis are conducted for better

understanding of the relationship

4 Empirical results

4.1 Unit Root Test

It is evident from the table 1 that our variables are non-stationary at their raw value but after

differencing for the first time, they become integrated of order (1) Therefore, co-integration

should be applied next to avoid spurious results

Table 1 The result of Unit Root Test 1

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Note: The tests are applied to the natural log of gold price and CPI The null hypothesis H 0 of all tests is having unit root (non-stationary) against

the alternatives of stationary series The equation contains both constant and time trend The maximum lag applied is 17 periods as followed the

previous research of Wang et al (2011) The optimal lags are selected according to Akaike Information Criterion (AIC) Four methods include

Augmented Dickey-Fuller test (ADF), Phillips-Perron test (PP), Dickey-Fuller – Generalized Least Squares test (DF-GLS), Ng and Perron (NP-

Statistic Value p_value Bandwidth

Statistic Value Lags

Statistic Value Lags

LNG -2.132627 0.5245 2 -2.067319 0.5608 4 -0.825813 2 -1.34529 2 LNCPI -1.663489 0.7641 13 -0.994318 0.9417 8 -1.089357 13 -3.1423 13

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4.2 Engle and Granger linear co-integration test

Table 2 The result of Linear Co-integration Test

Engle–Granger Co-integration test and Co-integration parameters

The result of linear co-integration test help us conclude on the relationship between Gold price

and Inflation in long-term:

• Regression equation for long-term relationship between Gold price and Inflation:

LNG = 7.896827 + 1.929461*LNCPI

θ1 = 1.929461: This value tells us that when CPI rises 1%, the gold price in Vietnam

dong rises 1.929%, showing the complete inflation hedge of gold.Even though the result

of Rଶ= 0.958598 and p-value = 0.0000are very good to conclude that this model is quite

fit to explain the relationship, both series are non-stationary so the outcome might be

spurious

Statistic Value P_Value Lags

Statistic Value P_Value Bandwidth

Statistic Value Lags

Statistic Value Lags

LNG -2.132627 0.5245 2 -2.067319 0.5608 4 -1.675022 2 -5.83283 2 LNCPI -3.415507 0.0518 2 -3.097124 0.1094 5 -1.436407 1 -4.48157 1

First difference

141.663*** 1

-∆LNC

PI -10.64494*** 0.0000 0 -10.68101*** 0.0000 2 -10.65683*** 0

102.846*** 0

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• Table 4 displays the result of Engle – Granger co-integration test With the p-values are not significant at any level, we cannot reject the null hypothesis of no linear co-integration Hence, there is no linear co-integration or long-run equilibrium between Gold price and CPI in Vietnam The similar result is found in Thailand

It is noted that as mentioned before, Engle – Granger linear co-integration test has drawback due

to not taking into account the asymmetric relationship of two variables This compels the author

to apply another technique to investigate the non-linear relationship of these variables

4.3 Non-linear co-integration Enders and Siklos test

Table 3 The result of Non-linear Co-integration Test

The results from table 3 uncover that in TAR model, the null hypothesis of no co-integration (଴∶ଵ= ଶ=0)can be rejected at 10% level of significance, which means there is non-linear

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relationship between gold price and inflation in long term The relationship illustrates the long run inflation-hedging effectiveness of gold However, the effectiveness of inflation hedging in long run may be not stable For further conclusion, the study employs the second test for null hypothesis of stable long run relationship We assess whether the adjustment to the long-run equilibrium is symmetric (଴ ∶ଵ= ଶ)or asymmetric (ଵ∶ଵ ≠ ଶ) The F-value equals

8.382464, significance at 5% level, suggests asymmetric adjustment for Gold price and CPI in long-run.The third row of table 3 reports the estimation result of the MTAR model We can only reject the null hypothesis of symmetric (଴∶ଵ= ଶ)at 5% significance level The null hypothesis

of no co-integration (଴∶ଵ= ଶ=0)cannot be rejected This implies the existence of slight

threshold co-integration for MTAR model

In the case of Thailand, the results from the similar testing procedure is inconsistent with the results from Vietnam The non-linear relationship is significantly only in one test t-Max (଴ ∶௜=

0) in MTAR model Consequently, there is no significant evidence of the presence of the

non-linear co-integration between Gold Return and Inflation in Thailand

The result points out the relationship between Gold price and CPI in Vietnam is not stable, proposing some interesting outcomes when investing the linkage between gold price and inflation in short run Therefore, the question needs to be studied further is how effectiveness of inflation hedging of gold in short run Error correction model will be employed to explore the short run adjustment of gold price and inflation The most common model is used for this kind of test is Error Correction Model (ECM) for linear short-run adjustment However, this research will apply more sophisticated correction model to capture entirely linkage between gold price and inflation in case the non-linear relationship of two variables exist

4.4 Linearity test for short-term adjustment