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

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) 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 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 cointegration test – threshold model to examine the long-run and short-run relationship between Gold price and Inflation in a case of emerging country like Vietnam, not developed countries as many previous studies had did To the best of author’s knowledge, only one research of Le Long, De Ceuster, Annaert, and Amonhaemanon (2013) has worked on this issue in Vietnam by using the conventional regression model Therefore, by allowing for non-linearity and discriminate between long-run and short-run dynamics, the research provides a useful measure of the effectiveness of inflation-hedging of gold over different time periods in Vietnam To have better view on the subject in developing countries, the research also conducts studies on Thailand since it is one of the major gold consumer country in the world like Vietnam and has quite similar economic backgrounds with Vietnam as well 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 cointegration or error-correction models, the earlier researches and studies havefound some initial 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 cointegration 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 (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 cointegration) on the relationship between CPI and the price of gold (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 cointegration 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, 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 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 not account for asymmetric effect that possibly exists in the Gold price – Inflation relation 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 Figure 11 Flow chart of testing procedure The first section applies linear co co-integration proposed by Engle and Granger (1987) as well as threshold co-integration integration test suggested by Enders and Siklos (2001) to o analyze long-run inflation hedging effectiveness of gold in Vietnam Vietnam The results from two types of techniques will tell us how well gold can act as an inflation hedge in long long-run run The testing procedure starts with the unit root test applied to natural llogarithm of both price of gold and CPI After two series are qualified to have the same order of integrated, linear co-integration integration tests is conducted first, If the findings show no significant evidence on linear co co-integration, non-linear linear threshold cointegration test is employed next to figure out what nature of the long long-term term relationship between gold price and inflation in Vietnam actually is Short-run run relationship will be analyzed in the second section The research will be based on the combination on of the nature of both long long-run and short-run run relationship to find the most applicable model for short-run run adjustment First of all, the linearity test for short-run short will be conducted to determine the nature of short short-run run relationship Then, there are two cases to be 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 (TCTVECM) is applied Finally, the Granger causality test and Impulse Response analysis are conducted for better understanding of the relationship Empirical results 4.1 Unit Root Test It is evident from the table 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 The result of Unit Root Test1 The result of Unit Root Test Vietnam ADF Level Statistic Value PP p_value Lags Statistic Value DF-GLS p_value Bandwidth Statistic Value NP-MZ Lags Statistic Value Lags LNG -2.132627 0.5245 -2.067319 0.5608 -0.825813 -1.34529 LNCPI -1.663489 0.7641 13 -0.994318 0.9417 -1.089357 13 -3.1423 13 First difference ∆LNG -11.2255*** 0.0000 -13.5632*** 0.0000 -11.2550*** -142.83*** -3.780174** 0.0193 12 -9.78560*** 0.0000 -1.481512 12 -2.33707 12 ∆LNC PI Thailand Level ADF PP DF-GLS NP-MZ Note: The tests are applied to the natural log of gold price and CPI The null hypothesis H0 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 (NPMZߙ) 10 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 (‫ܪ‬଴ ∶ ‫݌‬ଵ = ‫݌‬ଶ )or asymmetric (‫ܪ‬ଵ ∶ ‫݌‬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 reports the estimation result of the MTAR model We can only reject the null hypothesis of symmetric (‫ܪ‬଴ ∶ ‫݌‬ଵ = ‫݌‬ଶ )at 5% significance level The null hypothesis of no co-integration (‫ܪ‬଴ ∶ ‫݌‬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 (‫ܪ‬଴ ∶ ‫݌‬௜ = 0) in MTAR model Consequently, there is no significant evidence of the presence of the nonlinear 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 13 .04 03 Lowess Linear Fit (iters=4) Lowess Linear Fit (iters=4) Lowess Linear Fit (iters=4) D(LNCPI) 02 01 00 -.01 -.02 -.15 -.10 -.05 00 05 10 15 20 D(LNG) Figure The chart of ∆g and ∆p, Scatter Nearest Neighbor Fit Model2 It is observed that the relationship between ∆୥ and ∆୮ is non-linear in all three bandwidth spans: 0.15, 0.30 and 0.45 Therefore, the research apply the asymmetric short-run adjustment model TC-TVECM to verify the non-linear adjustment between the Gold Return and Inflation in short-run 4.5 Non-linear error-correction model The TC-TVECM is the combination of the vector error correction model (VECM) and the MTAR model, which is described as follow to infer the asymmetric short-run adjustment: (5) Note: the bandwidth span determines which observation should be included in the local regressions, and the span controls the smoothness of the local fit The research will use the same figure as in Wang et al (2011) research, which is three bandwidth spans: 0.15, 0.30 and 0.45; the polynomial degree is and the iteration number is 14 ‫ۓ‬ ߙ + ෍ ߙଵ,ଵ௜ ∆݃௧ି௜ + ෍ ߙଵ,ଶ௜ ∆‫݌‬௧ି௜ + ߱ଵଵ ‫ܯ‬௧ ‫ܶܥܧ‬௧ିଵ ۖ ଵ଴ ۖ ௜ୀଵ ௜ୀଵ ۖ + ߱ଵଶ ሺ1 − ‫ܯ‬௧ ሻ‫ܶܥܧ‬௧ିଵ + ݁௚ଵ௧, ∆‫ܶܥܧ‬௧ିௗ > ߛ ௣ ∆݃௧ = ௣ ‫۔‬ ۖߙଶ଴ + ෍ ߙଶ,ଶ௜ ∆݃௧ି௜ + ෍ ߙଶ,ଶ௜ ∆‫݌‬௧ି௜ + ߱ଶଵ ‫ܯ‬௧ ‫ܶܥܧ‬௧ିଵ ۖ ௜ୀଵ ௜ୀଵ ۖ + ߱ଶଶ ሺ1 − ‫ܯ‬௧ ሻ‫ܶܥܧ‬௧ିଵ + ݁௚ଶ௧, ∆‫ܶܥܧ‬௧ିௗ ≤ ߛ ‫ە‬ ௣ ௣ (6) ‫ۓ‬ ߚ + ෍ ߚଵ,ଵ௜ ∆݃௧ି௜ + ෍ ߚଵ,ଶ௜ ∆‫݌‬௧ି௜ + ߱ ഥଵଵ ‫ܯ‬௧ ‫ܶܥܧ‬௧ିଵ ۖ ଵ଴ ۖ ௜ୀଵ ௜ୀଵ ۖ +߱ ഥଵଶ ሺ1 − ‫ܯ‬௧ ሻ‫ܶܥܧ‬௧ିଵ + ݁௣ଵ௧, ∆‫ܶܥܧ‬௧ିௗ > ߛ ௣ = ௣ ‫۔‬ ഥଶଵ ‫ܯ‬௧ ‫ܶܥܧ‬௧ିଵ ۖߚଶ଴ + ෍ ߚଶ,ଶ௜ ∆݃௧ି௜ + ෍ ߚଶ,ଶ௜ ∆‫݌‬௧ି௜ + ߱ ۖ ௜ୀଵ ௜ୀଵ ۖ +߱ ഥଶଶ ሺ1 − ‫ܯ‬௧ ሻ‫ܶܥܧ‬௧ିଵ + ݁௣ଶ௧, ∆‫ܶܥܧ‬௧ିௗ ≤ ߛ ‫ە‬ ௣ ௣ Where ߙ, ߚ are the short-run estimated coefficients; ݁ଵ௧, ݁ଶ௧, represent the error terms of two regimes; ‫ܶܥܧ‬௧ିଵ = ݃௧ି௜ − ߠ଴ − ߠଵ ‫݌‬௧ିଵ, is the correction term of period t-1 in long-run equilibrium; d is the delay parameter ∆‫ܶܥܧ‬௧ିௗ > ߛ show that the adjustment momentum between gold price and consumer price is faster, which is called high momentum period ∆‫ܶܥܧ‬௧ିௗ ≤ ߛ show that the adjustment momentum between gold price and consumer price is slower, which is called low momentum period Furthermore, the error-correction mechanism is usually assumed to react immediately one period after some deviation from equilibrium, i.e., the delay parameter is usually assumed to equal one and the change in error correction term becomes ∆‫ܶܥܧ‬௧ିଵ (Ihle & von Cramon-Taubadel, 2008) The optimal lag for research’s model is 13 - significance in first two reliable test The estimated threshold value is identified at 0.036096 (Appendix A) The long-run co-integration equation in high regime is achieved from the short-run error correction model (Appendix A): D(LNG(-1)) = 4.34026075772*D(LNCPI(-1)) - 8.07434927e-18 The result displays the complete hedging ability of Gold for Inflation (coefficient = 4.34026075772) The model also has the high R2 (0.861588), indicating that the model above is 15 very appropriate to describe the relationship Furthermore, the coefficient of the error correction equation (co-integrated model) is C(1) = 41.80034, with p-value is significant at 1% level However, the coefficient or the speed of adjustment towards long-run equilibrium is positive, meaning that there is no long-run causality from Inflation to Gold price C(30) which is the coefficient for the model with CPI as dependent value also has the same result, significant but positive Thus, Gold price and CPI does not influence on each other in long-term within high regime The long-run co-integration equation in low regime (Appendix A) D(LNG(-1)) = 4.42053068555*D(LNCPI(-1)) - 0.0161863250971 Similarly, the result exhibits the complete hedging ability of Gold for Inflation (coefficient = 4.42053068555 with high R2 (0.889511) The coefficient C(1) and C(30) is significantly positive, meaning that there is no long-run causality for both directions between two variables in low regime as well In a nutshell, the TC-TVECM model gives the same conclusion as Enders and Siklos nonlinear co-integration test, which is in long-run, the gold price and inflation experience an asymmetric threshold co-integration (different adjustment coefficient) and gold with its inflation hedging effectiveness is a safe place to invest However, in the causality test for long-run, the research cannot find any significant signs of the influence between Gold price and CPI on each other This results implies that Gold investment in Vietnam is a useful tool to hedge against Inflation in long-run It is relevant with the previous research ofLe Long et al (2013) Nevertheless, different from the linear relationship in the research, this study observes a nonlinear co-integration relationship between Gold price and CPI The ability or level of hedging will vary depend on low and high period For Thailand, the threshold value is estimated at 0.035680 with the lag length number of Two long-run estimated equation in different regimes from TC-TVECM Model tell the same story: Gold price in Thailand can fully hedge against Inflation in long-term (Co-efficient = 2.16521115441 and 2.03392837135 in high and low momentum, respectively) The coefficients of the error correction equation in both regimes are negative and significant at 1%, suggesting 16 the opposite results compared with Vietnam, which is two-way causality between Gold price and Inflation in Thailand in long-term (Appendix B) 4.6 Short-run Granger Causality test Table The result of Short-run Granger Causality Test in Vietnam Depend ent High momentum regime w threshold co- Low momentum regime w threshold co- integration integration Null Hypothesis Ho variable Sum of coefficients ෍ ߙଵ,ଶ௜ Chi-square test Sum of coefficients Chi-square test 26.20875** ෍ ߙଶ,ଶ௜ 43.16393*** ௣ CPI does not cause Gold ௣ ௜ୀଵ (0.0159) 1419.04752 ∆lng MECT does not cause ∆lng (1-M)ECT does not cause ∆lng ߱ଵଵ = ߱ଵଶ = 15.74527 0.503155 (0.4781) ෍ ߚଵ,ଵ௜ MECT does not cause ∆lncpi (1-M)ECT does not cause ∆lncpi ߱ ഥଵଶ = 57.83648 (0.1380) 27.13145 ** ෍ ߚଶ,ଵ௜ 9.020681*** (0.0027) 60.01919*** (0.0000) ௣ ௜ୀଵ ߱ ഥଵଵ = ߱ଶଵ = ߱ଶଶ = -130.5878 2.200479 57.69097 (0.0119) -90.378133 ∆lncpi (0.0000) 1212.039063 ௣ Gold does not cause CPI ௜ୀଵ ௜ୀଵ 43.57975*** (0.0000) -72.760152 0.516584 4.196549 15.18013 (0.4723) 2.170054 (0.1407) ߱ ഥଶଵ = ߱ ഥଶଶ= 15.55259 -34.80486 9.413700*** (0.0022) 61.16586*** (0.0000) To confirm the causality of short-run dynamic effect and the inflation hedging ability of gold in short-run, we employ the Wald coefficient test to check the causality between variables (strong exogeneity) If the null hypothesis of Granger causality test is rejected and the coefficient sum is positive, the ability of hedging inflation of gold is effective If the null hypothesis of Granger causality test is rejected and the coefficient sum is positive, an increase of gold will lead to an increase in inflation 17 CPI does cause Gold In high momentum regime, the results proves the inflation hedging effectiveness of shortrun gold investment as the null hypothesis can be rejected at 5% level of significance (p-value = 0.0159) and the sum coefficients ∑୮୧ୀଵ αଵ,ଶ୧is positive CPI does cause gold in short-run in Vietnam In low momentum regime, inflation in Vietnam influences gold return very strongly (p- ෝଶ,ଶ୧ is positive, which indicates high value = 0.000) at 1% significant level The coefficient α ability of gold in hedging against inflation during short-run low period In Thailand, although the null hypothesis can be rejected at 1% level of significance, the accumulated coefficient is negative, gold cannot be used as effective tool hedging against inflation in high regime During low period, the coefficient is also negative, which means inflation increase causes overall negative impact on gold price Gold cannot hedge over inflation for low short-term regime in Thailand Gold price does cause Inflation Gold price also does Granger cause Inflation in short-run high momentum The effect of gold return on inflation is negative and significant at 5% level (p-value = 0.0119) For Thailand, the causality is also significant but the effect of gold return on inflation is positive Similarly, Gold price strongly influences Inflation in low momentum regime with 1% of significance level The coefficient sum ∑ β෠ ଶ,ଵ୧ is negative Therefore, it is evident that an increase in the price of gold is negatively correlated with an increase in inflation in short-run Additionally, by applying the weak exogeneity test through the significance of adjusting coefficient ߱ଵଵ , ߱ଵଶ, ߱ଶଵ and ߱ଶଶ of error-correction term, the study will verify the adjustment trend to the long-run equilibrium of each variables In addition, the model also can be used to examine the existence of rigidity adjustment of gold price in the short-run The result of weak exogeneity test in high momentum cannot provide any significant level of coefficient It illustrates that there is the elasticity of gold price in short term period in which gold price is highly fluctuated Gold price is resilient in adjustment to long-run equilibrium Similarly, adjustment of inflation toward long-run equilibrium in high momentum is automatic The same finding is also figured out in Thailand for both gold price and inflation adjustment 18 In low momentum, the results reveal that the adjustment coefficient ω ෝ ଶଶ of error correction term (1-M) ECT is negative with 1% significant level within low momentum regime Moreover, the adjustment coefficient ω ෝ ଶଵ of error correction term MECT is positive with 1% significant level also within low momentum |ωଶଶ |>|ωଶଵ | indicating that the Gold price needs to adjust upward for getting back to the long-run equilibrium and that the gold price presents the rigidity of downward adjustment In the second model of TC-TVECM in Eq.(6), |ω ഥ ଶଶ |>|ω ഥ ଶଵ | presents that the inflation needs to adjust upward for getting back to the long-run equilibrium and presents the downward rigidity of inflation Contradictory, in Thailand, both adjustment coefficients in high momentum are significant at percent |ωଶଵ |>|ωଶଶ | suggests gold price needs to adjust downward to long-run equilibrium, presenting the rigidity of upward adjustment, while in low momentum, |ω ഥ ଶଵ |>|ω ഥ ଶଶ | shows that the inflation needs to adjust downward or the upward rigidity of inflation 4.7 Impulse Response Analysis Both low and high regime have the same response in the Impulse Response Analysis, which are the significant reaction from Inflation to Gold and insignificant reaction from Gold to Inflation Specifically, the significant positive response of gold to CPI is only in period In contract, the response of inflation to gold oscillates wildly, starts from highly positive value in lag to deeply negative value in lag 2, then bounce back again to positive in lag After that, it fluctuates follow the sinuous pattern, around the zero point (Appendix A) Conclusion In general, the findings of this research suggest that the inflation hedge of Gold in Vietnam is effective in both long-term and short-term However, in short-term, if investors want to invest in Gold, they should be aware of different hedging ability of gold during high regime and low regime For extra safety, investors ought to choose the time of low momentum period or on the other hand, the time where Gold price responds to Inflation slowly This findings is contradictory to the findings from the original research of inflation hedging of gold in the U.S and Japan market In that research, they found out that in the nearly perfect market like the U.S or Japan, only in high momentum, when cross-elasticity between Gold price and CPI is high, the market becomes perfectly competitive, two variables almost adjust synchronously, the short-run 19 adjustment rigidity does not exist and investor could use the gold as an inflation hedge (Wang et al., 2011) Gold in the past had verified itself as a good protection against inflation From the traditional mindset to practical facts, Gold in Vietnam definitely keep its value during wars, crisis and changes of empires and government Before being strictly controlled, gold is an ideal portfolio holding for investors in monetary market Even now gold is no longer used for massive trading like house, land, etc, this situation is expected not last for long When the economy is less controlled, the role of gold will be back The contribution of this study is for both academic and practice From academic perspective, it is the first one that employs the non-linear method for this relationship in Vietnam It helps to enrich the existence literature of gold price and inflation relation in Vietnam to the thought of school of this issue in the world by adding another countries’ evidence, a young and immature market like Vietnam From the practice perspective, it provides a decision aid for making better asset allocation for portfolio not only in long-term but also in short-term and for the future as well Moreover, due to the fact that the price of gold is also an indicator of inflation pressure in the economy, understanding gold behavior during different timeframes is absolutely useful for policy makers, especially in the emerging market like Vietnam However, this study also has some limitations Firstly, available monthly data of 19 years does not actually bring enough convincible to the results This will be an evitable limitation of this research However, it covers almost the up and down period of Vietnam’s economic Hence, the empirical results hopefully still have practical meaning Secondly, the outcome might not reflect fully the fluctuation of Gold price due to the complexity of the economic Many economic variables effect on each other while the research focus only on two variables Gold price and Inflation 20 Appendix A Vietnam Lag length selection: Lag LogL LR FPE AIC SC HQ 1122.005 1157.020 1160.925 1165.264 1167.565 1168.357 1171.240 1173.265 1174.339 1175.022 NA 68.73907 7.594407 8.357456 4.389251 1.496779 5.394250 3.751750 1.969293 1.241424 1.15e-07 8.63e-08 8.63e-08 8.61e-08 8.74e-08 9.01e-08 9.10e-08 9.27e-08 9.53e-08 9.83e-08 -10.30419 -10.59005 -10.58917 -10.59229 -10.57663 -10.54707 -10.53677 -10.51857 -10.49160 -10.46104 -10.24189 -10.46544* -10.40227 -10.34308 -10.26512 -10.17325 -10.10066 -10.02015 -9.930881 -9.838014 -10.27903 -10.53971* -10.51367 -10.49162 -10.45079 -10.39606 -10.36060 -10.31723 -10.26509 -10.20936 10 11 12 13 14 15 16 17 1175.609 1180.203 1199.061 1217.222 1217.734 1218.724 1219.560 1225.611 1.054858 8.171872 33.19698 31.63499 0.882471 1.687694 1.409411 10.09480* 1.01e-07 1.01e-07 8.80e-08 7.73e-08* 7.99e-08 8.22e-08 8.47e-08 8.32e-08 -10.42958 -10.43505 -10.57199 -10.70251* -10.67036 -10.64262 -10.61345 -10.63236 -9.744255 -9.687428 -9.762065 -9.830277 -9.735828 -9.645782 -9.554315 -9.510919 -10.15274 -10.13304 -10.24482 -10.35016 -10.29285 -10.23994 -10.18561 -10.17934 * indicates lag order selected by the criterion LR: sequential modified LR test statistic (each test at 5% level) FPE: Final prediction error AIC: Akaike information criterion SC: Schwarz information criterion HQ: Hannan-Quinn information criterion The optimal lag for research’s model is 13 - significance in first two reliable test Threshold value γ estimation Lag LogL LR FPE AIC SC HQ 10 11 1122.005 1157.020 1160.925 1165.264 1167.565 1168.357 1171.240 1173.265 1174.339 1175.022 1175.609 1180.203 NA 68.73907 7.594407 8.357456 4.389251 1.496779 5.394250 3.751750 1.969293 1.241424 1.054858 8.171872 1.15e-07 8.63e-08 8.63e-08 8.61e-08 8.74e-08 9.01e-08 9.10e-08 9.27e-08 9.53e-08 9.83e-08 1.01e-07 1.01e-07 -10.30419 -10.59005 -10.58917 -10.59229 -10.57663 -10.54707 -10.53677 -10.51857 -10.49160 -10.46104 -10.42958 -10.43505 -10.24189 -10.46544* -10.40227 -10.34308 -10.26512 -10.17325 -10.10066 -10.02015 -9.930881 -9.838014 -9.744255 -9.687428 -10.27903 -10.53971* -10.51367 -10.49162 -10.45079 -10.39606 -10.36060 -10.31723 -10.26509 -10.20936 -10.15274 -10.13304 21 12 13 14 15 16 17 1199.061 1217.222 1217.734 1218.724 1219.560 1225.611 33.19698 31.63499 0.882471 1.687694 1.409411 10.09480* 8.80e-08 7.73e-08* 7.99e-08 8.22e-08 8.47e-08 8.32e-08 -10.57199 -10.70251* -10.67036 -10.64262 -10.61345 -10.63236 -9.762065 -9.830277 -9.735828 -9.645782 -9.554315 -9.510919 -10.24482 -10.35016 -10.29285 -10.23994 -10.18561 -10.17934 * indicates lag order selected by the criterion LR: sequential modified LR test statistic (each test at 5% level) FPE: Final prediction error AIC: Akaike information criterion SC: Schwarz information criterion HQ: Hannan-Quinn information criterion The estimated threshold value is identified at 0.036096 (Appendix A) The Impulse Response to Cholesky One S.D within high momentum Response to Cholesky One S.D Innovations Response of D(LNG) to D(LNG) Response of D(LNG) to D(LNCPI) 8 4 0 -4 -4 -8 -8 10 12 14 16 18 20 22 24 Response of D(LNCPI) to D(LNG) 10 12 14 16 18 20 22 24 22 24 Response of D(LNCPI) to D(LNCPI) 2 1 0 -1 -1 -2 -2 10 12 14 16 18 20 22 24 10 12 14 16 18 The Impulse Response to Cholesky One S.D within low momentum 22 20 Response to Cholesky One S.D Innovations Response of D(LNG) to D(LNG) Response of D(LNG) to D(LNCPI) 4 0 -4 -4 -8 -8 10 12 14 16 18 20 22 24 Response of D(LNCPI) to D(LNG) 10 12 14 16 18 20 22 24 22 24 Response of D(LNCPI) to D(LNCPI) 2 1 0 -1 -1 -2 -2 10 12 14 16 18 20 22 24 10 12 14 16 18 20 Appendix B Thailand Linearity test - Scatter Nearest Neighbor Fit Model 03 02 Lowess Linear Fit (iters=4) Lowess Linear Fit (iters=4) Lowess Linear Fit (iters=4) D(LNCPI) 01 00 -.01 -.02 -.03 -.04 -.2 -.1 D(LNG) Lag length selection Lag LogL LR FPE AIC SC HQ 1216.760 1231.660 1235.310 1236.579 1239.728 1239.792 NA 29.24935 7.099597 2.443103 6.007777 0.120736 4.79e-08 4.34e-08* 4.35e-08 4.46e-08 4.50e-08 4.66e-08 -11.17751 -11.27797* -11.27475 -11.24957 -11.24173 -11.20545 -11.11521 -11.15336* -11.08784 -11.00036 -10.93022 -10.83164 -11.15235 -11.22763* -11.19925 -11.14890 -11.11589 -11.05445 23 10 11 12 13 14 15 16 17 1244.957 1247.544 1254.778 1259.293 1259.920 1265.645 1273.431 1274.989 1276.821 1278.461 1279.552 1280.432 9.665009 4.792332 13.26727 8.198060 1.125897 10.18445 13.70659* 2.713231 3.157265 2.796324 1.840942 1.467011 4.61e-08 4.68e-08 4.54e-08 4.52e-08 4.66e-08 4.59e-08 4.44e-08 4.54e-08 4.63e-08 4.74e-08 4.87e-08 5.02e-08 -11.21620 -11.20317 -11.23298 -11.23772 -11.20663 -11.22254 -11.25743 -11.23492 -11.21494 -11.19319 -11.16638 -11.13762 -10.78008 -10.70476 -10.67226 -10.61470 -10.52131 -10.47491 -10.44750 -10.36269 -10.28040 -10.19635 -10.10724 -10.01618 -11.04002 -11.00183 -11.00647 -10.98605 -10.92979 -10.92052 -10.93025 -10.88257 -10.83742 -10.79051 -10.73853 -10.68460 * indicates lag order selected by the criterion LR: sequential modified LR test statistic (each test at 5% level) FPE: Final prediction error AIC: Akaike information criterion SC: Schwarz information criterion HQ: Hannan-Quinn information criterion Threshold value γ estimation Variable Coefficient Std Error Above Threshold Below Threshold Differenced Residuals(t-1) -1.294080 -0.930445 0.114920 0.112729 0.110491 0.064684 Threshold value (tau): F-equal: T-max value: F-joint (Phi): 0.035680 7.873732 -8.421005 78.134020 Estimated model High momentum D(LNG,2) = -46.1321624656*( D(LNG(-1)) - 2.16521115441*D(LNCPI(-1)) + 5.74253288599E-18 ) + 22.7149130515*D(LNG(-1),2) - 50.6591307943*D(LNCPI(-1),2) - 0.0361787914768 + 38.6818756417*ECT(-1) D(LNCPI,2) = -20.2330375195*( D(LNG(-1)) - 2.16521115441*D(LNCPI(-1)) + 5.74253288599E-18 ) + 10.2712429856*D(LNG(-1),2) - 22.9216290714*D(LNCPI(-1),2) - 0.0162887231058 + 17.4156829407*ECT(-1) Low momentum 24 D(LNG,2) = -23.4463249856*( D(LNG(-1)) - 2.03392837135*D(LNCPI(-1)) - 0.00107389496668 ) + 9.44994248538*D(LNG(-1),2) - 20.3001876218*D(LNCPI(-1),2) - 0.047195538435 51.1238508422*ECT(-1) D(LNCPI,2) = -10.4368430111*( D(LNG(-1)) - 2.03392837135*D(LNCPI(-1)) - 0.00107389496668 ) + 4.49703737187*D(LNG(-1),2) - 9.68920154866*D(LNCPI(-1),2) - 0.0209276355927 22.6116754651*ECT(-1) Short-run Granger Causality test High momentum regime w threshold co- Low momentum regime w threshold co- integration integration Depend ent Null Hypothesis Ho variable Sum of coefficients Chi-square test Sum of coefficients Chi-square test 56.05302*** 112.0628*** ∆lncpi x -> ∆lng -50.65913 (0.0000) -20.30019 2.550042 (0.0000) 73.71603*** ∆lng MECT x -> ∆lng ω11 = 27.26398 ( 0.1103) ω21 = -187.8699 0.998396 (1-M)ECT x -> ∆lng ω12 = -16.27580 (0.3177) (0.0000) 29.27415*** ω22 =-55.76496 (0.0000) 63.71463*** 107.4040*** ∆lng x -> ∆lncpi 10.27124 (0.0000) 4.497037 2.661874 (0.0000) 72.77744*** ∆lncpi MECT x -> ∆lncpi ϖ11 = 12.56469 (0.1028) ϖ21 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Engle and Granger linear co- integration test Table The result of Linear Co- integration Test Engle–Granger Co- integration test and Co- integration parameters Vietnam Dependent Variable θ0 θ1 ADF Test. .. of gold across South-east Asian countries Key words: Non- linear, Co- integration test model, Gold, Inflation hedging, Vietnam Introduction The economic role of gold has been recognized since ancient... 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 The result of Non- linear Co- integration Test