Can consumer price index predict gold price returns?

Economic Modelling 55 (2016) 269–278

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Can consumer price index predict gold price returns? Susan Sunila Sharma ⁎ Centre for Economics and Financial Econometrics Research, Faculty of Business and Law, Deakin University, 221 Burwood Highway, Burwood, Victoria 3125, Australia

a r t i c l e

i n f o

Article history: Accepted 12 February 2016 Available online xxxx Keywords: Gold price returns CPI In-sample Out-of-sample Predictability Forecasting

a b s t r a c t In this paper using data for 54 countries we test whether consumer price index (CPI) predicts gold price returns. Our test for predictability is based on a recently developed flexible generalised least squares estimator, which most importantly accommodates the endogeneity of CPI, its persistency and any heteroskedasticity in the model. We find limited evidence that CPI predicts gold price returns in in-sample tests; however, out-ofsample tests reveal relatively strong evidence that CPI predicts gold returns. These results are robust to different forecasting horizons. On the whole, we discover reasonable evidence that consumer prices predict gold price returns. © 2016 Elsevier B.V. All rights reserved.

1. Introduction The relationship between gold and inflation (see, inter alia, Tkacz, 2007; Pierdzioch et al., 2014a; Blose, 20101; Fortune, 1987; Christie-David et al., 2000; Adrangi et al., 2003; Ghosh et al., 2004; Levin et al., 2006; Mahdavi and Zhou, 1997; Tully and Lucey, 2007) has attracted significant interests because gold is regarded as an unusual asset, since it is both a commodity used, for example, in the production of jewellery and industrial applications, and also a financial asset, where it can be utilised as a store of value. Tkacz (2007) explains that as a financial asset, which represents about 12% of the gold market, the demand for gold can be seen as a function of the current and expected price of gold, the opportunity cost of holding gold, income, expected future inflation, and overall financial market stress. Theoretically, an increase in inflation expectations will reduce the perceived purchasing power of money, thus agents would divest themselves of money and can increase their holdings of gold. This literature has progressed along two lines. The first strand of the literature examines how inflation (CPI) affects gold prices (returns) (see, Pierdzioch et al., 2014a; Blose, 2010; Christie-David et al., 2000; Adrangi et al., 2003, among others). On the other hand, the other strand of the literature examines how gold prices affect CPI (inflation) (see Moore, 1990; Mahdavi and Zhou, 1997; Cui, 2009; Wherry, 2009; and Lehman, 2009). Both strands of the literature generally provide mixed results. For instance, Adrangi et al. (2003), Blose (2010), and Worthington and Pahlavani (2007) identify that the increasingly important role of gold acts as an inflation ⁎ Tel.: +61 392446871. E-mail address: [email protected]. 1 Blose (2010) presents a detailed survey of studies that examines the relationship between gold price and inflation.

http://dx.doi.org/10.1016/j.econmod.2016.02.014 0264-9993/© 2016 Elsevier B.V. All rights reserved.

hedge. In contrast, Lawrence (2003), Jaffe (1989), Mahdavi and Zhou (1997), and TKacz (2007) document that gold is not a leading indicator of inflation or is either uncorrelated or negatively correlated with expected inflation. From these literatures it is clear that the relationship between gold and inflation is endogenous. This is a relevant statistical issue that potentially impacts on the regression results. In this paper, we revisit the relationship between gold price returns and inflation. Our approach, however, is different from this literature in three ways. First, our approach follows a predictive regression framework: we test whether inflation (CPI) predicts gold price returns.2 Second, we use a newly developed estimator, proposed by Westerlund and Narayan (2015a), namely the flexible generalised least squares (WN-FGLS) estimator, to examine the null hypothesis of no predictability. The key advantage of the WN-FGLS is that it allows us to control for three statistical aspects of the data and model, which directly matter for the gold price and inflation relationship. These issues relate to; (i) endogeneity, already recognised as an issue in this literature, (ii) persistency of the predictor variable such that instead of diluting the information contained in consumer prices by taking the inflation rate as a predictor we can use the actual price variable as a predictor, and (ii) heteroskedasticity—an issue that is recognised as a stylised fact in financial time-series data. Through using the WN-FGLS

2 There are several studies which look at different determinants of gold returns. For instance, the common determinants of gold returns found in the literature are inflation rate (see Batten et al., 2014), the oil price (Zhang and Wei, 2010; Reboredo, 2013a), the exchange rate (Pukthuanthong and Roll, 2011 and Reboredo, 2013b), and business-cycle fluctuations (Pierdzioch et al., 2014b). However, our research question does not consider determinants of gold returns. Here, we look at the predictability of gold returns using CPI because we connect with an active strand of literature which has taken issue with the gold-CPI nexus.

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S.S. Sharma / Economic Modelling 55 (2016) 269–278

estimator, we account for all these statistical features that, as we will show later, characterise our data and predictive regression model. Third, we test for both in-sample and out-of-sample predictability. This is important because the relative roles and, therefore, importance of in-sample versus out-of-sample tests have occupied interest in the literature. Basically, there is no consensus: Some studies show preference for in-sample tests (see, for example, Foster et al., 1997; Lo and MacKinlay, 1990), while others support out-of-sample tests (see, Ashley et al., 1980; Rapach and Wohar, 2006). The main conclusion is that both are important and therefore undertaking both tests are important.3 Our approaches lead to three main findings. First, we discover weak evidence of in-sample predictability of gold price returns using CPI; evidence of predictability is only found for 10 countries. Second, we follow the literature and consider three (25%, 50%, and 75%) out-of-sample periods for out-of-sample forecasting evaluations. We use a constant returns model as our benchmark model. Our findings from out-ofsample evaluations reveal that there is strong evidence of out-ofsample predictability when we consider a short (25%) out-of-sample period compared to middle (50%) and long (75%) out-of-sample periods. In summary, we find that out of these 10 countries (where we find evidence of in-sample predictability), only for six countries the out-of-sample statistics (namely, Theil U and OOS_R2) for h = 1 support our proposed CPI-based predictive regression model. In addition, we find that out-of-sample predictability tests also support our proposed predictability model in the case of an additional 25 countries, where in-sample predictability test did not reject the null of no predictability. Third, to check the robustness of out-of sample predictability test, we compute Theil U and OOS_R2 statistics for a longer horizon (h = 6). From this exercise, we conclude that our results are robust. Our findings contribute to two different literatures. Our first finding that inflation predicts gold price returns supports earlier studies showing that; (a) inflation is a determinant of gold returns (see, Sherman, 1983; Moore, 1990; Christie-David et al., 2000), and (b) there is a cointegrating relationship between gold price and inflation (CPI) (see, Ghosh et al., 2004; Worthington and Pahlavani, 2007). Our second finding that in-sample and out-of-sample tests provide conflicting results is consistent with the bulk of the studies that undertake both in-sample and out-of-sample tests. For example, Bossaerts and Hillion (1999), Goyal and Welch (2003), Brennan and Xia (2005), Butler et al. (2005), and Ang and Bekaert (2007) document that financial ratios only predict stock returns mostly in in-sample tests than out-of-sample tests. By comparison, recent studies such as Westerlund and Narayan (2012, 2015b) show that out-of-sample tests perform as well as in-sample tests. When using a different predictor as opposed to financial ratios we discover evidence that support out-of-sample tests. This finding has implications for not only the gold market literature but also in other markets where predictability and forecasting are essential. The implication has been that out-of-sample evaluations should not be ignored. The rest of the paper is organised as follows. In the next section, we discuss the data used in this study and explain our estimation approach. Section three discusses the preliminary features of data and the main findings. The final section provides some concluding remarks. 2. Data and methodology This section contains two objectives. The first objective is to explain the data set. The second part of this section explains the in-sample predictive regression framework. 3 However, in this study we do not consider in-sample predictability tests for three subsample for which we have done the out-of-sample predictability tests. The reason is because the debate is about the out-of-sample predictability and not about in-sample predictability; see, for instance, Narayan et al. (2015a), Narayan and Sharma (2015), Phan et al. (2015), Narayan et al. (2014c), and Narayan et al. (2013a,b).

2.1. Data and preliminaries The data used in this study include monthly consumer price index (CPI)4 and London gold price for 54 countries. All data are sourced from the Global Financial Database. The sample size and the number of countries selected are dictated by data availability. The sample size ranges from as low as 774 observations in the case of Malta to as high as 1733 observations in the case of Germany. The gold price is measured in United States Dollars. The specific dates of data for each country are reported in the last column of Table 1. In columns 3 and 4 of Table 1, we report the mean and standard deviation of gold price returns and CPI (in natural logarithmic form) for each country. Considering the evidence for mean, we notice that CPI ranges from as low as − 24.82 in the case of Zimbabwe to as high as 5.697 in the case of Sri Lanka. By comparison, the most volatile CPI, based on the standard deviation, has been experienced by Brazil, followed by Greece, Argentina, and Germany. Tunisia, Thailand, Switzerland, Malta, and Malaysia have experienced the least volatility in CPI. 2.2. Methodology A recent study by O'Connor et al. (2015) presents a very detailed review of the literature on gold as an investment option. The main point here is that gold acts as a hedge against inflation. According to this survey, gold has a limited stock and a relatively inelastic supply in the short run, as it takes time to boost production through the introduction of new gold mines. This means that it is impossible to increase the supply of gold over a short time period. Gold, therefore, is considered as a hard currency, which holds its value as the purchasing power of other currencies decrease when faced with inflation. Feldstein (1980) provides hypothetical reasons as to how expected inflation is related to gold. His main argument is that the gold price will rise faster than the expected rate of inflation due to the fact that capital taxes will reduce any net payoff from selling gold. Additionally, Fortune (1987) builds this on this argument by explicitly suggesting a path through which gold prices are directly affected by inflation, which in also known as the substitution effect. Fortune (1987) hypothesis is built on the idea that the expectation of increases in future prices (inflation) encourages individuals to convert their assets, which indeed have a fixed nominal return, into gold. This increases the price of gold in that currency and it protects its residents from reductions in their purchasing power which is due to inflation. Finally, Levin et al. (1994, 2006) proposed an alternative inflationgold price channel which is based on an arbitrage model. This model argues that gold lease rates are equivalent to the world real interest rate. These studies assume that the general rate of inflation drives changes in gold extraction costs. They argue that in the long-term the gold price will rise in order to compensate miners for their increasing costs. In other words, this implies that there exists a causal relationship where causality runs from inflation to the cost of extraction to gold prices. Following these discussions supporting a relation between gold prices and inflation, we propose the following predictive regression model, where CPI is considered as a predictor of gold price returns, can be represented as follows: GRt ¼ α þ βCPI t−1 þ εGR;t

ð1Þ

Here, GR t is gold price returns in month t, computed as log(GPt/GPt − 1) ∗ 100, with GP being the gold price index. The predictor variable CPI is the natural logarithmic form of consumer price index. The null hypothesis of no predictability is tested by setting H0 : β = 0. As explained earlier, in the above specification, it is possible that CPI is endogenous. In case CPI is endogenous, a test for the null 4 It is worth noting while CPI for some countries like India has not been historically considered as the headline price index, it nonetheless captures the price movements.

S.S. Sharma / Economic Modelling 55 (2016) 269–278

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Table 1 Descriptive statistics and unit root test results. This table reports some commonly used descriptive statistics of the data. In columns 2 and 3, we conduct a test for unit roots based on the ADF unit root test. The null hypothesis is that there is a unit root. The ADF test is run with a maximum of eight lags. The Schwarz Information Criterion is then used to select the optimal lag length, which is reported beside the test statistics in square brackets. For the CPI series, we allow for both an intercept and a time trend, while for the gold price return series, we only allow for an intercept since it does not contain a time trend. In columns, 4 and 5, we report mean and standard deviation, respectively. In the final column, we report each countries time span of data. Country

Argentina Australia Barbados Brazil Canada Chile Colombia Congo Costa Rica Cyprus Dominican Republic Egypt Fiji Finland France Germany Greece Guatemala Guyana Iceland India Iran Israel Italy Jamaica Japan Kenya Korea Republic Malaysia Malta Mauritius Mexico Netherlands Norway Pakistan Paraguay Peru Philippines Portugal Senegal South Africa Sri Lanka Sweden Switzerland Thailand Trinidad and Tobago Tunisia Turkey Turkish Republic of Northern Cyprus UK Uruguay US Venezuela World Zimbabwe

Gold return

CPI

Mean

Std deviation

Dates

Test stat[LL]

p-value

Test stat[LL]

p-value

Gold return

CPI

Gold return

CPI

−30.005[0] −33.614[0] −26.963[0] −29.226[0] −33.280[0] −31.771[0] −30.723[0] −27.248[0] −29.414[0] −27.248[0] −28.832[0] −32.112[0] −26.945[0] −32.268[0] −33.116[0] −8.295[10] −31.799[0] −27.659[0] −26.945[0] −29.036[0] −32.164[0] −29.566[0] −31.842[0] −32.282[0] −28.888[0] −31.942[0] −27.151[0] −27.231[0] −27.242[0] −26.850[0] −27.029[0] −30.009[0] −32.486[0] −32.315[0] −26.955[0] −27.864[0] −31.621[0] −27.820[0] −30.537[0] −27.204[0] −32.093[0] −29.075[0] −32.951[0] −32.282[0] −27.231[0] −28.888[0] −27.368[0] −30.545[0] −3.438[0] −33.280[0] −29.226[0] −8.107[10] −28.942[0] −26.775[0] −30.545[0]

0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

−0.125[13] 0.391[12] −0.678[3] 0.226[2] 0.097[7] −0.737[16] 2.036[1] −2.259[0] 0.832[6] −1.104[12] 0.762[13] 1.446[12] −0.129[3] −1.433[4] −2.053[12] −1.237[17] −1.784[8] 1.684[4] −0.041[13] −0.935[12] 1.380[12] 0.003[1] −0.805[12] −1.103[13] 1.719[4] −1.860[24] 2.842[2] −6.518[0] −2.154[7] −1.258[0] −1.456[1] −1.321[5] −3.291[12] −3.247[14] −2.843[1] −2.303[6] −1.783[6] −5.235[5] −1.495[12] −3.037[0] 1.616[12] −1.763[0] −0.529[12] −0.307[13] −0.808[6] 1.042[1] −0.584[12] 0.644[13] 1.440[5] 0.144[13] −2.144[0] 1.919[4] 4.037[6] −0.600[13] 1.268[11]

0.945 0.983 0.850 0.974 0.966 0.835 1.000 0.186 0.995 0.716 0.993 0.999 0.944 0.567 0.264 0.660 0.389 1.000 0.954 0.777 0.999 0.958 0.817 0.717 1.000 0.674 1.000 0.000 0.514 0.897 0.844 0.882 0.068 0.076 0.182 0.431 0.713 0.000 0.831 0.032 1.000 0.399 0.883 0.921 0.816 0.997 0.871 0.991 0.999 0.969 0.227 1.000 1.000 0.868 0.999

0.423 0.336 0.442 0.394 0.343 0.377 0.404 0.427 0.389 0.427 0.406 0.369 0.430 0.365 0.347 0.228 0.376 0.432 0.430 0.399 0.368 0.385 0.375 0.365 0.403 0.373 0.420 0.428 0.428 0.443 0.438 0.377 0.361 0.365 0.441 0.429 0.381 0.427 0.409 0.428 0.370 0.398 0.350 0.365 0.428 0.403 0.429 0.408 0.427 0.343 0.394 0.239 0.393 0.446 0.408

−7.561 2.359 3.413 −8.735 3.173 −5.058 −0.679 2.962 0.849 3.551 0.961 1.266 3.382 2.292 2.044 −6.267 −5.662 2.068 1.887 1.329 2.353 0.489 −3.510 1.352 0.551 2.347 1.518 2.375 3.719 3.764 2.758 −1.646 3.200 3.035 2.604 0.951 −10.940 2.320 1.770 3.279 1.378 5.697 3.865 3.572 3.424 2.735 3.366 −5.410 2.861 2.680 3.360 3.299 3.497 3.676 −24.820

4.436 3.957 4.868 4.524 3.997 4.188 4.332 4.829 4.495 4.829 4.587 4.143 4.869 4.123 4.017 3.359 4.184 4.773 4.869 4.554 4.136 4.471 4.179 4.121 4.577 4.166 4.835 4.832 4.832 4.896 4.866 4.411 4.100 4.121 4.871 4.741 4.211 4.749 4.359 4.838 4.145 4.552 4.037 4.121 4.832 4.577 4.811 4.357 4.829 3.997 4.524 3.407 4.558 4.902 4.357

13.213 1.409 1.160 14.200 1.010 7.698 3.469 1.229 2.419 0.869 2.103 1.833 1.065 2.028 2.468 12.817 13.670 1.548 1.883 3.509 1.583 2.709 5.605 2.815 2.692 2.645 1.850 2.214 0.602 0.619 1.361 4.115 1.060 1.236 1.410 2.741 9.572 1.715 1.989 1.072 1.744 1.351 1.247 0.722 0.921 1.538 0.993 5.902 5.412 1.348 3.509 1.149 3.202 0.829 8.785

hypothesis of no predictability will be misleading (see, Westerlund and Narayan, 2012, 2014a). To avoid any bias inference resulting from an endogenous predictor variable, we follow Westerlund and Narayan (2012) and model CPI as follows: CPIt ¼ μ ð1−λÞ þ λCPIt−1 þ εCPI;t

1932m12–2014m04 1911m10–2014m03 1948m12–2014m02 1937m12–2014m04 1913m12–2014m04 1922m12–2014m04 1928m12–2014m04 1947m12–2014m04 1936m12–2014m04 1947m12–2014m04 1940m01–2014m04 1920m12–2014m04 1948m12–2013m12 1920m01–2014m04 1914m12–2014m04 1869m12–2014m04 1922m10–2014m04 1945m12–2014m04 1948m12–2013m12 1938m12–2014m04 1920m07–2014m03 1936m01–2014m03 1922m07–2014m04 1919m12–2014m04 1939m08–2014m03 1921m12–2014m04 1947m12–2013m12 1948m01–2014m04 1948m01–2014m04 1949m10–2014m03 1948m12–2014m03 1933m12–2014m04 1918m12–2014m04 1919m12–2014m04 1949m01–2014m02 1944m12–2014m04 1923m12–2014m04 1945m03–2014m04 1930m01–2014m04 1948m03–2014m04 1920m12–2014m03 1938m11–2014m04 1915m12–2014m04 1919m12–2014m04 1948m01–2014m04 1939m08–2014m03 1946m12–2013m12 1929m12–2014m04 1947m12–2014m04 1913m12–2014m04 1937m12–2014m04 1875m09–2014m04 1938m12–2013m12 1948m12–2014m01 1929m12–2014m04

order to allow for this possibility, we assume that the error terms are linearly related in the following way: εGR;t ¼ θε CPI;t þ ϵt

ð3Þ

ð2Þ 2 σCPI .

If the error terms from where εCPI,t is mean zero and with variance Eqs. (1) and (2) are correlated, then CPI is said to be endogenous. In

where ϵt is again mean zero and with variance σϵ2. We use bias-adjusted GLS estimator, which is based on making (1) conditional on (2), thereby removing the effect of the endogeneity.

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S.S. Sharma / Economic Modelling 55 (2016) 269–278

Table 2 Results for persistency and ARCH effects. In this table, we report the first-order autoregressive (AR(1)) coefficient of the CPI variable. We test the null hypothesis of ‘no ARCH’ at the lag of 12. This is done by filtering the data series by running at autoregressive model with 4 lags and then testing the null hypothesis of no ARCH. The F-statistics for the ARCH LM test are reported. *, *** denote statistical significance at the 10%, and 1% levels, respectively. Country

AR(1)

ARCH (F-Stat)

Country

CPI

CPI

Gold return

Argentina Australia Barbados Brazil Canada Chile Colombia Congo Costa Rica Cyprus Dominican Republic Egypt Fiji Finland France Germany Greece Guatemala Guyana Iceland India Iran Israel Italy Jamaica Japan Kenya

1.001 1.000 1.000 1.001 1.000 1.000 1.000 0.998 1.001 0.999 1.000 1.001 1.000 0.999 0.999 1.000 0.999 1.001 1.000 1.000 1.001 1.000 1.001 0.999 1.001 0.999 1.001

380.358*** 3.070* 147.983*** 1961.203*** 100.077*** 10.754*** 1.652 0.803 12.440*** 0.011 294.127*** 22.311*** 0.038 374.096*** 10.620*** 1301.920*** 917.231*** 51.552*** 14.294*** 0.029 173.594*** 0.000 513.140*** 0.060 101.236*** 11.611*** 1.504

48.737*** 72.882*** 34.100*** 45.571*** 70.458*** 60.110*** 53.267*** 35.259*** 46.709*** 35.259*** 43.195*** 62.401*** 34.107*** 63.454*** 69.304*** 121.059*** 60.300*** 36.879*** 34.107*** 44.434*** 62.800*** 47.675*** 60.587*** 63.549*** 43.599*** 61.255*** 35.154***

Korea Republic Malaysia Malta Mauritius Mexico Netherlands Norway Pakistan Paraguay Peru Philippines Portugal Senegal South Africa Sri Lanka Sweden Switzerland Thailand Trinidad and Tobago Tunisia Turkey Turkish Republic of Northern Cyprus UK Uruguay US Venezuela Zimbabwe

The resulting conditional predictive regression can be written as follows: GRt ¼ α−θμ ð1−λÞ þ βadj CPIt−1 þ θΔCPIt þ ϵt

ð4Þ

where ϵt is independent of εCPI,t by construction and βadj = β− θ(λ − 1). The key difference between this estimator and the one of Westerlund and Narayan (2012, 2014a) is the accounting for potential conditional heteroskedasticity in ϵt. This is done by assuming that ϵt has the following autoregressive conditional heteroskedastic (ARCH) structure: σ 2ϵt ¼ ψ0 þ

q X ψ j ϵ2t− j

ð5Þ

j¼1

where σϵt2 = var(ϵt | It − 1) and It is the information available at time t. The ARCH model in (5) can be obtained by fitting an autoregressive (AR) model to the squared OLS residuals obtained from regression (4), q 2 2 ̂ ¼ ψ̂0 þ ∑ j¼1 ψ̂ ϵ̂t− j , is ϵ̂t say. The fitted value from this AR model, σ ϵt j

a consistent estimator of σϵt2 and can, therefore, be used as a weight when using the GLS estimator. The Westerlund and Narayan (2012) test for predictability (or rather the absence thereof) is the resulting GLS t-statistic for testing H0 : βadj = 0 in (4).5 3. Empirical results This section is organised into three parts. In the first part, we discuss the key statistical features of the data. The emphasis here is on understanding the degree of persistency of the predictor variable, whether the predictor variable is endogenous, and whether the predictive 5 A referee of this journal suggested that we undertake a nonlinearity test. While this is a good suggestion, this is beyond the scope of this paper since the predictability test we use is a linear model. We, therefore, feel that future studies can extend the work we have done here to a nonlinear framework. In this regard our work here sets the motivation for any future work on this subject.

AR(1)

ARCH (F-Stat)

CPI

CPI

Gold return

0.995 1.000 0.999 1.000 1.000 1.000 1.001 1.001 0.998 1.001 1.001 1.000 0.998 1.001 0.995 1.000 1.001 0.993 1.000 0.998 1.001 1.001 1.000 0.991 1.001 1.002 1.005

0.001 183.913*** 93.222*** 107.849*** 103.256*** 0.064 33.887*** 70.488*** 28.572*** 13.103*** 97.365*** 7.322*** 68.795*** 80.458*** 0.001 8.276*** 436.117*** 262.028*** 263.632*** 3.833* 45.404*** 81.349*** 134.070*** 0.001 6.619*** 36.578*** 303.311***

35.165*** 35.165*** 33.236*** 34.135*** 50.115*** 64.698*** 63.549*** 34.002*** 37.874*** 58.966*** 37.656*** 52.038*** 34.999*** 62.322*** 44.529*** 68.151*** 63.549*** 35.165*** 43.599*** 35.733*** 52.132*** 35.259*** 70.458*** 45.571*** 115.244*** 44.330*** 52.132***

regression model is heteroskedastic. The second part of the results explains the findings from in-sample predictability test, while the final part concludes with an out-of-sample forecasting (of gold returns) evaluation. 3.1. Statistical features of the data Persistent and endogeneous predictors are common in predictive regression models and from recent studies it is clear that heteroskedasticity is also a strong characteristic of the predictive regression model. We check whether these statistical features are also present in our data set. We begin with the persistency of the CPI—the predictor variable. We do this by using the augmented Dickey and Fuller, 1981 unit root test, which examines the null hypothesis of a unit root. The results are reported in column 3 of Table 1; in column 2, we also test for a unit root in gold returns. The ADF regression model includes a constant and a time trend when CPI is used and includes only a constant when gold returns are used. This is because gold returns do not contain a time trend whereas the CPI series is trending. The test statistic and the p-value are reported for each series, as is the estimated lag length, which is obtained by using the Schwarz Information Criteria (starting with a maximum of eight lags). According to the ADF test, the unit root null is rejected for the CPI series of five countries, namely, Korea, Norway, the Netherlands, the Philippines, and Senegal. For the rest of the countries, CPI is found to be non-stationary. On the other hand, for the gold price returns (world), the unit root null is rejected at the 1% level for all different sample sizes. Even though one rejects the unit root null hypothesis, this does not imply lack of persistency. For this reason and to get a feel of the degree of persistency, we further examine the persistency of our predictor variable (CPI) for all 54 countries. In this pursuit, we report the estimated first-order autoregressive (AR) coefficient of the CPI variable in Table 2. We find that for all those countries for which the null is rejected, and similar to the 49 countries for which the null is not rejected, the AR coefficient is very close or equal to one. This is a sign of high persistency.

S.S. Sharma / Economic Modelling 55 (2016) 269–278

273

Table 3 Results for endogeneity test. This table reports endogeneity test results. This test is based on regressing the error term from the predictive regression model on the error term from the AR(1) model of the predictor variable. **, *** denote statistical significance at the 5%, and 1% levels, respectively. Country

θ

t-stat

p-value

Country

θ

t-stat

p-value

Argentina Australia Barbados Brazil Canada Chile Colombia Congo Costa Rica Cyprus Dominican Republic Egypt Fiji Finland France Germany Greece Guatemala Guyana Iceland India Iran Israel Italy Jamaica Japan Kenya

−2.130 7.698 37.272** −2.901 6.882 4.074 2.603 4.036 −17.682 5.255 0.512 −6.580 5.578 0.052 0.347 −0.050 −0.019 12.131 5.489 −1.300 −1.744 −2.845 2.856 1.338 14.827 1.693 10.665

−1.110 0.714 2.205 −1.374 0.407 1.153 0.369 0.550 −1.636 0.419 0.365 −0.861 0.338 0.037 0.066 −0.123 −0.035 0.991 0.829 −0.199 −0.226 −0.829 0.701 0.392 1.371 0.415 0.888

0.267 0.475 0.028 0.170 0.684 0.249 0.712 0.583 0.102 0.675 0.715 0.390 0.735 0.970 0.948 0.902 0.972 0.322 0.407 0.842 0.822 0.407 0.483 0.695 0.171 0.679 0.375

Korea Republic Malaysia Malta Mauritius Mexico Netherlands Norway Pakistan Paraguay Peru Philippines Portugal Senegal South Africa Sri Lanka Sweden Switzerland Thailand Trinidad and Tobago Tunisia Turkey Turkish Republic Of Northern Cyprus UK Uruguay US Venezuela Zimbabwe

4.726 69.277*** 6.166 19.373** 10.390 5.826 8.158 −10.270 8.166 −1.287 6.392 8.441 −10.540 13.400 −0.168 12.118 4.314 0.381 −1.452 −1.894 −6.220 12.577** 14.588 −0.082 23.488** −4.586 0.514

1.450 2.879 0.377 2.411 1.420 0.494 0.547 −0.681 1.176 −0.721 0.656 0.875 −1.113 0.699 −0.129 1.443 0.210 0.233 −0.132 −0.203 −1.118 2.100 1.304 −0.252 2.028 −0.663 0.614

0.147 0.004 0.706 0.016 0.156 0.621 0.585 0.496 0.240 0.471 0.512 0.382 0.266 0.485 0.898 0.149 0.834 0.816 0.895 0.839 0.264 0.036 0.192 0.801 0.043 0.508 0.539

Thus, we conclude that the CPI is in fact unit root non-stationary in all predictive regressions. We now turn to the results for heteroskedasticity reported in Table 2. We perform a Lagrange multiplier (LM) test for heteroskedasticity. We apply the LM test to CPI and gold price returns series by filtering each of these two series through a fourth-order AR model. According to the results, the null hypothesis of no ARCH in the gold price returns is rejected at the 1% level for all countries. The results for the CPI series are more mixed, with the no ARCH null hypothesis being rejected for only 42 countries. The evidence of heteroskedasticity in the CPI series is still strong. Finally, we search for the evidence that CPI is endogenous. Results on endogeneity test are reported in Table 3; specifically, we report the OLS estimates of θ in model (3) after replacing εGR ,t and εCPI,t with the estimated OLS residuals from (1) and (2), respectively. Our results indicate, unlike the strong evidence that CPI is persistent and are characterised by ARCH, that CPI is only endogenous for five countries, namely, Barbados, Malaysia, Mauritius, Turkish Republic of Northern Cyprus, and Uruguay. From these results, this is what we conclude. Overall, our findings indicate that while endogeneity is not a serious concern, CPI is strongly persistent and heteroskedastic.6 This implies the need for addressing these issues in estimating the predictive regression models. Thus, we conclude that using the procedure proposed by Westerlund and Narayan (2012) is ideal because it jointly accounts for persistency and heteroskeasticity. 3.2. In-sample predictability test results In Table 4, we report the in-sample WN-GLS predictability test results for horizon one, that is h = 1. We report the asymptotic GLS 6 Even though we find that endogeneity is not a serious concern, the change in the predictor variable is included by construction in the empirical framework as it deals with both persistency and endogeneity simultaneously. The idea is that if at least one of these two statistical issues are present, the change in the predictor variable (CPI) will need to be included in the predictive regression model. Therefore, if there is no endogeneity, as in our case, we do not compromise anything by including the change in the predictor variable.

coefficient and its corresponding t-statistic for each country. Our results reveal that CPI is able to predict gold price returns of only 10 countries. These countries are Australia, Canada, Germany, India, Sweden,

Table 4 In-sample predictability test results. This table reports in-sample predictability test results. The results are reported at horizon equal to one, h = 1. We report the t-statistics associated with the null hypothesis of no predictability. *, (**), *** denote statistical significance at the 10%, 5%, and 1% levels, respectively. Country

Coefficient t-value Country

Coefficient t-value

Argentina Australia Barbados Brazil Canada Chile Colombia Congo Costa Rica Cyprus Dominican Republic Egypt Fiji Finland France Germany Greece Guatemala Guyana Iceland India Iran

0.009 0.120** 0.107 0.011 0.158* 0.020 0.042 0.127 0.060 0.172 0.072

1.022 1.837 0.873 1.239 1.692 1.512 1.316 1.108 1.178 1.065 1.158

Korea Republic Malaysia Malta Mauritius Mexico Netherlands Norway Pakistan Paraguay Peru Philippines

0.076 0.200 0.191 0.073 0.036 0.161 0.129 0.108 0.056 0.014 0.084

1.220 0.839 0.816 0.679 1.267 1.752 1.610 1.048 1.119 1.257 1.064

0.084 0.119 0.070 0.057 0.010** 0.007 0.082 0.056 0.035 0.109* 0.070

1.479 0.893 1.475 1.565 2.142 0.997 0.892 0.722 1.002 1.689 1.546

0.061 0.133 0.094 0.105 0.130* 0.230* 0.138 0.093 0.120 0.028 0.028

1.073 1.020 1.584 1.151 1.693 1.684 0.902 1.129 0.842 1.421 1.008

Israel Italy Jamaica Japan Kenya

0.023 0.045 0.056 0.042 0.075

1.230 1.343 1.172 1.171 0.944

Portugal Senegal South Africa Sri Lanka Sweden Switzerland Thailand Trinidad and Tobago Tunisia Turkey Turkish Republic Of Northern Cyprus UK Uruguay US Venezuela Zimbabwe

0.119* 0.067* 0.166*** 0.050 0.026*

1.688 1.760 2.747 1.201 1.647

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Table 5 Out-of-sample evaluation — Theil U statistics. This table reports results on out-of-sample predictability based on the Theil U statistics. The Theil U statistic measures the performance of our predictive regression model vis-à-vis the constant returns model. The out-of-sample period for each country is set to 75%, 50%, and 25%, respectively. The results are reported for a one-period forecasting horizon, h=1. Country

Out-of-sample period

Theil U

Country

Out-of-sample period

Theil U

Argentina

1953M05–2014M04 1973M09–2014M04 1994M01–2014M04 1937M05–2014M03 1962M12–2014M03 1988M07–2014M03 1965M03–2014M02 1981M07–2014M02 1997M10–2014M02 1957M01–2014M04 1976M02–2014M04 1995M03–2014M04 1939M01–2014M04 1964M02–2014M04 1989M03–2014M04 1945M10–2014M04 1968M08–2014M04 1991M06–2014M04 1950M04–2014M04 1971M08–2014M04 1992M12–2014M04 1964M07–2014M04 1981M02–2014M04 1997M09–2014M04 1956M04–2014M04 1975M08–2014M04 1994M12–2014M04 1964M07–2014M04 1981M02–2014M04 1997M09–2014M04 1958M07–2014M04 1977M02–2014M04 1995M09–2014M04 1944M04–2014M04 1967M08–2014M04 1990M12–2014M04 1965M03–2013M12 1981M06–2013M12 1997M09–2013M12 1943M07–2014M04 1967M02–2014M04 1990M09–2014M04 1939M10–2014M04 1964M08–2014M04 1989M06–2014M04 1898M07–1984M04 1927M02–1984M04 1955M09–1984M04 1945M08–2014M04 1968M07–2014M04 1991M05–2014M04 1963M01–2014M04 1980M02–2014M04 1997M03–2014M04 1965M03–2013M12 1981M06–2013M12 1997M09–2013M12 1957M10–2014M04 1976M08–2014M04 1995M06–2014M04 1943M12–2014M03 1967M05–2014M03 1990M10–2014M03 1955M07–2014M03 1975M02–2014M03 1994M08–2014M03 1945M06–2014M04 1968M05–2014M04 1991M04–2014M04 1943M07–2014M04 1967M02–2014M04 1990M09–2014M04

1.118 1.089 1.000 1.000 0.995 0.995 1.269 1.033 0.997 1.140 1.093 1.000 1.063 1.016 0.998 1.052 1.012 1.001 1.009 1.007 0.997 1.029 1.042 0.991 1.005 1.000 0.997 1.297 1.154 0.997 1.003 1.001 0.997 0.997 0.997 0.994 1.471 1.077 0.997 0.996 0.995 0.992 0.996 0.996 0.993 1.083 1.001 1.000 1.000 1.001 1.000 1.050 1.053 1.004 0.999 1.010 1.001 1.005 1.000 0.997 0.997 0.994 0.991 1.003 1.000 0.995 1.061 1.026 1.000 0.998 0.998 0.995

Korea Republic

1964M07–2014M04 1981M02–2014M04 1997M09–2014M04 1964M07–2014M04 1981M02–2014M04 1997M09–2014M04 1965M11–2014M03 1981M12–2014M03 1998M01–2014M03 1965M03–2014M03 1981M07–2014M03 1997M11–2014M03 1954M01–2014M04 1974M02–2014M04 1994M03–2014M04 1942M10–2014M04 1966M08–2014M04 1990M06–2014M04 1943M07–2014M04 1967M02–2014M04 1990M09–2014M04 1965M04–2014M02 1981M07–2014M02 1997M10–2014M02 1962M04–2014M04 1979M08–2014M04 1996M12–2014M04 1946M07–2014M04 1969M02–2014M04 1991M09–2014M04 1962M06–2014M04 1979M09–2014M04 1996M12–2014M04 1951M01–2014M04 1972M02–2014M04 1993M03–2014M04 1964M09–2014M04 1981M03–2014M04 1997M09–2014M04 1944M03–2014M03 1967M07–2014M03 1990M11–2014M03 1957M09–2014M04 1976M07–2014M04 1995M05–2014M04 1940M07–2014M04 1965M02–2014M04 1989M09–2014M04 1943M07–2014M04 1967M02–2014M04 1990M09–2014M04 1964M07–2014M04 1981M02–2014M04 1997M09–2014M04 1958M03–2014M03 1976M11–2014M03 1995M07–2014M03 1963M09–2013M12 1980M06–2013M12 1997M03–2013M12 1951M01–2014M04 1972M02–2014M04 1993M03–2014M04 1964M07–2014M04 1981M02–2014M04 1997M09–2014M04 1939M01–2014M04 1964M02–2014M04 1989M03–2014M04 1957M01–2014M04 1976M02–2014M04 1995M03–2014M04

0.993 0.996 0.989 2.017 1.290 1.035 1.741 1.110 1.025 1.316 1.024 1.009 1.022 1.015 0.999 1.021 1.000 0.992 1.014 0.999 0.994 1.063 1.017 0.997 1.000 0.999 0.996 1.510 1.145 1.002 1.015 1.021 0.994 0.996 0.995 0.995 1.058 1.057 0.993 0.995 0.995 0.993 1.143 1.126 0.998 1.044 1.013 0.998 1.110 1.057 1.017 1.122 1.081 1.003 1.010 1.010 0.995 1.138 1.194 0.998 1.107 1.070 1.001 1.172 0.999 0.999 1.015 1.001 0.994 0.992 0.995 0.987

Australia

Barbados

Brazil

Canada

Chile

Colombia

Congo

Costa Rica

Cyprus

Dominican Republic

Egypt

Fiji

Finland

France

Germany

Greece

Guatemala

Guyana

Iceland

India

Iran

Israel

Italy

Malaysia

Malta

Mauritius

Mexico

Netherlands

Norway

Pakistan

Paraguay

Peru

Philippines

Portugal

Senegal

South Africa

Sri Lanka

Sweden

Switzerland

Thailand

Trinidad and Tobago

Tunisia

Turkey

Turkish Republic of Northern Cyprus

UK

Uruguay

S.S. Sharma / Economic Modelling 55 (2016) 269–278

275

Table 5 (continued) Country

Out-of-sample period

Theil U

Country

Out-of-sample period

Theil U

Jamaica

1958M03–2014M03 1976M11–2014M03 1995M07–2014M03 1945M01–2014M04 1968M02–2014M04 1991M03–2014M04 1964M06–2013M12 1980M12–2013M12 1997M06–2013M12

1.014 1.005 0.997 0.997 0.997 0.994 1.003 1.008 0.998

US

1904M04–1990M01 1932M11–1990M01 1961M06–1990M01 1957M09–2013M12 1976M06–2013M12 1995M03–2013M12 1951M01–2014M04 1972M02–2014M04 1993M03–2014M04

1.000 1.000 1.010 1.006 1.009 1.001 3.538 2.398 1.144

Japan

Kenya

Venezuela

Zimbabwe

Switzerland, the UK, Uruguay, the US, and Zimbabwe. For the rest of the 44 countries, we find that the null hypothesis of no predictability cannot be rejected.7 3.3. Out-of-sample predictability test results The controversy regarding in-sample and out-of-sample evidence of predictability is now well-known (see Inoue and Kilian, 2004). Several relatively recent studies on stock return predictability find that insample evidence of predictability is not corroborated by out-ofsample tests. Welch and Goyal (2008), among others, document the poor out-of-sample forecasting power of financial ratios in predicting returns. Yet, there are others, such as Rapach et al. (2010), who show that out-of-sample return predictability outperforms random walk models. In short, there is tension on this front, and consensus has not been established when it comes to in-sample and out-of-sample predictability. In this section, we consider the out-of-sample forecasting evaluation. Here, we test the performance of the CPI-based predictability model against the constant returns (benchmark model) model. We follow the literature and consider three out-of-sample periods (25%, 50%, and 75%) for evaluation. Given that different countries have different sample periods, the out-of-sample periods are dependent on data availability for different countries. We compute out-of-sample forecasts based on unrestricted model which in our case is given by Eq. (1). We then restrict the unrestricted model by setting β = 0, which then becomes a constant returns model (restricted model): GRtþ1 ¼ α þ εtþ1

ð6Þ

We follow Westerlund and Narayan (2012) and use FGLS to obtain the in-sample estimates of the parameters of Eq. (1), which we then use to forecast out-of-sample. We repeat the same step for the restricted model. Thus, this allows us to compare the forecasting performance of a constant returns model with our proposed predictive regression model, where we use CPI as a predictor variable. To make the comparison between these two models, we use two commonly-known forecasting evaluation statistics, namely, the relative Theil U and out-of-sample R2 (OOS_R2) statistics. The relative Theil U statistic is simply the ratio of the root mean squared forecast error (RMSFE) for the CPI-based predictive regression model (restricted model) forecasts to the RMSFE for the constant returns model forecasts. Given this, if the Theil U statistic is equal to the value one, then both restricted and unrestricted models are equally good at predicting gold returns, whereas if the Theil U statistic is larger than the value one, then the restricted model is considered superior and vice versa. These results are reported in Table 5. The results are estimated and recorded over three different out-of-sample periods and these out-of-sample periods are reported in column 2. 7 In this study, we have also considered the Narayan and Popp (2010) test to extract two structural break dates for each country's gold price returns. We then used the break dates as dummy variables in the predictive regression model (Eq. (4)). The structural break-based predictive regression model did not perform well, suggesting that there is no role for structural breaks in our hypothesis test. Tabulated results are available upon request.

Reading the results when we consider a short out-of-sample (25%) period, we find that the Theil U statistic is greater than the value one and equal to the value one in the case of 13 and five countries, respectively. This implies that the constant predictive regression model outperforms the unrestricted model (or preferred CPI-based model) for 13 countries. These countries are Chile, Guatemala, Guyana, Malaysia, Malta, Mauritius, Peru, Switzerland, Thailand, Turkey, Venezuela, the US, and Zimbabwe. Moreover, in the case of five countries (Argentina, Brazil, Germany, Israel, and Greece) both statistics from restricted and unrestricted models are equally good at predicting gold price returns. For the rest of the 36 countries, we find that the CPI-based predictive regression model is able to outperform the constant returns model. However, when we consider 50% and 75% out-of-sample periods, we find weak evidence that the unrestricted model outperforms the restricted model. For instance, when we consider a 50% out-of-sample period, the CPI-based predictive regression model outperforms the constant returns model in the case of 14 countries, and when we consider 75% out-of-sample period, the unrestricted model outperforms the restricted model for only 11 countries. Next, we also use the relatively more popular out-of-sample R2 (OOS_R2) test developed by Campbell and Thompson (2008). This test statistic is now widely used in empirical applications in the financial economics literature (see Narayan et al., 2013a, 2014a,b). One can interpret the OOS_R2 statistic as follows. If the OOS_R2 is positive, this implies that the unrestricted model outperforms the restricted model. In other words, the predictive regression has a lower average meansquared prediction error than the historical average return. The OOS_R2 is computed as follows: 2 XT  GRt −GR ̂t t¼1 OOS R ¼ 1− X  2 T GRt −GRt t¼1 2

ð7Þ

where GR ̂ is the fitted value from the predictive regression estimated through period t − 1, and GR is the historical average return estimated through period t − 1. The result on OOS_R2 is reported in Table 6. When we consider a relatively short out-of-sample period (25%), the OOS_R2 is positive at h= 1 in the case of 39 countries. This implies that for these 39 countries (except in the case of Chile, Germany, Greece, Guatemala, Guyana, Malaysia, Malta, Mauritius, Peru, Switzerland, Thailand, Turkey, the US, Venezuela, and Zimbabwe), our proposed predictive regression model is able to outperform the constant returns model. However, when we consider long (75%) and balanced (50%) out-of-sample periods, the OOS_R2 statistic is only positive in the case of 13 and 19 countries, respectively. Finally, to check the robustness of our out-of-sample predictability results, we evaluate both Theil U and OOS_R2 statistics by setting a longer horizon, that is h = 6. The robustness check results are reported in Table 7. The Theil U and OOS_R2 statistics at h = 6 are fairly consistent with the findings we reported at h = 1. For instance, reading the results when we consider a short out-of-sample period (25%), we find that the Theil U statistic is less than the value one in the case of 30 countries. Similarly, the OOS_R2 is found to be positive in the case of 33 countries.

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Table 6 Out-of-sample R2 statistics. This table reports results on out-of-sample predictability based on Campbell and Thompson OOS_R2 statistic. The OOS_R2 statistic measures the performance of our predictive regression model vis-à-vis the constant returns model. The out-of-sample period for each country is set to 75%, 50%, and 25%, respectively. The results are reported for one-period forecasting horizon, h=1. Country

Out-of-sample period

OOS_R2

Country

Out-of-sample period

Argentina

1953M05–2014M04 1973M09–2014M04 1994M01–2014M04 1937M05–2014M03 1962M12–2014M03 1988M07–2014M03 1965M03–2014M02 1981M07–2014M02 1997M10–2014M02 1957M01–2014M04 1976M02–2014M04 1995M03–2014M04 1939M01–2014M04 1964M02–2014M04 1989M03–2014M04 1945M10–2014M04 1968M08–2014M04 1991M06–2014M04 1950M04–2014M04 1971M08–2014M04 1992M12–2014M04 1964M07–2014M04 1981M02–2014M04 1997M09–2014M04 1956M04–2014M04 1975M08–2014M04 1994M12–2014M04 1964M07–2014M04 1981M02–2014M04 1997M09–2014M04 1958M07–2014M04 1977M02–2014M04 1995M09–2014M04 1944M04–2014M04 1967M08–2014M04 1990M12–2014M04 1965M03–2013M12 1981M06–2013M12 1997M09–2013M12 1943M07–2014M04 1967M02–2014M04 1990M09–2014M04 1939M10–2014M04 1964M08–2014M04 1989M06–2014M04 7/1/1898–1984M04 1927M02–1984M04 1955M09–1984M04 1945M08–2014M04 1968M07–2014M04 1991M05–2014M04 1963M01–2014M04 1980M02–2014M04 1997M03–2014M04 1965M03–2013M12 1981M06–2013M12 1997M09–2013M12 1957M10–2014M04 1976M08–2014M04 1995M06–2014M04 1943M12–2014M03 1967M05–2014M03 1990M10–2014M03 1955M07–2014M03 1975M02–2014M03 1994M08–2014M03 1945M06–2014M04 1968M05–2014M04 1991M04–2014M04 1943M07–2014M04 1967M02–2014M04 1990M09–2014M04

−0.249 −0.186 0.001 −0.001 0.011 0.011 −0.609 −0.067 0.007 −0.301 −0.194 0.001 −0.131 −0.032 0.004 −0.108 −0.025 −0.002 −0.019 −0.013 0.005 −0.058 −0.085 0.018 −0.010 0.000 0.007 −0.681 −0.332 0.005 −0.007 −0.001 0.007 0.006 0.006 0.012 −1.164 −0.160 0.006 0.009 0.010 0.016 0.007 0.008 0.014 −0.174 −0.001 −0.001 −0.001 −0.001 −0.001 −0.102 −0.108 −0.007 0.003 −0.020 −0.002 −0.009 0.000 0.007 0.005 0.013 0.017 −0.005 0.001 0.011 −0.125 −0.053 0.000 0.005 0.005 0.010

Korea Republic

1964M07–2014M04 1981M02–2014M04 1997M09–2014M04 1964M07–2014M04 1981M02–2014M04 1997M09–2014M04 1965M11–2014M03 1981M12–2014M03 1998M01–2014M03 1965M03–2014M03 1981M07–2014M03 1997M11–2014M03 1954M01–2014M04 1974M02–2014M04 1994M03–2014M04 1942M10–2014M04 1966M08–2014M04 1990M06–2014M04 1943M07–2014M04 1967M02–2014M04 1990M09–2014M04 1965M04–201M02 1981M07–2014M02 1997M10–2014M02 1962M04–2014M04 1979M08–2014M04 1996M12–2014M04 1946M07–2014M04 1969M02–2014M04 1991M09–2014M04 1962M06–2014M04 1979M09–2014M04 1996M12–2014M04 1951M01–2014M04 1972M02–2014M04 1993M03–2014M04 1964M09–2014M04 1981M03–2014M04 1997M09–2014M04 1944M03–2014M03 1967M07–2014M03 1990M11–2014M03 1957M09–2014M04 1976M07–2014M04 1995M05–2014M04 1940M07–2014M04 1965M02–2014M04 1989M09–2014M04 1943M07–2014M04 1967M02–2014M04 1990M09–2014M04 1964M07–2014M04 1981M02–2014M04 1997M09–2014M04 1958M03–2014M03 1976M11–2014M03 1995M07–2014M03 1963M09–2013M12 1980M06–2013M12 1997M03–2013M12 1951M01–2014M04 1972M02–2014M04 1993M03–2014M04 1964M07–2014M04 1981M02–2014M04 1997M09–2014M04 1939M01–2014M04 1964M02–2014M04 1989M03–2014M04 1957M01–2014M04 1976M02–2014M04 1995M03–2014M04

Australia

Barbados

Brazil

Canada

Chile

Colombia

Congo

Costa Rica

Cyprus

Dominican Republic

Egypt

Fiji

Finland

France

Germany

Greece

Guatemala

Guyana

Iceland

India

Iran

Israel

Italy

Malaysia

Malta

Mauritius

Mexico

Netherlands

Norway

Pakistan

Paraguay

Peru

Philippines

Portugal

Senegal

South Africa

Sri Lanka

Sweden

Switzerland

Thailand

Trinidad and Tobago

Tunisia

Turkey

Turkish Republic of Northern Cyprus

UK

Uruguay

OOS_R2 0.015 0.007 0.022 −3.069 −0.663 −0.071 −2.030 −0.233 −0.051 −0.731 −0.049 −0.017 −0.045 −0.030 0.003 −0.043 0.001 0.015 −0.028 0.003 0.013 −0.130 −0.034 0.006 0.000 0.003 0.008 −1.279 −0.311 −0.003 −0.031 −0.043 0.011 0.009 0.009 0.009 −0.119 −0.118 0.014 0.011 0.010 0.013 −0.307 −0.269 0.004 −0.089 −0.026 0.005 −0.233 −0.118 −0.034 −0.260 −0.169 −0.006 −0.020 −0.020 0.010 −0.296 −0.425 0.004 −0.225 −0.154 −0.002 −0.375 0.002 0.002 −0.029 −0.001 0.012 0.015 0.010 0.025

S.S. Sharma / Economic Modelling 55 (2016) 269–278

277

Table 6 (continued) Country

Out-of-sample period

OOS_R2

Country

Out-of-sample period

OOS_R2

Jamaica

1958M03–2014M03 1976M11–2014M03 1995M07–2014M03 1945M01–2014M04 1968M02–2014M04 1991M03–2014M04 1964M06–2013M12 1980M12–2013M12 1997M06–2013M12

−0.028 −0.010 0.006 0.006 0.006 0.013 −0.007 −0.016 0.004

US

1904M04–1990M01 1932M11–1990M01 1961M06–1990M01 1957M09–2013M12 1976M06–2013M12 1995M03–2013M12 1951M01–2014M04 1972M02–2014M04 1993M03–2014M04

0.000 0.000 −0.020 −0.013 −0.018 −0.002 −11.518 −4.752 −0.308

Japan

Kenya

Venezuela

Zimbabwe

The Theil U and OOS_R2statistics at h = 6 do not support our proposed CPI-based predictive regression model, whereas it was supported when the horizon was set at h = 1, only in the case of five countries, namely, Barbados, Cyprus, Fiji, Pakistan, and the Turkish Republic of Northern Cyprus. There are four key messages emerging from the overall predictability analysis of gold price returns using CPI as a predictor variable. First, we find weak evidence that CPI can predict gold returns using a popular predictive regression model based on the FGLS estimator. This evidence that CPI predicts gold price returns is only supported in the case of 10 countries. These countries are Australia, Canada, Germany, India, Sweden, Switzerland, the UK, Uruguay, the US, and Zimbabwe. Second, we find that out of these 10 countries for which predictability is found only for six countries (Australia, Canada, India, Sweden, Uruguay and the UK) predictability is supported by the out-of-sample matrices, namely, the Theil U and OOS_R2 statistics. For the rest of the four countries (Zimbabwe, Germany, Switzerland, and the US) the out-of-sample predictability tests fail to support the fact that our proposed CPI-based predictability model predicts gold price returns. Third, out of 44 countries where we do not reject the null of no predictability using the in-sample predictability test, the out-of-sample matrices (both Theil U and OOS_R2) provide strong evidence that our proposed CPI-based predictive regression model outperforms the constant returns model in the case of 25 countries when we set the out-of-sample period to 25%. It is important to note that Rapach et al. (2010), Westerlund and Narayan (2012, 2015b), Narayan et al.

(2014a,b), and Makin et al. (2014) argue that either 25%, 50% or 75% out-of-sample periods should be sufficient to address the question of whether or not there is out-of sample predictability. Thus, in light of our small sample size, we choose 25% out of sample period to conclude our results considering the fact that our analysis is done using data with small sample size. This seems to work best in finite samples. 4. Concluding remarks In this paper, we test whether CPI can predict gold price returns. Our empirical analysis is based on monthly data and covers a large number of countries. We have a sample of 54 countries. We use a newly developed predictive regression estimator that tests the null hypothesis of no predictability. Our in-sample predictability test results reveal that CPI can predict gold price returns for only 10 countries, namely, Australia, Canada, Germany, India, Sweden, Switzerland, the UK, Uruguay, the US, and Zimbabwe. We also evaluate the out-of-sample forecasts on a pair-wise basis using the well-known Theil U statistic and the popular OOS_R2 statistic. Our proposed CPI-based predictive regression model is compared with the constant returns model (benchmark model). Models are evaluated using three different out-of-sample periods, that is, 25%, 50%, and 75%, and at two different horizons, h= 1 and h= 6 in order to gauge the robustness of the results. Our results suggest that an out-of-sample size set to 25% offers greater and stronger (relatively to in-sample evidence) evidence of gold price return predictability.

Table 7 Robustness test. This table reports out-of-sample relative Theil U and Campbell and Thompson OOS_R2 statistics at h=6. Country

Out-of-sample period

Theil U

OOS_R2

Country

Out-of-sample period

Theil U

OOS_R2

Argentina Australia Barbados Brazil Canada Chile Colombia Congo Costa Rica Cyprus Dominican Republic Egypt Fiji Finland France Germany Greece Guatemala Guyana Iceland India Iran Israel Italy Jamaica Japan Kenya

1994M01–2014M04 1988M07–2014M03 1997M10–2014M02 1995M03–2014M04 1989M03–2014M04 1991M06–2014M04 1992M12–2014M04 1997M09–2014M04 1994M12–2014M04 1997M09–2014M04 1995M09–2014M04 1990M12–2014M04 1997M09–2013M12 1990M09–2014M04 1989M06–2014M04 1955M09–1984M04 1991M05–2014M04 1997M03–2014M04 1997M09–2013M12 1995M06–2014M04 1990M10–2014M03 1994M08–2014M03 1991M04–2014M04 1990M09–2014M04 1995M07–2014M03 1991M03–2014M04 1997M06–2013M12

1 0.993 1.002 1 0.995 1.001 0.997 0.991 0.997 1 0.997 0.994 1.003 0.991 0.993 1 1 1.006 1.004 0.997 0.99 0.995 1 0.995 0.997 0.994 0.999

0.001 0.014 −0.004 0.001 0.01 −0.002 0.005 0.018 0.006 −0.001 0.006 0.013 −0.005 0.017 0.014 −0.001 −0.001 −0.012 −0.008 0.006 0.019 0.009 0 0.01 0.006 0.012 0.002

Korea Republic Malaysia Malta Mauritius Mexico Netherlands Norway Pakistan Paraguay Peru Philippines Portugal Senegal South Africa Sri Lanka Sweden Switzerland Thailand Trinidad and Tobago Tunisia Turkey Turkish Republic of Northern Cyprus UK Uruguay US Venezuela Zimbabwe

1997M09–2014M04 1997M09–2014M04 1998M01–2014M03 1997M11–2014M03 1994M03–2014M04 1990M06–2014M04 1990M09–2014M04 1997M10–2014M02 1996M12–2014M04 1991M09–2014M04 1996M12–2014M04 1993M03–2014M04 1997M09–2014M04 1990M11–2014M03 1995M05–2014M04 1989M09–2014M04 1990M09–2014M04 1997M09–2014M04 1995M07–2014M03 1997M03–2013M12 1993M03–2014M04 1997M09–2014M04 1989M03–2014M04 1995M03–2014M04 1961M06–1990M01 1995M03–2013M12 1993M03–2014M04

0.987 1.045 1.026 1.013 0.999 0.993 0.991 1.001 0.995 1.002 0.994 0.996 0.992 0.992 1.002 0.999 1.009 1.006 0.997 0.997 1.001 1 0.992 0.986 1.024 1.002 1.163

0.026 −0.092 −0.053 −0.025 0.003 0.013 0.019 −0.003 0.009 −0.004 0.013 0.009 0.016 0.015 −0.005 0.003 −0.018 −0.012 0.007 0.006 −0.002 −0.001 0.016 0.028 −0.048 −0.003 −0.353

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On the whole, we find reasonable evidence that gold price returns are predictable using CPI. There are two main implications of our findings. The first implication is that one should not just depend on insample tests for predictability. As the applied econometrics literature argues, both in-sample and out-of-sample tests are important, and in fact the applied forecasting literature shows that out-of-sample tests offer stronger outcomes in favour of predictability. Our results support both the applied and theoretical literature on forecasting returns. The second implication is that because gold price returns are predictable, successful trading strategies can be devised by investors in the gold market. This finding is supported by studies which actually estimate profits in the gold market; see, for instance, Narayan et al. (2013a, 2015b). Acknowledgement I acknowledge helpful comments and suggestions from two anonymous referees of this journal. Helpful comments on earlier versions of this paper from Dr. Sagarika Mishra, Dr. Kannan Thuraisamy, and Dr. Dinh Phan are also acknowledged. References Adrangi, B., Chatrath, A., Raffiee, 2003. Economic activity, inflation, and hedging: the case of gold and silver investments. J. Wealth Manag. 6, 60–77. Ang, A., Bekaert, G., 2007. Return predictability: is it there? Rev. Financ. Stud. 20, 651–707. Ashley, R., Granger, C.W.J., Schmalensee, R., 1980. Advertising and aggregate consumption: an analysis of causality. Econometrica 48, 1149–1167. Batten, J.A., Ciner, C., Lucey, B.M., 2014. On the economic determinants of the goldinflation relation. Res. Policy 41, 101–108. Blose, L.E., 2010. Gold prices, cost of carry, and expected inflation. J. Econ. Bus. 62, 35–47. Bossaerts, P., Hillion, P., 1999. Implementing statistical criteria to select return forecasting models: what do we learn? Rev. Financ. Stud. 12, 405–428. Brennan, M., Xia, Y., 2005. Tay's as good as cay. Finance Res. Lett. 2, 1–14. Butler, A., Grullon, G., Weston, J., 2005. Can managers forecast aggregate market return? J. Financ. 60, 963–986. Campbell, J.Y., Thompson, S.B., 2008. Predicting excess stock returns out of sample: can anything beat the historical average? Rev. Financ. Stud. 21 (4), 1509–1531. Christie-David, R., Chaudhry, M., Koch, T.W., 2000. Do macroeconomics news releases affect gold and silver prices? J. Econ. Bus. 52, 405–421. Cui, C., 2009. Gold Retains Its Allure. Eastern ed. Wall Street J. 253(75) p. C9. Dickey, D.A., Fuller, W.A., 1981. Distribution of the estimators for autoregressive time series with a unit root. Econometrica 49, 1057–1072. Feldstein, M., 1980. Inflation, tax rules, and the prices of land and gold. J. Public Econ. 14, 309–317. Fortune, J.N., 1987. The inflation rate of the price of gold, expected prices and interest rates. J. Macroecon. 9, 71–82. Foster, F.D., Smith, T., Whaley, R.E., 1997. Assessing goodness-of-fit of asset pricing models: the distribution of the maximal R2. J. Financ. 53, 591–607. Ghosh, D., Levin, E.J., Macmillan, P., Wright, R.E., 2004. Gold as an inflation hedge? Stud. Econ. Finance 22, 1–25. Goyal, A., Welch, I., 2003. Predicting the equity premium with dividend ratios. Manag. Sci. 49, 639–654. Inoue, A., Kilian, L., 2004. In-sample or out-of-sample tests of predictability: which one should we use? Econ. Rev. 23, 371–402. Jaffe, J., 1989. Gold and Gold Stocks as Investments for Institutional Portfolios. Financial Analysts Journal 45, 53–59. Lawrence, C. (2003). Why is gold different from other assets? an empirical investigation. In Research manuscript. London, UK: World Gold Council. Lehman, R., 2009. Prepare for inflation. Forbes 183 (7), 106.

Levin, E.J., Montagnoli, A., Wright, R.E., 2006. Short-run and long-run determinants of the price of gold. World Gold Council. Research Study No. 32. Levin, E., Abhyankar, A., Ghosh, D., 1994. Does the gold market reveal real interest rates? Manch. Sch. 62, 93–103. Lo, A.W., MacKinlay, A.C., 1990. Data-snooping biases in tests of financial asset pricing models. Rev. Financ. Stud. 3, 431–467. Mahdavi, S., Zhou, S., 1997. Gold and commodity prices as leading indicators of inflation: tests of long-run relationship and predictive performance. J. Econ. Bus. 49, 475–489. Makin, A.J., Narayan, P.K., Narayan, S., 2014. What expenditure does Anglosphere foreign borrowing fund? J. Int. Money Financ. 40, 63–78. Moore, G.H., 1990. Gold prices and a leading index of inflation. Challenge 33, 52–56. Narayan, P.K., Sharma, S.S., 2015. Is carbon emissions trading profitable? Econ. Model. 47, 84–92. Narayan, P.K., Sharma, S.S., Thuraisamy, K.S., 2015a. Can governance quality predict stock market returns? New global evidence. Pac. Basin Financ. J. 35, 367–380. Narayan, P., Narayan, S., Sharma, S., 2013a. An analysis of commodity markets: what gain for investors? J. Bank. Financ. 37 (10), 3878–3889. Narayan, P., Sharma, S., Bannigidadmath, D., 2013b. Does tourism predict macroeconomic performance in Pacific Island countries? Econ. Model. 33, 780–786. Narayan, P., Sharma, S., Poon, W., Westerlund, J., 2014c. Do oil prices predict economic growth? New global evidence. Energy Econ. 41, 137–146. Narayan, P.K., Popp, S., 2010. A new unit root test with two structural breaks in level and slope at unknown time. J. Appl. Stat. 37 (9), 1425–1438. Narayan, P.K., Ahmed, H.A., Sharma, S., K.P., Prabheesh, 2014b. How profitable is the Indian stock market? Pac. Basin Financ. J. 30, 44–61. Narayan, P.K., Narayan, S., Thuraisamy, K.S., 2014a. Can institutions and macroeconomic factors predict stock returns in emerging markets? Emerg. Mark. Rev. 19, 77–95. Narayan, P.K., Ahmed, H.A., Narayan, S., 2015b. Do momentum-based trading strategies work in the commodity futures markets? J. Futur. Mark. 35, 868–891. O'Connor, F.A., Lucey, B.M., Batten, J.A., Baur, D.G., 2015. The financial economics of gold — a survey. Int. Rev. Financ. Anal. 41, 186–205. Phan, D.H.B., Sharma, S.S., Narayan, P.K., 2015. Stock return forecasting: some new evidence. Int. Rev. Financ. Anal. 40, 38–51. Pierdzioch, C., Risse, M., Rohloff, S., 2014a. On the efficiency of the gold market: results of a real-time forecasting approach. Int. Rev. Financ. Anal. 32, 95–108. Pierdzioch, C., Risse, M., Rohloff, S., 2014b. The international business cycle and gold-price fluctuations. Q. Rev. Econ. Finance 54, 292–305. Pukthuanthong, K., Roll, R., 2011. Gold and the dollar (and the euro, pound, and yen). J. Bank. Financ. 35, 2070–2083. Rapach, D.E., Wohar, M.E., 2006. In-sample vs. out-of-sample tests of stock return predictability in the context of data mining. J. Emp. Finance 13, 231–247. Rapach, D.E., Strauss, J.K., Zhou, G., 2010. Out-of-sample equity premium prediction: combination forecasts and links to the real economy. Rev. Financ. Stud. 23, 821–862. Reboredo, J.C., 2013a. Is gold a hedge or safe haven against oil price movements? Res. Policy 38, 130–137. Reboredo, J.C., 2013b. Is gold a safe haven or a hedge for the US dollar? Implications for risk management. J. Bank. Financ. 37, 2665–2676. Sherman, E.J., 1983. A gold pricing model. J. Portf. Manag. 9, 68–70. Tkacz, G., 2007. Gold prices and inflation. Bank of Canada Working Paper 2007–35. Tully, E., Lucey, B.M., 2007. A power GARCH examination of the gold market. Res. Int. Bus. Finance 21, 316–325. Welch, I., Goyal, A., 2008. A comprehensive look at the empirical performance of equity premium prediction. Rev. Financ. Stud. 21, 1455–1472. Westerlund, J., Narayan, P., 2015a. Testing for predictability in conditionally heteroskedastic stock returns. J. Financ. Econ 13, 342–375. Westerlund, J., Narayan, P., 2015b. A random coefficient approach to the predictability of stock returns in panels. J. Financ. Econ 13, 605–664. Westerlund, J., Narayan, P.K., 2012. Does the choice of estimator matter when forecasting returns? J. Bank. Financ. 36, 2632–2640. Wherry, R., 2009. Gold Has a Wild Ride: What's Next? Eastern ed. Wall Street J. 253(15) p. B10. Worthington, A.C., Pahlavani, M., 2007. Gold investment as an inflationary hedge: cointegration evidence with allowance for endogenous structural breaks. Appl. Financ. Econ. Lett. 3, 259–262. Zhang, Y.J., Wei, Y.M., 2010. The crude oil market and the gold market: Evidence for cointegration, causality and price discovery. Resour. Policy 35, 168–177.