The drivers of physical demand for gold

While modelling the demand for physical gold can be done relying on the same classical tools used when modelling the total demand market, the task remains very complicated due to the lim

The drivers of physical demand for gold

Results for total gold demand indicate a positive relationship with short-term yields and economic uncertainty, while the exact opposite is observed for industrial gold demand, where a positive relationship with economic activity is observed Furthermore, results indicate a rising luxury demand linked to increases in national wealth, and towards a positive relationship between investment demand for gold and both inflation and economic uncertainty More specifically, we break a common myth by proving that global investors protect themselves from inflation by investing into physical gold rather than through buying jewellery

Keywords: gold; physical demand

1 Introduction

Financial research about precious metals draws conclusions about empirical behaviour

and aspects of gold by considering the official price originating on stock markets In this

case, the demand is aggregated; no difference is made between institutional and institutional investors, between the private and the public sector, between demand originating from consumers and producers

non-However, the alleged safety character of gold is the very definition of the asset’s nature; one would think that this would only truly come to light by means of a physical investment into gold While indeed an exposure to gold through holding it in an investor’s portfolio is beneficial for multiple reasons (see Baur and Lucey (2010) and Batten et al (2014)), the real safety of gold lies in holding it physically as a last resort asset in extreme situations (Starr and Tran (2008)) Financial research on gold can be divided into different categories, each considering different aspects of the precious metals (O’Connor

et al (2015)) A very predominant field is on the relationship between gold and inflation; here an alleged relationship is believed to exist based on gold’s definition as both: an international currency and a production asset If gold is considered to be an international currency, an increase in expected inflation would lead to a reduction of the anticipated purchasing power, which would lead to investors driving down their proportion of cash and invest in gold, hence pushing the price upwards (Lucey et al (2016)) On the other hand, if gold is considered to be a regular asset, then its price would rise alongside the rate of inflation since the definition of inflation is that the dollar price of a typical good rises (Jaffe (1989)) The reaction to inflation from investors is therefore proactive while the reaction from producers is reactive - an obvious difference in the behaviour of demand should therefore be observable A similar reasoning can be applied for the safe haven theory proposed by Baur and Lucey (2010): gold offers protection to investors during financial turmoils, which should positively impact investors demand while it should, if anything, diminish the demand from producers who are facing an economic downturn Again, a different impact on investor and producer demand can be expected

While modelling the demand for physical gold can be done relying on the same classical tools used when modelling the total demand market, the task remains very complicated due to the limited availability of data and the manual allocation of the demand Extracting these figures is a very cumbersome and labour-intensive task which

can only be done by looking into the annual surveys of the past decades computed by the Gold Fields Mineral Services Ltd and available only in physical copies at their offices in London

Non-Government physical demand for gold can be broken down into three different categories:

• Industrial Demand: reflecting the demand for precious metals as a production

input in electronics, dentistry etc

• Investment Demand: the demand for bars and coins, targeting mostly

investors attracted by the safety aspects of precious metals

• Luxury Demand: gold needed for the production of jewellery

Important country effects might affect the physical demand for gold by influencing some of the three categories more than others In order to try and derive empirical results instead of running country-specific models, we propose working with different panel approaches and formally test whether or not pooled Ordinary Least Squares (OLS) procedures could accurately fit the data while deleting country-specific effects

The choice of country is made in regard to the country’s relative importance on both the offer and/or the demand market of gold The following countries are considered: Australia, Canada, China, Egypt, Germany, India, Italy, Japan, Mexico, Russia, Saudi Arabia, South Korea, Switzerland, Thailand, Turkey, the United Kingdom of Great Britain and Northern Ireland, and finally, the United States of America

This paper contributes to the field by being the first to look at physical demand for gold, breaking down the demand into different types We work with a clean and thorough methodology and derive insightful results into the effect of macroeconomic variables on the physical demand for gold

The rest of this paper is organised as follows: Section 2 offers a brief overview of the related literature in order to defend the choice of data, Section 3 presents the methodology, while Section 4 outlines and discusses the empirical results Finally, Section

5 concludes

2 Literature Review and Data Presentation

FERGAL LITERATURE

The annual Gold Fields Mineral Services (GFMS) surveys published Thomson Reuters provide an overview of the amount of gold supplied and demanded across various countries over the past calendar year

Plotting the demand for gold and silver respectively (Figures 1) indicates a shift in the demand towards a rising importance of the investment side, the graphs are also revealing that jewellery consumption is the most important factor in demand for physical gold

It should be noted that Figures 1 is computed taking into account the global demand for gold However, the regression results in this paper are computed considering only a subset of countries, which were chosen because of their relative importance on either the supply or the demand side of the gold market respectively The countries are: Australia, Canada, China, Egypt, Germany, India, Italy, Japan, Mexico, Russia, Saudi Arabia, South Korea, Switzerland, Thailand, Turkey, the United Kingdom of Great Britain and Northern Ireland, and finally, the United States of America

While the research of Starr and Tran (2008) is the only paper focused on the drivers

of physical demand for gold, it is indeed the only source that can be used as a steppingstone when deciding what data to consider In line with Starr and Tran (2008), the CPI, the GDP and the exchange rate to the US Dollar have been considered

Figure 1: Global Demand for Gold by Type in Tonnes

The level of the national equity indices have also been considered, as well as both long term and short term interest rates in order to get a feeling for the state of the underlying economy Here, the short term interest rates considered are the 3 Months Interbank Lending Rate, while 10 Years Government Bond Yields are used as a proxy for long term interest rates The dataset is also augmented with narrow money supply as well as the Economic Uncertainty Index if such an index is available for the country considered All data are annually and run from 1990 to 2015

3 Methodology

3.1 Identifying Heteroscedasticity through Residuals

A major assumption of linear regression procedures is that the variance of the error

terms u is constant, the assumption of homoscedasticity ( Brooks (2014)) Breusch and

Pagan (1979) propose a testing procedure to detect the presence of possible heteroscedasticity in linear regression models by building upon a classical regression model of the form:

where a set of residuals uˆ can be obtained, while an Ordinary Least Squares procedure

would constrain their mean value to be 0 In the case that this assumption might fail, the variance of the residuals might be linearly related to independent variables and the model could be examined by regressing the squared residuals on the independent variables ( Brooks (2014)):

v x

H0 : α2 = = α p = 0 (4)

and therefore z t0α = α1 so that σ t2 = h(α1) = σ2 is constant

3.2 Evaluating Estimator Consistency

Hausman (1978) proposes a test that evaluates the known consistency of an estimator

1

ˆ

q with another estimator q efficient under the assumption being tested Theoretically, ˆ2

the procedure is based on the expectation that for a standard regression of the type:

The basic null hypothesis is that θˆ2 is both an efficient and consistent estimator of the

true parameters So if a comparison of the estimates from estimator θˆ2 with the efficient

estimator θˆ1 assumed in Equation 6 can be made, and noting that their differences is

uncorrelated with estimator θˆ1 under the null hypothesis, Equation 5 can be reformulated as:

v x

)(

)(

e c e c e

where β c is the coefficient vector from the consistent estimator θˆ1 and β e

is the coefficient vector from the efficient estimator θˆ2 Furthermore, V c is the

covariance matrix of the consistent estimator θˆ1 and V e is the covariance matrix of the

efficient estimator θˆ2

3.3 Determining Serial Correlation in the Idiosyncratic Error Term

Serial correlation in panel data leads to biased standard errors and to less efficient results; Wooldridge (2002) therefore proposes a testing procedure that identifies serial correlation in the idiosyncratic error term in both random- and fixed-effects models Assume the following model:

}{1,2, ,}

{1,2, ,

where y it is the dependent variable and α, β1, and β2 are 1 + K1 + K2 parameters (Drukker

(2003)) Xit is a (1 ∗ K1) vector of time-varying covariates and Zi is a (1 ∗ K2) vector of

time-invariant covariates, while µ i is the individual level effect and it is the idiosyncratic error

In the case that the µ i are correlated with the Xit or the Zi, then the coefficients on the

time-varying covariates Xit can be consistently estimated by a regression on either the within-transformed data or the first-differenced data

In the case that the µ i are uncorrelated with the Xit and the Zi, the coefficients on both time-varying and time-invariant covariates can be estimated consistently and efficiently using the feasible generalised least squares method known as random-effects regression

(Drukker (2003)) A discussion on the estimators of the coefficients of the covariates Xit

and Zi can be found in Wooldridge (2002) and Baltagi (2013)

Assuming that there is no serial correlation in the idiosyncratic errors, or assuming that ] = 0 for all s 6= t, Wooldridge (2002) relies on the residuals obtained from a

regression in first-differences of the form:

it it

it

it it it

it it

it

X y

X X y

y

e b

e e b

D+DD

+-

-1

1 1

1 1

=

)(

=

(11)

where ∆ is the first-difference operator (Drukker (2003)) The Wooldridge (2002)

procedure estimates the parameters β1 by regressing ∆y it on ∆Xit and obtains the residuals

eˆ it In case the it are not serially correlated, then

5 (Drukker (2003)) Wooldridge (2002) therefore

regresses the residuals eˆ it on their lags and tests that the coefficient on the lagged

residuals is equal to −0.5 while accounting for within-panel correlation in the regression

of eˆ it on eˆ it−1 by adjusting the variance-covariance matrix for clustering at the panel level (Drukker (2003))

3.4 Linear Panel Data Models

Assuming a model of the following form:

=

2 1

=

)(

i

x y

Q a b åe å -a-b

so that the estimators αˆ and βˆ are defined as:

][

],[

=)(

))(

=

1

=

x Var

y x Cov x

x

y y x x

x y

i n

i

i i

n

i

-

where x¯ and y¯ indicate the average value of x and y respectively ( Brooks (2014))

It is possible to fit regression models to panel data in regard to both fixed effects and random effects estimators, but is surprisingly complex to model econometrically

Building upon a basic model of the form:

where ε it is the error term of the system and v i the panel-specific error term, the question

of interest that remains is the estimation of β So in the light that v i differs between units but is constant within the unit, the following must hold:

i i i

where y¯ i is defined as , while x¯ i is calculated by In this sense, it follows that

ε¯ i is obtained through So subtracting Equation 15 from Equation 14 yields:

)(

)(

)}

(){(1)

()(1

ˆ1

=ˆ

e

ess

sq

u i T

Corporation (2013)) It should be noted that in case σ v2 = 0, implying that v i is always

0, it follows that θ = 0 and that Equation 14 can be directly estimated by an Ordinary

Least Squares procedures

The popular R2 procedure can be used to evaluate goodness of fit of the model, where

the classical measure is predicted on:

=)ˆˆ

=

ˆ~

i it i it

Asiedu and Lien (2011) on the impact of democracy on foreign direct investments, and finally, in Aisen and Veiga (2013) on the determinants of economic growth

3.5 Dynamic Panel Data Models

In the light of unobserved fixed or random specific effects, linear dynamic

panel-data models include p lags of the dependent variable y as covariates However, this might

lead to an inconsistency of standard estimators, given that the unobserved panel-level

effects are correlated with the values of the lagged variable y (Stata Corporation (2013))

In order to tackle this problem, the following section highlights four different paneldata estimation models building upon previously presented formal testing procedures for linear regressions

Throughout the section, the following classical linear dynamic paneldata model shall

be considered (Stata Corporation (2013)):

i it

i it it

j t j

++

+-

with N the sample of individual time series and T the observation periods x it is a 1 ∗ k1

vector of strictly exogenous covariates and w it is a 1 ∗ k2 vector of predetermined and

exogenous covariates β1 and β2 are respective k1 ∗ 1 and k2 ∗ 1 vectors of parameters to be

estimated, while v i are panellevel effects and it independent and identically distributed

over the entire sample with variance The independence of v i and it is assumed for each

i over all t

3.5.1 Linear Dynamic Panel Data Modeling

Based upon the works of Anderson and Hsiao (1981, 1982) on dynamic models, and of Holtz-Eakin et al (1988) on vector autoregression coefficients in panel-data, Arellano and Bond (1991) build their methodology upon the Generalised Method of Moments (GMM) and propose a procedure designed for datasets with many panels but few observation periods, with the only requirement that no autocorrelation is present in the idiosyncratic

errors The GMM estimator αˆ is based on the sample moments N−1Z0v¯

so that:

1 1

1

'

'

=)()'(

=

ˆ

-

y Z ZA y v Z A Z v argmin

N

N N

a

where ¯ is a N(T − 2) ∗ 1 vector and Z =

matrix (Arellano and Bond (1991)) A N needs

to be set to A N = (N−1Pi Z i0HZ i)−1 where H is a (T − 2) square matrix in order to obtain the one-step estimator αˆ1 while the two-step estimator αˆ2 is obtained by setting A N =

VˆN−1 (Hansen (1982))

Regarding the GMM estimator βˆ, it can be obtained by:

y Z ZA X X Z ZA

where X¯ is a stacked (T −2)N ∗k matrix of observations on x¯ it and the

alternative choices of A N will produce one-step and two-step estimators

The procedure proposed by Arellano and Bond (1991) assures estimator consistency

by removing panel-level effects through first-differentiation and by forming moment conditions derived from the first-difference errors of Equation 21

Due to its availability in different economic and statistical software packages, the procedure proposed by Arellano and Bond (1991) has been widely applied in financial research Examples can be found in Podrecca and Carmeci (2001) on economic growth,

in Castells and Sol´e-Oll´e (2005) on regional allocation of infrastructure investment, in Liu (2006) on financial structure, corporate finance and growth of manufacturing firms

in Taiwan, in Naud´e and Krugell (2007) on determinants of foreign direct investment in Africa, and finally, in Chang et al (2011) on the relationship between military expenditure and economic growth

3.5.2 Linear Dynamic Panel Data Modeling with Additional Moment Con-

ditions

In the light of possible model limitations highlighted by Arellano and Bover (1995), Blundell and Bond (1998) propose a related estimator to Arellano and Bond (1991) using additional moment conditions in assuring estimator consistency under the only additional

condition that E = [v i ∆y i2 ] = 0 holds for all i in Equation 21 Building upon a classical

dynamic panel-data model as presented in Equation 21, Blundell and Bond (1998) argue that the lagged-level instrument in the Arellano and Bond (1991) estimator becomes weak

in two cases: first, if the autoregressive process becomes too persistent, and second, if the

ratio of the variance of the panel-effects v i to the variance of the idiosyncratic error it

becomes too large (Stata Corporation (2013))

Building upon the work of Arellano and Bover (1995), Blundell and Bond (1998) propose to use moments conditions that use lagged differences as instruments for the level equation in addition to the moment conditions of lagged levels as instruments for the differenced equations - hence resulting in an additional moment estimator

Econometrically, their procedure results in a GMM estimator αˆ of the following form:

(24)

where ¯ is the (T − 2) vector (∆y i3 , ∆y i4 , , ∆y iT ) and ¯ is the (T − 2) vector (∆y i2 ,

∆y i3 , , ∆y i,T−1) (Blundell and Bond (1998))

In the same fashion as Arellano and Bond (1991), the definition of the matrix A N is

essential in determining αˆ Blundell and Bond (1998) define the optimal weights of A N

as:

1 1

3.5.3 A Linear Dynamic Panel Data Model allowing for Autocorrelation in the Idiosyncratic Errors

As mentioned above, Arellano and Bond (1991) propose one-step and two-step GMM estimator using moment conditions relying on lagged levels of the dependent and predetermined variables This procedure is augmented by Blundell and Bond (1998) who

show that the lagged-level instruments in the Arellano and Bond (1991) estimator become weak in two cases: either as the autoregressive process becomes too persistent or if the

ratio of the panel-level effect variance v t to the variance of the idiosyncratic error it

becomes too large

Both procedures require that there be no autocorrelation in the idiosyncratic errors, hence limiting there field of application A linear dynamic panel data procedure can however be respecified as such, that the correlation in the idiosyncratic errors follows a low-order Moving-Average ( MA ) process, hence tackling the restriction imposed by Arellano and Bond (1991) and Blundell and Bond (1998)

Mathematically, a panel-data model like that in Equation 21 can be considered, where

x and w might contain both lagged independent variables and time dummies Define X L it

= (y i,t−1 , y i,t−2 , , y i,t−p , x it , w it ) as the 1 ∗ K vector of covariates for i at time t where K = p + k1 + k2 and define p as the number of lags included, k1 as the number of strictly

exogenous variables in x it , and k2 as the number of predermined variables in w it in order

to rewrite Equation 21 as a set of T i equations for each individual (Stata Corporation (2013)):

(26)

where L stands for levels and T i is the number of observations available

for individual i y i , ι i and i are all T1 ∗ 1 while Xi is T i ∗ K

Given a value of i, stacking the transformed and untransformed matrices of the

covariates yields:

÷

÷

÷ø

öç

öç

d i i

di

I D

Z

00

where Zdi is the matrix of the GMM-type instrument for the difference equation and ZLi is

the matrix of the GMM-type instruments for the level equation Di is the matrix of

standard instruments for the difference equation, while Li is the matrix of standard

instruments for the level equation Finally, Id i is the matrix of standard instruments from

the difference and level equations for the differenced errors, while IL i is the matrix of standard instruments from the difference and level equations for the level errors

Now, the one-step estimator βˆ1 can be defined as:

zy

xz A Q Q

Likewise, the two-step estimator βˆ2 can be defined as:

zy

xz A Q Q

More information about the procedure, as well as an excellent mathematical derivation

of the bias-corrected estimator for the robust standard errors of two-step GMM estimators can be found in Windmeijer (2005)

3.5.4 A Bias Corrected Least-Squares Dummy Variable Dynamic Panel Data Estimator

A final renowned panel-data estimation procedure is the bias-corrected

Least-Squares Dummy Variable (LSDV) procedure initially proposed by Nickell (1981) and that assures consistency of the estimates in a scenario in which the amount of panels rises towards infinity

Formally, an LSDV procedure transforms Equation 21 into a matrix format:

(31)

where y and W = (y t−1 ..X) are (NT ∗1) and (NT ∗k) matrices of stacked observations respectively (Bruno (2005b)) Furthermore, D = I N ⊗ι T is the (NT ∗ N) matrix of

individual dummies with ι T the (T ∗ 1) vector of all unity elements Finally, η is the (N ∗ 1) vector of individual effects, while is the (NT ∗1) vector of disturbances and δ = (α ..β0)

is the (k ∗1) vector of coefficients

Building upon the exogenous selection procedure of Bun and Kiviet (2003) applied to unbalanced panels, Bruno (2005a) proposes a more general approximation procedure for

the coefficients in Equation 21 valid for the observation interval [0,T] Bruno (2005a) defines a selection indicator r it such that r it = 1 if (y it ,x it ) is observed, and r it = 0 otherwise

in order to define a dynamic selection rule s(r it ,r i,t−1) that only includes observations for which both the current value and the lagged value are observable Formally:

T t

and N i

otherwise

r r if

þý

üî

í

-(32)

so that for any i, the number of usable observations is given by T i = while the

total number of usable observations is given by n = and denotes the

average group size For every i, Bruno

(2005b) defines a (T ∗ 1) vector s i = [s i1 , ,s iT ]0, a (T ∗ T) diagonal matrix S i that has

the vector s i on its diagonal, and a (NT ∗ NT) block-diagonal matrix S = diag(S i) so that Equation 31 can be rewritten:

(33) The LSDV estimator is defined as:

where M s = S{I − D(D0SD)−1D0}S is the symmetric and idempotent (NT ∗ NT) matrix

deleting individual means and selecting usable observations (Bruno (2005b))

Further discussions on the Least-Squares Dummy Variable procedure can be found in Kiviet (1995), in Kao (1999), and finally, in Bun and Carree (2005)

4 Empirical Results

While a large amount of research exists on the implications and the effects of certain macroeconomic variables on the price of gold, only one formal investigation exists on the drivers of physical country demand for gold (Starr and Tran (2008)) In order to provide

more detailed results, the demand for gold is broken down into different categories, depending on the final usage of the precious metal

4.1 Total Demand

The total demand is the aggregated sum of gold demand required for jewellery production, investment purposes, and industrial production, mainly in electronics

An important question to raise in the light of the data on hand is to see how it should

be modelled, the Lagrange Multiplier test by Breusch and Pagan (1979) is used to test for linear misspecification in the model

The test results displayed in Table 1 advice to reject the null hypothesis and suggest that the variance of the unobserved fixed effects is different than 0 - a pooled OLS regression might therefore not be the appropriate model to use

In order to build a good model that fits the physical gold demand data of the 17 countries in the system, an essential question is to understand if the data should be fitted

in a random effect or a fixed effect model, relying on the Hausman Specification Test (Hausman (1978))

Table 2

Hausman Specification Test: Total Demand for Gold

(b) Fixed

(B) Random

(b-B) Difference

sqrt(diag(V b-V B)) S.E