Substitution between monetary assets and consumer goods: New evidence on the monetary transmission mechanism

Journal of Banking & Finance 34 (2010) 2811–2821

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Substitution between monetary assets and consumer goods: New evidence on the monetary transmission mechanism Leigh Drake a,*, Adrian R. Fleissig b a b

Nottingham University Business School, Nottingham, United Kingdom Department of Economics, California State University, Fullerton, United States

a r t i c l e

i n f o

Article history: Received 11 December 2008 Accepted 8 June 2010 Available online 11 June 2010 JEL classification: C14 C43 E52 Keywords: Monetary transmission mechanism Morishima elasticities Fourier demand system

a b s t r a c t This paper presents important new evidence on the monetary transmission mechanism in the context of the degree of substitution across UK monetary assets and consumption goods. Specifically, our empirical results show that durable goods expenditures are a relatively powerful element of the monetary transmission mechanism with semi-durables consumption having a somewhat smaller impact. Our results also provide an explanation for the ‘‘puzzle” that the nominal expenditure share of durables has remained relatively stable in recent years while the real expenditure share has increased dramatically. In addition, this paper demonstrates that the potential bias in substitution estimates from using artificial breakadjusted monetary data can be reduced by using the relatively new non-break adjusted monetary data produced by the Bank of England. Ó 2010 Elsevier B.V. All rights reserved.

1. Introduction Consumer spending is a key element of aggregate demand and is influenced by monetary policy through the monetary transmission mechanism. When the Bank of England varies the short term policy interest rate, typically referred to as Bank Rate, it generally affects all interest rates by different magnitudes and causes consumers to adjust their expenditure decisions on goods as well as monetary assets, in response to changes in the relative prices or user costs of these goods and assets. How monetary policy affects consumption through the monetary transmission mechanism depends on the differential impact that Bank Rate has on the relative price/user cost of goods and monetary assets and also on the degree of substitution between the various categories of consumption goods and monetary assets. Consequently, for the Bank of England (BOE) to determine how monetary policy will affect consumer spending, the policymaker requires reliable estimates of the substitution between goods and assets, which may well vary over time. The BOE has recently begun to focus more attention on the composition and determinants of expenditure across durables, * Corresponding author. Tel.: +44 (0)115 9515505; fax: +44 (0)115 9515527. E-mail addresses: [email protected] (L. Drake), afleissig@fullerton. edu (A.R. Fleissig). 0378-4266/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.jbankfin.2010.06.002

non-durables and services, as well as the ‘‘puzzle” that the nominal expenditure share of durables has remained relatively stable in recent years while the real expenditure share has increased dramatically (see Hamilton and Morris, 2002 and Power, 2004). Empirical studies, however, typically assume that expenditure on goods and services is independent from consumer’s financial decisions. Furthermore, the degree of substitution between durables and nondurable goods is often assumed to be constant or equal to unity, as in Power (2004). The former assumption is rather surprising given that theoretical work on money demand typically stresses strong links between money and consumption. The traditional role of money as a means of exchange, for example, implies a complementary relationship which is epitomized in the cash-in-advance models of Lucas and Stokey (1983, 1987) and Cooley and Hansen (1989). In contrast, the asset demand approach of Friedman (1956) asserts that monetary assets are likely to be substitutes for a wide range of both financial and real assets, including durable goods. This ‘‘money view” of the transmission mechanism, as personified by Friedman (1956), recognized that an exogenous increase in the money supply via open market operations (or equivalently, a reduction in the policy interest rate) would operate not only via the traditional Keynesian interest rate mechanism on the demand for real capital goods, but may also increase the demand for durable goods. This increase in the demand for durable goods is

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attributable to a real balance or wealth effect and/or a portfolio balance effect and implies a relatively high elasticity of substitution between money and durable goods (Friedman and Schwartz, 1963). It is the consumer, however, who determines if monetary assets, durable goods, semi-durable goods, non-durables and services are substitutes or complements in demand and hence this is an empirical issue with important policy implications.1 A key objective of this paper is to provide more precise estimates and policy implications for this important aspect of the monetary transmission mechanism, which has been relatively neglected in recent years with more attention being focused on the analysis of the various credit channels of the transmission mechanism (Kashyap et al., 1994; Bernanke and Gertler, 1995; Goddard et al., 2007; Basistha and Kurov, 2008). In order to produce accurate estimates of the degree of substitution between goods and monetary assets, however, we require robust aggregate measures of consumer goods and services and of broad money. With respect to the latter, the BOE continues to strive to produce more accurate measures of broad monetary aggregates. An important development in this context was the introduction of Divisia monetary aggregates in 1993.2 The conversion of many large building societies from mutual to plc status during the mid-1990s, however, resulted in large jumps in the levels of the unadjusted data when Building Society Deposits were re-classified into the appropriate category of bank deposits. In an attempt to address these data problems in the context of its Divisia monetary aggregation project, the BOE initially introduced artificial break adjustments in order to eliminate the large jumps in the data.3 It is highly unlikely that the break-adjusted levels will correctly reflect the consumer choices across monetary assets and goods. In recognition of this problem, therefore, the BOE changed their Divisia monetary aggregation methodology and now apply any break adjustments only to the flow data, but not to the underlying levels data (see Hancock, 2005). Hence, from the perspective of this paper, the most significant change was the switch from using artificial break-adjusted data on the levels of the component assets to non-break adjusted data. Consequently, previous studies based on the break-adjusted data may give misleading conclusions and biased estimates of elasticities of substitution involving monetary assets. While the Divisia index methodology has been widely adopted by central banks, it is seldom employed in consumption studies. In the UK, for example, the Office for National Statistics (ONS) typically computes total consumer expenditure for non-durables and services as the sum of all the sub-components of expenditure within each category. Thus the official aggregates for non-durable

expenditure and services expenditure may fail to accurately measure consumer choices because they are not constructed using a superlative index. In addition, durable and semi-durable consumption are typically reported as expenditures whereas a well specified economic analysis of consumer purchasing decisions for such goods relates to the net stocks and user costs of durables and semi-durables. Failing to use the net stocks of both durable and semi-durable goods and superlative indices to aggregate both consumption and monetary data may further bias estimates of substitution. A key objective of this study is to try to ensure that data based biases are not introduced into the estimation of the elasticities of substitution across monetary assets and goods and that policy implications relating to the monetary transmission mechanism, for example, are robust. Consequently, this study uses disaggregated data for monetary assets, non-durables and services as well as the net stocks of durables and semi-durables in order to analyze optimal consumer behavior. We also follow the non-parametric approach established by Swofford and Whitney (1987, 1988) to test if data are consistent with utility maximization. This approach has been applied to UK data by Patterson (1991), Drake (1997), Drake et al. (2003) and Elger et al. (2008).4 After establishing utility maximization for the assets and goods, we construct Divisia aggregates from the monetary assets, non-durable goods and services expenditure. Finally, rather than imposing a-priori restrictions such as a unitary elasticity of substitution between durables and nondurables, as assumed in Power (2004), we estimate Morishima elasticities of substitution across monetary assets and consumer goods from a system of Fourier demand equations. In using a well specified demand system, such as the Fourier flexible form, and Divisia aggregates the results are less likely to be subject to the ‘‘Barnett Critique” as defined by Chrystal and MacDonald (1994).5 2. Data In a consumer optimization, the agent gains utility from both consumer goods and the service flows from monetary assets.6 The monetary assets and consumption series used relate to the UK household sector. These quarterly data consist of disaggregated series of monetary assets, services expenditure, non-durables expenditure and we also compute the net stock of both durable and semidurable goods. In this study, the utility function U() consists of vectors of service flows of 25 variables from the BOE and the ONS.

Uðmonetary assets; non-durables; services; stock of durables; stock of semi-durablesÞ:

1 Although intertemporal substitution in consumption has been examined by Hall (1988), Eichenbaum and Hansen (1990) and Atkeson and Ogaki (1996), few studies estimate intratemporal elasticities between the categories of consumption such as durables, semi-durables, non-durables and services. The US studies of Fleissig (1997), Ogaki and Reinhart (1998) and Fisher et al. (2001) estimate intratemporal elasticities but use only a subset of the consumption data. The UK studies of Drake and Fleissig (2006, 2007) also use a subset of the consumption data and use the artificially break adjusted monetary data which may bias results. 2 The Divisia methodology weights the various component assets according to their monetary transactions services rather than giving them an equal weight of unity as in simple sum aggregation. The Bank of England introduced Divisia monetary aggregates in 1993 in order to overcome some of the shortcomings of the simple sum monetary aggregates. The importance of constructing a Divisia aggregate of monetary assets was first shown by Barnett (1980, 1982, 1987) using the superlative index approach of Diewert (1976, 1978) which links index number and aggregation theory. In January 2005, however, the Bank of England made a number of changes to its methodology in an effort to make the Divisia measure more consistent with economic theory (Hancock, 2005). 3 A shortcoming of the artificial break adjusted data is that the deposits of the converted building societies are treated as bank deposits both prior to and after the conversion process. This has the implication, for example, that the break adjusted holdings of building society deposits are much lower during the 1980s and the early to mid 1990s than their true historic levels.

ð1Þ

In line with the micro-foundations approach the quantity series are converted into real per household terms using data on the total number of households obtained from The Office of Population and Census Studies. All quantity data are seasonally adjusted and cover the period 1977:1–2005:3. The monetary asset categories from the Bank of England are: NC – notes and coins NIBS – non-interest-bearing sight deposits IBS – interest bearing sight deposits

4 Studies using US data include Swofford and Whitney (1987, 1988), Barnett et al. (1992), Belongia (1996), Belongia and Chalfant (1989), Fleissig and Swofford (1996), Fisher and Fleissig (1997), Jones et al. (2005). 5 The ‘‘Barnett Critique” emphasizes using well defined monetary and consumption aggregates, such as Divisia aggregates, and flexible functional forms that reduces bias in estimates. 6 This approach is used by Samuelson and Sato (1984), Barnett et al. (1992), Fisher and Fleissig (1997), Fleissig and Swofford (1996), Drake et al. (2003) and Drake and Fleissig (2006, 2008).

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Artifical Break Adjusted

non-break adjusted

9

8

7

6

5

4

3

2 1990.2

1991.2

1992.2

1993.2

1994.2

1995.2

1996.2

1997.2

1998.2

1999.2

2000.2

2001.2

2002.2

2003.2

2004.2

2005.2

Chart 1. Building Society Deposits.

TD – Bank Time Deposits BSD – Building Society Deposits.7 These assets are converted into real quantities using the total consumer expenditure deflator. Liquidity service flows from monetary assets are assumed to be proportional to the real per household stock of monetary asset holdings. The assets correspond broadly to UK M4, the official broad money aggregate adopted following the abandonment of £M3 (approximately M4 less BSD) targeting in the mid 1980s. As highlighted previously, the conversion of many large mutual building societies into plc banks during the mid-1990s had a major impact on the monetary data. With respect to Building Society Deposits, it is clear from Chart 1 that there can be very large differences between the artificially break-adjusted data and the new non-break adjusted data. Consequently, it is unlikely that the break-adjusted levels will correctly reflect the consumer choices across monetary assets and goods which we endeavour to investigate. As emphasized previously, in recognition of this problem, the Bank of England changed their methodology and now apply any break adjustments only to the flow data, but not to the underlying levels data (see Hancock, 2005). The one period holding cost, or user cost of monetary assets, derived by Barnett (1978) and Donovan (1978) is RPit = Pt(Rt  rit)/ (1 + Rt) where Rt is the yield available on a benchmark asset, Pt is a price index and rit is the market yield on the ith monetary asset.8 The interest rate series (rit), such as bank interest bearing sight and time deposits, reflect rates paid to the household sector. Details of the own rates of return for interest bearing assets are discussed by Fisher et al. (1993) and the Bank of England (2005). The annual percentage interest rate data were transformed into quarterly returns by dividing by 400. The own rates of return on notes and coins and non-interest bearing sight deposits are zero although the opportunity cost of holding these assets is not zero. We follow the methodology of the Bank of England (2005) in using the envelope approach to determine the benchmark rate of return. Since NC and

7 The Government introduced Cash individual savings accounts (ISAs) in 1999.2 as part of an initiative to stimulate savings. Since Cash ISA deposits are not available over most of the sample, they are omitted from the analysis. 8 In monetary studies, this user cost is used by Belongia and Chalfant (1989), Barnett et al. (1992), Belongia and Chrystal (1991), Patterson (1991), Swofford and Whitney (1987, 1988), Drake and Chrystal (1994, 1997), Drake (1996), Belongia (1996), Drake et al. (2003) and Drake and Fleissig (2006, 2008).

NIBS have identical user costs, they make up a Hicksian composite good and can be added together and referred to as Non-Interest Bearing M1 (NIBM1). The consumption data consist of nine components of non-durable expenditure, ten components of services expenditure and the net stocks of both durable and semi-durable goods. The series for non-durables expenditure and services expenditure (in constant prices) are obtained from the ONS.9 Prices for non-durable goods and services are derived as the implicit price deflator from the ratio of current to constant price expenditure. The stock of durables is calculated using real expenditures on durables, together with the depreciation rate calculated using unpublished data obtained from the ONS on the assumed average life length for durables and using the short life-length assumption. There are no such data are available for semi-durable goods. As semi-durable goods include the clothing and footwear category (which was previously classified as durables expenditure by the ONS), and in the absence of any specific information on the average life-length of semi-durables, we assume that all semi-durables have an average two year life length based on data previously provided by the ONS for the clothing and footwear category. The user cost for both durable and semi-durable goods is calculated using the formula of Diewert (1974) and Patterson (1991) with the assumed average life lengths used to calculate the appropriate depreciation rates (see Drake and Fleissig, 2008), and using the benchmark rate of return derived for monetary assets.10

3. Substitution and estimation of the demand system To evaluate if the monetary and consumption data are consistent with optimal consumer behavior, the data are often tested for consistency with the Generalized Axiom of Revealed Preference (GARP) using the non-parametric procedure of Varian (1982). The 9 The ONS data consist of: nondurables: food and non-alcoholic beverages; alcoholic beverages; tobacco; household utilities (water, electricity, gas, other fuels, etc.); furnishings and household equipment; health; transport; recreation and culture; miscellaneous goods and services. Services: clothing and footwear, household utilities (water, electricity, gas, other fuels, etc.); furnishings and household equipment; health; transport; communications; recreation and culture; education; restaurants and hotels; miscellaneous goods and services. 10 The user cost is pit  (1 + Rt)1(1  d)Etpit+1 where R is the nominal interest rate, d is the depreciation rate, pit is the price of good i, and Etpit+1 is the expected price of good i.

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data violate revealed preference over the sample 1977.1–2005.3 as in Drake and Fleissig (2008) and Elger et al. (2008). Thus conclusions about optimal consumer behavior over the sample 1977.1– 2005.3 are a joint test of utility optimization and misspecification of the utility function. In contrast, when the data satisfy GARP, then there exists a utility function that can rationalize the data. There are advantages and disadvantages of the revealed preference approach. The advantage of the GARP approach is that the test is performed without having to specify the functional form. A disadvantage of the approach is that it is nonstochastic and this limitation is discussed in Barnett and Choi (1989), Bronars (1987) and others. Given the conversion of many large building societies into plc banks, using a sample where the data are consistent with GARP is likely to provide more precise estimates of substitution because the data can be rationalized by a data generating function. Consequently, we follow the approach of Belongia and Chalfant (1989), Swofford and Whitney (1987, 1988), Drake and Fleissig (2008) and Elger et al. (2008) to establish a sample that is consistent with utility optimization. Additional testing established that the data are consistent with GARP over the period 1990.1–2005.3 which implies that there exists a utility function over this sample that rationalizes the data. Our aim is to analyze substitution between aggregated monetary assets holdings and consumption goods over this GARP consistent period. The intention is to evaluate potential differences in the estimates emanating from the use of non-break adjusted rather than break-adjusted monetary asset data. This is an important empirical issue and is also highly relevant from a policy perspective as the monetary transmission mechanism depends, at least in part, on the substitution between monetary assets and the various categories of consumption in response to changes in interest rates/user costs. It is also important to note that superlative indices of monetary assets and goods should be used in conjunction with a well specified econometric model, such as the Fourier flexible form, in order to minimize any potential violations of what Chrystal and MacDonald (1994) have called the ‘‘Barnett critique” in monetary economics. Specifically, in using the Fourier flexible form and superlative indices, a stable structure is less likely to appear to be unstable. In the demand systems approach the goal is to derive and estimate demand share equations and elasticities of substitution from the unknown indirect utility function. The indirect utility function is approximated using the Fourier flexible form which has been used in money demand studies by Ewis and Fisher, 1985; Fisher, 1992; Barnett et al., 1992; Fisher and Fleissig, 1997; Drake and Fleissig, 2008). The Fourier flexible form can globally approximate the levels and partial derivatives of a continuous utility function and give unconstrained estimates of substitution.11 In contrast, locally flexible forms such as the Translog provide a local approximation to the data generating function in a delta neighborhood of an unknown and possibly small size.12 The Fourier indirect utility function is (Gallant, 1981):

11 The Fourier flexible form is dense in a Sobolev norm and can asymptotically approximate the levels and partial derivatives of a data generating function accurately, Gallant (1981). A semi-nonparametric function refers to the use of a truncated series expansion that is dense in a Sobolev norm, see El badawi et al. (1983). 12 Some examples of monetary studies using locally flexible forms include the translog for US data by Ewis and Fisher (1984), Serletis (1987, 1988) and Drake (1992) for UK data, and the Almost Ideal Demand System to analyze UK data by Barr and Cuthbertson (1991). The Fourier flexible form has also been used in preference to locally flexible forms such as the Translog (in the context of cost function specifications) in numerous studies of costs and efficiency in banks and other financial institutions (Beccalli, 2007; Fenn et al., 2008; Kauko, 2009.).

1 0 v Cv 2 ! J A X X 0 0 þ u0a þ 2 ½uja cosðjka v Þ  wja sinðjka v Þ ; 0

f ðÞ ¼ u0 þ b v þ

a¼1

ð2Þ

j¼1

P 0 where C ¼  Aa¼1 u0a ka ka and {b}, {uja} and {wja} are the parameters to be estimated. A multi-index, ka, is an n vector of integers denoting partial differentiation of the utility function. Approximating the partial derivatives accurately is important when estimating substitution which requires second order derivatives. The variables x and p are vectors of the quantities and user costs of non-durables, services, stock of durables, stock of semi-durables and monetary assets, and v = p/p0 x is a vector of expenditure normalized prices or user costs. The parameters A and J determine the degree of the Fourier polynomials and are determined by empirical testing. The Fourier share equations are:  P  P v i bi  Aa¼1 u0a v 0 ka þ 2 Jj¼1 ½uja sinðjk0a v Þ þ wja cosðjk0a v Þ kia v i  st ðÞ ¼ : PA  PJ 0 0 0 0 b v  a¼1 u0a v 0 ka þ 2 j¼1 j½uja sinðjka v Þ þ wja cosðjka v Þ ka v ð3Þ

The system of equations is estimated by assuming additive errors which is preferable to multiplicative errors (McElroy, 1987):

St ¼ f ðÞ þ et ;

ð4Þ

where et is a multivariate normal. Since the budget shares sum to unity the disturbance covariance matrix is singular and Barten (1969) shows that unique maximum likelihood estimates can be obtained by dropping any equation. All estimation was performed using the nonlinear LSQ multivariate regression procedure from International TSP 4.4. In the initial estimates, there was positive serial correlation which is a common result, especially in the monetary literature and is also found by (Serletis, 1988; Fleissig and Swofford, 1996, 1997; Fisher and Fleissig, 1997; Fleissig, 1997; Drake et al., 2003; Drake and Fleissig, 2008). We follow the approach in these studies and use a first-order autoregressive process et = Ret1 + et where R = [Rij] is a matrix of unknown parameters, et are the estimated residuals per equation, and et is a non-autocorrelated vector disturbance term with constant covariance matrix. Berndt and Savin (1975) show that results will be invariant to which equation is deleted in the estimation by constraining the diagonal coefficients of R to be equal and setting the remaining coefficients to zero. Numerous starting values were used to ensure convergence to the global optimum. The number of terms included in the Fourier is determined by A and J and the nonlinearity of the data. The upward F-test of (Eastwood, 1991) was used to determine the degree and number of parameters used for the Fourier polynomials. The Fourier flexible form fits the data well giving high Rsquares, low mean square errors, no evidence of autocorrelation and with most of the parameters statistically significant. The parameter estimates using the Divisia aggregates are in Appendices A and B. This study estimates and analyzes Morishima elasticities of substitution between consumer goods and monetary assets which is now examined. When there are more than two variables, Blackorby and Russell (1989) show that the Allen–Uzawa calculation is incorrect. They show that the Morishima elasticity of substitution MEij ¼ si ðraji  raii Þ, where si is the share of expenditure from variable i and raji are the Allen–Uzawa elasticities of substitution, can be non-symmetric and gives the correct measure of substitution. The Morishima measure shows that changes in the optimal quantity ratio (xi/xj) in response to changes in relative prices (pi/pj) depend on whether the price change is in the ith or jth co-ordinate direction and has been used extensively in the monetary literature (Davis

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and Gauger, 1996; Fisher and Fleissig, 1997; Fisher et al., 2001; Drake et al., 2003; Drake and Fleissig, 2008). The possibility of finding non-symmetric elasticities of substitution is particularly important when analyzing the substitution between goods and money. Specifically, changes in the Bank of England’s Bank Rate, to the extent that it affects other interest rates (and the benchmark rate), will affect all of the user costs of durable goods, semi-durable goods and monetary assets but not necessarily to the same extent. Hence, any non-symmetry in the substitution between monetary assets, durable goods and semi-durable goods could have implications for the consumption element of the monetary transmission mechanism. This issue is examined further in the following sections.

4. Estimated substitution between goods and assets The focus is on the Morishima estimates of substitution between durables (Dur), semi-durables (Semi-Dur), non-durables (Nond), services, and monetary assets (Money) using the Divisia aggregated non-break adjusted data. While it is the agent who determines whether categories of consumption goods and monetary assets are substitutes or complements in demand, empirical results may nevertheless be misleading when inappropriate data are utilised. Thus by contrasting these estimates with those obtained using the artificially break-adjusted data, we can ascertain the extent of any potential biases.

4.1. Divisia (non-break) adjusted monetary and consumption aggregates Given the theoretical advantages of constructing aggregates using a superlative index, we examine the Morishima elasticities between goods and money estimated from the Divisia aggregated data (see Appendix 1c). The estimates show that goods and money are substitutes in demand with the largest degree of substitution (max 4.103; mean 2.836) between the Divisia aggregate of nondurables and the Divisia monetary aggregate during 2005.1, when the price of non-durable goods changes (ME13 in Appendix 1c). The lowest degree (at the mean) of substitution (min 0.839; mean 0.970) is between the Divisia aggregates of non-durable goods and services during 2004.3, when the price of services changes (ME21 in Appendix 1c).

In the context of the monetary transmission mechanism, it is important to note that monetary assets and consumption goods (for changes in the relative user cost/price due to changes in the user cost of monetary assets) are always substitutes in demand as shown in Chart 2. Specifically, the Morishima elasticities all tend to be above unity with respect to durables, semi-durables, nondurables and services. Furthermore, as the Morishima elasticities are reasonably stable over the sample period, these results strongly support the use of the non-break adjusted monetary data, in lieu of the artificially constructed break-adjusted data. The non-break adjusted data are much more likely to provide more precise measures of the degree of substitution between monetary assets and consumption goods, and do not appear to be compromised by the problems associated with the building society conversion process after the mid-1990s. In addition, the estimates are in line with apriori expectations in the sense that monetary assets and durable goods are relatively strong substitutes in demand. Interestingly, this result does not extend to semi-durables where the degree of substitution with monetary assets appears to be similar to that of services. Finally, the degree of substitution between monetary assets and non-durables is relatively stronger and generally falls mid-way between that of durables on the one hand and services and semi-durables on the other. 4.2. Changes in the user cost of durable goods Given the dramatic increase in the real share of durables expenditure in recent years, a good deal of attention has been directed at the degree of substitution between durables and non-durables in both the UK and US However, the boost in durable goods spending in real terms has not been mirrored by an increase in the nominal expenditure share. This is typically attributed to the large decline in the relative price of durable goods, a feature of both the UK and US economies. As the recent analysis conducted by the Bank of England (Power, 2004) recognizes, this explanation relies on the untested assumption that the elasticity of substitution between durables and non-durables is equal to unity. Power argues, for example, that: ‘‘There is little or no UK micro literature on the elasticity of substitution between durable and non-durable spending. But the US literature suggests an elasticity of substitution around 1. Such an elasticity implies that a 1% rise in the relative price of

1.5 Money-Nond

Money-Services

Money-Durables

Money-Semi-Dur

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1

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Chart 2. Substitution for Divisia aggregates changes in the user cost of money.

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Dur-Services

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Chart 3. Substitution for Divisia aggregates changes in the user cost of durable goods.

durable goods will cause demand to shift away from durable goods by 1%. As a result, the nominal expenditure share of durable goods is unaffected by relative price movements.” (p. 25). Our study not only provides estimates of the degree of substitution between durables and non-durables, but also allows this substitution to potentially vary over time in response to changing economic conditions. It is evident from Chart 3 that the degree of substitution between durables and non-durables, for changes in the user cost of durables, is relatively stable over time. More significantly, the elasticity of substitution between durables and both non-durables and services is slightly above unity with means of 1.133 (ME41 in Appendix 1c) and 1.069 (ME42 in Appendix 1c), respectively. This is consistent with the typical findings in the US literature. Ogaki and Reinhart (1998), for example, estimate an elasticity of substitution between durables and non-durables of 1.17 for the US. The results also support the assumption of Power (2004). This is a significant result as it suggests that the relative stability in the nominal expenditure share of durables in the face of the declining relative price of durables can indeed be attributed to a unitary elasticity of substitution between durables and non-durables (when the user cost of durables changes). As might be expected, semi-durables are greater substitutes in demand for durables than are either non-durables or services. Chart 3 indicates that substitution between durables and semidurables (ME45 in Appendix 1c) is fairly stable at around 1.298 throughout the sample period. Finally, the results confirm the importance of calculating the Morishima elasticities of substitution, which allow for the possibility of non-symmetry in the substitution relationship. Specifically, substitutability between monetary assets and durable goods (ME43 in Appendix 1c) ranges from 1.988 to just less than 3.980 (mean, 2.742) for changes in the user cost of durable goods. This is considerably larger than the estimated substitution between durable goods and monetary assets which range between 1.252 and 1.349 (mean, 1.298, ME34 in Appendix 1c) when the user cost of monetary assets changes (Chart 2). There is also a sustained trend increase in this substitutability over time as the elasticity of substitution between durable goods and monetary assets was typically close to 2 in the early 1990s but increased to around 4 by the end of the sample period. This evidence of non-symmetry is extremely important in the context of monetary policy and the monetary transmission mechanism, particularly given the recent attention paid by the Bank of

England to consumption, and especially to durables expenditure. More specifically, any change in monetary policy implemented by the Bank of England’s Monetary Policy Committee (MPC) via changes in Bank Rate will influence both the user cost of money and the user cost of durables by virtue of the impact on the benchmark interest rate. Hence, any reduction in the user cost of money (via a reduction in Bank Rate), for example, will reduce the user costs of both money and durables. According to the estimated Morishima elasticity ME34, this would produce a substitution away from durable goods and into monetary assets, while according to ME43 this would produce a substitution away from monetary assets and into durable goods. Clearly, as these effects could potentially cancel each other out, the implication would be a relatively weak transmission mechanism from interest rates to durables consumption expenditure. However, as is evident from Charts 2 and 3, the degree of substitutability between monetary assets and durable goods is considerably larger for ME43 as compared to ME34. Hence, the substitution away from monetary assets and into durable goods consumption is likely to dominate in respect of any loosening of monetary policy, and vice-versa. Furthermore, any change in Bank Rate which impacts on benchmark interest rates is likely to have a much larger impact on the user cost of durables than on the user cost of monetary assets. The reason being that any change in Bank Rate will also tend to produce adjustments in the own rates of return on interest bearing monetary assets, as well as in the benchmark interest rate. Consequently, this adjustment in own rates will tend to counteract at least some of the impact of changes in the Bank Rate on the user cost of money. This offset will not be present in the context of the user cost of durables. For both of the reasons advanced above, therefore, the influence of the monetary/interest rate transmission mechanism via the traditional ‘‘money channel” may be much more powerful than has hitherto been recognized. Furthermore, the evidence of a strong and sustained trend increase in the degree of substitutability between durable goods and money suggests that this channel of the monetary transmission mechanism is actually becoming more powerful over time (ME43 in Appendix 1c). Previous studies that hold substitution constant over time may therefore fail to capture this strong support for the traditional ‘‘money channel” of the monetary transmission mechanism. In addition, there may also be powerful ‘‘credit channels” linking durable goods consumption with official interest rate changes, although this analysis falls outside the scope of this paper.

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Semi Dur-Services

Semi Dur-Money

Semi Dur-Dur

1.5

1.3

1.1

0.9

0.7 90.3

91.3

92.3

93.3

94.3

95.3

96.3

97.3

98.3

99.3

00.3

01.3

02.3

03.3

04.3

05.3

Chart 4. Substitution for Divisia aggregates changes in the user cost of durable goods.

4.3. Changes in the user cost of semi-durables Few studies to date examine the consumption of semi-durable goods. Analyzing expenditure on semi-durable goods is important given the similarities between semi-durables and durables and the considerable attention directed to durable goods consumption in recent years from a policy perspective (see Power, 2004). Hence, this section examines the degree of substitution between semidurables and other consumption goods and monetary assets, when the user cost of semi-durables changes. Chart 4 shows that semi-durables and durables appear to be relatively strong substitutes in demand, also evident when examining the impact of changes in the user cost of durable goods in Chart 3. The Morishima elasticities between semi-durables and durables also appear to be symmetrical in the sense that both ME45 and ME54 are relatively stable at just below 1.3 throughout the sample period. In contrast, the degree of substitution between semi-durables and non-durables and services is somewhat lower, with both ME51 and ME52 close to unity throughout the sample period. Turning now to the substitution between semi-durables and monetary assets for changes in the user cost of semi-durable (ME53 in Appendix 1c), the estimates indicate relatively larger substitution, although not as great as the substitution evident between durable goods and monetary assets (Chart 3). Notwithstanding the increased variability since 1998, the results presented in Chart 4 suggest that semi-durables and money have become closer substitutes in recent years with substitution increasing from just over unity in 2002 to around 1.3 by the end of the sample period. As with the relationship between durables and monetary assets, the degree of substitution between semi-durables and money appears to be non-symmetric given that, for changes in the user cost of monetary assets, ME35 in Appendix 1c shows little variability at just over unity over the sample. Hence, it appears that there may also be an important monetary transmission channel which operates via reductions in Bank Rate, subsequent adjustments in the user costs of both monetary assets and semi-durables, and a net substitution away from monetary assets and into semi-durables consumption. However, given that our estimates of the substitution between durables and monetary assets (ME43 in Appendix 1c) fluctuate between 3 and 4 since 2001, while the substitution between semi-durables and monetary assets (ME53 in Appendix 1c) only varies between 1.04 and 1.3, this suggests that durable goods consumption plays a much more significant role in the monetary transmission mechanism compared to semi-durable expenditure. Once again, this is an important empirical result in the context of the implementation of monetary policy by the Bank of

England, and suggests that the Bank is correct in paying particular attention to the role of durable goods expenditure. Our empirical results also confirm the approach of Friedman (1956) and Friedman and Schwartz (1963) which proposed an important role for durable goods in the context of the ‘‘money view” of the transmission mechanism and predicted a relatively high elasticity of substitution between monetary assets and durable goods.

5. Artificially adjusted data and substitution estimates It is important to evaluate the effect on substitution, and thus on the monetary transmission mechanism, of the Bank of England’s decision to replace the artificially break-adjusted data with the non-break adjusted data. We repeat the analysis previously conducted and use the break-adjusted data. As in the case of the non-break adjusted monetary data, the results show that goods and money are substitutes in demand (Appendix 1d) with no evidence of complementarity in demand. The largest degree of substitution (max 1.635; mean 1.556) is between the Divisia aggregate of services and the stock of semi-durable goods during 2001.1 (ME25 in Appendix 1d). This maximum amount of substitution is considerably less than the corresponding relatively large amount of substitution (max 4.103; mean 2.836) between the Divisia aggregate of non-durables and the Divisia monetary aggregate from the non-break adjusted monetary data (ME13 in Appendix 1c). Significantly, for the break-adjusted data, ME13 actually exhibits the minimum amount of substitution (min 0.431; mean 0.715) during 2003.3. It is also evident that the substitution between monetary assets and consumption goods, based on the artificially break-adjusted data (Chart 5) differ markedly from the corresponding estimates in Chart 2 based on non-break adjusted data. While the estimates from the non-break adjusted data generally exceed unity, the substitution estimates from the break-adjusted data are very close to or below unity. In the context of our focus on the monetary transmission mechanism, this potential bias appears to be most serious in the case of the substitution between money and durable goods, for changes in the user cost of durable goods as shown in Chart 6. While the estimated substitution between monetary assets and durable goods is close to unity for the artificially break-adjusted data, the corresponding estimates from the non-break adjusted data show substitution generally increasing from around 2.0 in the 1990s to around 4.0 in the third quarter of 2005. In the context of the monetary transmission mechanism, therefore, it is very evident that estimates

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Money-Services

Money-Durables

Money-Semi-Dur

1.02

1

0.98

0.96

0.94

0.92 91.2

92.2

93.2

94.2

95.2

96.2

97.2

98.2

99.2

00.2

01.2

02.2

03.2

04.2

05.2

Chart 5. Substitution for Divisia aggregates changes in the user cost of money.

4.5 Non-Break Adjusted

Break Adjusted

4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 90.2

91.2

92.2

93.2

94.2

95.2

96.2

97.2

98.2

99.2

00.2

01.2

02.2

03.2

04.2

05.2

Chart 6. Substitution durable goods and monetary assets changes in the user cost of durable goods.

based on the artificially break-adjusted data considerably underestimate the true extent of the substitution. Hence, it is clear that the use of artificial break-adjusted data introduces considerable biases into the estimated elasticities of substitution, both between money and goods and between the various categories of consumption goods. 6. Conclusion This paper produces empirical results which are important from the perspective of the implementation of the Bank of England’s monetary policy. Given the potential role of consumption in the monetary transmission mechanism, the estimates of substitution between monetary assets and durable goods consumption produced in this paper suggest that consumption is a relatively powerful element in the monetary transmission mechanism. These results imply that the traditional ‘‘money/interest rate channel” of the monetary transmission mechanism may be more powerful than has hitherto been appreciated. Substitution between monetary assets and semi-durables consumption appears to be a less powerful, although still potentially important, channel in the transmission mechanism. Hence, our estimates support the

increasing attention which central banks, such as the Bank of England, have been paying to the role of durable consumption expenditure in recent years. Secondly, our results confirm the assumption made in the Bank of England analysis of consumption (see Power, 2004), that the elasticity of substitution between durables and non-durables (and services) is approximately unity. This result can explain the ‘‘puzzle” that the nominal expenditure share of durables in the UK has remained relatively stable in the face of a sharp decline in the relative price of durables, while the real expenditure share of durables has increased dramatically. Our estimates suggest that this assumption does not hold in the case of semi-durables. Finally, this paper also provides important new evidence on potential data-driven sources of bias in estimates of substitution across UK monetary assets and consumption goods (non-durables, services and the net stock of durables and semi-durables), and the consequences for policy. Specifically, it is clear from our empirical results that a major source of bias can occur from using artificial break-adjusted monetary data and our results support the Bank of England’s decision to switch from the artificial break-adjusted data to the non-break adjusted data in order to make the Divisia measure more consistent with economic theory (Hancock, 2005).

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Appendix 1a

Appendix 1b (continued)

Fourier estimates divisia aggregates non-break adjusted monetary data

Fourier estimates Divisia aggregates break-adjusted monetary data

Parameter

Estimate

Standard error

t-Statistic

P-value

Parameter

Estimate

Standard error

t-statistic

P-value

U05 U15 V15 U04 U14 V14 U03 U13 V13 U02 U12 V12 U01 U11 V11 B4 B3 B2 B1

0.0163 0.0022 0.0008 0.0321 0.0002 0.0000 0.0362 0.0001 0.0003 0.0432 0.0212 0.0057 0.0006 0.0004 0.0013 2.6530 0.8362 0.7187 0.4834 0.894

0.002 0.001 0.001 0.003 0.001 0.001 0.005 0.001 0.001 0.022 0.004 0.012 0.007 0.001 0.001 0.324 0.073 0.344 0.312 0.169

7.888 2.460 1.190 10.797 0.189 0.047 7.197 0.129 0.378 1.955 5.997 0.483 0.092 0.306 0.917 8.182 11.477 2.090 1.550 5.285

0.000 0.014 0.234 0.000 0.850 0.9620 0.000 0.897 0.705 0.051 0.000 0.629 0.927 0.760 0.359 0.000 0.000 0.037 0.121 0.000

U11 V11 B4 B3 B2 B1

0.0024 0.0104 0.3798 0.1384 1.0594 1.7377 0.876

0.004 0.006 0.043 0.017 0.021 0.154 0.131

0.555 1.868 8.807 8.217 49.405 11.320 6.681

0.579 0.062 0.000 0.000 0.000 0.000 0.000

q

(1) All estimation was performed using the nonlinear LSQ procedure from International TSP 4.4 with convergence set at 0.00001. Multiple starting values and multi-indexes were used to ensure convergence to the global optimum. Budget shares from the Divisia data are the same as from the actual data. (2) The parameter estimates are from estimating the system of equations using Divisia aggregates for monetary assets and consumer goods. The upward F-test procedure of Eastwood (1991) is used to determine the degree of the Fourier polynomials and finds that A = 4 and J = 1. (3) The Lagrange multiplier test for serial correlation was performed by regressing the residuals from each equation on the exogenous variables and the lagged residuals from the ith share equation as in Fisher et al. (2001). Using four lagged values gives a v2-test-statistic of 9.49 at the 5% level. There is no evidence of serial correlation given the estimated LM values of 19.386 (Divisia aggregate for nondurable goods), 13.598 (Divisia aggregate for monetary assets), 19.986 (Divisia aggregate for services), 22.874 (Stock of durable goods), and 21.857 (Stock semidurables).

Appendix 1b Fourier estimates Divisia aggregates break-adjusted monetary data Parameter

Estimate

Standard error

t-statistic

P-value

U05 U15 V15 U04 U14 V14 U03 U13 V13 U02 U12 V12 U01

0.0008 0.0012 0.0001 0.0051 0.0001 0.0006 0.0127 0.0009 0.0007 0.1055 0.0096 0.0110 0.0556

0.000 0.000 0.000 0.001 0.000 0.000 0.001 0.000 0.000 0.009 0.003 0.002 0.013

2.716 6.964 1.210 7.538 0.522 3.610 9.776 2.319 2.241 11.853 3.036 5.088 4.316

0.007 0.000 0.226 0.000 0.601 0.000 0.000 0.020 0.025 0.000 0.002 0.000 0.000

q

(1) All estimation was performed using the nonlinear LSQ procedure from International TSP 4.4 with convergence set at 0.00001. Multiple starting values and multi-indexes were used to ensure convergence to the global optimum. Budget shares from the Divisia data are the same as from the actual data. (2) The parameter estimates are from estimating the system of equations using Divisia aggregates for monetary assets and consumer goods. The upward F-test procedure of Eastwood (1991) is used to determine the degree of the Fourier polynomials and finds that A = 4 and J = 1. (3) The Lagrange multiplier test for serial correlation was performed by regressing the residuals from each equation on the exogenous variables and the lagged residuals from the ith share equation as in Fisher et al. (2001). Using four lagged values gives a v2-test-statistic of 9.49 at the 5% level. There is no evidence of serial correlation given the estimated LM values of 21.681 (Divisia aggregate for nondurable goods), 15.815 (Divisia aggregate for monetary assets), 17.506 (Divisia aggregate for services), 18.813 (Stock of durable goods), and 19.090 (Stock semidurables).

Appendix 1c Non-break adjusted monetary data Morishima elasticities of substitution (Divisia aggregates) Morishima

Mean

Std. dev.

Minimum

Maximum

ME31 ME32 ME34 ME35 ME41 ME42 ME43 ME45 ME51 ME52 ME53 ME54 ME12 ME13 ME14 ME15 ME21 ME23 ME24 ME25

1.139 1.007 1.286 1.024 1.133 1.069 2.742 1.298 0.999 1.013 1.127 1.286 0.979 2.836 1.301 1.002 0.970 1.158 1.308 1.076

0.007 0.007 0.017 0.015 0.008 0.005 0.522 0.024 0.002 0.004 0.081 0.017 0.047 0.498 0.016 0.006 0.089 0.136 0.021 0.018

1.125 0.994 1.252 1.004 1.121 1.061 1.988 1.252 0.997 1.008 1.036 1.252 0.914 1.948 1.264 0.992 0.839 0.843 1.265 1.051

1.153 1.020 1.323 1.053 1.147 1.082 3.980 1.349 1.002 1.020 1.336 1.322 1.051 4.103 1.329 1.016 1.101 1.364 1.351 1.111

MEij = Morishima elasticity between variables i and j when the user cost/price of variable i changes. 1 = Divisia aggregate for non-durable goods. 2 = Divisia aggregate for services. 3 = Divisia aggregate for monetary assets. 4 = stock of durable goods. 5 = stock semi-durables.

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Appendix 1d Artificially break-adjusted monetary data Morishima elasticities of substitution (Divisia aggregates) Morishima

Mean

Std. dev.

Minimum

Maximum

ME31 ME32 ME34 ME35 ME41 ME42 ME43 ME45 ME51 ME52 ME53 ME54 ME12 ME13 ME14 ME15 ME21 ME23 ME24 ME25

0.980 0.989 1.012 0.953 0.954 0.975 1.002 0.893 0.990 1.134 0.732 0.894 1.155 0.715 0.875 0.942 1.310 0.721 0.881 1.556

0.008 0.003 0.002 0.007 0.007 0.003 0.000 0.012 0.086 0.011 0.084 0.012 0.034 0.145 0.014 0.191 0.100 0.144 0.014 0.045

0.967 0.984 1.008 0.942 0.939 0.971 1.001 0.871 0.897 1.112 0.572 0.865 1.113 0.431 0.844 0.736 1.207 0.439 0.850 1.474

0.988 0.993 1.015 0.966 0.964 0.980 1.002 0.914 1.115 1.149 0.891 0.908 1.203 0.863 0.893 1.205 1.461 0.867 0.898 1.635

MEij = Morishima elasticity between variables i and j when the user cost/price of variable i changes. 1 = Divisia aggregate for non-durable goods. 2 = Divisia aggregate for services. 3 = Divisia aggregate for monetary assets. 4 = stock of durable goods. 5 = stock semi-durables.

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