Time deformation in UK consumers’ expenditure: an empirical analysis of highly disaggregated data

Abstract

The literature on testing for the presence of cyclical asymmetry in consumers’ expenditure is extended via the application of tests for time deformation to UK data subject to a high degree of disaggregation. The initial empirical findings provide evidence of significant time deformation in total, durables and semi-durables expenditures. Closer examination of highly disaggregated expenditure further reveals that time deformation is an intrinsic property of a particular set of expenditure categories including household fittings and furnishings, communication and information technology, vehicles and utilities. These results suggest that such consumers’ expenditures ‘speed up’ during expansions, most likely being driven by the relaxation of credit rationing constraints due to transient income windfalls or the easing of credit conditions, and possibly associated with housing market conditions subsequent to financial market liberalization.

Notes

¹ See Psaradakis (2000) for discussion of a number of commonly employed tests of asymmetry and non-linearity.

² Relatedly, Cook (2000b) reports evidence of significant inverse steepness in Australian total consumers’ expenditure, while Cook (2000c) reports the results of asymmetry tests applied to total consumers’ expenditure for seven major OECD economies, with mixed results. Cook (1999b) confirms significant deepness and steepness asymmetry in US consumer expenditure on durable goods, and insignificant test results for non-durable goods expenditure.

³ More fully, Holly and Stannett (1995) reported evidence of significant (negative) deepness in aggregate UK consumers’ expenditure while, in an extension of that initial study, Speight and McMillan (1997) examined the behaviour of 13 broadly disaggregated components of UK consumers’ expenditure, finding durables in particular to exhibit significant asymmetric steepness. Cook (2000a) extended the consideration of UK consumers’ expenditure to a longer run of annual frequency data across the three broad categories of durable, non-durable and total consumers’ expenditure and found durable consumption alone to display asymmetric steepness though not deepness asymmetry, but found the significance of the former to be dependent on the manner in which the trend filter is applied. Cook and Speight (2005) have extended this literature through application of an alternative test of asymmetric adjustment due to Randles et al . (1980) which has been shown to be robust to outliers (Eubank et al ., 1992) and by examining consumers’ expenditure at a much higher level of disaggregation, covering 101 separate categories of UK consumers’ expenditure in addition to two aggregate measures. The results obtained depict a positive relationship between the durability of goods and the degree of asymmetry they exhibit at an intermediate level of disaggregation, while at high levels of disaggregation it is found that evidence of deepness asymmetry is driven by a relatively small number of expenditures, prominent among which are durable and semi-durable good expenditures relating to housing fittings and communication.

⁴ Despite the novelty of the framework described here, the use of alternative time scales has a precursor in the phase averaging procedures employed at the National Bureau of Economic Research. Such phase averaging, whereby data are averaged across different phases of the business cycle, has a long history with Burns and Mitchell (1946) and Friedman and Schwartz (1982) offering early and more recent examples of this approach.

⁵ The two aggregate series considered are ‘national’ and ‘domestic’ measures. The series differ as a consequence of the latter's inclusion of net tourist expenditure.

⁶ Consumer Trends four character identifiers for these series, in the order listed in the results tables, are as follows: Table 1: ABJR, ZAKW, ZAKY, ZALA, ZAVO, ZAVW, ZAWC, ZAWM, ZAWW, ZAXA, ZAXS, ZAYG, ZWUN, ZWUT; Table 2: UTIH, UTID, UTIT, UTIL, UTIP; Table 3: ATQX, ATRD, ATRR, ATRV, ATRZ, ATSD, LLKX, LLKY, LLKZ, LLLA, LLLB, LLLC, TMMI, TMML, TMMZ, TMNB, TMNO, UWIC, XYJP, XYJR, XYJT, ZAYM; Table 4: ATQV, ATRF, ATRJ, ATSH, ATSL, ATSX, AWUW, CDZQ, LLLZ, LLMA, LLMB, LLMC, LLMD, XYJN, XYJO, XYJQ, XYJS, XYJU, XYJX, ZAVK; Table 5: ATSP, ATUA, AWUX, CCTK, CCTL, CCTM, CCTN, CCTO, CCTT, CCTU, CCTY, CCUA, CDZY, JRBA, LLLL, LLLM, LLLN, LLLO, LLLP, LLLQ, LTZA, LTZC, TTAB, UTHW, UTXP, UTZN, UUIS, UUVG, UWBK, UWBL, UWFD, UWFX, UWGH, UWGI, UWHO, UWIB, UWKQ, XYJW, ZAKY, ZWUN, ZWUP, ZWUR.

⁷ It should be noted that although some components, for example ‘Transport’, appear under durable, semi-durable and non-durable expenditure, in each case expenditure is defined as that part of the component relating to the classification (durable, semi-durable and non-durable) being considered. It may nonetheless be the case that such expenditures are not separable across these categories as a practical matter.

⁸ As a consequence of the stationarity requirement of the time deformation tests, augmented Dickey–Fuller tests were applied to all of the above series to determine their orders of integration. It was found that the unit root null hypothesis was rejected for only three series (clothing materials; newspapers, books and stationery; electricity, gas and other fuels) at the 5% level of significance. Therefore, in these instances the logarithmic values of the series in question are employed for the time deformation tests, while for all other series first differences of the logarithmic values are employed. Full details of unit root test results are available from the authors on request.

⁹ To avoid potential problems resulting from the presence of serial correlation and/or heteroskedasticity, the Newey–West (1987) heteroskedasticity and autocorrelation consistent (HAC) covariance matrix estimator is employed to assess the significance of the alternative F-tests of time deformation.

¹⁰ As Psaradakis and Sola (2003) show, tests of asymmetry may possess low power when applied to the business cycle component of macroeconomic time series, and we therefore consider test statistic significance up to a threshold of 10% rather than the conventional significance level of 5%.

¹¹ Although these results cover a larger number of expenditure categories, they offer confirmation of the preliminary time deformation test results for UK consumers’ expenditure previously reported in Cook (1999a).

¹² Furniture and furnishings; furnishings and household equipment; carpets and other floor coverings; photographic and optical equipment; information processing equipment; transport; vehicles; motor cars; bicycles.

¹³ Household textiles; transport; motor vehicle spares; small tools; electrical appliances for personal care; books.

¹⁴ Materials for maintenance and repair of dwelling; vehicle fuels and lubricants; electricity; gas; solid fuels; electricity, gas and other fuels; newspapers, books and stationery; health; meat; oils and fats; coffee, tea and cocoa; fruit; spirits; beer; other food; other medical products; pets and related products.

¹⁵ As noted previously in the literature, such asymmetries are not easily reconciled with the genre of intertemporal rational expectations permanent income models unless the role of transaction costs, precautionary savings under income uncertainty, habit formation, non-separabilities in utility derived from durable and non-durable goods, or liquidity constraints are acknowledged (Messinis et al ., 2002; Sarantis and Stewart, 2003).