Multicointegration in US consumption data

Abstract

The present study tests for the existence of multicointegration between real per capita private consumption expenditure and real per capita disposable personal income in the USA. In doing so, the study exploits the fact that the flows of disposable income and consumption expenditure on the one hand, and the stock of consumers' wealth, which can be considered as cumulative past discrepancies between the flows of income and expenditure, on the other hand, can be thought of as a stock-flow model, in which multicointegration is likely to occur. Recently developed I(2) techniques are applied for testing for multicointegrating relations and find supporting evidence for the existence of multicointegration in US consumption data.

Acknowledgements

I would like to thank Tom Engsted, Philip Hans Franses, Paul Gregory, Niels Haldrup, Michael Jansson, and most of all Hans Christian Kongsted, as well as the participants of the Centre for Nonlinear Modelling in Economics (CNME) seminar in Svinkløv (Denmark), and the workshop on the I(2) analysis in Bertinoro (Italy), for thoughtful comments. The usual disclaimer applies.

Notes

¹Muellbauer and Lattimore (1995) summarize the economic role of assets an the consumption decisions.

² We would like to distinguish between multi- and polynomial cointegration. The former refers to the situation when the focus is the long-run relations between the original I(1) variables and their I(2) transformation, whereas the latter – and the long-run relations between the original I(2) variables and its first differences or some other I(1) variables. For recent examples of polynomial cointegration analysis see Kongsted (2003), Nielsen (2002), and Banerjee et al. (2001).

³ Zero initial values are assumed for y_t and c_t . Such scaling has no implications for the further analysis, except that proper allowance for deterministic components in the model will be needed.

⁴ The I(2) analysis in VAR models is technically involved. Therefore, in the further discourse the Skeleton of the inference and estimation procedures used are mainly presented. For a recent review of the I(2) analysis as well as for the further technical details, see e.g. Haldrup (1998) and references therein.

⁵ Observe that by using the I(2) formulation of the problem the single multicointegrating relation involves the two layers of cointegration that follow from the usual I(1) analysis.

⁶ This point has been made by Hans Christian Kongsted.

⁷ In the common stochastic trends representation we omit the nuisance parameters introduced by the initial conditions, see Johansen (1995).

⁸ This dataset has been used extensively in the literature, for example, in Blinder and Deaton (1985), Campbell and Deaton (1989), Flavin (1993), and Vahid and Engle (1993).

⁹ As pointed out by Muellbauer and Lattimore (1995), when modelling the consumption function one should be concerned with the possibility that the error term grows with the scale of consumption. Consequentially, they suggest using the log transformations of the consumption and explanatory variables in order to remedy this potential problem. Fortunately, this effects are absent in our data, see Fig. 1. Therefore in the subsequent analysis one proceeds with the variables measured in the natural units. Further advantage of using the data in the present form is that in the framework of the multicointegration analysis it is easier to interpret the measure of wealth in terms of the cumulative savings.

¹⁰ All I(2) analysis has been performed using the I(2) procedure written by Clara M. J⊘rgensen for the CATS in RATS package (available online http://www.estima.com/procs/i2index.htm).