Consumers' Expenditure
In modelling UK consumers' expenditure, David adopted a modelling approach similar to that in Hendry and Anderson (1977) by seeking a consumption function that served to interpret the equations from the major UK macro-models and explain why their proprietors had picked their particular specifications.
The resulting paper—Davidson, Hendry, Srba and Yeo (1978), often referred to as DHSY—has become one of David's most cited papers. DHSY adopted a “detective story” approach, using a nesting model for the different models' variables, valid for both seasonally adjusted and unadjusted data, and with up to five lags on all the variables to capture dynamics. Reformulation of that nesting model delivered an equation that Hendry and von Ungern-Sternberg (1981) later reinterpreted in light of Phillips (1954, 1957) and called an error correction model. Under error correction, if consumers made an error relative to their plan by overspending in a given quarter, they would later correct that error.Some historical background helps illuminate DHSY's approach. David first had access to computer graphics in the early 1970s, and he was astonished by the graphs of real UK consumers' expenditure and income. Expenditure manifested vast seasonality, with double-digit percentage changes between quarters, whereas income had virtually no seasonality. Those seasonal patterns meant that expenditure was much more volatile than income on a quarter-to- quarter basis. Two implications followed. First, it would not work to fit a model with first-order lags (as David had done in Hendry (1974)) and hope that seasonal dummies plus the slight seasonality in income would explain the seasonality in expenditure. Second, the general class of consumptionsmoothing theories such as the permanent-income and life-cycle hypotheses seemed misfocused. Consumers were inducing volatility into the economy by large inter-quarter shifts in their expenditure, so the business sector must be a stabilising influence.
Moreover, as discussed in Section 4.1, the equation for consumers’ expenditure in Hendry (1974) had dramatically misforecast the first two quarters of 1968, suggesting the need for respecification.In developing their own model, DHSY examined several ingredients that were necessary to explain other modellers’ model selections: their modelling approaches, data measurements, seasonal adjustment procedures, choice of estimators, maximum lag lengths, and misspecification tests. DHSY first standardised on unadjusted data and replicated models on that. While seasonal filters leave a model invariant when the model is known, they can distort the lag patterns if the model is data-based. DHSY then investigated both least squares and instrumental variables estimation but found little difference. Few of the then reported evaluation statistics were valid for dynamic models, so such tests could mislead. Most extant models had a maximum lag of one, and they had short-run marginal propensities to consume that seemed too small to reflect agent behaviour. DHSY tried many blind alleys (including measurement errors) to explain these low marginal propensities to consume. DHSY then showed that equilibrium correction explained the low marginal propensities to consume by the induced biases in partial adjustment models. DHSY designed a nesting model, which explained all the previous findings, but with the puzzle that it simplified to a differenced specification, with no long-run term in the levels of the variables. Resolving that conundrum led to the equilibrium correction mechanism. DHSY’s “Sherlock Holmes” approach was extremely time-consuming and was rarely repeated subsequently; but it did stimulate research into encompassing, that is, trying to explain other models’ results from a given model’s perspective.
Even with DHSY’s wide-ranging and highly systematic modelling approach, a significant model reformulation occurred just before publication. An earlier version of DHSY’s model explained real consumers’ expenditure given real income, and that model significantly over-predicted expenditure through the 1973-1974 oil crisis.
Angus Deaton (1977) had just established a role for inflation in a consumption function if agents were uncertain as to whether relative prices or absolute prices were changing. Deaton's formulation suggested adding inflation and its lags to that earlier DHSY specification. Doing so explained the over-prediction. This result was the opposite to what some other economic theories suggested—namely, that high inflation should induce pre-emptive spending because inflation is an opportunity cost of holding money. Inflation did not reflect money illusion. Rather, it implied the erosion of the real value of liquid assets. Consumers did not treat the nominal component of after-tax interest as income, whereas the UK government's statistical office did, and so disposable income was being mismeasured. Adding inflation to DHSY's equation corrected that.DHSY made enormous advances empirically and methodologically. However, it did miss some key issues, including the equivalence of equilibrium correction models and cointegration (discussed in Section 2.2); the implications of seasonality in the data for annual differences in the model; the role of liquid assets in determining consumers' expenditure; and the insights of Phillips (1954, 1957) on proportional, integral, and derivative control rules. Collaboration with Thomas von Ungern-Sternberg identified and sorted through the last three issues and resulted in Hendry and von Ungern- Sternberg (1981), or HUS.
In DHSY, the equilibrium correction term was the four-quarter lag of the log of the ratio of expenditure to income, and it was highly seasonal. However, seasonal dummy variables were insignificant if one used Scheffe's method. About a week after DHSY's publication, Thomas von Ungern-Sternberg added seasonal dummies to that equation and, with conventional /-tests, found that they were highly significant. Care was clearly required with multiple-testing procedures. Those results on seasonality stimulated an industry on time-varying seasonal patterns, periodic seasonality, and periodic behaviour, with many contributions by Denise Osborn (1988, 1991).
Also, DHSY found that liquid assets were not significant in their model: that result arose from a subtle form of misspecification. HUS showed that, in an equilibrium correction formulation, imposing a long-run unit elasticity of expenditure with respect to income leaves no room for liquid assets. Methodologically speaking, DHSY were testing from simple to general, and not general enough. Once the long-run income elasticity was derestricted, liquid assets were significant in DHSY's equation. HUS interpreted the role of liquid assets as a Phillips-type integral correction mechanism. Moreover, the combined effect of liquid assets and real income on expenditure added up to unity in the long run.
After DHSY and HUS, David produced a whole series of papers on consumers' expenditure. Davidson and Hendry (1981) found that lagged variables, as derived from HUS, were significant in explaining current changes in UK consumers’ expenditure. HUS’s model thus encompassed the Euler- equation approach in Hall (1978). Subsequent papers by David checked the constancy of the models and extended them. Hendry (1983) modelled annual inter-war UK consumers’ expenditure, obtaining results similar to the postwar quarterly relations in DHSY and HUS, despite large changes in the correlation structure of the data. Mizon and Hendry (1980) and Hendry (1992a) developed models of consumers’ expenditure in Canada and France respectively; Hendry (1999) modelled inter-war and post-war US food expenditure; and Hendry (1994) revisited HUS with yet additional data. Hendry, Muellbauer and Murphy (1990) re-examined DHSY on an extended information set, finding that additional variables mattered—a result consistent with econometric theory in Sargan (1975) and White (1990). With an increasing sample size or information set, noncentral /-statistics become more significant, so models expand. These results also highlighted some of the challenges of empirical work. General-to-specific methodology provides guidelines for building encompassing models, but advances between studies are frequently simple-to-general, putting a premium on creative thinking.
5.3