The Practice of Econometrics

In order to accurately assess the impact of important individual characteristics such as income, demographic structure, location, wages and prices on commodity expenditure it is most advantageous to work with survey data at the individual level. However, all surveys on individual or household expenditures cover purchases over a limited period of time. Indeed, the more accurate the measurement in terms of precise diary records the shorter the period over which the survey can be afforded and the more likely the occurrence of reported zero expenditures. Even where the expenditure in question relates to an item or group of items for which actual consumption is positive, infrequency of purchase or the ‘durability’ of the good may result in a recorded zero expenditure. Here we wish to develop a bivariate model for the joint determination of the purchase and expenditure decision. We shall focus on the particular example of a commodity which is continuously consumed but only infrequently purchased.

Since the introduction of the Almost Ideal Demand System (AIDS) in the seminal paper by Deaton and Muellbauer (1980), few applications of their model have been reported. This may be due partly to the relatively complicated structure of the model and the associated estimation problems but it may also be due to the fact that the simplified versions of AIDS recommended by Deaton and Muellbauer have been used instead. More specifically, when it is possible to approximate a highly nonlinear price index (deflator) by a much simpler index such as the Stone (1953) index and hence reduce the level of computational difficulty to that of, say, the Rotterdam model, it is not surprising that researchers choose not to employ the AIDS model but use instead a model based on the simpler index.

This was the point of view expressed by Cramer in 1961 near the conclusion of his elegant monograph on ‘The Ownership of Major Consumer Durables’. It is arguable that job separation is an elementary, though far from simple, economic phenomenon — and we have tried to be patient.

I take particular pleasure in celebrating through the theme of this paper Cramer’s contributions to the study of household behaviour. Of these, I might specifically mention his 1957 paper which contains the first exposition of the neoclassical theory of the demand for durables, his 1962 book on the ownership of durables and his 1969 text. Particularly memorable for me from the latter’s very nice exposition of Engel curves is his clear treatment of the identification problem in the Prais-Houthakker (1955) method of constructing household equivalence scales from Engel curves incorporating household composition effects. Though no great issues arise in the treatment of household composition effects in the Engel curves which I estimate below, I hope that he will enjoy the paradoxes of the paper that follows.

The conventional approach to consumption theory considers only one consumer. His preferences are represented by a utility function, which is maximized subject to a budget constraint. Under appropriate conditions this leads to a system of demand equations, one for each good.

One of the more intractable problems in the area of monetary economics is the measurement of cash payments. In recent years, interest in cash payments has been revived as a direct result of their alleged role in lubricating the ‘underground’ economy. Because cash payments rarely leave a ‘paper’ trail, they are an effective medium of exchange for those seeking to avoid the payment of income or consumption taxes. But the importance of cash payments goes well beyond the issue of the underground economy. Indeed, the appropriate measurement of cash payments, and more particularly, the turnover or velocity of cash, is essential for the coherent development of monetary theory, and for measuring the effects of monetary changes on all macroeconomic activity.

The denominational mix of currency in circulation is part of the fine structure of a monetary economy. Although Chen (1976) has argued that the denominational mix has macroeconomic consequences, the prevailing view seems to be that the combination of banknotes and coins of different nominal values into the aggregate termed currency is a convenient, relatively harmless analytical simplification. This is evidenced by the fact that the denominational mix is seldom discussed in the monetary literature.

Cramer prefers to explore unmapped territory, doing research that presents all the challenge and excitement of discovery. From estimators, parameters and distributions to motor-cars and bank notes. Unfettered by convention and inspired by a high degree of originality. Doubly fascinated when the search is difficult, tracing that rock-solid parameter or that cast-iron constant or those many ‘missing’ Dutch 1000-guilder bank notes.

This paper is based on a consultancy project for the Dutch Postal Clearing Service, the ‘Giro’. The Giro plays an important part in transactions in the Netherlands. Specifically salary payments to households are important. As most of these take place on rather fixed days each month, and also have yearly patterns, the balance of the giro shows strong calendar variations and seasonality. Apart from that there are clearly trend movements. To develop a model to forecast all these movements was the goal of the project. This succeeded but the resulting model appeared much more complex than expected. Instead of the balance several flows of money going into and out of the system were modelled. Moreover each flow was decomposed into monthly aggregates showing trends and seasonality and the distribution of the aggregates over the days in each month showing all kinds of calendar effects. For all the submodels several possibilities have been tried, evolving from ad hoc solutions based on traditional time-series models to solutions based on the Kalman-filter. Around 1983 we discovered the latter possibilities, mainly due to the work of Harvey (1981). The Kalman-filter has a great appeal as a unified framework. Moreover the certainty that the specified models are optimally estimated — often not possible with ad hoc solutions — is reassuring.

According to Lange (1968) the first econometric study has been Pareto’s analysis of the personal income distribution. It appeared first in the Giornale degli Economisti of January 1895. Over the last twenty five years the personal income distribution has also been one of the topics of interest of Cramer, see Cramer (1969,1976,1978) and Ransom and Cramer (1983). Most authors deal with the problem from a normative point of view. They compare the given distribution with some preconceived idea of how the distribution should look like. Cramer is more at home among positivists who aim at a concise description of actual distributions.

Policy makers and economists have long been interested in the effect of economic growth on the size distribution of incomes. Some economists believe that economic development in countries can come only at the expense of greater distributional inequality, suggesting that policies that encourage economic growth should be accompanied by redistributional policies. Others feel that economic growth will naturally result in a more equitable distribution of income, as all groups benefit from growth.

R², the coefficient of determination or the squared correlation coefficient, is a recurrent theme in statistics. Kendall (1960) calls it an evergreen. Sooner or later any empirical analyst has to deal with some aspect of R² which appears not to have been treated satisfactorily in the known literature. Some like Hotelling (cf. Kendall (I960)) or Cramer (1964, 1984) even do it sooner and later. Also the present contribution is prompted by the problem that the usual expressions for R² may yield unacceptable values in regressions without a constant term. The purpose is to obtain an expression which avoids this problem and at the same time is as analogous as possible for regressions with and without intercept.

Market research very often considers different time series simultaneously and analyses their interdependence within the regression framework. The most prominent example is the relationship between sales and advertisement of which the carryover effect of advertising on sales has attracted much interest. Clarke’s (1976) well-known survey lists 69 studies up to 1975 and Aaker & Carman (1982) review several additional studies since then. The main emphasis in these studies has been on proper statistical modelling of the lag structure in the spirit of the empirical-econometrics tradition. The most common statistical specification has been the Koyck model for adaptive behaviour.

In a recent book Zellner (1982, p. 26) reviews some basic issues in econometrics, past and present. He recalls the discussion between Keynes and Tinbergen in the 1930s on the appropriateness of applying statistical methods to non-experimental economic time-series data, on the possible incorrect specification of relationships, and on the suitability of econometric methods and models for succesfull prediction and policy making; Zellner also briefly mentions a few other controversial basic issues in econometrics, viz. the causal interpretation of econometric models, the appropriateness of probability statements made in econometric analysis, and the claimed success of rather simple time-series models in comparison with elaborate econometric models. On many of these fundamental issues various conflicting opinions are still propounded in the literature. At the same time in most leading textbooks — that according to their titles deal with the foundations, principles, theory and analysis of models, methods and techniques of econometrics — many of the above-mentioned fundamental matters are not treated explicitly at all.

For a great many years, and certainly for as long as Cramer has held the chair of econometrics at the University of Amsterdam, the simultaneous-equation model has represented, to econometric theorists, what Kuhn, the author of a famous monograph on the Structure of Scientific Revolutions (1972) would describe as a central paradigm of their science.