econometrics
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1 What is Econometrics?
Econometrics is a rapidly developing branch of economics which, broadly speaking, aims to give empirical content to economic relations. The term ‘econometrics’ appears to have been first used by Pawel Ciompa as early as 1910; although it is Ragnar Frisch, one of the founders of the Econometric Society, who should be given the credit for coining the term, and for establishing it as a subject in the sense in which it is known today (see Frisch, 1936, p. 95). Econometrics can be defined generally as ‘the application of mathematics and statistical methods to the analysis of economic data’, or more precisely in the words of Samuelson, Koopmans and Stone (1954),
... as the quantitative analysis of actual economic phenomena based on the concurrent development of theory and observation, related by appropriate methods of inference (p. 142).
Other similar descriptions of what econometrics entails can be found in the preface or the introduction to most texts in econometrics. Malinvaud (1966), for example, interprets econometrics broadly to include ‘every application of mathematics or of statistical methods to the study of economic phenomena’. Christ (1966) takes the objective of econometrics to be ‘the production of quantitative economic statements that either explain the behaviour of variables we have already seen, or forecast (i.e. predict) behaviour that we have not yet seen, or both’. Chow (1983) in a more recent textbook succinctly defines econometrics ‘as the art and science of using statistical methods for the measurement of economic relations’.
By emphasizing the quantitative aspects of economic problems, econometrics calls for a ‘unification’ of measurement and theory in economics. Theory without measurement, being primarily a branch of logic, can only have limited relevance for the analysis of actual economic problems. While measurement without theory, being devoid of a framework necessary for the interpretation of the statistical observations, is unlikely to result in a satisfactory explanation of the way economic forces interact with each other. Neither ‘theory’ nor ‘measurement’ on their own is sufficient to further our understanding of economic phenomena. Frisch was fully aware of the importance of such a unification for the future development of economics as a whole, and it is the recognition of this fact that lies at the heart of econometrics. This view of econometrics is expounded most eloquently by Frisch (1933a) in his editorial statement and is worth quoting in full:
... econometrics is by no means the same as economic statistics. Nor is it identical with what we call general economic theory, although a considerable portion of this theory has a definitely quantitative character. Nor should econometrics be taken as synonymous with the application of mathematics to economics. Experience has shown that each of these three view-points, that of statistics, economic theory, and mathematics, is a necessary, but not by itself a sufficient, condition for a real understanding of the quantitative relations in modern economic life. It is the unification of all three that is powerful. And it is this unification that constitutes econometrics.
This unification is more necessary today than at any previous stage in economics. Statistical information is currently accumulating at an unprecedented rate. But no amount of statistical information, however complete and exact, can by itself explain economic phenomena. If we are not to get lost in the overwhelming, bewildering mass of statistical data that are now becoming available, we need the guidance and help of a powerful theoretical framework. Without this no significant interpretation and coordination of our observations will be possible.
The theoretical structure that shall help us out in this situation must, however, be more precise, more realistic, and, in many respects, more complex, than any heretofore available. Theory, in formulating its abstract quantitative nations, must be inspired to a larger extent by the technique of observation. And fresh statistical and other factual studies must be the healthy element of disturbance that constantly threatens and disquiets the theorist and prevents him from coming to rest on some inherited, obsolete set of assumptions.
This mutual penetration of quantitative economic theory and statistical observation is the essence of econometrics (p. 2).
Whether other founding members of the Econometric Society shared Frisch’s viewpoint with the same degree of conviction is, however, debatable, and even today there are no doubt economists who regard such a viewpoint as either ill-conceived or impractical. Nevertheless, in this survey I shall follow Frisch and consider the evolution of econometrics from the unification viewpoint.
2 Early Attempts at Quantitative Research in Economics
Empirical analysis in economics has had a long and fertile history, the origins of which can be traced at least as far back as the work of the 16th-century Political Arithmeticians such as William Petty, Gregory King and Charles Davenant. The political arithmeticians, led by Sir William Petty, were the first group to make systematic use of facts and figures in their studies. (See, for example, Stone (1984) on the origins of national income accounting.) They were primarily interested in the practical issues of their time, ranging from problems of taxation and money to those of international trade and finance. The hallmark of their approach was undoubtedly quantitative and it was this which distinguished them from the rest of their contemporaries. Political arithmetic, according to Davenant (1698, Part I, p. 2) was ‘the art of reasoning, by figures, upon things relating to government’, which has a striking resemblance to what might be offered today as a description of econometric policy analysis. Although the political arithmeticians were primarily and understandably preoccupied with statistical measurement of economic phenomena, the work of Petty, and that of King in particular, represented perhaps the first examples of a unified quantitative/theoretical approach to economics. Indeed Schumpeter in his History of Economic Analysis (1954) goes as far as to say that the works of the political arithmeticians ‘illustrate to perfection, what Econometrics is and what Econometricians are trying to do’ (p. 209).
The first attempt at quantitative economic analysis is attributed to Gregory King, who is credited with a price-quantity schedule representing the relationship between deficiencies in the corn harvest and the associated changes in corn prices. This demand schedule, commonly known as ‘Gregory King’s law’, was published by Charles Davenant in 1699. The King data are remarkable not only because they are the first of their kind, but also because they yield a perfectly fitting cubic regression of price changes on quantity changes, as was subsequently discovered independently by Whewell (1850), Wicksteed (1889) and by Yule (1915). An interesting account of the origins and nature of ‘King’s law’ is given in Creedy (1986).
One important consideration in the empirical work of King and others in this early period seems to have been the discovery of ‘laws’ in economics, very much like those in physics and other natural sciences. This quest for economic laws was, and to a large extent still is, rooted in the desire to give economics the status that Newton had achieved for physics. This was in turn reflected in the conscious adoption of the method of the physical sciences as the dominant mode of empirical enquiry in economics. The Newtonian revolution in physics, and the philosophy of ‘physical determinism’ that came to be generally accepted in its aftermath, had far-reaching consequences for the method as well as the objectives of research in economics. The uncertain nature of economic relations only began to be fully appreciated with the birth of modern statistics in the late 19th century and as more statistical observations on economic variables started to become available. King’s law, for example, was viewed favourably for almost two centuries before it was questioned by Ernest Engel in 1861 in his study of the demand for rye in Prussia (see Stigler, 1954, p. 104).
The development of statistical theory at the hands of Galton, Edgeworth and Pearson was taken up in economics with speed and diligence. The earliest applications of simple correlation analysis in economics appear to have been carried out by Yule (1895, 1896) on the relationship between pauperism and the method of providing relief, and by Hooker (1901) on the relationship between the marriage-rate and the general level of prosperity in the United Kingdom, measured by a variety of economic indicators such as imports, exports, and the movement in corn prices. In his applications Hooker is clearly aware of the limitations of the method of correlation analysis, especially when economic time series are involved, and begins his contribution by an important warning which continues to have direct bearing on the way econometrics is practised today:
The application of the theory of correlation to economic phenomena frequently presents many difficulties, more especially where the element of time is involved; and it by no means follows as a matter of course that a high correlation coefficient is a proof of causal connection between any two variables, or that a low coefficient is to be interpreted as demonstrating the absence of such connection (p. 485).
It is also worth noting that Hooker seems to have been the first to use time lags and de-trending methods in economics for the specific purpose of avoiding the time-series problems of spurious or hidden correlation that were later emphasized and discussed formally by Yule (1926).
Benini (1907), the Italian statistician, according to Stigler (1954) was the first to make use of the method of multiple regression in economics. He estimated a demand function for coffee in Italy as a function of coffee and sugar prices. But as argued in Stigler (1954, 1962) and more recently detailed in Christ (1985), it is Henry Moore (1914, 1917) who was the first to place the statistical estimation of economic relations at the centre of quantitative analysis in economics. Through his relentless efforts, and those of his disciples and followers Paul Douglas, Henry Schultz, Holbrook Working, Fred Waugh and others, Moore in effect laid the foundations of ‘statistical economics’, the precursor of econometrics. Moore’s own work was, however, marred by his rather cavalier treatment of the theoretical basis of his regressions, and it was therefore left to others to provide a more satisfactory theoretical and statistical framework for the analysis of economic data. The monumental work of Schultz, The Theory and the Measurement of Demand (1938), in the United States and that of Allen and Bowley, Family Expenditure (1935), in the United Kingdom, and the pioneering works of Lenoir (1913), Wright (1915, 1928), Working (1927), Tinbergen (1930) and Frisch (1933b) on the problem of ‘identification’ represented major steps towards this objective. The work of Schultz was exemplary in the way it attempted a unification of theory and measurement in demand analysis; whilst the work on identification highlighted the importance of ‘structural estimation’ in econometrics and was a crucial factor in the subsequent developments of econometric methods under the auspices of the Cowles Commission for Research in Economics.
Early empirical research in economics was by no means confined to demand analysis. Another important area was research on business cycles, which in effect provided the basis of the later development in time-series analysis and macroeconometric model building and forecasting. Although, through the work of Sir William Petty and other early writers, economists had been aware of the existence of cycles in economic time series, it was not until the early 19th century that the phenomenon of business cycles began to attract the attention that it deserved. (An interesting account of the early developments in the analysis of economic time series is given in Nerlove and others, 1979.) Clement Juglar (1819–1905), the French physician turned economist, was the first to make systematic use of time-series data for the specific purpose of studying business cycles, and is credited with the discovery of an investment cycle of about 7–11 years duration, commonly known as the Juglar cycle. Other economists such as Kitchin, Kuznets and Kondratieff followed Juglar’s lead and discovered the inventory cycle (3–5 years duration), the building cycle (15–25 years duration) and the long wave (45–60 years duration), respectively. The emphasis of this early research was on the morphology of cycles and the identification of periodicities. Little attention was paid to the quantification of the relationships that may have underlain the cycles. Indeed, economists working in the National Bureau of Economic Research under the direction of Wesley Mitchell regarded each business cycle as a unique phenomenon and were therefore reluctant to use statistical methods except in a non-parametric manner and for purely descriptive purposes (see, for example, Mitchell, 1928 and Burns and Mitchell, 1947). This view of business cycle research stood in sharp contrast to the econometric approach of Frisch and Tinbergen and culminated in the famous methodological interchange between Tjalling Koopmans and Rutledge Vining about the roles of theory and measurement in applied economics in general and business cycle research in particular. (This interchange appeared in the August 1947 and May 1949 issues of The Review of Economics and Statistics.)
3 The Birth of Econometrics
Although, as I have argued above, quantitative economic analysis is a good three centuries old, econometrics as a recognized branch of economics only began to emerge in the 1930s and the 1940s with the foundation of the Econometric Society, the Cowles Commission in the United States, and the Department of Applied Economics (DAE) under the directorship of Richard Stone in the United Kingdom. (A highly readable blow-by-blow account of the founding of the first two organizations can be found in Christ (1952, 1983), while the history of the DAE is covered in Stone, 1978.) The reasons for the lapse of more than two centuries between the pioneering work of Petty and the recognition of econometrics as a branch of economics are complex, and are best understood in conjunction with, and in the light of, histories of the development of theoretical economics, national income accounting, mathematical statistics, and computing. Such a task is clearly beyond the scope of the present paper. However, one thing is clear: given the multi-disciplinary nature of econometrics, it would have been extremely unlikely that it would have emerged as a serious branch of economics had it not been for the almost synchronous development of mathematical economics and the theories of estimation and statistical inference in the late 19th century and the early part of the 20th century. (An interesting account of the history of statistical methods can be found in Kendall, 1968.)
Of the four components of econometrics, namely, a priori theory, data, econometric methods and computing techniques, it was, and to a large extent still is, the problem of econometric method which has attracted most attention. The first major debate over econometric method concerned the applicability of the probability calculus and the newly developed sampling theory of R.A. Fisher to the analysis of economic data. As Morgan (1986) argues in some detail, prior to the 1930s the application of mathematical theories of probability to economic data was rejected by the majority in the profession, irrespective of whether they were involved in research on demand analysis or on business cycles. Even Frisch was highly sceptical of the value of sampling theory and significance tests in econometrics. His objection to the use of significance tests was not, however, based on the epistemological reasons that lay behind Robbins’s and Keynes’s criticisms of econometrics. He was more concerned with the problems of multicollinearity and measurement errors which he believed, along with many others, afflicted all economic variables observed under non-controlled experimental conditions. By drawing attention to the fictitious determinateness created by random errors of observations, Frisch (1934) launched a severe attack on regression and correlation analysis which remains as valid now as it was then. With characteristic clarity and boldness Frisch stated:
As a matter of fact I believe that a substantial part of the regression and correlation analyses which have been made on economic data in recent years is nonsense for this very reason [the random errors of measurement] (1934, p. 6).
In order to deal with the measurement error problem Frisch developed his confluence analysis and the method of ‘bunch maps’. Although his method was used by some econometricians, notably Tinbergen (1939) and Stone (1945), it did not find much favour with the profession at large. This was due, firstly, to the indeterminate nature of confluence analysis and, secondly, to the alternative probabilistic rationalizations of regression analysis which were advanced by Koopmans (1937) and Haavelmo (1944). Koopmans proposed a synthesis of the two approaches to the estimation of economic relations, namely the error-in-variables approach of Frisch and the error-in-equation approach of Fisher, using the likelihood framework; thus rejecting the view prevalent at the time that the presence of measurement errors per se invalidates the application of the ‘sampling theory’ to the analysis of economic data. In his words
It is the conviction of the author that the essentials of Frisch’s criticism of the use of Fisher’s specification in economic analysis may also be formulated and illustrated from the conceptual scheme and in the terminology of the sampling theory, and the present investigation is an attempt to do so (p. 30).
The formulation of the error-in-variables model in terms of a probability model did not, however, mean that Frisch’s criticisms of regression analysis were unimportant, or that they could be ignored. Just the opposite was the case. The probabilistic formulation helped to focus attention on the reasons for the indeterminacy of Frisch’s proposed solution to the problem. It showed also that without some a priori information, for example, on the relative importance of the measurement errors in different variables, a determinate solution to the estimation problem would not be possible. What was important, and with hindsight path-breaking, about Koopmans’s contribution was the fact that it demonstrated the possibility of the probabilistic characterization of economic relations, even in circumstances where important deviations from the classical regression framework were necessitated by the nature of the economic data.
Koopmans did not, however, emphasize the wider issue of the use of stochastic models in econometrics. It was Haavelmo who exploited the idea to the full, and argued forcefully for an explicit probability approach to the estimation and testing of economic relations. In his classic paper published as a supplement to Econometrica in 1944, Haavelmo defended the probability approach on two grounds: firstly, he argued that the use of statistical measures such as means, standard errors and correlation coefficients for inferential purposes is justified only if the process generating the data can be cast in terms of a probability model: ‘For no tool developed in the theory of statistics has any meaning - except, perhaps, for descriptive purposes - without being referred to some stochastic scheme’ (p. iii). Secondly, he argued that the probability approach, far from being limited in its application to economic data, because of its generality is in fact particularly suited for the analysis of ‘dependent’ and ‘non-homogeneous’ observations often encountered in economic research. He believed what is needed is