Prediction and Forecasting, Economic

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Prediction and Forecasting, Economic

Historical background

Types and methods of forecasting

Evaluaton of forecasts


A forecast can be defined generally as a statement about an unknown and uncertain event— most often, but not necessarily, a future event. Such a statement may vary greatly in form and content: it can be qualitative or quantitative, conditional or unconditional, explicit or silent on the probabilities involved. A reasonable requirement, however, is that the forecast should be verifiable, at least in principle; trivial predictions that are so broad or vague that they could never be found incorrect merit no consideration, and the same applies to predictions that are rendered meaningless by relying on entirely improbable assumptions or conditions. As for the “event” that is being predicted, it too is to be interpreted very broadly. Thus the forecast may refer to one particular or several interrelated situations (single versus multiple predictions). It may identify a single value or a range of values likely to be assumed by a certain variable (point versus interval predictions). Various combinations of these categories are possible, and some are interesting; for example, an unconditional interval prediction can be viewed as a set of conditional point predictions (that is, the forecaster estimates the range of probable outcomes by setting limits to the variation in the underlying conditions).

In principle, the unknown event that is the target of a prediction could pertain to the past or the present, but it is the future that is of primary concern to the forecaster. Information about the past and present is often incomplete and inadequate, but it is as a rule far richer and firmer than whatever may be “knowable” about the future. In fact, inferences from the past are the sole basic source for the expectations of events that are beyond the forecaster’s control. And the quality of these expectations (forecasts) is clearly a major determinant of the quality of plans and decisions that refer to factors over which the maker or user of the forecast does have substantial control.

Economic forecasts refer to the economic aspects of unknown events. Looking into the future, these predictions may be classified into short-run (with spans or distances to the target period of up to one or two years), intermediate (two to five years), and long-term (relating to more persistent developments or distant occurrences). Forecasts in all these categories are made for purposes of business planning, of aiding economic policies of governments, and of testing generalizations of economic theory. It is true that business forecasts deal largely with the near future, because this is both what is most needed and what stands a better chance of relative success in the reduction of avoidable business risks. Nonetheless, in certain areas, such as planning new industrial plant construction or acquisition of new businesses, prediction of rather long developments is needed, and lately business forecasters seem to have grown bolder in undertaking to project long trends in the economy. With the recent emphasis on growth objectives, longrange forecasts are also gaining ground as tools of governmental planning and decision making.

Important generalizations of economic theory typically imply qualitative conditional predictions; for example, the “law of demand” predicts that a decline in the price of a good will lead consumers to purchase more of that good. In the history of economic thought one also finds another type of prediction, in which the author presents as a forecast of things to come what is essentially an empirical hypothesis based on assumptions that may only have been valid at the time or may be questioned altogether. Predictions of secular developments by the classical economists provide several major examples, such as the law of historically diminishing returns and the Malthusian population principle. (Marx’s projections of a falling rate of profit and increasing pauperization and crises belong in the same logical category.) History dealt harshly with some of these prognostications, while many others were left untested by events and must often be viewed as inconclusive or lacking in present interest. In any case, these so-called evolutionary laws and other predictions of such a general nature are not included in the subject matter of this article, which will concentrate on more limited, specific, and, in particular, quantitative forecasts.

Historical background

It is clear from the preceding that prediction in the general sense has always been one of the products of economic thought; indeed, the ideal aim of any scientific generalization is to establish regularities or relationships that would hold not only for the past but also for the future observations of the same phenomena. Specific quantitative prediction, however, is of a much more recent origin in economics, having had to await the development of empirically oriented research and its statistical and mathematical tools. Two contributions of enduring influence in this development were Ernst Engel’s analysis of cross-section data on workers’ household budgets, which appeared in 1883, and Clement Juglar’s study of time series data on prices and finance, which appeared in 1862 and introduced the idea of observable “cycles” in business activity.

Growing interest in the persistent and disturbing phenomenon of business cycles gave considerable impetus to the collection and analysis of a variety of economic time series. A succession of significant studies of business cycles, with frequent references to historical and statistical materials, appeared between 1898 and 1925: works by Wicksell, Tugan-Baranovskii, Aftalion, Spiethoff, and Schumpeter in Europe, and by Mitchell in the United States. In the course of his later work on business cycles, Mitchell developed a strong (though healthily skeptical) concern about the possibilities of predicting the near-term fortunes of the economy. His 1938 paper on statistical indicators of cyclical revivals, written with Arthur F. Burns, initiated a series of several studies by the National Bureau of Economic Research (NBER), which produced tools that have recently been widely used in practical forecasting. [See the biography ofMitchell.]

Another flow of important contributions to the present-day techniques of economic forecasting had its source in the development of new methods of statistical inference, which were first applied in the physical and biological sciences and soon attracted the attention of those interested in social and economic data. Early illustrations of such work are found in Henry L. Moore’s studies on economic cycles and forecasting, which appeared in 1914 and 1917. Moore’s work stimulated the use of regression methods in forecasting prices and production of individual (particularly agricultural) commodities. Irving Fisher’s major achievements in monetary economics, index numbers, the study of distributed lags, etc., have long been acknowledged as early models of what came to be known as econometric research. Other pioneers in this approach include Paul H. Douglas (production functions, wages), Henry Schultz (demand functions), Ragnar Frisch (marginal utility measurement), Charles F. Roos (automobile and housing demand), and Jan Tinbergen (statistical tests of business cycle theories). Modern analysts and forecasters who use econometric models clearly owe a major debt to the work of these men.

More directly concerned with forecasting of short-term changes in general business conditions were the efforts of Warren M. Persons (1931) and the Harvard University Committee on Economic Research to identify time series that tend to move cyclically and would therefore help to anticipate what was ahead for the economy. The result was the Harvard Index Chart, consisting of three curves: (A) speculation (stock prices); (B) business (wholesale prices, later bank debits); and (C) money market (short-term interest rates). The Harvard chart was first published in 1919 for the last decade before World War i, then extended back to 1875; but the first extensive use of the underlying relationship was made by one of the early commercial business forecasting services, J. H. Brookmire, in 1911. The A-B-C sequence was found to have occurred with substantial regularity in the period before World War i. In the 1920s, the three-curve barometer proved less consistently successful, and it was considerably modified and often used in combination with other statistical devices. The Harvard service did not survive the great depression, although the index was published periodically in the Review of Economic Statistics until 1941. However, a recent unpublished evaluation shows that the sequence underlying the Harvard ABC curves persisted over a long period, not only in the interwar years but also in the post-World War u years. The Brookmire-Harvard method, for all its shortcomings, deserves to be acknowledged as an early forerunner of the present indicator techniques and also as a highly influential factor in the evolution of business cycle forecasting in Europe during the interwar period.

For men of affairs, prediction in some (not necessarily explicit) form must have always been unavoidable. Most decisions made in business and many decisions made in government imply or follow some forecasts of economic conditions. Economic and business forecasting as a specialized activity, however, is a relatively recent phenomenon which made its appearance largely in the twentieth century and developed rapidly only after World War i and, particularly, after World War II. In the latter postwar period forecasts have become both more abundant and more ambitious than ever before. Increasingly, forecasts of such comprehensive aggregates as the gross national product (GNP) and its major components, industrial production, and total employment are being made in numerical form not only for the next year but often also over a sequence of short periods, say the next four or six quarters. The spread of such predictions was stimulated by two recent developments: the rise of active interest in the application of macroeconomic theory, and the corresponding accumulation and improvement of aggregative data. The former can be attributed largely to the intensive work done by economists in the last thirty years— since Keynes’s General Theory—on problems in the determination of aggregate income, employment, and the price level. The latter goes back to the development of concepts and data on national income accounts by Simon Kuznets and others at the NBER and in the government statistical agencies. Very recently, the rapid growth of electronic computer technology has greatly accelerated the rate at which economic data (the raw materials for the forecaster) are compiled and processed. The same factor also had some more direct effects —without the computer, for example, the largescale econometric models could not have been produced, and hence output of forecasts of the econometric variety would have been severely limited.

Types and methods of forecasting

It is instructive to classify forecasts by several different criteria. First, one may distinguish between forecasts that are based solely on the past and current values of the variable to be predicted and forecasts that rely on postulated or observed relationships between the variable to be predicted and other variables. The former type of forecast will be referred to as an extrapolation. Second, the degree to which formalized methods are used establishes at least in principle a whole gradation ranging from informal judgment forecasts to predictions based on fully specified and strictly implemented econometric models. And third, one may distinguish between forecasts constructed by a single source, which could be an individual or a team (say, the staff of a business, or government agency), and forecasts derived as weighted or unweighted averages of different predictions made by a few or many individuals or organizations (the latter category includes opinion polls, surveys of businessmen’s anticipations, etc.).

These various classes of forecasts overlap and can be combined in various ways. For example, a forecast of next year’s GNP and its major components by a business economist may consist of any or all of the following ingredients: (1) extrapolation, of some kind, of the past behavior of the given series; (2) relation of the series to be predicted to known or estimated values of some other variables; (3) other external information considered relevant, such as a survey of investment intentions or a government budget estimate; and (4) the judgment of the forecaster. Also, it should be noted that a group forecast, say an opinion poll, will incorporate as many different techniques as are used by the different respondents. Any single classification of forecasting methods that cuts across the different criteria is likely to have only limited application to actual forecasts, which are built much more often on a combination of methods than on one particular technique.

Increasingly, starting with the early post-World War ii forecasts, the analysis of factors affecting the course of the economy is being carried on in terms of the major components of GNP. [SeeNational Income and Product Accounts.] This framework is thought to have the advantages of (a) ensuring that none of the main components of “aggregate effective demand” will be overlooked in the forecast, since they are all represented in the expenditure categories of the GNP accounts; (b) steering the forecaster to think in terms of the basic determinants of spending decisions by consumers, business, government, and foreign buyers; and (c) providing some safeguards that the various parts of the forecast, being constructed according to the internally consistent GNP system, will not be inconsistent with each other. However, there are also some disadvantages in an exclusive reliance on data such as those for GNP, which are highly aggregative, subject to frequent and often substantial revisions, and available only annually (with a relatively short dependable historical record) and quarterly (for the recent years).

A few mechanical forecasting techniques that were once fairly popular can be quickly disposed of as having little scientific basis or empirical soundness. For example, the method that assumes periodic cycles of given duration founders on the fact that cycles in business activity are far from being strictly periodic. The device of equalizing the areas below and above trend, or predicting that a business index will turn once it deviates from the “normal” by some critical amount, is unlikely to score well because trends are difficult to determine on a current basis and need not have the connotation of “normal” or “equilibrium” levels even when they are satisfactorily identified.

Judgment, in the broad sense of the word, is, of course, a necessary ingredient of all types of prediction: the forecaster must “judge” what information and methods of analysis to use and how to interpret and evaluate the results. Thus, judgment is bound to enter the forecasting process at various stages, but its proper role is to be a complement to, not a substitute for, a competent economic and statistical analysis. Informed judgment can go far in making forecasts more consistent and dependable, while pure guesswork can only rely on luck for success. It is well to recognize, however, that the ability to reach “good judgments” is not a well-defined, technical, transferable skill but rather a puzzling function of personal talent, experience, and training.

Many economic forecasts, particularly from business sources, are not based on formal models and do not disclose the underlying assumptions and methods. Some are likely to be little more than products of intuition, yet most seem presently to take the specific form of numerical point forecasts. However, there is no general presumption that the informal judgmental forecasts are largely hunches; on the contrary, at least the better ones among them originate in the application of various analytical techniques as well as judgment to diverse and substantial bodies of information.

Judgmental inferences from data samples and from any other evidence that the forecaster may have and regard as pertinent involve probability distributions. It would be informative and helpful for the appraisal of predictions if forecasters stated the odds they attach to the expected outcomes (the practice is frequent in weather forecasts, for example). The step from interval to distribution forecasting is, in principle, short. However, probabilistic distribution predictions appear to be regrettably rare in practical business and economic forecasting.

After eliminating those forecasting procedures that have little relevance currently, the following seem to merit further discussion: (1) extrapolative techniques; (2) surveys of intentions or anticipations; (3) business cycle indicators; and (4) econometric models. Typically, forecasters are using one or another of these approaches, or more likely some combination of them, for the most part tempering their results with considerable doses of “judgment.”


The term “extrapolations” will be used here as a shorthand expression for “extrapolations of the past behavior of the series to be predicted.” (The term is often applied in a broader sense to include projections of relationships between different variables, but such forecasts are more conveniently discussed under other headings—“econometric models” and to some extent also “business cycle indicators.” To be sure, extrapolative elements can be combined with the others, as in an econometric model in which, say, xt is associated with both xt-2 and yt-1.) Being restricted to the history of just one variable or process, extrapolations make only minimal or no use of economic theory, which deals largely with relations between different factors. Technically, however, extrapolations can vary a great deal, from very simple to very complicated forms. The simplest “naive models” project the last-known level or the last-known change in the series, that is, they assume that next period’s value of the series will equal this period’s value or that it will equal this period’s value plus the change from the preceding to this period. Few, if any, forecasters would cast their predictions in the form of such crude extrapolations, but the naive models are useful as minimum standards against which to measure the performance of forecasts proper.

Since trends are common in many economic time series because of the pervasive influence of growth in the economy, trend extrapolations usually provide more effective predictions and are therefore more demanding as criteria for forecast evaluation. Particularly in application to long-term forecasts, trend fittings and projections are widely used. The trends are usually conceived as smooth (often but not always monotonic) functions of time; the methods of describing them vary greatly, from visual freehand projections and long-period moving averages to diverse (for example, exponential, logistic) curves fitted by mathematical formulas. In the short-run context, the other typical components of economic time series become of primary importance, namely, the cyclical, seasonal, and purely “irregular” or random movements. (However, for some series, trends are substantial even over short periods, and in such cases it is especially rewarding for the forecaster to approximate them well.) [SeeTime Series.]

Strictly periodic, repetitive fluctuations are, like persistent trends, relatively easy to extrapolate: stable seasonal movements would often be more or less of this type. Average ratios of raw (say, monthly) data to smoothed values of the series representing mainly the longer-term movements (a centered 12-month moving average is the simplest example) are most commonly employed as a set of “seasonal indexes.” Extrapolations of these indexes then serve as forecasts of the seasonal movements. Since such movements are a major source of instability for business firms, their projection is particularly important in industrial and sales forecasting. Complications arise when the seasonal patterns are not very pronounced and not very stable, hence difficult to isolate from other component movements. Forecasters whose interest is mainly in the other movements often try to work around the seasonal effects by predicting changes in the seasonally adjusted series.

This leaves the cyclical and irregular components as the major objects of concern for the shortterm forecaster. Looking forward, it is usually anything but easy to distinguish the cyclical from the random element in the movement of an economic time series, although retrospectively it is often possible to do so with fair results (by decomposing the time series and testing the residually obtained estimates of the irregular component for randomness).

The forecasting errors that are directly traceable to very short random movements must be accepted as unavoidable. The forecaster can hardly be expected to predict an event generally regarded as unforeseeable, such as an outbreak of a war or a strike started without advance warning. However, although such “shocks” cannot themselves be predicted individually with the tools of economics and statistics, their more significant effects on the economy are, of course, the proper concern of the forecaster. In probabilistic predictions, which aim at the distribution of unknown parameters and outcomes rather than at point forecasts of future events, the effects of shocks and other random errors would be taken into account as an important part of the system to be analyzed. The role of random impulses in propagating business cycles has been given considerable attention in recent simulation studies of aggregative econometric models. [SeeSimulation, article oneconomic processes.]

For sequences of successive point predictions, which are the most common type of economic forecasts, the requirement of a good forecast is, in brief, that it predict well the systematic movements —trends and cycles—not that it predict perfectly the actual values of economic series, which, as a rule, contain random elements. Smoothing techniques can reveal the past patterns of systematic changes in the given series, and extrapolations can help the forecaster in his task to the extent that they preserve these patterns and to the extent that the patterns continue to apply. But, in regard to economic and related social events, the future seldom reproduces the past without significant modifications, and the historical “patterns” are often complex enough to elude efficient extrapolation.

In particular, extrapolations are by and large incapable of signalizing the turning points in business. The turns in extrapolations will as a rule lag behind those in the actual values; the strength of a good projection lies almost entirely in that it may predict well the longer-term trends. This contributes to the fact that, along with the short random variations, it is the cyclical fluctuations, not the longer trends, that produce the greatest difficulties in short-term forecasting. These fluctuations are recurrent but nonperiodic; they vary greatly in duration and amplitude; and calling them cyclical should convey neither more nor less than that they reflect mainly the participation of the given economic factor in “the business cycle.”

Important mathematical studies of smoothing and extrapolation of time series (by A. Kolmogoroff and by Norbert Wiener) appeared in the early 1940s. The method of autocorrelation, or the extrapolation of a series by means of a correlation of the series with itself at different points of time, was added and related to the methods of trend projection and harmonic analysis of the residuals from trend. It is an essential feature of dynamic process analysis in economics that variables at different points of time are functionally (usually stochastically) related; this approach may result in difference equations which generate their own solutions, as in the multiplier–accelerator models that yield a dependence of the current value of national income on the past values of national income. Thus, there is a strain of theoretical thought here that suggests the use of autoregressive extrapolation functions in aggregate income forecasting.

More recent developments have led to application of such functions in the analysis of how expectations are formed and how lagged adjustments are made. In particular, functions in which the weights decline geometrically as one goes back to progressively earlier past period values have been used in a variety of problems involving either expectation or partial adaptation to change. [SeeDistributed lags.] Forecasts derived from such exponentially declining weighted averages were found to have certain desirable properties for a class of autoregressive time series. But these are “optimum” predictions only if the structure of the series is known to belong in the given class and only if the past values of the series are all that one has to go on. These conditions are seldom fulfilled or relevant. As one of the pioneers in econometric forecasting methods has observed: “Mathematical processing or analysis can never substitute for sophistication. And until one understands the forces that built a particular structure in an economic time series and how these forces are currently changing, he cannot forecast with confidence even though by chance he scores a preponderance of successes” (Roos 1955, pp. 368–369).

Surveys of anticipations or intentions

The collection and evaluation of expectational data for the U.S. economy did not develop on a large scale until after World War II, but since then work in this area has proceeded at a rapid pace. The data relate to future consumer expenditures, planned or anticipated capital outlays of business firms, business expectations about “operating variables,” and government budget estimates.

Reports dealing with purchases of household appliances and automobiles are published periodically by the Survey Research Center of the University of Michigan. They currently include quarterly measures of consumer attitudes and inclinations to buy as well as annual financial data. Since 1959, a quarterly household survey has also been conducted by the Bureau of the Census.

The surveys of business plans and anticipations relating to future expenditures on plant and equipment include one that is carried on annually and quarterly as a joint enterprise by the U.S. Department of Commerce and the Securities and Exchange Commission (SEC) and another that is conducted annually by the McGraw-Hill Publishing Company. Since 1955, a quarterly survey of new and unspent capital appropriations has been conducted by the National Industrial Conference Board.

The oldest of the current surveys of businessmen’s expectations in the United States is the Railroad Shippers’ Forecast, which has given quarterly anticipations for carloadings by commodity since 1927. The Fortune magazine program, which started in the 1950s, includes surveys of “business expectations and mood,” retail sales, farm spending, homebuilding, inventories, and capital goods production (all of these are now semiannual, except for the annual farm and the quarterly inventory surveys). Data on manufacturers’ sales expectations have been gathered since 1948 in the course of the U.S. Department of Commerce–SEC survey of investment anticipations; quarterly figures on manufacturers’ sales and inventory expectations are now published regularly by the Department of Commerce in a program initiated in 1957.

Two other sources of data on business expectations about operating variables can be grouped together inasmuch as their output takes the special form of “diffusion indexes.” Such data indicate, for each successive forecast period, the percentage of respondents in the sample who expect either rises or declines or no change in the given variable. The Dun and Bradstreet surveys of manufacturers, wholesalers, and retailers cover employment, inventories, prices, new orders, sales, and profits; they started in the 1950s, are quarterly, and refer in each case to businessmen’s expectations for the impending six-month period. The monthly questionnaire of the National Association of Purchasing Agents, first issued in 1947, is addressed to participating members, covers production, new orders, commodity prices, inventories, and employment, and asks how the month ahead is going to compare with the preceding month (whether it will be better, worse, or the same).

Surveys of enterprise expectations have also spread in other countries, originating apparently with the IFO-Institute for Economic Research in Munich at the beginning of 1950. This institute sends monthly questionnaires to a large number of companies in West Germany and on the basis of replies from executives compiles diffusion data on the actual and expected directions of change in several important economic variables. By 1959, eight European countries, as well as Japan, South Africa, and Australia, adopted methods of entrepreneurial surveys similar to the IFO procedure.

Business expectations have been classified into intentions (plans for action where the firm can make binding decisions), market anticipations (relating to the interplay between the firm’s actions and its environment), and outlook (expectations about conditions which the firm cannot significantly influence but which will affect the markets). To illustrate, new capital appropriations or plans regarding next year’s outlays for plant and equipment fall into the first category, as does the scheduling over shorter periods of production and employment. The firm’s sales forecast, which depends on customers’ reaction to the terms offered, advertising efforts, etc., belongs to the second category, as do the expectations concerning financing, inventories, and selling prices (for firms that are not able to set their own prices). Finally, the class labeled “outlook” includes forecasts of the general situation of the economy or industry.

Consumer intentions to buy are in principle akin to business plans to acquire productive resources, but in practice they are often more vague and attitudinal and usually less firmly budgeted. Government budget estimates also represent intentions: they document what the central administration would undertake to spend for diverse specified purposes, subject to approval by the legislature. In government, as well as in many large business companies, the process of forming “expectations” or forecasts is often highly decentralized and complex, as is indeed the related process of reaching decisions.

The distinction between intentions, market anticipations, and outlook is of significance for the question of the predictive value of expectational data. It is plausible that accuracy will tend to be higher the greater the degree of control that those holding the expectation have over the variable concerned. This suggests that intentions should be on the whole more accurate than market anticipations, and the outlook estimates should be the least accurate. There is some evidence consistent with this view, notably the fact that business anticipations of plant and equipment expenditures have a much better forecasting record than business sales anticipations (as shown by the U.S. Department of Commerce–SEC sample surveys). However, there are other relevant factors which can modify such comparisons, such as the variabilities of the predicted series (forecasts of a very stable aggregate, classifiable as outlook, may be better than market anticipations for a variable which is highly volatile and therefore difficult to predict) and span of forecast (surveys looking far enough ahead, even for largely “controllable” variables, will be more in the nature of market anticipations and less of intentions, and they could well be less accurate than outlook surveys for the very near future).

Clearly, expectations of all kinds always involve some degree of uncertainty. They are presumably based in part on historical evidence, such as extrapolation of past behavior of the given series and inferences from observed relations with other series; but they are unlikely to incorporate only such evidence. As a result of expert insight or mere hunches, they may well include some additional information not contained in the patterns of the past. Hence, even where expectations are not very efficient when used alone as a direct forecast, they may still have a net predictive value as an ingredient in a forecasting process that combines expectational with other inputs.

In long-run forecasting, informed judgment or expectations play a major role along with extrapolative techniques. In large part, these forecasts are growth projections, which have been described as tools for exploring economic potentials. They are not intended to provide predictions of actual conditions in a distant year but rather estimates of likely conditions under some specified assumptions regarded as more or less reasonable. Attempts are often made to allow for the uncertainties of the future by constructing alternative projections that assume several different paths of economic developments within the range considered plausible. These forecasts are thus essentially concerned with trends of the economy at full employment. The variables projected are typically population, labor force, hours of work, and productivity on the supply side; expenditures on the major GNP components on the demand side; income, saving, and investment; and price level movements (which are often only implicitly considered, the projections being expressed in constant dollars).

Business cycle indicators

Business cycle indicators, which are used in analyzing and forecasting short-term economic developments, are time series selected for the relative consistency of their timing at cyclical revivals and recessions (other criteria being the economic significance of the series in relation to business cycles, their statistical adequacy, historical conformity to general movements of the economy, smoothness, and currency). The series are selected from large collections of quarterly and monthly economic series and then subjected to detailed analysis and repeated examinations of the quality of their performance as cyclical indicators. Such selections, based on studies of 500–800 series and successive reviews of the results, were made at the National Bureau of Economic Research in 1938 (by Mitchell and Burns), in 1950 and 1960 (by Geoffrey H. Moore), and in 1965 (by Moore and Shiskin). The first list included only indicators of cyclical revivals; the later ones covered indicators of both revivals and recessions, classified into those that tend to lead the turns in general business activity, those that tend to coincide roughly with these turns, and those that tend to lag. Further revisions and extensions of the list have been prompted by the appearance of new and improvement of old data, the accumulation of knowledge about the behavior of the series and the processes they represent, and the great increase in efficiency with which time series can be processed and analyzed. These reviews resulted in many significant changes, but the core of the list has not been essentially altered as to its composition in terms of the represented processes. In the most recent list, this core consists of the following:

Leading indicators (14 series)—average work week in manufacturing, nonagricultural job placements, new building permits for private housing, net business formation, new orders for durable goods, contracts for plant and equipment; change in unfilled orders for durables, change in manufacturers’ and trade inventories; industrial materials prices, stock prices, corporate profits after taxes, ratio of price to unit labor costs in manufacturing; change in consumer installment debt, liabilities of business failures.

Roughly coincident indicators (8 series)—nonagricultural employment, unemployment rate, GNP in constant dollars, industrial production, personal income, retail sales, manufacturing and trade sales, wholesale price index.

Lagging indicators (6 series)—long-duration unemployment, book value of manufacturers’ and trade inventories, labor cost per unit of output in manufacturing, business expenditures on new plant and equipment, bank rates on short-term business loans, commercial and industrial bank loans outstanding.

While the selection is based mainly on historical evidence, it is also broadly supported by general economic considerations and logic. Thus the aggregative series on production, employment, and income measure approximately the general level of business or economic activity whose major fluctuations are defined as the business cycle; hence, these series could hardly fail to be “roughly coincident.” The leaders include series that anticipate production and employment, such as hours worked, job vacancies, and new orders and contracts. For example, an increase in demand calling for additional labor input is likely to be met first by lengthening the work week and only later, if still needed, by hiring new workers (the former adjustment is less binding and costly than the latter). New orders precede production and employment by sizable intervals for goods made largely in response to prior offers or commitments to buy. Most durable manufactured goods belong in this category and, particularly, the capital equipment items which are as a rule produced to fill advance orders; construction of industrial and commercial plant is similarly anticipated by building contracts. The execution of these new investment orders and contracts takes time, however, and so the expenditures on plant and equipment is a roughly coincident or slightly lagging series.

Another type of sequence arises from the fact that a stock series often undergoes retardation before reversal; hence the corresponding flow series (or rate of change in the stock) tends to turn ahead of the stock. Thus, inventory changes lead at business cycle turns, while total inventories lag. Still other sequences are recognized when downturns in some indicators are related to upturns in others. For example, the decline in inventories lags behind, and is a possible consequence of, the downturns in the comprehensive measures of economic activity (such as GNP, industrial production, and retail sales); but the downturn in inventories also leads, and may be contributing to, the later upturns in these and other series (as the need for the stocks to be ultimately replenished will stimulate orders and help to bring about the next business recovery). Such considerations suggest that the coinciders and laggers are not merely of value as confirming indicators; some of them also play an active role as links in the continuous round of business cycle developments.

In addition to the 28 series identified above, more than sixty other series are included in the full list of indicators of business expansions and contractions. Up-to-date charts and tabulations and various summary measures for the entire set of indicators have been published since 1961 by the Bureau of the Census in the monthly report Business Cycle Developments. The full list contains several related series for each type of economic process having significance for business cycle analysis and forecasting. Most of the series are monthly (less than 20 per cent are quarterly), and more than half of those classified by timing are leaders. Change in money supply, a series with long leads and rather pronounced irregular component movements, deserves a special reference in view of the hypothesis that this variable is a fundamental factor in initiating business downturns and upturns.

The indicators are used mainly to reduce the lag in the recognition of cyclical turning points. The lead time provided by the indicators is, on the whole, short; often, especially when the economy reverses its course in a relatively abrupt manner, the best obtainable result seems to be to recognize the cyclical turning point at about the time it is reached. Even this is not a negligible achievement, however, since revivals and recessions are generally not recognized as such until several months after they have occurred.

The greatest difficulty in using indicators for forecasting purposes arises from the need to establish on the current basis the direction in which these series are moving or the dates of their turning points. This is because the trend and cyclical movements in many indicators are typically overlaid and often obscured by other short-period variations, partly of a seasonal but mainly of an erratic nature. Seasonal adjustment and subsequent smoothing of the series can help to distinguish its cyclical from its shorter irregular movements, but these are essentially descriptive-historical procedures which are not very efficient and which cause losses in up-to-dateness when applied currently.

The leading indicators, in particular, are highly sensitive to all kinds of short-term influences and not only to the forces making for the general cyclical movements. They have anticipated marked retardations in business activity as well as the major recessions and revivals. Skilled (or lucky) judgment of the user could sometimes succeed in distinguishing between these different episodes, but no mechanical, replicable method of applying the indicators has been able to do so.

Individual indicators occasionally fail to signalize the approach of a general business reversal, and their leads often vary a great deal in length from one recession or revival to another. The evidence of groups of indicators is considered to be on the whole more reliable than the evidence of any single indicator. Accordingly, the degree of consensus in the behavior of these series attracts considerable attention of business analysts and forecasters. Several measures of the consensus are in use, including diffusion and other composite indexes for groups of the indicator series.

Econometric model forecasts

Aggregate econometric models are systems of equations designed to represent the basic quantitative relationships among, and the behavior over time of, such major economic variables as national income and product, consumption, investment, employment, and price level. Such models are used for forecasting and also for other purposes (simulation of the likely effects of alternative fiscal and monetary policies, tests of hypotheses, etc.). In recent years, intensive work in this area has been done in several universities and government agencies in the United States and abroad, notably by Lawrence R. Klein and his associates.

The equations in econometric models describe the behavior of consumers, producers, investors, and other groups of economic agents; they also describe the market characteristics, institutional conditions, and technological requirements that guide and constrain economic action. They include variables selected to represent important systematic factors entering each of these functions and relate these variables by means of statistical estimates of their net marginal effects. The estimation of these unknown values (called parameters and taken, as a rule, to be constant) is based on the assumption that all the major factors affecting the relationship have been properly identified, leaving only random disturbances with expected values of zero. Ideally, the residual disturbance terms, which entail the net effect of all influences other than those of the specified explanatory variables, should be small, not serially correlated, and not associated with the systematic factors. In practice, the model builder hopes that the disturbances will be at least approximately random and relatively small, that is, that economic theory or other insights will lead him to a sufficiently good specification of a few principal determinants in each of these relationships.

In contrast to these “stochastic” equations, which are supposed to hold only approximately, the remaining equations of the model are accounting “identities,” which are based on definitions and are therefore supposed to hold exactly. The stochastic equations and the identities together form a description of the structure of the economy.

The unknown variables that are to be determined by the model are called the jointly dependent or current endogenous variables; their number equals that of the equations in the complete system. To solve for these variables, each of them is expressed as a function of the estimated structural parameters, the disturbances, and the predetermined variables. The predetermined variables are inputs required by the model and consist of (a) the values of those variables (labeled exogenous) that are viewed as determined by factors outside the model; and (b) the lagged values of the endogenous variables, which are given by outside estimates or by the past operation of the system. It is the jointly determined estimates of the current endogenous variables, all of which are functions of the predetermined variables with disturbances typically assumed to be zero, that represent the forecasting output or the “reduced form” of the model.

If the predetermined variables are taken as given, say at their reported ex post values, forecasts made from the reduced form will be conditional upon these data. “Unconditional” forecasts of the jointly dependent variables will be obtained when the unknown future values of the predetermined variables are themselves predicted (which for the exogenous factors necessarily means prediction outside the model). A closely related distinction is between alternative hypothetical forecasts (for example, of GNP next year, assuming 5 or 7 or 10 per cent increases in government expenditures) and the single preferred forecast (that government expenditures will be up 7 per cent and GNP will be such and such).

It follows that unconditional forecasts could have substantial errors because of wrong projections of exogenous variables, even if the specification and solution of the model were essentially correct. The accuracy of the conditional forecasts, on the other hand, depends (apart from any effects of errors in the data to which the equations are fitted) only on the errors that occur in the construction and solution of the model. These may arise for several different reasons: (1) incorrect specification of the behavioral or other economic relationships, that is, failure to use the right explanatory variables in their proper form; (2) deficient methods of statistical inference, for example, inability to measure well the separate effects of several closely interrelated exogenous variables; (3) errors in the parameter estimates resulting from sampling fluctuations, that is, from the presence of the disturbance terms which obscure the underlying relationships; and (4) discrepancies between predictions and realizations that result from the assumption that the disturbance terms vanish—in any particular period these terms may differ from zero, even though their expected values are zero.

Statistical inferences as to the probabilistic meaning of the parameter estimates, the goodness of fit to the data in the sample period, the presence or absence of autocorrelation in the disturbance terms, etc., can be used to evaluate the severity of the errors resulting from sampling variations and the inefficiency of the estimation methods employed. As far as the appraisal of the model per se is concerned, however, misspecifications are clearly the decisive sources of error, and these are more difficult to detect and evaluate. Theoretical and other a priori considerations can tell us something about the correctness of some of a model’s specifications; but the correctness of the specifications for the forecast period and not just the sample period must be judged primarily from the quality of the conditional forecasts made with a model that proved satisfactory on the other statistical tests just mentioned.

The unit time period varies from a quarter to a year in different models; for the purpose of analyzing and forecasting near-term developments, short unit periods are desirable, and aggregate econometric models have recently progressed from annual to quarterly units. Models also vary greatly in size and complexity. One view is that simple small-scale models can be sufficient for forecasting the broad course of the economy in the near future and indeed that they may be preferable in this role to large models which present greater opportunities for error by taxing heavily the present inadequate knowledge and data. But, while small models with as few as five equations have recently been proposed, the trend appears to be in the direction of ever larger and more complex systems.

It should be noted that conditional forecasts of particular variables are sometimes obtained by econometricians from one-equation systems. If the equation is unlagged, it merely shifts the burden of prediction in that, to get an authentic ex ante forecast of the dependent variable, the independent variable(s) must somehow be predicted outside the model. If the dependent variable is taken with a lag, it can be predicted from the equation inasmuch as the earlier values of the explanatory factors are known or treated as known. The single equation approach is strictly applicable only to cause-effect relations where one variable, say x, depends on others, y1, y2… but the y’s do not depend on x. If the variables depend on each other, a multiequation model should be applied.

An econometric forecasting model can in principle be so constructed and annotated as to be available for production of successive forecasts, replication by users other than the authors of the model, and continuous inspection and testing. This possibility holds out the promise of scientific advance, but it is difficult to achieve in practice for complex models with large requirements in terms of data and methods, especially when the data and methods are themselves subject to frequent and substantial changes. Moreover, some econometric forecasters wish to use their models in a flexible manner, modifying them repeatedly so as to take advantage of additional information. Thus, anticipatory data from surveys, indicators, etc., are introduced into the models as exogenous variables, or judgment about the probable effects of a recent event is used to alter the constant term in an individual equation. Such modifications are often informal and sometimes unrecorded; they may (although they need not) improve any particular forecast, but they certainly increase the difficulty of replicating and evaluating the models.

Input-output tables. Input-output analysis, which was developed by Wassily Leontief and first presented in 1941, involves a relatively detailed division of the commodity-producing sector of the economy into individual industries and estimation of the relations between these industries. In a statistical input-output table, each row shows the sales made by a given industry to every other industry, and each column shows what one industry purchased from every other industry. If the quantity of each input per unit of output is treated as a structural constant (which implies constant returns to scale and, a particularly drastic assumption, absence of substitution among inputs when relative prices change), then a system of linear equations can be set up describing the interdependence between the outputs of the different industries by means of these “technical coefficients” of production. Such a model can be used to make conditional predictions of the values of industry outputs, given the estimates or projections of the “bill of goods,” that is, of purchases by the autonomous sectors— consumers, government, and foreign countries. [SeeInput-output analysis.]

Evaluaton of forecasts

Despite the widespread and apparently increasing use of economic forecasts in business, government, and research, surprisingly little has been done to test these forecasts in a systematic and comprehensive way. Yet it is clear that forecasts must be properly evaluated if their makers are to learn from past errors and if their users are to be able to discriminate intelligently among the available sources and methods. Without dependable assessments of forecasting accuracy, informed comparisons of costs and returns associated with forecasting are clearly impossible.

Conceivably, the effectiveness of forecasts could be such as to complicate seriously their evaluation. Forecasts may influence economic behavior and, in particular, the variables being predicted; to the extent that this happens, the forecasts may validate or invalidate themselves. For example, if almost everyone predicted better economic conditions in the period ahead, this very consensus of optimistic expectations could contribute to the stimulation of the economy. Or, conversely, if the government accepted the forecast that the economy is threatened by recession, it would probably adopt policies designed to avert or at least postpone the undesired outcome initially foreseen.

It is easy to exaggerate or misjudge such feedback effects. Of the limited theoretical work on the problem, some is highly abstract and speculative. The best result appears to negate the thesis that public announcements must necessarily invalidate an otherwise accurate prediction. Under some plausible assumptions (notably that the predicted variable has a lower and an upper bound), if unpublished forecasts can be accurate, so can published forecasts, because the reaction to them can conceptually be known and taken into account.

Actually, the changes in GNP and other macro-variables that are predicted by different sources for any given period show sufficiently large dispersion to suggest that no single forecast is generally accepted (the evidence comes from a recent NBER study of American forecasts referred to below).For groups of forecasters, average forecasts are in the long run typically more accurate than most of the forecasts of the individual members because of compensating errors among the latter. Consistently superior forecasts are evidently hard to find. Some predictions are much more influential than others (and the special significance of official government forecasts is widely recognized), but there is no single authoritative source that enjoys unquestioned leadership.

A careful appraisal of American business forecasts presented by Cox (1929) was one of the few early studies in this area. The years following World War ii produced a number of particularly unsatisfactory forecasts (reflecting expectations of serious unemployment), which became the subject of some instructive reviews. Christ (see Conference on Business Cycles …1951) published a test of an early econometric model constructed by Klein. Essays concerned with the development and appraisal of different forecasting approaches were collected in several volumes by the National Bureau of Economic Research (Conference on Models of Income Determination 1964; Conference on Research in Income and Wealth 1954; 1955; Universities-National Bureau Committee for Economic Research 1960; Moore 1961). In Europe, Henri Theil and his associates (1958) produced a major analysis of the methodology and quality of forecasts, directed to both business surveys and econometric models. A comprehensive study of accuracy and other properties of short-term forecasts of economic activity in the United States has been conducted since 1963 at the National Bureau of Economic Research, and several reports on methods and results of this evaluation have been prepared.

Judging from the over-all results of most of these studies, the record of economic forecasters in general leaves a great deal to be desired, although it also includes some significant achievements and may be capable of further improvements. According to the current NBER study, the annual GNP predictions for 1953–1963 made by some three hundred to four hundred forecasters (company staffs and groups of economists from various industries, government, and academic institutions) had errors averaging $10 billion. Although this amounts to only about 2 per cent of the average level of GNP, the errors were big enough to make the difference between a good and a bad business year. The average annual change in GNP in this period was approximately $22 billion. Hence, the errors were, according to absolute averages, not quite one-half the size of those errors that would be produced by assuming that next year’s GNP will be the same as last year’s (since the error in assuming no change is equal to the actual change). Had the forecasters assumed that GNP would advance next year by the average amount it had advanced in the preceding postwar years, the resulting average error would not have been greater than $12 billion. However, while it is true that in terms of the absolute average errors some forecasts of GNP have not been significantly better than simple trend extrapolations, the forecasts were typically superior in terms of correlations with actual changes. In fact, recent forecasts of aggregate economic activity in the coming year, whether measured by GNP or industrial production, have generally been more accurate than both the simple extrapolations of the last level or change and the considerably more effective models of trend projection and autoregression.

Forecasters, then, were able to make a net predictive contribution over and above what could be obtained by means of mechanical extrapolations alone. This is a favorable result that is by no means always attained—for example, simple trend projections would have done better than the recorded forecasts that envisaged a serious business depression in 1947–1948. It is not a major achievement, however, since the course of the economy has been relatively smooth in recent years and therefore, on the whole, probably less difficult to predict than the developments in the earlier part of the postwar period. In the decade after 1953, there were fewer and smaller exogenous “shocks” of the type represented, say, by the outbreak of the Korean War in 1950. Also, the timing of recent business downturns was early enough to make the presence of the recessions rather widely known by the ends of the peak years (1953, 1957, and 1960), and most forecasts are made at the end of the year. This, plus the presumption that the contractions would continue to be short, made predicting the direction of the year-to-year changes in aggregate economic activity relatively easy.

By and large, the business economists’ forecasts covered by this analysis are informal, eclectic, and framed loosely in terms of the GNP accounts. The econometric model forecasts for GNP in the years since 1953 appear to have been about as accurate as the better business forecasts. It must be noted, however, that very few ex ante econometric forecasts are available for such tests, since most of the models now in use have been constructed only in the last few years and their accuracy beyond the sample periods cannot as yet be evaluated with any confidence. The econometric forecasts that do lend themselves to this appraisal come mainly from a series of closely related models used in a flexible manner, with many judgmental modifications.

Many forecasts show a bias of underrating the growth of the economy; the declines are much less frequently underestimated than the increases. The charge that forecasters tend to be too cautious or conservative seems, in this sense, to be justified. Since such series as GNP or industrial production have strong upward trends, their future levels as well as their changes have been understated most of the time (underestimation of increases typically results in underestimation of the ensuing levels).

Forecast errors are also affected by the cyclical characteristics of the forecast period. The levels of GNP and industrial production are underestimated most in the first year of expansion, when the increases in these series tend to be very large. Later in the expansions, when the increases are usually smaller, the levels are underestimated much less. In contractions, the predicted levels are as a rule too high, often because the downturn was missed and sometimes because the decline turned out to be larger than foreseen.

The forecasts of total GNP are often substantially better, in the sense of having smaller percentage change errors, than the forecasts of most major GNP expenditure components from the same source. Apparently, the over-all forecasts benefit from a partial cancellation of errors in forecasts of the components. This is definitely preferable to the opposite case of positively correlated and mutually reinforcing errors, but gross inaccuracies in the component forecasts are, of course, disturbing, even if these errors happen to be largely compensating.

Errors in predicting percentage changes in personal consumption expenditures are considerably smaller than those in corresponding forecasts of gross private domestic investment, while errors in predicting government spending are of intermediate size. Consumption forecasts have suffered from a pronounced tendency toward underestimation. In contrast, changes in series that fluctuate more and grow less strongly, notably the components of investment, have been as often overestimated as underestimated.

Although the errors of consumption forecasts are smaller than those for the other major GNP components when measured in deviations of percentage changes, they are large relative to the errors of some extrapolations. The consumption series, including those for nondurable goods and services, are smoothly growing series that could have been predicted very well in recent years by simple trend projections; and, indeed, the average errors of the latter have often been smaller than those of recorded consumption forecasts.

Aggregation of short-term expectations or plans of business concerns about their outlays on plant and equipment, as developed in periodic intentions surveys, results in better predictions of total business capital expenditures than those made independently for the entire economy. This can be inferred from comparisons between investment forecasts made before and after the McGraw-Hill investment intentions survey and also from comparisons involving the U.S. Department of Commerce–SEC anticipations data.

The average accuracy of short-term forecasts diminishes as they reach further into the future: the various series covered are all predicted better over the next three months than over the next six and better over six months than over nine or twelve. However, the errors increase less than proportionately to the extension of the span. Most extrapolations also tend to worsen with the lengthening of their span, and the simplest among them (the naive models) usually show the fastest deterioration. While forecasts of three to nine months (which includes the annual forecasts whose average spans are little more than six months) are generally superior to all kinds of extrapolations, the longer forecasts, which aim at targets 12 to 18 months ahead, are often worse than some of the relatively efficient types of trend projections and autoregressive extrapolations.

Conditional forecasts from formal models appear to produce errors that are similarly related to the time span of prediction. Thus, a recent analysis of input–output tables for the Netherlands during the period 1949–1958 concluded that predictions based on this method were on the whole better than extrapolations when the tables used were less than two or three years older than the extrapolation data. The input-output forecasts of industry output values for three or more years ahead (given the actual final demand schedules) proved inferior to the results of some fairly simple mechanical extrapolations.

Forecasts made frequently for sequences of two or more short intervals (for example, quarterly, for four successive quarters each) are more relevant for an appraisal of turning-point errors than are the annual forecasts, and they present a rather unfavorable picture. There are very few indications in the record of an ability to forecast turning dates several months ahead. Not only were actual turns missed, but some turns were predicted that did not occur. Reports by observers of the economic scene in business and financial periodicals are consistent with this finding in that they commonly show substantial lags in recognizing revivals and recessions. Business cycle indicators have at times demonstrably reduced these lags for competent users, but they also occasionally gave signals of retardations or minor declines that were misread as forewarning recession.

Multiperiod forecasts also provide data that lend themselves to an analysis of forecast revisions, that is, changes in predictions for a given target period made at dates successively closer to that period. These revisions do tend to improve the forecasts in most cases, and they appear to be related to errors in previous forecasts. Positive correlations between forecast revisions and errors of forecast have been interpreted as evidence of “adaptive behavior,” or “learning from past errors.” Such correlations, however, could also be due to autoregressive elements in some forecasts, since they are implied in fixed-weight autoregressive extrapolations.

Better statistical data and better utilization of the historical content of the predicted series could lead to significant improvements of the forecasts (as indicated, in particular, by the relative success of some types of extrapolations in predicting consumption and also price levels). Improvements in the record-keeping practices of forecasters are definitely needed. The records should include the estimates of the level of the series at the time the forecast was made, as errors in these base values are as a rule substantial and their measurability is important for the appraisal of forecasts.

Victor Zarnowitz

[Directly related are the entriesBusiness cycles; Econometric models, aggregate; Survey analysis, article onapplications in economics.]


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