Forecasting

Forecasting

Forecasting Kenneth C Land, Department of Sociology, Duke University, Durham, NC, USA Ó 2015 Elsevier Ltd. All rights reserved. Abstract Forecasting ...

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Forecasting Kenneth C Land, Department of Sociology, Duke University, Durham, NC, USA Ó 2015 Elsevier Ltd. All rights reserved.

Abstract Forecasting comprises of the formation of expectations about future states or processes of social entities, such as populations or subpopulations thereof, and associated entities, such as economies and political and social institutions. This article commences by describing and giving examples of empirical applications of four methods of forecasting that have been developed, and are widely used, in the social sciences: leading indicators, quantitative trend analysis, formal forecasting models, and qualitative (theoretical–institutional–scenario) analysis and forecasts. This is followed by a section on limitations of forecasting. All social science forecasts are subject to deterioration of their accuracy with increasing temporal distance from the initiation point of the forecasts. This is due to the complexity of social systems to which forecasting models and the data from which they are estimated are only an approximation, the evolving nature of such systems, and the fact that the forecasts sometimes are just elements in the social system to which some actors respond, thus changing their behavior. It is concluded that forecasts should incorporate prediction intervals that grow with increases in the forecast horizon and the forecasts should be updated frequently.

Introduction Forecasting refers to the formation of expectations about future states or processes of specific historical entities. Forecasting involves the estimation or calculation of expected future events or developments from a conceptual model. At the most informal level, the conceptual model can be a heuristic model based on individuals’ life experiences and the particular social, cultural, and economic circumstances in which they live, as in the formation of expectations about the routine activities and rituals to take place on a given day. At the other end of the spectrum, the conceptual model can be analytic, formal, and complex based on numerical measurements, equations, simulations, and projections. The most widely known forecasts by social scientists are economic and demographic forecasts, whereas natural scientists are associated with weather, climate, earthquake, and ecological forecasts (Land and Schneider, 1987). But these disciplines produce forecasts of many other social and natural phenomena and there are interstitial topics, such as energy, transportation, and technological forecasting, to which both have contributed. The subject of forecasting, encompassing both methods of forecast construction and substantive applications thereof, is very large and would require a large volume for adequate description. Accordingly, this article will be highly focused. The next section describes four widely used methods of forecast construction. This is followed by a section on limitations of forecasting. For purposes of this article, forecasting will refer to the formation of expectations on outcomes of study in the social sciences for social entities, such as populations or subpopulations thereof, and associated entities, such as economies and political and social institutions. This excludes applications of forecasting tools in clinical settings wherein the focus is on expected trajectories of health or behavioral outcomes for individuals. Within this specified context, forecasts can be made for single-outcome variables or multidimensional distributions

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of outcomes at a specific time or time horizon into the future from the date of the forecast. The methods of construction of forecasts range from combining simple extrapolations of past performance with human judgment to elaborate methodological formalisms based on universal laws or accounting identities, or some combination of lawful behavior, extrapolation, and judgment. The ‘future’ forecasted can be near or distant. The scope of forecasts can encompass the world’s physical/ social/economic systems or a single local phenomenon. The uses of forecasts range from their fulfillment of a statutory requirement for practical policy uses to an assessment of their explanatory value in a scientific sense.

Methods of Forecasting To focus the exposition, four methods of forecasting that have been developed, and are widely used, in the social sciences and business will now be described: leading indicators, quantitative trend analysis and extrapolation, formal forecasting models, and qualitative (theoretical–institutional–scenario) analysis and forecasts. Examples of empirical applications of each method will be included in the descriptions.

Leading Indicators The leading indicator approach to forecasting in the social sciences has been most extensively developed and applied to economic and business forecasting, due very much to the work of the National Bureau of Economic Research (NBER) and one of its founders Wesley Mitchell (1927). It is based on the view that market-oriented economies experience business cycles of expansion and contraction within which repetitive sequences occur and that these sequences underlie the generation of the business cycle itself (Lahiri and Moore, 1991). The leading economic indicator (LEI) approach focuses on finding repetitive sequences, explaining them, and using them to forecast emerging stages of the current business cycle.

International Encyclopedia of the Social & Behavioral Sciences, 2nd edition, Volume 9

http://dx.doi.org/10.1016/B978-0-08-097086-8.10544-6

Forecasting

The LEI approach differs from efforts to construct structural models of the economy – econometric models (described in more detail below) – which do not differentiate business cycles from other economic fluctuations, except possibly seasonal variation (Lahiri and Moore, 1991). The LEI construct has no fixed requirements on the duration of expansions or contractions, their amplitude, or their scope because the observed sequences – leads and lags – can be quite variable over time and are often systematically different at peaks and troughs, and because cycle phases vary widely in duration. The LEI emphasis on cycles has contributed to its longevity and helped it to spread around the world. Early signals of recession or recovery are of high salience to the actions of business officers, policy makers, job seekers, and investors. In the 1930s and 1940s, a group of NBER economists, including Moses Abramovitz, Arthur Burns, Milton Friedman, Gottfried Haberler, Wesley Mitchell, and Geoffrey Moore, developed a system of leading, coincident, and lagging indicators of business cycles. For the United States, the system is maintained and published monthly by the Conference Board, a global independent business membership and research association. The components of the Conference Board’s Leading Economic Indicators Index are the following statistics: 1. Average weekly hours (manufacturing) – Average weekly hours is a leading statistical indicator for changes in unemployment, as adjustments to the working hours of existing employees are usually made in advance of new hires or layoffs. 2. Average weekly jobless claims for unemployment insurance – The Conference Board reverses the value of this component statistic from positive to negative because a positive reading indicates a loss in jobs. 3. Manufacturers’ new orders for consumer goods/materials – Increases (decreases) in new orders for consumer goods and materials usually mean positive (negative) changes in actual production, which makes this a useful leading indicator. 4. Vendor performance (slower deliveries diffusion index) – Vendor performance is estimated from a monthly survey conducted by the National Association of Purchasing Managers (NAPM). This statistics measures the time it takes to deliver orders to industrial companies. Vendor performance leads the business cycle because an increase in delivery time can indicate rising demand for manufacturing supplies. 5. Manufacturers’ new orders for non-defense capital goods – As stated above, new orders lead the business cycle because increases (decreases) in orders usually mean positive (negative) changes in actual production and perhaps rising demand. This statistic is the producer’s counterpart of new orders for consumer goods/materials component. 6. Building permits for new private housing units. An increase (decrease) in this statistic is indicative of more (less) activity in housing construction. 7. The Standard & Poor’s 500 (S&P 500) stock index – The S&P 500 is considered a leading indicator because increases (decreases) in stock prices reflect investor’s expectations for the future of the economy and interest rates.

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8. Money Supply (M2) – The money supply statistic measures demand deposits, traveler’s checks, savings deposits, currency, money market accounts, and small-denomination time deposits. M2 is adjusted for inflation by means of the deflator published by the federal government in the periodic Gross Domestic Product (GDP) report. Bank lending, a factor contributing to account deposits, usually declines when inflation increases faster than the money supply, which can make economic expansion more difficult. Thus, an increase in demand deposits is indicative of expectations that inflation will rise, resulting in a decrease in bank lending and an increase in savings. 9. Interest rate spread (10-year Treasury vs Federal Funds target) – The interest rate spread (often referred to as the yield curve) indicates the expected direction of short-, medium-, and long-term interest rates. Changes in the yield curve have been the most accurate predictors of downturns in the economic cycle. This is particularly true when the curve becomes inverted, that is, when the longterm returns are expected to be less than the short rates. 10. Index of consumer expectations – This is the only component of the leading indicators that is based solely on expectations. This statistic leads the business cycle because consumer expectations can indicate future consumer spending or tightening. The data for this component come from sample surveys conducted by the University of Michigan Survey Research Center and is released once a month. Figure 1 contains graphical representations of the Conference Board’s Leading and Coincident Economic Indices from January 1999 through May 2014. Periods of economic recessions are shaded in gray. It can be seen that the Leading Economic Index turns down, signaling the oncoming 2008– 09 Great Recession well before the Coincident Economic Index, the downturn of which marks the official beginning of the recession. The Leading Economic Index also turns up, signaling an oncoming economic expansion well before the Coincident Economic Index, an upturn of which marks the official beginning of an expansionary period. At the international comparative level, the Organisation for Economic Cooperation and Development (OECD) in Paris, France, publishes leading indices monthly for 34 OECD member countries plus Brazil, China, India, Indonesia, Russian Federation, and South Africa. The LEI approach to economic forecasting persists because of its ability to survive repeated evaluations of its performance (Lahiri and Moore, 1991, pp. 2, 3). This does not mean that all of the indicators remain unchanged forever. Indeed, the need to change the list of indicators in the LEI occurs every few years because new indicators and time series become available, because research has produced some new results, or because the economy has changed. In brief, two important aspects of the LEI are that they are easy to understand and every component indicator needs periodic review.

Quantitative Trend Analysis and Extrapolation Quantitative trend analysis and extrapolation is a second major approach to forecasting. Among other empirical applications,

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Figure 1

Forecasting

The Conference Board’s Leading Economic Index, June 2014. Source: The Conference Board.

quantitative trend analysis and extrapolation is a part of the methodology of the technical analysis of stock market trends. In technical analysis, the developmental characteristics (e.g., gaps, reversals, trend lines of highs and lows, and trend channels) of prices of corporate stock equities traded in stock exchange markets, using both visual and quantitative properties, have been developed and applied for several decades (Edwards et al., 2013). There also is a tradition of application of logistic and other S-curve models to time trends of data in order to extrapolate/forecast population growth, life expectancy, the spread of a new disease such as AIDS, energy prices, the diffusion of innovations and new products/devices, and so forth (see, e.g., Modis, 1992). In the social sciences more generally, population projections are a prototypical empirical application of quantitative trend analysis and extrapolation. For instance, the U.S. Census Bureau periodically produces projections of the United States resident population by age, sex, race, and Hispanic origin. These projections are produced using a cohort-component method that decomposes changes in the age–sex–race/ethnicity counts of the population obtained from a decennial census year into three components of change from year to year: births into the population at age zero, age-specific deaths to the population, and age-specific net international migrants (immigrants into the population minus emigrants from the population) into the population (U.S. Bureau of the Census, 2012). Application of this method to the production of annual age–sex–race/ ethnic-specific population projections from a base year thus requires assumptions about yearly changes in these three

demographic components of change (future births, deaths, and net international migration). As a specific example, the Census Bureau National Projections for the years 2012–60 were produced using a cohortcomponent method beginning with an estimated base population for July 1, 2011 as follows (U.S. Bureau of the Census, 2012). First, components of population change (mortality, fertility, and net international migration) were projected. Next, for each passing year, the population was advanced 1 year of age and the new age categories were updated using the projected survival rates and levels of net international migration for that year. A new birth cohort was then added to form the population under 1 year of age by applying projected age-specific fertility rates to the average female population aged 10–54 years and updating the new cohort for the effects of mortality and net international migration. The assumptions for the components of change were based on time-series analysis of historical trends as follows. Age-specific fertility rates were calculated and projected for women aged 10–54 years from birth registration data for 1989–2009, which were compiled by the U.S. National Center for Health Statistics (NCHS). The birth registration data were used in conjunction with the Census Bureau’s Intercensal Estimates to produce a series of age-specific fertility rates by mother’s race and Hispanic origin for five race- and Hispanicorigin groups: (1) non-Hispanic white, (2) non-Hispanic black, (3) non-Hispanic American Indian or Alaska Native (AIAN), (4) non-Hispanic Asian or Pacific Islander (API), and (5) Hispanic (of any race). Race and Hispanic origin was assigned

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to projected births based on the race of the mother, the racial composition of men in the projected population, and the 2010 Census distribution of race and ethnicity of women and men with children less than 18 years of age in the household. Sex was assigned to projected births within each race- and Hispanic-origin group. The sex ratios (males per 100 females) of future births were set to equal the average of the sex ratios of births for the period from 1989 to 2009, within each of the five race- and Hispanic-origin groups. The age-specific fertility rates then were projected to 2060 by assuming convergence by 2100 of the age-specific fertility rates of all five raceand Hispanic-origin groups to the average age-specific fertility rates of the non-Hispanic white group for the years 1989– 2009 (1.83 births per woman). Only one series of mortality rates was projected for the 2012 National Projections. Mortality rates were calculated from NCHS-compiled death registration data for 1989 to 2009. These rates were used in conjunction with the Population Estimates Program’s Intercensal Estimates to produce a series of mortality rates by age and sex for three race- and Hispanicorigin groupings. Mortality was projected based on projections of the life expectancy at birth (e0) by sex. Changes in life expectancy at birth by sex were modeled assuming that the complement of the life expectancy (difference between an upper bound value, A, and life expectancy values) would decline exponentially: CðtÞ ¼ A  e0 ðtÞ

[1]

where C(t) ¼ the observed complement of life expectancy at birth at time t, A ¼ the upper asymptote of life expectancy, and e0(t) ¼ the life expectancy at birth at time t. The complement of life expectancy was then projected for future dates as: b ¼ Cðt b 0 Þerðtt0 Þ CðtÞ

[2]

b ¼ the observed complement of life expectancy at where CðtÞ birth at time t, r ¼ the rate of change in the complement of life b 0 Þ ¼ the model complement of life expectancy at birth, and Cðt b 0 Þ, and A were expectancy at time t0. The parameters r, Cðt estimated simultaneously by minimizing the sum of squared errors (SSE) between the model and the observed values of life expectancy, by sex, for the years 1999 through 2009. It was assumed that the complement of life expectancy for each of the three race- and Hispanic-origin groups would change at the same rate as for the total country for each sex. Projected values for the complement of life expectancy for each group for selected years from 2010 through 2060 were produced by assuming that the rate of change in the complement of e0 is the same for each subpopulation as it is for the total country. Mortality rates by age were then produced using the most recent observed rates by sex- and race-origin group, the trajectory of life expectancy values, and an ultimate life table. To get an ultimate age pattern of mortality by sex, the United Nations’ single age versions of the extended Coale and Demeny model life tables were used (United Nations, 2010). The West model mortality rates with life expectancy values of 87 for males and 91 for females were selected. Using the Coale–Demeny West model, age-specific central death rates were projected for each of the three race-origin groups by sex using a Census Bureau algorithm, which creates life tables for years that have intermediate life expectancy estimates by

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finding the interpolation factors for the most recent and next death rate inputs that would result in the desired life expectancy at birth value (Arriaga and Associates, 2003). The interpolation is done on the logarithms of the death rate values. The 2012 National Projections include a Middle/Main series and three alternative series. These four series of projections provide results for differing assumptions for net international migration. The alternative series were based on assumptions of Low, High, and Constant levels of net international migration. The Constant series was produced by holding the level of net international migration from the Middle series for 2012 constant from 2012 to 2060. The High and Low series were produced by varying the level of net international migration of the foreignborn from the projection used in the Middle series, 30%, respectively. All other methodology and assumptions used in the Low, High, and Constant series are the same as those used in the Middle series. The three alternative series are useful for analyzing potential outcomes of different levels of net international migration relative to the Middle series. Table 1 presents the resulting projections of the resident population for 2012 through 2060 for the Middle series and the three alternative series based on Constant, High, and Low projections of international migration. In the Middle series, the population is projected to increase from 314 million in 2012 to 420 million in 2060. The Constant Migration series lowers the 2060 projected count to 393 million, the High Migration series raises this to 442 million, and the Low Migration series yields 398 million. The 2012 Census Bureau National Population projections have been described and presented in some detail in order to illustrate an important application of quantitative trend forecasting in the social sciences. In addition to the National Population projections, the Census Bureau produces subnational projections for each of the US states. The cohort-component method recently has been generalized and extended to the projection of both national and regional populations by household structures/composition (Zeng et al., 2013, 2014). Key features of these demographic and other applications of quantitative trend analysis and projections are the application of relatively simple statistical models (e.g., minimum leastsquares estimates of time trends) and the presence of an accounting identity that coordinates the various component projected series combined with considerable expert substantive knowledge of the subject matter of the forecast.

Formal Forecasting Models Formal forecasting models, based on mathematical and statistical equations with empirically estimated parameters, are another widely used tool for forecasting. As noted by Land and Schneider (1987, pp. 9–12), forecasts in the social and natural sciences using formal models often are based on one or more universal laws or identities. An example is the classical accounting identity used on econometric models: Ct þ It hYt

[3]

which states that, by definition, aggregated consumption (C) for some collectivity (such as a nation) plus aggregate investment (I) is identically equal to aggregate income (Y) in

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Table 1

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Projections of population for the United States, 2015–60

Year

Middle series population estimates

Constant net international migration estimates

High international migration series

Low international migration series

2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 2025 2026 2027 2028 2029 2030 2031 2032 2033 2034 2035 2036 2037 2038 2039 2040 2041 2042 2043 2044 2045 2046 2047 2048 2049 2050 2051 2052 2053 2054 2055 2056 2057 2058 2059 2060

321 363 323 849 326 348 328 857 331 375 333 896 336 416 338 930 341 436 343 929 346 407 348 867 351 304 353 718 356 107 358 471 360 792 363 070 365 307 367 503 369 662 371 788 373 883 375 950 377 993 380 016 382 021 384 012 385 992 387 965 389 934 391 902 393 869 395 841 397 818 399 803 401 796 403 798 405 811 407 835 409 873 411 923 413 989 416 068 418 161 420 268

321 219 323 606 325 979 328 335 330 671 332 981 335 260 337 504 339 707 341 866 343 977 346 036 348 041 349 987 351 875 353 704 355 473 357 185 358 841 360 443 361 992 363 494 364 950 366 365 367 741 369 081 370 390 371 670 372 925 374 158 375 374 376 574 377 759 378 934 380 101 381 262 382 416 383 566 384 712 385 857 387 001 388 146 389 293 390 442 391 593 392 746

321 595 324 200 326 844 329 524 332 238 334 983 337 754 340 548 343 361 346 190 349 032 351 885 354 745 357 611 360 482 363 358 366 194 368 991 371 749 374 471 377 158 379 816 382 447 385 054 387 640 390 210 392 766 395 313 397 853 400 391 402 929 405 471 408 016 410 570 413 136 415 714 418 305 420 910 423 531 426 168 428 823 431 497 434 189 436 900 439 629 442 374

321 130 323 497 325 851 328 191 330 511 332 808 335 077 337 312 339 511 341 669 343 782 345 848 347 863 349 824 351 731 353 584 355 390 357 149 358 864 360 536 362 166 363 759 365 318 366 846 368 346 369 821 371 274 372 710 374 129 375 538 376 939 378 333 379 722 381 110 382 500 383 892 385 287 386 686 388 091 389 502 390 922 392 350 393 788 395 236 396 694 398 160

Ct ¼ a þ cYt

Source: U.S. Census Bureau, Population Division, Release Date: December 2012.

any time period (t). The National Income and Product Accounts contain this and other identities. Another example: Systems of national and regional demographic accounts – counts of stocks and flows of people among demographic and/or social statuses such as age and occupational categories (Long and McMillen, 1987) – lead to the population transformation identity: It1;t hPt1;t Ot1;t þ Bt

This identity says that a column vector of population inflows into a fixed geographical unit (such as a nation) from time period t  1 to period t (It1,t) is identically equal to the product of an outflow transition proportions matrix from t  1 to t (Pt1,t) times a column vector of population outflows (survivors) from t  1 to t (Ot1,t) plus a column vector of births and net migrants in period t(Bt). In scalar form for total population aggregates, eqn [4] is the population accounting identity that lies beneath the population trends/projection analyses reviewed in the previous section. When members of the population are classified by demographic and/or social statuses (e.g., age, location of residence, employment status, occupational category, marital/union status, etc.), the full vector–matrix representation of eqn [4] is necessary. From a physical science point of view, identities such as those in eqns [3] and [4] are specific instances of the law of conservation of mass. More generally, conservation laws are the natural science analog of social science accounting identities (Land and Schneider, 1987, p. 10). Both in natural science and in social science forecasting, formal models proceed by specifying parametric models/equations for one or more elements of the accounting identities. An econometric example is the classical Keynesian parameterization of the Ct in eqn. [3] as a linear function of current national income (Yt):

[4]

[5]

where a and c are constants that can be estimated by simultaneous equation econometric methods. This parameterization, termed a behavioral equation, expresses the Keynesian specification that, in the short run such as a year, aggregate consumption is the sum of autonomous consumption (a) plus the current national income scaled by the marginal propensity to consume (cYt). When combined with the specification that aggregate net investment (It) is fixed or autonomous in the short run, eqns [3] and [5] can be solved to determine Ct and Yt (see, e.g., Brems, 1968). The foregoing exposition illustrates two key properties of the structural models approach to forecasting (termed econometric models when applied to model the economy) to the development of formal forecasting models, be they of social or natural phenomena. First, the models often include one or more accounting identities/conservation laws. Second, the models incorporate parametric representations of one or more of the component elements of the accounting identities. Illustrative of this, Pescatori and Zaman (2011) describe three broad categories of models that have been developed and used by the U.S. Federal Reserve Board to forecast the US and world economies over the past 50 years, each with its own strengths and weaknesses: structural, nonstructural, and large-scale models. Structural macroeconomic models are built using the fundamental principles of economic theory, often at the expense of the model’s ability to predict key macroeconomic variables like GDP, prices, or employment. Nonstructural models are primarily statistical time-series models (taking the form of Auto-Regressive Integrated Moving Average (ARIMA) for single time series or Vector AutoRegressive (VAR) models for multiple time series or variations thereon; see, e.g., Granger and Newbold 1986; Woodward et al. 2012) – that is, they represent correlations of historical data that incorporate very little economic

Forecasting structure, and this fact gives them enough flexibility to capture the force of history in the forecasts they generate. Indeed, it has been shown that the accuracy in various substantive contexts that the accuracy of single-period-ahead forecasts from ARIMA models is extremely difficult to beat (Nelson, 1973). In macroeconomic forecasting, these statistical time-series models are used to produce unconditional forecasts that generate the expected future paths of economic variables and provide the most accurate forecasts if the overall monetary policy regime does not change. The third category, large-scale models, is a kind of middle ground between the structural and nonstructural models. They are like nonstructural models in that they are built from many equations, which describe relationships derived from empirical data, and they are like structural models in that they also use economic theory, namely to limit the complexity of the equations. Their large size has the advantage that relationships can be selected from a huge variety of data series, making it possible to provide a thorough description of the economic condition of interest. For example, structural models rarely feature highly specific variables such as ‘car sales,’ while large-scale models often do. This characterization of macroeconomic forecasting models, especially the distinction between structural models and nonstructural/statistical time series models, applies generally across forecasting in the social sciences. Briefly, structural models seek to represent behavioral and other structural relationships between exogenous variables determined outside the system being modeled and as well as the internal relationships among the endogenous or outcome variables of the system. By contrast, statistical time series models seek to model one or more time series of observations on the outcome variables in terms of their systematic properties purely as temporal phenomena. Articles on formal models of forecasting, both structural and time series, with applications to business, economic, demographic, and social phenomena are published in the International Journal of Forecasting and Foresight: The International Journal of Applied Forecasting by the International Institute of Forecasters (http://forecasters.org/), which was founded in 1981 for the objective of developing and furthering the generation, distribution, and use of knowledge on forecasting.

Qualitative Trend Analysis and Forecasts A fourth general class of approaches to forecasting can be termed qualitative trend analysis methods. These methods pertain to the forecasting of general features of society and take the form of theoretical–institutional–scenario analyses. Daniel Bell’s (1973) treatise, The Coming of Post-Industrial Society, on the transition in the late-twentieth century from an industrial societal form to a postindustrial form is a leading example. Bell posited that the United States in the late-1960s and 1970s was transitioning from an industrial form of society to a postindustrial form characterized by three key elements: (1) a shift from economy based on manufacturing to one based on services, especially the creation, processing, and distribution of information; (2) the increasing importance of theoretical knowledge and centrality of new science-based industries; and (3) the rise of new technical elites and the advent of a new principle of stratification that emphasize the

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dominance of the professional and technical classes – and that other developed societies would follow a similar transition. Bell’s analysis was based, in part, on quantitative data on employment trends in the mid-twentieth century United States, but it largely was a social forecast about a change in the social framework of society “. the structures of the major social institutions that order the lives of individuals in a society” (Bell, 1973, p. 8), especially the distribution of persons by occupation, the education of the young, and the regulation of political conflict. A decade later, John Naisbitt (1982) published Megatrends, in which he identified 10 major trends shaping the evolution of American society in the last quarter of the twentieth century. These included transitions from a national economy to a world economy, from hierarchical forms of organization to networking, and from either/or personal choices (e.g., either we get married in a male/female union or we do not) to multiple options (many forms of domestic unions from traditional heterosexual marriage to cohabitation to serial marriages/unions to same sex marriage). The qualitative, institutional–structural transitions forecasted by Bell and Naisbitt have been highly evident in societal evolution over the decades since 1970. These forecasts are part of the innovation and development of a field of scholarly inquiry termed futurology or futurism. Just as the International Institute of Forecasters was established to further the development of formal forecasting models and methods, the World Future Society (http://www.wfs.org/) and its journal, The Futurist, was established in 1966 to foster the development of ideas about the future, including forecasts (especially qualitative forecasts), recommendations, scenarios, and alternatives. The body of qualitative trend analyses and forecasts produced by futurists over the past four or five decades is huge, of which the examples cited here are only illustrative. The methods of analysis used in futurist studies also are quite diverse. Bell (1973), for example, based his projections of the postindustrial society very much on a theoretical–conceptual analysis of changes in the nature of economic production and the implications this would have for occupational structures and for the educational system and its relation to occupational success and stratification systems. This is illustrative of one class of approaches to futurist studies, namely, a theoretical– conceptual–institutional analysis of implications of technological, demographic, or political changes. Related to this is the use of possible scenarios of futures that might develop as a consequence of scientific technological advances, demographic, or political changes; an example is Mayes (2014) in which possible scenarios for recent developments in synthetic genomics/ biology (¼ biology þ engineering/editing of genomic structures) are sketched. A third approach is that on which Naisbitt’s (1982) research was based, namely the content analysis of the verbal content of more than 2 million articles published in some 6000 local US newspapers during a 12-year period. Content analysis is a method of identifying specified characteristics of messages that has its roots in US intelligence efforts in World War II, led by the sociologist Paul Lazarsfeld and the political scientist Harold Lasswell, to obtain information on enemy nations from their published newspapers. Since the 1970s, qualitative trend followers such as Naisbitt have made extensive use of this method. With the

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development and widespread use of the Internet, similar content-based trend-identification tools have also been developed by providers of major search engines. An example is Google Trends (http://www.google.com/trends/), which tracks how often a particular search term is entered relative to the total search volume across various regions of the world and in various languages.

Limitations of Forecasting All demographic, economic, and social forecasts have limitations with respect to accuracy. Demographic forecasts of national and other large populations, as noted above, deal with movements of demographic processes of fertility, mortality, net migration, and multistate status changes from time period to time period. These processes change relatively slowly. Even so, demographers consider population projections for up to a decade or so beyond the initiating time period to have informative forecasting information, whereas projections beyond this time horizon are considered to be scenarios that may or may not develop (Zeng et al., 2014). While the time horizon for macroeconomic forecasts typically is shorter (monthly or quarterly) than that for annual population projections, their limitations are even stronger. As Pescatori and Zaman (2011) noted, it is unlikely that macroeconomic models will ever provide perfectly accurate forecasts, because forecasts are ultimately just another variable in a system in which there are many rational actors (e.g., managers of production and distribution corporate units, bank managers, investors) for whom an economic forecast may change their behavior. In fact, the economic actors who attend most closely to forecasts are the people whose behavior is most likely to affect the future course of the variables forecasted. Both the structural and nonstructural varieties of economic forecasting models have been extensively developed and improved since the 1970s. However, most models, including the Federal Reserve Board’s models (Greenspan, 2013, p. 7), failed to predict the financial crisis of September 2008 that led to the Great Recession of 2008–2009. This failure may be partly attributed to the models’ failure to fully incorporate the growing role of the financial sector or the worldwide financial and trade linkages that globalization has generated. A key point is that economic systems evolve and change over time and it is difficult to incorporate these changes into the macroeconomic models until a forecasting crisis has raised their salience. Even so, the lack of forecasting ability does not prevent models from being useful devices that can help policy makers in making decisions. Similar considerations apply to the accuracy of forecasts based on qualitative trend analyses. That is, while the accuracy of qualitative forecasts is more difficult to assess because of their more ephemeral nature (the author knows of no existing large-scale systematic assessment), it likely is the case that some such forecasts hit the mark, some do not, and some work temporarily but lose their accuracy as the system being forecasted evolves. For instance, of the 10 major trends shaping the evolution of American society in the last quarter of the twentieth century identified by Naisbitt (1982), a fair assessment is that 5 have evolved and lasted in the

long-run (Industrial Society > Information Society, National Economy > World Economy, Hierarchies > Networking, More Development in the north United States > More Development in the south United States, and Either/ Or > Multiple Options), while 5 may have had some staying power in the 1980s but have not been as widespread or lasted as strongly or long (Forced Technology > High Tech/High Touch, Short-Term > Long-Term, Centralization > Decentralization, Institutional Help > Self-Help, Representative Democracy > Participatory Democracy). To understand these limits to forecasting accuracy, it is helpful to recall Land and Schneider’s (1987, pp. 17–19) analysis of the accuracy of weather and social science forecasting. Briefly, weather forecasts are based on nonlinear partial differential equations of hydrodynamic flow that depend continuously on both boundary and initial conditions. To produce accurate forecasts of indefinitely long range from such equations would require perfect boundary specifications and an observational net of weather stations finer than the radius of the smallest atmospheric eddy; otherwise, small weather events ‘hidden beneath the net’ eventually become amplified, with time into the forecast horizon from the initiation point, into larger uncertainties by inherent instabilities in the nonlinear system. In brief, the finite resolution of observations on weather variables (such as temperature, barometric pressure, relative humidity, wind speed) is due to the fact that atmospheric measurements are available at only a finite number of grid points at which there are weather stations. Forecasts then are based on initial conditions that assume that the weather variables for points between stations are equal to the average or interpolated values between the stations. Because the interpolated values of the initial conditions on the grid often deviate from atmospheric microevents (e.g., thunderstorms) that lie within the grid, the resulting ‘errors in initial conditions’ in weather forecasting models ultimately places limits on their accuracy. Observational and theoretical studies have found that the limit of weather predictability is about 2 weeks (Somerville, 1987). In the social sciences, corresponding limits to forecasting accuracy are due to the fact that, no matter how much disaggregation and cross-classification is introduced into the forecasting models and data, at some point a statistical average value must be estimated for each subcategory or subpopulation. But such an average, even if it is not subject to measurement or sampling error, likely ignores some population heterogeneity that is ‘hidden’ relative to the specified resolution of the model. This, combined with the property that social science models often are based on linear approximations to underlying nonlinear, multilevel interactive mechanisms, produces forecast errors that, again, become amplified with time into the forecast horizon from the initiation point. Accordingly, it is not surprising that demographic, economic, and social forecasts, whether quantitative or qualitative, have errors that deteriorate with an increasing forecast horizon from the point of initiation. In brief, limits to forecasting accuracy are the reason that forecasters emphasize the need to incorporate uncertainty into forecasts (Goodwin, 2014). Uncertainty can be due to several sources, including uncertainty in the structure of models, errors in measurement of variables, and errors in estimation of model parameters. To the extent possible, therefore,

Forecasting

forecasts should incorporate prediction intervals that grow with increases in the forecast horizon, such as the high and low bounds on the U.S. Census Bureau National Population projections described above, if possible, these intervals should be based on probabilistic analyses, and the forecasts should be updated frequently.

See also: Data Bases and Statistical Systems: Applied Social Research; Demography: History Since 1900; Economics, History of; Population Forecasts; Social Changes: Models; Structural Equation Modeling; Time Series: General.

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