Granger, Sir Clive William John (1934–2009),
economist, was born on 4 September 1934 at Sketty Nursing Home, Swansea, the only child of Edward John Granger (1904–1974), commercial traveller, and his wife, Evelyn Agnes,
née Hessey (1909–1991). His paternal grandfather made and sold shoes in his own shop, a successful small business in Cambridge. His maternal grandfather was a gardener at Windsor Castle, where his maternal grandmother was a cook. At the time of his birth registration his parents lived at 40 Glanbrydan Avenue, Swansea. His father worked for Chivers, manufacturers of jams, marmalades, and jellies, and soon after Granger's first birthday the family moved to Lincoln. During the Second World War his father served with the RAF, driving large support vehicles, and Granger and his mother moved to Cambridge to live first with his maternal grandmother and then with his paternal grandparents, who also still lived in the city. He went to primary school in Cambridge, where a teacher told his mother that he ‘would never become successful’ (which, Granger wryly observed, ‘illustrates the difficulties of long-run forecasting on inadequate data’; Nobel prize autobiography). He nevertheless passed the eleven-plus to enter Cambridgeshire High School for Boys. In 1946 his father returned from the war and the family moved to West Bridgford, Nottingham, and Granger transferred to the grammar school there. His mathematical ability became more apparent at that school, nurtured by two excellent teachers, whom Granger credited with sparking his interest in the subject and equipping him and his fellows with a thorough grasp of mathematical principles. He stayed on to take A-levels in pure mathematics, applied mathematics, and physics.
Interested in the practical applications of mathematics, Granger applied successfully for a place on a new degree course at Nottingham University in mathematics and economics. (He was the first member of his family to go to university.) After a year he switched to a mathematics degree but, after graduating in 1955 and having been persuaded to stay on to study for a PhD, he decided to study a mathematical topic with relevance to economics and, having discovered that there was relatively little mathematical work on the subject, chose economic time series. His supervisor was Harry Pitt, a renowned pure mathematician and probabilist who nevertheless gave him an excellent grounding in statistics.
Granger completed his PhD in 1959, by which time he had already spent three years as a lecturer in statistics at Nottingham (having, he later claimed with typical modesty, got the job because the only other candidate had spent the interview arguing with the university's vice-chancellor). He became a reader in econometrics at Nottingham in 1964, and professor the following year. In 1959–60 he spent a year at Princeton working with Oskar Morgenstern, John Tukey, and Michio Hatanaka thanks to a Harkness fellowship, the terms of which included a stipulation that he spend the last three months travelling around the United States. This he did with his wife, Patricia Anne,
née Loveland (
b. 1938), whom he had met when she was a research assistant to David Chambers, an economic historian at Nottingham, and whom he married in Princeton University Chapel in 1960. They had a son, Mark (
b. 1964), and a daughter, Claire (
b. 1968). In 1974 they moved permanently to the United States, when Granger took up a research professorship in the department of economics at the University of California, San Diego, where he remained until his retirement in 2003.
Non-stationarity and spectral analyses
Granger's PhD thesis concerned testing for non-stationarity. A time series is stationary if the distribution from which the data are drawn remains the same over time. Consequently the mean and variance of that distribution need to remain constant. If the distribution or any of its moments shift over time, then the process is non-stationary. Almost all macroeconomic time series are non-stationary. In particular the presence of a trend in economic time series reveals a changing mean, although it is logically possible that the series is stationary once that trend has been removed. It is often assumed that the first differences of (or period-to-period changes in) macroeconomic data are stationary. However, there are many possible causes of non-stationarity, the financial crisis of 2008 being an example that shifted the means of many economic variables (including interest rates and the government deficit among many others).
Using United Kingdom macroeconomic data since 1860 as examples of non-stationary time series, average annual wages have increased by 55,000 per cent, prices by 8500 per cent, average age of death by about 75 per cent (close to a weekend longer every week for 150 years), and the purchasing power of incomes by roughly 650 per cent. Their variability has also changed greatly over that period. Nevertheless, the dominant assumption in both theoretical and applied econometrics at the time was that such data were stationary, so Granger was at the forefront in tackling the difficult issue of non-stationarity, an area in which he was to make significant advances.
In Princeton, Granger worked on the spectral properties of economic data, initially applied to New York stock market prices (with Morgenstern, 1963), and resulting in his first book,
Spectral Analysis of Economic Time Series, in 1964 (with Hatanaka), which was important both for extending the economist's toolkit, and because frequency-domain thinking played an important part in Granger's general approach to econometric problems. That book became a citation classic, and notably contained a substantial discussion of non-stationarity, providing a lead into his new formulation of causality. An influential paper in
Econometrica in 1966 (‘The typical spectral shape of an economic variable’) revealed a dominant mode in the spectrum close to the origin for many macroeconomic levels, which is a shape similar to that of a random walk, a process where the change is random, so the level wanders, and is non-stationary.
The biologist Robert Brown in 1828 first described the random movements of pollen grains floating on water, now called Brownian motion. Expressed as a random walk, this process has been used as a model for equity price movements since the suggestion by Louis Bachelier in his thesis in 1900. Equity prices and commodity prices are still often treated as random walks, implying that their changes are unpredictable. Granger's interest in stock markets was followed up in work with Morgenstern (
Predictability of Stock Market Prices, 1970), and with Walter Labys on commodity markets (
Speculation, Hedging and Forecasts of Commodity Prices, 1970). Economic forecasting
per se, and its role in evaluating econometric models, became one of the recurring themes of Granger's later research.
Causality
The next major research that Granger undertook concerned causal relationships between economic variables (‘Investigating causal relations by econometric models and cross-spectral methods’,
Econometrica, 1969), building on both earlier themes of spectral analysis and forecasting. He noted that previous definitions of causality in econometrics concerned causal interpretations within simultaneous equations systems, namely ‘instantaneous’ causality. Granger now gave stochastic variables and the ‘arrow of time’ central roles in his definition (excluding purely deterministic processes from the discussion), but reverted to stationary series. His new definition of causality was based on the prediction variance of a subset of observable variables: if the joint distribution of that subset is altered by eliminating the history of any other variables then that second group causes the first. Consequently the first group of economic variables can be predicted more accurately using the second set of variables than without them. To make his idea operational he proposed testing if the removal of the second group of variables from a model of the first group reduced their predictability. If so he argued that the second group caused the first. This notion made it possible to test the hypothesis of non-causality between economic variables by statistical methods, an idea followed up by Christopher Sims, later a Nobel laureate. Such an apparently easy implementation made his definition popular, and stimulated considerable empirical research. The concept also created controversy as to whether it was a general definition of causality or just an example thereof, and for clarity Granger's definition is usually referred to as ‘Granger causality’.
Independently of whether or not Granger's notion was ‘genuine causality’ or just incremental predictability it became an important concept in empirical economic research, reappeared in the concept of cointegration, and was applied in other observational disciplines. In a chapter for Granger's Festschrift volume, edited by his colleagues Robert F. Engle and Halbert White at the University of California, San Diego (
Cointegration, Causality and Forecasting, 1999), David Hendry and Grayham Mizon analysed ten areas of econometric modelling in which ‘Granger causality’ could be seen to play an important role: marginalizing; conditioning; distributions of estimators and tests; inference via simulation; cointegration; encompassing; forecasting; policy analysis; dynamic simulation; and impulse-response analysis. The common theme connecting these apparently disparate topics would not have been obvious had Granger not formulated his notion. Conversely Hendry and Mizon argued that his original notion was not operational, as it required knowledge of the joint distribution of all variables to be sure that reduced predictability on the elimination of some variables was due to those, and not correlations of those with the ‘real causes’ when only a subset of all the variables was included, as inevitably happened in practice.
Non-stationarity revisited
Nonsense correlations, such as that between the annual UK birth rate and the number of storks nesting that year in Stockholm, had puzzled early users of Francis Galton's recently developed statistical methods. The first formal analysis of such correlations was presented by Udny Yule in his presidential address to the Royal Statistical Society in 1926, where he explained the source as being due to the non-stationarity of the time series. Contemporaneously Bradford Smith proposed a model formulation to handle that problem (in the
Journal of the American Statistical Association, 1926), but neither paper was remembered after the Second World War, so both the problem and its solution had to be rediscovered.
In work with his former student Paul Newbold published in the
Journal of Econometrics in 1974 Granger illustrated the difficulty for conventional econometric models of what they called ‘spurious regressions’. Yule had discussed ‘spurious correlations’ in 1897, where two variables were apparently related, but only because each was related to a third. That early research was the source of the remark in 1940 by John Maynard Keynes when criticizing Jan Tinbergen's League of Nations book (
Statistical Testing of Business-Cycle Theories, 1940) about the ‘mine [Mr Yule] sprang under the contraptions of optimistic statisticians’, a comment Keynes would doubtless have applied to much post-war empirical research. Nevertheless, the name ‘spurious regressions’ stuck. Granger and Newbold showed that if one random walk was regressed on another to which it was unrelated the regression coefficient estimates would appear to be ‘significant’ far more often than in unrelated stationary processes (about 75 per cent versus the anticipated 5 per cent for two independent stationary variables). They observed that empirical econometric equations could have excellent goodness-of-fit, yet would also have non-random residuals (correlations between successive deviations from the regression line), which should act as a warning sign that the relation might be spurious.
As a result Granger and Newbold proposed differencing the variables to reduce the non-stationarity before testing for a relationship between them. This was not only a step back from Bradford Smith's forgotten formulation, but also from the proportional, integral, and derivative control mechanisms introduced to economics by Bill Phillips (later more famous for his eponymous curve), and the ‘error-correction’ proposal of Denis Sargan in his chapter in the Colston Research Society volume
Econometric Analysis for National Economic Planning (1964). Lawrence Klein, later a Nobel laureate, had already expressed a version of this idea in his
Textbook of Econometrics (1953) in terms of ‘great ratios’, where the non-stationarity in individual series such as consumers' expenditure and income cancelled in their (log) ratio, which was non-trending and well behaved in comparison. On the other hand, the autoregressive-moving average (ARMA) model proposed by George Box and Gwilym Jenkins (
Time Series Analysis: Forecasting and Control, 1970) also argued for removing one form of non-stationarity by using the differences of the variables. The autoregressive model had first been proposed by Yule in 1927, whereas moving averages were invented by the Bank of England in 1797 to conceal the perilous state of its bullion reserves (an early example of creative accounting), and developed by Eugene Slutsky in 1937 (translated from a Russian version of 1927). Box and Jenkins combined these ideas, but also emphasized the need to difference time series that appeared to be non-stationary, and such a ‘solution’ began to be adopted.
Spurious or nonsense relations occurred when the current-dated levels of variables were correlated. Smith and Sargan among others had earlier proposed formulating dynamic models where the previous values of the variables were also included, which precluded any spurious correlations. However, Granger doubted the statistical legitimacy of analysing the levels of non-stationary time series by such models. It was already known from statistical theory that the distributions of estimators of parameters in random walks were non-standard and non-normal, and that larger critical values were needed for tests of significance. The literature on ‘error-correction’ mechanisms did not seem to address that problem, so Granger set out to prove that spurious results would still occur, a task that would take him more than five years, and lead to the opposite conclusion—with momentous consequences for econometrics. In the meantime Granger returned to his earlier research theme of forecasting.
Economic forecasting
In his 1969 paper with John Bates, Granger showed that a combination of several forecasts of an economic variable could be more accurate than any of the individual predictions in that combination. Such a result seems counter-intuitive: a combination should certainly be more accurate than the worst forecast, but how could it beat the best when it included poor forecasts in the average? However, in 1906 Galton had already noted that the average of a group of forecasts (in his case villagers guessing the weight of an ox at a fair) could be remarkably accurate when none of the individual forecasts was. Granger correctly suspected that differential biases in forecasts would cancel on combining, which prompted him to propose various weighting systems for combining forecasts, initiating a literature on combining forecasts.
Consistent with Granger's view that many empirical economic relationships were spurious, the large econometric models of the time often produced less accurate forecasts than simple atheoretic time-series devices, usually with important random-walk components, further stimulating the search for an improved approach to alleviate such a problem. His joint book with Newbold,
Forecasting Economic Time Series (1977; 2nd edn, 1986), summarized most of what was known at the time about forecasting, and the role of forecasts in evaluating models.
To judge any economic forecast—combined or otherwise—one has to know how to evaluate it. It may be a surprise that this task is far from straightforward. For example forecasts for the changes in a variable can be accurate while the forecasts of the level are very poor; and forecasts of each of two variables may be very inaccurate, yet the forecasts of their differential be spot on (e.g. imports and exports versus the balance of trade). What aspects should be taken into account when evaluating forecast accuracy? Granger argued that users would know the costs of inaccurate forecasts, so he investigated a variety of measures of those costs and how they might influence the choice of forecasting method, including their impacts on econometric modelling methods. In related work with Hashem Pesaran he also studied how alternative cost functions might affect both the estimation of parameters in models and the evaluation of those models. That extension was an important development beyond mechanistic forecast evaluation, and brought economic analysis into the judgement of the costs of forecast errors and the benefits from more accurate forecasts.
Cointegration
The notion of ‘co-integration’ settled the debate about the legitimacy of analysing the levels of non-stationary economic time series. (Cointegration is now usually written without a hyphen, but pronounced as if the hyphen were there, following a long tradition where co-relation was the origin of correlation.) Research at the University of California, San Diego, especially with his colleague Engle, whom Granger had attracted there, showed that non-stationary time series can move together because they share common trends. Granger later used a simple demonstration of this idea. Imagine spilling a handful of pearls onto a table; then they will usually scatter in all directions. However, if the pearls are strung along a necklace they will move together when the necklace is dropped on the table—the pearls are ‘cointegrated’. Of course the shape of the necklace will differ on different occasions, but the distances between neighbouring pearls will stay the same.
If two economic variables are driven by the same non-stationary force then a combination of those variables exists which eliminates that non-stationarity, and hence could be stationary. The real breakthrough was showing that if the two economic variables shared a single ‘error-correction’ feedback of the kind Smith, Phillips, and Sargan had pioneered, then they would be both non-stationary and cointegrated. This provided economics with an internal mechanism for generating non-stationarity, which previously had been posited to arise from outside the economic system. The epithet ‘error correction’ seemed appropriate as deviations from the long-run equilibrium would be corrected by the feedback, and although Granger himself thought ‘equilibrium correction’ might be more appropriate (as later transpired to be the case), to relate to the earlier literature, ‘error correction’ was retained.
The paper by Engle and Granger published in
Econometrica in 1987 (‘Co-integration and error-correction: representation, estimation and testing’) achieved what its title proclaimed. In addition to the result just discussed it presented a representation for cointegrated time series (later known as the Granger representation), provided methods of estimating cointegrated relations, and derived tests for the presence of cointegration. Their approach took account of the non-standard distributions that occurred in non-stationary processes, so earlier worries about spurious relations could be resolved by establishing whether or not the variables under analysis were cointegrated. Engle's and Granger's paper became one of the most frequently cited papers in the history of econometrics. It was in recognition of this research that Granger was awarded the Sveriges Riksbank prize in economic science in memory of Alfred Nobel (popularly known as the Nobel prize for economics) in October 2003, shared with Engle for his invention of the autoregressive conditional heteroskedasticity (ARCH) model.
Long memory, non-linearity, and econometric modelling
At the end of the 1970s Granger began investigating processes with long memory. These processes have the property that their autocorrelations decay at a much slower rate than that of a linear ARMA process. Benoit Mandelbrot had suggested using rescaled range (R/S) analysis to detect long-term dependence, an idea he applied to fluctuations of water levels in the Nile and of stock prices. In work with Roselyn Joyeux, Granger defined new concepts of fractional integration and fractional differencing, and showed how fractionally differenced variables could have a long-memory property. A possible model for fractionally integrated processes was based on aggregating autoregressive processes. With the increased availability of long financial time series the importance of long-memory models in econometrics subsequently grew, and was applied to modelling conditional variances where their considerable persistence is consistent with long memory in volatility. Granger also demonstrated that when decomposing a high-frequency return time series (such as a stock return) into the product of its sign and its absolute value only the latter process has long memory, whereas the sign is nearly unpredictable. The forecastability of the absolute-value series could help control financial risk.
Granger was again one of the first econometricians to investigate non-linear time-series models, commencing in 1978 through research with Allan Andersen on bilinear models. That work soon became a standard reference, and was influential in econometrics via the analysis of non-linear models in empirical macroeconomics. It was also an important stimulus to his close colleague, Engle, in the creation of the ARCH model. The class of ARCH, and later generalized ARCH (GARCH), models was often applied to forecasting volatility in stock markets.
Granger even proposed forecasting white noise, supposedly unpredictable, through non-linear interactions. When Granger and Tae-Hwy Lee generalized cointegration to multi-cointegration in 1989, they also defined a form of non-linear cointegration. Empirical work such as Granger's on non-linearities alerted economists to the fact that some important relationships are non-linear—with implications for economic theory—and conversely that it is not always necessary to linearize theoretical relationships where non-linear models are anticipated. A book by Granger and Timo Teräsvirta,
Modelling Nonlinear Economic Relationships (1993), provided a magisterial overview, followed up later with Teräsvirta and Dag Tjøstheim in
Modelling Nonlinear Economics Time Series (2010). Most of Granger's work on non-linearities concentrated on the modelling of conditional first moments, but he also contributed to methods for modelling conditional variances, linking back to his joint research with Engle.
Although he only devoted one book to the topic of empirical modelling (
Empirical Modeling in Economics, 1999) underpinning Granger's many contributions was his long-term research agenda of improving the quality of econometric model building by a better match between empirical models and the data evidence. This required careful specification of the model to be estimated and thorough evaluation of its properties. He focused on doing so mainly through forecast performance, as that was outside the control of the model builder. However, he was also interested in model selection, and in the growing literature on computer-based methods for doing so.
Granger had a long-lasting interest in trying to understand and build models of trends, and the last paper he wrote was on that topic (with White). Stochastic and deterministic trends can occur, and these can be linear or non-linear, constant or evolving, or even subject to sudden shifts. Thus much of his research both directly and indirectly addressed trends in their many manifestations.
Granger was eclectic in the subjects he studied, with early interests in astronomy (numbers of sunspots), and in experimental economics, a subject which later became popular, with both laboratory and field experiments being conducted to test economic theory propositions. Macroeconomics is inherently about aggregate data, and Granger addressed that issue in several publications, as well as seasonal fluctuations in higher-frequency observations. With André Gabor he conducted experiments in supermarkets, altering the prices of products and recording changes in sales, which led to several articles on price formation and consumers' attitudes to prices. Later he worked on the future of the Amazon rainforests, and contributed to
The Dynamics of Deforestation and Economic Growth in the Brazilian Amazon (2002, with four collaborators).
Legacy and honours
Granger's research spawned a veritable industry of procedures and applications both in economics and in many other disciplines. First his concept of cointegration provided a unified framework for economic theories of long-run equilibrium relationships to be combined with dynamic econometric models of short-run behaviour. This was a substantial advance in the empirical analysis of macroeconomic relationships, and in testing macroeconomic theories, extending to non-stationary macroeconomic time series the formulations by the Nobel laureates Ragnar Frisch and Trygve Haavelmo of an economy as a system of simultaneous stochastic relationships. Economic policy agencies around the world came to use empirical econometric models in which cointegrated relations determined the long-run outcomes.
Second a cointegrated representation automatically separates the short-term effects (expressed as changes in variables) from the long-term effects (cointegrated levels, capturing underlying trends). In retrospect that was essentially the model proposed by Bradford Smith in 1926, but now with appropriate statistical methods for non-stationarity arising from random-walk components. Importantly, and a reflection of the spurious correlations problem, most economic time series are highly inter-correlated, a phenomenon called collinearity following Frisch (
Statistical Confluence Analysis by Means of Complete Regression Systems, 1934). The cointegrated specification removed most collinearity, as changes in variables are much less inter-correlated, as are the cointegrated relations, or ‘error corrections’, themselves.
Third expressing a model in cointegrated form as an ‘error correction’ also appeared to improve its forecasting performance. This transpired to be partly due to the use of differences in both the formulation and the evaluation. Unfortunately a second type of non-stationarity soon intruded, namely shifts in relationships from major policy and legislative changes, wars, large technological advances, and crises. These induced shifts of the equilibrium, to the new value of which ‘error correction’ did not correct. Rather it corrected back to the previous equilibrium, and by doing so led to large, systematic forecast errors. An excellent example of this was the ‘boom and bust’ in the UK economy in the late 1980s and early 1990s, arising from changes in the structure of finance that led to changes in aggregate expenditure patterns. Large forecast errors resulted, well expressed by the failure to appear of the ‘green shoots of recovery’ repeatedly promised by the chancellor of the exchequer, Norman Lamont. Apart from the failure to remember such lessons before the 2008 financial crisis ‘equilibrium correction’ was seen to be a more appropriate name as it emphasized correction within, but not between, equilibria.
Fourth Granger's research was applied by many other scholars outside economics, including in biology, engineering, and the environment, to topics such as river flooding and deforestation, climate change, paleobiology, and paleoclimatology. Other areas influenced by his research included business science, political science, sociology, and marketing.
Fifth Granger attracted many visitors to the University of California at San Diego and would discuss the ideas of others constructively at the weekly econometrics lunches he helped organize. He delighted in collaborating with other researchers, and had about ninety different co-authors, as well as supervising a large number of successful doctoral students. Thus he invested a considerable proportion of his time and energy in successor generations.
The overall outcome was one of the most successful research programmes in the history of econometrics, making many lasting contributions to that discipline. At the time of his death, he had more than 40,000 citations to his published work, a total that continued to rise in subsequent years.
Granger received many honorary doctorates in recognition of his work, starting with one from the University of Nottingham in 1992, and including Universidad Carlos III de Madrid, Stockholm School of Economics, University of Loughborough, and Aarhus and Aristotle universities. He was given a Festschrift,
Cointegration, Causality, and Forecasting, in 1999, co-edited by Robert F. Engle and Halbert White, and in 2001 his collected papers were published in two volumes as
Essays in Econometrics. He was elected a fellow of the Econometric Society and the American Academy of Arts and Sciences, and an honorary fellow of the International Institute of Forecasters, as well as a foreign member of the Finnish Society of Sciences and Letters. He was also elected a corresponding fellow of the British Academy in 2002, the same year he was made a distinguished fellow of the American Economic Association. When he and Engle were jointly awarded the Bank of Sweden Nobel memorial prize in economic sciences in 2003 Granger was in New Zealand as a visiting professor at the University of Canterbury. He received a phone call at 3 a.m. telling him of the award, but at first thought the call was a hoax. He was knighted in 2005, and in the same year the University of Nottingham renamed the building housing its economics and geography departments the Sir Clive Granger Building and created the Granger Centre for Time Series Econometrics. He was delighted in 2004 to be voted one of the 100 Welsh heroes.
Granger was made an honorary fellow of Trinity College, and greatly enjoyed the privilege, as it brought back happy memories of his childhood years in Cambridge. He was a member of the advisory board of the
Journal of Applied Econometrics for many years, and helped younger authors in numerous ways, including his joint editorship of the Oxford University Press
Advanced Texts in Econometrics series with Grayham Mizon.
From the time of his trip to the United States in 1959–60 Granger sported a beard. Blessed with a wry, gentle, and self-deprecating sense of humour, he was liked as well as respected by those who worked with him. He liked to take a short power nap each afternoon, when a ‘do not disturb’ sign would be displayed on his door, but at all other times his door would be open to all to call in. He showed particular interest in the ideas and careers of younger colleagues. In California he enjoyed body surfing on the beaches near the university; he also enjoyed hiking, tennis, reading, and art. He died at the Scripps Memorial Hospital in La Jolla, California, on 27 May 2009 of complications arising from a brain tumour, and was survived by his wife, Patricia, and their children, Mark, a computer software developer, and Claire, a science writer.
David F. Hendry