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G.S. Maddala (universally known as ‘G.S.’) was born on 21 May 1933 in the south Indian state of Andhra Pradesh, where he had his high-school education. G.S. held the University Eminent Chair at the Ohio State University when he died on 4 June 1999 due to congestive heart failure.

G.S.’s father was a schoolteacher of modest means, and his mother, though having only an elementary education, was well versed in Sanskrit and the works of the great Indian philosopher Sankara. After graduating from high school in 1947, G.S. had to drop out of college for a few years due to health and other reasons. In 1955 he graduated first in his class from Andhra University with a BA in mathematics, and went on to graduate in First Class from Bombay University with an MA in statistics in 1957. With a Fulbright Fellowship, G.S. travelled to the University of Chicago in 1960 and completed his Ph.D. in 1963 under the supervision of the late Zvi Griliches. In that year, he was offered the job of Assistant Professor of Economics at Stanford University. Before joining Ohio State in 1993, G.S. taught at the University of Rochester (1967–1975) and at the University of Florida (1975–1993). He also held visiting appointments at Cornell, Yale, CORE, Monash, Columbia, Caltech (as the Fairchild Distinguished Scholar), Emory and Oakridge Labs. The fascinating narration of his journey from an early college dropout in a remote Indian village in 1947 to a faculty position at Stanford in 1963 can be found in the Introduction (‘How I Became an Econometrician’) to the two-volume selected works of Maddala (1994). More detailed biographical information, his life story and philosophy can be found in Lahiri and Phillips (1999), Lahiri (1999), Griliches (1999), Rosen (2000) and Hsiao (2003).

Beginning with his first published paper (with Zvi Griliches, Robert Lucas, and Neil Wallace) in 1962, through the next four decades, G.S. published 12 books and more than 110 articles covering almost every emerging area of econometrics – distributed lags, generalized least squares, panel data, simultaneous equations, measurement errors, tests of significance, switching and disequilibrium models, qualitative and limited dependent variable models, selection and self-selection models, exact small sample distributions of estimators, outliers and bootstrap methods, robust estimators, and more. The list is practically endless. Throughout his career G.S. used sample theory and Bayesian techniques freely in his research, a rarity in the econometrics profession, and was one of the early proponents of Bayesian approach in econometrics. Through his many books and the breadth of his own research, G.S. became a veritable textbook himself – a pre-eminent teacher in econometrics and an authority on almost every econometrics topic. Not surprisingly, according to the Social Science Citation Index, G.S. was one of the top five most-cited econometricians during each of the years 1988–1993, and he was cited more times in 1994 and 1996 than each of the six econometricians who won the Clark Medal during 1970–2000.

During the 1960s, G.S. contributed heavily towards the formulation and estimation of production functions and technical change. His doctoral dissertation was on productivity and technical change in the US bituminous coal industry. His two papers with Jay Kadane in 1966 and 1967 considered, respectively, the importance of alternative exogeneity assumptions in the estimation of the constant elasticity of substitution production functions parameters inclusive of the share equations; and the bias in the estimation of the returns to scale parameter when the production function is incorrectly specified as a Cobb Douglas. The rigour and depth in these papers were undoubtedly ahead of their time.

The early 1970s saw a flurry of activity on efficient estimation methods of alternative distributed lag models. One of G.S.’s widely cited papers (1971a) showed why certain commonly used two-step procedures are asymptotically less efficient than the maximum likelihood estimator in the presence of lagged dependent variables as regressors. This sort of problem is encountered also in dynamic panel data models with individual heterogeneity. The key result in this paper is that in these models the information matrix of the slope parameters and the parameters embedded in the covariance matrix of residuals are not diagonal. Using this as a starting point, Pagan (1986) developed a more thorough and modern characterization of numerous two-step procedures with estimated covariance matrix in the context of various econometric models.

With Dave Grether in 1973, G.S. studied the effects of errors in variables in distributed lag models with serial correlation. They showed analytically that the estimated speed of adjustment can be severely biased, and can give the spurious appearance of a long lag in adjustment. In two influential papers with A.S. Rao in 1971 and 1973, G.S. developed maximum likelihood procedures for Solow’s Pascal lag and Jorgenson’s rational distributed lag models, and compared the power of tests for serial correlation in regression models with lagged dependent variables. One important conclusion that emerged from the latter study was that the nature of the autocorrelation and trend in the exogenous variable is crucial in determining the small sample behaviour of the test statistics and the estimators – hinting at much of the work on integrated variables that would come in the 1980s.

During the early 1970s G.S. also produced a number of important papers on the use and estimation of panel data models, and rightfully became one of the three ‘fathers’ (together with Yair Mundlak and Marc Nerlove) of modern panel data analysis in econometrics. In his influential Econometrica (1971b) paper, G.S. demonstrated – with his characteristic clarity – that the error component estimator is a weighted combination of within and between estimators, and thus the use of dummies entails substantial loss of information by ignoring the ‘between’ variation in the data. In another Econometrica (1971c) paper, G.S. discussed the problem of pooling cross-section and time series data, and emphasized tests for consistency between time series and cross-section information. The paper contains a very deep analysis of an alternative Bayesian approach with diffuse priors and concludes that the two approaches should be complementary. (Publishing three full-length articles in Econometrica in a year has to be some kind of a record for an economist!) The profession quickly saw the enduring value of these publications and elected G.S. a fellow of the Econometric Society in 1975.

During the 1970s, like many other econometrics stalwarts of the period, G.S. was also involved in the development of econometric methodology in simultaneous equations models. He worked on appropriate estimation strategies in large and medium-size econometric models (1971d), and studied the power characteristics of alternative tests of significance associated with simultaneous equation estimation (1974a). His Econometrica (1974b) paper showed that ‘diffuse’ and ‘non-informative’ priors might lead to sharp posterior distributions even in under-identified models. Only recently have Chao and Phillips (2002) fully solved the so-called ‘Maddala paradox’ using Jeffreys prior. They interpret the pathological result in terms of a naive use of the diffuse prior that fails to downweight sufficiently that part of the parameter space where the rank condition either fails or nearly fails. In another potent contribution to an important recent work on weak instruments, Maddala and Jeong (1992) correctly showed that the bimodal distribution of the instrumental variable estimator obtained in the literature is merely due to the illustrative model used, where the correlation between the structural and the first-stage errors is perfect. Phillips (2006) gives a complete characterization of the bimodality problem when instruments are weak.

From the mid-1970s, G.S. was primarily focused on developing estimation and test procedures for qualitative and limited dependent variable models, and produced nearly 40 articles. This line of research also dealt with models with selection, self-selection, disequilibrium and controlled prices. His work at Rochester with Forrest Nelson (1974) on disequilibrium models and with Lung-Fei Lee (1976) on recursive models with qualitative endogenous variables and generalized selection models represents a long and very fruitful period of research on this topic. His 1983 Econometric Society monograph, Limited Dependent and Qualitative Variables in Econometrics, was an immediate best-seller and was declared a citation classic in Current Contents (vol. 30, 16 July 1993). It has fuelled much of the innovative applied and theoretical research using these tools since the mid-1980s, and has served as a bible to empirical researchers in applied microeconomics. The strength of the book lies in its comprehensiveness, expositional simplicity, and depth. As of June 2006, the Google Scholar reports a record 3,721 citations of this advanced monograph. G.S. also wrote a number of theoretical and empirical papers analysing limited dependent and qualitative variable models with panel data, and wrote widely cited expository articles for use in other disciplines such as accounting, finance, transportation, and health.

It is notable that G.S. can jointly claim a statistical distribution – the Singh–Maddala (1976) distribution – a much better name than the Burr type 12 to which it is related. Maddala and Singh’s proposed statistical distribution has triggered much research in describing the actual size distribution of incomes, and is a generalization of the Pareto distribution and the Weibull distribution used in analysis of equipment failures. As aptly noted by Sherwin Rosen (2000) while delivering the first Maddala lecture at Ohio State University on 26 April 2000, ‘Coase may have his Theorem, Stigler his Laws, Black and Scholes their Formula, and Lucas his critique, but what economist aside from Pareto (who was just as much a sociologist and political scientist and only one third economist) has half ownership of a distribution? And what an elegant economic derivation it has.’

G.S. had a deep interest in rational expectations models, in the validity of the hypothesis that can be gleaned from recorded survey data, and in how econometric disequilibrium models play out in this framework. Maddala, Fishe and Lahiri (1983) developed methods to estimate aggregate expectations when available survey data are partly qualitative and partly quantitative. He had done pioneering work (Maddala, 1983a) on the estimation for models with bounded price variation, and with Scott Shonkwiler (1985) applied the methodology to the corn market. With Steve Donald (1992), G.S. studied the disequilibrium model with upper and lower bounds on prices under rational expectations. The latter paper foreshadowed much work on exchange rate determination in a target zone in the 1990s. Undoubtedly, the full potential of this line of research initiated by G.S. is yet to be realized.

With failing health, G.S. spent much of the 1990s working primarily on bootstrap techniques and time series models with cointegration and structural breaks. During this period, he also wrote important papers on tests of unit roots in panel data models, robust inference, errors in variables problems in finance, Bayesian shrinkage estimation, outliers and influential observations, neural nets, and many others. Thus, ill health neither slowed down his research nor dampened his passion for mentoring and supervising Ph.D. students. In total G.S. supervised close to 60 doctoral students, co-authoring more than 65 published articles with them.

While testing the rationality of survey data on interest rate expectations in the context of a multiple-indicator single index model with heteroskedasticity, Maddala and Jeong in the mid-1990s used the weighted double bootstrap method to implement the Wald test in finite samples. His work with Hongyi Li in 1996 explored the use of different bootstrap techniques in cointegration regressions, financial and non-linear models. With Wu (1999) on panel data unit root test, G.S. suggested the use of a novel Fisher test that combines N individual tests with bootstrap-based critical values. Since much remains to be done to extend the Fisher approach to combining individual tests that are correlated, further generalizations of the Maddala–Wu test are certainly to come.

Much of his work on modern time series analysis has been summarized in his seminal book with In-Moo Kim (1998). This book also presents a comprehensive and lucid review of unit root and cointegration tests, and estimation with integrated variables. It discusses problems of unit root tests and cointegration under structural change, outliers, robust methods, the Markov switching model, and Harvey’s structural time series model. The book contains a welcome chapter on the Bayesian approach to many of these problems and bootstrap methods for small-sample inference.

G.S. contributed to a number of purely policy-oriented and applied areas. Some of these topics include consumption, production and cost functions, money demand, regulation, pseudo-data, returns to college education, housing markets, energy demand, stock prices, international macro, and cross-country growth analysis. In all these papers, G.S. made serious attempts to grapple with substantive and important issues of the day. However, one common characteristic that flows through all these papers is that they unfailingly reflect the discriminating judgement of a consummate econometrician.

G.S. had the gift of a brilliant expositor – the ability to cut through the technical superstructure to reveal only essential details, while retaining the nerve centre of the subject matter he sought to explain. He loved to write econometrics in plain English. There was magic in how he could cut to the core, strip away all the irrelevant details and illuminate the essence of the issue in a quiet and unassuming way. This exceptional expository capability made him revered by applied and theoretical econometricians alike. This skill was apparent in all his writing and was a central element in his textbook expositions. His 1977 econometrics text redefined the boundaries of econometrics that could be integrated into graduate teaching, and became a new standard for subsequent econometrics textbooks. His advanced undergraduate textbook An Introduction to Econometrics has gone into its third edition (2000), and all his textbooks have been translated into a number of foreign languages.

G.S.’s style was to take a critical but constructive look at evolving econometric techniques – in particular those that have little practical significance. In this, G.S. had something that was close to perfect pitch in econometrics. He was one of the few econometricians who constantly asked whether the questions being answered were worth asking – always maintaining a clear perspective on a wide range of issues in econometrics and their relationship to economic problems. In doing so, he never hesitated to go against the tide of the profession. While much of his work was undoubtedly constructive, much was also critical of many current fads in econometrics. That is also a very important contribution.

See Also

Selected Works

  • 1962. (With Griliches, Z., R.E. Lucas, and N. Wallace.) Notes on estimated aggregate consumption functions. Econometrica 30: 491–500.

  • 1965. Productivity change in the bituminous coal industry. Journal of Political Economy 73: 352–365.

  • 1966. (With Kadane, J.R.) Notes on the estimation of elasticity of substitution. Review of Economics and Statistics 48: 340–344.

  • 1967. (With Kadane, J.R.) Estimation of returns to scale and elasticity of substitution. Econometrica 35: 419–423.

  • 1971a. Generalized least squares with an estimated covariance matrix. Econometrica 39: 23–33.

  • 1971b. On the use of variance component models in pooling cross-section and time series data. Econometrica 39: 341–358.

  • 1971c. The likelihood approach to pooling cross-section and time series data. Econometrica 39: 939–953.

  • 1971d. Simultaneous equations methods for large and medium-sized econometric models. Review of Economic Studies 38: 435–445.

  • 1971. (With Rao, A.S.) Maximum likelihood estimation of Solow’s and Jorgenson’s distributed lag models. Review of Economics and Statistics 53: 80–88.

  • 1972. (With Grether, D.M.) On the asymptotic properties of two-step procedures used in the estimation of distributed lag models. International Economic Review 13: 737–744.

  • 1973a. (With Grether, D.M.) Errors in variables and serially correlated residuals in distributed lag models. Econometrica 41: 255–262.

  • 1973b. (With Rao, A.S.) Tests for serial correlation in regression models with lagged dependent variables and serially correlated errors. Econometrica 41: 255–262.

  • 1974a. Some small sample evidence on tests of significance in simultaneous models. Econometrica 42: 841–851.

  • 1974b. Weak priors and sharp posteriors in simultaneous equation models. Econometrica 44: 345–351.

  • 1974c. (With Nelson, F.D.) Maximum likelihood methods for models of markets in disequilibrium. Econometrica 42: 1013–1030.

  • 1976a. (With Lee, L.-F.) Recursive models with qualitative endogenous variables. Annals of Social and Economic Measurement 5: 525–545.

  • 1976b. (With Singh, S.K.) A function for size distribution of incomes. Econometrica 44: 963–970.

  • 1977. Econometrics. New York: McGraw Hill.

  • 1983a. Methods for models of markets with bounded price variation. International Economic Review 24: 361–378.

  • 1983b. Limited dependent and qualitative variables in econometrics. Cambridge: Cambridge University Press.

  • 1983c. (With Fishe, R.P., and K. Lahiri.) A time series analysis of popular expectations data. In Economic applications of time-series analysis, ed. A. Zellner. Washington, DC: U.S. Census Bureau.

  • 1985. (With Shonkwiler, J.S.) Modeling expectations of bounded prices: An application to the market for corn. Review of Economics and Statistics 67: 697–702.

  • 1992a. (With Jeong, J.) On the exact small sample distribution of the instrumental variable estimator. Econometrica 60: 181–183.

  • 1992b. (With Donald, S.) A note on the estimation of limited dependent variable models under rational expectations. Economics Letters 38: 17–23.

  • 1994. Econometric methods and applications: Selected papers of G.S. Maddala, volume 2. Aldershot: Edward Elgar.

  • 1996. (With Li, H.) Bootstrapping time series models (with discussion). Econometric Reviews 15: 115–195.

  • 1998. (With Kim, I.-M.) Unit roots, cointegration and structural change. Cambridge: Cambridge University Press.

  • 1999. (With Wu, S.) A comparative study of unit root tests with panel data and a new simple test. Oxford Bulletin of Economics and Statistics 61: 631–652.

  • 2000. An introduction to econometrics, 3rd edn. Chichester: Wiley.