Trygve Haavelmo Research Articles

Nonlinear growth model with long memory: generalization of Haavelmo model

The Haavelmo economic growth model is one of the most famous nonlinear macroeconomic models proposed by Trygve Haavelmo, who received the Alfred Nobel Memorial Prize in Economic Sciences in 1989. In this paper, we proposed a generalization of the Haavelmo growth model, in which we take into account the fading memory and variable parameters. Equation of the proposed model is described by nonlinear fractional differential equation, in which the Caputo fractional derivative of non-integer order are used to take into account long memory with power-law fading. The paper proposes an exact solution for the nonlinear equation of the suggested model with memory. The conditions of the existence of the suggested exact solution for this nonlinear fractional differential equation are described. These conditions impose restrictions on the nonlinear economic dynamics with memory. For proposed model, expressions for the warranted rate of growth with power-law memory are derived.

Some tendencies in modern econometrics

All analytical subjects, probably all scholarly fields of investigation, for the matter, should be exploring new avenues of research and seeking new findings. In economics, generally, there is an explosion of research activity, associated with new information, new devices, new scholarly journals, and new professional opportunities. Econometrics, which greatly expanded as a sub-dis? cipline of economics in the second half of this century, is presently branching out in many directions, some of which appear to be fruitful and some of which do not. There are now several books and articles on the historical development of econometrics from sparse early roots in the 19th century and much more significant growth activity in the 20th century. It is worth while to reconsider some earlier research, in relation to recent developments. The subject grew quite naturally as formal economics and mathematical statistics expanded, but a breakthrough occurred that came to be known as the 'Haavelmo Revolution'. A manuscript authored by Trygve Haavelmo circulated among academic economists and statisticians in the late 1930s and early 1940s; it was published as a supplement to Econometrica in 19441. An important interpretation of Haavelmo's contribution, viewed largely from the side of mathematical statistics, has been published by Theodore W. Anderson on the occasion of the award of the prize in memory of Alfred Nobel to Haavelmo in 1989.2 In order to assess some recent developments in econometrics, I want to emphasize a few important aspects of Haavelmo's contribution, which indeed has many facets. Essentially, Haavelmo placed econometric methodology in the midst of developments that were taking place, or had already taken place, in statistical inference. Statistics in economics, which was already well established, but under development at the time of Haavelmo's work, was largely concenrned with descriptive statistics. The main problems were those of describing the economy in quantitative terms. Haavelmo's approach showed how to relate mathematical specifications of economic relationships to probability interpretations of statistical estimates of the specified relationships. All econometrics does not deal with the estimation of behavioural relationships or economic decision-making, but a large portion of the discipline is involved in analyzing economic behaviour, and this forms the focus for the present discussion. To show how probability and economic relationships are involved together, let us consider the fundamental, but general, model that formed the basis for Haavelmo's approach.

Searching for a Theory That Fits the Data: A Personal Research Odyssey

This survey paper discusses the Cointegrated VAR methodology and how it has evolved over the last 30 years. first section is a description of major steps in the econometric development of the CVAR model that facilitated serious real world applications. next three sections are primarily methodological and discuss (i) difficulties and puzzles when confronting theory with the data, (ii) the formulation of a viable link between theory and the data, a so called theory-consistent CVAR scenario, and (iii) how all this was inspired by Trygve Haavelmo and his Nobel prize winning monograph The Probability Approach to Economics. next two sections discuss early applications of the Cointegrated VAR model to monetary transmission mechanisms, international transmission mechanisms and wage, price and unemployment dynamics. They report puzzling evidence, discuss the need for new theory, and propose a method for combining partial CVAR analyses into a larger macroeconomic model. following sections propose a new, empirically-based, approach to macroeconomics in which imperfect knowledge based expectations replace so called rational expectations and in which the financial sector plays a key role for understanding the long persistent movements in the data. last section argues that the CVAR can act as a design of experiment for passive observations and illustrates with several applications including unemployment dynamics under crises periods and aid effectiveness in South Saharan African countries.

Lawrence R. Klein and the Making of Large-Scale Macro-Econometric Modeling, 1938-1955

Lawrence R. Klein was the father of macro-econometric modeling, the scientific practice that dominated macroeconomics throughout the second half of the twentieth century. Therefore, understanding how Klein developed his identity as a macro-econometrician and how he conceived and forged macro-econometric modeling at the same time, is essential to draw a clear picture of the origins and subsequent development of this scientific practice in the United States. To this aim, I focus on Klein’s early trajectory as a student of economics and as an economist (from 1938-1955), and I particularly examine the extent to which the people and institutions Klein encountered helped him shape his professional identity. Klein’s experience at places like Berkeley, MIT, Cowles, and the University of Michigan, as well as his early acquaintance with people such as Griffith Evans, Paul Samuelson, and Trygve Haavelmo were decisive in the formation of his idea on how econometrics, expert knowledge, mathematical rigor, and a specific institutional configuration should enter macro-econometric modeling. Although Klein’s identity defined some of the most important characteristics of this practice, by the end of the 1950s, macro-econometric modeling became a scientific practice independent of Klein’s enthusiasm and with a “life of its own,” ready to be further developed and adapted to specific contexts by the community of macroeconomists.

2016 HES PRESIDENTIAL ADDRESS: STATISTICAL INFERENCE IN ECONOMICS, 1920–1965: CHANGES IN MEANING AND PRACTICE

I review changes over time in the meaning that economists in the US attributed to the phrase “statistical inference,” as well as changes in how inference was conducted. Prior to WWII, leading statistical economists rejected probability theory as a source of measures and procedures to be used in statistical inference. Trygve Haavelmo and the early Cowles Commission econometricians developed an approach to statistical inference based on probability theory, but the arguments they offered in defense of this approach were not always responsive to the concerns of earlier empirical economists that the data available to economists did not satisfy the assumptions required for such an approach. Despite this, after a period of about twenty-five years, a consensus developed that methods of inference derived from probability theory were an almost essential part of empirical research in economics. I conclude with some speculation on possible reasons for this transformation in thinking about statistical inference.

The Status of Bridge Principles in Applied Econometrics

The paper begins with a figurative representation of the contrast between present-day and formal applied econometrics. An explication of the status of bridge principles in applied econometrics follows. To illustrate the concepts used in the explication, the paper presents a simultaneous-equation model of the equilibrium configurations of a perfectly competitive commodity market. With artificially generated data I carry out two empirical analyses of such a market that contrast the prescriptions of formal econometrics in the tradition of Ragnar Frisch with the commands of present-day econometrics in the tradition of Trygve Haavelmo. At the end I demonstrate that the bridge principles I use in the formal-econometric analysis are valid in the Real World—that is in the world in which my data reside.

Methodological institutionalism as a transformation of structural econometrics

ABSTRACTI agree with Nell and Errouaki that an econometrics based on neoclassical economic theory fails to develop any insight into deep structures. But my methodology differs slightly from theirs because of my view that an econometrics based on any economic theory would fail in this sense. Economics is an inexact science, incapable of providing a complete set of causal factors to explain any economic phenomenon. I arrive at a different call for more fieldwork in econometrics due to a somewhat different reading of the criticisms of Trygve Haavelmo, Wassily Leontief, the young Tjalling Koopmans and Oskar Morgenstern. These economists not only shared the idea that economic structure is different in nature from natural laws and that statistical analysis alone is not enough to arrive at knowledge of this structure, but also that economic theory as an additional source of knowledge would not be sufficient either. Another additional source of knowledge is needed—that is, field expertise.

Econometrics and equilibrium models

ABSTRACTIn Rational Econometric Man, Edward Nell and Karim Errouaki present a welcome and timely case for the view that econometrics and econometric model-building may not be the magic tools to solve all empirical questions despite what many seem to have thought they were in the 1960s. Here I examine some possible problems with econometric models that have to do with their usually taking the form of equilibrium models. Some of these problems were recognized by Trygve Haavelmo decades ago. And as Aris Spanos has recently discussed, the problems are often the result of what we say in our textbooks. Some problems have to do with what we mean by econometric parameters and others with how we use probabilities.

Lawrence R. Klein 1920–2013: Notes on the early years

Klein can well be said to have created the field of macroeconometric modeling almost singlehandedly. His international influence started at an early stage. The article offers scattered archive observations on Klein's early years from undergraduate study to the University of Pennsylvania in 1958. Klein was in 1944 recruited by the Cowles Commission in Chicago to construct the first macroeconomic model in the USA, drawing on the experiences of the interwar modeling work of Jan Tinbergen and the new path-breaking econometric methods developed by Trygve Haavelmo. The first Klein model was taken into use at the end of 1945 to shed light on the prospects for the US economy in the transition from war to peace. After two-three years in Chicago Chicago, Klein traveled for a year in Europe and initiated macroeconometric modeling work in Canada, at the University of Michigan, and at Oxford University. This was only the beginning of the lifelong influence exerted on modelers around the globe. The article pays attention to Klein's relation to Paul Samuelson, Jacob Marschak, Trygve Haavelmo, Ragnar Frisch, and others.

TRYGVE HAAVELMO’S EXPERIMENTAL METHODOLOGY AND SCENARIO ANALYSIS IN A COINTEGRATED VECTOR AUTOREGRESSION

The paper provides a careful, analytical account of Trygve Haavelmo’s use of the analogy between controlled experiments common in the natural sciences and econometric techniques. The experimental analogy forms the linchpin of the methodology for passive observation that he develops in his famous monograph,The Probability Approach in Econometrics(1944). Contrary to some recent interpretations of Haavelmo’s method, the experimental analogy does not commit Haavelmo to a strong apriorism in which econometrics can only test and reject theoretical hypotheses, rather it supports the acquisition of knowledge through a two-way exchange between theory and empirical evidence. Once the details of the analogy are systematically understood, the experimental analogy can be used to shed light on theory-consistent cointegrated vector autoregression (CVAR) scenario analyses. A CVAR scenario analysis can be interpreted as a clear example of Haavelmo’s ‘experimental’ approach; and, in turn, it can be shown to extend and develop Haavelmo’s methodology and to address issues that Haavelmo regarded as unresolved.

HAAVELMO’S PROBABILITY APPROACH AND THE COINTEGRATED VAR

Some key econometric concepts and problems of great importance to Trygve Haavelmo and Ragnar Frisch are discussed within the general framework of a cointegrated VAR. The focus is on problems typical of time-series data such as multicollinearity, spurious correlation and regression, time dependent residuals, model selection, missing simultaneity, autonomy, and identification. The paper argues that the more recent development of unit root econometrics has been instrumental for a solution to the above problems.

VAR INTERPRETATIONS OF HAAVELMO’S MARKET MODEL OF CAPITAL AND INVESTMENT

In the paper attempts are made to integrate two parts of Trygve Haavelmo’s work: investment theory and dynamic econometric models of interrelated markets. Specifically, the duality in the representation of the capital service price and the capital quantity in relation to the investment price and quantity are brought to the forefront and confronted with elements from simultaneous equation modeling of vector autoregressive systems containing exogenous variables (VARX), using linear four-equation models. The role of the interest rate and the modeling of the expectation element in the capital service price and the capital’s retirement pattern, and their joint effect on the model’s investment quantity and price dynamics are discussed. Stability conditions are illustrated by examples. Extensions relaxing geometric decay and ways of accounting for forward-looking behavior, including rational expectations, are outlined. Some remarks on the theory-data confrontation of this kind of model are given.

TRYGVE HAAVELMO AT THE COWLES COMMISSION

The article reviews the early history of the Cowles Commission (CC), its close and intertwined relations with the Econometric Society (ES), and the influence and guidance of Ragnar Frisch. It provides detail on three rounds of choosing a research director for CC in 1937–38, in 1939 and, particularly, at the end of 1942. Haavelmo’s work in the early 1940s came to play a major role for the econometric research at the Cowles Commission under Jacob Marschak as research director 1943–48. The article points to the importance of Abraham Wald and Jacob Marschak for the success of Haavelmo’s venture and its influence and tells the story of how it came about that Haavelmo’s ideas were adopted, applied, and disseminated by the Cowles Commission. Thus the mention of Trygve Haavelmo in the title is referring also to his econometric ideas. The ideas themselves and their further evolvement at the CC have been a dominating theme in the history of econometrics literature, e.g., Hildreth (1986), Epstein (1987), Morgan (1990), Qin (1993), and Christ (1994). The article discusses the recruitment, the inner workings, and various other concerns of the Cowles econometricians, from Marxism to Black Magic. It recounts at some length the efforts made by Marschak to recruit Abraham Wald to the University of Chicago and the Cowles Commission. The article can be read as a sequel to Bjerkholt (2005, 2007).

MODEL DISCOVERY AND TRYGVE HAAVELMO’S LEGACY

Trygve Haavelmo’sProbability Approachaimed to implement economic theories, but he later recognized their incompleteness. Although he did not explicitly consider model selection, we apply it when theory-relevant variables, {Xt}, are retained without selection while selecting other candidate variables, {Wt}. Under the null that the {Wt} are irrelevant, by orthogonalizing with respect to the {Xt}, the estimator distributions of theXt’s parameters are unaffected by selection even for more variables than observations and for endogenous variables. Under the alternative, when the joint model nests the generating process, an improved outcome results from selection. This implements Haavelmo’s program relatively costlessly.

Trygve Haavelmo and the Emergence of Causal Calculus

Haavelmo was the first to recognize the capacity of economic models to guide policies. This paper describes some of the barriers that Haavelmo’s ideas have had (and still have) to overcome, and lays out a logical framework that has evolved from Haavelmo’s insight and matured into a coherent and comprehensive account of the relationships between theory, data and policy questions. The mathematical tools that emerge from this framework now enable investigators to answer complex policy and counterfactual questions using embarrassingly simple routines, some by mere inspection of the model’s structure. Several such problems are illustrated by examples, including misspecification tests, nonparametric identification, mediation analysis, and introspection. Finally, we observe that economists are largely unaware of the benefits that Haavelmo’s ideas bestow upon them and, to close this gap, we identify concrete recent advances in causal analysis that economists can utilize in research and education.

MY REMINISCENCES OF TRYGVE HAAVELMO AT THE COWLES COMMISSION

Trygve Haavelmo and the author were colleagues at the Cowles Commission for Research in Economics during the academic year 1945–46. The econometric analysis of simultaneous equation models and its uses in economic analysis were explored.

Haavelmo’s Epistemology for an Inexact Science

The first two chapters of Trygve Haavelmo’s Probability Approach provide a very rich epistemological framework for understanding what is involved in finding laws outside the laboratory. Even though these laws will be inexact, a framework was developed to specify for which conditions laws could be found. Therefore, Haavelmo defined two different kinds of influences, potential and factual influences. To decide whether a regression equation represents a law, it is not the strengths of the factual influences that are relevant, but whether the potential influences are significant. Unfortunately, by passive observations only it is difficult to obtain knowledge about potential influences, particularly when they have not revealed their strengths (yet).

Lawrence R. Klein 1920-2013: Notes on the Early Years

Lawrence R. Klein can well be said to have created the field of macroeconometric modelling and his international influence started at an early stage. The article offers scattered observations on Klein’s early years from undergraduate study to the University of Pennsylvania in 1958. Klein was in 1944 hired by the Cowles Commission in Chicago to construct the first macroeconomic models in the USA, drawing on the experiences of the interwar modeling work of Jan Tinbergen and the new path-breaking econometric methods developed by Trygve Haavelmo. The first Klein model was taken into use at the end of 1945 to shed light on the prospect for the US economy in the transition from war to peace. After three years in Chicago, Klein travelled for a year in Europe and initiated macroeconometric modeling work in Canada, the University of Michigan, and Oxford University. This was only the beginning of the lifelong influence Klein exerted on modelers around the globe. The article pays attention to Klein’s relations with Paul Samuelson, Jacob Marschak, Trygve Haavelmo, Ragnar Frisch, and others.

Overdeterminacy and Endogenous Cycles: Trygve Haavelmo's Business Cycle Model

AbstractThe econometrician Trygve Haavelmo pursued a research programme in macroeconomic theory that was highly original for its time. We present his macro model for an economy with deregulated financial markets and a policy determined interest rate path. Disequilibria arise in the interface between asset markets and the real economy. A mismatch between the marginal return to capital and investors' required rate generates endogenous switching between recession and full employment regimes. Haavelmo regarded the ‘switching mechanism’ as a substitute for liquidity constraints, and together with his ideas of price dynamics, there is a clear Keynesian and Wicksellian influence on his macroeconomic theorizing.

Trygve Haavelmo at the Cowles Commission

The article reviews the early history of the Cowles Commission (CC), its close and intertwined relations with the Econometric Society (ES), and the influence and guidance of Ragnar Frisch. It provides detail on three rounds of choosing a research director for CC in 1937-38, in 1939 and, particularly, at the end of 1942. Haavelmo’s work in the early 1940s came to play a major role for the econometric research at the Cowles Commission under Jacob Marschak as research director 1943-48. The article points to the importance of Abraham Wald and Jacob Marschak for the success of Haavelmo’s venture and its influence and tells the story of how it came about that Haavelmo’s ideas were adopted, applied and disseminated by the Cowles Commission. Thus the mention of Trygve Haavelmo in the title is referring also to his econometric ideas. The ideas themselves and their further evolvement at the CC have been a dominating theme in the history of econometrics literature, e.g. Hildreth (1986), Epstein (1987), Morgan (1990), Qin (1993) and Christ (1994). The article discusses the recruitment, the inner workings and various other concerns of the Cowles econometricians, from Marxism to Black Magic. It recounts at some length the efforts made by Marschak to recruit Abraham Wald to the University of Chicago and the Cowles Commission. The article can be read as a sequel to Bjerkholt (2005, 2007). It will appear in Econometric Theory.