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.

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.

This paper surveys Trygve Haavelmo’s contributions to econometrics. A brief summary of his 1944 monograph is followed by an analysis of the six important papers he contributed during 1943–47. Four of them were devoted to macroeconomic models including estimation of the Keynesian marginal propensity to consume; the first two introduced the methodology of a system of structural equations; the third marked a milestone in econometric method by deriving the reduced form of such a system; and the fourth analyzed the contrast between time-series and cross-section analysis. The fifth (joint with M.A. Girshick) on the demand for food provided a definitive treatment of estimation of demand and supply functions; it carried out the execution of a five-equation structural model of the U.S. economy. The sixth was an interesting policy model of the interrelationship between the agricultural and the rural sector of the economy, which was fitted to U.S. data and addressed to questions of policy.

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.

Much of modern econometrics stems directly from the post-1940 works of Haavelmo and the Cowles Commission (CC) Monograph 10. This paper examines the consolidation process of the Haavelmo-CC research program mainly during the 1950–70 period from three aspects: (i) developments of econometrics textbooks, (ii) emerging themes and trends in econometric research, and (iii) the contribution of the program to empirical modeling of real-world issues. The examination reveals that the program has gained dominance primarily through its adherence to the scientific banner and style rather than its empirical relevance. The adoption of the hard science methodology is decisive in winning over the academic community; the taxonomy of econometrics into steps involving primarily specification, identification, and estimation has played a pivotal role in generating compartmentalized research topics with manageable technical challenge and also in facilitating the educational need for compiling self-contained subjects and definitely soluble questions.

We consider an omnibus test for the correct specification of the dynamics of a sequence $\left\{ {x\left( t \right)} \right\}_{t \in Z^d } $ in a lattice. As it happens with causal models and d = 1, its asymptotic distribution is not pivotal and depends on the estimator of the unknown parameters of the model under the null hypothesis. One first main goal of the paper is to provide a transformation to obtain an asymptotic distribution that is free of nuisance parameters. Secondly, we propose a bootstrap analog of the transformation and show its validity. Thirdly, we discuss the results when $\left\{ {x\left( t \right)} \right\}_{t \in Z^d } $ are the errors of a parametric regression model. As a by product, we also discuss the asymptotic normality of the least squares estimator of the parameters of the regression model under very mild conditions. Finally, we present a small Monte Carlo experiment to shed some light on the finite sample behavior of our test.

This paper develops uniform approximations for the integrated mean squared error (IMSE) of nonparametric series regression estimators, including both least-squares and averaging least-squares estimators. To develop these approximations, we also generalize an important probability inequality of Rosenthal (1970, Israel Journal of Mathematics 8, 273–303; 1972, Sixth Berkeley Symposium on Mathematical Statistics and Probability, vol. 2, pp. 149–167. University of California Press) to the case of Hilbert-space valued random variables.

Volatility component models have received considerable attention recently, not only because of their ability to capture complex dynamics via a parsimonious parameter structure, but also because it is believed that they can handle well structural breaks or nonstationarities in asset price volatility. This paper revisits component volatility models from a statistical perspective and attempts to explore the stationarity of the underlying processes. There is a clear need for such an analysis, since any discussion about nonstationarity presumes we know when component models are stationary. As it turns out, this is not the case and the purpose of the paper is to rectify this. We also look into the sampling behavior of the maximum likelihood estimates of recently proposed volatility component models and establish their consistency and asymptotic normality.

Data envelopment analysis (DEA) and free disposal hull (FDH) estimators are widely used to estimate efficiencies of production units. In applications, both efficiency scores for individual units as well as average efficiency scores are typically reported. While several bootstrap methods have been developed for making inference about the efficiencies of individual units, until now no methods have existed for making inference about mean efficiency levels. This paper shows that standard central limit theorems do not apply in the case of means of DEA or FDH efficiency scores due to the bias of the individual scores, which is of larger order than either the variance or covariances among individual scores. The main difficulty comes from the fact that such statistics depend on efficiency estimators evaluated at random points. Here, new central limit theorems are developed for means of DEA and FDH scores, and their efficacy for inference about mean efficiency levels is examined via Monte Carlo experiments.