Popper and Production: Testing Parametric Restrictions in Systems under Nonstationarity

Abstract

This study tests symmetry and homogeneity restrictions on a system of factor demand equations for central and western Canadian agriculture under the assumption that the variables are integrated processes and the demands represent cointegrating relationships. It is well known that the distribution of F‐statistics derived from ordinary least squares estimates in such systems are not distributed as the ratio of two independent χ2 random variables normalized by their degrees of freedom even asymptotically. Indeed, the use of traditional critical values of F‐statistics in such cases will severely underestimate the true critical values and therefore use of traditional critical values would tend to overreject symmetry and homogeneity restrictions. Bootstrapping techniques are employed to generate the true distribution of the F‐statistic so that the proper critical values can be compared with the calculated F‐statistic on symmetry and homogeneity. For both regions, the calculated F‐statistic is not rejected using the proper critical values but would have been strongly rejected using standard critical values. Results are consistent with the argument that the regularity of rejection of the parametric restrictions of symmetry and homogeneity found by Fox and Kivanda may be due to inappropriate assumptions regarding the time series properties of the data rather than a rejection of neoclassical production theory. This interpretation is consistent with arguments made by Clark and Coyle in their comments on Fox and Kivanda. Nous testons les constraintes de symétrie et d'homogénéité sur un système d'équations de demande de facteurs de production pour le secteur agricole du centre et de I‘ouest du Canada, en postulant que les variables sont des processus intégrés et que les demandes représentent des rapports cointegrants. Il est admis que dans des systèmes de ce genre les valeurs F dérivées des calculs des carrés latins ordinaires ne sont pas distribués comme le rapport de deux variables aléatoires χ2 indépendantes normalisées par leur degré de liberté, me soit ‐ce que de façon asymptotique. De fait, l'emploi, dans pareil cas, des valeurs critiques classiques de l'analyse statistique basée sur F comporte une grave sous‐estimation des vraies valeurs critiques, de sorte qu‘il risque de sur‐rejeter les constraintes de symétrie et d'homogénéité. Les techniques de rééchantillonnage bootstrap sont utilisées pour produire la vraie distribution des valeurs F, de telle sorte que les valeurs critiques convenables puissent être comparées aux valeurs F calculées, quant à la symétrie et à l'homogénéité. Pour les deux régions mentionnées plus haul, les valeurs F calculées ne sont pas rejetées lorsqu‘on utilise les valeurs critiques appropriées, mais elles le seraient fortement si on utilisait les valeurs critiques standards. Les résultats s‘accordent avec l‘hypothèse selon laquelle la régularité du rejet des restrictions paramétriques de symétrie et d'homogénéite observée par Fox et Kivanda s'expliquerait par des postulats erronés relatifs aux...

Metropolitan Evidence Regarding Small Commercial and Industrial Electricity Consumption

“…That is helpful because of shortcomings that may arise within the context of static modeling approaches (Fox and Kivanda, 1994). This study employs time series data and the decisions of CIS firms are likely to be better modeled within dynamic frameworks (Clark and Grant, 2000;Boonsaeng and Wohlgenant, 2006). Additionally, the data-based approach is able to account for dynamic variations in CIS electricity demand over time, as it allows sample information to select the underlying data-generating process and capture the long-run equilibrium structure (Reziti and Ozanne, 1999).…”

Simultaneous Estimation of Cost and Distance Function Share Equations

“…Indeed, all variables are considered endogeneous in cointegrated systems that arise from vector autoregressions (VARs) (e.g., Pesaran and Shin 2002). Estimation of primal and dual models in cases where data are nonstationary include Clark and Youngblood (1992) and Clark and Grant (2000) and, for demand systems, Pesaran and Shin (2002) and Lewbel and Ng (2005). Estimation of primal and dual models in cases where data are nonstationary include Clark and Youngblood (1992) and Clark and Grant (2000) and, for demand systems, Pesaran and Shin (2002) and Lewbel and Ng (2005).…”

“…The distance function, which we will call the "primal" approach, develops a set of primal conditional factor demands from which elasticities of complementarity can be calculated (e.g., Karagiannis et al 2004;Kumbhakar and Tsionas 2005;Coelli et al 2008). The cost function, which we will call the "dual" approach, develops a set of conditional factor demands from which elasticities of substitution can be calculated (e.g., Appelbaum 1978;Lopez 1980;Taylor 1989;Clark and Youngblood 1992;Clark and Grant 2000). The distance function and the cost function are dual to one another meaning that the information contained in one function is identical to the other (Deaton 1979).…”

“…In addition, asymptotically efficient estimators derived from cointegrating systems, like ordinary least squares (e.g., Engle and Granger 1987) and maximum likelihood (Johansen 1991), are "superconsistent" in the sense that they converge at rate T rather than at rate T 1/2 , as is the case for estimates derived from stationary data. Estimation of primal and dual models in cases where data are nonstationary include Clark and Youngblood (1992) and Clark and Grant (2000) and, for demand systems, Pesaran and Shin (2002) and Lewbel and Ng (2005).…”