Moving-Average Transformations in Classical Linear Models

Economists are frequently compelled to use data which take inappropriate forms. One particular deficiency is discussed in the paper below; namely, the prior adjustment of economic time-series by moving average transformations. This discussion is restricted to regression analyses and data which satisfy the conditions for the classical linear model.

Temporal Spillover and Autocorrelation in Some Aggregate Models of Wage-Determination

In a recent paper, we discussed the possible availability of prior information with respect to the source of the moving-average components of mixed moving-average autoregressive processes in the context of empirical investigations of wage-determination. The earlier discussion of this generalization of the Yule-Slutsky effect ignores the possible presence of lagged endogenous variables, which may be due to explicit temporal spillovers between different wage-bargains in the labour market. This omission is remedied in this paper, and several final equations for models with temporal spillovers are given below. These can be contrasted with the final equation for a simple model in which the spillover feedback is restricted to autoregressive processes for the stochastic errors of theoretical relations. Also, in this paper the different specifications can be associated with a collection of linear hypotheses for which conventional least-squares statistics provide suitable test statistics if samples of data are sufficiently large. Knowledge of the weights for the moving-average components is an essential framework for the procedures which are outlined.

Known Moving-Average Transformations and Autoregressive Processes

The errors in the linear models which are used so widely by economists may be generated by mixed moving-average autoregressive processes. If errors on an aggregative equation are generated by a mixed moving-average autoregressive process and the weights of the moving-average component of this process are known, then the least-squares procedure can yield consistent estimators of both signal and autoregressive parameters if two adjustments are made to the equation. The autoregressive transformation is combined with pre-multiplication by a Moore-Penrose inverse based on the known weights of the moving-average component.

The Sensitivity of Quarterly Models of Wage Determination to Aggregation Assumptions

In his A.E.A. Presidential Address, Tobin points out that due to the continuing controversy over the concept of a stable Phillips curve, the institutional features of the labour market have been largely ignored. Hence, the purpose of this paper is twofold: (1) to present an analytical framework for the empirical investigation of these institutional labour market features, and (2) to present some empirical results demonstrating the gravity of the problem.

Autocorrelation in Empirical Studies of Wage Determination

The need for careful specification in econometric analyses is well-known. If some component of a particular specification is incorrect, then conventional inferential procedures may be invalid. In particular, the presence of autocorrelation in linear economic models may lead to the use of inappropriate formulae for estimates of standard errors of estimated coefficients and for F-statistics which provide the bases for tests of significance. Concern over this problem has generally been represented in recent years by two checks of sensitivity, namely, the calculation of Durbin-Watson d-statistics and the use of either autoregressive transformations of the type introduced by Cochrane and Orcutt (1949) or similar approaches such as the Hildreth-Lu (1960) scan procedure, which can be associated with maximum likelihood methods. At the same time, econometric studies of wage determination provide an excellent illustration of certain specific deficiencies which may be introduced by conventional checks of sensitivity. Clarification of the quantitative significance of these deficiencies depends critically upon adequate investigation of institutional features of the labour market, and we cannot claim to have achieved this final goal. However, incompleteness of knowledge does not preclude a demonstration that current practices in empirical studies of wage-determination leave much to be desired. Two well-known studies of Phillips curves, those of Perry and Bodkin et al., provide the bases for discussion.

The Specification of Institutional Features in the Determination of Wages in Canadian Manufacturing Industries

As demonstrated in a recent paper, quarterly models of wage determination are highly sensitive, both with respect to parametric estimates and statistical inferences, to the specification of institutional features in the labour market. In the context of these sensitivities, this paper attempts to eliminate a severe deficiency in relevant data by the provision, in tabular form, of time-series which summarize evidence for critical institutional features of the Canadian labour market. The first section contains a brief overview of the data set and examines certain issues such as the coverage of the sample, seasonal patterns in bargaining, and the average lengths of contracts. This overview is followed in the second section by an account of a particular analytical model which incorporates these institutional features in a form appropriate for estimation of behavioural parameters. Finally, some statistics for the institutional characteristics of the labour market (by reference to the analytical model) are provided in the form of a collection of variable weights. These weights will be employed in a subsequent paper for which the behavioural parameters of the market will be estimated.

A Second Look at the Roles of Quit Rates and Exceptional Variables in the Determination of Money Wages

In his recent discussion of wage-determination in the U.S. manufacturing industry and its durable and non-durable components, Arthur Donner attempts to explore the short-run interaction of labour turnover and inflationary expectations by incorporating this interaction into a "a two-equation model suitable for econometric testing". His tentative conclusions concern both the direct roles of these variables and the speeds of adjustment of wage changes to prior expectational changes. Since theoretical analyses cannot establish the quantitative significance of biases and false inferences, our numerical results provide important results with respect to the robustness of Donner's estimates. They appear to confirm a significant role for excess demand, but the effect of inflationary price expectations remains uncertain in the absence of prior information with respect to the speeds of adjustment to such expectations. In his list of tentative conclusions, Donner cites one particular result which he had not anticipated. "The implication that the wholesale price index fits into the estimating equation slightly better than the consumer prices is somewhat startling at first, but may present some support for the hypothesis that prices and wages are raised when labour supply tightens--and particularly when vacancies rise above their steady-state values. There appears to be some tentative support in these findings for the hypothesis that the money illusion exists in the short-run." Our results suggest that the use of the wholesale price index (WPI) leads to substantially better fits than the use of the consumer price index (CPI) for both total manufacturing and its separate components. Finally, a model which contains the unusual specification of wage expectations as an explanatory variable for money wage changes is conclusively rejected by our results.

Quarterly Models of Wage Determination: Some New Efficient Estimates

The concept of stable Phillips curves and their economic implications have been the subject of a series of disputes in recent years. Since Phillips introduced his simple disequilibrium model,empirical research in the field of wage determination has indicated a wide spectrum of explanatory variables which expands and contracts almost randomly in published studies. Apart from this difficulty in specification, the intertemporal instability of estimated coefficients for Phillips curve variants is particularly disturbing. In addition, the theoretical bases for many of these variants are unclear, and several economists have participated in a neo-classical counter-attack on the existence and stability of Phillips curves from a theoretical viewpoint. The objectives of this paper are to examine the consequences of certain invalid statistical procedures which are employed in many of these studies and to provide some empirical evidence of their effect. In particular, we focus attention on the implications of the aggregate procedure which provides the basis for the use of a "four quarter overlapping change" representation of the dependent variable in quarterly studies of wage determination and, also, for the use of moving averages of explanatory variables.

Novel metallic states at low temperatures

We present an overview of unconventional metallic states arising close to magnetic quantum critical points with a focus on d-electron systems. The applicability and potential breakdowns of traditional self-consistent field theories of such materials are discussed as well as related phenomena in other systems

On the mechanisms governing gas penetration into a tokamak plasma during a massive gas injection

A new 1D radial fluid code, IMAGINE, is used to simulate the penetration of gas into a tokamak plasma during a massive gas injection (MGI). The main result is that the gas is in general strongly braked as it reaches the plasma, due to mechanisms related to charge exchange and (to a smaller extent) recombination. As a result, only a fraction of the gas penetrates into the plasma. Also, a shock wave is created in the gas which propagates away from the plasma, braking and compressing the incoming gas. Simulation results are quantitatively consistent, at least in terms of orders of magnitude, with experimental data for a D 2 MGI into a JET Ohmic plasma. Simulations of MGI into the background plasma surrounding a runaway electron beam show that if the background electron density is too high, the gas may not penetrate, suggesting a possible explanation for the recent results of Reux et al in JET (2015 Nucl. Fusion 55 093013)