Comparison of Robust and Varying Parameter Estimates of a Macroeconometric Model

Four estimators of econometric models are compared for predictive accuracy. Two estimators assume that the parameters of the equations are subject to variation over time. The first of these, the adaptive regression technique (ADR), assumes that the intercept varies overtime, while the other, a varying-parameter regression technique (VPR), assumes that all parameters may be subject to variation. The other two estimators are ordinary least squares (OLS) and a robust estimator that gives less weight to large residuals. The vehicle for these experiments is the econometric model developed by Ray Fair. The main conclusion is that varying parameter techniques appear promising for the estimation of econometric models. They are clearly superior in the present context for short term forecasts. Of the two varying parameter techniques considered, ADR is superior over longer prediction intervals.

Executive Compensation: Facts

In this paper we describe the important features of executive compensation in the US from 1993 to 2006. Some confirm what has been found for earlier periods and some are novel. Notable facts are that: the compensation distribution is highly skewed; each year, a sizeable fraction of chief executives lose money; the use of security grants has increased over time; the income accruing to CEOs from the sale of stock increased; regardless of the measure we adopt, compensation responds strongly to innovations in shareholder wealth; measured as dollar changes in compensation, incentives have strengthened over time, measured as percentage changes in wealth, they have not changed in any appreciable way.CEO, Pay–Performance Sensitivity, Stock, Options

Executive Compensation: Facts

In this paper we describe the important features of executive compensation in the US from 1993 to 2006. Some confirm what has been found for earlier periods and some are novel. Notable facts are that: the compensation distribution is highly skewed; each year, a sizeable fraction of chief executives lose money; the use of security grants has increased over time; the income accruing to CEOs from the sale of stock increased; regardless of the measure we adopt, compensation responds strongly to innovations in shareholder wealth; measured as dollar changes in compensation, incentives have strengthened over time, measured as percentage changes in wealth, they have not changed in any appreciable way.CEO, Pay–Performance Sensitivity, Stock, Options

Identification Theory for Time Varying Models

The identification of time-varying coefficient regression models is investigated using an analysis of the classical information matrix. The variable coefficients are characterized by autoregressive stochastic processes, allowing the entire model to be case in state space form. Thus the unknown stochastic specification parameters and priors can be interpreted in terms of the coefficient matrices and initial state vector. Concentration of the likelihood function on these quantities allows the identification of each to be considered separately. Suitable restriction of the form of the state space model, coupled with the concept of controllability, lead to sufficient conditions for the identification of the coefficient transition parameters. Partial identification of the variance-covariance matrix for the random disturbances on the coefficients is established in a like manner. Introducing the additional concept of observability then provides for necessary and sufficient conditions for identification of the unknown priors. The results so obtained are completely analogous to those already established in the econometric literature, namely, that the coefficients of the reduced form are always identified subject to the absence of multicollinearity. Some consistency results are also presented which derive from the above approach.

On the Identification of Time Varying Structures

The identifiability of reduced form econometric models with variable coefficients is investigated using the control theoretic concepts of uniform complete observability and uniform complete controllability. First, a variant of the state space representation of the traditional reduced form is introduced which transcribes the underlying non-stationary estimation problem into one particularly suited to a Kalman filtering solution. Using such a formulation, observability and controllability can be called upon to obtain a necessary and sufficient condition for identification of the specific parameterization. The results so obtained are completely analogous to those already established in the econometric literature, namely, that the parameters of the reduced form are always identified subject to the absence of multicollinearity(referred to as "persistent excitation" in the control literature). How-ever, now the multicollinearity condition is seen to depend on the structure of the parameter variations as well as the statistical nature of the explanatory variables. The verification of identifiability thus reduces to a check for uniform complete observability which can always be affected in econometric applications. Some consistency results are also presented which derive from the above approach.

Varying-Parameter Supply Functions and the Sources of Economic Distress in American Agriculture, 1866-1914

The agrarian unrest in the United States at the end of the nineteenth century is examined. This unrest is often viewed as stemming from the inability of farmers to adapt to changing conditions in world agriculture. This hypothesis is tested in the context of a distributed lag supply function. Varying parameter estimation methods are used to trace the history of the parameters in the supply function and to decompose observed prices into permanent and transitory components over time. The patterns of variation are tested for conformity with a model of rational price-expectation formation. The conclusion is that farmers behaved as economic theory would predict, but that neither theory nor practice gave them relief from the troubles which plagued them.

Aggregate Consequences of Limited Contract Enforceability

We study a general equilibrium model in which entrepreneurs finance investment with optimal financial contracts. Because of enforceability problems, contracts are constrained efficient. We show that limited enforceability amplifies the impact of technological innovations on aggregate output. More generally, we show that lower enforceability of contracts will be associated with greater aggregate volatility. A key assumption for this result is that defaulting entrepreneurs are not excluded from the market.

Unanticipated Money

The role of unanticipated changes in money growth for aggregate fluctuations is reexamined using the methods of quantitative equilibrium business cycle theory. A stochastic growth model with money is constructed that has the feature, following Lucas (1972, 1975), that production and trade take place in spatially separated markets (islands). Individuals must infer changes in the aggregate price level from observing local relative prices. This causes individuals to react to changes in the average price level, due to unanticipated changes in the aggregate money supply, as though they were changes in market specific relative prices. We show that this mechanism can lead to quantitatively large fluctuations in real economic activity. The statistical properties of these fluctuations, however, are quite different from the properties of fluctuations observed in the U.S. economy.Business Cycles, Monetary Policy, Aggregate Fluctuations, Real Business Cycles