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.

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.

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

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.

A Note on Optimal Smoothing for Time Varying Coefficient Problems

An algorithm is presented which provides a complete solution to the optimal estimation problem for time-varying parameters when no proper prior distribution is specified. The key ideas involve a combination of the information-form Kalman filter with the two-filter interpretation of the optimal smoother. The algorithm produces efficient estimates of the parameter trajectories over the entire sample, arid is equally applicable when a proper prior distribution has been specified.

The Farm, the City and the Emergence of Social Security

In this paper we study the social, demographic and economic origins of social security. The data for the U.S. and for a cross section of countries make it clear that urbanization and industrialization are strongly associated with the rise of social insurance. We describe a model economy in which demographics, technology, and social security are linked together. We study an economy with two locations (sectors), the farm (agricultural) and the city (industrial). The decision to migrate from rural to urban locations is endogenous and linked to productivity differences between the two locations and survival probabilities. Furthermore, the level of social security is determined by majority voting. We show that a calibrated version of this economy is consistent with the historical transformation in the United States. Initially a majority of voters live on the farm and do not want to implement social security. Once a majority of the voters move to the city, the median voter prefers a positive social security tax. In the model social security emerges and is sustained over time as a political and economic equilibrium. Modeling the political economy of social security within a model of structural change leads to a rich economic environment in which the median voter is identified by both age and location

The Farm, the City, and the Emergence of Social Security

In this paper we study the social, demographic and economic origins of social security. The data for the U.S. and for a cross section of countries make it clear that urbanization and industrialization are strongly associated with the rise of social insurance. We describe a model economy in which demographics, technology, and social security are linked together. We study an economy with two locations (sectors), the farm (agricultural) and the city (industrial). The decision to migrate from rural to urban locations is endogenous and linked to productivity differences between the two locations and survival probabilities. Furthermore, the level of social security is determined by majority voting. We show that a calibrated version of this economy is consistent with the historical transformation in the United States. Initially a majority of voters live on the farm and do not want to implement social security. Once a majority of the voters move to the city, the median voter prefers a positive social security tax. In the model social security emerges and is sustained over time as a political and economic equilibrium. Modeling the political economy of social security within a model of structural change leads to a rich economic environment in which the median voter is identified by both age and location.social security, political economy, structural change, migration