Are Errors in Official U.S. Budget Receipts Forecasts Just Noise?

Existing evidence suggests that U.S. Government budget receipts forecasts are unbiased and efficient. Our study is an attempt to examine the veracity of these findings. The time series framework employed in this study is distinguished from previous work in three ways. First, we build a model that explicitly admits serial correlation in the residuals by allowing for autoregressive, moving-average, serial correlation. Second, we employ the nonparametric Monte-Carlo bootstrap to free ourselves from reliance on asymptotic distribution theory which is suspect given the short data series available for this study. Third, we control for errors in the macroeconomic and financial assumptions used to produce the U.S. Government's budget forecasts. We find that the U.S. Government's annual, one-year ahead, budget receipts forecasts for fiscal years 1963 through 2003 are biased and inefficient. In addition, we find that these forecasts exhibit serial correlation in their errors and thus do not efficiently exploit all available information. Finally, we find evidence that is consistent with strategic bias that may reflect the political goals of the Administration in power. Working Paper 07-2

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.

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.

Interequation Constraint and the Specification of Dynamic Structure

This note considers the effect of a class of linear inter-equation constraints in the specification of the lag structure in econometric models. In particular, attention is focused on the linear summing, or "adding up�, constraints which arise between equations in factor shares analysis. The consequences of such constraints on the specification of lag structures for models with dynamic adjustments and autoregressive or moving-average disturbances are presented in the form of linear restrictions which result in singular coefficient matrices . Thus, the structural (lag) specification of one equation depends on the structure of all other equations in the model.

FIML Estimation of Rational Distributed Lag Structural Form Models

The Rational Distributed Lag Structural Form (RSF) representation of an econometric model is introduced and its relationship to several standard forms of representation is discussed. The FIML estimation problem for the RSF is then considered and formulated as a nonlinear, unconstrained optimization problem. A solution to the relation optimization problem is then obtained by an application of the Davidon-Fletcher-Powell variable metric method using simple first difference approximations for the necessary gradients. This approach requires a minimum of effort on the part of the model builder since there is no longer any need to analytically determine, and then program, the gradient expressions. The feasibility of the method is demonstrated with several examples.

Rational Distributed Lag Structural Form--A General Econometric Model

The Rational Distributed Lag Structural Form of an econometric model is introduced, and its relationship to several traditional forms of representation is discussed. The traditional forms are viewed as special cases of the Rational Structural Form. Thus, the latter provides a unified framework for any treatment of the linear, time invariant modeling problem. In particular, a solution of the estimation problem for the Rational Structural Form leads to the solution of the estimation problem for all traditional forms.