The Covariance Matrices of Reduced-Form Coefficients and of Forecasts for a Structural Econometric Model

A Note on Dynamic Simulation Forecasts and Stochastic Forecast-Period Exogenous Variables

“…We note that the asymptotic covariance matrix of 9A iS y~~~~~~ (9) 12 + (IoZ,)-T(10Z1)'; T see Goldberger, Nagar and Odeh [2]. Here (1/ T)f is the asymptotic covariance matrix of P(lt), where P(Jt) is the vector formed by "stacking" the columns of 4t.…”

“…The asymptotic covariance matrix of these forecasts has been derived by Goldberger, Nagar, and Odeh [2].…”

Preliminary Data Errors and Their Impact on the Forecast Error of Simultaneous-Equations Models

“…Models (1) and (2) bances, the two components of the forecast error are independent. Therefore, the asymptotic covariance matrix of the vector of forecast errors is simply the sum of the covariance matrices of the two components and can be written as where F = I, C3 z;', g = m + n being the number of observable variables, and T-';R. is the rg2 x rg2 asymptotic covariance matrix of restricted reduced-form coefficients, computed using the methods of Dhrymes (1973) or Goldberger, Nagar, and Odeh (1961). [Note that, in the framework of (3) and (9, the distinction between current endogenous and exogenous variables and between ex-ante and ex-post forecasting is no more meaningful.…”

The Error of Forecast in Econometric Models when the Forecast-Period Exogenous Variables are Stochastic

“…Goldberger et al [4] have shown how the matrices of approximate covariances between every pair of reduced form coefficients can be calculated from the structural equation covariance matrices by using the usual approximation for the covariance between two nonlinear functions of several random variables. The authors then use these covariance matrices to define forecast standard errors on the assumption that the XiF'S are known constants.…”