Forecasting with log-linear (S)VAR models: Incorporating annual growth rate conditions

This note explores conditional forecasting under conditions on annual growth rates, where variables enter a (possibly structural) vector autoregressive (VAR) model in logarithms or logarithmic first differences. For example, imposing conditions on the annual growth rate of quarterly real GDP modeled in logarithms is challenging be- cause annual growth rates are nonlinear functions of the log variables. We address this by approximating the annual growth rate with a linear function of the model variables, enabling the use of standard conditional forecasting methods. An approximation error arises since the condition is not imposed directly; to mitigate this, we iteratively adjust the condition until the error is acceptable. We provide MATLAB companion code that also accepts other types of conditions: (1) conditions on the path of variables entering the VAR, (2) conditions on the path of structural shocks, and (3) conditions on sums of successive variable observations.