Empirical Estimation and the Quarterly Projection Model: An Example Focusing on the External Sector

In this paper, we offer one possible way to estimate a key feature of the Bank of Canada’s main macroeconomic model, the Quarterly Projection Model or QPM. The key feature which is the focus of this study is the so-called "short-run equilibrium values" or SREQs which link the dynamic portion of QPM to its steady state. Our estimation is motivated by an unsatisfying feature of the current version of the SREQs. That is, they are produced using a mechanical filter which does not capture the influence of movements in other variables on the filtered time series. In other words, the current SREQs are exogenous. The estimation approach detailed in this paper attempts to make the SREQs endogenous with respect to fluctuations in key economic variables. The first part of this paper demonstrates how we are able to rewrite the external sector of QPM in a form that allows empirical estimation based on cointegration analysis. The second part of the paper then considers the implications for QPM of estimated, endogenous SREQs via both impulse response functions and stochastic simulations. In this latter part of the paper, we also present what we believe are novel approaches for estimating stochastic shocks for calibrated macroeconomic models.