Suppose instead that the model has a consistent one period lag, so Y(t)=R(X(t-1)). And suppose that Statistics Canada reports all data on X immediately. Now we can use the model for genuine forecasting of the future. Statistics Canada tells us what X is today, and we use the model to tell us what Y will be one period in the future. But the model can tell us nothing about what Y will be two periods in the future, because Statistics Canada can't tell us what X will be one period in the future. And yet I keep hearing about model-based forecasts for one, two, three, four, etc., periods in the future.Steve Malpezzi, Walter Barnes and I wrote a paper some years ago that tried to come to grips with this very issue. The context was office market forecasts, and we worked on developing confidence intervals for estimates of future office demand for a number of metropolitan areas. In developing the confidence interval, we used a technique from a 1971 Martin Feldstein Econometrica paper that takes into account the fact that to forecast Ys, one needs to forecast Xs as well.

To make a long story short, after a couple of quarters, the confidence intervals blow up (I don't have the paper at home, but when I go in to the office this week I will scan some pictures from it), meaning that after a few quarters, metropolitan office demand could be just about anything. Local office markets are much less complicated than an entire national economy.