# If y = A*x where x is exogenous and not shocked in the Policy run, how can y have a nonzero value in the deviation results?

Here we are considering a dynamic model solved via RunDynam/RunMONASH etc. Suppose that the variable x is exogenous in the Policy run and is not shocked in the Policy shocks. Suppose also that your model contains a linear equation of the form y = A*x. How can y have a nonzero value in the deviation results? That is, how can the Policy result for y be different from the Rerun (or Base) result for y?

First you need to realise the circumstances in which the Policy result for x can be nonzero. If x is also exogenous in one period (year) of the Base case and not shocked there, then the Policy result for x will also be zero in that period. But if x is endogenous in that period, the Policy result for x in that period will be the same as the endogenous value in the Base as explained elsewhere.

So now suppose that x is endogenous in one period of the Base. Then, from the equation y = A*x, we expect the result for y to be nonzero in that period of the Policy. But the value for x in that period of the Rerun (or of the Base if you don't do the Rerun) will be the same as in that period of the Policy. So you would expect the equation y=A*x to give the same result for y in the Rerun and in the Policy. Hence you would expect the deviation result (the difference between the Policy and the Rerun results) to be zero.

That will be the case if the Coefficient A is a paremeter - that is, if the value of A stays constant in any simulation.

But if A is not a parameter, the result for y in the Policy may be different from the Rerun result, as we explain below.

To see how, consider a 2-step Euler calculation for the first period in which Policy shocks are applied. Suppose that the value of A is equal to A0 at the start of the first period in the Policy. Then it will have the same value A1 at the start of that period in the Rerun. So, on the first Euler step, the y result will equal A0*(x/2) since, in the first Euler step of a 2-step, the shock to x is half of the total shock.

What about the second step? Suppose that the shock to x in this step is x2 (which will be a little less than x/2 if x is a percent change variable); of course the same shock will be given to x in the second step of the Rerun as in that step of the Policy. Now the value of A at the start of the second step will change in accordance with the shocks. But the Policy shocks are different from those in the Rerun so that the value A1P of A after the first Euler step in the Policy may be different from the value A1R of A after the first Euler step in the Rerun. The result for y in the second step of the Policy is y=A1P*x2 whereas the result for y in the second step of the Rerun is y=A1R*x2. Since A1P and A1R may be different, the second step results for y may bbe different. Hence the whole 2-step result for y (obtained by compounding the results from the first and second steps) in the Policy may be different from the 2-step result in the Rerun. Hence the deviation result for y may be nonzero.

The key to the puzzle is that, in any period, the values of A may be different in the Policy from the Rerun.

Above we discussed the first period in which Policy shocks were applied. The value of A at the start of that period is the same in the Policy as in the Rerun. But in later periods, the value of A at the start of the Policy may already be different from at the start of the same period of the Rerun. That is because of the effects of the Policy shocks which have been applied in previous periods. Accordingly, the Policy and Rerun results for y may me even more different in those periods.

Example. Consider the case where A is equal to say the total value of employment. Suppose that the Policy is one which increases employment gradually over the years of the simulation. Then, if the endogenous values of x (from the Base) are all positive, you would expect the deviation results for y to become increasingly greater across the periods. That is because the A values will be higher in any year of the Policy that in the corresponding year of the Rerun. Hence, even though the x values are the same in the Policy and Rerun, the y=A*x values will be greater in the Policy than in the Rerun because of the larger A values in the Policy.

Supplementary Question. Why can't I see the truth when I load the results into AnalyseGE?

Even if you load the results for one year (say the first year in which the Policy shocks are applied) into AnalyseGE, you are hard pressed to see the truth. The explanation above depends on changing values of a Coefficient A, indeed of the changes in A during one simulation, or across the whole of the Policy run. But AnalyseGE only shows you the value of A at one time, usually at the start of the relevant simulation (though it can show post-simulation values which may help understanding puzzles like the one described here). While AnalyseGE can help with some result understanding, subtle differences may not show up there.

Go back to
GEMPACK FAQ Page