fiscal, fiscal-policyWhy is cutting spending in a recession considered pro-cyclical: the answer seems obvious, but what is the mathematical basis behind this reasoning?
For example, if we simply modelled the economy as a having inertia, and a governments fiscal balance as one of the forces acting on it, then spending (a restorative force) during the downside of a business cycle would be pro-cyclical.
So what are the standard quantitative explanations behind the simple answer?
I’m not shure that I really understand the question, but I try my best.
Using standard notation, you have $Y = C + I + G + Ex$. Then differences can be seen as $dY = dC + dI + dG + dEx$. Let’s assume worsening terms of trade, leading to $dEx <0$. If all other components stay equal ($dC = dI = dG = 0$), you have $dY < 0$. If the terms of trade would be in equilibrium again after the initial worsening, the economy would return to equilibrium as well, with $dY = 0$. If, on the other hand, government would cut spending as reaction to the recession, you would have $dG < 0 \rightarrow dY < 0$, which would prolong the recession. Now, if you had a government policy that would cut spending every time you have a recession, you see that its reaction would be to cut spending in every period, until a different shock to Consumption, Investment or net Export would equalize its cuts.
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