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  1. In the attached picture below, shocks associated with GDP are demand shocks and shocks associated with inflation are supply shocks.

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  1. Here, shocks associated with GDP are rather supply shocks, and shocks associated with unemployment are demand shocks.

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  1. Here, demand shocks are IS and LM shocks. enter image description here

Where we call GDP aggregate demand or aggregate supply in the model is our choice? In my mind, I will call shocks to GDP as aggregate supply shocks, and shocks to inflation as aggregate demand shocks. Is that wrong?

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You don't provide much information. Here is what I see here.

The theoretical background for the first case is the AS-AD model. The exact specification seems to be an A-type VAR. A positive aggregate demand shock has a positive effect on both $\Delta y$ ($\Rightarrow a_{11} >0$) and $\pi$ ($\Rightarrow a_{21} >0$).

A positive supply shock has a positive effect on $\Delta y$($\Rightarrow a_{12} >0$) and a negative effect on $\pi$($\Rightarrow a_{22} < 0$).

The second case is a type-B model with no intercept and no lags. That is a static SEM in the shocks. The inverse from the formula is:

$\frac{1}{a} \begin{bmatrix} 1 & a \\ 0 & 1 \end{bmatrix}$

Thus the effect of a positive AS-shock on $\Delta gdp$ is $\frac{1}{a}$ and o $ur$ ist 0. The effect of a positive AD-shock on $\Delta gdp$ is 1 and on $ur$ is $\frac{1}{a}$.

The theoretical motivation for the third model is the IS-LM. The IS-LM equilibrium is about demand equalling production. There are no supply shocks here. The shocks are shifters of the IS and LM curve respectively.

As you see the terms AS-shock and AD-shocks have a clear context dependent meaning.

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How you call your shocks should not be based alone on which variable they hit, but also how, exactly, they hit it. What matters here is the structure of the impact matrix, such as in your example 2. I assume it shows the long-run impact (although I cannot be sure). On a higher levels, how to interpret the shocks also depends on the angle of analysis.

If it shows the long-run impact, the model assumes no permanent impact of the second shock on GDP, whereas there is a permanent impact from the first shock. So, how do we interpret the shocks and call them? It comes from economic theory. What determines long-term GDP growth? Theory suggests it is exclusively determined by the supply side (the impact of the other shock 2 is zero), hence we could call it supply shock.

How to call the second shock is more tricky and open to interpretation. Calling it demand shock is a little loose, in my view. But as the label "supply shock" is already taken, and demand shocks are another key driver of economic dynamics, it makes sense (sort of) to give it the label "demand" shock.

Note that, if the analysis focuses on the drivers of GDP growth, the shocks could as easily be labelled "permanent" and "transitory".

Finally, imposing the structure of the impact matrices and labelling shocks in a suggestive way based on conventional theory makes it that much harder to advance the theory from data analysis. If your empirical model gives dubious results, it's much easier to conclude that there is a paradox, rather than that the theory might be wrong. Indeed, linking back to supply vs demand, there are analyses that suggest demand shocks may have a permanent impact on long-term growth, in which case the labelling in your examples might turn out to be misinformed.

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