would then be the residual from that equation We can then regress on and to get

Would then be the residual from that equation we can

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would then be the residual from that equation. We can then regress 𝑒 𝑚,? on 𝑢 𝑑,? and 𝑢 ?,? to get 𝜑 𝑚𝑑 and 𝜑 𝑚? , while 𝑢 𝑚,? would be the residual from that equation. b. Consider first monetary policy and the monetary shock. Following the lectures, we might assume that that because of information lags, the central bank cannot respond immediately to developments in output and inflation. In that case, we would have: 𝜑 𝑚𝑑 = 𝜑 𝑚? = 0 . Alternatively, we might assume that it takes time for monetary policy shocks to have an impact on output and inflation. In that case we would have: 𝜑 𝑦𝑚 = 𝜑 𝜋𝑚 = 0 (i.e. as above). What about the third assumption? We need this to disentangle demand and supply shocks and their influences. One option would be to assume that demand shocks have no contemporaneous effect on inflation (i.e. aggregate supply is completely elastic in the short run); that would correspond to 𝜑 𝜋𝑑 = 0 . Note that all these assumptions become less plausible, the longer the time period; they are more defensible for e.g. monthly data than they are for annual data. c. If we accept the Classical dichotomy holds in the long run, it is tempting to assume instead that both monetary policy and demand shocks have no long-run effect on output. Such assumptions would allow us to dispense with assumptions about their short-run impact. (VARs with long-run restrictions were first
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