《国际经济学辅助资料》（英文版） proof

a sketch of a proof for why fiscal policy does not work under flexible exchange rates (by special request from Messrs. Eubank and Heidlage) The easiest way to show that fiscal policy does not work under flexible exchange rates was the one we covered in class on Monday! There is a different way, but it is more difficult. Essentially, it is a proof by contradiction. I illustrate how the proof is constructed below. Note that the long-run solution of the model is not going to be affected at all by any of this. An increase in government spending from 20 to 21 will still have the exact same long-run implications we discussed in class. In particular, Y must be 97.5, e must be 1. 15 i must be 4%. and P must be 1 Suppose that (as in the IslM diagram above)the increase in government spending(g) does succee in raising the economy's output above 97.5 in the short run. the interest rate is also up and higher than the foreign interest rate of 4% Exactly what happens to the nominal exchange rate? There are 2 things that can happen. First, it might appreciate somewhat from the original level of 1.25 but not all the way to 1. 15. For the sake of argument, let's say that in the short run e appreciates to 1. 20. Second, perhaps e overshoots in the short run(as suggested by Ben Heidlage). For the sake of argument, let 's say that e goes all the way to 1. 10 in the short run. In both cases, however, e must ultimately go to 1. 15 in the long run. Lets discuss each of the 2 cases separately Case e e= 1.20 OK, in the short run this economy is producing more than 97.5, the interest rate is up, and the exchange rate has appreciated from 1.25 to 1. 20. In the adjustment to the long run, the interest rate will be falling back toward the world interest rate(4%)and the exchange rate will be appreciating further toward 1.15 But wait, something is wrong here! Why would anybody hold the foreign currency during the adjustment toward the long run?? The domestic currency is paying a higher interest rate(more than 4%). It is also expected to appreciate, so that will make domestic currency deposits an even sweeter deal. In essence, we are in violation of UIP here. In reality, what is likely to happen is that the Electronic Herd will dump the foreign currency and start buying the domestic currency This will cause the exchange rate to appreciate and the domestic interest rate to fall. The Electronic Herd will

A sketch of a proof for why fiscal policy does not work under flexible exchange rates (by special request from Messrs. Eubank and Heidlage) The easiest way to show that fiscal policy does not work under flexible exchange rates was the one we covered in class on Monday! There is a different way, but it is more difficult. Essentially, it is a proof by contradiction. I illustrate how the proof is constructed below. Note that the long-run solution of the model is not going to be affected at all by any of this. An increase in government spending from 20 to 21 will still have the exact same long-run implications we discussed in class. In particular, Y must be 97.5, e must be 1.15, i must be 4%, and P must be 1. Suppose that (as in the ISLM diagram above) the increase in government spending (G) does succeed in raising the economy’s output above 97.5 in the short run. The interest rate is also up and higher than the foreign interest rate of 4%. Exactly what happens to the nominal exchange rate? There are 2 things that can happen. First, it might appreciate somewhat from the original level of 1.25 but not all the way to 1.15. For the sake of argument, let’s say that in the short run e appreciates to 1.20. Second, perhaps e overshoots in the short run (as suggested by Ben Heidlage). For the sake of argument, let’s say that e goes all the way to 1.10 in the short run. In both cases, however, e must ultimately go to 1.15 in the long run. Let’s discuss each of the 2 cases separately: Case I: e = 1.20 OK, in the short run this economy is producing more than 97.5, the interest rate is up, and the exchange rate has appreciated from 1.25 to 1.20. In the adjustment to the long run, the interest rate will be falling back toward the world interest rate (4%) and the exchange rate will be appreciating further toward 1.15. But wait, something is wrong here!! Why would anybody hold the foreign currency during the adjustment toward the long run?? The domestic currency is paying a higher interest rate (more than 4%). It is also expected to appreciate, so that will make domestic currency deposits an even sweeter deal. In essence, we are in violation of UIP here. In reality, what is likely to happen is that the Electronic Herd will dump the foreign currency and start buying the domestic currency. This will cause the exchange rate to appreciate and the domestic interest rate to fall. The Electronic Herd will

not relent until the exchange rate appreciates all the way to 1. 15 and the interest rate falls back to 4% Only then, the Electronic Herd will become indifferent between holding domestic deposits and foreign deposits. Because, capital moves in and out very fast, this adjustment is going to happen almost instantaneously. So the short-run equilibrium really involves e going to 1. 15 right away, i staying at 4%, and the output level not budging from 97.5 Case ll:e= l10 OK, here in the short run this economy is producing more than 97.5, the interest rate is up, and the exchange rate has appreciated from 1.25 to 1. 10. In the adjustment to the long run, the interest rate will be falling back toward the world interest rate(4%)and the exchange rate will be depreciating back toward 1.15 But wait, something is wrong here! If the interest rate is expected to be falling over the adjustment that means investment I will be going up. And if the nominal exchange rate is expected to depreciate from 1.10 to 1.15, while the price level P is stuck at I all throughout, then the real exchange rate R will also be depreciating. So then this economy will start exporting more and importing less. OK,so during the adjustment investment will be increasing and net exports will also be increasing. So then the output level should be increasing as well. Instead of falling back toward 97. 5, it will be going higher and further away from 97.5. Instead of converging back to "full employment"and"potential GDO, this economy will diverge and end up even further away from its normal level of output. But that is a contradiction To conclude, the only short-run solution that does not create any internal contradictions in the model is for the output level and the interest rate to remain fixed, and for the nominal exchange rate to immediately appreciate to its long-run equilibrium level

not relent until the exchange rate appreciates all the way to 1.15 and the interest rate falls back to 4%. Only then, the Electronic Herd will become indifferent between holding domestic deposits and foreign deposits. Because, capital moves in and out very fast, this adjustment is going to happen almost instantaneously. So the short-run equilibrium really involves e going to 1.15 right away, i staying at 4%, and the output level not budging from 97.5 Case II: e = 1.10 OK, here in the short run this economy is producing more than 97.5, the interest rate is up, and the exchange rate has appreciated from 1.25 to 1.10. In the adjustment to the long run, the interest rate will be falling back toward the world interest rate (4%) and the exchange rate will be depreciating back toward 1.15. But wait, something is wrong here!! If the interest rate is expected to be falling over the adjustment, that means investment I will be going up. And if the nominal exchange rate is expected to depreciate from 1.10 to 1.15, while the price level P is stuck at 1 all throughout, then the real exchange rate R will also be depreciating. So then this economy will start exporting more and importing less. OK, so during the adjustment investment will be increasing and net exports will also be increasing. So then the output level should be increasing as well. Instead of falling back toward 97.5, it will be going higher and further away from 97.5. Instead of converging back to “full employment” and “potential GDO,” this economy will diverge and end up even further away from its normal level of output. But that is a contradiction! To conclude, the only short-run solution that does not create any internal contradictions in the model is for the output level and the interest rate to remain fixed, and for the nominal exchange rate to immediately appreciate to its long-run equilibrium level