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 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,
(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 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,
