International Finance – Assignment 2, Spring 2018
Richard Walker, Northwestern University
To be returned on Monday May28th 30th in class.
There are 65 points available. Write your answers in the spaces provided.
Consider the framework of exchange rate determination from class, augmented in the following way. Instead of being exogenous, investmentIis decreasing in the domestic interest rateR. So,I=I[R], with a rise inR implying a fall inI. We will assume that investment depends on the nominal interest rate, rather than the real interest rate, purely for simplicity.
Our LRGME and LRMME equations are thus:
Y=C[YT] +I[Rf] +G+NX
Y,Yf, EPf P
The LRMME equation is unchanged from class. The world interest rateRfnow appears on the right-hand side of the LRGME equation, though; in the long run, with the domestic exchange rateEconstant and expected to remain so, the domestic interest rateRmust be equal toRffor uncovered-interest parity to hold. We will assume there are no risk premia associated with exchange rates, so that UIP will hold in its pure form.
The SRGME and SRMME equations may be written:
Y+(PPe) =C[YT] +I
The SRMME equation is unchanged from class. The SRGME equation now reflects the dependence of investment upon the domestic interest rate, as well as the fact that uncovered interest parity must hold.
Given thatRfis exogenous, there will still be only one single value ofNX, and thus a single value of the real exchange rateEPPf, that solves our LRGME equation. As a result our LRGME/LRMME diagram will resemble that from class:
P 1 =Pe
E 1 =ET=Ee
The domestic central bank is pursuing an exchange rate targetET. This fixed-exchange-rate regime is initially successful and credible, so that the initial long-run equilibrium is at point 1 withE 1 =ET=EeandP 1 =Pe. The position of the SRMME line reflects the fact that, at least initially, forex markets expect the peg to persist.
(i) Redraw the diagram above to include the SRGME line, incorporating the initial expectation that the exchange rate will continue to be equal toET=Ee. Explain the lines position and slope. Will the SRGME line be steeper or flatter than the LRGME line if investment is very sensitive to the interest rate? Assume hereafter that investmentisvery sensitive to the interest rate.(5 marks)
(ii) Now the foreign interest rate unexpectedly rises, fromRf^1 toR^2 f. The domestic government, anticipating a
painful peg defence, raises government spending fromG^1 toG^2 to cushion the blow. Show on a new diagram (below) what (if anything) happens to the LRGME and LRMME lines. Denote their intersection as point 2, and the nominal exchange rate associated with this intersection asE 2. [Note: you should assume that the rise in government spending is smaller in absolute terms than the fall in investment that would result from a rise in the interest rate fromR^1 ftoR^2 f. That is:I[R^1 f]I[R^2 f]> G^2 G^1 .](5 marks)
(iii) Following the changes inRfandGforex traders maintain their confidence in the peg, andEeremains equal toE 1 =ET. Show on a new diagram below what happens to the SRMME and SRGME lines, thinking particularly carefully about the position of the SRGME line. Note that you may treatPeas fixed atP 1 , as wage contracts have yet to be rewritten. You must explain your answer; dont just draw the new lines but justify their positions.Update: for future reference [see footnote to part(vii)] call the intersection of the new SRMME and SRGME lines point Q.(10 marks)
[Hint: the SRMME line must as usual cut the LRMME line at the expected exchange rate. As for the SRGME line: what (roughly) mustEbe to satisfy our SRGME equation ifP=Pe? That is, in what range will the new SRGME line cross the old LRMME line? The reason this is a useful exercise is that by fixing P=Pewe are fixing the left-hand-side of the SRGME equation, atY=Y; so, we then just need to find (roughly) theEsuch that the sum of the right-hand-side variables is also unchanged from the initial level, following the change in fiscal policy. Once youve figured that out, ask a similar question in the vertical plane: in what range mustPbe to satisfy our SRGME equation ifE=Ee=E 1 =ET?]
(iv) Continue to assume thatPeis fixed and thatEeremains atE 1 =ET. The central bank acts to maintain the peg, i.e. keepEequal toET, by changing the money supply in an appropriate manner. Show the resulting shift in the LRMME and SRMME curves, and indicate the new short-run equilibrium point (call this point 3). What has happened toI,NXandY, compared to their levels before the changes inRfandG? Explain your answers. [Note: you might want to draw this on a new diagram below; just make sure the points are clearly labelled.](12 marks)
(v) How does the effect on outputYof the peg defence in part (iv) depend on the sensitivity of net exports to the real exchange rate, on the sensitivity of investment to the interest rate, and on the marginal propensity to consume? Also, did the increase in government spending make the peg defence less painful or not?( marks)
(vi) The central bank abandons the current peg, and decides to adopt a new nominal exchange rate ofE 2 (note thatE 2 was defined in part (ii) above). The central bank changes the money supply so that the LRMME intersects the current LRGME atE 2 (i.e. it reverses the peg defence). Suppose the new peg is credible, so that forex traders change expectations and nowEe=E 2. Assume thatPeis still fixed at the original level. What happens to the SRMME and SRGME lines, and where is the new short-run equilibrium? [Draw this on a diagram below, and label the new short-run equilibrium point 4.](9 marks)
(vii) There are no further changes in policy or in exchange-rate expectationsEe. Eventually (following gradual renegotiation of nominal wage contracts) the economy settles down into a long-run equilibrium involving the new target exchange rateE 2. Indicate the equilibrium path on a new diagram below (i.e. another SRGME/SRMME/LRGME/LRMME picture). Then draw separate timepaths (like I have done in class) for the variablesY,NX, andR(Im looking for three separate pictures with timeton the horizontal axis). Note that these latter three timepaths should show the evolution of the three variables from the very first shock, the changes toRfandGin part (ii). [To be clear on the timing of events here:westartatpoint 1 inthe initialequilibrium;thentheshockstoRfandGhitandthebank(simultaneously)defendsthepeg,sowe jumptopoint 3 (i.e.theeconomyneveractuallygoestopoint2);afteraspellatpoint2)thecentralbank abandonsthepegandwegotopoint4;andfinallytheeconomygraduallyevolvestowardsthefinallong-run equilibrium.]Thats not clear at all. Ill try again. We start at point 1 in the initial equilibrium; then the shocks toRfandGhit and the bank simultaneously defends the peg, so we jump to point 3^1 ; after a spell at point 3 the central bank abandons the peg and we go to point 4; and finally the economy gradually evolves towards the final long-run equilibrium.(12 marks)
(^1) So the economy never actually goes to point Q, defined in the update to part (iii).