Exchange Rate Theories1

Exchange Rate Theories All pages references below refer to Hallwood and MacDonald, International Money and Finance (Blackwell Publishing, ISBN 0631204628) unless otherwise stated. The main exchange rate models or approaches are: • Keynesian o Elasticities (balance of trade on goods and services) o Absorption • Modern Asset View o Flexible Price Monetary Model (FLMA) (PPP holds) o Sticky Price Monetary Model (SPMA) (Overshooting) o Currency Substitution o Portfolio Balance (not a “monetary” model)

Pages

Traditional Flow View Keynesian Elasticities Absorptio n 24 52-56, 156-9

Model Author(s)

Hicks

Modern Asset View Monetary FLMA SPMA 179 9.7 p 181 Frenkel, Mussa, Bilson

188

Currency Sub 193-8

Dornbusch, McKinno Frankel n

Portfolio Balance 226, ST 115 p. 230 W = M+B+SF Branson, McKinnon, etc

Relevance LDCs PPP Yes No No - SR, Yes – LR holds? Note: ST is Sarno and Taylor “Economics of Exchange Rates” (http://www.cambridge.org/uk/catalogue/catalogue.asp?isbn=0521485843) Keynesian models Elasticities Approach (or Balance of Payments Approach), page 24. “The exchange rate is determined by the flow of currency through the foreign exchange market.” This approach focuses on the current capital and NOT the capital account. It is more relevant in describing developing economies since they attract relatively little international capital flows. Model (p. 157) B=X–M B = current account balance (flow) X = exports, M = imports Some basic equations

eP * P DC e FC Y C  I G X M A  C  I G NX  X  M



 Foreign demand (for X): X  M  M   , Y        Domestic demand (for M): M  M   , Y    * Trade balance (TB) NX  M   , Y    M   , Y  *

*





*

The first term represents the value of exports and the second term represetns the value of imports (in domestic currency). eP * M Recall:  M  P * Hence, NX  NX   , Y , Y  NX NX NX  0;  0; ?0 * Y Y  Note: TB can deteriorate if ρ increases (though it’s counter-intuitive). Define:

M *   0  M * M   0 Price elasticity of domestic demand for M:     M Price elasticity of foreign demand for X:

* 

Differentiating the TB with respect to ρ:   NX M * M M*  M   M  *    1  M   *    1    M   Marshall-Lerner Condition NX 0 if α*+α-1>0, or α*+a>1 (sum of elasticities is >1)     * If Marshall-Lerner holds, then NX  NX   , Y , Y    Goods market equilibrium is given by:    *    Y  A  Y , K  NX   , Y , Y     

Graph in Y, ρ space, there is an upward sloping YY line (since the M-L condition holds) and a flatter, but upward sloping NX=0 line. The point of intersection indicates internal balance. Assuming the Marshall-Lerner condition holds, then a devaluation (depreciation) must lead to an increase in B (improvement of balance of trade). Interest Rates The model can be used to address capital flows from disparities between the domestic interest rate (i) and the world interest rate (i*). Note: these results are the opposite of the results using the asset approach (monetary approach). If i>i*, then there are capital inflows and the exchange rate appreciates. If i
Absorption Approach Model (basic Keynesian model) Y= C + I + G + (X – M) A= C+ I+G B = X – M (same as above) Y=A+B Or, B =Y–A B = current account balance (flow) Y = income A = (domestic) absorption B = Y – A = - If If = capital flows (<0 indicates an outflow) Using the leakage-injection terminology S+M+T=I+X+G (S – I) + (T – G) = (X – M) Net national savings is equal to the current account surplus. (Used for the “Twin Deficits problem” p. 58-9) B = Y – A = net national savings = - If The trade balance can only improve when income is increased relative to absorption (Y>A). This might require expenditure switching (devaluation) and expenditurereducing policies (p. 157). Returning equilibrium when there is a balance of trade deficit. Two methods, real balance effect (laissez-faire) or activist policy.

The real balance effect stipulates that price level movements are all that are required to get the economy back into equilibrium, however these may can a long time. Activist policies could be used to eliminate a trade deficit and avoid inflation. “Expenditure switching switches demand toward home produced goods. Devaluation is the best policy but import tariffs and quotas could also be used. Expenditure reduction policies reduce the level of domestic adsorption...through higher interest rates and higher taxes or lower government spending” (p. 54).

Monetary Monetary models are based on the proposition that exchange rates are determined by the supply and demand for the national money in each nation. Monetary models, unlike the Mundell-Fleming model, ignore the flow implications. That is to say, overshooting affects the real exchange rate and current account, but ignores the wealth implications. Monetary approaches do not include the current account, but rather focus on the capital account, thus they are inappropriate to analyze exchange changes from trade deficits (or surpluses), except for the portfolio balance approach. ∆F = B + K ∆F = change in reserves B = current account balance (flow) K = capital account balance (flow) Thus, the models are equivalent if K=0, as the Keynesian models assume. ∆F = B = X – M = Y – A = ∆M – ∆D Where, ∆M = change in money stock, and ∆D = change in domestic credit expansion. PPP R=SP*/P q=lnR, s=lnS, p=lnP, p*=lnP* q=s-p+p* or s = p – p*

Flexible Price Monetary Approach (FLMA) Expanded PPP to include exchange rates and the quantity theory on money (Monetary policy is inflationary). See also King, p. 245. 1. s = p – p* Assume: monies are non-substitutable and bonds are perfect substitutes, portfolios are adjusted instantly—capital is perfectly mobile, and UIRP holds. ste1   i  i   2. UIRP t

(If i>i*, then in the following period, the expected exchange rate will depreciate, s up).

Wealth constraint (on domestic residents) W  M  B  B 3. W  M V M = money supply B = domestic bonds V = B + B* Agents hold wealth in money, domestic bonds, and foreign bonds. Based on the assumption, bonds are perfect substitutes, so they can be written as V. Following Walras’ Law, if the money market is in equilibrium, then so is the bonds market, thus the model only focuses on the money market. Cagan money demand functions (p.180) D 4. mt  pt  1 yt   2it D    5. mt  pt  1 yt   2it α1 is an income elasticity and α2 is a semi-elasticity (since i is expressed as proportion, not a log).

Money demand = money supply mtD  mtS  mt 6. D mt  mtS   mt Substituting (6 into 4 and 5) and solving for prices     7. pt  pt  mt  mt  1  y  y    2  i  i  t

t

Substituting into the PPP equation (s=p-p*), we get the reduced-form equation of the FPMM    8. s  mt  mt  1  y  y    2  i  i  t

t

Predictions: If m increases, then s will increase (depreciate). [Because of the quantity theory, we expect that inflation will increase from monetary expansion, leading to depreciation.] dy>0, ds<0 the currency appreciates (unlike in the Keynesian models) di>0, ds>0 the currency depreciates (unlike in the Keynesian models) Why the difference? First, the model is of money demand—the exchange rate is determined by money demand (not demand for goods).    L  L Y,i  An increase in Y, increases L due to transactions demand.  

 m the nominal money supply is fixed. An increase in L (because Y   p up) can only be balanced through a decrease in P. Recall equation 1. s = p – p* Thus appreciation is needed for the domestic price to fall. Concerning the interest rate If the interest rate increases this reduces the demand for money (L) and thus P needs to increase to maintain money market equilibrium. Since PPP holds, the domestic price level can only rise if the exchange rate depreciates. To make the link between interest rates and prices, one can substitute prices into the equation for interest rates. Assume the real interest rates are the same between countries. it  rt  pte1 9. Fisher Equations  it  rt  pte1 And L  

  e e 8’. s  mt  mt  1  y  y  t   2  p  p  t 1

Sticky-Price Monetary Model (SPMM) Dornbusch Overshooting Model Sources: Lecture notes and handout: 2 February 2005, Obstfeld and Rogoff p. 609-618, Hallwood and MacDonald p. 188-193, Sarno and Taylor p. 104-108 Note: the equation and page numbers reflect those in O&R, not the lecture notes. Model (Mundell-Fleming with sticky prices) Uncovered Interest Rate Parity must hold: (1) it 1  i *   et 1  et  Note on UIRP: if et 1  et  it 1  i * Money demand equation in log-form (2) mt  pt   it 1   yt

where η is the interest rate sensitivity of money demand and  is the income sensitivity of money demand. The IS curve d (3) yt  y    et  p *  pt  q  Purchasing power parity (R=ep*/p) and lnR=q (4) q  e  p *  p q is the (long-run) equilibrium real exchange rate consistent with full employment, where q =0 Expectation Augmented Phillips Curve (role of inflation) d % (5) Pt 1  pt    yt  y    p% t 1  pt 

* Expected inflation: p% t  et  pt  q (price level if the output market cleared) If PPP really holds, then e adjusts from a change in p expectations. “The first term on the right-hand side of (5) embodies the price inflation caused by date t excess demand, while the second term provides for the price-level adjustment needed to keep up with expected inflation or productivity growth. That is, the second term captures the movement in prices that would be needed to keep y  y if the output market were in equilibrium” (O&R p 611-612).

Note that (5) implies: d (6) Pt 1  pt    yt  y   et 1  et Dynamic Equations To solve, insert (3) and (4) into (6) d (3) yt  y    et  p *  pt  q  (4) p *  p  qt  et

(6)’ Pt 1  pt      et  p *  pt  q    et 1  et (6)’’ qt  et      qt  et  et  q    et 1  et

(7) qt 1  qt 1  qt    qt  q  assume  <1 (shocks to the real exchange rate damp out over time) Substitute (1), (3), and (4) into (2) and let p*  y  i*  0 (2)’ mt   et  qt  p *    i *   et 1  et      qt  q  (8) mt  et  qt    et 1  et     qt  q 

et  1    qt   q  mt          Notice that (7) and (9) constitute the two first-order differences of equations in q and e. ∆q =0 (or vertical on the graph) when q  q . Thus the speed of anticipated real adjustment is independent of nominal factors. The ∆e=0 has a vertical-axis intercept of  q  mt , and it is upward sloping if  <1 (the slope must be below 45 degrees). or (9) et 1  et 1  et 

Implications: SR PPP is violated An unanticipated increase in money supply, initially causes a more than proportional exchange rate depreciation (e up). “The nominal depreciation of domestic currency implies a real depreciation (since prices are sticky). This real depreciation raises aggregate demand, so output rises temporarily above its steady state value” p. 616. Short-comings: While the real exchange rate changes and thus the current account balance and wealth do not have an effect on aggregate demand.

Currency Substitution p. 196 Since corporations, investors, and speculators have incentives to hold a basket of currencies to minimize risk, the previous assumption of agents holding no foreign currency and monies are non-substitutable is no longer valid. Note: currency substitution has been implicated as a factor reducing the stability of money demand in the 1970s, thus reducing the effectiveness of monetary targets. “For example, the Swiss and German monetary authorities set money supply targets of 5 and 8 percent, respectively, for the period 1977-9. The actual money supply outcome was an increase of 16.2 in Switzerland and 11.4 percent in Germany. These overshoots of the money supplies were blamed on a shift in foreign and domestic demand for financial assets based in deutschmarks and Swiss francs (in particular a shift away from the US dollar which was argued to be overvalued). Since the Swiss and German authorities were unwilling to let the exchange rate take the adjustment (i.e. this would imply, on assumption that prices are sticky, a real exchange rate change) by appreciating, they intervened in the foreign exchange markets to supply Swiss francs and German marks. Since the monetary consequences of this were not sterilized, increased money supplies inevitably resulted. These monetary overshoots led to the non-announcement of monetary targets by the Swiss authorities in 1979 and a more flexible target by German authorities in 1979” (p. 195-6). Portfolio Balance Approach This models allows agents to hold domestic and foreign bonds and for the current account (and capital account) to affect the exchange rate. Bonds are imperfect substitutes and thus there is portfolio diversification in terms of bonds between countries. ‘International transactors are likely to hold a portfolio of currencies to minimize exchange rate risk and risk-averse international investors will wish to hold a portfolio of non-monetary assets—depending on risk-return factors.’ (p.228) Thus uncovered interest rate parity is NOT expected to hold. UIRP needs a risk premium attached to it to hold. where λ is the risk premium   i  i   s e If λ<0, then foreign assets are viewed as more risky and offer a relatively higher return. If investors decide that the currency has also become riskier, then they will diversify away form the currency—depreciation. [e.g. USD depreciated relative to DEM and JPY in 1977-8 as Us assets were seen as more riskier.] W = M+B+SF Wealth comes from domestic money, domestic bonds, and foreign bonds. Wealth could influence the exchange rate if...  Consumption is a function of wealth (life-cycle theory) income and demand for money will also change.  Money demand is a function of wealth (not just Y and i as before), then it can affect the exchange rate.  Agents are risk-averse, they will hold a greater proportion of domestic bonds to foreign (home country bias).