- Assume demand side currency substitution as opposed to supply side currency substitution which occurs under fixed exchange rates where central banks look to maintain fixed exchange rates.
- Monetary currency substitution models contrast to global models in that the former interpret current balance surpluses (deficits) as an excess demand (supply) for foreign currency by domestic residents (where capital account and capital markets are ignored because there are no interest bearing assets in these models). The latter view the relevant money supply as the world money supply within the context of a highly developed and interdependent world capital market. The value of diverse money holdings relates then to the liquidity services money provides.
- Motive for diversifying money holdings across currencies of denomination is 1. transactions based 2. speculative (incl. hedging)
- 3 types of global currency substitution models are subdivided by the way they represent domestic residents' porfolios of assets.
- Two-stage portfolio allocation model
- First stage - portfolio divided between money and bonds.
- Second stage - divide bonds between domestic and foreign and money between domestic and foreign.
- Thus only need to consider the domestic/foreign allocation because bonds & money is already fixed.
- Offers a restricted set of portfolio choices and currency substitution arises from switching different currencies in the liquid asset portfolio. This is independent of the non-liquid asset position.
- Thus M=M_D+M_F & M*=M*_D+M*_F
- Demand for each money K depends on price level P, level of income and both domestic and foreign rates of interest r & r*
- Money market equilibrium conditions
- M_D+M_F=PK_D(r, r*)Y+PK_F(r, r*)Y*
- M*_D+M*_F = P*K*_D(r,r*)Y+P*K*_F(r, r*)Y*
- where under Miles M_F=M*_F=0 i.e. focusing solely on domestic demand
- Thus M_D/M*_D=PK_D(r, r*)Y/P*K*_D(r, r*)Y where assuming purchasing power parity the real income terms cancel to M_D/eM*_D=K_D(r, r*)/K*_D(r,r*)
- This can be approximated by (after taking logarithms) log(M_D/eM*_D)=σlog(θ_1/θ_2)+σlog((1+r*)/(1+r)) where σ represents the degree of currency substitution where σ is positive such that the ratio of domestic to foreign currency balances held by domestic residents depends directly upon the foreign rate of interest and inversely on the domestic rate.
- Single-stage portfolio allocation
- All four assets available.
- Optimize return subject to a minimal level of risk in a single-decision process.
- Fraction of real resources necessary for transactions (V) is inversely related to the level of money services S such that V=V(S)
- Where level of money services S = S(M/P, M*/P*)
- Consumer seeks to maximise utility from consumption subject to a wealth constraint and a savings/asset accumulation constraint such that:
- S_1(M/P,M*/P*)/S_2(M/P, M*/P*)=(P/eP*)(r/(r*(1+ε)).
- Assuming constant electricity of substitution you can take logs to get log(M/eM*)=log(θ_1/θ_2)+σlog(P/(eP*)-σlog(r/(r*(1+ε))
- Portfolio balance model
- All four assets available.
- No constraints (except obviously total wealth= total asset stocks)
- Two-stage portfolio allocation model - σ is positive such that the ratio of domestic to foreign currency balances held by domestic residents depends directly upon the foreign rate of interest and inversely on the domestic rate.
- Also known as money services model.
- An alternative specification of the Two-stage portfolio model M_F=M*_F=0 is the restriction that M*_D=0 i.e. domestic residents do not hold foreign money but foreign residents hold domestic money. Thus all currency substitution is undertaken by foreign residents. thus M_F/P=K_D(r, r*)Y*. One advantage of this specification is it includes Y* and that it doesn't require the assumption of purchasing power parity. Again like previous specification the interest rate captures the currency substitution.