Liquidity and Exchange Rates

Questions & answers

Q1. What gap does the paper fill, and how does its asset-market cash-in-advance constraint differ from prior open-economy liquidity models?

The paper’s objective is “to analyze the open economy implications of models in which money is used both for transactions in the goods markets and for transactions in the asset markets,” extending Lucas’s (1988) closed-economy cash-in-advance framework for asset prices to two countries (Section 1, Introduction). The authors are explicit about how their mechanism differs from the paper’s “important predecessor,” Helpman and Razin (1985): “while in Helpman and Razin, it is the borrower that faces a cash in advance constraint (at the time of repayment), in our model it is the lender that faces a cash in advance constraint (at the time she purchases assets). Moreover, in our model, the current account is always balanced and thus there is no relation between the current account and the exchange rate” – the exchange rate effect here runs entirely through portfolio liquidity, not through current-account financing needs.

Q2. How is the household’s transaction technology set up, and why does this allow a cleaner model of capital controls than earlier approaches?

Following Lucas (1988), each representative household is modeled as three members who separate for the period and pool resources at the end: one sells the period’s endowment, one uses a share of money to buy domestic and foreign goods (subject to separate cash-in-advance constraints, Eqs. 2.c-2.d), and one carries the remaining cash to the securities market to buy domestic and foreign bonds (subject to separate cash-in-advance constraints, Eqs. 2.a-2.b) (Section 2). Because domestic and foreign bonds must each be bought with their own currency, the model can represent a capital control as “a tax (τ) on the cash-in-advance constraint relative to foreign asset transactions” rather than, as in Greenwood and Kimbrough (1987) and Stockman and Hernandez (1988), as something “equivalent to restrictions on current account transactions” – the paper argues this is a more faithful representation of how real-world capital controls, which are overwhelmingly asset-transaction taxes rather than goods tariffs, actually operate (Section 1, Section 3).

Q3. What is the paper’s central comparative-statics result linking the exchange rate to asset-market liquidity?

Solving the certainty version of the model, the equilibrium nominal exchange rate is given by e = [(1−z¹)/(1−z²)]·(M¹/M²)·(y²/y¹)·(U₂/U₁) (Eq. 17), where z^i is the equilibrium share of country i’s money held for asset-market transactions. The authors state the mechanism plainly: “part of the money supply is held for use in the asset market, and thus, does not enter in the determination of the goods prices,” so a larger z (more money tied up buying bonds) means less money bidding up domestic goods prices, a lower price level, and – via goods-market arbitrage – a more appreciated currency (Section 2). The paper also shows ∂z^i/∂x^i < 1: a permanent increase in the rate of bond creation x^i raises the asset-transaction money share by less than one-for-one, which also implies a lower bond price and a higher nominal interest rate.

Q4. How does the model generate the result that capital controls appreciate the taxing country’s currency?

Imposing a tax τ on domestic residents’ foreign-bond purchases reduces the equilibrium share z² of foreign money held for asset transactions (Eq. 31.b, shown to be a decreasing function of τ), which frees up more foreign money to chase foreign goods, raising the foreign price level relative to the home price level and so appreciating the home currency (Eq. 33). The authors explicitly contrast the mechanism with that in prior capital-control models: “In the other models, foreign exchange controls act as a tariff on goods purchases…the effect on the exchange rate is through a change in terms of trade…In our model, instead, there is no change in the relative price of the two goods or in their allocation across countries: capital controls are neutral from that point of view” – the appreciation comes purely through the reallocation of money across the goods and asset markets, not through altered real trade flows (Section 3). The paper notes the policy corollary directly: “a liberalization of capital restrictions is likely to lead to a depreciation of the currency that is being liberalized,” and suggests this may explain why capital controls “in a number of EMS countries might have been effective in limiting exchange rate depreciations resulting from divergent economic policies among the member countries.”

Q5. How does the paper connect public debt maturity structure to the exchange rate, and why does this differ from the Giavazzi-Pagano mechanism?

Extending the model to multi-period bonds, the paper derives that the equilibrium asset-transaction money share for n-period bonds spread evenly over maturities is strictly smaller than for one-period bonds financing the same present value of debt (Eq. 40): z(n-period) = [(1−β)/(1−βⁿ)]·βD₁ < βD₁ = z(1-period). Because a smaller z means a less appreciated currency, “the longer is the maturity structure of the debt, the smaller will be the equilibrium share (z) of money holdings used for asset transactions…in the case of longer maturity bonds the exchange rate will be more depreciated” (Section 4). The authors flag this as a different channel from Giavazzi and Pagano’s (1989) well-known maturity-structure result: “In Giavazzi and Pagano (1989), a longer maturity of the debt reduces the probability of a devaluation…Our model, however, suggest[s] that, if liquidity constraints in the asset markets are important, the monetary authorities should also consider the effects of a longer maturity on the exchange rate through the reduction in the share of money used for security purchases” – a liquidity channel, not a default-risk channel. The paper offers this as a candidate explanation for why Italy, with a historically short debt maturity, had a relatively strong lira “in spite of…large money creation.”

Q6. How does the paper extend the model to uncertainty, and what is the resulting “excess volatility” result for exchange rates?

Under uncertainty about the size of each period’s bond issuance (x¹, x² i.i.d.), the log nominal exchange rate decomposes into a constant “fundamental” component plus a stochastic liquidity component driven purely by the realized bond-creation shocks: ln(e) = k + ln(x²) − ln(x¹) (Eq. 53), so that Var(s) = Var[ln(x¹)] + Var[ln(x²)] even though every real variable in the economy – output, consumption allocations, money holdings, and price levels – is held constant by construction (Section 5). The authors state this is the open-economy counterpart of Lucas’s closed-economy result: “We therefore find for the exchange rate the same excess volatility result as found by Lucas for the interest rate… the excess volatility of interest rates found by Lucas for a closed economy spills over in an open economy on the exchange rate.” The same shocks also move the real exchange rate one-for-one with the nominal rate (Eq. 59, Var(ln(re)) = Var(s)), which the authors note “is consistent with the empirical evidence about the high correlation between nominal and real exchange rates (e.g. Mussa (1987))” – achieved here, notably, in a flexible-price model with no nominal rigidity. The paper shows this volatility could in principle be eliminated: “the variance of the exchange rate can be reduced to the variance of its fundamental value (i.e. zero) if the monetary policies of the two countries are coordinated so that x¹ and x² are perfectly correlated” (Eq. 55), implying “only a very tight coordination of the monetary policies of two countries can assure the stability of the exchange rate in the presence of these stochastic liquidity effects” (Section 6, Conclusions).

Q7. What simplifying assumption keeps the current account from confounding the exchange-rate results, and what does it cost the analysis?

To isolate the liquidity channel from ordinary borrowing/lending dynamics, the paper assumes the foreign country’s discount factor is set so that each country’s rate of time preference exactly equals its net (after-tax) real return on assets, which “guarantees the equality between each country’s rate of time preference and the net rate of return on financial assets while preventing the divergence between the two countries[’] rates of time preference from creating incentives to borrow or lend” (Section 3, footnote), a device the authors compare explicitly to Svensson’s (1988, 1989) treatment of cross-country differences in risk aversion. The paper is explicit that this is a modeling simplification rather than a result: alternative approaches (a finite-horizon or overlapping-generations model) “would introduce dynamic effects such as borrowing and lending from which we want to abstract.”