Appendix Two-Country Model
The Consumer’s Problem
For the home country, agent i’s utility function is given as follows:
where Ci is a consumption basket of home and foreign goods, Mi represents money holdings of home currency (no currency substitution), Q is the domestic consumer price index, and
In the case of intersectoral trade, agents have CES subutilities over home and foreign varieties of goods, respectively. Explicitly, Ci is given as
In these last two subutility expressions,
Consider now the case of intraindustry trade. Home and foreign goods no longer belong to separate commodity groups as countries exchange goods within the same industry. To modify preferences accordingly, equations (A2) through (A4) are replaced with:
where β measures home goods preference. Although agents consider home and foreign varieties to be of the same product type, residents in each country still prefer local goods.
The budget constraint, identical in both instances, completes the formulation of the consumer’s problem facing the home agent:
where Pj is the price of home good j (in home currency) and
Solving the consumer’s problem by maximizing (Al), given equations (A2) through (A4), with respect to
Again, solving the consumer’s problem by maximizing equation (Al) subject to equation (A6), but given equation (A5) instead, one can write the individual demands for each home and foreign variety under two-way trade as
Money demand remains unchanged from that under interindustry trade in equation (A9). Summing up individual demands for each home variety in equation (A7) or (A 10) over all home consumers along with the equivalent export demands over foreign consumers yields the product demands facing the representative domestic producer as a function of relative price and real wealth at home and abroad.
The Producers Problem
Producer i“s revenues plus his or her initial money holdings make up the individual’s nominal wealth:
For stability, “marginal cost”—in terms of the marginal disutility of output— must be non-decreasing, requiring γ - 1 ≥ 0. Hence, scale economies in production in the model refer to decreasing average rather than marginal costs. The producer’s problem can be stated as maximizing the modified profit function (A12) with respect to each price given demand for output in each market shown in Table 1. The explicit solutions to the producer’s problem are shown (in logs) in Table 2.
The following conditions characterize general equilibrium under both patterns of trade.
Money Market Equilibrium
Using the money demand function in equation (A9) and the definition of wealth, domestic money market equilibrium is given by
where the total money stock held by home agents equals aggregate money demand and is proportional to nominal GNP. Using this quantity equation relationship at home and similarly abroad, one can derive the demand facing each home producer in both the local and export market shown in Table 1, where
Goods Market Equilibrium
In symmetric equilibrium at the industry level, identical producers set identical prices. Consequently, the following relative prices are unity in general equilibrium:
where quantity variables without; subscripts indicate measures summed over all home agents (e.g., C = ΣC). Note that goods market equilibrium in (A14) equates GNP at market prices with aggregate consumption, requiring balanced trade (NX = 0) in the absence of capital mobility.
Exchange Rate Equilibrium
Given goods and money market clearing and balanced trade
The exchange rate adjusts to ensure balance of payments equilibrium. In symmetric equilibrium at the country level, national money supplies are assumed to be equal and, hence, local and export prices are also equal at home and abroad, respectively. Thus, the initial symmetric steady-state equilibrium has both the nominal and real exchange rate equal to unity (E = R = 1).
Relative Price Dynamics
To proceed, note that the consumption-based (log) real exchange rate r—defined simply as the currency-adjusted ratio of CPIs in each country—can be written as a weighted measure of relative local and export prices (in logs): r = α (e + p2* — p1) + (1 — α)(p2 — e — p1*).39 Using this measure of the real exchange rate and defining a measure of domestic-foreign price differentials, d = α(x2* - x1) + (1 - α)(x2 - x1*), the difference equation governing the dynamics of nominal price differentials under both patterns of trade can be written as
Note that in equation (A16), the “homogeneity” condition ψ0 + ψ1 + ψ2 = 1 is not satisfied. The implication of this result is that monetary disturbances will have permanent effects on relative prices (long-run non-neutrality).40 Thus, PPP fails to hold under market segmentation (see below).
Solving the second-order difference equation in (2), the (non-explosive) fundamental solution is given by
Using the fact that r = e + 0.5d + 0.5d-1, the dynamic solution for the real exchange rate is
Assuming home and foreign money, and consequently the exchange rate, are martingale processes (i.e., tmt + i = 0 for i ≥ 0) in equation (A 18), one can obtain the specific solution for the real exchange rate shown in (2), where
The steady-state or long-run impact of a monetary shock on the real exchange rate from equation (2) is measured by (ω1 + ω2)/(1 - λ), which equals 1 - (ψ1 + ψ2)/(1 - ψ0).
Hence, long-run PPP (monetary neutrality) is violated unless the homogeneity condition ψ0 + ψ1 + ψ2 = 1 is satisfied. Under the law of one price, this homogeneity condition is indeed met (see Faruqee (1994)), but is no longer assured under market segmentation. Instead, a domestic monetary expansion will usually lead to a lasting nominal and real depreciation with pricing to market.41
Adams, Charles, and Bankim Ghadha, “Real and Nominal Exchange Rates in the Long Run,” IMF Working Paper 91/63 (Washington: International Monetary Fund, June 1991).
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Ball, Laurence, and David Romer, “Real Rigidities and the Non-Neutrality of Money,” Review of Economic Studies, Vol. 57 (April 1990), pp. 183–203.
Blanchard, Olivier J., “Price Asynchronization and Price-Level Inertia,” in Inflation, Debt, and Indexation, ed. by Rudiger Dornbusch and Mario Henrique Simonsen (Cambridge: MIT Press, 1983), pp. 3–24.
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Breuer, Janice Boucher, “An Assessment of the Evidence on Purchasing Power Parity,” in Estimating Equilibrium Exchange Rates, ed. by John Williamson (Washington: Institute of International Economics, 1994), pp. 245–77.
Cooper, Russell, and Andrew John, “Coordinating Coordination Failures in Keynesian Models,” Quarterly Journal of Economics, Vol. 103 (August 1988), pp. 441–63.
Delgado, Francisco A., “Hysteresis, Menu Costs and Pricing with Random Exchange Rates,” Journal of Monetary Economics, Vol. 28 (December 1991), pp. 461–84.
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Engel, Charles, “Real Exchange Rates and Relative Prices: An Empirical Investigation,” Journal of Monetary Economics, Vol. 32 (August 1993), pp. 35–50.
Faruqee, Hamid, “Real Exchange Rates and the Pattern of Trade: Comparative Dynamics for North and South” (Ph.D. dissertation; Princeton, New Jersey: Princeton University, 1994; and Journal of International Money and Finance (forthcoming)).
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Goldstein, Morris, and Mohsin Khan, “Income and Price Effects in Foreign Trade,” Chapter 20 in Handbook of International Economics, Vol. 2, ed. by Ronald W. Jones and Peter B. Kenen (Amsterdam: North-Holland, 1985).
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Hooper, Peter, and Catherine L. Mann, The U.S. External Deficit: Its Causes and Persistence, Board of Governors of the Federal Reserve System International Finance Discussion Paper No. 316 (Washington: Federal Reserve Board, November 1987).
Knetter, Michael M., “Price Discrimination by U.S. and German Exporters,” American Economic Review, Vol. 79 (March 1989), pp. 198–210.
Knetter, Michael M., “International Comparisons of Pricing-To-Market Behavior,” American Economic Review, Vol. 83 (June 1993), pp. 473–86.
Krugman, Paul R., “The International Role of the Dollar: Theory and Prospect,” in Exchange Rate Theory and Practice, ed. by John F.O. Bilson and Richard C. Marston, NBER Conference Report (Chicago: University of Chicago Press, 1984), pp. 261–78.
Krugman, Paul R., “Pricing to Market When the Exchange Rate Changes,” in Real-Financial Linkages Among Open Economies, ed. by Sven W. Arndt and J. David Richardson (Cambridge: MIT Press, 1987), pp. 49–70.
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Hamid Faruqee is an Economist in the Research Department. He received his Ph.D. from Princeton University. Work on this paper began while the author was a lecturer in the Woodrow Wilson School of Public and International Affairs. He would like to thank William Branson, Larry Ball, Rex Ghosh, Michael Knetter, and IMF Research Department Seminar participants for helpful comments and discussions.
Comparing the relative price of different goods within the same country versus the relative price of the same good across different countries, Engel (1993) finds the former measure to be less variable in all but a few cases such as energy prices and primary commodities. Moreover, the second relative price tends to be several times more variable on average, confirming that the local prices prevailing in a given market destination remain comparatively quite stable.
See Engel (1993) for a study on the G-7 countries. Giovannini (1988) and Marston (1990) document evidence of pricing to market practices within particular Japanese industries. Other studies on the failure of one price include Isard (1977), Mann (1986), and Knetter (1989 and 1993).
Krugman (1989, p. 43) summarizes this dissatisfaction:
[W]e must now admit that international Keynesianism, while more like reality than international monetarism, itself turns out to have a problem: It does not go far enough in rejecting international arbitrage. Not only does the Law of One Price fail to hold at the level of aggregate national price indices... it doesn’t even hold at the level of individual goods.
Aizenman (1984), for example, illustrates that when transport or information costs impede arbitrage over the very short term, PPP holds up to constant plus white noise. However, it is the persistence of relative-price movements that dominate the time series of the real exchange rate that requires further explanation.
During the dollar upswing between 1980 and 1985, Dornbusch (1987, p. 104) observes the following fact regarding U.S. import prices:
[T]he order of magnitude of the decline [in import prices] remains relatively small compared to the change in relative unit labor costs. With a change in relative unit labor costs of more than 40 percent, the decline in the relative price is in most cases less than 20 percent. That is not at all out of line with the theory once some degree of “pricing to the American market” is taken into account....
For the period 1985-87, when the dollar fell precipitously, Hooper and Mann (1987) find that import-price increases, in percentage terms, were well short of the nominal depreciation. Krugman (1989) reports a similar finding in the specific case of Japanese exports in manufactures, finding that export prices (in dollars) were relatively stable in the destination market despite sharply rising unit labor costs (in dollars) at the point of origin.
A partial exception is Delgado (1991), which develops a dynamic menu cost model of pricing to market, albeit in a partial equilibrium setting.
Under imperfect integration in world markets for goods and services, countries differ in their national consumption patterns and in the units of account in which they set prices—favoring both their own goods and their own currency. However, the law of one price still equates currency-adjusted prices across markets. For a general discussion of imperfect integration, see Krugman (1989).
See Faruqee (1994).
See Appendix for details and the basic setup of the model.
See Appendix for details.
More precisely, with interindustry trade, the domestic CPI is a function of prevailing home and foreign producer prices given by
where α is the exact expenditure share on home goods. Under intraindustry trade. the home CPI and expenditure share on home goods are
Given relative producer prices in general equilibrium, β is chosen so that
There are many justifications for the premise of differential costs. If there exist market specific costs in transportation, distribution, production, advertising and/or servicing, then costs can differ at the margin for the home and exported good. For example, foreign markets may require different product specifications and/or have different governmental regulations that differentiate costs of production; producing the export good may even take place in the destination country itself, involving a completely separate plant and production run. These and similar explanations may also help explain why markets are actually segmented in the first place.
Constant differential markups could be introduced into this CES framework by assuming differential elasticities of substitution across markets (ϵ ≠ ϵ*). In that case, there would exist a constant degree of pricing to market.
Typically, with differential markups, demand is less convex than the constant elasticity case. See Marston (1990).
Krugman (1984) finds that most countries invoice exports in terms of domestic currency when relative country-size differences are not significant. The exception is developing country exports, which are predominantly invoiced in U.S. dollars.
Based on taste parameters, the coefficients in Table 2 are given by
where both coefficients and their sum are between (0,1).
Pass-through abroad is defined as
Applying L’Hôpital’s rule to preferences described in the Appendix verifies this equivalence result in the limit as ϵ → 1.
An alternate but related definition of pricing to market used elsewhere when considering multiple markets is the discrepancy between various export prices for a given producer. See, for example, Krugman (1987) and Knetter (1993).
Agents are not risk neutral here, and equation (1) omits a risk premium that is a function of the conditional distribution of all nominal variables. For example, if money, prices, and the exchange rate are log-normal, the risk premium is a constant (comprised of variance and covariance terms) and can be ignored. Alternatively, the dynamics can be interpreted as deviations from a (stochastic) trend reflecting time-varying risk—which has very little impact on relative prices through symmetry across home and foreign price setters.
In a general sense, one can view equation (1) as the outcome of minimizing a quadratic kiss function defined by squared deviations in actual price from optimal price over the period for which prices are predetermined.
The behavior of the nominal exchange rate is identical across both trade patterns. Given money market clearing and balanced trade (see Appendix), the (log) nominal exchange rate is given by
Comparing this expression to equation (2), which follows, highlights the fact that asset market prices and goods markets prices adjust at differential rates.
That is, it is assumed that
(where ν, ν* are random disturbances), in which case the nominal exchange rate will also follow a random walk.
One can show that
In a closed-economy context, Ball and Romer (1990) show that real rigidities—such as efficiency wages—reinforce the effects of nominal rigidities, inducing a greater degree of persistence in domestic prices. In an open economy, pricing to market provides the source of real rigidity—allowing firms to stabilize relative prices in each market—which increases the degree of stickiness in nominal prices (in terms of local currency) and magnifies the degree of persistence in the real exchange rate.
The equivalent solution for intersectoral trade under one price for the degree of inertia is (2α — 1)λ, compared with λ under market segmentation. In a closed economy (α = 1), the dynamics in the two instances are identical, as one would expect. Meanwhile, when α = 0.75, inertia under one price is half that under pricing to market, and the increase in persistence is even larger for intraindustry trade. See Faruqee (1994).
The steady-state value (denoted with a bar) for the real exchange rate as seen from equation (2) is given by
where the coefficient in this expression measures the king-run impact of a permanent monetary shock. See Appendix for details.
The model thus includes a role for monetary factors in determining equilibrium real exchange rates, so long as markets remain segmented. See Krugman (1990) for a recent discussion on real determinants of equilibrium exchange rates.
With two-way trade, this definition serves as a linear approximation. Out of steady state, spending patterns are constant under the approximation, neglecting the (typically second-order) effects of relative price movements on budget shares under intraindustry trade. See also footnote 15.
Real quantities are of course also affected. In general equilibrium, the composition of (log) output is related to the steady-state real exchange rate by r = α(y1-y2*)+(1 - α)(y1* - y2).
One can show that ψ0 + ψ1 + ψ2 ≤ 1 since 2(α - 1) ≤ γ - 1, suggesting that nominal and real exchange rates exhibit positive long-run comovements from monetary shocks. In the second condition, the left-hand side is bounded above by zero (local goods preference) while the right-hand side is bounded below by zero (rising marginal costs). Homogeneity obtains in the knife-edge case when both expressions hold as equalities.