APPENDIX: The Basic Model
For the home country, producer-consumer 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, I replace equations (A2) through (A4) 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 P*j is the price of foreign good j (in foreign currency) prevailing in the home market (designated later by a superscript 1), E is the nominal exchange rate (home currency price of foreign currency), and Ii is agent i’s level of nominal wealth.
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Southeast Asia and Pacific Department, International Monetary Fund. Work on this paper began while the author was a lecturer in the Woodrow Wilson School of the Public and International Affairs and was completed when he was in the Research Department. The author would like to thank Michael Knetter, Laurence Ball, and IMF Research Department Seminar participants for helpful comments and discussions. The views expressed and the errors remaining are the author’s sole responsibility.
Comparing the relative price of different goods within the same country versus the relative price of same good across different countries, Engle (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 Engle (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), Knetter (1989, 1992).
See Breuer (1994) for a recent survey of the PPP literature.
“[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) 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 dominates the time-series of the real exchange rate which requires further explanation.
“[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 in most cases was 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 ensuing period from 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 currency. However, the law of one price still equates currency-adjusted prices across markets. See Faruqee (1992). For a general discussion of imperfect integration see Krugman (1989).
See Appendix for details and the basic set-up 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 which 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 LDC 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,
In Armington (1969), goods are imperfect substitutes according to country rather than industry.
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 loss function defined by squared deviations in actual price from optimal price over the period for which prices are predetermined.
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 1, page 6.
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).
Furthermore, one can show that ψ0+ψ1+ψ2<1 unless 2(α-l)=γ-1 in which case homogeneity obtains. In the knife-edge 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).
The behavior of the nominal exchange rate is also 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 (4) highlights the fact that asset market prices and goods markets prices adjust at differential rates. By further specifying the law of motion for m and m* (forcing variables), one can then obtain closed form solutions based on (4)
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 local 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 (2a-l)A compared to A under market segmentation. And in a closed economy (a=l), the dynamics are the identical in the two instances. Meanwhile, when a=0.75, inertia under one price is half that under pricing to market, and for intraindustry trade the increase in persistence can be shown to be larger still. See Faruqee (1992).
Provided that market segmentation exists in steady state.
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.