Comment on "The Effects of Exchange Rate Adjustment on International Investments" by Dennis E. Logue and Thomas D. Willett

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— INTERNATIONAL. FINANCE DISCUSSION PAPERS |

COMMENT ON-"THE EFFECTS OF EXCHANGE RATE ADJUSTHENT OW SNTERNATIONAL INVESTMENT? BY DENNTS EB. LOGUE” AND THOMAS D. WILLETTE”

Guy V.G. Stevens”

_ Discussion Paper ¥Ko._53, September 19, 1974

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Division of International Finance

Board of Governors of the Federal Reserve System

The analysis and conclusions of this paper represent the views of the author and should not be interpreted as reflecting the views of the Board of Governors of the Federal Reserve System or its staff. Discussion papers in many cases are circulated in preliminary form to stimulate discussion and comment and are not to be cited or quoted without the permission of the author °

This comment will concentrate exclusively on the direct invest-

ment aspects of the Logue & Willett- paper. "Throughout the paper the

authors make a number of theoretical and empirical statements applicable to the analysis of foreign investment. Their general conclusion, albeit tentative, is that both theory and fact imply that a devaluation of the dollar will discourage U.S. direct investment” outflows and encourage direct investment into the United States. Thus, on pase 1

they point to the trade-off_between production abroad by U.S. subsidiaries and exports, stating: “During the period. of. overvaluation of the dollar, U.S. direct tnvestnent abroad was artificially stimulated in relation to exports: whereas foreign investment in the U.S. was discouraged relative fo exporting to the U.S." Later in section III.C they come to the same conclusion for apparently different theoretical reasons, emphasizing the lower foreign currency price of existing

American assets-after the U.S. devaluation. Finally in section II1.€ they adduce empirical evidence to support the same overail result.

I do not want to deny the authors conclusion. However , my position is that such a conclusion is much less obvious than the above arguments suggest; in fact, depending on the alternative ways 2 devaluation of the dollar can affect the costs and revenues of direct investors, one can make 2 plausible theoretical case for any outcome: the devalua-

tion may discourage U.S. direct investment abroad, encourage it or

leave it unchanged. We can arrive at such differing conclusions be-

cause there are 4 number of different ways that

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devaluations can affect the revenver-znd-conts of foreign subsidiaries.

Perhaps it will help to clarify the issues to explore the effects

_of exchange-rate changes in the context of a~simple model of the pro-

fit-maximizing international firn.> The main point will be to trace

the effect of exchange-rate changes on the output of a U.S. foreign

subsidiary; although I will not trace the subsequent effects in this

comment, changes in output will have effects in the same direction on the capital stock of the subsidiary and, presumably, the financing of investment by capital outflows from the U.S.: U.S. direct investment.

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The analysis will be partial‘ equilibrium, which can of course lead to

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errors; but, unfortunately, none of our research has gone beyond this point.

| We need consider only the simplest kind of model. The profits (P) of a given foreign affiliate at any time t are equal to its revenues (R) minus it costs (C). Revenues are assumed -equal to price

time output (pQ), and costs aré some increasing function of output

[C(Q)]. An important question is in what currencies these revenues and costs are denominated.

The first case, leading to a conclusion that a devaluation has no effect at all, is that of a subsidiary which sells all its output in a given foreign market and incurs all its costs in foreign currencies: Lie. it employs only foreign labor and buys its capital inputs abroad ( a very common phenomenon). Letting the subscript f£

stand for..foreign_currency units and $ for magnitudes expressed in

* Eons eel

oe create eR: RT Oe OR

! oa . dollars, for.this case the profits of the subsidiary are initially

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wholly in foreign currency:

Pe = PQ - C(Q) (1)

. The U.S. owners, we assume, ultimately want only dollars; so the

value of these profits to a U.S. owner is the foreign currency value

times the exchange rate (dollars per unit of foreign currency):

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Assuming that the U.S.-owned firm maximizes dollar profits, the

output of the foreign subsidiary will be set so that marginal revenues in dollars will equal marginal costs in dollars. But in this case, since the exchange rate simply multiplies both revenues and costs in

foreign currencies, the optimal point is reached when marginal revenue

equal marginal cost denominated in foreign currency:

a = x(MRe - MCe) = 0, or MRe - NC. = 0 Oe (3) Equation (3) shows that the exchange rate does not enter into the marginal equation determining optimal output; hence exchange rate changes in any direction will not affect the level of output, capital stock,

or direct investment of sucha subsidairy. This is true even though

the value of such a firm or asset to its U.S. owners is definitely increased by a devaluation (an increase in x). Letting r be the discount rate, the value of this firm Vina perfect market will be the

present value of its future profits:

| — Ve) =x f Pelee ae . — —. @& -- t=o

Clearly a given percentage change in the exchange rate leads to

the same percentage change in the dollar value of the'asset. However,

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this need not, and does not in this case lead to a change in direct in-

vestment. Such results may seem paradoxical, but they. aren't if we remember that the exchange rate has_changed nothing at the margin, increasing, rather, the rate of profit on all intra-marginal units. Further, the rate of return on the firm will not change, since the

dollar value of both profits and the value of the firm Have changed by the same percentage; the only real change is that the owner of the firm at the time of the devalucticon has reaped a once-and-for-all windfall gain. In fact, Logue and Willett implicately recognize this case when they analyze portfolio investment ~section IIIL.A};~however, they

did not consider-its application to direct investment. . :

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One can get different results by having the exchange rate affect the profits of the foreign affiliate in more complicated ways. The 2 = key is whether the exchange rate affects directly the profits of the foreign affiliate (P,) before they are changed into dollars to be remitted to the U.S. owners. A simple case, showing that a dollar de- 5 valuation can have a positive effect on output and direct investment is that where the foreign subsidiary uses an input imported from the United States. We can represent this by splitting the subsidiary's cost function into two parts: costs initially denominated in foreign _

currency [Cc .(Q)] and U.S. currency [C.(Q)]. As the dollar depreciates,

the foreigh ‘currency cost of this latter input decreases_as can be.

seen by the modified expression for subsidiary profits (in foreign

currency units):

~ €,(Q) . ; s - _—_s

Contrary to the previous model, the optimal level of output is

affected by the exchange rate? -

oP oe XC, (Q) ; = =0 “35 {x P 2 - *£,(Q) - = — } which implies xMK, = xMC, + MC, -- a oo. (6)

Intuitively we. can see that as * increases (the dollar is devalued), the dollar marginal revenue is now greater than the total marginal cost in dollars (XMC + MCe). Hence, we would expect output to expend until the equality is re-established. This-ean be established

rigorously _by differentiating the marginal condition (6) with respect

“Fr -_ =

to the exchange rate (x), and solving for dQ/dx.

wR. +X dMRe @ oc + xdMC - a, dM. ac £ dQ dx £ dq dx dQ dx Hence dQ. UR ¢ _ MC ¢ (7) dx x dC, : MC. _ OR dQ dQ dQ

The second order condition for a profit maximum implies that

the denominator of (7) must be positive (marginal revenue is decrea-

sing faster than total marginal cost). And equation (6) shows that

UR e - MC is greater than zero, hence a must also be positive - - as

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-- we deduced intuitively. But this is a conclusier—opposite to that of

Logue and Willett, since direct investment will increase as Q in-

creases. Finally, the Logue-Willett conclusion can be supported in the following two ways, both of which cause the revenues of the foreign-

produced good to be reduced. First, what if the international firm

supplies the same market by both exporting from the United States and

producing the same commodity abroad? Second, what if U.S. firms

export products that~are imperfect substitutes for the production of foreign affiliates? -

To keep the analysis simple and comparable to the previous example, assume first that an identical good is produced in both

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locations.” The total amount sold in the foreign market is, as before,

Q; but this amount is made up of a part, Q) produced in the United States and a part, G» produced abroad. Of -course Q, + % =Q. If we assume that the marginal costs of producing are increasing, then we get a interior maximum. The fir maximizes profits as before, but now there are two interrelated problems: how much to produce (Q) and where to produce it (the division of Q between Q, and Q,)+ Substituting Q + Q, for Q, the firm maximizes profits with respect to Q, and

Qo» where P now equals: _ _Pg = * pp(Q * [Q + 1 - x C,(Q,) - Cy (Q)) (8) ‘Maximizing with respect to Qy and Qo» we get two marginal

equations (note that so = 1): i

-7ap, . 3c Pe - _ —% 7,787 xg (a FQ) + PP BP (9) BPs oP. aC, 7, 7 07 * sg IO +O) + Pe) > FQ, (10)

Since the first term in parentheses is -equal-to- marginal revenue,

we have the familiar condition that marginal cost in each location is

set equal to the common marginal revenue (MR). Note-also that the ex-

change rate does not cancel fron equation (9)- cee

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To find the effect of a dollar devaluation on direct investment, we again calculate the effect of a change in x on foreign output, Q-

A standard comparative static analysis shows that dQ, /dx equals the

following: - 4Q, | MR_(@MR/2Q) = dx [x dMR/dQ - SATE = aXC,/dQ,] - ERTEO)” (11)

Since MR > 0, and since 9MR/3Q can be of any sign, we see that the effect of the exchange rate on foreign subsidiary output is ambiguous; but for the usual case where marginal revenue is decreasing (aMR/3Q<0). a devaluation will decrease foreign output and direct investment.

It is instructive to look at this effect. as the exchange rate affecting the marginal revenue curve of the foreign subsidiary. Thus»

in the case where perfect competition prevails, increased exports from

“the United States will not affect the price at which foreign subsidiary

output will be sold (8MR/9Q=0); hence 2 0.

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It might be noted that’ commodities need not—be. perfect substi-

tutes for effects such as those in equation (11) to be observed. U.S. exports may be imperfect substitutes for U.S. foreign subsidiary production e.g. big American cars and little European cars produced by U.S. affiliates) ; nevertheless, as long as there is. some cross-elasti-

.city of demand, changes in U.S. exports brought on by devaluation will

affect foreign subsidiary output and direct investment. F

In summary, the theoretical story of the effect of.a devaluation on direct. investment is, in my opinion, ambiguous. It should be

emphasized, further, that all-the analysis, so far, has been partial

wrest ere ry tens

equilibrium in nature; much more can happen as we move to the overall

general equilibrium solution.

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In view of this theoretical ambiguity, the ball would seem to

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be in the court of the empiricists. Unfortunately, as I am sure

tered tae.

Messrs. Logue and Wilkett would agree, we have-as yet virtually nothing on the empirical side to aid in the choice of the right theoretical

model. The authors tentatively point to data on foreign investment

into and out of the United States as support for their thesis that a

devaluation decreases outflows of direct investment and increase inflows. I know nothing about the upsurge in inflows reported by the authors. On the outflow evidence, however, there are alternative conjectures at least as plausible as that of Logue and Willett. Other qualified observers attribute the pattem of 1973 to a high

speculative outflow in the beginning of the year in anticipation of

the subsequent devaluation; following the devaluation there were lower-

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than normal outflows, not because foreign subsidiary output had been

cut, but because the higher anticipatory outfiows had reduced financial needs for the remainder of 1973. Thus if investors anticipated the devaluation, the. flows observed in 1973 could -have occurred under any of the hypotheses set out above. | -- ee

\ \ FOOTNOTES ‘ ‘ "

—1, The paper by Logue and Willett and the following comment

“were delivered at the Conference on the Effects of Exchange Rate - Adjustments, sponsored by the Treasury Department and the Federal

Reserve Board, and held April 4 and 5, 1974, Both pieces will be published in Peter Clark, D. Logue and R. Sweeney, eds., The Effects

of Exchange Rate Adjustments, (U.S. Government Printing Office, 1974).

2.. Chief, Quantitative Studies, International Division, Federal Reserve Board. Many of the ideas presented below were developed over the years in conversation or colloboration with others. 1 would like to recognize, in particular, Michael Adler, with whom I wrote the article cited in footnote 4 and my colleagues, Dale Henderson and Ray Lubitz,. . _ .

3. The modéls discussed below (for what they are worth) were ‘developed over a long period of time. I was not aware of any published literature in this area, but I assumed there must be some. After delivering this comment at the Treasury Conference, I had the good fortune to read an excellent paper by Susan Alexander of Southern Methodist University (dated Dec. 10, 1973). In her review of the literature Ms. Alexander confirms that economists have generally reglected the effects of devaluation on direct investment, but she does point to a few treatments by Meade, Sidney Alexander, H.P. Gray and Houthakker. According to Ms. Alexander all but Houthakker reach the conclusion of the first case discussed_below: that devaluation does not affect direct investment. Houthakker, alone, "hints" at a negative effect, but presents no real_analysis in support of the conclusion.

. Ms. Alexander, by the way, hits the nail on the head by maintaining that one mist do a careful analysis of the currencies in which revenues and costs are denominated.

The full references for the works cited above are:

James Meade, The Balance of Payments, (Oxford Univ. Press,1951) Chapters V and VIII.

Sidney Alexander, "Effects of a Devaluation

on the Trade Balance," IMF Staff Papers, April,1952,pp.263-278. H.P. Gray’, "U.S. Foreign Investment and the

Dollar Exchange Rate,'' Economia Internazionale,

August, 1966, pp. 10-12.

H.S. Houthakker, "Should we Devalue the Dollar?"

Challenge, October, 1962, pp. 10-12.

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4, It is’easy to show that there will be production in both locations only if one or both marginal cost curves are increasing. With constant returns to scale in both locations we would never see

“production of an identical good in both plates; exchange rate changes might, however, have an effect by causing a total shift in production from one location.to another. For a full development of this point me in the analytically similar case of tariffs, see Thomas Horst, "The me Theory of the Multinational Firm: Optimal Behavior Under Different Pe

Tariff and Tax Rates," Journal of Political Economy, September/October 1971, pp. 1059-1072.

5. See Michael Adler and Guy Stevens, "Direct Investment and Trade: An Analysis of the Export Displacement Effect," Discussion Paper #41, Division of International Finance, Federal Reserve Board (forth-

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coming, May 1974, in the Journal of Finance). —