Direct Investment and Trade: An Analysis of the Export Displacement Effect
(#714 in RFD Series)
INTERNATIONAL FINANCE DISCUSSION PAPERS
DIRECT INVESTMENT AND TRADE: AN ANALYSIS OF THE EXPORT DISPLACEMENT EFFECT
by
Michael Adler Columbia University
Guy V.G. Stevens Board of Governors of the Federal Reserve System
Discussion Paper No. 41, February 1, 1974
Division of International Finance
Board of Governors of the Federal Reserve System
This paper was presented at the Annual Meeting of the American Economic Association in New York, December 28-30, 1974. The views expressed are those of the authors and do not necessarily represent those of the institutions at which they are em
loyed.
Direct Investment and Trade: An Analysis of the Export Displacement Effect*
Michael Adler* Guy V.G. Stevens
*The authors are respectively, Associate Professor, Graduate School of Business, Columbia University and Chief, Quantitative Studies, Division of International Finance, Board of Governors of the Federal Reserve System. Financial support was provided by the U.S. Department of State and the Board of Governors of the Federal Reserve System, Neither organization shares responsibility for the opinions expressed in this paper. The authors wish to thank Stephen Preston and Walter Enders of Columbia University, who co-authored with them an antecedent study of native firm cost-functions, and Richard Berner, Howard Howe and P.A.V.B. Swamy of the Fed for very helpful comments and discussions. Arnold Gilbert of the Bureau of Economic Analysis, U.S. Department of “ Commerce provided invaluable assistance in programming and running : regressions for us on BEA's Multinational Data System, Our thanks go also to Terry Coble, Cora Flaifel and Sam Parrillo for expert research assistance,
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I. Introduction
The multinational corporation (MNC) has the choice of supplying foreign markets via either exports from the home market (US) or local production by a foreign subsidiary (FS). If the final (as distinguished from intermediate)U.S.-made and FS-produced goods are not identical the firm may do both. Two important questions in the analysis of the balance of payments impact of direct investment then arise. What determines this choice? And what is the impact of an increase in sales of the FS-product on sales of MNC exports? The purpose of this paper is to investigate these issues and especially the latter, the question of export displacement.
To date, the export displacement phenomenon has largely escaped theoretical or empirical analysis. The major exception is Hufbauer and Adler's (H-A) [12 ] analysis of the balance of payments consequences of U.S. direct private investment overseas. Depending on their interest, most observers have tended to assert either that F.S. sales compete very little with U.S, exports or that they fully displace them, | The assertion of these opposite points of view has frequently been grounded in two sets of assumptions which too frequently have been confused. On the one hand, minimizers of the export displacement effect seem to have argued that U.S. exports and the goods produced by F.S, are non-substitutes or complements in demand, while their opponents have supposed the goods to be perfect substitutes. These product-substitutability assumptions should be kept distinct from the implicit presumptions made by the opposing sides, on the other hand, regarding a different question: What would have happened to U.S. exports in the absence of
F.S. production, i.e. what is the "alternative position?" Typically those
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who dismiss the export displacement effect as insignificant do so in conjuction with the assumption that in the FS's absence its goods would have been produced and sold by some other native or third-country firm, That is, they adopt what H-A called the "reverse classical" alternative position in which any increase in F.S. sales displaces only native-firm sales and has no effect on imports at all. Those who emphasize the importance of export-displacement, however, implicitly adopt H-A's classical hypothesis in which native firms do not supplant F,S. sales. In this case, increases in F.S. sales impact exclusively against imports. In short the debate
over export-displacement has largely taken place within the framework of H-A's extreme assumptions and in the absence of any attempt except by conflicting assertion to determine which, or whether some mixture, of
the assumptions as to product substitutability or the alternative position ~~ is better suited to empirical fact.”
Our paper grapples with and attempts to resolve some of these questions theoretically and empirically in the context of a two tier micro- theoretical model of market conditions abroad, as set forth in section II and the appendix. The first tier is a model of a global-profit-maximizing MNC which produces two non-identical, partially substitutable products, one in the U.S. for home consumption and export and one abroad, for foreign consumption only. The second tier is added by nesting the MNC model ina model of the foreign market, in which the MNC's two products compete with, and partially or perfectly substitute for, goods produced for local consumption by native firms and products imported from third countries, There are
several innovations in this partial-equilibrium approach from which subse-
-3quent benefits emerge.
Section II, which lays out the full model structure, introduces a precise and flexible definition of the export displacement effect. It is precise in the sense that it flows unambiguously from the comparative statics of the model and involves parameters which in principle can be measured empirically. It is flexible because it can be made to accommodate any number of competitors to the MNC, alternative assumptions with respect to product substitutability (the "associated export effect") and can if necessary be extended to include intermediate goods (the "parts and components effect"). When intermediates are ignored, our analysis suggests that neither the classical nor the reverse-classical hypothesis will accurately portray the alternative position against which the export displacement effect actually takes place.
Our assumptions with respect to product homogeneity and the inclusion of market behavior distinguish our model from Horst's [ 11] excellent treatment of the MNC taken in isolation. Horst assumed that his MNC exported and produced abroad identical products. In contrast, we assume, perhaps more realistically for the markets we consider below that the MNC's exports and the goods produced by FS and native firms are non-identical, partial substitutes: their price cross-elasticities may be large but need not be infinite.° There are several reasons for our different choice of setting. /
First and most importantly, it is impossible fully to investigate export displacement in a model, such as Horst's, which excludes native firms,
One can certainly analyse the trade-off between exporting and producing
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abroad in the single-firm context while ignoring other firms, as we do
in Section II. But assuming identical goods, (Horst's case) is equivalent to the forced assumption, ab - initio of (a modification of) the classical position, In the absence of native firm or other products, increases in FS sales will necessarily reduce MNC exports of the same good exclusively. Even in Horst's model, the impact will not generally be one for one (the classical case), In our model, however, the effect can even disappear, as shown below.
Our model, on the other hand, incorporates a modified version of reverse classical behavior. Perfect classical behavior is excluded, for with native firms producing substitutes, U.S. exports will not alone bear the brunt of the displacement effect. Equally, perfect reverse classical behavior is unlikely, for in the presence of U.S, exports, increases in ~~ F.S, sales will not react exclusively against native firms. This consistent admixture of possibilities seems reasonable especially since the "classical" and "reverse classical" positions were chosen by H-A [ 12] in the first instance as polar extremes and not as representative of reality.
In the second place, it will be recalled that Horst's model produced interior solutions, with the MNC both producing in two locations and exporting, only when the sum of the slopes of the marginal cost functions was positive, Under the alternative assumptions of constant or decreasing costs, radically different patterns, emerged. These corner solutions involved either production in both places with no trade, or production in one with the second supplied exclusively by trade. Our model, however, provides interior solutions for the empirically relevant case of constant returns to scale. Nonetheless,
the existence of interior solutions, the size of the export displacement
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effect and the impact of changes in other exogenous variables do depend critically on the equilibrium values and slopes of the underlying cost and demand functions. We therefore devote Section III to an empirical examination of the structure of the production functions and the consequent cost functions of U.S. foreign subsidiaries and native firms in the chemical and electrical engineering industries in Germany, Canada and Japan.
Section IV presents a preliminary empirical analysis of the export displacement effect and the effects on the MNC's optimum of changes in other key factors, such as the cost of capital and foreign tax and tariff rates, in the full, four-firm, three - good, market nexus, Our technique is to estimate the effects on the equilibrium outputs of each competitor caused by a small change in some underlying parameter. These comparative statics are calculated at the point which represents the 1966 equilibrium values of the variables in the model. Of course, rather than use the 1966 equilibrium values as the point of reference, one could alternatively solve for equilibrium for any given values of the exogenous parameters. However, this would require solving a set of simultaneous, non-linear equations and will not be attempted here. When the MNC is considered alone, it is relatively straightforward to assess the signs and sizes of the determinant of the relevant Hessian and all its principle minors. When the MNC is embedded in the broader setting, however, these signs and sizes generally remain ambiguous. Consequently, the 1966 equilibrium levels and the conmparative statics at that point are calculated numerically. A concluding section summarizes, discusses caveats and suggests promising directions for
future research.
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II. The MNC in the Foreign Market
A. Model Structure
The objective of this section is to set forth the theoretical structure of our model of the MNC in the foreign market strictly in conformity with the empirical requirements of the data analyzed below. For these purposes it is sufficient to consider a static, one-period model of a MNC, with production and sales operations in two countries, involving the parent in country 1 (the U.S) and a subsidiary in country 2. The MNC behaves as a maximizer of its long-run profits from the sale of two differentiated products. Good 1 is produced by the MNC in the U.S, in the amount QQ of which Si1 is sold in the U.S, while Sj2 is exported to country
2: Qi = S14 + Si9- Good 2 is produced and sold by the F.S. in country 2;
The two goods sold by the MNC in country 2 compete with two additional differentiated products: sales in the quantity S39 of goods produced by and imported from third country firms; and S40 of the products of native firms. Because price-data are not presently, or ever likely to be, available separately for U.S, subsidiaries and native firms, we are forced for empirical purposes to assume that Soo and S42 represent an identical
good, the total sales of which are S.. = S
T2 22 + Si0° In this case we assume
that U.S. subsidiaries and native firms behave as Cournot-type imperfect competitors with respect to their common product; that is, they ignore the effects of their actions on the sales of their competitors. It is a small step from this convenient assumption to the general model of totally differentiated products, and in section IV alternative calculations are presented for
both the general and Cournot cases,
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The demand for each distinct product in the country 2 market is most easily estimated as a function of its own prices, the prices of competing goods and income. Letting the vector Po = (Py 9>Pp22P39) Sia = S;9(Pos¥) i=1,...,4 where own price-elasticities are negative and price cross-elasticities are positive if the products are substitutes; all income elasticities are positive. For purposes of the theoretical development, howevér, the demand functions are more conveniently employed in their inverse forn.
Letting the vector $5 = (S)92S72 539)» Pio = Py9(So)> where all partial derivatives will be negative if the several products are gross substitutes’ Sales revenues from product i in market 2 are therefore given by
Reo = S59P;0 (S89) = Ry9(So)- For simplicity, we assume that U.S. sales of
the MNC's good 1 depend on its own price alone: 8,1 = $441) and, inverting, P 111 p° Similarly the home (i.e. country 3) market price of the goods
ll reduced by third-country firms,
P33 = P44 (S33)- We may now proceed to model the market system by writing the profit-maximands of the three firms which compete in the second market.
The MNe's after-tax net revenues ariseing in country 1 from selling good 1 are: q) L Soy Pyy(Sqi) + M812 - ©2111 + S12) | (1-ty), where Cy = C1(Qz) is the cost function of good I, Ty is the export transfer price of good 1 set
by the MNC and t, is the tax rate in country 1. MNC (dollar) profits from 1
selling geod 1 in 2 are
T 1 (2) [ S12 Pio (So) - a+ To) FH $15 | (1-t,)£, where To and to are country
2's tariff and tax rates, respectively, and f) is the exchange rate between
1 and 2.
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The MNC also profits from selling good 2 in 2:
(3) L S22P22($2) - €2(So9) late
Summing expressions (1)-(3), total MNC profits may be rewritten as
4) B11 Spy) > S11 + 8p) ] =e) + [Ryp (Sp) = Cy(Sp9) + Ryp(Sp).] C1-t_r£,-7 T1549 where Ty) = To (1-ty) - (ty-t,). This expression is similar in several respects to Horst's [11] and preserves his insight that the MNC will set 1, as low as possible if Tt) > 0, i.e. if Ty > (ty-ty) / (1-ty). Note that Roo = So oPpo (So) In a similar fashion, the objective function of the third country firm may be written as the sum of their after-tax profits from producing and selling their good 3 at home and from exporting it to country 2, as
follows:
-¢Cc . eed . (5) [53 (S5) 3835 * s,.)| (l-t,)+£,(1-t5) [ 85268) | 73T3535 where T3 = T, (ity) - (t,-t3)
Finally, the maximand of the native firms which for simplicity do no exporting ~
may be written as:
(6) LBa2“S2) - 4 Sgo) ] (1-to)
where R
42 = S19? p9 (So) and the cost functions C,(Q) and C,@,) differ.
The first order necessary conditions for market equilibrium are established when each firm maximizes its own objective function with respect to its own decision variables, while holding the other firms' decisions
constant, Firms, that is, take no account of the effects of their actions
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on others. The commonality of this assumption to all firms is guaranteed by the previous assumption of Cournot behavior on the part of U.S. subsidiaries and native firms.
The MNC maximize ith res t to S S and §S iving: e max zes W pec Ce) Ww? °12 99° giving
7 ' . ' _ = (7a) (R 1 mp) (1 t)) 0 °
1
- t - - - =
(7b) fa t,) (Ri> + ORo» / 0S)5) mT, (1 t) Cy 0 - ? - t s
(7c) £0 t,) (Roo + oRio / Sn Cc) 0
where R},* OR, J 08,57 Pyyt Sqy OP i; / d845 > 03 OR» / 2849 *
Si OP, / O85 <0, i#j. Note that 0C, / 084, ° dc, / dQ, since
oa, / oS, , = 1, j=1,2 and that oR y / Soa = ORs / dS since d855 / dSoo71, i=1,2.
Similarly, third-country exporters maximize with respect to S43
and S
. °
32 (8a) (Ry, - cy) (1-t,) = 0
£ et ' 2. ¢1- too = (8b) 3¢t 2) Bao ql tc, T,T, 0
Finally, native firms maximize with respect to S,9°
(9) (Ry, - C4) (I-t,) = 0
where R' =P +S, dP i = ere 42 12 42 re) 72 / 0S.5 since S5 / os, 1
The simultaneous solution of the six equations in (7), (8) and (9) produces the point of market equilibrium, The simultaneity arises from the
presence of interactive terms produced by the dependence of the demand function
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for each good on the quantities sold of the other goods. This equilibrium is clearly much more complex than Horst's [ 11] case which is somewhat similar to the three equations in (7) but without the cross-derivative temns owing to his assumption that Si5 and S50 represent identical products.
The market will reach equilibrium if each firm is in equilibrium. It is therefore required, and we assume, that each firm's second-order, Hessian matrix is negative définite. The set of partial derivatives of each firm's first order conditions with respect to its own and the other firms' decision variables produces the 6x6 matrix of second-order conditions for market equilibrium set forth in Table 1, Note that the matrix is assymetric and is not a Hessian. The Hessians for each of the competitors are outlined diagonally. The restriction that these diagonal blocks are negative-definite is not, however, sufficient unambiguously to determine the sign, let alone the size of the determinant of the market-matrix. © In the actual event, it is therefore necessary to estimate its components empirically and to evaluate numerically the relevant comparative statics
around the 1966 equilibrium, as we do in Section IV.
B. Export Displacement As noted in the introduction, two sets of arguments have been adduced to provide a basis for the existence of the export displacement effect. One is rooted in the perfect, partial or non-substitutabfility of the goods produced at home and abroad by the MNC and its FS, ignoring foreign market conditions, The second set involves hypotheses relating both to the degree of substitutability between the kinds of products sold, on the
one hand, by native firms and those produced by the MNC and its affiliates,
-1l1-
ose Le gelgg Tr zy 0 [ aia (74-1) (23-1) 0 SI 2%, z C65 7). n0(°%I-T) LE cgtlcg ZEgQiT gg ey (24-1) &3 Eo(*a-1) - Ey 9 (23-1) "3 [ yg (Ca-vs Csr “_ poe _ [ Clo QvEg zz eg tog ¥z8 Clcr + Ty |(-D) 3 T5(44-1- ZIsqQ c I ZI wo(ta-1)- | “ose z T_ It. | 11 To tae1- (°3-T) Gud- Wd) sP II oP ep cep €€cp Clcp elcp SP en mm mmmmemaend JoyACH OY} AOF XFIIVW AepAO puosss T e71qeL +)
ds
ds
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11
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22
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on the other; and to the market-behavioral reactions of native firms to changes in the decisions of U.S, subsidiaries. In principle, both sets of issues can be investigated in the framework of comparative static analysis. For illustrative purposes we shall focus initially on the first because of the analytical intractability of the assymmetric 6x6 matrix of market second-order conditions.
Consider, then, the symmetric, negative-definite. second order
matrix, M, for a MNC maximum, taken in isolation from the market as a whole.
d ds Shy S12 22
(1-t,) iy - ey) - (1-t,) cy
2 2 2 do” R oR d°R - (1-t_) cH £, (1-t,.) (RM + 22 £ (1-t,)C Biz + o°R22 ~(1-t;) ci tee
2 2 R R 2 d “12 0 “22 R £, (1-ty) ( + ____)} £, (1-t,) (RY, + eee) C3)
08, dS 08) 208.55
12° °T2 T2
Will increasing foreign sales displace U.S. exports? In other words, what is the MNC's trade-off between exporting and producing abroad? Intuitively, the answer should depend on the changes in the relevant marginal revenues and costs caused by shifting sales from one location to the other, Taking the context of balance of payments regulation let us examine the effect on S19 of relaxing a restriction that has had the effect of holding. Ss
22 some constant level, Soo. which is suboptimal for the MNC. We seek the ‘ene
to
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sign of dS, / dS... The effect of the assumed constraint is to remove the third of the three first order equations in (7). The remaining relevant conditions are (7a) and (7b) which we differentiate totally with respect to
549° producing
(10)
(1-0, ) (RY) = cy) ~(i-t,) ct
2 ~£,(1-t,) [2 Roo
2. —_ - OR ~(1-t,) cy £,(1-t,) (RY + —# dSq2 0812 . . . . R. ~(1-t, cn" 12 +> Bi 0879951
The determinant, D, of the leftmost matrix is necessarily positive according
to the second order conditions. Using Cramer's rule, the export displacement
effect (11) - w oC au as (1-t,) (RY, = CHD 0 12 — et { f 2 / 71 <0 ds. DY} -(1-t,)cr - p(l-ty)/d Rao ' St2 0812 J
2 + OR, / Sq 28,0!
2 2 Since 0 Ryo / OSpo O08y9 < 0 and d Ryo / Spo 8,5 < 0 if So, and Sj). are gross substitutes. Parenthetically, our apparatus points to a second effect, the existence of which has been completely ignored to date. It might be called
the "home-output displacement effect" of foreign direct investment and is
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obtained by solving equation (10) for:
12) dsj, / dS,, = Lj 44. ' /,2 \ 2) A441 B09 = —— | --tyyoy (Let) 8, (2°R,, + d-Ri» | OSp d8y9 OSp9 0849
Clearly the sign of dsi4 / dS. is determined by the sign of Cy: the effect will be zero under constant returns to scale.?
The result that the export displacement effect is negative when the MNC is considered in isolation might not seem surprising in view of our introductory remarks, But here the conclusion has a different basis from that of most arguments which incorporate the presumption that Si and Soo are homogeneous products. In our case the export displacement effect arises directly from the (partial) substitutability assumption. The effect will disappear, i.e. dS, / d5g, = 0, if the goods are indepen dent in consumption, a question which can be addressed empirically.
We adopt dS49 / dS50 as the relevant measure of export displacement because it embodies two essential requirements: it takes account of the alternative position and it is related to the MNC's optimal decisions. The requisite quantity reflects what would happen to MNC exports in the absence of additional direct investment (which assuming constant output/ capital ratios will produce proportionate FS sales increases). In the more precise language of our model this amounts to determining the shifts in the equilibrium value of S19 caused by relaxing the constraint on Soo if initially S99 is constrained to a suboptimal fixed value, given the presence of other competing products,
Our definition has the further advantage of flexibility over previous concepts. It is not restricted to extreme situations: rather,
its magnitude may vary depending on the empirical substitutability
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relationships between U.S, export goods and other competing products in foreign markets. It can readily accomodate complementarities (the “associated export effect") should they exist as well as independent goods. It could be modified to take account of intermediate goods - the compensating increase in U.S, exports of parts and components to subsidiaries as Soo rises to displace S10 - which we are forced to omit owing to data deficiencies.” Most importantly, it is directly extensible to the total market setting in which MNC exports and FS products compete with other goods in foreign markets. This last extension requires that we investigate the shift in
the MNC's equilibrium S,, decision when the constraint on Soo is lifted
12 under circumstances where competing firms equilibrium decisions may also change as a consequence and in turn affect the MNC and its FS. That is, we must employ the full, 6x6, set of market second order conditions. The difficulties of establishing directions and magnitudes for the comparative statics in this case have already been mentioned. We therefore perform this extension numerically in Section IV, where we seek to compute the signs and sizes of the export-displacement and such other, more traditional comparative static effects as the impact on the various outputs of changes in capital costs and tax, tariff and exchange rates. These signs and sizes, which are the important information for policy, depend exclusively on the parameters of the included cost and demand functions. In Section III we
present the relevant estimates.
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III, Empirical Estimates of Cost, Production and Demand Functions
In this section we present the results of our attempt to estimate empirically the cost and demand function parameters suggested by the model of Section II, Clearly the results can only be treated as rough estimates, as the reader will readily observe. However, despite the ever present problem of comparability, discussed below, the results in the area where we tried the hardest--the estimation of cost functions for competitors--are, we think, encouraging. In any case, we hope that a description of our trials, tribulations and triumphs will in itself be of use to economists and policy-makers, For it cannot be repeated enough: if you want to estimate the effects we discuss, you must estimate, in some way, the magnitudes we sought.
A. The Production Functions and Cost Curves
We have estimated production functions, from which we have derived cost functions, for five markets: the chemicals market in Germany, Canada, and Japan and the electrical machinery market in Germany and Japan. In each market the production functions were estimated for three of the four major classes of competitors: for U.S, exporters, and for native firms and U.S. controlled subsidiaries in the host country. The one class of competitor that we have not adequately covered is the exporters to these markets from third countries, If we had cost estimates for all major exporting countries, then this problem could be | solved, either by generalizing our theoretical framework to a multicountry model or by weighting the cost functions of major exporters by their share of trade in a given market, Where it is necessary to estimate the
marginal cost of third-country exporters below, we use an average of
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the costs of the two relevant of our three countries, weighted by their total exports.
The major problems in getting the estimates that we need revolved, as one would expect, around the availability and international comparability of data, Naturally we need data disaggregated by classes of competitors, Further, to investigate the market for commodities that we suspected were close but not perfect substitutes, we felt it important to get data disaggregated as far as possible by product; the selection of the chemical and electrical machinery industries, S.I.T.C. 5 and 72; was an undesired choice made necessary by the unavailability of capital stock and other data at a greater degree of industrial disaggregation for countries other than the United States, Similarly our choice of countries was limited by the same data deficiencies.
The innovation in our empirical work has been to exploit a newly available source of micro-economic data on the costs and production of U.S. foreign subsidiaries. These data, available at present in crosssections for 1966 and 1970, were made available to us as one of the first users of the Multinational Data System developed at the Bureau of Economic Analysis, U.S. Department of Commerce!
The results presented in this paper are for 1966, the last full Census year. Rather complete balance sheet and income statement data were available, as is indicated inthe Appendix. Although limited in some respects, as is most cross-section data--for example, in the unavailability of a deflated measure of real capital stock--the data and our results compare favorably with recent attempts to estimate production functions from cross-section sources (cf, Griliches and
Ringstad [ 8 ]).
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For this paper separate regressions were run for subsidiaries in each industry and country; in most cases there were ample degrees of freedom, 20 or more; the major exception was the Japanese electrical machinery industry, where our exclusionary rules had to be relaxed to get even 14 observations.
A multitude of sources were used to collect data on native or indigenous producers in each country. The relevant data tables and sources are presented in the Appendix. These data, unfortunately, have several weaknesses: the time series are fairly short, primarily because capital stock data are usually unavailable for years prior to 1957 or so. A fundamental drawback with these series is that the data are aggregates of the operations of both native firms and U.S. foreign subsidiaries. Owing to the lack of comparable time-series on foreign subsidiary operations, it is impossible to obtain clean series for native firms alone. The following table indicates the seriousness of
this aggregation problem for each of our cases:
Table 2
12/
Ratio of Foreign Subsidiary Sales to Total Market Sales 1966 — Chemicals Electrical Machinery Germany 06 13 \
Japan 005 O01 Canada 86
Clearly the major problem is that in Canada it is hard to talk at all about a native sector in the chemical industry. Fortunately our cost
results indicate that there is little difference between the cost estimates
eh, f
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for the foreign subsidiary sample and the so-called native firm timeseries. The impossibility of clearly isolating native firm characteristics from those of U.S. foreign subsidiaries will persist until either the United States or the host countries decide to provide time-series of adequate production and cost statistics for one class or the other or, preferably, both. Results for Production Functions
Our major finding was that there was no evidence of increasing returns to scale in either sample. Further, the preponderance of the evidence points to constant returns to scale for each class of competitor. This, of course, is an important result if it holds up. It should be
recalled that many of the possible patterns of behavior discussed in
‘the context of theoretical models such as our own and Horst's depend
importantly on the presence or absence of increasing or decreasing returns to scale in production, In Horst's model [{ 11], discussed above, the finding of constant costs implies that there will be no interior maximum, Except where tariffs cause distortions, we would observe all production occurring in that locale with the lowest costs of production. In our models, constant costs do not necessarily imply a corner solution of the above sort. However, the slope of the marginal cost curve appears in the second order conditions for each firm and in the matrix of second order conditions for the market as a whole; with constant costs the slope of these marginal cost curves all are equal to zero; hence only the slopes of marginal revenue curves remain in the second order conditions. This, of course, does not mean that costs affect
nothing in the model, Marginal cost terms appear in the numerator of
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many of the comparative static calculations. They also affect the final equilibrium levels of all the outputs of the four classes of competitors. The results for the native firm regressions were generally so weak that virtually no sensible hypothesis on returns to scale could be rejected, For foreign subsidiaries the results were much more interesting. When materials (plus components) was used as an independent variable along with labor and capital, all three coefficients were usually significantly different from zero; and in the vast majority of cases constant returns to scale could not be rejected at the 5% level of significance, When materials were dropped from the production function, significant decreasing returns to scale were detected for virtually all specifications, unlike the results presented for many previous crosssection studies (e.g., Griliches and Ringstad [ g ]). However, we feel that the statistical results favor the regressions which include materials, First, the R*'s are greater for these variables--for the same dependent variable, output. Second, and most important, the significance of the coefficient of the materials variable tends to reject the hypotheses that justify the alternative regressions using labor and capital alone: i.e., that materials are (1) linearly related to output or (2) that materials enter in the production process in fixed proportion to output .22/ Fortunately, we found also that our best production functions also produced our best cost functions. ‘ The results for the best foreign subsidiary and native firm regressions are present in Table 3 below. All such results are for
the Cobb-Douglas specification of the production function:
Q= AL2gby!-2-b | Constant elasticity production functions were also
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-21-
fitted for some specifications for both sets of data. However, for
the n ‘ive firm regressions, Cobb-Douglas forms proved superior to all CES forms; both to maintain symmetry with the native firm results and because one cannot apply CES forms to production functions with more than two inputs without further assumptions ~~” we have so far limited our investigation of the functions which include materials as a variable to the Cobb-Douglas form, Future work with more general production functions may prove useful: However, Griliches and Ringstad [8 ] found that, in virtually all cases, the CES did not improve upon the Cobb- Douglas results (p. 63).
In the native firm regressions, as the following tables show, a variety of dependent variables and measures of the capital stock were used; the latter variety was forced upon us by the limited availability of data. In all cases, however, the measure of labor input that seemed to perform best was some form of total payroll--rather than number of employees,
For the foreign subsidiary regressions, a single form performed as well as or better than all others in each country; this used output as the dependent variable and payroll, net capital stock plus inven-
15/
tories and a measure of purchased inputs as the independent variables, Cost Functions
Although it is possible to develop the theory of Section II entirely in terms of production functions, we have chosen to do so in terms of cost functions, thus fitting our model into a familiar theoretical framework, This means we have to derive cost functions, either by
oie
direct regressions or by deriving them from our production functions, ~~
“et
wee,
-22-
We have chosen the latter path, thus allowing us to calculate the effects on costs of changes in input and output prices and permitting an independent check on the validity of the production function results.
From the Cobb-Douglas production functions with constant returns to scale, it is well knownee! that cost functions of the following forms can be derived, making costs a function of the parameters A, a and b of the production function and the prices of labor (w), materials (P) and capital services (ccap). Form(13) below corresponds to the production function estimated with materials included and form(14) with materials excluded:
w? ccap? pst
l-a (4c) = ers Q+ Pp, M
(1-a) In the Table below we present our estimates of the average and marginal costsez/ for 1966. for each of our four classes of competitors in our five markets. ‘These are derived from the cost function corresponding to the best production functions presented above. Each estimate assumes that 1966 wage rates and prices of materials prevail; as can be seen in the Appendix these prices cause us no trouble because they are embedded in our estimate of the constant term of the cost function and the 1966 materials/output ratio. However, deriving a figure for the cost of capital services is another, more difficult story. Since in our estimates
we, like all other researchers, use measures of the capital stock as
inputs and since there are virtually no payments for the annual rental
-23-
of capital stock, we must derive an independent estimate for the cost
of t... capital services that are produced annually by the firm's
capital stock, As Jorgenson and others have discussed at length, 22!
the annual rental price (ccap) in models such as ours of any asset should equal: r+d-q/q, where r is the firm's cost of capital, d the depreciation rate on the asset and q/q the rate of increase of the price (q) of a unit of the asset.
Estimates of the actual depreciation rates on capital assets vary widely. For the U.S. manufacturing sector, rates between 13 and 16% have typically been used 22! But, in a recent article, Coen=2/ has noted that for the industries we are studying the Treasury Department's average useful lives calculations imply the overall depreciation rates of 8,3% and 6.5% for the electrical machinery and chemical industries
respectively.
Any estimate of the cost of capital, r, depends importantly on “ the assumption concerning the financial theory of the firm, the existence of perfect or imperfect capital markets and the like. Little has been done to link the theoretical variations to specific numerical estimates .22/ Here of necessity we shall, like most other empiricists, assume that
the firm exists in a perfect capital market, Even so this does not
make things much easier; estimates of r for 1966 have varied from .104 (Jorgenson and Hall) down to the Moodies Industrial Bond yield (.053)
or even to the average 1966 dividend/price ratio for U.S. manufacturing
stocks (.035).
For the United States in 1966, if we exclude the term -4/q as most’.
others have, these estimates lead to a possible range of r+d from .0971
-24-
to .264, For expository purposes we present estimated costs for the U.S. subsidiaries and parents for a value of ccap equal to .25 for the gross capital stock measure (the measure clccest to the domestic measures), This estimate is on the high side of our range, but for the U.S. subs leads to values of predicted costs that are closer to our estimates of actual costs. This value, .25, is also close to the value for native firms that allowed the best prediction for 1966[ 2 ].
A note should be added here on the final column of the succeeding table . The calculation of the derivation of actual from predicted costs is based upon an estimate both of actual as well as predicted costs. Costs reported by the companies and subsidiaries do not report actual costs related to capital services in any sense acceptable to economists; depreciation does not reflect, in many cases, actual economic deterioration; and profits need not measure well the cost of capital, Hence for our estimate of "actual" capital costs we have substituted our own figure, ccap times the capital stock measure. This procedure is explained at greater length in the Appendix.
B. The Problem of Demand Function Estimates
For reasons explained briefly below, the estimates of the comparative statics presented in Section IV do not rely on our empirical demand function parameters. Rather, they employ putatively reasonable values of the income, own-price and cross elasticities, The basis for these assumed values is as follows.
Recall from Section II that our theory requires parameters for inverse demand functions of the form Pay = Pi4($)) where i is subscripts
products and j, markets, while Sj is the relevant goods vector in
-25=
country j. The requisite parameters can be obtained by inversion from direct demand functions of the form S35 = 8; 5 (Bj. ¥4) where Bj is the relevant price vector and Yj denotes income, both in market j. Loglog regressions were used to estimate Cobb-Douglas renditions of
the direct demand equations for each of the three products, S39.
i= 1, T, 3, in each foreign market:
(15) S;5 = 4569 pil? Pa Pye yy, where
Pig = U.S. wholesale price index for the relevant good;
Pro = Country 2 wholesale price index for the relevant good;
P39 = Average of the wholesale prices of major exporters other than
5 the U.S. weighted by their share in exports to 2;23/ and the 8552
4 are the elasticities such that 2 a. = 0 in the absence of money
1 ij2~ illusion. No regressions were run for home-market sales of either U.S, MNC's or third-country firms,
The partial price elasticities may be arrayed to form the 3x3 matrix Ay: Pi2s Pras P32
S19 4112 7172 4439 7142 Sq2 “712 7rr2 2732] = Ags and S42 = 9742 S35 *312 4372 3332 a19
is the column vector of income elasticities, Note that Ay is not sym- 24/
metric.” The system of demand equations in country 2 may now be
rewritten in log-log form
log Sy = I log agp + Ag log poy + By log Yo
where underlining denotes a vector of logs, I is the identity matrix, 4,2 is the vector of demand-equation constants from above and B, isa
diagonal matrix with 4j42 in the ith diagonal element and zeros elsewhexe,
Noe
COUNTRY AND INDUSTRY
Cost of Capital Production Costs Total Costs per $
Class of Services (Gross per $ of Output of Output Producer Capital Basis) (1966 prices) (1966 prices) United States & Native Native Native
Toreign sub2/
Foreign Sub(best
Japan ectfica
Native 3/ Foreign Sub
Foreign Sub (best
Native Native Native €orei gn sub2! Foreiga gub(bes t
German Chemicals
Native Firm 225 79
3/ ; Foreign Sub™ .25 092 95
Foreign Sub(best .25 . 83 86
Canada Chemical
Native 25 80 98
3/ Foreign Sub- =.25 84 85
Foreign Sub(best
1 Y sources! Production functions in Table 3
2/Revalued net fixed assets used; thig value was omewhat greater than the book val
function.
Calculated Error of relevant cost prediction for 1966.
(Actual-Pred)/ Actual
17%
not calculated for sample
+2.47 +17%
+10%
+1%
18%
-3%
not calculated for sample
+20.6%
+9.8%
1%
11%
“21% +19%
+112
of net fixed assets,
3/This fuhction used the same form and, wherever possible, the same variables as "| best nazive firm production
-26-
Solving for the log price vector is a simple computational procedure:
_ acl -l -1 (16) log pp = Ag log Sy - Ag B log YQ - Ag I log apo | If the goods are substitutes, we know that the elements of A5t, denoted e442 will be negative for all i, j[ 10 , p. 182]. The matrix (a7!) will be diagonal, Its ith row elements, C;5 = €;494j42> will be negative since asn2 ? 0, as will the coefficients of the constant terms. These provisions are expressed in the signs of the exponents and constants of the ith inverse demand function corresponding to the
25/
Cobb-Douglas specification above:— GQ) pp = Crop8tnte sit? 5/132 vi where C42 = (antilog aio2) tt. Since the marginal revenues of all the competing firms at equilibrium must be positive, we would expect for any reasonable set of estimates of as 52? that 0 < eij2 < 1. This expectation is confirmed by the e442 values which we compute via equation (16) from pre-set price elasticities in Section IV.
In practice, the OLS regressions used to estimate the parameters of equation (1) usually failed to produce significant own-price or cross elasticity coefficients. In two instances, own-price elasticities had significantly negative signs while the cross elasticities did not significantly differ from zero. Equally usually, however, the income elasticities were positive and in the case of both import categories frequently exceeded one by a significant margin,22/ These empirical results are largely useless for our purposes, which, because we are supposing a market of substitutes, require negative own-price elasticities
and admit zero cross-elasticities (independent goods) only as a special, Oe
-27-
somewhat unlikely case. Our alternative for this paper was to pick the
plausible elasticity values as specified in Section IV.
~28-
IV. Comparative Statics This section presents the calculations for the changes in the output levels of the multinational firm and its competitors induced by
changes in various exogenous variables. First, as detailed above we
model the export displacement effect by constraining the output level of the foreign subsidiary and calculating the effects as the constraint is relaxed by one unit. Besides the export displacement effect we have calculated the effects of a (small) change in tariff and income tax rates
of the foreign country, the exchange rate of the United States and the cost of capital of the multinational firm.
All such calculations are for small changes in the exogeneous variables at the 1966 equilibrium for either the 6-good market set out above (determining the comparative statics ds,,/dx, dS, 5/dx, dS5o/dX, ds, /ax, ds, ,/dx, ds, ,/ax, where X is the exogeneous variable) or for the multinational firm alone (determining ds, ,/ax, ds,_/dXx, dS, ./dx in isolation).
Technically speaking, as is fairly well known the comparative ~ statics of the system of lst order conditions (7) alone or (7), (8) and (9) of Section II -- are calculated according to Cramer's rule as a ratio of two determinants.” The denominator is the determinant of second derivatives of the system -- for the full system the determinant of the matrix set out in Table 1 above; the numerator is that determinant with one ccivwm replaced by the column of derivatives of the first order conditions with respect to the exogenous variable, X.
In calculating numerical values for these determinants we have assumed the 1966 values of the prices, quantities, costs and levels of
exogenous variables, Thus our estimates attempt to portray a small Nee
-29-
displacement from the 1966 equilibrium.
We shall use the best cost estimates presented in the last section. AS a consequence we assume constant returns to scale and all the cost terms (cr ) in the matrix of Table 1 become zero. Thus the denominator of our comparative static calculations is a function of slopes of marginal revenue curves and exogeneous variables alone. We shall see below that the effects, particularly their sizes, are very sensitive to the revenue curves assumed.
For all alternative demand curves we have scaled the constant term so that the equation is satisfied for 1966 values. This scaling involved two choices of units of measurement which we do not think affected any of the results, Since our demand functions are Cobb-Douglas, the constant term B. was defined so that P Ss, =B (S y* cy, y> r (Ss 5
| i 1,66 "i,66 i° 1,66 ° 1,66 jay f° >” where P and S are price and output, Y is national income and the 66 subscripts indicate 1966 values; a and b, and the c,'s are the assumed elasticities of revenue with respect to quantities and income. Quantities were measured in 1966 price units in the currency of the country where the good was sold. Prices were measured as an index of 1966 prices; hence the actual 1966
price becomes 1.
A. Demand Alternatives and Their Effects As discussed in the last section we have no demand curve estimates that we believe with any confidence. Hence in the simulations a number of alternatives were tried. One of the most noteworthy developments
in our calculations was that variations in the size of the own and cross-
-30-
elasticities of demand had very marked effects on the results we got; this © was true even though in every case all goods remained gross substitutes and the Cobb-Douglas form was maintained.
The demand cases we tried can be described by (1) the absolute size of the own and cross-elasticities (2) their relative size and (3) whether money illusions was present (whether the sum of the price and income elasiticities was different from zero). The spectrum is defined in the following table. The elasticities for a typical equation are presented for each of the cases; the own elasticity is the largest
number in absolute value, appearing in the leftmost column,
Demand Alternatives: General Case Case Price Elasticities Income le Normal; no money illusion -4 +1 +1 +1 +1 2. Normal; money illusion -2..2 .2 .2 +1
3. Small Cross Elasticities; no money illusion -2 .05 .05 .05 1.85
4. Large elasticities; money illusion -7 2.0 1.0 1.0 1,2
As will be seen below, these small cross-elasticities turned out to be virtually necessary conditions to get all the effects of sign and size that have been customarily assumed in the literature on direct investment.
Cases 1 and 4 led to the violation of the second order conditions
for the MNC, as will be discussed more fully below. Consequently,
TABLE 5
Export Displacement Effect
(Small Cross Elasticities; No Money Illusion)
Electrical Chemicals Industr Machinery Canada German Japan German Japan
S92 & S42 Identical
481/48), 0 0 0 0
481 9/ dS -0.04 | -0.06 — |-0.05 -0.05
dS4,/ dS)5 -0.001 | 0.0005 | 0.0002 0.0003
dS33/ 4855 0
aS,/ 48,5 1.08 All Goods Different
4511/89 0 fo
dS; 5/ dSoo -0.04 |-0.11
dS4,/ dS,, -0.03 | -0.04
dS33/ dS oo 0 0
ds, ,/ 435, -0.52 | -6,32 MNC Alone
dS 11 / aSp9 0
dS, 5/ dSo0 -0.11
| |
Notes:
a. The relevant vector of derivatives of first-order conditions is omitted here since it was derived in essence in Section Il.
TABLE 6
The Export Displacement Effect
(Normal Elasticities Case; Money Illusion)
| Electrical Chemicals Industr Machiner Canada Japan German Japan S99 & Syo Identical ds, 1/4899 0 0 dsj 5/4829 -0.84 | -0.26 dS4,/4529 0.32 | 0.01 dS 33/4899 0 0 dS,,5/485, 6.32 | 3.07 All Goods Different 4811/9895 0 ds; 9/4899 -0.51' dS4,/45,, -1,13 dS 33/4855 0 a,,/*22 -23.8 : | “MNC Alone dS 11/4899 x 0 0 0 0 481/522 x -0.58 | -0.35 || -1.10 | -0.57
Note: (*) Asterisks indicate that the second order conditions for an MNC manimum are not satisfied.
-31-
the Tables and discussion below concentrate on cases 2 and 3,
Cases 1 and 4 demonstrated that the choice of the demand curve often had a significant effect on the second order conditions for the multinational firm, In a number of cases, what we thought were. plausible elasticities turned the upper left hand 3x3 block in Table 1 into a positive definite sub-determinant, which implies that the equilibrium is a profit minimum rather than a maximum for the MNC, The major culprit was the second diagonal term which should have been negative: f, al - to) Ryo + 3°R 9/284): The last element of this term, which is always positive, must be outweighed by Rig? which is always negative. This frequently was not the case, particularly when the size of the F.S. sales (Roo) were large relative to exports from the United States, This can be appreciated by noting that for the Cobb-
j R woe. . Douglas case, Rj» = €149 61 €112) so and 12
3°Ry9/ Ss, = -€949(-€919 -1)R9/Si95 where €,, is good Sj9's ownquantity. elasticity and €012 is the cross-quantity elasticity of good
2 with respect to good 1, Since 1 - e;;9 must be > 0, Ryo is negative. Now if for 1966 the revenue from foreign subsidiary sales (Roo) is much greater than the revenue from U.S. exports (Rj 9)> then unless e€5, is very near zero, the second positive term will outweigh the negative term. This seems to indicate that we cannot have both the Cobb-Douglas demand case, a rather high cross-elasticity of demand, and observed sales levels that are widely different. The disparate levels of sales that in fact existed in 1966 are also probably responsible for some
derivatives that are surprisingly large in absolute (though not percentage)
-32-
terms--even when all second order conditions are satisfied.
The entire set of comparative statics analyses are presented in Tables 5 through 14. There are two tables for each effect, reflecting the selection of the two different sets of assumptions regarding elasticities as discussed above. The format of the tables is identical. Each presents results for three separate models: (a) the market when S99 and Syo are treated as identical goods without separate demand parameters; (b) the market allowing S99 and S42 to be distinct products with, however, the same own and cross elasticities as the others; and (c) the MNC in isolation. For reference we set forth in the table margins the column of derivatives of the first-order conditions with respect to the given exogenous variable, which replaces successive columns in the determinant of the relevant matrix of second-order conditions as each comparative statics effect is calculated.
wee
The Export Displacement Effect —_— Tables 5 and 6 present the comparative statics for a unit relaxation of the constraint on foreign subsidiary sales, The disparity of the patterns in these tables reveal the variability of this effect, in particular, with respect to demand conditions abroad. As one would expect, the smaller the cross elasticities, the smaller will be the shifts in the equilibrium quantities caused by dS59. The “home-output displacement effect," dS14/dS505 is zero everywhere, since we incorporate our finding of constant marginal costs, Reading from the bottom, the results for the MNC considered in isolation hold few surprises.
The export displacement effect, dSj9/dSo55 is invariably negative if
the goods are substitutes as predicted by equation (11) above. If
-yo-
the cross elasticities are sufficiently large, however, we get the unusual possibility for the Table 6-cases of the German and Canadian chemicals industries,when cross elasticities are relatively large, that dSj5/dSo9 <-1l. This outcome is probably unlikely in practice andis not observed in Table5 . It doubtless arises as a result both of the Cobb-Douglas specification of the demand functions and the particular numerical relationships among the specified own-price and cross elasticities which affect the size and can change the sign of the second diagonal element of the market matrix in Table l, as mentioned above.
The sensitivity to specification underlies the variety of patterns which are revealed in the full-market context, When all four products are assumed to be differentiated and cross-elasticities are relatively small, the Table 5shifts in all equilibrium sales values with respect to dS» are negative as one might surmise on prior grounds, A puzzle is the large displacement of native firm sales in the Japanese electrical machinery industry which is repeated in the comparable case in Table 6 . What disturbs preconceptions, however, is that when cross elasticities grow relative to own elasticities and all products are differentiated Table 6 shows that the universal negativity of all effects breaks down. Several unfamiliar patterns emerge. While U.S. exports seem always to be diminished, the effect on native firm sales and third country exports can become either negative or, startlingly, positive. Similar positivity is evident when Soo and Sy9 are constrained to be identical.28/
While the demand assumptions seem reasonable and have been used
by others some of our results seem empirically implausible. Consider
= 2be
the case where dS,5/dS22 <0, 0 < dS3o/dSj5 < 1 and dS4o/dSo9 > 1. Baldly interpreted, a unit increase in FS sales will displace U.S. exports, encourage host country imports from third countries and generate additional native firm sales of more than one unit. Are F.S. sales an engine of growth? We think not. But we do not hesitate to point out that our results reveal exceptions to common expectations and to insist that the demand-parameter measurements we seek are a prerequisite for policy to be aimed accurately. Exchange Rate Changes.
Tables 7 and g provide the comparative statics for a devaluation of the dollar relative to all other currencies. Our analysis is necessarily incomplete for our model excludes macro-economic policy relationships and therefore omits all considerations relating to price and income changes flowing from the international adjustment process. A consequence of this omission is that both exporters' home-market sales, $i and $33» remain unaffected by the devaluation.
Nonetheless, the results tend both to camfirm simple prior expectations and therefore to reinforce belief in our approach. Ceteris paribus, one would expect a dollar devaluation to increase optimal MNC exports and to reduce its equilibrium level of foreign production. This pattern is apparent in all instances, under both sets of elasticity assumptions. One would also expect optimal third country exports, S39> and native firm sales, S42 to decline. Generally this is indeed the case. The possibility remains ( Canadian chemicals and Japanese electrial machinery) that interactive demand effecss can reduce the incidence of the devaluation on S35 to the point ~
that dS3o/éf, > 0.
-34a-
The magnitudes in Tables 7 and8 are meaningless without further interpretation. The derivatives are expressed in millions of currency units of good Say per dollar change in the exchange rate, f,- Clearly a dollar change in the 1966 exchange rate for any of these countries would have been an enormous one (e.g. about a 400% increase in the German case). However, we can use the derivative to calculate the effect of more realistic changes, say a 10% devaluation of the dollar with respect to each currency. The absolute effect of such a devaluation would be found by multiplying the respective columns by the following constants: .0926; .0251; .000276; .0251; .000276.
In many cases the sizes of these effects seem quite reasonable. Thus, taking the effect on U.S. exports to the host country as an example, the absolute effects in the first non-zero row of Table 7 imply the following percentage changes in export quantities (measured in 1966 dollars) for a 10% devaluation of the dollar: 23% for Canadian chemicals; 22.5% for German chemicals; 21% for Japanese chemicals; 23.5% for German
electrical machinery; 20% for Japanese electrical machinery. (see Table
A4).
Table 7
Comparative Statics for a Change in Country 2's Exchange Rate® (Small Cross Elasticities: No Money Illusion)
Chemicals Industry Electrical Machinery Canada Germany Japan si“ ss«SGermany Japan S99 & Sao Identical ds, ,/d£, 0 0 0 0 0 ds, ,/afy O.11x10+ 064x100" 0.60x10° 0.41x10¢ 0.22x10° aS,5/4fy -0.014x10* -0,008x10 -0.003x108 -0,005x10% -0. 38x10" ds,,/4f, -0,0007x10" -0,063x10° -0,020x10® -0.041x10* —-0. 25x10" 4s4,/4f | 0 0 0 0 9 as,,/4f, -0.0001x10* -0.43x10* -0.52x10® = -0,69x10* = -0. 44x10 All Goods Different ds, ,/4fy 0 0 0 0 0 a8, 5/44; 0.11x104 0.61x10* 5835x104 38x10¢ 2207.. JM ds,,/ af, -0.013x10* -0.052x104 -369..x10% ~.040x104 -91x104 4845/ 4f 0.0007x10* -0.059x10% — -190.x104 -.037x104 -22x104 dS33/ df) 0 0 ) 0 0 as,,/ af, -.0011x10 -0,45x104 = -5267.10* ~~. 67x04 -3929x10 MNC Alone ds,,/ 4%; 0 0 0 0 0 as, 9/4 O.l1xl0t 6 1x10+ 5827x10 —0,38x10* + 2205x104 48 9/ ~-0,013x104 — -0,054x10 — -379,x10* —-0, 042x10% 92. x1 04
o —— te
Note (a) The relevant derivatives of the first-order conditions in (7), (8) and (9) taken with respect to fy, and transposed to form a row vector are:
0, -(1-ty) (dRg2/dSjo+dR12/dS12), 0, 0, 0, 01
Table 8
Comparative Statics for a Change in Country 2's Exchange Rate
(Normal Elasticities Case: No Money Illusion) ,
rr rear nrenetn e t ereeeneeeenecenneee
. Chemicals Industry Electrical Machinery
Canada Germany Japan Germany Japan Soo & S,o Identical © . ,
as, ,/4f, 0 0 0 0 0
ds, ,/4f, 2.09x104 1.30x104 -85x108 1,34x10° | .24x10°
as, / af -.87x104 -.069x10% -,016x108 -.06x104 -,00018x108
és,/4f, -.05x104 -.52x10¢ =, 11x10° -.54x10¢ —_-,01x10°
d8,,/4£, 0 0 0 0 0
as,,/ df -.006x10" -3.51x10° -2.93x108 --8.89x104 = -1.89x10°
a Enema nee -A1ll Goods Different
* 0 0 0 0 dS ,/ 44, . as, ,/4f . * 1.40x10° .83x10° 369x104 1.20x108 ds,,/ 48, * -.58x10' -,.282x10® = -1. 78x10" —-1.91x10° 4 4845/ 4£ * - 50x10 -,093x108 —-1, 36x10* »245x10° * 0 0 0 0 as ,/ 48, * --3,82x10* = -2 57x10 -24.52x104 43.56x108 MNC Alone | * 0 0 0 0 as,/4f) . 1.35x104 .81x10° 3.34x10¢ 1.17x10 a 8 4 8 a809/ dE . . - 64x10" -,30x10 -1.87x10 -1.66x10
NOTE: Asterisks indicate cases where the second order conditions for an MNC profit maximum are not satisfied
Table 9
Comparative Statics for Tariff Change in Country 2.=
a/
(Small Cross Elasticities; No Money Illusion)
Chemicals Industry Electrical Machinery Canada Germany Japan Germany Japan Soo & S42 Identical as. ./dr, -0.22e10 = -1,21x10% = -1.15x10® = -0.77x10# = 41. 74x10 12 &849/4ty 0.03x10* 0.02x10* 0,005x10 0.01x10+ 0.007x1( as,,/dr, -0.04x10* -0,90x10% —0,03x10® = 053x104 0.42x10' 32 0 0 0 0 0 4844/dt5 , as,,/47, 0.0006x10* — 1.00x10 1.00x10° 1,54x104 83.03x10° All Goods Different ds, ,/4T) 0 0 0 0 | 0... ds,,/4r, -0.22x10* -1,22n10% —-1.15x10° -0.78x10* -41.92x10° dS,./dro 0.0410" 0.12x10% 00 7x108 0.09x10* 1.73x10° as,,/4r, -0.04x10" -0.91x104 0.03x10° -0.53x107 0.37x10° aS53/dt) 0 0 0 0 0 ds,5/4t, 0.004x107 1.11x104 1.04x10° 1.66x10" 74..84x10° MNC Alone as, ,/ar2 -0.23x10" -1.23x10* -1,15x10° -0.79x10* 42.0x10° 4859/4 0.03x10* 0.11x104 0.07x10° 0.09x10" 0.2x10° a/ The relevant derivatives of the first-order conditions in (7), (8), and (9),
taken with respect to tg and arranged as a row_vector. | t
1 10, (L-ty) 2, 0, (1-tg) ¢3, 0, 0 |
-35-
Increasing Tariffs in Country 2.
The comparative statics analysis of this case appears in Tables 9 and10. All other things being equal one would expect a tariff increase in country 2 to reduce the MNC's optimal exports to country 2 and to raise the equilibrium level of its FS sales. This expectation is confirmed unambiguously in all cases. One would also expect the tariff increase to protect native firms and cause the optimal level of Si to rise. This expectation is also largely confirmed with Japan's electrical machinery industry being a possible exception. |
Somehow, a uniform tariff increase might be expected to reduce imports from all sources especially when the import products are similar, though not identical. Our model, however, tells us clearly that this need not be the case. There are several instances where dS3/drg > 0. When cross elasticities are small, these cases are confined to Japan. But when the cross elasticities are larger (Table 10) dS35/dto turns positive more frequently. There is no obvious explanation for this unusual result.
The Effect of a Rise in Country 2's Tax Rate.
Tables 11 and 12 set forth the relevant comparative statics. All others exogenous factors held constant, one would expect a rise in ty to raise equilibrium MNC exports and reduce optimal F.S. sales. This result is apparent in all versions of the model under both sets of elasticity assumptions.
: It is interesting that the effect on native firm sales,
dSyo/dt, is usually also negative. It is well known that corporate
Table 10
Comparative Statics for a Rise in Country 2's Tariff Rate _
(Normal Elasticities Case: No Money Illusion)
Chemicals Industry Electrical Machinery Canada Germany Japan Germany Japan
So & S42 Identical
ds, ,/dro 0 0 0 0 0 ds, ,/ary -3,.82x10¢ -2.39x10+ -1,64x10° -2.44x107 -.458x10° 8 ds,./dt» 164x107 142x104 .032x10° .117x10% .0003x10 é84,/dr, 055x107 - 082x107 .218x108 .358x10¢ 020x108 0 0 0 0 0 ds,/dro 4 4 8 4 8 All Goods Different * 0 0 0 0 dsj ,/dr, ‘ 4 8 4 8 8 d8,/dr, * 1.71x10% .685x10° 5.94x10" 3.91x10 ds,,/dr * 356x104 .221x10°® 3.86x10" -.502x10° 4 8 _ 4A 8 d5,9/d7, * 11.72x10 6.25x10 82.08x10' -89,0x10 MNC Alone 4 8 4 8 a8, ,/ ar, * -3.89x10 -1,98x10 -11.16x10 -2.39x10 as, 4/ dry & 1.83x10° .735x10° 623x103, 39x10" NOTE: Asterisks indicate cases where the second-order conditions for an MNC
profit maximum are not satisfied.
Table 11
Comparative Statics for an Increase in Country 2's Tax Rate2/ (Small Cross Elasticities: No Money Illusion)
a NNR
Chemicals Industry Electrical Machiner Canada Germany Japan” Germany _Japal Soo & Sy,o Identical , | ds,,/dt, 0 0 0 0 0 as, ,/at, 0.31x10% 1.94x10¢ 2.55x10° L.2hx10% 1.02x10° 4s,,/at, -0.05x104 -0,03x10" -0.01x108 —-0,02x10 0, 02107 ds, /dt 0.05x104 0.77x10* -0,08x10° 0.43x10* — -0.. 11x10! as,,/dt, 0 0 0 0 0 dS,,5/dty -0.001x10¢ -1.48x104 -2.21x10° -2.29x10% -2.04x10° a | | All Goods Different dS, ,/dt, 0 0 0 ; 0 — _0 ~ ds, ,/aty 0.34x104 1.98x10* 2.56x10° 1.27x10° 1.03x10° s,/aty -0,06x10* -0,18x10 + -0,16x10"— -0.14xl0* —-0. 04x10! 4845 /aty 0.05x10¢ 0.78x10+ — -0.08x10° 0.43x10* — -0, O01x1( dS5/dt, 0 0 0 0 0 d5,5/ dt, -0,005x10* -1.66x10* §-2.31x108 = -2.48x104 = -1. 84x10 MNC Alone ds,,/at, 0 | 0 0 0 0 as, ,/atg 0.34x10+ 1.98x10° 2.56x10° 1.27x10* 1,03x10' : aSy9/ ay . -0.04x104 -0.18x10° -0.17x10° -0.14x10° ~0. 04x10
ee NO a/ The relevant vector of derivatives of first order conditions, (7), (8) and (9), with respect to ty is transposed:
Lo, £1 (8R22/dS12 +dRy2/dS12) - (1-T9)¢}, 0, fo (8839/2532) - (1479)C3, 0, 0
-36-
income tax changes do not change the optimal output decisions of one-country firms considered in isolation. Clearly, an exception to this rule may emerge when the firms are considered in a market context, as a consequence of the shift of demand to imports.
This shift is not complete, however. For reasons that are not obvious, the tax-rate change may move the equilibrium level of
S39 either upwards or downwards.
Comparative Statics for a Change in the Cost of Capital
The cost of capital, denoted above by r, is just another cost, one element of the annual rental price of a unit of a firm's capital stock (CCAP). This annual rental price appears in the Cobb-Douglas cost functions, equations (13) and (14) above. The rate of change of costs with respect to changes in r is a function of the capital elasticity b: 3c/ar = bC/ccap.
For a single firm producing one product whose price and marginal revenue is unaffected by changes in r, it is clear that an increase in the cost of capital causes a reduction in the equilibrium output of the firm. However, there can be many variations on this theme when a production process becomes one of many in a multinational firm, First is the question of the dependence of the marginal revenue curve of a given product on the prices of substitutes, these latter perhaps being affected by the increased cost of capital. Second is the question of whe ther the cost of capital for operations in one locale is related to, independent of, or identical to that in another, Independence, of course, will be the rule if the international capital market is perfect.
It might be true only for all operations of a given MNC if the MNC can
-37-
overcome imperfections that beset smaller, native firms,
In this comparative static calculation we assume that all operations of the MNC possess the same cost of capital, .25 on a gross capital basis, but that it is at least partially independent of the cost of capital of native and third-country firms. Of course, alternative variations can easily be computed.
In the small elasticities case, Table 13, we see that, if the multinational firm is taken in isolation, the sign of the changes of sales is negative apart from two exceptions. One would expect these exceptions to the one good case to multiply as one gave fuller play to cross elasticities of demand--by either increasing the cross-elasticities directly or embedding the MNC in a wider market.
And that is what we see in the tables, In the normal elasticities case, Table 14, the exceptions increase to four, still taking the MNC in isolation. In the 6x6 market, even when cross elasticities are small, there are numerous cases of dS, 5/dr and dS,,/dr being greater
than zero,
TABLE 12
Comparative Statics for an Increase in Country 2's Tax Rate f (Normal Elasticities Case: No Money Illusion)
. Chemicals Industry Electrical Machinery Canada Germany Japan Germany Japan Soo & Syp Identical ds, ,/dt, 0 0 0 0 0 /dt as ene 5 .45%10¢ 3.93%104 3.65x10° 401x104 1.13%10° dt , dS99/4ty 2.344107 - .22%104 - .07%108 - .19%104 - ,0008%108 dS,,/dt, .08%10 - .56%10" - 49x10° -1,03%10" = .05 10° (dS,,/dt, 0 0 0 0 0 4 4 8 4 8 dS ,/dty - ,02%10° -11.3 »10 -12.66*10 -27.56*10 -8,94*10 All Goods Different dS, ,/dt, * 0 0: ; o 9 dS, ,/dty * 6.64%10" 4.48*10° 20.68*10" 6.04%10° dS, 0/dty * -2,82%10° -1.52*10° -10.05*10" -9 ,60*10° dS4,/dt, * -1.34%10" - .50810° ==: 7.0410" -1.23«10° dS33/dt, * 0 0 0 0 dS ,./ dt» * -19,.07*10" -13,86*10° -138.56*10' — 218,50+*10° MNC Alone dS, ,/dty 0 0 0 0 ds_,/dt 12/ dt2 * 6.50*10¢ 4.39*10° —18.86*10° 5. 87*10° d dSy2/dtz * -3,05*107 -1,63*10° -10.53*10' -8.31*19° Note:
*Asterisks indicate that the second order conditions for an MNC profit maximum are not satisfied. .
Table 13 Comparative Statics for a Change in the MNC's Cost of Capital (Small Cross Elasticities; No Money Illusion)
. Chemicals Industry ' Electrical Machinery Canada: Germany Japan Germany Japan Soo & Syo Identical | . ,
ds,,/dr -17.93 -17.93 -17.93 -18.25 -18.25 as, /at 0.53 “1.16 -1.25x104 -0.74 -0.45x104 . . 4
dS,_/dr -17.51 -1.75 36.35 -1.18 -0.47x10 ; 4
ds,,/ dr 0.02 0.12 417.1 0.08 0.51x10 ds,,/dr- 0 . 0 ° 0 °
Ce
411 Goods Different
~ d8,,/dr -17.93 - -17.93 -17.93 _ 718.26 -18.26 ~ ds,,/ar 1.10. -1.02 1.25104 -0.66 0.45x104 dS5_/ a -32.66 5.78 0.07x10% -3.79 0.02x104 484, /dr 5.03 0.35 0.04x104 0.19 0,45x102 dSga/dr o o- 0 0 0 dS,9/ ar 7.85 a.72 1.14x104 3.45 0.8x104 MNC_ Alone dS,,/dr “17.93 = -17.93 -17.93 18.25 718.25 ds, ,/ar 1.11 “1.02 =1,25x104 -0.65 70.45x104 A8o9/ dr - 132-62 -5.77 0.07x10-4 -3.79 0.02104
rd
9) The relevant derivatives of the first-order conditions in (7), (8) and (9), taken with respect to the cost of capital, r, and transposed into a vow vector . are:
F ca-tqre} cy /oe), (-tg V0} (1Hry)0G4/dx, £y(1-ty)C%D0" for. 0, 0, 0 |
Table 14
Comparative Statics foran Increase in the MNC's Cost of Capital (Normal Elasticities Case: No Money Illusion)
. Chemicals Industry Electrical Machinery Canada Germany Japan Germany Japan S50 & S49 Identical © . , Z ds,,/4r ~14,90*10" -14.90*10" -14,90*104 -15.25*10% -15.25*10 . 8 ds, ,/ ar -3.63*10" -2.83*10" -1,98*10 -2.92#10° 54910" dSoo/ dr 1.13*10¢ . .036*10° .036*10°8 .054*10" .0003*10° ds,_/ dr .093*10" 1.13*10" .267*10° 1.17*10° .025*10° ds,,/ dr 0 . 0 0 0 . 0 , 8 ds,5/ dr .040*107 7.57*10" 6.86*10 19,27*10 4,36
a LL SS SSeS ss ss SSS All Goods Different 4 4
ds, ,/ ar -14.90%10* —-14.90*10 —-15.25#10" —~15.25».0" ds, >/ ar * -4.26*10° -=2.4310° = -13,. 28104 ~~ -2. 9410 ds,,/ dr * 1.24107 -0, 81*10° 6.09*10* 2.94108 ds,,/ dr * 1.62*10¢ .27*108 4.95*10% | -.598x10° dS33/dr * 0 0 0 0
as,o/ 42 : * 12,421 04 7.53*10° 89.08*10 -106.16*10€
MNC Alone
as,,/ a . -14,90#10' —-14,90*10" == -15.25"10* 15, 25*10° és,,/oF * a4stze10 ~—-2, 384108 =~ --12, 0110" 2, 86108 dSoo/ 2 1.43*10* .87*108 6.39%10¢ ge 498
ee
NOTE: Asterisks indicate that the second-order conditions for an MNC profit maximum are not satisfied.
-38-
V. Concluding Remarks
The comparative static results are the end of our story. They reveal to policy-makers, we think, the dangers of ignoring market interactions between the MNC and its competitors and acting on simple assumptions which do not take these effects into account.
To economists and policy-makers we hope a further, theoretical, implication comes through. It is possible to model the trade-direct investment nexus, By deriving and estimating the demand and cost functions of the major competitors in a market, it is then possible to answer the question so many have despaired of answering: what would have happened if the direct investment had not been made?
But successful prediction requires an accurate picture of the world, As is so often the case, the accuracy of our view of the trade-direct investment nexus is marred by severe empirical problems, To fully test this model we especially need the data to permit more refined estimates of demand functions. it is to be hoped that modern demand theory, the thrust of which is to estimate demand systems rather than functions for individual products in isolation, can find a useful application here,
In the matter of cost function estimates, too, further advances are required though we believe our work has made useful progress. It is too frequently asserted that MNC's enjoy scale economies, and too many predictions are based on this assumption, for our finding of everywhere constant returns to scale to go unquestioned, And if MNC's produce identical goods at home and abroad, data refinements will
have to be sought to make comparable cost function estimates from
-39-
different parts of the world, This last is an important issue in the Study of the causes and balance of payments and employment effects of the international migration of specific industries.
Finally, a few caveats. Our work is hardly the last word on export displacement. Our model perforce elided the problem of trade in intermediate goods. It cannot accommodate the macro-economic changes which accompany the international adjustment process, It also is non-dynamic and thus does not incorporate restrictions on substitutability that might be required for dynamic Stability, In its present version it ignores uncertainty, Finally, we have calculated only the effects of small changes in exogenous variables; we have not solved the model for its equilibrium values or simulated the effects of large displacements from an initial equilibrium, These sins of omission should be corrected
in future work, We hope to have made a fruitful beginning,
-Al-
Appendix
The Cobb-Douglas cost function as described above (equation (13)),
makes costs (C) a function of output (Q) and:
w = the wage.rate ccap = the rental price of capital services Pm = the price of a unit of raw materials A = the constant term of the corresponding Cobb-Douglas pro-
duction function
a,b,c = the elasticities of output with respect to labor, capital and raw materials; since returns to scale are constant ec=l-a-b.
Thus we have the functional relationship:
(Al) CQ) = ( egere ee Par) Q A a@ pP ce
It would appear that once A, a, b, and c are estimated from the production function it should be an easy matter to plug in the proper values for wages and the costs of other inputs and then calculate costs for any level of output.
However, there are intricate problems of scaling A, w, ccap and Pm that have made the derivation of our cost functions a difficult task. The major problem is that the estimate of A for the production function is affected by the units of measurement of all the independent variables entering into the production function, The size and the units of measurement of A change as the definitions and/or units of measurement of A change. The problem of deriving cost functions from the production function estimates really boils down to making the proper transformations on either the received values of A or the input prices
,
(w, ccap, Pm) in order to express the composite term bracketed in
-A2-
equation Al in the units , dollars per unit of output. This unit of output must correspond to the units in which output is measured.
A detailed discussion of the scaling transformations necessitated in this study can be found in Adler, et al. [ 2 ], Chapter II. Here we will briefly go through our procedures,
As mentioned in Section III, labor input was measured as the wage bill; this can be interpreted as a weighted average of labor inputs of different qualities [I w, Ly] or as the wage times labor input of a single skill category. We assumed the former, but for illustrative purposes will here assume the latter. It can easily be shown that, for a Cobb-Douglas production function, measuring labor inputs in dollar values (at some base year price, W) does not change the estimate of the elasticity a but does change the estimate of A by the factor =, where bis the estimated value of the true labor elasticity, a. This can be understood heuristically by noting how the constant term can be changed inQ=A L? > when wL is substituted for L; we then have:
Q= aq ie = aw) i = ab i3e’, where al now equals AW’, Likewise, in a regression for this type of function, multiplying any variable by a constant (k) changes the value of the estimated regression constant term by the factor k’, where e is the exponent of the variable in the production function,
In our regressions all variables were expressed in base year price units; let P> @> v, Pm be the base year price unit for output, the capital stock, labor and materials. We also have an added problem that we need a measure of capital services, cs , rather than a measure of
capital stock, By arguments identical to the previous one, it can be
ral
-A3-
shown that the estimated constant term of the production function (Ay is related to the estimate we desire and would get if everything were
measured in quantity units (A*) by the following formula:
Nos
wdqpPp, where all the symbols have been introduced except x, the ratio of capital services (cs) to capital stock: cs = xK.
We need A* in the denominator of the cost function and we do not have x and the base year prices, P> W; ds Pn that are distorting the estimate A, We can, however, undo the effect on A* by expressing the price variables in the cost function as appropriate price indices--thus basically multiplying or dividing factors that multiply A in equation Al, rather than changing A itself. It can be verified that if we express each input price in equation Al as an index with the same base as was used in the estimation of the production function (i.e., with bases W, q> Pm)? then the overall cost function will be identical to the one in
equation Al, Thus we calculate costs, for any spectrum of input prices
and output levels, using the following: A A A
ey (xcean)’ (Pa) (a2) CQ) = ZS ae — @Q)
A ar hhc
It should be noted that the value x times ccap is the cost of a
unit of capital service times the number of units of capital services per unit of capital stock: i.e., the cost of the value of capital services produced by one unit of capital stock. This latter is equal, under our assumptions, to q(r +d - q/q)> as defined in Section III.
Finally, it should be noted that when calculating costs for the
-A4-
input prices that existed in the base year, the term w/w and Pin! Pin both become 1, and x-ccap/q becomes r+d-q/q.
II, Data
The first table in this section shows the balance sheet and income statement data gathered from foreign subsidiaries in the 1966 Census. Succeeding this are the1966 values for Bios Soo> S39 and So for each of the five country-industry cases, Finally, we report data
used to estimate the native firm production functions.
~A5-
Foreign Subsidiary Data
Table Al _ 12-31-66 (or date)
In currency used on [tem books of allied foreign organization (Specify)
Note: Lines n and ct should equal line }.
ASSETS Cash, government securities and other cash items . Trade accounts receivable Invenctorics « Other current assets
. Total current assets (line a -d)
1% jaja joo
Investments in& advances to subsidiaries, affiliates & branches g. Property, plant and equipment, at cost h. Less: Accumulated reserves
i. Deferred charges and other assets
j. Total assets (line e-1)
LIABILITIES k. Current liabilities 1. Long-term debt m. Other licbilities, including underlying minority interests
n. Total liabilities (line k - m)
NET WORTH OR SHAREHOLDERS’ EQUITY eo. Capital stock
p. Capital surplus
q. Retained earnings or earned surplus
r. Surplus reserves
s. Home office account of branches, net proprietorship account, or partnership account
t. Total net worth or shareholders’ equity (line 0 - s)
oo. — _ , | Year ended 12-31-66 (
In currency used or books of foreign
Item organization (Specify)
ec A
INCOME 38 Net sales of goods or services, total
es of goods oF services, on Dividends, interest, profits, royalties and fees received from foreign secondary operations ei eS aCe Te Sey ees) ey ee ON
Other income (Identify principal type)
Total income (lines a - c) COSTS AND EXPENSES
Costs of goods and services purchased
Compensation of employees
Depreciation, amortization and retirement of property, plant and equipment Depletion of natural resources
ee nee en
Interest
Taxes other than income taxes (include excise taxes levied on company if included in line a)
Provision for forcign income taxes
Je sosts and charges, including adjustment for underlying minority interest share in profit or loss (Sis oy major items)
Total costs and expenses” (lines e- 1)
Net income after foreign income taxcs
Net income acre ee Unrealized profit or loss on books of parent organization resulting from exchange revaluation
Net income after adjustment for exchange revaluation eee OT ne
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Footnotes
1 Compare, for example, the contrasting views of Benoit {5] and
Barber [4]. Zan exception to this rule is Branson [6].
>this assumption of partial substitutability admits the claim made by industry that goods manufactured abroad by American and native firms may be specially designed for local markets. This "local model" thesis however, may not be as plausible for chemicals as it is for electrical machinery. The unlikely possibility of complementarity between pairs of product aggregates as large as the ones we deal with can be incorporated via negative cross-elasticities.
4s tevens [16] has shown that a world-wide profit-maximization model served better to explain the direct investment activities of U.S. MNC's than several alternative hypotheses. Horst [11] also adopts this behavioral assumption. In analyses of domestic investment it is customary to make the model operational by asserting that the firm maximizes the
present value of its cash flow = (90 - wL - qi - rB + dB/dt)e reat subject to a production function constraint. Assuming that market parameters are independent of the firm's investment rate and given perfect capital markets so that r is constant and dB/dt - rB drop out, the objective reduces to the myopic maximization of profits during each period with respect to labor, capital and price where profits =
pQ - wL - K(r + d - q/q). Stevens [17] has recently shown that under uncertainty, somewhat similar expressions, including means and covariances of random variables, can be substituted for these hypothetical objectives. In the context of the MNC, Adler [1] has argued that the — perfect capital market assumption is equivalent to assuming that exchangerisk can be hedged costlessly, no constraints on money-capital flows
and that stockholders all reside in one country. Under certainty, restrictions on capital flows can be incorporated in the form of a money capital constraint on the financing of the FS. Under uncertainty they produce an optimal foreign investment decision after which global maximization can proceed, These nuances of imperfect markets are omitted below.
>The possibility that the FS, produces for export to the U.S. or third countries merely produces analytical complexity without additional insight. It is therefore omitted for convenience.
6cf, Henderson and Quandt [10], p. 182 and Allen [ 3], p.359,
"Cournot duopoly reaction equations could be specified by solving (7a), (7b) and (7c) for Soo in terms of S42 and (9) for S42 as a function of So9. We omit this exercise because it adds nothing to our investigation. In particular, such reaction equations would not serve to identify or illuminate the alternative position,
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Ban atialysis of the requirements for the dynamic stability of the system can probably determine the sign of the determinant, particularly since we assume that the goods in this market are gross substitutes,
a case for which many theorems on dynamic stability exist (see, e.g., Quirk and Soposnik [19], pp. 210-215). In fact, in all relevant cases the sign of the 6x6 determinant turned out to be positive, the sign required by Metzler's theorem on stability.
However, we are reluctant to assert that the determinant of the market matrix must be positive without considerable further analysis. Since our system is one of imperfect competitors it cannot immediately be analyzed out of equilibrium in terms of excess demand functions. Second, the usual procedure for a dynamic analysis is to assume prices as the independent variables; we have taken the alternative route making quantities the independent variables, thus necessitating a transformation of our system or the available stability theorems.
; For example, if returns to scale are diminishing at the margin, cC’ >0. An increase in Soo will reduce S and also cause marginal ptoduction costs, Ci> to fall. Pap must therefore rise in order to
: au ‘ ° . * * maintain R, = Cy as is required. e case of increasing returns to scale is symmetric,
10theoretically it is not difficult to introduce an input into the production of S99 exported from the home country--perhaps part of the production of Q, = 84, + Si9- Then the total export effect of direct investment becomes the sum of the intermediate effect and our export displacement effect.
It has been impossible for us to separate exports from the U.S. in our industries into intermediates to subsidiaries and other sales; therefore we have attributed all exports to S,,, sales to unaffiliated parties. Naturally, for precise estimates of the various effects we
seek it is necessary to separate U.S. exports and materials inputs for subsidiaries into their components.
llye would like to reiterate our gratefulness to the people at BEA who supported and implemented the idea to develop a system which made research possible while preserving the confidentiality of the underlying data. Dave Devlin, formerly Assistant Director for International Economic Analysis, played the major role in promoting the System. Arnold Gilbert has done and is doing an excellent job in developing the necessary computer programs and is overseeing the completion of the actual research projects.
total market sales were obtained from the sources indicated in the Appendix for each country table. Foreign subsidiary sales are preliminary figures obtained from the Bureau of Economic Analysis.
3 there is a possible third justification for our preference. Our data do not distinguish between raw materials and processed or manufactured inputs. The latter may substitute for labor and capital. Consider a refrigerator manufacturer, If outside suppliers deliver his sealed motors, they will substitute for the labor and capital that would otherwise have had to be used in their own manufacture. Further, manufactured inputs can be used in varying proportions: outside suppliers could provide shelves and racks as well, In short, one would expect the coefficients of labor and capital to add to less than one in this case. However, this would not be evidence of declining returns to scale. Stevens wishes to disassociate himself from this footnote since the cases where materials can be validly excluded from the regression need have nothing to do with the degree to which they have
; eae a
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l4me measure of purchased inputs, referred to above as materials was constructed in two alternative ways, both of which led to virtually identical results. A measure of "costs of goods and services purchased" was collected directly in the 1966 Census, Since the instructions to this entry were somewhat ambiguous, we also measured purchased inputs directly as a measure of output minus value added, The latter performed consistently, but marginally, better in terms of R“ and t-ratios, so it was used in the "best" regressions.
15 See, e.g., Walters[(18], l6these, of course, are equal for constant returns to scale,
l7since none of the production functions estimated with native firm data was uniformly superior to the others, one of the criteria used to choose the best production function was its ability to explain 1966 costs with reasonable values of the cost of capital. For the foreign subsidiary sample, the best production function also turned out to explain sample costs the best, in terms of the average error of prediction for the sample.
19 orgenson {13].
20 Hall and Jorgenson [9],
2 teoen [7 }, P-184
22perfect capital market models such as Lintner's [14 ] can be extended to the international setting by including exchange risk which produces the equivalent of heterogeneous expectations. Theoretically, the MNC's cost of capital will then be invariant to financial decisions which do not introduce any risk of default. The cost of capital will not, however, be invariant to investment decisions which change the firm's systematic risk, a nebulous concept which cannot be measured with ex post data when expectations are not homogeneous, In the face of these difficulties and in the absence of appropriate data, we are forced to rely on others' estimates.
23 . .
The S,. were measured as values in constant 1966 prices, It should be clear that P,5 and P35 are merely proxies for the relevant prices, i.e., the locat selling price of U.S. and other countries’ exports, These latter, of course, were unavailable, Further, national income is a proxy for the relevant activity variable: owing to multicollinearity we chose not to employ total local consumption, i.e., total sales-exports,. S,5 was corrected for exports and therefore represents total local output for local use. Sources of quantity and income data are given.in the Appendix, Price data and trade weights were provided by Helen Junz.
The inadequacies of data availability, e.g., short time-series and high levels of aggregation further prevented any attempt to estimate the demand functions as a system. Consequently, the regression for each product was run independently, without constraints on the coefficients,
-F4-
Ze can express the price cross elasticities, 0S;/ep;> in terms of the Slutsky compensated price elasticities, of ;/ 2p; = at j/ epi» and income elasticities: i/Op, = df4/Op4y + $4Sj/BY = Of; /0pj ~ SjSiaj4/¥ when Sj is defined as in the text. “It then follows for i # j, 08;/®p,4 = 8S; / pj + S48; (aj4 - ai4)/Y. The cross elasticities will differ if the income elasticities differ. The size of the difference will also depend on S;S;/Y. For large product groups such as ours, this quantity may not be less than 1.
*55ince the likelihood of multicollinearity in the inverse demand function is so very high, it is not a useful empirical specification.
26oward Howe pointed out to us that these results could be the outcome of capacity constraints in the foreign markets. In the face of such constraints, measured price elasticities would appear to be low while income elasticities especially for imports might appear to exceed 1 owing to scarcity. While this explanation seems plausible it is unsuitable, for our model assumes that "normal conditions" prevail. In addition, however, many other problems plague our demand estimates. Data deficiencies have already been mentioned, Moreover, there may be errors of specification. Clearly, fruitful work remains to be done in this area.
27 see, e.g., Samuelson [ 15], p. 63 ff.
28positivity of dS,5/ds may result in a scenario such as the following, The rise in S59 Will produce decreases in- R59 and P99. The price of S,. must then decline merely to maintain Soo at a constant equilibrium level. If, however, the result of relaxing the constraint on Soo is to reduce the MNC's optimal exports, S} 9, then P12 will rise. Erstwhile customers of Sj9 will then turn to S,9, the equilibrium level of which will also rise. The net effect of these offsetting forces leaves the sign of dS12/dSo9 generally ambiguous.
-Ri-
References
(1) Adler, M. "The Cost of Capital and Valuation of a Two Country Firm," The Journal of Finance, March 1974, forthcoming.
(2) Adler, M., Enders, W., Preston, S, and G, Stevens. "Production Costs in the Chemical and Electrical Machinery Industries: Estimates of Cost Functions Derived from Production Functions in U.S., Canada, Japan, West Germany, France, Sweden and Australia," mimeo, 1973.
(3) Allen, R.G.D. Mathematical Analysis for Economists (London: Macmillan and Co. Ltd., 1960).
(4) Barber, R.J. "Big, Bigger, Biggest," The New Republic, April 30, 1966,
(5) Benoit, Emile, Statement in House Ways and Means Committee, 87th Congress, lst Session, pp. 3186-3190.
(6) Branson, W.H. Book review, The Journal of Finance, June 1969, pp. 583-585.
(7) Coen, R.M. "The Effect of Cash Flow on the Speed of Adjustment,"
Chapter IV in Tax Incentives and Capital Spending, ed, Gary Fromm (Washington, D.C.: The Brookings Institution, 1971).
(8) Griliches, Z. and V. Ringstad. Returns to Scale and the Form of the Production Function (Amsterdam: North Holland Publishing Co., .972).
(9) Hall, R.E. and D.W., Jorgenson, ''Tax Policy and Investment Behavior," American Economic Review, vol. 59 (June 1969), pp. 388-401.
(10) Henderson, J.M. and R.E. Quandt, Micro Economic Theory, lst ed. (New York: McGraw-Hill, Inc., 1958).
(11) Horst, T. "The Theory of the Multinational Firm: Optimal Behavior Under Different Tariff and Tax Rates," Journal of Political Economy, September/Cctober 1971, pp. 1059-1072.
(12) Hufbauer, G.C. and M. Adler. ‘Overseas Manufacturing Investment and the Balance of Payments," U.S. Treasury Tax Policy Research Study No, 1 (Washington, D.C., USGPO, 1968).
(13) Jorgenson, D. "Anticipations and Investment Behavior," Chapter 2 in The Brookings Quarterly Econometric Model of the United States, edited by Duesenberry, et al. (Chicago: Rand McNally, 1965).
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(14) Lintner, J. "The Aggregation of Investors' Diverse Judgments and Preference in Purely Competitive Security Markets," Journal
of Financial and Quantitative Analysis, December 1969, pp. 347-400.
(15) Samuelson, P. Foundations of Economic Analysis (Cambridge, Mass.: Harvard University Press, 1958).
(16) Stevens, G.V.G. "Fixed Investment Expenditures of Foreign Manufacturing Affiliates of U.S. Firms: Theoretical Models and Empirical Evidence," Yale Economic Essays, vol, 9, no. l, Spring 1969, pp. 137-198.
(17) Stevens, G.V.G. "On the Impact of Uncertainty on the Value and Investment of the Neoclassical Firm," American Economic Review, forthcoming, June 1974,
(18) Walters, A.A. "Production and Cost Functions: An Econometric Survey," Econometrica, vol. 31, 1963, pp. 1-66. (19)
Quirk, J. and R. Saposik, Introduction to General Equilibrium Theory and Welfare Economics (New York: McGraw-Hill, 1968).
Cite this document
Federal Reserve (1974, January 31). Direct Investment and Trade: An Analysis of the Export Displacement Effect. Ifdp, Federal Reserve. https://whenthefedspeaks.com/doc/ifdp_1974-41
@misc{wtfs_ifdp_1974_41,
author = {Federal Reserve},
title = {Direct Investment and Trade: An Analysis of the Export Displacement Effect},
year = {1974},
month = {Jan},
howpublished = {Ifdp, Federal Reserve},
url = {https://whenthefedspeaks.com/doc/ifdp_1974-41},
note = {Retrieved via When the Fed Speaks corpus}
}