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Commercial policy, growth and the distribution of income in a dynamic trade model
Journal of Development Economics 37 (1992) l-30. North-Holland
Commercial policy, growth and the distribution of income in a dynamic trade model Edward F. Bufie* Vanderbilt University, Nashville, TN 37235, USA Received March 1990, final version received November 1990
This paper analyzes the effects of commercial policy in a dynamic thrf.e-factor, three-sector model that allows for endogenous capital accumulation, nontraded goods and both consumption and capital good imports. Simple, well-defined conditions are derived under which different trade strategies raise or lower the real wage and are effective in promoting capital accumulation.
1. Introduction
Since the appeals of Haberler and Bhagwati in their influential survey papers [Haberler (1961), Bhagwati (1964)] considerable progress has been made in extending the pure theory of international trade to growing economies. The impact of free trade on steady-state welfare has been the subject of papers by Johnson (1971), Vanek (1971), Corden (1971), Pattanaik (1974), Togan (1975), Bertrand (1975), and Smith (1976, 1977, 19791, while the implications of capital accumulation for the terms of trade and the changing pattern of comparative advantage and specialization has been analyzed in Oniki and Uzawa (1965), Bardhan (1970, chapters 2, 4, 6), and Findlay (1970, 1973, chapter 5). Despite these impressive advances, it is fair to say that existing theory remains inadequate for the purpose of analyzing the interactions between trade policy and growth in LDCs. Al! of the aforementiorred papers, except those of Findlay, employ some variant of the two-sector neoclassical growth model in which the economy produces a single consumption good and a
*I am indebted to two anonymous referees, Howard Pack and participants in economic development workshops at Cornell University and Vanderbilt University for helpful comments. 030&3878/91/!IO3.50 0
1991-Elsevier
Science Publishers B.V. All rights reserved
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E.F. Bufl;e, Commercial
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single investment good. l While Derhaps appropriate for developed economies, this model does not capture the structural characteristics of less developed economies where imports comprise both competitive consumption goods and noncompetitive capital goods and a significant share of aggregate consumption is often nontraded. Findlay’s work is more suitable in this regard. Findlay (1970) develops a three-sector model with traded consumption goods and a nontraded investment good. A dualistic LDC that produces a primary export good and a manufactured consumer goad is analyzed in Findlay (1973, chapter 5). These two papers are rich in insights, but neither allows for nontradables consumption and both adhere to the neoclassical growth model’s ad hoc assumption of an exogenously fixed propensity to save (out of profits or aggregate income).2 A second major limitation of the existing literattIre from the vantage point of development economics is that a satisfactory framework has not yet been developed for the evaluation of commercial policy in dynamic trade models. The massive OECD and NBER studies [Little, Scitovsky and Scott (1970), Ehagwati (1978), Krueger (1978)] have inveighed against the tendency of many LDCs to subsidize capital imports through escalated structures of protection, but the discussion is informal and lacks explicit theoretical foundations. Findlay has demonstrated in a recent paper [Findlay ( 1982)] that protection necessarily lowers the steady-state growth rate. This result is based, however, on a dualistic version of the two-sector neoclassical growth model and accordingly is subject to the reservations mentioned earlier. Moreover, protection in the Findlay model is, of ncccssity, a tariff on imported capital goods. This does not faithfully reflect the nature of protection in most LDCs, where tariffs on capital imports are kept low compared with those on consumption imports in an effort to promote investment and growth. This paper analyzes the effects of commercial policy in a tractable yet general dynamic model of a small economy. The analysis improves on the existing literature in several important respects. The productive structure is mere general and realistic than that of the two-sector neoclassical growth model. Three goods are produced domestically, an export good, an import-
‘Smith (1976) and Corden (1971j also introduce some distinctive features into their models. Smith compares steady-state consumption levels under autarky and free trade in input-output and vista:: models as well as the conventional two-sector nzockissical growth model. The savings rate is not constant, but instead is assumed to adjust so as to keep the steady-state profit rate constant. Corden employs a two-tiered production structure in which iwo iraded intermediate inputs produced by capitnl and labor are used. in turn. to produce either a consumption good or an investment good. ‘Smith (1976) points out that the assumption of a ftxed propensity to save often gives rise to implausible results.
E.F. Buj$e,
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competing final good and a nontraded good. There exist both consumption and capital good imrcrts and, besides capital and labor, land is an important factor of production. Investment is determined not by some exogenously specified savings rate, but instead is derived from the utility maximizing behavior of capitalist households endowed with perfect foresight. Finally, in contrast to much of the literature, no restrictions are placed on the nature of demand or production functions. Duality theory is employed to permit the use of general specifications for demand and technology. The next section lays out the basic model while section 3 analyzes the repercussions of protectionist policies. Section 3.1 explores how an escalated structure of protection affects the real wage. The distributional outcome differs sharply from those that obtain in the standard Hecksher-Ohlin or specific-factor models where the aggregate capital stock is fixed. With endogenously determi red cap&t stocks, a tariff on imports of conbJmer goods is unambiguously favorable to labor. Clear, well-defined results also emerge for trade strategies combining different degrees of import-substitution and export-promotion. Section 3.2 investigates the impact of protection on capital accum;ziation. Sarrpri! ingly, notwithstanding the complexities inherent in a three-factor model with three en&genously determined capital stocks it is possible to derive very simple sufficient conditions lrnder which the aggregate capital stock rises or falls. It is shown, for example, that, starting from an initial position of free trade. a small tariff on consumer imports ra.ises the aggregate capital stock when: (1) there exists an enclave export sector or (2) the importcompeting good is the most capital-intensive good produced in the economy and the nontraded and export goods are compensated substitutes in consumption. Section 3.3 focuses an dynamics, analyzing how investment, the aggregate capital stock and the real wage evolve over time. A notable result emerging from the dynamic analysis is that there may be no time period over which the distributional conclusions of the sta:ic Heckscher-Ohlin or RicardoViner models are valid: even when the import-competing sector is the most capital intensive sector in the economy, under certain conditions a tariff will result in an unambiguously higher real wage on impact and at ail points on the transition path connecting steady-state equilibria. Export-oriented policies are briefly examined in section 4. There is a strong presumption that export promotion will inducz aggregate capital decumulation. And, as with protection, the long-run distribvti-anal outco is very sharply defined. Across steady-states, an export silbsidy lowers the real wage. The final section discusses the implications of the results for the over the merits of inward- vs. outward-looking trade policie; in L
E.F. Bufie,
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Commercial
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2. The model Apart from the distinctive features described earlier, the model is cast along familiar lines. The stocks of ;and and labor are fixed and there is no technical progress or external borrowing (either in the form of bank loans or direct foreign investment).3 Capital and labor are intersectorally mobile and flexible goods and factor prices ensure full employment and market clearing in the nontradables sector. The assumption that capital is intersectorally capilai stock can be mobile over the time period in which t he GggiQait: treated as fixed is, admittedly, a strong one. However, the alternative approach of postulating installed capital to be sector specific entails specifying three sectoral investment functions and results in either ad hoc or equiliintractable dynamics.4 The analysis of a moving Heckscher-Bhlin brium no doubt overlooks certain short-run effects, but should suffice to capture the broad impact of commercial policy on the incentive to accumulate capital and the interactions between capital accumulation and the distribution of income through time.
2.1. Prices In each sector, constaat returns to scaie prevaii and output is produced by perfectly competitive firms. With competitive firms, the zero profit condition obtains Pi= C’(2),
i=
ll, Ill, X,
(1)
where R, rr and x refer, respectively, to the nontraded, import and export sectors; Pi is the price of good i; C’ is the unit cost function in sector i; and g’ is a vector of factor prices. All three sectors utilize capital K’ and labor L’, but the exportable is a composite manufactured--primary good which requires land T as an additional input. Accordingly, in the export sector the relevant factor prices are the wage w, the capital rental r, and the land rental u, while only w and Y appear in the cost functions for the nontradables and import-competing sectors. The economy- is small and units are chosen so that al! world market prices 3Al!owingfor trade in finzncial assets would not alter any of the results that follow if the country is raiioned in its access to foreign loans. The assumption of credit rationing seems empiricaily plausible and accords with the consensus view in the debt literature that repudiation risk and other factors result in the impcsiiiort of rationing !ong before ihe icturn on domes& capitai approaches the lending rate of interest [Gersovitz (1985), Cooper and Sachs (1985)J The assumption that physical capital is not internationally mobile is dis -ussed at the end of section 2.3. 4For example,under the assumption of perfect foresight, the dynamic system is 6 x 6. (Three co-state variables accompany the three capital stocks.)
E.F. Bufjie,
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equal unity. Letting t and s represent the ad valorem tariff rate on consumption imports and subsidy rate on exports, the domestic prices are P,=l+t, P,=l
+s.
(3)
Along the lines of two-gap models [Chenery and Bruno (1962), McKinnon (1964), Chenery and Strout (1966) Chenery and Ma&wan (1966), Chenery and Eckstein (19X))], capital is specified to be a composite good produced by combining a noncompetitive import with a nontraded component (construction) in fixed proportions. 5 The imported capital good (i.e., machinery) is thus a pure intermediate input, or a ‘middle product’ in the terminoiogy of Sanyal and Jones (1982). Since the model is homogeneous of degree zero in the prices of the three traded goods, one of the traded goods may be selected as a numeraire. Given that most LDCs have opted for an escalated structure of protection, it is natural to choose the imported capital good as the numeraire and fix its price at unity (i.e., capital imports enter duty free). Denoting by b, and b, the respective input-output coefficients for the imported and nontraded components, the supply price of an aggregate capital good P, is P,=b,+b,P,. 2.2. Factor demands Letting Q’ stand for output in sector i and using Shephard’s sectoral capital and labor demands can be expressed as L’r Ki
lemma, the
C;(g')Q', = (7$gi)Q’.
Factor prices are flexible enough to ensure full employment:
‘The assumption that imported and nontraded components are used in fixed proportions is not critical. The dynamic analysis of section 3.3 is qualitatively unchanged and the resdts in sectron . 2.1 on the distribution of income hold exactly since, by the envelope theorem, dP, = 6, dP, regardless of whether the bi are constants or variabie. Tine resu?:s in section 4 also do not depend on the fixed proportions assumption because, when on!y the export subsidy varies, P, is constant. The general solution for the impact of a tariff on capita? acccumulatian is affected by the ftxed proportions assumption, but all of the results of section 3.2 generalize. This can be seen by replacing P’s, in (25) by (@“E” +@{), where @=b,,GK/Q”< 1 and <=&/~~<
E.F. Buffie, Commercial policp. growth
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and income
distribution
(9!
K”+K”+K”=K,
where K is the aggregate capital stock and L and ‘i are, respectively, the fixed domestic labor force and the fixed stock of land. Eq. (9), the market clearing condition for the capital stock, applies only in the short run; in the long run, K is a choice variable of firms.
2.3. Demand Consumption and investment expenditures are made by a representative family firm having homothetic preferences.6 Again, the most compact specification is achieved through the use of duality theory. Let D’jF, u), E(F, U) and R(P, K) represent, respective!y, the compensated demand, ex:enditure and revenue functions of the family firm, where P is the price vector (P,,,, P,, P,) and u is current utility. The expenditure and revenue functions possess the well-known properties E,=D’, &= Q’ and R,=r, where Ei z JE/aPi and RiEaR/(?Pi. Thus, with 1 denoting aggregate investment, market ciearing in the nontradables sector requires D”( P,u) = R,( F, K) - b,l.
(10)
Consistent with the assumption that capital is intersectorally mobile, the representative family firm can invest in import-competing, export or nontradables production. Capital markets do not exist and tirercforo all investment is financed out of retained profits. The family firm possesses ptrfect foresight and selects the investment plan that maximizes an additively separable utility function:
max T V(P, E) e -p1dt, (1.E) 0
subject to E+ P,i=
R(P, K)+t[D”(p,
u)-Q”]
-s[Q”-D”(I’,
u,]?
!12)
‘A single representative agent Is postulated solely to simplify the algebra. The steady-state results are independent of whether just capitalists, a combined capitalist-landlord class, or a single representative agent saves because net saving is zero across steady stat,?. Nor is the dynamic analysts substantively affected; ail of the dynamic results are qualitatively unchanged as the steady state remains a saddle point.
E.F. BuJk,
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where p and 6 are the constant private discount rate and the depreciation rate of a capital good; an overdot stands for a time derivative; and current utility is represented by the indirect utility function V( -) [i.e., u = V( . )J Eq. (12), the budget constraint, states that the sum of consumption and investment expenditure cannot exceed net national income, where the latter equals net national product plus tariff revenues less the cost of export subsidies. Net trade revenues are distributed to the family firm in a lumpsum fashion. The solution to (1 Z) will be discussed later in section 3.3 when the time paths of I and K are analyzed. For the moment, it is suficient to note that across steady states l=dK,
(14)
r=(p+S)P,.
(15)
Eq. (14) reflects the condition that net investment be zero in the steady state while (15) defines the long-run rental rat; (i.e., the rental rate that obtains when the demand price of a capital good equals its supply price). Eqs. (l)-( 15) describe the complete model. Before proceeding fttrther, some of the stronger assumptions underlying the mode1 should be discussed more fully. The purpose of the perfect foresight assumption is to capture in a simple but rigorous way the notion that capital accumulation is driven by forward-looking behavior. Under perfect foresight, the investment decision is made on the basis of how the actual paths of future prices affect the return to capital. While this may well exaggerate the family firm’s forecasting ability, it is difficult to find an acceptable, alternative method of modelling expectations. If ad hoc forecasting schemes are rejected for the usual reasons, the sole alternative to assuming perfect foresight is to model the process by which agents attempt to learn the true structure of the economy. Unfortunnitely, theory has rrot made much progress in this direction to date. Grdogenous learning has been incorporated only in very simple and primitive models, not in multi-sector dynamic general equilibrium models of t.he type I have formulated here. .A second important assumption concerns foreign investment. 1 have ignored the possibility that perfect international capital mobility might equalize domestic and foreign rates of return out of a conviction that this is rlzalistic. Direct foreign investment is subject to government controls almost everywhere in the Third World and seldom accounts for more than a very small fraction of total domestic investment. For a few countries, of course, the assumption of perfect capital mobility may be approximately correct. In this ca~:~ tire model KILM he extended to mcluae a specification of t dynamics of foreign investment. Since the cdpital retrial is fIxed fn the Iong
8
E.F. Bugle, Commercial policg, poolvth and income thsrribution
run, the steady-state distributional outcome is the same as in the model when all capital goods are imported (which results in constant). Once the increase in foreign owned capital is determined, the soiution for the aggregate domestic capital stock is obtained by ~o~~~wi~ same procedure as in section 3.2.?
3.
stectionist trade regimes
The trade regime is labeled protectionist simply if t >s. Sections 3.1 and 3.2 analyze the impact of protectionist policies on the steady-state real wage and capital accumulation. Section 3.3 completes the analysts by c~~racterizinr the nature of the transition path the economy ~o~~o~vs ~~etw~enskadys&e equilibria.
In ana?yzing the distributional outcome here and later concentrate solely on how trade pulicy affects the real wage. enough to work out results for the impact on the real c rentals, these are of lesser interest from a distributiona! point of view. The steady-state equilibrium Is defined by (l)--(8), (1 ), (12). (14) and (15), 18 equations that can be solved for the 18 nnknow~s Q’. Pi, K”, L”, w, r9 1‘.U, P, and i as a function of t, s, L and 7: Though large and seemingly complex, the model is easy to manipulate because of its basically block recursive structure. Observe first from (4) and (15) that
where a circumflex denotes the percentazc &ngC in 3 ~ri&!~ 2.nd a!-b,P,jPk, the cost share of nontradables in the pro cQion of an aggregate capital good. Now define 0: to be the cost share of tor j in sector i and differentiate eqs. (I). After using (I@, there emerges
‘Eq. (23) is altered to read der=pP~l -h)dK, where h=dK”/d is the fraction of the increase in the aggregate capital stock accounted for by foreign owried capital K”. (If the country is a net exporter of capital, h measures the decrease in foreign assets owned by domestic residents.) Also, the sohtion ~“=~~~~Q~~~~is substituted into (22).
in r is less than the CQprofii condition nontradables sector that the wage- rental ratio must increase (6~ FormaIZy, om (16). (19) and (20)
Aside from the limiting and unrealistic case (for LDCs) in which capital is produced entirely in the nontradables sector (I = I), the wage-rental ratio must increase, with the magnitude of the increase being Larger the more dependent the economy is on imported capital goods (i.e.>the smaller is r). A higher wage-ren;aI ratio imp!ies that the real wage rises measured in terms of importables and nontradables. It is also clear that the real wage rises measured in terms of exportables since &> P,,,> p,. Protectionist trade 7~gi,nes are t’nus tinambiguousiy favorable to labor.
ositionB contrasls
stri
In static models fferences in sectorai facto by protection either lowers or exerts an am is likely to worsen t
es-Ed al outcome IS
in statictrade
sector
is typically capital int3sive in L
models conclude that the real wage fall n terms of s goods.8 When the capital stock is variable behavigr, real factor rewa ariner. The key facfegkprice to In a static model th capital rental v fixed capita3 stock, y contrast, with ,a behavior constrains tbe long-run increase increase in the supply price of a capital good. increases, in turn, depends on the tee reflected by the parameter r. As long as s (crl
‘In a 2 x 2 Heckscher-Oh’.- (HO) model the increase in the real capital rental is accompanied by an unambiguous decrease I the real wage, while in a Ricardo-Viner (RV) model the wage rises in terms of the exportable but declines in terms of the importable. The current model is a more complicated mixed I-IO-RV model that allows for nontraded goods, but in a static setting it yields broadly similar conclusions. Under the weak assumption that the ex Ort and noqtraded goods are compensared substitutes in consumption, the real wage MIS measured in terms of importables and nontradables whenever the import sector is the most cap intensive sector in the economy. If the nontradables sc~tor is suficiently labor intensive, the side of the model dominates: the nominal wage falls, pri?xcing an unambiguous decrease in the real wage.
~QF trade
theorists
have succeeded
in f~~~~ati
follows sheuld go a long way toward clarifying this debate: it is possible in the three-factor, three-sector general e~~~~~br~~rnmodel use here, TV derive simple conditions under which various commercial poficie are effective in promoting aggregate capital accumwlation.
To compare import-substituting and export-oriented policies some mark is needed. The anly fair benchmark woufd appear to be free Accordingly, the results in this and the following section -=~e in the tariff starting from an initka impact of a small inc,,,_ where t=s=O.
The policy implications of t e results are 0 As laid out in section 2, the imperfections. This makes i
model
d
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E.F. Bugle, Commercial policy. growth and income distribution
private agents may cause the private discount rate to exceed the social discount rate, as in Blanchard (1985). Under either of these interpretations of the model, the results indicate the sign of the optimal second-best tariff or export subsidy.gv’O I will preccnt the results in a st;ictiy pasitivc hght; the reader can decide for himself whether they constitute a valid rationale for departing from free trade. Turning to the task at hand, the most economical solution procedure exploits the fact that across steady states the change in the aggregates capital stock must be consistent with equilibrium in the nontradable market. Endogenizing E through the expenditure function E(F, u), choosing units so that E,= 1 and differentiating (10) and (12) yields” c, dw+(&,I’, - P,R& dK
=Q L(fln-(P”&,)~~+(~,--~&,)~~+(n,-~”E,)8,], -n-
du=pP,d.K,
(22) (23)
where @*= F/Q”, ci denotes the marginal propensity to consu the compensated elasticity of demand for nontradables with respect to Pi; and rti~ PiRt:i,lQ”,the elasticity of nontradables supply with respect to Pi. Substituting for du and p,, in (22) from (19) and (23) gives
-
+
(& -
@“&JPx.
(24)
‘When there is a p ro p ortional tax T on net income, r = f~( I -T)- ’ + 6]P, across steady states and eq. (23) is replaced by du=ptl -r)- ’ dK. With finitely-lived agents as modeled in Blanchard (1985) greater modifications are required in the model because P is a function of K across steady states. Consequently, P, is also a function of K in the long run. Variations in P, induced by variations in K represent, however, second-round effects that do not alter the qualitative nature of the conclusions. [Extra terms appear in the coeficient multiplying dK in (24).] For the welfare analysis. what is crucial is that aggregate behavior yields p<(r-6)lP,
E.F. Bufj’ie.Comnercial policy. growth and
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ote from (7) and (9) that P,R, =(p -kfi)P,, of steady-state equilibrium.” Using this retationship and the conditions qn= - )~m---c)* and E,= -E,=+, (24) can be rewritten as
=b=-@“~“)(1-N(
m
where c~=c,+c,. Now “(Q~--@%J is the change in excess supply of nowtradables caused by a rise in Ip,. En& $j, --.$pl”&Y,) > 0.’ 3 (25) states that when s”t> (+a; a tariff increases sne aggregate c+ta! stock provid nontradables and exportables are not overly strong genera! equ~ljb~~rn complements (substitutes). Proposition 2. if the import-competin g sector is capita? (labor) intensive relative to the nontradables sector.
is the necescq capital stock.
and su_$cient condition @r a tariff to increase the aggregate
Corollary 2.1. If the import-competing sector is capital (iabor) intensive relative to the nontradables sector and nontradables and exportabks are general equilibrium substitutes (compbments), then a taii.fJ increases the aggregate capital stork.
Proposition 2 is a general result involving no explicit ~est~~~~o~s 02 technology or demand. To go further, it is necessary to ex terms of more primitive supply parameters. In the nosy. analysis is complicated by the presence of various te 12fL is found by solving for the change in Q” that results when 5 changes and all goods prices are kept fixed. With fixed goods prices, factor prices are constart. (Fmm the zero conditions in sectors m and n, w and r are constant. then foIlvws from the zero profit an condition in sector x that c is unchanged.) Eq. (18) thus (9) can be solved for 0” and 0”’ as a functioa? of K. Alte Kr;= ri/p” and solve eqs. (1) for r as a function of P,. 13The expression for qn will be presented later. Under very weak r tic2ions. qs is posit+= When qfl is negative, ~ro~os~t~o~ 2 and Cordlary 2.1 hold subject to ~~2~i~~at~Q~ that ihe nomradabks market exhibit Walrasian stability.
degrees of substitutabiiity between capital, iabor and land in ex~ortab~~s production. To astract from these terms, which are generally s ambiguous in sign, I will confine the analysis to the plausible case of a f~~~~ separable CES production function in the export sector. In the appendix it is shown that with this technology,
where t/~~zP@/f,Q”; k,=K”/L”; and t# is the elasticity of subbtitution in sector i (between capita! and labor in sectors na ar.d II and between capital, labor and land in sector x). Replacing ~7”and q, in (25) by the above expressions yields the following critical condition:
(26)
Eq. (26) isolates three crucial determinants of the aggregate capital stock. The first term measures the increase in capital accumulation arising from substitution towards capital induced by the increase in the wage-rental ratio [see (21)]. The second term captures the effect of the import sector drawing resources away from the nontradables sector. Not surprisingly, this tends to promote capital accumulation if the import sector is relatively capital intensive. Finally, the last term reflects the impact of the reallocating resources from the export to the import sector. Again, this reallocation favors capital accumulation when the import sector is relatively capital intensive > k,!. y inspection, it is easily seen that the two ~ea~~ocat~o~ e substitution effect when k,> k,, k, and E, ~0.
cts reinforce the
f e, > O), then a
tarijfinei eases the
The ~ond~tjon bst~tutes serves t
is clear from t in many countries It
contraction in the capital intensive nontradabtes sector is capable of lowering the aggregate capital stock. This outcome, however, requires quite small sectoral elasticities of substitution so that the substitu:.ion elect toward capital accumulation operates weakly. To see this, rewrite the second term in (26) as
In the normal case where goods are compensated substitutes, the first term is positive and the second is negative. The latter term, however, will be dominated by the term in (26) involving CF”if cf’(1-r) > @%l( I -@Y/F,), This gives Proposiiion 4. When the import-competing sector is capita! intensice relatice to the export sector and the nontraded good is a compensated substitute with both traded goods, tf’( 1 -x) > dQx( 1 - 838%) is a sufficient condition for a tariff to increase the aggregate capital stock. The logic underlying Proposition 4 is fairly straightforward. condition guarantees that #” increases when the ~o~trada most capital-intensive sector in the economy. For a give smaller is E, the more steeply sloped is the nontradab~es de e more steeply slo falls less than other effect [measured by G”(I- r)] dominates tke output e
The su
E.F. SufJie, Commercial policy, growth and income distribution
16
compensated substitutes at a high level of aggregation, Proposition 3 shoul apply in a large number of cases. Furthermore, in those cases where k, < k,, making Proposition 3 inapplicable, there is a reasonable chance that *he sufftcient condition in Proposition 4 will be valid. Though little is known about the magnitude of the cross-price elasticity E,, production function estimates invariably place the elasticity of substitution in the range of 0.5-1.2 [White (19X$)]. And even when the sufficient condition fails to hold, the capital stock does not decrease unless the single negative cross-price term is large enough to dominate all of the positive terms in (26). The most significant qualification in Propositions 3 and 4 is that the export sector be labor intensive relative to the import sector. In countries where exports are predominantly capital-intensive natural resource goods, protection may induce capital decumutation. Given the great diversity among LDCs, one additional result is of interest. A prototype that has received a great deal of attention in the development literature is the Enclave Export (EE) economy. The distinguishing feature of an EE economy is that interdependencies between the export sector and the rest oi the economy are at a minimum. In the current model, this notion is captured by setting cY=sX=O, which effectively severs all links between the export sector on the one hand and the import and nontradables on the other. Turning back to (25) [or (26)3, in the case of an EE economy the second term on the right-hand side disappears, giving rise to a completely unqualified result. Proposition 5. stock.
In an EE economy, a tar[ff increases the aggregate
capital
The intuitive rationale for this result is simply that a tariff on consumer imports alone acts as a differential capital subsidy in the non-export sectors by lowering Pk relative to P, and P,. In the EE economy, K” is fixed and therefore the stimulus to capital accumulation in the non-export sectors is sufficient to ensure an increase in the aggregate capita! stock.
3.3. The transition path was shown earlier that an escalated structure of protection always raises the real wage in the long run when the capital stock has reached its equilibrium level. This result directly contradicts the conventional wisdom, which argues that there is a strong presumption the real wage will decrease if, as in most LDCs, the import-competing sector is relatively capital intensive. Since the conventional wisdom is based on static trade models It
which assume a fixed aggregate capital st k, it is natup-al to canj=t the two results can be reconciledas refle ng the different short.. a run effects of protecti. n. The central aim of this section is to demonstr invariably correct. Accordingly, the analysis w~~i a tariff on capital accumulation and real in Proposition 3: k,> k, k, and E,>Q. 4 the most relevant case.) ven in this case, where is the most capital intensive sector in the econo plausible conditions protection generates an una at all points on the transition path betw condition for this outcome is z> c,, a con Behaviorally speaking, %>c,, means that an increase in investment spending raises the demand for nontradables: since a one dollar increase in investment is financed by a one dollar increase in saving, demand for nontraded consumer goods falls by c, at the same time as purchases of nontraded capital goods increase by r; the ove,all impact on demand thus tiirns on sign of a-cc,.14 In the appendix, I solve the famify firm’s intertemporal optimization problem and d~?lKXiStia~C that the steady state is a saddle point with a unique convergent path to equilibrium. The dynamic-; of the adjustment process are depicted in fig. I. The KK and II schedules denote loci for which sitively the capital stock and the level of investment ;ire constant. KK is sloped because the level of replacement investment rises with K. To the left of KK net investment is positive and K is increasing while to its right net investment is negative and K is falling. The If schedule may be positively or negatively sloped, but when positively sloped it cuts KK from above as in fig. l? Investment is increasing above 11 and decreasing below it, giving rise to a positively sloped saddle path. All of the results that follow also hold when the saddle path is negatively sloped. The relationship between the real wage C and the capital stock OPIth transition path is tracked by the WW schedule in the Given that a>c, and km> k,, I? and K must mov This follows from the dual nature of the Stolper-Samuelso theorems. P, increases on the transition path s’ the demand for nontradables while (from the capital stock results in a contraction in no tun, produces a magnified increase in the nomin the real wage rises regardless of the basket of goods workers consume. e initi Now consider once more the re ercussions of a t 14See eq. (A.1 1) in the appendix. ’ 5Theslope of the saddle ath is
T[
d- 6,
wkre
n is the
syste
I
I
S
S
I
I
I
!
W
\v
Fig. 1
brium is (iGo,I,, K,) in fig. 2.
tariff raises the
relative to nontradables. orem: an increase in
T the
good. The time path followe on the relative
state
of excess
E.F. Buffie, Commercial policy, growth and income distribution
20
Since P, has increased relative to P,, the change in nontradables supply is given by -qX: P,=
P,.
Nontradables supply increases as long as cY>O so that the export sector releases some factors to the rest of the economy. However, in view of the jump in investment spending, it is also possible that nontradables demand will have increased. At P,=P,, the overall change in ncntradables demand is given by (a -en) dl - D”E,~,.
The higher P, reduces consumption demand for nontradables but the rise in I pulls in the opposite direction. Bringing the supply and demand changes together, it is seen that the relative price of the nontradable is likely to increas: on ;&nycrciwhen: (a) nontradables and exports are weak substitutes both in production and consumption (c?, E, small - in the EE economy the real wage always increases on impact); (b) the iabor intensity of nontradables production is high relative to the average labor intensity of tradables production is small]; (c) the employment share of the nontradables l&z-U/&--k,) sector is large compared to the export sector; and (d) I rises strongly. Should any combination of (a)-(d) bring about an increase in the relative price of the nontradable, there wi!l be an unambiguous increase in the real wage on impact and at all points on the transition path between steady-states. Immediately following the imposition of the tariff, an investment boom produces a strong increase in the demand for labor intensive nontradables that shifts the WW schedule to the right and provokes a discrete, upward jump in the real wage from w0 and wi. The initial jump in the real wage is followed by further increases as a growing capital stock strengthens the demand for Loor. It may seem counterintuitive that investment rises initially given that the real wage increase forces r to decline relative to P, and P,. The simultaneous increase in I and fall in r/P,,, and r/P,, however, is easily explained. In deciding whether to invest the family firm compares, not the current capital rental to P, and P,, but rather the shadow price of capital ,l to the supply price of a capital good. The shadow price of capital equals the present discounted value of the marginal utility of the entire future stream of rentals generated by an extra unit of capital. Since r declines on the transition path and i- Pk in the new steady state, it is clear that on im act il rises by more
E.F. Bugle, Commercial
potrcy, growth
and income distribution
21
than P,. Firms endowed with perfect foresrght calculate the true vaiue of i. and respond by increasing I.
4. Export promotion In a pure export-oriented trade regime where s > t =O, the steady-state distributional outcome is well defined. Since ti> pX> 6 = P,,,= ?n = ? =O, landowners gain unambiguously while capitalists and workers lose to the extent that they consume the export good. Proposition 6. In a pure export-oriented trade regime, the real wage declines across steady states if the export gsod is consumed domestically.
When export promotion is accompanied by protection (SB t ~0): the distributional repercussions are possibly quite different. The real wage may increase unambiguously, an outcome that cannot occur in conventional static models. With t>O, the real wage rises in terms of nontradables and importables, but may fall measured in units of exportables (ti> pE p FJ. Even in strongly export-oriented regimes, however, it is likely that the export sector product wage will rise. Define the degree of export-oriented bias by p&P,> 1. After slight manipulation, (20) then yields
(27) from which we have Proposition 7. In an export-oriented measured m units of any good if
trade regime, the real wage increases
W)
For plausible parameter vahtes, (28) will be satisfied by values of /I< 1.5. Since few, if any, LDCs have pursued ex orb ~rornot~Q~ to t much exceeds unity, it seems safe to onclude that. i oriented trade regimes have been favorable to labor. kS liV6: however, to the fact that export su substantial measure of protection.
The
counterpart
to
(26) is
As an export subsidy does not alter the wage-re substitution effect toward capital ~~c~rn~~~a~~~ come is determined by just the two r~a~~~~i~~ determines the direction of tRe resource transfer kt nontradables secitors. If E,>O, the ~~~~radab~~s sector ex resources at the expense of the import SecfOP.ConYers?!yq nontradables autos contrasts, releasing resources as two reallocation efkcts work in the same direction (k,-k,) share the same sign.
Since normally E, >O, t e practical import of ~~@~~sition 9 k Bhat an export subsidy is sure ts p mote capital a~c~~n~~~t~~~~~~~ in the rare LDC in whida the import sector is the most labor intensive sector in the economy. In the much more common ease where the import set intensive sector in the econon y, an export tax is re accumu!ation. Finally, the interested reader can deve ic analysis for vari cases by proceeding along the same lines as in suction 3.3.
It is a cliche in the development literature istribtition of income of a given policy rank as high concetns abou demonstrates ~~~se~ue~~~s trade model that incor
regimesdse
m eseal
structure
tial studies of LittEe. S&msky
sf protection enhances
aggregate
and Scott, and Bhagwati and Krueger, which
not contradict this literature. The in this paper shows only that a case can
ts
“he 0
ea~jta~
agwati has stressed (1978), their trad only in ihe sense that export subsidies hav offset the anticxporl bias supply price of capital
is accompanied by continually rising real wa,ga an tion of income. l6 What eG3sting anal by the protectionist component substitution trade policy of countri unaided export subsidy triggers capi in the 1’ongrun. To make further progress towards outward-oriented trade strategies in L evaluate other arglamenb that have oriented trade strategy. This paper which commerciat polky afkts gro final word on the issue of which benefits. There are numerous ot growth might occur. It is frequent growth is fueled by gains from induced by greater contact with w must be carefullv, fiCWin;m c - - ....=ed befo trade regime is most conducive to growth.
on onward- vs.
Since t =s=O initially, the trade revenue terms in the budget constraint (12) may be ignored when solving the family firm‘s maximization problem. Hence, after substituting for E in the indirect utility function (12), the maximization problem ( 11) becomes
subject to ‘%nce supply and demand functions are horn nontradables supply and consumption demand for n Hence, if AI,> k, and the Increase in investment sp (2 > c,), then, on impact, k > Pm> B, = B,.
where A”
is the
arshallian demand function for the nontraded go Iv,= i”V/ZP,. Differentiating with respect to E yields in the case of ~~~ut~et~~ demand (i.e.*an unitary expenditure elasticity) B= H(1 -!- VEsr/V'EA")t W
0, the elasticity of the ~arg~~a~
W
iture.
~etu~~i~g to (A.rC),factor out VE/Pn, note that of (AS) to get
where a=~P,b,/Pk, the cost share of the production 0% an aggregate capital good. Slime tastes a P,A”/E SC,,, where c, is the marginat pro Thus, after collecting terms on 9, i and k (A.6) reads
where
essary to know to c~~~~es in I required reduced-form solutions are obtained from qs. (~~~~0~ and (124. which define the temporary equilibrium. ENS,(1) yiel Samueison solutions:
To complete the dynamic analysis, it is with P, and how the latter in turn respo
More efbrt is needed to obtain N, and N,. After tedious emerges
there
N,IP,= r&8”, + c,eyy
(A-10)
N,/P, = P,( 3( - c,)/f.
(A.1 I) -@/pm> 0, the elasticity of excess supply of rradabies sector 1s
in no
es
E.F. B&e,
28
Commercial policy, growth and income distribution
where yl=b;+Pk
V,(cx-
c”)2
-v,,
f
1
93,
1.
r2v&en,+ c&y-ae; +( I- o!)qq p () fE-m2
The determinant of the coefficient matrix in (A. 15) is negative. The steady state, therefore, is saddle-point stable. A.I.
The general equilibrium supply elasticities
Uzawa (1962) has shown that the Allen partial elasticity of substitution between factors i and j, Oij, equals C,C/CiCj. Logarithmically differentiating eqs. (j)-(6) and making use of Uzawa’s result and the adding-up condition %PKK= &CI, where 0 is the c!asticity of substitution between capital and labor - we obtain *. L’ = - ,i(&( 6 - i’)+ Qi, ki = &‘,(G _ ;) +
(A.16)
Qi,
(A.17)
for i=n, m. From (A.8)-(A.9), ti-i=(p,-p,)/B. gives
ei=~&~l3-~(b,-P~)+~~, i=n,m, Ki
=
-&$-yp,-p")+Qi,
i=n,m.
Substituting into (16)-(17)
(A.18) (A.19)
Similar manipulations of (5), (6) and (8) yield the following solutions for K* and L” in the case of a non-nested CES production function:
B,,
(A.20)
-$dx,
jA.21)
i‘=a‘elPn+tYe2Pm+$ T
Rx= cxe3P,
+ cXe4Bm$
T
where
E.F.
Bufie,
CommerciaS policy, growth and income distribution
29
Differentiating (7) and (9) and making use of (A.18)dA.21) now gives two equations that can be solved for Q” and Q” as a function P,, Pm and Y,: Lmom+ Ln@ = d,& + d,b, -
( Lxcr=/~“,)~x,
(A.22) (A.23)
where do = B- ‘(#LV;t + o”Lm8;) - LWe,, dl z I?- ‘(a”K’Y?~+ amKmQ)- Kxaxef, d2 3 B- l(cPLnO~+ a”lL”@) - L”a”e,,
The solutions for 9” and qX on page 14 in the text can be obtained in a straightforward manner from (A.22)-(A.23). References Bardhan, P.. 1970, Economic growth, development and foreign trade (Wiley, New York). Bertrand, T., 1975, The gains from trade: An analysis of steady-state solutions in an open economy, Quarterly Journal of Economics 89, 555-568. Bhagwati, J., 1964, The pure theory of international trade: A survey, Economic Journal 74, !-84. Bhagwati, J., 1971, The generalized theory of distortions and welfare. in: J. Bhagwati et al.. eds.. Trade, balance of payments. and growth (North-Holland, Amsterdam). Bhagwati, J., 1978. Anatomy and consequences of exchange control regimes (Baiiinger. Cambridge, MA). Bhagwati, J. and T.N. Srinivasan, 1969. Optimal intervention to achieve noneconomic objectives. Review of Economics Studies 36,27-38. Bhagwati, J. and T.N. Srinivasan, 1980, Trade and welfare in a steady state, in: J. Chipman and C.P. Kindieberger, eds., Fiexibie exchange rates and the bcaiance of payments: Essays in memory of Egon Sohmen (North-Holland, Amsterdam). Bianchard, O., 1985, Debt, deficits and finite horizons, Journ&! of Poiiticai Economy 93. 223-247. Chenery, H. and M. Bruno. 1962, Development alternatives in an open economy. Economic Journal 72,89-103. Chenery. H. and P.B. Eckstein, 1970, Alternative policies for Latin America, Journa) of Pohtical. Economy 78,9661006. Chenery, H. and A. MacEwan. 1966. Optimal patterns of growth and aid: The case of P in: I. Adeiman and E. Thorbecke, eds.. The theory and design of economic devcl (Johns Hopkins University Press. Baltimore, MD). Chenery, H. and A. Strout, 1966, Foreign assistance and economic ,levelopment, American Economic Review 56,679-733. Cooper. R. and J. Sachs, 1985. Borrowing abroad: The btor’s perceptive. in: G.W. ~eloping countries (The W J.T. Cuddington, &., i~ter~ationai debt and the Washington, DC). .. cdi.. :i et Corden, W.M., 14 ti, ‘The effects oi tratie nor o,i sn Trade, balance of payments and grow Charles P. K.ind!eberger ~N~~tb-~o~~a~~, New York).
30
E.F.
Su~re,
Commercial
policy,
growrh
and income
distribution
Corden, WM., 1974, Diaz-Alejan&o, CF.,
Trade policy and economic welfare (Oxford University Press, Glasgow). 1975, Trade policies and economic development, in: Peter B. Kenen. ed., trade and finance: Frontiers for research (Cambridge University Press.
International London). Findlay, R., 1370, Factor p isportions and comparative advantages in the long-run Journal of Political Economy 78, 27-34. Findlay, R., 1973, International trade and development theory (Columbia University Press, New York). Findlay, R., 1982, Protection and growth in a dual economy, in: M. Getsovitz et al., eds., The theory and experience of economic development (George Allen and Unwin, London). Findlay, R., 1984, Growth and development in trade models, in: R. Jones and P.B. Kenen, eds., Handbook of international economics, vol. I (North-Holland, Amsterdam). Gersovitt, M., 1985, Banks’ international lending decisions: What we know and implications for future research, in: G.W. Smith and J.T. Cuddington, International debt and the developing countries (The World Bank, Washington, DC). Haberler, G., 1961, A survey of international trade theory, Special papers in international economics (Princeton University Press, Princeton, NJ). Johnson, H.G., 1965, Optimal trade intervention in the presence of domestic distortions, in: R. Caves, H.G. Johnson and P. Kenen, eds., Trade, growth and the balance of payments (Rand McNally, New York). Johnson, H.G., 1971, Trade and growth: A geometrical exposition, Journal of International Economics 1,83-102. Jung, W.S. and P.J. Marshall, 1985, Exports, growth and causality in developing countries, Journal of Development Economics 18, 1-13. Krueger, A., 1978, Liberalization attempts and consequences (Ballinger, Cambridge, MA). Krueger, A. et al., 1982, Trade and employment in developing countries: Individual studies (University of Chicago Press, Chicago, IL). Little, I., T. Scitovsky and M. Scott, 1970, Industry and trade in some developing countries (Oxford University Press, London). Luedde-Neurath, R., 1986, Import controls and export-oriented development: A reassessment of the South Korean case (Westview Press, London). McKinnon, R.I., 1964, Foreign exchange constraints in economic development and efficient aid allocation, Economic Journai 74, 388-409. Oniki, H. and H. Uzawa, 1965, Patterns of trade and Investment in a dynamic model of international trade, Review of Economic Studies 32. Pattanaik, P., 1974, Trade, distribution and saving, Journal of International Economics 4, 77-82. Samuelson, P., 1975, Trade pattern reversals in time-phased Ricardian systems and intertemporal efftciency, Journal of Internationa! Economics 5. 309. Samuelson, P., 1978, Free trade’s intertemporal Pareto optimality, Journal of International Economics 8, 147-149. Sanyal, K. and R. Jones, 1982, The theory of trade in middle products, American Economic Review 72, 16-31. Smith, M.S., 1976, Trade, growth and consumption in alternative models of capital accumulation, Journal of International Economics 6, 371-384. Smith, M.S., 1977, Capital accumulation in the open two-sector economy, Economic Journal 87, 273-282. Smith, M.S., 1979, International gains from trade, Journal of International Economics ‘3, 239-248. Togan, S., 1975, The gains from international trade in the context of a growing economy, Journal of International Economics 5, 229-238. Uzawa, H., 1962, Production functions with constant elasticities of substitutions, Review of Economic Studies 29, 291-299. Vanek, J., 1971, Economic growth and international trade in pure theory, Quarterly Journal of Economics 85, 377-390. White, L., 1978, Evidence on appropriate factor proportions for manufacturing in less developed countries, Economic Deve!opment and Cultural Change 27, 27-59.
Commercial policy, growth and the distribution of income in a dynamic trade model Edward F. Bufie* Vanderbilt University, Nashville, TN 37235, USA Received March 1990, final version received November 1990
This paper analyzes the effects of commercial policy in a dynamic thrf.e-factor, three-sector model that allows for endogenous capital accumulation, nontraded goods and both consumption and capital good imports. Simple, well-defined conditions are derived under which different trade strategies raise or lower the real wage and are effective in promoting capital accumulation.
1. Introduction
Since the appeals of Haberler and Bhagwati in their influential survey papers [Haberler (1961), Bhagwati (1964)] considerable progress has been made in extending the pure theory of international trade to growing economies. The impact of free trade on steady-state welfare has been the subject of papers by Johnson (1971), Vanek (1971), Corden (1971), Pattanaik (1974), Togan (1975), Bertrand (1975), and Smith (1976, 1977, 19791, while the implications of capital accumulation for the terms of trade and the changing pattern of comparative advantage and specialization has been analyzed in Oniki and Uzawa (1965), Bardhan (1970, chapters 2, 4, 6), and Findlay (1970, 1973, chapter 5). Despite these impressive advances, it is fair to say that existing theory remains inadequate for the purpose of analyzing the interactions between trade policy and growth in LDCs. Al! of the aforementiorred papers, except those of Findlay, employ some variant of the two-sector neoclassical growth model in which the economy produces a single consumption good and a
*I am indebted to two anonymous referees, Howard Pack and participants in economic development workshops at Cornell University and Vanderbilt University for helpful comments. 030&3878/91/!IO3.50 0
1991-Elsevier
Science Publishers B.V. All rights reserved
2
E.F. Bufl;e, Commercial
policy, growth
.md
income distribution
single investment good. l While Derhaps appropriate for developed economies, this model does not capture the structural characteristics of less developed economies where imports comprise both competitive consumption goods and noncompetitive capital goods and a significant share of aggregate consumption is often nontraded. Findlay’s work is more suitable in this regard. Findlay (1970) develops a three-sector model with traded consumption goods and a nontraded investment good. A dualistic LDC that produces a primary export good and a manufactured consumer goad is analyzed in Findlay (1973, chapter 5). These two papers are rich in insights, but neither allows for nontradables consumption and both adhere to the neoclassical growth model’s ad hoc assumption of an exogenously fixed propensity to save (out of profits or aggregate income).2 A second major limitation of the existing literattIre from the vantage point of development economics is that a satisfactory framework has not yet been developed for the evaluation of commercial policy in dynamic trade models. The massive OECD and NBER studies [Little, Scitovsky and Scott (1970), Ehagwati (1978), Krueger (1978)] have inveighed against the tendency of many LDCs to subsidize capital imports through escalated structures of protection, but the discussion is informal and lacks explicit theoretical foundations. Findlay has demonstrated in a recent paper [Findlay ( 1982)] that protection necessarily lowers the steady-state growth rate. This result is based, however, on a dualistic version of the two-sector neoclassical growth model and accordingly is subject to the reservations mentioned earlier. Moreover, protection in the Findlay model is, of ncccssity, a tariff on imported capital goods. This does not faithfully reflect the nature of protection in most LDCs, where tariffs on capital imports are kept low compared with those on consumption imports in an effort to promote investment and growth. This paper analyzes the effects of commercial policy in a tractable yet general dynamic model of a small economy. The analysis improves on the existing literature in several important respects. The productive structure is mere general and realistic than that of the two-sector neoclassical growth model. Three goods are produced domestically, an export good, an import-
‘Smith (1976) and Corden (1971j also introduce some distinctive features into their models. Smith compares steady-state consumption levels under autarky and free trade in input-output and vista:: models as well as the conventional two-sector nzockissical growth model. The savings rate is not constant, but instead is assumed to adjust so as to keep the steady-state profit rate constant. Corden employs a two-tiered production structure in which iwo iraded intermediate inputs produced by capitnl and labor are used. in turn. to produce either a consumption good or an investment good. ‘Smith (1976) points out that the assumption of a ftxed propensity to save often gives rise to implausible results.
E.F. Buj$e,
Commercial
policy. growth and income distrihurion
3
competing final good and a nontraded good. There exist both consumption and capital good imrcrts and, besides capital and labor, land is an important factor of production. Investment is determined not by some exogenously specified savings rate, but instead is derived from the utility maximizing behavior of capitalist households endowed with perfect foresight. Finally, in contrast to much of the literature, no restrictions are placed on the nature of demand or production functions. Duality theory is employed to permit the use of general specifications for demand and technology. The next section lays out the basic model while section 3 analyzes the repercussions of protectionist policies. Section 3.1 explores how an escalated structure of protection affects the real wage. The distributional outcome differs sharply from those that obtain in the standard Hecksher-Ohlin or specific-factor models where the aggregate capital stock is fixed. With endogenously determi red cap&t stocks, a tariff on imports of conbJmer goods is unambiguously favorable to labor. Clear, well-defined results also emerge for trade strategies combining different degrees of import-substitution and export-promotion. Section 3.2 investigates the impact of protection on capital accum;ziation. Sarrpri! ingly, notwithstanding the complexities inherent in a three-factor model with three en&genously determined capital stocks it is possible to derive very simple sufficient conditions lrnder which the aggregate capital stock rises or falls. It is shown, for example, that, starting from an initial position of free trade. a small tariff on consumer imports ra.ises the aggregate capital stock when: (1) there exists an enclave export sector or (2) the importcompeting good is the most capital-intensive good produced in the economy and the nontraded and export goods are compensated substitutes in consumption. Section 3.3 focuses an dynamics, analyzing how investment, the aggregate capital stock and the real wage evolve over time. A notable result emerging from the dynamic analysis is that there may be no time period over which the distributional conclusions of the sta:ic Heckscher-Ohlin or RicardoViner models are valid: even when the import-competing sector is the most capital intensive sector in the economy, under certain conditions a tariff will result in an unambiguously higher real wage on impact and at ail points on the transition path connecting steady-state equilibria. Export-oriented policies are briefly examined in section 4. There is a strong presumption that export promotion will inducz aggregate capital decumulation. And, as with protection, the long-run distribvti-anal outco is very sharply defined. Across steady-states, an export silbsidy lowers the real wage. The final section discusses the implications of the results for the over the merits of inward- vs. outward-looking trade policie; in L
E.F. Bufie,
4
Commercial
policy, growth and income distribution
2. The model Apart from the distinctive features described earlier, the model is cast along familiar lines. The stocks of ;and and labor are fixed and there is no technical progress or external borrowing (either in the form of bank loans or direct foreign investment).3 Capital and labor are intersectorally mobile and flexible goods and factor prices ensure full employment and market clearing in the nontradables sector. The assumption that capital is intersectorally capilai stock can be mobile over the time period in which t he GggiQait: treated as fixed is, admittedly, a strong one. However, the alternative approach of postulating installed capital to be sector specific entails specifying three sectoral investment functions and results in either ad hoc or equiliintractable dynamics.4 The analysis of a moving Heckscher-Bhlin brium no doubt overlooks certain short-run effects, but should suffice to capture the broad impact of commercial policy on the incentive to accumulate capital and the interactions between capital accumulation and the distribution of income through time.
2.1. Prices In each sector, constaat returns to scaie prevaii and output is produced by perfectly competitive firms. With competitive firms, the zero profit condition obtains Pi= C’(2),
i=
ll, Ill, X,
(1)
where R, rr and x refer, respectively, to the nontraded, import and export sectors; Pi is the price of good i; C’ is the unit cost function in sector i; and g’ is a vector of factor prices. All three sectors utilize capital K’ and labor L’, but the exportable is a composite manufactured--primary good which requires land T as an additional input. Accordingly, in the export sector the relevant factor prices are the wage w, the capital rental r, and the land rental u, while only w and Y appear in the cost functions for the nontradables and import-competing sectors. The economy- is small and units are chosen so that al! world market prices 3Al!owingfor trade in finzncial assets would not alter any of the results that follow if the country is raiioned in its access to foreign loans. The assumption of credit rationing seems empiricaily plausible and accords with the consensus view in the debt literature that repudiation risk and other factors result in the impcsiiiort of rationing !ong before ihe icturn on domes& capitai approaches the lending rate of interest [Gersovitz (1985), Cooper and Sachs (1985)J The assumption that physical capital is not internationally mobile is dis -ussed at the end of section 2.3. 4For example,under the assumption of perfect foresight, the dynamic system is 6 x 6. (Three co-state variables accompany the three capital stocks.)
E.F. Bufjie,
Commercial
poky.
growth
and income distribution
5
equal unity. Letting t and s represent the ad valorem tariff rate on consumption imports and subsidy rate on exports, the domestic prices are P,=l+t, P,=l
+s.
(3)
Along the lines of two-gap models [Chenery and Bruno (1962), McKinnon (1964), Chenery and Strout (1966) Chenery and Ma&wan (1966), Chenery and Eckstein (19X))], capital is specified to be a composite good produced by combining a noncompetitive import with a nontraded component (construction) in fixed proportions. 5 The imported capital good (i.e., machinery) is thus a pure intermediate input, or a ‘middle product’ in the terminoiogy of Sanyal and Jones (1982). Since the model is homogeneous of degree zero in the prices of the three traded goods, one of the traded goods may be selected as a numeraire. Given that most LDCs have opted for an escalated structure of protection, it is natural to choose the imported capital good as the numeraire and fix its price at unity (i.e., capital imports enter duty free). Denoting by b, and b, the respective input-output coefficients for the imported and nontraded components, the supply price of an aggregate capital good P, is P,=b,+b,P,. 2.2. Factor demands Letting Q’ stand for output in sector i and using Shephard’s sectoral capital and labor demands can be expressed as L’r Ki
lemma, the
C;(g')Q', = (7$gi)Q’.
Factor prices are flexible enough to ensure full employment:
‘The assumption that imported and nontraded components are used in fixed proportions is not critical. The dynamic analysis of section 3.3 is qualitatively unchanged and the resdts in sectron . 2.1 on the distribution of income hold exactly since, by the envelope theorem, dP, = 6, dP, regardless of whether the bi are constants or variabie. Tine resu?:s in section 4 also do not depend on the fixed proportions assumption because, when on!y the export subsidy varies, P, is constant. The general solution for the impact of a tariff on capita? acccumulatian is affected by the ftxed proportions assumption, but all of the results of section 3.2 generalize. This can be seen by replacing P’s, in (25) by (@“E” +@{), where @=b,,GK/Q”< 1 and <=&/~~<
E.F. Buffie, Commercial policp. growth
6
and income
distribution
(9!
K”+K”+K”=K,
where K is the aggregate capital stock and L and ‘i are, respectively, the fixed domestic labor force and the fixed stock of land. Eq. (9), the market clearing condition for the capital stock, applies only in the short run; in the long run, K is a choice variable of firms.
2.3. Demand Consumption and investment expenditures are made by a representative family firm having homothetic preferences.6 Again, the most compact specification is achieved through the use of duality theory. Let D’jF, u), E(F, U) and R(P, K) represent, respective!y, the compensated demand, ex:enditure and revenue functions of the family firm, where P is the price vector (P,,,, P,, P,) and u is current utility. The expenditure and revenue functions possess the well-known properties E,=D’, &= Q’ and R,=r, where Ei z JE/aPi and RiEaR/(?Pi. Thus, with 1 denoting aggregate investment, market ciearing in the nontradables sector requires D”( P,u) = R,( F, K) - b,l.
(10)
Consistent with the assumption that capital is intersectorally mobile, the representative family firm can invest in import-competing, export or nontradables production. Capital markets do not exist and tirercforo all investment is financed out of retained profits. The family firm possesses ptrfect foresight and selects the investment plan that maximizes an additively separable utility function:
max T V(P, E) e -p1dt, (1.E) 0
subject to E+ P,i=
R(P, K)+t[D”(p,
u)-Q”]
-s[Q”-D”(I’,
u,]?
!12)
‘A single representative agent Is postulated solely to simplify the algebra. The steady-state results are independent of whether just capitalists, a combined capitalist-landlord class, or a single representative agent saves because net saving is zero across steady stat,?. Nor is the dynamic analysts substantively affected; ail of the dynamic results are qualitatively unchanged as the steady state remains a saddle point.
E.F. BuJk,
Commercial
policy. growth and income distribution
7
where p and 6 are the constant private discount rate and the depreciation rate of a capital good; an overdot stands for a time derivative; and current utility is represented by the indirect utility function V( -) [i.e., u = V( . )J Eq. (12), the budget constraint, states that the sum of consumption and investment expenditure cannot exceed net national income, where the latter equals net national product plus tariff revenues less the cost of export subsidies. Net trade revenues are distributed to the family firm in a lumpsum fashion. The solution to (1 Z) will be discussed later in section 3.3 when the time paths of I and K are analyzed. For the moment, it is suficient to note that across steady states l=dK,
(14)
r=(p+S)P,.
(15)
Eq. (14) reflects the condition that net investment be zero in the steady state while (15) defines the long-run rental rat; (i.e., the rental rate that obtains when the demand price of a capital good equals its supply price). Eqs. (l)-( 15) describe the complete model. Before proceeding fttrther, some of the stronger assumptions underlying the mode1 should be discussed more fully. The purpose of the perfect foresight assumption is to capture in a simple but rigorous way the notion that capital accumulation is driven by forward-looking behavior. Under perfect foresight, the investment decision is made on the basis of how the actual paths of future prices affect the return to capital. While this may well exaggerate the family firm’s forecasting ability, it is difficult to find an acceptable, alternative method of modelling expectations. If ad hoc forecasting schemes are rejected for the usual reasons, the sole alternative to assuming perfect foresight is to model the process by which agents attempt to learn the true structure of the economy. Unfortunnitely, theory has rrot made much progress in this direction to date. Grdogenous learning has been incorporated only in very simple and primitive models, not in multi-sector dynamic general equilibrium models of t.he type I have formulated here. .A second important assumption concerns foreign investment. 1 have ignored the possibility that perfect international capital mobility might equalize domestic and foreign rates of return out of a conviction that this is rlzalistic. Direct foreign investment is subject to government controls almost everywhere in the Third World and seldom accounts for more than a very small fraction of total domestic investment. For a few countries, of course, the assumption of perfect capital mobility may be approximately correct. In this ca~:~ tire model KILM he extended to mcluae a specification of t dynamics of foreign investment. Since the cdpital retrial is fIxed fn the Iong
8
E.F. Bugle, Commercial policg, poolvth and income thsrribution
run, the steady-state distributional outcome is the same as in the model when all capital goods are imported (which results in constant). Once the increase in foreign owned capital is determined, the soiution for the aggregate domestic capital stock is obtained by ~o~~~wi~ same procedure as in section 3.2.?
3.
stectionist trade regimes
The trade regime is labeled protectionist simply if t >s. Sections 3.1 and 3.2 analyze the impact of protectionist policies on the steady-state real wage and capital accumulation. Section 3.3 completes the analysts by c~~racterizinr the nature of the transition path the economy ~o~~o~vs ~~etw~enskadys&e equilibria.
In ana?yzing the distributional outcome here and later concentrate solely on how trade pulicy affects the real wage. enough to work out results for the impact on the real c rentals, these are of lesser interest from a distributiona! point of view. The steady-state equilibrium Is defined by (l)--(8), (1 ), (12). (14) and (15), 18 equations that can be solved for the 18 nnknow~s Q’. Pi, K”, L”, w, r9 1‘.U, P, and i as a function of t, s, L and 7: Though large and seemingly complex, the model is easy to manipulate because of its basically block recursive structure. Observe first from (4) and (15) that
where a circumflex denotes the percentazc &ngC in 3 ~ri&!~ 2.nd a!-b,P,jPk, the cost share of nontradables in the pro cQion of an aggregate capital good. Now define 0: to be the cost share of tor j in sector i and differentiate eqs. (I). After using (I@, there emerges
‘Eq. (23) is altered to read der=pP~l -h)dK, where h=dK”/d is the fraction of the increase in the aggregate capital stock accounted for by foreign owried capital K”. (If the country is a net exporter of capital, h measures the decrease in foreign assets owned by domestic residents.) Also, the sohtion ~“=~~~~Q~~~~is substituted into (22).
in r is less than the CQprofii condition nontradables sector that the wage- rental ratio must increase (6~ FormaIZy, om (16). (19) and (20)
Aside from the limiting and unrealistic case (for LDCs) in which capital is produced entirely in the nontradables sector (I = I), the wage-rental ratio must increase, with the magnitude of the increase being Larger the more dependent the economy is on imported capital goods (i.e.>the smaller is r). A higher wage-ren;aI ratio imp!ies that the real wage rises measured in terms of importables and nontradables. It is also clear that the real wage rises measured in terms of exportables since &> P,,,> p,. Protectionist trade 7~gi,nes are t’nus tinambiguousiy favorable to labor.
ositionB contrasls
stri
In static models fferences in sectorai facto by protection either lowers or exerts an am is likely to worsen t
es-Ed al outcome IS
in statictrade
sector
is typically capital int3sive in L
models conclude that the real wage fall n terms of s goods.8 When the capital stock is variable behavigr, real factor rewa ariner. The key facfegkprice to In a static model th capital rental v fixed capita3 stock, y contrast, with ,a behavior constrains tbe long-run increase increase in the supply price of a capital good. increases, in turn, depends on the tee reflected by the parameter r. As long as s (crl
‘In a 2 x 2 Heckscher-Oh’.- (HO) model the increase in the real capital rental is accompanied by an unambiguous decrease I the real wage, while in a Ricardo-Viner (RV) model the wage rises in terms of the exportable but declines in terms of the importable. The current model is a more complicated mixed I-IO-RV model that allows for nontraded goods, but in a static setting it yields broadly similar conclusions. Under the weak assumption that the ex Ort and noqtraded goods are compensared substitutes in consumption, the real wage MIS measured in terms of importables and nontradables whenever the import sector is the most cap intensive sector in the economy. If the nontradables sc~tor is suficiently labor intensive, the side of the model dominates: the nominal wage falls, pri?xcing an unambiguous decrease in the real wage.
~QF trade
theorists
have succeeded
in f~~~~ati
follows sheuld go a long way toward clarifying this debate: it is possible in the three-factor, three-sector general e~~~~~br~~rnmodel use here, TV derive simple conditions under which various commercial poficie are effective in promoting aggregate capital accumwlation.
To compare import-substituting and export-oriented policies some mark is needed. The anly fair benchmark woufd appear to be free Accordingly, the results in this and the following section -=~e in the tariff starting from an initka impact of a small inc,,,_ where t=s=O.
The policy implications of t e results are 0 As laid out in section 2, the imperfections. This makes i
model
d
12
E.F. Bugle, Commercial policy. growth and income distribution
private agents may cause the private discount rate to exceed the social discount rate, as in Blanchard (1985). Under either of these interpretations of the model, the results indicate the sign of the optimal second-best tariff or export subsidy.gv’O I will preccnt the results in a st;ictiy pasitivc hght; the reader can decide for himself whether they constitute a valid rationale for departing from free trade. Turning to the task at hand, the most economical solution procedure exploits the fact that across steady states the change in the aggregates capital stock must be consistent with equilibrium in the nontradable market. Endogenizing E through the expenditure function E(F, u), choosing units so that E,= 1 and differentiating (10) and (12) yields” c, dw+(&,I’, - P,R& dK
=Q L(fln-(P”&,)~~+(~,--~&,)~~+(n,-~”E,)8,], -n-
du=pP,d.K,
(22) (23)
where @*= F/Q”, ci denotes the marginal propensity to consu the compensated elasticity of demand for nontradables with respect to Pi; and rti~ PiRt:i,lQ”,the elasticity of nontradables supply with respect to Pi. Substituting for du and p,, in (22) from (19) and (23) gives
-
+
(& -
@“&JPx.
(24)
‘When there is a p ro p ortional tax T on net income, r = f~( I -T)- ’ + 6]P, across steady states and eq. (23) is replaced by du=ptl -r)- ’ dK. With finitely-lived agents as modeled in Blanchard (1985) greater modifications are required in the model because P is a function of K across steady states. Consequently, P, is also a function of K in the long run. Variations in P, induced by variations in K represent, however, second-round effects that do not alter the qualitative nature of the conclusions. [Extra terms appear in the coeficient multiplying dK in (24).] For the welfare analysis. what is crucial is that aggregate behavior yields p<(r-6)lP,
E.F. Bufj’ie.Comnercial policy. growth and
income distribution
ote from (7) and (9) that P,R, =(p -kfi)P,, of steady-state equilibrium.” Using this retationship and the conditions qn= - )~m---c)* and E,= -E,=+, (24) can be rewritten as
=b=-@“~“)(1-N(
m
where c~=c,+c,. Now “(Q~--@%J is the change in excess supply of nowtradables caused by a rise in Ip,. En& $j, --.$pl”&Y,) > 0.’ 3 (25) states that when s”t> (+a; a tariff increases sne aggregate c+ta! stock provid nontradables and exportables are not overly strong genera! equ~ljb~~rn complements (substitutes). Proposition 2. if the import-competin g sector is capita? (labor) intensive relative to the nontradables sector.
is the necescq capital stock.
and su_$cient condition @r a tariff to increase the aggregate
Corollary 2.1. If the import-competing sector is capital (iabor) intensive relative to the nontradables sector and nontradables and exportabks are general equilibrium substitutes (compbments), then a taii.fJ increases the aggregate capital stork.
Proposition 2 is a general result involving no explicit ~est~~~~o~s 02 technology or demand. To go further, it is necessary to ex terms of more primitive supply parameters. In the nosy. analysis is complicated by the presence of various te 12fL is found by solving for the change in Q” that results when 5 changes and all goods prices are kept fixed. With fixed goods prices, factor prices are constart. (Fmm the zero conditions in sectors m and n, w and r are constant. then foIlvws from the zero profit an condition in sector x that c is unchanged.) Eq. (18) thus (9) can be solved for 0” and 0”’ as a functioa? of K. Alte Kr;= ri/p” and solve eqs. (1) for r as a function of P,. 13The expression for qn will be presented later. Under very weak r tic2ions. qs is posit+= When qfl is negative, ~ro~os~t~o~ 2 and Cordlary 2.1 hold subject to ~~2~i~~at~Q~ that ihe nomradabks market exhibit Walrasian stability.
degrees of substitutabiiity between capital, iabor and land in ex~ortab~~s production. To astract from these terms, which are generally s ambiguous in sign, I will confine the analysis to the plausible case of a f~~~~ separable CES production function in the export sector. In the appendix it is shown that with this technology,
where t/~~zP@/f,Q”; k,=K”/L”; and t# is the elasticity of subbtitution in sector i (between capita! and labor in sectors na ar.d II and between capital, labor and land in sector x). Replacing ~7”and q, in (25) by the above expressions yields the following critical condition:
(26)
Eq. (26) isolates three crucial determinants of the aggregate capital stock. The first term measures the increase in capital accumulation arising from substitution towards capital induced by the increase in the wage-rental ratio [see (21)]. The second term captures the effect of the import sector drawing resources away from the nontradables sector. Not surprisingly, this tends to promote capital accumulation if the import sector is relatively capital intensive. Finally, the last term reflects the impact of the reallocating resources from the export to the import sector. Again, this reallocation favors capital accumulation when the import sector is relatively capital intensive > k,!. y inspection, it is easily seen that the two ~ea~~ocat~o~ e substitution effect when k,> k,, k, and E, ~0.
cts reinforce the
f e, > O), then a
tarijfinei eases the
The ~ond~tjon bst~tutes serves t
is clear from t in many countries It
contraction in the capital intensive nontradabtes sector is capable of lowering the aggregate capital stock. This outcome, however, requires quite small sectoral elasticities of substitution so that the substitu:.ion elect toward capital accumulation operates weakly. To see this, rewrite the second term in (26) as
In the normal case where goods are compensated substitutes, the first term is positive and the second is negative. The latter term, however, will be dominated by the term in (26) involving CF”if cf’(1-r) > @%l( I -@Y/F,), This gives Proposiiion 4. When the import-competing sector is capita! intensice relatice to the export sector and the nontraded good is a compensated substitute with both traded goods, tf’( 1 -x) > dQx( 1 - 838%) is a sufficient condition for a tariff to increase the aggregate capital stock. The logic underlying Proposition 4 is fairly straightforward. condition guarantees that #” increases when the ~o~trada most capital-intensive sector in the economy. For a give smaller is E, the more steeply sloped is the nontradab~es de e more steeply slo falls less than other effect [measured by G”(I- r)] dominates tke output e
The su
E.F. SufJie, Commercial policy, growth and income distribution
16
compensated substitutes at a high level of aggregation, Proposition 3 shoul apply in a large number of cases. Furthermore, in those cases where k, < k,, making Proposition 3 inapplicable, there is a reasonable chance that *he sufftcient condition in Proposition 4 will be valid. Though little is known about the magnitude of the cross-price elasticity E,, production function estimates invariably place the elasticity of substitution in the range of 0.5-1.2 [White (19X$)]. And even when the sufficient condition fails to hold, the capital stock does not decrease unless the single negative cross-price term is large enough to dominate all of the positive terms in (26). The most significant qualification in Propositions 3 and 4 is that the export sector be labor intensive relative to the import sector. In countries where exports are predominantly capital-intensive natural resource goods, protection may induce capital decumutation. Given the great diversity among LDCs, one additional result is of interest. A prototype that has received a great deal of attention in the development literature is the Enclave Export (EE) economy. The distinguishing feature of an EE economy is that interdependencies between the export sector and the rest oi the economy are at a minimum. In the current model, this notion is captured by setting cY=sX=O, which effectively severs all links between the export sector on the one hand and the import and nontradables on the other. Turning back to (25) [or (26)3, in the case of an EE economy the second term on the right-hand side disappears, giving rise to a completely unqualified result. Proposition 5. stock.
In an EE economy, a tar[ff increases the aggregate
capital
The intuitive rationale for this result is simply that a tariff on consumer imports alone acts as a differential capital subsidy in the non-export sectors by lowering Pk relative to P, and P,. In the EE economy, K” is fixed and therefore the stimulus to capital accumulation in the non-export sectors is sufficient to ensure an increase in the aggregate capita! stock.
3.3. The transition path was shown earlier that an escalated structure of protection always raises the real wage in the long run when the capital stock has reached its equilibrium level. This result directly contradicts the conventional wisdom, which argues that there is a strong presumption the real wage will decrease if, as in most LDCs, the import-competing sector is relatively capital intensive. Since the conventional wisdom is based on static trade models It
which assume a fixed aggregate capital st k, it is natup-al to canj=t the two results can be reconciledas refle ng the different short.. a run effects of protecti. n. The central aim of this section is to demonstr invariably correct. Accordingly, the analysis w~~i a tariff on capital accumulation and real in Proposition 3: k,> k, k, and E,>Q. 4 the most relevant case.) ven in this case, where is the most capital intensive sector in the econo plausible conditions protection generates an una at all points on the transition path betw condition for this outcome is z> c,, a con Behaviorally speaking, %>c,, means that an increase in investment spending raises the demand for nontradables: since a one dollar increase in investment is financed by a one dollar increase in saving, demand for nontraded consumer goods falls by c, at the same time as purchases of nontraded capital goods increase by r; the ove,all impact on demand thus tiirns on sign of a-cc,.14 In the appendix, I solve the famify firm’s intertemporal optimization problem and d~?lKXiStia~C that the steady state is a saddle point with a unique convergent path to equilibrium. The dynamic-; of the adjustment process are depicted in fig. I. The KK and II schedules denote loci for which sitively the capital stock and the level of investment ;ire constant. KK is sloped because the level of replacement investment rises with K. To the left of KK net investment is positive and K is increasing while to its right net investment is negative and K is falling. The If schedule may be positively or negatively sloped, but when positively sloped it cuts KK from above as in fig. l? Investment is increasing above 11 and decreasing below it, giving rise to a positively sloped saddle path. All of the results that follow also hold when the saddle path is negatively sloped. The relationship between the real wage C and the capital stock OPIth transition path is tracked by the WW schedule in the Given that a>c, and km> k,, I? and K must mov This follows from the dual nature of the Stolper-Samuelso theorems. P, increases on the transition path s’ the demand for nontradables while (from the capital stock results in a contraction in no tun, produces a magnified increase in the nomin the real wage rises regardless of the basket of goods workers consume. e initi Now consider once more the re ercussions of a t 14See eq. (A.1 1) in the appendix. ’ 5Theslope of the saddle ath is
T[
d- 6,
wkre
n is the
syste
I
I
S
S
I
I
I
!
W
\v
Fig. 1
brium is (iGo,I,, K,) in fig. 2.
tariff raises the
relative to nontradables. orem: an increase in
T the
good. The time path followe on the relative
state
of excess
E.F. Buffie, Commercial policy, growth and income distribution
20
Since P, has increased relative to P,, the change in nontradables supply is given by -qX: P,=
P,.
Nontradables supply increases as long as cY>O so that the export sector releases some factors to the rest of the economy. However, in view of the jump in investment spending, it is also possible that nontradables demand will have increased. At P,=P,, the overall change in ncntradables demand is given by (a -en) dl - D”E,~,.
The higher P, reduces consumption demand for nontradables but the rise in I pulls in the opposite direction. Bringing the supply and demand changes together, it is seen that the relative price of the nontradable is likely to increas: on ;&nycrciwhen: (a) nontradables and exports are weak substitutes both in production and consumption (c?, E, small - in the EE economy the real wage always increases on impact); (b) the iabor intensity of nontradables production is high relative to the average labor intensity of tradables production is small]; (c) the employment share of the nontradables l&z-U/&--k,) sector is large compared to the export sector; and (d) I rises strongly. Should any combination of (a)-(d) bring about an increase in the relative price of the nontradable, there wi!l be an unambiguous increase in the real wage on impact and at all points on the transition path between steady-states. Immediately following the imposition of the tariff, an investment boom produces a strong increase in the demand for labor intensive nontradables that shifts the WW schedule to the right and provokes a discrete, upward jump in the real wage from w0 and wi. The initial jump in the real wage is followed by further increases as a growing capital stock strengthens the demand for Loor. It may seem counterintuitive that investment rises initially given that the real wage increase forces r to decline relative to P, and P,. The simultaneous increase in I and fall in r/P,,, and r/P,, however, is easily explained. In deciding whether to invest the family firm compares, not the current capital rental to P, and P,, but rather the shadow price of capital ,l to the supply price of a capital good. The shadow price of capital equals the present discounted value of the marginal utility of the entire future stream of rentals generated by an extra unit of capital. Since r declines on the transition path and i- Pk in the new steady state, it is clear that on im act il rises by more
E.F. Bugle, Commercial
potrcy, growth
and income distribution
21
than P,. Firms endowed with perfect foresrght calculate the true vaiue of i. and respond by increasing I.
4. Export promotion In a pure export-oriented trade regime where s > t =O, the steady-state distributional outcome is well defined. Since ti> pX> 6 = P,,,= ?n = ? =O, landowners gain unambiguously while capitalists and workers lose to the extent that they consume the export good. Proposition 6. In a pure export-oriented trade regime, the real wage declines across steady states if the export gsod is consumed domestically.
When export promotion is accompanied by protection (SB t ~0): the distributional repercussions are possibly quite different. The real wage may increase unambiguously, an outcome that cannot occur in conventional static models. With t>O, the real wage rises in terms of nontradables and importables, but may fall measured in units of exportables (ti> pE p FJ. Even in strongly export-oriented regimes, however, it is likely that the export sector product wage will rise. Define the degree of export-oriented bias by p&P,> 1. After slight manipulation, (20) then yields
(27) from which we have Proposition 7. In an export-oriented measured m units of any good if
trade regime, the real wage increases
W)
For plausible parameter vahtes, (28) will be satisfied by values of /I< 1.5. Since few, if any, LDCs have pursued ex orb ~rornot~Q~ to t much exceeds unity, it seems safe to onclude that. i oriented trade regimes have been favorable to labor. kS liV6: however, to the fact that export su substantial measure of protection.
The
counterpart
to
(26) is
As an export subsidy does not alter the wage-re substitution effect toward capital ~~c~rn~~~a~~~ come is determined by just the two r~a~~~~i~~ determines the direction of tRe resource transfer kt nontradables secitors. If E,>O, the ~~~~radab~~s sector ex resources at the expense of the import SecfOP.ConYers?!yq nontradables autos contrasts, releasing resources as two reallocation efkcts work in the same direction (k,-k,) share the same sign.
Since normally E, >O, t e practical import of ~~@~~sition 9 k Bhat an export subsidy is sure ts p mote capital a~c~~n~~~t~~~~~~~ in the rare LDC in whida the import sector is the most labor intensive sector in the economy. In the much more common ease where the import set intensive sector in the econon y, an export tax is re accumu!ation. Finally, the interested reader can deve ic analysis for vari cases by proceeding along the same lines as in suction 3.3.
It is a cliche in the development literature istribtition of income of a given policy rank as high concetns abou demonstrates ~~~se~ue~~~s trade model that incor
regimesdse
m eseal
structure
tial studies of LittEe. S&msky
sf protection enhances
aggregate
and Scott, and Bhagwati and Krueger, which
not contradict this literature. The in this paper shows only that a case can
ts
“he 0
ea~jta~
agwati has stressed (1978), their trad only in ihe sense that export subsidies hav offset the anticxporl bias supply price of capital
is accompanied by continually rising real wa,ga an tion of income. l6 What eG3sting anal by the protectionist component substitution trade policy of countri unaided export subsidy triggers capi in the 1’ongrun. To make further progress towards outward-oriented trade strategies in L evaluate other arglamenb that have oriented trade strategy. This paper which commerciat polky afkts gro final word on the issue of which benefits. There are numerous ot growth might occur. It is frequent growth is fueled by gains from induced by greater contact with w must be carefullv, fiCWin;m c - - ....=ed befo trade regime is most conducive to growth.
on onward- vs.
Since t =s=O initially, the trade revenue terms in the budget constraint (12) may be ignored when solving the family firm‘s maximization problem. Hence, after substituting for E in the indirect utility function (12), the maximization problem ( 11) becomes
subject to ‘%nce supply and demand functions are horn nontradables supply and consumption demand for n Hence, if AI,> k, and the Increase in investment sp (2 > c,), then, on impact, k > Pm> B, = B,.
where A”
is the
arshallian demand function for the nontraded go Iv,= i”V/ZP,. Differentiating with respect to E yields in the case of ~~~ut~et~~ demand (i.e.*an unitary expenditure elasticity) B= H(1 -!- VEsr/V'EA")t W
0, the elasticity of the ~arg~~a~
W
iture.
~etu~~i~g to (A.rC),factor out VE/Pn, note that of (AS) to get
where a=~P,b,/Pk, the cost share of the production 0% an aggregate capital good. Slime tastes a P,A”/E SC,,, where c, is the marginat pro Thus, after collecting terms on 9, i and k (A.6) reads
where
essary to know to c~~~~es in I required reduced-form solutions are obtained from qs. (~~~~0~ and (124. which define the temporary equilibrium. ENS,(1) yiel Samueison solutions:
To complete the dynamic analysis, it is with P, and how the latter in turn respo
More efbrt is needed to obtain N, and N,. After tedious emerges
there
N,IP,= r&8”, + c,eyy
(A-10)
N,/P, = P,( 3( - c,)/f.
(A.1 I) -@/pm> 0, the elasticity of excess supply of rradabies sector 1s
in no
es
E.F. B&e,
28
Commercial policy, growth and income distribution
where yl=b;+Pk
V,(cx-
c”)2
-v,,
f
1
93,
1.
r2v&en,+ c&y-ae; +( I- o!)qq p () fE-m2
The determinant of the coefficient matrix in (A. 15) is negative. The steady state, therefore, is saddle-point stable. A.I.
The general equilibrium supply elasticities
Uzawa (1962) has shown that the Allen partial elasticity of substitution between factors i and j, Oij, equals C,C/CiCj. Logarithmically differentiating eqs. (j)-(6) and making use of Uzawa’s result and the adding-up condition %PKK= &CI, where 0 is the c!asticity of substitution between capital and labor - we obtain *. L’ = - ,i(&( 6 - i’)+ Qi, ki = &‘,(G _ ;) +
(A.16)
Qi,
(A.17)
for i=n, m. From (A.8)-(A.9), ti-i=(p,-p,)/B. gives
ei=~&~l3-~(b,-P~)+~~, i=n,m, Ki
=
-&$-yp,-p")+Qi,
i=n,m.
Substituting into (16)-(17)
(A.18) (A.19)
Similar manipulations of (5), (6) and (8) yield the following solutions for K* and L” in the case of a non-nested CES production function:
B,,
(A.20)
-$dx,
jA.21)
i‘=a‘elPn+tYe2Pm+$ T
Rx= cxe3P,
+ cXe4Bm$
T
where
E.F.
Bufie,
CommerciaS policy, growth and income distribution
29
Differentiating (7) and (9) and making use of (A.18)dA.21) now gives two equations that can be solved for Q” and Q” as a function P,, Pm and Y,: Lmom+ Ln@ = d,& + d,b, -
( Lxcr=/~“,)~x,
(A.22) (A.23)
where do = B- ‘(#LV;t + o”Lm8;) - LWe,, dl z I?- ‘(a”K’Y?~+ amKmQ)- Kxaxef, d2 3 B- l(cPLnO~+ a”lL”@) - L”a”e,,
The solutions for 9” and qX on page 14 in the text can be obtained in a straightforward manner from (A.22)-(A.23). References Bardhan, P.. 1970, Economic growth, development and foreign trade (Wiley, New York). Bertrand, T., 1975, The gains from trade: An analysis of steady-state solutions in an open economy, Quarterly Journal of Economics 89, 555-568. Bhagwati, J., 1964, The pure theory of international trade: A survey, Economic Journal 74, !-84. Bhagwati, J., 1971, The generalized theory of distortions and welfare. in: J. Bhagwati et al.. eds.. Trade, balance of payments. and growth (North-Holland, Amsterdam). Bhagwati, J., 1978. Anatomy and consequences of exchange control regimes (Baiiinger. Cambridge, MA). Bhagwati, J. and T.N. Srinivasan, 1969. Optimal intervention to achieve noneconomic objectives. Review of Economics Studies 36,27-38. Bhagwati, J. and T.N. Srinivasan, 1980, Trade and welfare in a steady state, in: J. Chipman and C.P. Kindieberger, eds., Fiexibie exchange rates and the bcaiance of payments: Essays in memory of Egon Sohmen (North-Holland, Amsterdam). Bianchard, O., 1985, Debt, deficits and finite horizons, Journ&! of Poiiticai Economy 93. 223-247. Chenery, H. and M. Bruno. 1962, Development alternatives in an open economy. Economic Journal 72,89-103. Chenery. H. and P.B. Eckstein, 1970, Alternative policies for Latin America, Journa) of Pohtical. Economy 78,9661006. Chenery, H. and A. MacEwan. 1966. Optimal patterns of growth and aid: The case of P in: I. Adeiman and E. Thorbecke, eds.. The theory and design of economic devcl (Johns Hopkins University Press. Baltimore, MD). Chenery, H. and A. Strout, 1966, Foreign assistance and economic ,levelopment, American Economic Review 56,679-733. Cooper. R. and J. Sachs, 1985. Borrowing abroad: The btor’s perceptive. in: G.W. ~eloping countries (The W J.T. Cuddington, &., i~ter~ationai debt and the Washington, DC). .. cdi.. :i et Corden, W.M., 14 ti, ‘The effects oi tratie nor o,i sn Trade, balance of payments and grow Charles P. K.ind!eberger ~N~~tb-~o~~a~~, New York).
30
E.F.
Su~re,
Commercial
policy,
growrh
and income
distribution
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