Me4- vie ,,ft?6,4 UV;

MODELLING RESEARCH GROUP

FOUNDATION OF GIANNINI AGRICULTURAL ONOMICB UB i,PR 2 71987

DEPARTMENT OF ,' UNIVERSITY OF SOUTHERN CALIFORNIA UNIVERSITY PARK LOS ANGELES, CALIFORNIA 90089-0152 M'4 we ?60 UV;

MODELLING RESEARCH GROUP

THE NORTH'S DEMAND FOR SOUTHERN EXPORTS AND IMMISERIZATION OF THE SOUTH

ABDELHAMID MAHBOB

JEFFREY B. NUGENT*

MRG WORKING PAPER #M8624

FOUNDATION OF JIANNINI ONOMICS AGRICULTURAL LIB tYP% 'PR 2 71987

DEPARTMENT OF ECONOMICSA UNIVERSITY OF SOUTHERN CALIFORNIA UNIVERSITY PARK LOS ANGELES, CALIFORNIA 90089-0152 THE NORTH'S DEMAND FOR SOUTHERN EXPORTS AND IMMISERIZATION OF THE SOUTH

ABDELHAMID MAHBOB JEFFREY B. NUGENT*

MRG WORKING PAPER #M8624

May 1986

ABSTRACT

This paper constructs an alternative model of North-South to the controversial one of Chichilnisky for purposes of demonstrating that export-led growth can be immis- erizing for the South even when the source of export growth is an increase in the North's demand for the South's export. The model relies on a dualistic labor , a relatively substantial urban rate and a Harris-Todaro migration function which serves as an adjustment mechanism additional to that of the terms of trade. Since the dualis- tic labor market constitutes a distortion, the model represents another special case of Bhagwati's "general theory of immiserizing growth". 1. Introduction The identification of conditions under which export growth would be

immiserizing has been a popular pastime for for some time. The

factors initiating immiserization would seem to be of two main types:

(a) those in which, in the presence of a distortion, growth itself is the

initiating sourcel and (b) those in which a change in policy regime, typically

moving from autarky to free trade, but also from one level of trade to another,

is the initiating source.2 Models in which the latter source of immiseriza-

tion is featured can in turn be broken down into two classes, namely single

country models and two-region models of the North-South variety in which

asymmetries in technology and structure exist. In view of the widespread appreciation for the enviable export-led growth

performance of the "gang of four" East Asian countries (Taiwan, Korea, Hong

Kong and Singapore) the claims of Chichilnisky (1981, 1984a, 1984b) and Heal

and McLeod (1984) suggesting that export growth can be immiserizing even if

the initial impetus is increased external demand for the South's exportables

have quite understandably received much attention. Thus far, however, the

issue has been clouded by numerous confusions and ambiguities, leaving the

jury split on whether or not the argument has been successfully demonstrated.3

Recently, Lysy (1985) removed some shortcomings in Chichilnisky's model

and carefully reconstructed her argument. He demonstrated that an exogenous

shift in Northern demand could immiserize the South in the sense that in the

new equilibrium a higher volume of Southern exports may be more than offset by

the resulting deterioration in the terms of trade. Nevertheless, this demon-

stration was for the intuitively obvious case in which the initiating force is

an increase in the North's demand for its own export (i.e., a decrease in its

demand for the South's export). 2

The purpose of this paper is not to reenter the debate as to the adequacy of Chichilnisky's model but rather to construct an alternative model substan- tiating the original claim of Chichilnisky (1981, 1984ai-1984b) -and-Heal_and

McLeod (1984) that immiserization can occur even when the initial change is an increase in the North's demand for the South's export. Since our model relies on a dualistic labor market, which can be interpreted as a distortion, our demonstration provides yet another example in support of Bhagwati's "general theory of immiserizing growth." While in other respects our model deliber- ately follows (although generalizing slightly) the Lysy-Chichilnisky model, its most important innovation is the inclusion of a migration function of the

Harris-Todaro type which serves as a second adjustment mechanism (in addition to that of the terms of trade). The addition of this second adjustment mechanism is crucial for immiserization because otherwise the export demand shift would improve the South's terms of trade and income and that would be that. With it, however, it can trigger adjustments in the labor market which under certain conditions can lower the South's terms of trade and income.

Specifically, if the South's exportable (B) is labor-intensive and urban unemployment exists, an improvement in the South's terms of trade (P) induced by the North's increased demand for B could trigger in the South a reduction in urban unemployment (U), excess supply in the market for B and hence a subsequent decline in P. With P and U falling simultaneously, but U still sufficiently high, as will be' explained below, the fall in U can under certain conditions have the effect of lowering the expected urban rate, thereby delaying restoration of equilibrium (i6 the sense of no further change in the

unemployment rate) until P has fallen sufficiently far below its initial equilibrium as to cause the South's income to fall. 3

2. The Model Let the South be producing two ; a basic (primary) good (6) and a

manufactured good (M), combining labor L and capital K in constant returns to

scale production functions

B B (1) B = L 0(k ); 0 > 0, 0" < 0 and 0(0) = 0,

(2) M = LMf(kM); f' > 0, f" < 0 and f(0) = 0,

B where k and kM represent the capital-labor ratios in the two sectors. With

perfect prevailing everywhere, in each sector entrepreneurs will

hire units of the two factors up to the point of equality between the real

factor and their marginal physical products. We take the manufactured

good M as a numeraire (the nominal of which is normalized to 1).

Although the two factors are perfectly mobile within the economy, we follow M B Harris and Todaro in assuming wage rate dualism, w > w , which coexists with urban unemployment. The industrial wage rate wM is set by minimum wage legis- B lation and is designated by w M. Both w and w are measured in units of M.

Denoting by P the price of B in term of units of M, the marginal productivity

conditions are as follows.

1413 [0(kB) 030.(kB) ]p (3)

(4) WM = f(kM) kMf'(kM)

M 113 (5) f'(k )= Ol(k P = r 4

Although for simplicity the factor endowments are assumed fixed, there is suf-

ficient time for these endowments to be reallocated between sectors. Hence,

we can write:

(6) LB + LM + U = E; u >

(7) kBLB + kMLM = R

where U is the number unemployed in the urban sector. Equation (4) implies _m that at w there will never be an excess demand for labor. The marginal rural

worker considering migration to the city would expect to earn the wage rate:

e -m m m (8) w = w L +U)

Thus far the model is similar to that of Harris and Todaro (1970) but

without the equality condition wB = we and without the fixity of Ln which

follows from the fixity of sector-specific capital. The system of equations

(1)-(8) can be solved in terms of the state variables P and U. We will assume _m dw = 0 and that dK = dL = 0, i.e., that the factor endowments remain

constant.

Before solving the model, note that equation (4) implies the fixity of kM _11 in terms of w and that equation (5) yields:

-. (9) dk =( 4) /4 )dP

B implying that the relationship between k and P is positive. From equations

(3) and (9), after some manipulation, we obtain: 5

B (10) dw =

The factor supply constraints (6) and (7) together with equation (9) can B be used to solve for employment in the two sectors L and LM as follows:

(11) (kM-kB)dLB = (-LBOVP0")dP - kMdU

(12) (kM-kB)dLM = (L801/4")dP + kBdU

M B If we assume a la Hechscher-Ohlin that (k -k ) > 0, an increase in P or a B decrease in U would cause L to rise and LM to fall. From equations (1) and

(2) it can be seen that the output-price responses would be:

B B dB/dP = LOl dk /dP + OdL /dP, and

m m dM/dP = fdL /dP (k is independent of P)

With the aid of equations (9), (11) and (12) and after some manipulation,

we obtain:

M B (_0.1_13/0.,p2)(wB÷rkM .-_ (13) (k-k)c113 = )aP 01(MdU

M B B B (14) (k -k )dM = (O'L /0"P)dP + fk dU

The "perverse output-price response" case of Bhagwati and Srinivasan (1971) is M B ruled out by assuming that k -k > 0; i.e., that B is more labor intensive

than M. Hence, in this case the effects of factor growth on production in the two sectors follows from Rybczinsky's theorem. Specifically, since a change in U can be treated as a change in the effective supply of labor, a decrease in U would result in an increase (decrease) in the supply of the more (less) labor-intensive good, B(M).

The final point to be made in this section concerns the wage rate (we) migrants would expect to receive if they were to move to the urban sector. e Since w is formed from observations on U and L in a dynamic world, seemingly perverse responses can be obtained. For example, were U to increase, from e M B equation (8) the direct effect would be to reduce w but, as long as k > k , as noted above it would also increase LM which would tend to raise we. It is possible that the latter effect would dominate the former and hence that the unorthodox result in which U and we would rise together would obtain. If so, despite the rising U, rural-urban migration would be induced. In order to identify precisely the condition(s) under which this would occur, let us totally differentiate equation (8):

e -M M 2 M M dw = [w +U) ](UdL -L dU)

With the aid of equation (12), this yields:

kBLM);114/01.u)2(kM_ kB). dwe/dU = (kBU - kMLM +

M B that of the terms As long as k -k > 0, the sign of this derivative would be within the first set of parentheses which can be rewritten as:

B M M M B M M k (U+L )- k L = k L - - k L (since U+LM = L-0)

B = k L - K (since kBLB + kMLM = K) 7

Using Jones' (1965) definition of relative factor intensity wherein sector B

is relatively more labor intensive than sector M when the percentage of labor

used in (or allocated to) sector B is greater than the percentage of capital

used in (or allocated to) that sector, the labor intensity of sector B

implies:

B B B B B B L /(L-U) > k L /K or 1/(L-U) > k /K or k L - K < k U.

We then can state the following condition.

B (C.1) dwe/dU 0 according as k L-K 0.

e B When U = 0, the orthodox result dw /dU < 0 must hold since k L-K is neces-

sarily negative. However, the larger the value of U, the wider will be the B range over which k L-1( > 0 would hold. Since in reality urban unemployment

seems to be sizeable in most developing countries, this would seem to be a

distinct possibility.

To facilitate the subsequent analysis, from equation (12) the full

expression for the total variation in we can be written as:

e -M M 2 M B B B (15) dw = [w /(L 411) (k -k )][(UL cps/Pcp")dP (k L-K)dU

3. Equilibration, Comparative Dynamics and,Immiserization

As noted above, the attainment of "equilibrium" in our model is driven by

two adjustment mechanisms, namely, the elimination of labor migration via

adjustment in the allocation of labor so as to satisfy we = wB and the clear-

ance of the product markets via adjustment in P. The first adjustment mechan- 8

ism can be expressed as:

= H(we_w6); H, (16) H(0) = 0 and 0 = dU/dt.

At equilibrium, 0 = 0. We can, therefore, obtain a curve in the P-U plane along which no further migration occurs and urban unemployment is constant.

This "0 = 0" curve can be written as:

+ H dU = 0, (16') H dP u where H = H l dwe/dP - H I ciwB/dP < 0 [from equations (10) and (15)], and e B Hu = Hiciw /dU 0 according as k L-K 0. (Condition (C.1))

Turning now to the second adjustment mechanism, and assuming that the

South is an exporter of B and an importer of M, the terms of trade P would come to rest when the value of the North's imports (of 0 is equal to the value of the South's imports (of M), i.e., when the con- straint of each region is satisfied. This condition guarantees the clearance of the world market for one of the products (and by Walras law also the other). For simplicity and without any loss of generality, let us assume the

North's import demand for B to be m(P,a) where mp < 0, and mu > 0 such that a can be interpreted as a shift parameter in the m function. We postulate also B -M M the South's consumption function for M as 40 L , w L , rk, P). One may

regard this function as the sum of the consumption functions of rural workers,

urban workers and all capitalists. All partial derivatives are assumed to be

positive, i.e., all groups consider M as a normal good. The equation of

motion of P can be written as:

(17) = G(m - Op-MVP); G' > 0, G(0) = 0 and 0 = dP/dt. 9

If we start from equilibrium, = 0. The argument of the G(-) function repre- sents the world excess demand for B after making use of the South's budget constraint (or its balance of payments condition). Hence, the terms of trade

(or the relative price of B) must grow when the world excess demand for B rises above its initial value of zero. Setting = 0 and taking the total differential, we can derive the "P = 0 curve" in the P-U plane as:

G + G dU = (17') dP u

where Gp = G'qmp + (tp-M)/P2 - (1/P)d(&ls-M)/dP] < 0 and G = (-GI/P)

(tpiwBdLB/dU - (f-tp2AdLM/dU) > 0. The negativity of Gp is required for the

stability of static equilibrium (in the Walrasian sense) which is the

Marshall-Lerner stability condition. As for the sign of Gu, notice that the (f-ip w ) must be positive since f > w from equation (4) and tp repre- term 2 2 sents the urban workers' marginal propensity to consume the importable good M,

and hence 0 < 4J2 < 1. Even if the tp(-) function is amended to include the

effects of transfers received by the unemployed, Gu > 0 would still hold.4

The system of differential equations (16) and (17) reaches a locally

stable equilibriums if and only if both the following conditions are satis-

fied: H + G < 0 , and (i) the trace condition: u P (ii) the determinant condition: HuGp - HpGu > 0 ,

where all these derivatives are evaluated at the equilibrium values of P and

U. Since Gp < 0, Gu > 0 and Hp < 0, it is sufficient that Hu < 0 in order for

both conditions to be satisfied. But this is not necessary. The economy can

still reach a stable equilibrium even if Hu > 0 as long as the absolute value

is not very large. of Hu 10

For understanding the comparative dynamics, phase diagrams can be of use.

The determinant condition above can be rearranged to give: -Hu/Hp < -Gu/Gp.

This means (from equations (16') and (17')) that the slope of the 0 = 0 curve of = 0 curve. The latter is always positive. must be less than the slope P C. The former could be positive (Figure 1) or negative (Figure 2) depending on the sign of Hu. In the case of Figure 1, stability requires that the 0 = 0 curve be flatter than the 0 = 0 curve.

At this point, we have all the ingredients to demonstrate export-led immiserization. To do so, we show, first, that the terms of trade could be worsened by the exogenous increase in the North's demand for B and., then, that the result could be a decrease in the South's income.

An increase in the North's demand for B would be represented by an increase in the shift parameter a in the m(-) function defined above. As can be seen from equation (17) above, this would shift upwards the P = 0 curve as shown in Figures 1 and 2. That is, if we start at some equilibrium point such

E in either Figure 1 or Figure 2, this external shock will have the effect as 0 of increasing P initially at the current value of U. If Hu < 0 as in Figure

2, the final effect will be the orthodox one of an increase in P. If, how- ever, Hu > 0 as in Figure 1, the new equilibrium point El will be to the of E implying that the South's terms of trade are negatively Southwest 0' affected by the initial increase in the North's import demand.

In order to explain this result, assume that Hu > 0 (i.e., dwe/dU > 0). 0 = The initial effect of the increase in m(-) is an upward shift in the the curve. The economy would operate at ome point like E2. In spite of B and equilibrium in the product markets, the new higher P would raise w depress we (from equations (10) and (15)), hence making 0 negative. Moreover, in the as U falls, P becomes negative since Gu > 0; i.e., an excess supply 11

world market for B develops. Hence, both P and U would now be falling. The

fall in P would help narrow the gap initially created between we and wB and

also would help eliminate the excess supply in the market for B. This pro- to ) cess, however, would be frustrated by the fall in U which would tend decrease we (from Condition (C.1)) and to increase the excess supply of B. This is why a large reduction in P is needed in order to restore equilibrium e at E in Figure 1. On the other hand, if dw /du < 0, the fall in U would as 1 B e accelerate the closing of the gap between w and w and less of a fall in P

would be needed to restore equilibrium as at E1 in Figure 2.

. Moreover, as long as Hu > 0, the initial increase in m(-) will result in B B -M M a decrease in the South's income defined asY=w L +w L + rK. Sincer=

fl(kM) and kM depends only on WM, it is clear that capitalists' income rK is

not affected. With aggregate income falling but capitalists' income unaf-

fected, it is implied that the effect of variations in P and U fall completely income. The total differential of Y can be obtained as: _ on labor

dy 1.13dwB 4. w13--dLB m m . + Cra-

\

13 - M B M [(wM- B-wB M M B = L OP + [(w -w )31_ /3P]dP + k k )/(k -k )]dU

where use is made of equations (10), (11) and (12). From equation (8) and 13 e realizing that at equilibrium w = w , one can obtain:

WM-wB = WM - WMLMALM+U) -=;'WMUALM+U) and

_ ] cimkB - wBkM = WMkB - WMOLMALM+U) = [kB(LM+U) - OILM -411/(LM+U)

B -M M = (k L-K)w /(L +U)

_ 12

Thus, after using the expression for dwe/dU from equation (15), dY can be expressed as:

-M M M e dY = LBqdP + [w U/(L +M(aLM/aP)dP + [(L +08w /30dU:

Equations (16') and (17') can be used to substitute du for dP and dU. It is easy to show that dP = (-G s motHu/D) and dU = (Glmai-lp/D) where D = GpHu - GuHp

> 0 by the determinant condition for dynamic stability. Using the definitions

H and H stated above, it can be shown (after some manipulation) that: of u

(18) dY/dcy = (-141-11/D)awe/DU < 0 [Q.E.D.]

We can also notice that:

m dLM aLM . dP dU der 3P der 3U da

Then, replacing dP/dot and dU/dcy by (-GlmotHu)/D and (G'motHp)/D, respec- tively, and collecting terms after making use of equations (15) and (16'), we can get:

M G'm H' - M dL _ wL aLM (19) D, 2 . V der (LM+U)

By inspection of the signs of the relevant terms in equation (19), it can be seen that dLM/da < 0. Hence, the *conditions under which an increase in foreign demand for the South's export would immiserize the South also imply that the South would experience declines in manufacturing employment and urban unemployment and an increase in rural employment. In other words, under the 13

specified conditions, the rise in the North's demand for B would set off a reaction chain wherein at the new equilibrium the South's terms of trade and income would be lower than they were before the increase, the of income would be further biased against the working class and the direction of migration would be reversed.

Just as Lysy made no claim for the likelihood that export immiserization would occur in the case in which the North's demand for M rises, we make no claim as to the empirical validity of immiserization of the South when the

North's demand for B increases, let alone one that there is evidence support- ing our particular explanation for it. Nevertheless, it is interesting to

note that several authors6 have attributed all of these results to the

increased demand for 13 in the North associated with the expansion of colonial-

ism in the late nineteenth century.

It is important to emphasize that the model and the export-immiserizing

conclusions derived from it arise only when urban unemployment is relatively

large as it is frequently argued to be in contemporary LDCs. Indeed, it is

the fact that the conditions for immiserization are most likely to arise when

urban unemployment is relatively high which gives the model and its outcome

some potential relevance and importance. Should open urban unemployment be

relatively unimportant but employment in a nontraded informal sector rela-

tively important, and should there exist relatively strong positive linkages

between the formal and informal urban sectors, as Cole and Sanders (1985) have

argued, the model would change considerably and export immiserization results

not necessarily obtain.

15

Footnotes

*The authors wish to thank Graciela Chichilnisky, Jan Gunning and Anup Sinha for useful suggestions.

1. See Bhagwati (1971).

2. See, e.g., Johnson (1965), Batra and Pattanaik (1970), Batra and Scully (1971), Brecher and Diaz-Alejandro (1977), Bhagwati and Brecher (1980), Bhagwati and Tironi (1980).

3. On the "con" side see Ranney (1984), Gunning (1984), Saavedra-Rivano (1984), Findlay (1984) and Srinivasan and Bhagwati (1984) on the "pro" side see Chichilnisky (1981, 1984) and Heal and McLeod (1983, 1984). B 4. The unemployed receive some transfer s < w < w. The function would now be amended to include sU which would appear as tits in the term Gu in equation (17'). As long as 4,5 and s are small so as to be dominated by the other positive terms in Gu, the results will not be affected.

5. It is noteworthy that this equilibrium is not only locally stable, since H G but globally stable as well. The Olech's conditions are satisfied u P and H G 0 See Sydsaeter (1981). 0 P u 6. See especially Resnick (1970) and Birnberg and Resnick (1975). 16

References

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M8530: MICHAEL J. P. MAGILL and WAYNE J. SHAFER: Equilibrium and Efficiency in a Canonical Asset Market Model. M8531: DENNIS J. AIGNER and PIETRO BALESTRA: On the Optimal Experimental Design for Error Commponents Models. M8532: ROGER GUESNERIE: Stationary Sunspot Equilibria in an N Commodity World. M8601: JOHN M. VEITCH: Repudiations and Confiscations _by the Medieval State. M8602: MARIO D. TELLO: Imperfect International Markets, Multinational Enter- prises and Manufactured Exports from Developing Countries. M8603: JEFFREY B. NUGENT: Arab Multinationals: Problems, Potential and Policies. M8604: RICHARD H. DAY and T.-Y. LIN: Irregular Fluctuations and Comparative Policy Dynamics in the Keynesian Regime. M8605: RICHARD M. GOODWIN:—TRe Economy as an Evolutionary Pulsator. M8606: Z.M. BERREBI and J. SILBER: Interquantile Differences, Income Inequal- ity Measurement and the Gini Concentration Index. M8607: JOSEPH G. HIRSCHBERG: A Comparison of Three Flexible Cost Functions Using Establishment Level Electricity Use Data. M8608: IAN E. NOVOS and MICHAEL WALDMAN: Complementarity and Partial Non- excludability: An Analysis of the Software/Computer Market. M8609: ARNOLD ZELLNER: Further Results on Bayesian Minimum Expected Loss (MELO) Estimates and Poste Distributions for Structural Coeffi- cients. M8610: ARNOLD ZELLNER: Bayesian Analysis in . M8611: ARNOLD ZELLNER: A Tale of Forecasting 1001 Series: The Bayesian Knight Strikes Again. M8612: ARNOLD ZELLNER: Biased Predictors, Rationality and the Evaluation of Forecasts. M8613: ARNOLD ZELLNER: Bayesian Estimation and Prediction Using Asymmetric Loss Functions. M8614: RICHARD H. DAY, SUDIPTO DASGUPTA, SAMAR K. DATTA, and JEFFREY B. NUGENT: A Note on Instability in Rural-Urban Migration. M8615: DENNIS J. AIGNER, FRIEDRICH SCHNEIDER and DAMAYANTI GHOSH: Me and tlz Shadow: Estimating the Size of the U.S. Underground Economy from Time Series Data. M8616: ROBERT KALABA and LEIGH TESFATSION: Flexible Least Squares. M8617: JOHN M. VEITCH: Wavering Virgins, the Deficit and Gramm-Rudman. M8618: TIMUR KURAN: Chameleon Voters and . M8619: RICHARD H. DAY: The Evolving Economy. M8620: JACQUES SILBER: Factor Components, Income Classes and the Computation of the Gini Index'of Inequality. M8621: MARIO D. TELLO: Manufactured Exports from Developing Countries and Government Policy Under Imperfect International Markets: Corporate Income Taxes and Exchange Rate. M8622: DANIEL F. SPULBER: The Second Best Core. M8623: DANIEL F. SPULBER: ValWand Efficiency: with Nonlinear Price Schedules. M8624: ABDELHAMID MAHBOB and JEFFREY B. NUGENT: The North's Demand for Southern Exports and Immiserization of the South. M8625: IAN E. NOVOS and MICHAEL WALDMAN: The Emergence of Copying Technolo- gies: What Have We Learned. M8626: REZAUL KHANDKER: Offer Heterogeneity in a Two State Model of Sequential Search. A

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