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Was Britain immiserized during the industrial revolution?
EXPLORATIONS
IN ECONOMIC
HISTORY
28,
121-124 (1991)
NOTE Was Britain lmmiserized
during the industrial Revolution?”
DOUGLAS International
Finance
Division,
Federal
A. IRWIN Reserve
Board,
Washington,
D. C. 20551
Economic historians have been cautious in ruling out, or have ruled out for the wrong reasons, the possibility that Britain was immiserized in the early 19th century. This note suggests that the notion that Britain was, or came close to being, immiserized can be rejected. Q 1~1 Academic press, I~C.
The theory of immiserizing growth examines the conditions under which economic growth concentrated in a country’s export sector could so deteriorate its terms of trade as to reduce national welfare.’ While few economists have suggested actual examples of this phenomena, one possible case appears to be that of Britain in the early 19th century. As a consequence of the industrial revolution, Britain experienced tremendous growth in the output of its exportables, particularly cotton textiles. This sharply reduced export prices and led to a deterioration in Britain’s terms of trade of nearly 30% between 1821 and 1841.2 Several of the classical economists observed this situation with concern and passages in their writings resemble anticipations of the concept of immiserizing growthq3 Economic historians have been tentative in ruling out the possibility of immiserizing growth for this period of British history. Some such as Matthews (19.54) have suggested that Britain may have been immiserized if foreign demand for cotton textiles was price inelastic. Recent estimates of trade elasticities for the period in Irwin (1988) suggest that this assumption may be reasonable. Others more skeptical about the possibility of immiserization, such as Hartwell and Engerman (1975), present data showing improved standards-of-living for labor. Yet immiserization cannot * I thank N. F. R. Crafts for helpful discussions and a referee for useful comments. ’ Originally dubbed “damnifying growth” by Edgeworth (1894), the modern theory has been set forth by Bhagwati (1958). ’ See Crafts (1985), p. 147, and Findlay (1982). 3 See the papers by Bloomfield. 121 00144983/91 $3.00 Copyright 0 1991 by Academic Press, Inc. Ail rights of reproduction in any form reserved.
122
DOUGLAS
A. IRWIN
be ruled out on this basis: if Britain specialized in producing capitalintensive goods for export, as there is reason to believe, the StolperSamuelson theorem (1941) tells us that an adverse terms-of-trade shift will increase the real return to the scarce factor, i.e., the real wage of labor. Crafts (1985) recently examined the issue in the context of a twosector model of international trade. Although he finds that there was no immiserization, Crafts maintains that agriculture played a pivotal role in this result; without an expansion in agriculture, he argues (p. 150), the model “conceivably could have implied immiserizing growth and would certainly have worsened the terms of trade.” The purpose of this note is to suggest that the possibility that Britain was immiserized during this period can be ruled out in general, regardless of the role played by demand inelasticities, agricultural production, or other factors. A slight variant on the model used by Crafts (in Caves and Jones, 1977) provides the framework for the analysis. Export and import volumes respond both to changes in the terms of trade, from which the offer curve is derived, and to shifts in the offer curve, considered here as the change in trade volume that would occur at constant relative prices. Thus, the change in home (or Britain’s) imports and foreign imports (Britain’s exports) can be decomposed as follows:
rii = ej? +
Al,,
ii?* = e*p^ + iG*Ip,
(1) (2)
where M (M*) is the volume of home (foreign) imports, e (e*) is the elasticity of the home (foreign) offer curve, and p is Britain’s terms of trade, or relative price of its exportables. (Hats denote relative rates of change, i.e., j? = tip/p.) The first terms of (1) and (2) are the elasticity of imports to terms-of-trade changes along the offer curve, while the second terms are shifts in the offer curves at constant prices. After totally differentiating and rearranging the balance of trade identity,
p^+itP=ii2, and substituting
(3)
(1) and (2) into (3), solving for p^ yields
where A = e - e* - 1 and is positive to meet the Marshall-Lerner condition for stability. Consider the case of export-led growth in Britain, where at constant terms of trade the output of the exportable expands while that of the importable does not, i.e., dxX > 0 and dxw = 0, where xx (xM) is domestic production of the exportable (importable). Also assume that the foreign offer curve remains fixed, i.e., &I*/, = 0. These two assumptions increase the likelihood of immiserization. Home demand for the importable in-
BRITAIN
AND INDUSTRIAL
REVOLUTION
123
creases because of the output expansion at initial prices such that dM = mpdx,, where m is the marginal propensity to import and pdxx is the change in income. Substituting this relation into (4) we have j? = -mpdxX/MA.
C-9
Note that p^ is indirectly related to dx,; i.e., an increase in the output of the exportable decreases the relative price of exports. The change in the country’s welfare can be written as dy = FM + (pdx, + dxw),
(6)
the first term representing the terms-of-trade effect and the second term representing the effect of changes in production (which equals zero for a movement along the production possibilities frontier, but here becomes simply pdx,). After substituting (5) into (6) we have dy = - (m/A)pdxX
+ pdxx,
m
which demonstrates the ambiguity of the change in welfare resulting from increased output of the exportable. The second term indicates that at constant prices welfare rises by the amount of the additional output, while the first term indicates that the terms of trade deteriorate commensurate with the increased output. Immiserization requires only that m > A. The reason Crafts attributes such an important role to agriculture in averting immiserization is that he believes the marginal propensity to import would have been large in the absence of a prosperous British agriculture. Crafts also suspects the price elasticities of British trade to have been small. Taking e and e” to be the demand elasticities of British trade and assuming that they were somewhat inelastic, he found that the parameters came quite close to meeting the condition for immiserization. Crafts’ assumption about the values of the import and export demand elasticities, as pointed out above, has been generally validated by evidence in Irwin (1988). However, e and e* in A are not the price elasticities of British trade as he suggests, but the elasticities of the offer curve. The offer-curve elasticities can be decomposed into the price elasticities of import demand and export supply, such that e = -r) 3 E and e* = 7I” - E” , where q (q*) is the home (foreign) price elasticity of import demand and E (E*) is the home (foreign) price elasticity of export ~upply.~ Thus, Crafts concludes that Britain would have come perilously close to being immiserized in the absence of a prosperous agriculture partly because supply elasticities were excluded from consideration. In fact, the sum of 4 Note that e > 0 because import demand rises along the offer curve with an increase in the relative price of home exportables, dhile e* < 0 because foreign import demand falls with a rise in the relative price of its importables (the home country’s exportable). This leadstoe = -r) + &>Oande* = q* - E* < 0, where r), q* < 0, and E, E* > 0. See Bhagwati and Srinivasan (1983), pp. 403-404.
124
DOUGLAS
A. IRWIN
the trade elasticities must be extremely small, and the marginal propensity to import must be very close to one, for the immiserization condition to be met. The estimates of the trade elasticities for the period (which are probably downward biased) are sufficiently large to imply that Britain never came close to being immiserized, even if the marginal propensity to import was unity. The short-run British export supply elasticity, for example, was close to 1.5 in Irwin (1988), and both the import and the export demand elasticities were close to unity. It is clear that Britain never confronted the possibility of immiserizing the growth once it is understood that the condition for immiserization is extremely stringent and that it was almost certainly not met by parameters relevant to Britain’s trade during this period. Furthermore, if one were to take foreign growth into account, in terms of a shift in the foreign offer curve, the adverse terms-of-trade movement for Britain is somewhat mitigated and the results here are reinforced. It appears safe to conclude that, regardless of the role played by inelastic foreign demand or by agriculture during the industrial revolution, Britain never faced the prospect of reduced national welfare from growth in the production of its exportables. REFERENCES Bhagwati, J. (1958) “Immiserizing Studies
Growth:
A Geometrical
Note.” Review
of Economic
2.5, 201-205.
Bhagwati, J., and Srinivasan, T. N. (1983), Lectures on Znternational Trade. Cambridge: MIT Press. Bloomfield, A. I. (1978). “The Impact of Growth and Technology on Trade in Nineteenth Century British Thought.” History of Political Economy 10, 608-635. Bloomfield, A. I. (1981), “An Early Anticipation of the Concept of Immiserizing Growth.” Journal
of International
Economics
11, 423-427.
Bloomfield, A. I. (19&l), “Effects of Growth on the Terms of Trade: Some Early Views.” Economica 51, 187-193. Caves, R. E., and Jones, R. W. (1977), World Trade and Payments. Boston: Little, Brown, 2nd ed. Crafts, N. F. R. (1985), British Economic Growth During the Industrial Revolution. New York: Clarendon Press. Edgeworth, F. Y. (1894), “The Theory of International Values.” Economic Journal 4, 3550.
Findlay, R. (1982), “Trade and Growth in the Industrial Revolution.” In C. P. Kindleberger and G. Tella (Eds.), Economics in the Long View: Essays in Honor of W. W. Rostow, Vol. 1, Models and Methodology. New York: New York Univ. Press. Hartwell, R. M., and Engerman, S. (1975), “Models of Immiserization: The Theoretical Basis of Pessimism.” In A. J. Taylor (Ed.), The Standard of Living in Britain in the Industrial Revolution. London: Methuen. Irwin, D. A. (1988), “Welfare Effects of British Free Trade: Debate and Evidence from the 1840s.” Journal of Political Economy 96, 1142-1164. Matthews, R. C. 0. (1954), A Study in Trade-Cycle History: Economic Fluctuations in Great Britain, 1833-1842. Cambridge: Cambridge Univ. Press. Stolper, W., and Samuelson, P. A. (1941), “Protection and Real Wages.” Review of Economic
Studies
9. 58-73.
IN ECONOMIC
HISTORY
28,
121-124 (1991)
NOTE Was Britain lmmiserized
during the industrial Revolution?”
DOUGLAS International
Finance
Division,
Federal
A. IRWIN Reserve
Board,
Washington,
D. C. 20551
Economic historians have been cautious in ruling out, or have ruled out for the wrong reasons, the possibility that Britain was immiserized in the early 19th century. This note suggests that the notion that Britain was, or came close to being, immiserized can be rejected. Q 1~1 Academic press, I~C.
The theory of immiserizing growth examines the conditions under which economic growth concentrated in a country’s export sector could so deteriorate its terms of trade as to reduce national welfare.’ While few economists have suggested actual examples of this phenomena, one possible case appears to be that of Britain in the early 19th century. As a consequence of the industrial revolution, Britain experienced tremendous growth in the output of its exportables, particularly cotton textiles. This sharply reduced export prices and led to a deterioration in Britain’s terms of trade of nearly 30% between 1821 and 1841.2 Several of the classical economists observed this situation with concern and passages in their writings resemble anticipations of the concept of immiserizing growthq3 Economic historians have been tentative in ruling out the possibility of immiserizing growth for this period of British history. Some such as Matthews (19.54) have suggested that Britain may have been immiserized if foreign demand for cotton textiles was price inelastic. Recent estimates of trade elasticities for the period in Irwin (1988) suggest that this assumption may be reasonable. Others more skeptical about the possibility of immiserization, such as Hartwell and Engerman (1975), present data showing improved standards-of-living for labor. Yet immiserization cannot * I thank N. F. R. Crafts for helpful discussions and a referee for useful comments. ’ Originally dubbed “damnifying growth” by Edgeworth (1894), the modern theory has been set forth by Bhagwati (1958). ’ See Crafts (1985), p. 147, and Findlay (1982). 3 See the papers by Bloomfield. 121 00144983/91 $3.00 Copyright 0 1991 by Academic Press, Inc. Ail rights of reproduction in any form reserved.
122
DOUGLAS
A. IRWIN
be ruled out on this basis: if Britain specialized in producing capitalintensive goods for export, as there is reason to believe, the StolperSamuelson theorem (1941) tells us that an adverse terms-of-trade shift will increase the real return to the scarce factor, i.e., the real wage of labor. Crafts (1985) recently examined the issue in the context of a twosector model of international trade. Although he finds that there was no immiserization, Crafts maintains that agriculture played a pivotal role in this result; without an expansion in agriculture, he argues (p. 150), the model “conceivably could have implied immiserizing growth and would certainly have worsened the terms of trade.” The purpose of this note is to suggest that the possibility that Britain was immiserized during this period can be ruled out in general, regardless of the role played by demand inelasticities, agricultural production, or other factors. A slight variant on the model used by Crafts (in Caves and Jones, 1977) provides the framework for the analysis. Export and import volumes respond both to changes in the terms of trade, from which the offer curve is derived, and to shifts in the offer curve, considered here as the change in trade volume that would occur at constant relative prices. Thus, the change in home (or Britain’s) imports and foreign imports (Britain’s exports) can be decomposed as follows:
rii = ej? +
Al,,
ii?* = e*p^ + iG*Ip,
(1) (2)
where M (M*) is the volume of home (foreign) imports, e (e*) is the elasticity of the home (foreign) offer curve, and p is Britain’s terms of trade, or relative price of its exportables. (Hats denote relative rates of change, i.e., j? = tip/p.) The first terms of (1) and (2) are the elasticity of imports to terms-of-trade changes along the offer curve, while the second terms are shifts in the offer curves at constant prices. After totally differentiating and rearranging the balance of trade identity,
p^+itP=ii2, and substituting
(3)
(1) and (2) into (3), solving for p^ yields
where A = e - e* - 1 and is positive to meet the Marshall-Lerner condition for stability. Consider the case of export-led growth in Britain, where at constant terms of trade the output of the exportable expands while that of the importable does not, i.e., dxX > 0 and dxw = 0, where xx (xM) is domestic production of the exportable (importable). Also assume that the foreign offer curve remains fixed, i.e., &I*/, = 0. These two assumptions increase the likelihood of immiserization. Home demand for the importable in-
BRITAIN
AND INDUSTRIAL
REVOLUTION
123
creases because of the output expansion at initial prices such that dM = mpdx,, where m is the marginal propensity to import and pdxx is the change in income. Substituting this relation into (4) we have j? = -mpdxX/MA.
C-9
Note that p^ is indirectly related to dx,; i.e., an increase in the output of the exportable decreases the relative price of exports. The change in the country’s welfare can be written as dy = FM + (pdx, + dxw),
(6)
the first term representing the terms-of-trade effect and the second term representing the effect of changes in production (which equals zero for a movement along the production possibilities frontier, but here becomes simply pdx,). After substituting (5) into (6) we have dy = - (m/A)pdxX
+ pdxx,
m
which demonstrates the ambiguity of the change in welfare resulting from increased output of the exportable. The second term indicates that at constant prices welfare rises by the amount of the additional output, while the first term indicates that the terms of trade deteriorate commensurate with the increased output. Immiserization requires only that m > A. The reason Crafts attributes such an important role to agriculture in averting immiserization is that he believes the marginal propensity to import would have been large in the absence of a prosperous British agriculture. Crafts also suspects the price elasticities of British trade to have been small. Taking e and e” to be the demand elasticities of British trade and assuming that they were somewhat inelastic, he found that the parameters came quite close to meeting the condition for immiserization. Crafts’ assumption about the values of the import and export demand elasticities, as pointed out above, has been generally validated by evidence in Irwin (1988). However, e and e* in A are not the price elasticities of British trade as he suggests, but the elasticities of the offer curve. The offer-curve elasticities can be decomposed into the price elasticities of import demand and export supply, such that e = -r) 3 E and e* = 7I” - E” , where q (q*) is the home (foreign) price elasticity of import demand and E (E*) is the home (foreign) price elasticity of export ~upply.~ Thus, Crafts concludes that Britain would have come perilously close to being immiserized in the absence of a prosperous agriculture partly because supply elasticities were excluded from consideration. In fact, the sum of 4 Note that e > 0 because import demand rises along the offer curve with an increase in the relative price of home exportables, dhile e* < 0 because foreign import demand falls with a rise in the relative price of its importables (the home country’s exportable). This leadstoe = -r) + &>Oande* = q* - E* < 0, where r), q* < 0, and E, E* > 0. See Bhagwati and Srinivasan (1983), pp. 403-404.
124
DOUGLAS
A. IRWIN
the trade elasticities must be extremely small, and the marginal propensity to import must be very close to one, for the immiserization condition to be met. The estimates of the trade elasticities for the period (which are probably downward biased) are sufficiently large to imply that Britain never came close to being immiserized, even if the marginal propensity to import was unity. The short-run British export supply elasticity, for example, was close to 1.5 in Irwin (1988), and both the import and the export demand elasticities were close to unity. It is clear that Britain never confronted the possibility of immiserizing the growth once it is understood that the condition for immiserization is extremely stringent and that it was almost certainly not met by parameters relevant to Britain’s trade during this period. Furthermore, if one were to take foreign growth into account, in terms of a shift in the foreign offer curve, the adverse terms-of-trade movement for Britain is somewhat mitigated and the results here are reinforced. It appears safe to conclude that, regardless of the role played by inelastic foreign demand or by agriculture during the industrial revolution, Britain never faced the prospect of reduced national welfare from growth in the production of its exportables. REFERENCES Bhagwati, J. (1958) “Immiserizing Studies
Growth:
A Geometrical
Note.” Review
of Economic
2.5, 201-205.
Bhagwati, J., and Srinivasan, T. N. (1983), Lectures on Znternational Trade. Cambridge: MIT Press. Bloomfield, A. I. (1978). “The Impact of Growth and Technology on Trade in Nineteenth Century British Thought.” History of Political Economy 10, 608-635. Bloomfield, A. I. (1981), “An Early Anticipation of the Concept of Immiserizing Growth.” Journal
of International
Economics
11, 423-427.
Bloomfield, A. I. (19&l), “Effects of Growth on the Terms of Trade: Some Early Views.” Economica 51, 187-193. Caves, R. E., and Jones, R. W. (1977), World Trade and Payments. Boston: Little, Brown, 2nd ed. Crafts, N. F. R. (1985), British Economic Growth During the Industrial Revolution. New York: Clarendon Press. Edgeworth, F. Y. (1894), “The Theory of International Values.” Economic Journal 4, 3550.
Findlay, R. (1982), “Trade and Growth in the Industrial Revolution.” In C. P. Kindleberger and G. Tella (Eds.), Economics in the Long View: Essays in Honor of W. W. Rostow, Vol. 1, Models and Methodology. New York: New York Univ. Press. Hartwell, R. M., and Engerman, S. (1975), “Models of Immiserization: The Theoretical Basis of Pessimism.” In A. J. Taylor (Ed.), The Standard of Living in Britain in the Industrial Revolution. London: Methuen. Irwin, D. A. (1988), “Welfare Effects of British Free Trade: Debate and Evidence from the 1840s.” Journal of Political Economy 96, 1142-1164. Matthews, R. C. 0. (1954), A Study in Trade-Cycle History: Economic Fluctuations in Great Britain, 1833-1842. Cambridge: Cambridge Univ. Press. Stolper, W., and Samuelson, P. A. (1941), “Protection and Real Wages.” Review of Economic
Studies
9. 58-73.