Applied Economics Letters, 2009, 16, 1501–1504

The labour scarcity paradox reconsidered: a simple growth theoretic explanation Qiang Chen

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School of Economics, Shandong University E-mail: [email protected]

By calibrating a Solow model augmented by natural resources, this paper offers a simple explanation of the labor scarcity paradox during the process of America’s catching up with Britain, which static models have difficulties in accounting for so far.

I. Introduction America’s rapid industrialization in the nineteenth century as compared to Britain has intrigued many scholars. Rothbarth (1946) and Habakkuk (1962) surmised that this was largely due to America’s abundant land and hence scarce labour, which gave an incentive to install labour-saving equipments. Temin (1966) found an unpleasant consequence of the RothbarthHabakkuk thesis. While land abundance implies labour scarcity (higher wages), it also implies capital abundance (lower interest rates), which was contradicted by historical evidence (Homer, 1963; Rosenberg, 1967; Adams, 1970). However, Fogel (1967) showed Temin’s specification to be flawed. Summers and Clarke (1980) broadened the discussion to include international trade and capital flow. James and Skinner (1985) was an ambitious effort to resolve this paradox. Using 1849 US census data, they constructed a 3-good-4-factor general equilibrium model to explain the following three empirical regularities for the antebellum period: ‘(1) The United States was relatively capital intensive only in a limited number of manufacturing

1 2

industries; (2) Both the nominal and the real wage rates were higher in the United States than in Britain; and (3) Both the nominal and the real costs of capital were higher in the United States than in Britain.’1 However, despite its complexity, James and Skinner (1985)’s model was still static, and missed the broad picture of comparative American and British performance. Their reliance on ‘skilled workers’ to explain the labour scarcity paradox is also unsatisfactory, as ‘skilled labour’ is usually endogenous in the long run. This article shows that a calibrated Solow model augmented by natural resources offers a straightforward explanation of all empirical regularities of ‘labour scarcity’ while accounting for the dynamic process of America overtaking Britain.

II. The Solow Model Augmented by Natural Resources Because there was minimal restriction on technology transfer between America and Britain during most part of the nineteenth century,2 it seems reasonable

James and Skinner (1985), p. 517. Habakkuk (1962), p. 9697. Applied Economics Letters ISSN 1350–4851 print/ISSN 1466–4291 online ß 2009 Taylor & Francis http://www.informaworld.com DOI: 10.1080/13504850701578843

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Q. Chen

1502 to assume that both the rate of technological progress and level of technology were the same between US and Britain.3 The importance of natural resources in American industrialization through land, raw materials and cheap energy has been emphasized by Ames and Rosenberg (1968), Christensen (1981), and Wright (1990), Rosenberg (1977), (1969) and Romer (1996), among others. Natural resources are assumed to be immobile between countries. This is plausible for the nineteenth century when the cost of transportation was high and the scale of international trade in natural resources was small. Hence, I follow Solow (1999) to set up a three-factor production function.

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Y ¼ K  ðALÞ R 1

ð1Þ

A critical assumption is the presence of natural resources R, which is assumed to be fixed and inexhaustible. As in the standard Solow model, technology level A and labour force L grow at constant rates of g and n, respectively. The saving rate is fixed at s. In the standard Solow model, the trick to simplify the solution is to normalize the capital stock K by the efficient unit of AL. Under the present setting, it turns out that the proper scaling is provided by ðALÞ=ð1Þ . Define effective capital and effective output respectively by, k¼

K 

ð2Þ



ð3Þ

ðALÞ1 y¼

Y ðALÞ1

It is straightforward to show that the effective capital k converges monotonically to a unique steady state level of k , 

k ¼

sR1 ðnþgÞ 1

þ

1 !1

ð4Þ

Obviously, a higher level of natural resources R would raise the steady state value of k . If we just blindly assume that all parameter values between US and Britain were the same except natural resources R, then ultimately the US economy, starting from a lower level of k, would eventually converge to a higher level of k than Britain. Assuming that factors

are paid their marginal products, then real interest rate and real wage are given by, r¼

@Y R1 ¼ @K k1

@Y R ¼ Ak w¼ 1 @L ðALÞ1

ð5Þ

!1 ð6Þ

From (5), it is clear that before converging to the steady state, America’s real interest rate would be higher than Britain’s for two reasons. A usual reason was America’s lower effective capital stock. Another reason was America’s abundant natural resources, which raised capital’s marginal efficiency. From (6), we see that despite the lower initial US capital stock, real wage in US was boosted by abundant natural resources, and it was possible for US to have both a higher real wage and a higher real interest rate than Britain.

III. Calibration To estimate the ratio of US natural resources to Britain’s in 1850, I take its upper bound to be ‘acres of land in agriculture’, which was 293.6 million acres for US in 1849, and 38.8 million acres for Britain in 1851,4 implying an upper bound of 7.57. On the other hand, I take the lower bound to be ‘primary energy consumption per $1000 of real GDP, GDP in 1970 US relative prices, energy in tons of oil equivalent’ in 1850, which was 4.63 and 2.55 for US and Britain, respectively,5 implying a lower bound of 1.82. A sensible estimate should fall between 1.82 and 7.57. Due to the paucity of data, I cannot estimate production function parameters  and  by regression.6 I have to calibrate these parameters from income shares. Britain’s labour income share had been quite stable. It was 0.63 in 1843, 0.625 in 1913 and again 0.625 in 1938. On the other hand, labour’s income share in America had been declining from 0.80 in 1850 to 0.74 in 1910, then to 0.665 in 1938.7 Habakkuk (1962) argued that ‘the fall is almost certainly to be explained by the decline in the

3 It may seem odd that they happened to be exactly the same. Yet it is a good baseline case until we find evidence suggesting otherwise. 4 James and Skinner (1985), p. 527. 5 Maddison (1982), Table 3.3, p. 48. 6 I tried running regressions using data from Maddison (1982) for Great Britain, but the parameter estimates don’t make much sense with  ¼ 0.66, and  ¼ 1.2. One reason is that the sample size is too small (every ten years from 1820 to 1913). 7 Habakkuk (1962), p. 111.

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Labour scarcity paradox reconsidered number of self-employed persons as the result of the relative increase of industry . . .’. If this is true, then the primary reason for America’s high labour income share in 1850 was because it included returns from natural resources (such as land) owned mostly by self-employed individuals.8 If this is the case, then the difference of labour’s income shares between America and Britain may proxy the income share for natural resources, which is 0.80  0.63 ¼ 0.17 around 1850. The rest of 0.2 (i.e. 1  0.8) is capital’s income share. As a baseline case, I assume the production parameters to be uniform across US and Britain in 1850,9 with capital share  ¼ 0.2, labour share  ¼ 0.63 and resource share 1   ¼ 0.17. James and Skinner (1985, p. 527) put total labour forces for America and Britain at 5.47 million (1849) and 5.3 million (1851), respectively. To adjust to the same year of 1850, I use population growth rate of 1.5% for America10 and 0.65% for Britain,11 respectively. Assuming constant labour participation rates, the total labour forces were estimated at 5.55 million and 5.26 million in 1850 for America and Britain, respectively. James and Skinner (1985, p. 527)’s estimates of total capital stocks for the US and Britain in 1849 and 1851, respectively were problematic, as they used current par exchange rate. To use PPP exchange rates, I start with Maddison (1982, Table 3.5, p. 54)’s estimates of US and Britain’s capital stock per worker in 187012 based on dollars of 1970 US purchasing power, which were $5066 and $6068, respectively. The US and British labour forces are estimated to be 7.48 million and 5.99 million in 1870, respectively.13 Multiplying capital stock per worker by total labour force, the US and British capital stocks in 1870 were estimated at $37 882.53 million and $36 373.41 million in 1970 PPP US$, respectively. I then extrapolate the capital stocks back to 1850 8

1503 through their growth rates during that period, which were 4.74% for US14 and 2.304% for Britain,15 respectively. In the end, the estimated US and Britain total capital stocks in 1850 were $15 003.32 million and $23 063.85 million in 1970 PPP US$, respectively. Therefore, the American capital stock was about 65.1% of the Britain’s in 1850 instead of 42.3% estimated by James and Skinner (1985). The real interest rates for US and Britain during 18411860 were 5.255% and 3.51%, respectively.16 So the US interest rate was about 50% higher than the Britain’s. Assuming uniform technology level and growth rate, the effective capital stock can be calculated as k ¼ K=L=ð1Þ by normalizing the technology level in 1850 to unity. Therefore, the US and British effective capital stocks were $3889.79 and $4379.93, respectively. So in 1850, the American effective capital stock was about 88.8% of the Britain’s. From Equation 5, it is easy to derive the implied natural resources ratio R ¼ 6.14, which was a sensible value between 1.82 and 7.57. With R ¼ 6.14 at hand, from Equation 6 we can calculate the implied ratio of US real wage to British real wage as 1.32, which is broadly consistent with various estimates in the literature ranging from 1.25 to 1.52.17 Was the American steady state level of effective capital stock higher than the Britain’s? America’s higher level of natural resources R and higher saving rate (11.5% compared with Britain’s 8%18) both had positive effects. However, these effects were partly offset by America’s higher population growth rate of 1.5% vs. the Britain’s 0.65%. If we assume the same annual rates of technical progress at 2% and depreciation at 5% for both countries, then from Equation 4 America’s steady state effective capital stock K* was about 2.07 times higher than Britain’s.

In 1870, 50% of the total employment was in the agricultural sector in America, while the British counterpart was only 22.7%. This gap would have been larger in 1850. Source: Maddison (1982), Table C5, p. 205. 9 This is a sensible assumption if they were using the same technology. 10 I take the arithmetic average of the US population growth rates of 1.2% (during 17001820) and 1.8% (during 18201979). Source: Maddison (1982, Table 3.4, p. 49). 11 I take the arithmetic average of the British population growth rates of 0.7% (during 17001820) and 0.6% (during 18201979). Source: Maddison (1982, Table 3.4, p. 49). 12 Unfortunately no direct data for 1850 is available. 13 I use the above data of America’s labour force in 1849, Britain’s labour force in 1851, and the population growth rates during that period for both countries for extrapolations. 14 This is calculated from Maddison (1982, Table D13, p. 232), which indicates the US capital stocks as 6.52 and 10.36 in 1870 and 1880, respectively with 1950 ¼ 100. 15 This is calculated from Maddison (1982, Table D12, p. 231), which indicates the British capital stocks as 16.13 and 31.95 in 1830 and 1860, respectively with 1950 ¼ 100. 16 I take arithmetic average of real interest rates between 18411850 and 18511860. Source: James and Skinner (1985, p. 539). 17 James and Skinner (1985, p. 537). 18 Both US and Britain data are for 18711880 as ‘ratio of gross fixed nonresidential investment to GDP at current market price from Maddison (1985), Table 2.3, p. 40.

Q. Chen

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1504 Finally, if the US overall capital stock was only about 2/3 of that of Britain around 1850, why did several US industries actually have higher capital intensity, which surprised British visitors to begin with? Habakkuk (1962) enumerated these exceptional US industries as agriculture implements, doors, furniture, other woodwork, boots and shoes, ploughs, mowing machines, wood screws, files, nails, biscuits, locks, clocks, small arms, nuts and bolts.19 James and Skinner (1985) characterized these industries as a skilled sector, but were forced to exclude ‘boots and shoes and cotton textiles’ ad hoc because of their small ratios of skilled workers relative to total employment. Apparently, many of these industries were resource intensive. To the extent that natural resources and capital are complements (higher resource level leads to higher steady state capital stock and faster convergence), the complementarity between skilled labour and capital implies that more skilled workers would be employed in these resource-intensive industries. In this view, skilled labour was not the ultimate cause of these American industries’ early edge over Britain, but an intermediate cause at best. Another important factor was demand. As emphasized by Habakkuk (1962), the more homogenous US population made standardized parts possible and aided the American mechanization process. Many of the above ‘exceptional’ industries (e.g. small arms) were characterized by the importance of ‘standardized parts’ in their production processes.

IV. Conclusion Neoclassical growth model is one of the most robust models in economics, and has become a workhorse in macroeconomics for decades. This article again demonstrates its power in organizing our understanding of the comparative US-Britain economic performance in the nineteenth century. The apparently complex interactions among the three productive factors of capital, labour and natural resources in America, known as the ‘labour scarcity paradox’, become transparent through a Solow model augmented by natural resources. Calibration results match all empirical regularities of the American and British economy around 1850. It is hard to imagine how we

19

Habakkuk (1962), p. 4.

could gain this clarity of understanding without a growth framework. Overall, it is a success of the Neoclassical growth model.

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