Engels’ Pause: A Pessimist’s Guide to the British Industrial Revolution Bob Allen Department of Economics Oxford University 2007

Our knowledge of the macro-economics of the British I.R. is much greater than 50 years ago: Growth rate of per capita income was low (less than 1.5% per annum) but sustained, so income rose 82% between 1760 and Investment rate rose from 6% to 12%. However, growth accounting shows productivity growth accounts for the rise in income per head. Nevertheless, it is important to remember how bad the data are!

What about inequality? We can measure it with variables in 1850s prices. Indices of real GDP, wages, and rents are used to run 1850s values back to 1760—giving series in 1850s prices. Real input series: occupied population, acres of improved farm land, and capital stock in 1850s prices. Capital income, rate of return, and factor shares computed from these figures.

Inequality followed a two-stage process as described by Kuznets and Lewis. Up to the 1840s, wages did not keep up with output per worker, the profit rate rose, and factor shares shifted against labour. After the 1840s, wages rose in pace with output, profits and factor shares stabilized. Why did the economy function like this?

Two phase development process implied by Allen’s revision of Feinstein’s real wage series: < = Wages falling behind output growthWages rising with output = > Engels’ Pause

Historical Factor Shares,

Historical Profit Rate,

How can the two phase history of inequality be explained? Lewis proposed a two sector model—many problems. –Zero marginal product of labour in agriculture? –Agriculture was only 35% of British economy in –I retain the assumption that savings come out of profits. Marx emphasized labour augmenting technical change. Malthus emphasized induced population growth.

A standard one sector macro model with savings a function of property income explains the essential facts: Alternative, Kalecki or Kaldor savings function:

Marginal products equal input prices, which are also related to shares: With the I=sY savings function, ‘growth’ and ‘distribution’ are separable. With the Kaldor function, they are interdependent.

Calibrating the Savings Function For the simple Keynesian function I = sY, s is computed as the time series of I/Y. The Kaldor function fits the data better: –Budget data show workers did not save. –The ratio of savings to property income was largely trendless.

Historical Savings Rate out of Property Income

Regression with data for shows a slightly greater propensity to save out of profits than rents: I/Y =.138 φ T φ K (.013) (.014) This regression, slightly modified for , was used in simulations.

Two production functions considered. Cobb-Douglas: The problem with the Cobb-Douglas is that it imposes constant shares.

So I use the translog:

Logarithmic differentiation gives the share equations: These are the basis for calibrating the model.

The translog production function was calibrated in two stages. First a Cobb-Douglas was calibrated and used to work out the trajectory of labour augmenting technological change: – :.3% per year – : 1.5% per year – : 1.7% per year These values were used to calibrated the translog.

Calibrating the translog Substituting values for two years (1760 and 1860) gives six equations in six unknowns. The other parameters can be calculated from the restrictions.

Values of translog coefficients:

How well does the translog work? actual and simulated GDP

To test the model as a whole, we must see if it replicates the key features of the industrial revolution. The model does a good job!

Actual and Simulated Investment Rate

The model simulates the two phase pattern of British industrialization:

The model does pretty well simulating factor shares:

And the profit rate:

And the rent of land:

Why did inequality rise ( ) and then stabilize ? The answer turns on properties of the production function and savings function.

The translog production function has a special property with important implications: Elasticity of substitution between capital and labour is very low (about.2). This means that technical progress required capital accumulation to be effective. The low elasticity of substitution is also a key to explaining why inequality rose.

Translog and Cobb-Douglas Isoquants in 1810 illustrate low elasticity of substitution:

The elasticity of substitution and the process of economic growth: By itself, neither the rise in savings nor the rise in productivity growth would have caused per capita income to increase much. This is because of the low elasticity of substitution between capital and labour. Without complementary capital formation, the rise in productivity would not have raised output. The ‘sources of growth’ identified by growth accounting are artificial.

Alternative Growth Simulations

The low elasticity of substitution is also key to explaining inequality. Productivity growth accelerated after 1800 raising the ratio of augmented labour to capital. Hence, the marginal product of capital rose. Low elasticity of substitution meant that the share of capital rose. This explains the rise in inequality.

The rise in inequality was undone by the same forces. The rise in the share of capital increased saving since it depended on property income. More savings raised investment in response to the increase in its demand due to the productivity growth. Capital/augmented labour rose and converged to steady state growth with rising real wages and constant shares. This is why inequality went through two phases.

What about the explanations of Marx and Malthus? We can explore them by simulating the model. Marx’s view is tested by eliminating labour augmenting technical change. Malthus’ view is tested by eliminating population growth. Both factors were necessary for the rise in inequality.

Without the productivity growth, factor shares would have been much more stable: But there wouldn’t have been an Industrial Revolution either!

Productivity growth without population growth is the more interesting scenario: Output per worker would have risen at historical rates. The real wage would have risen at the historical rate: no Engels’ pause. Unchanged factor shares Only a modest rise in the savings rate since capital was not needed to house and equip a growing population.

Compare simulated output per worker and real wage, which now rise together:

With constant population, factor shares would also have remained constant:

Two points on Malthus & Marx It looks like Malthus was right and population growth explains wage stagnation, but population grew almost as fast after 1850 as before. The problem is that rapid population growth plus labour augmenting TC cut capital per efficiency unit of labour. This moved the economy off a steady state growth path. Rising inequality led to more investment, which brought the economy back to steady state growth even with rapid population growth. Marx was right that rising inequality and capital acccumulation were interconnected pre-1848, but the sequel was rising real wages as accumulation caught up with augmented labour—not further immiseration and revolution! The model of this paper explains history better than Malthus and Marx.

We can tell the story of the IR like this: Rise in productivity was the prime mover. It increased the demand for capital. The upsurge in population also increased the demand for capital. Rate of return rose and shifted income to capitalists since the elasticity of substitution was so low. The income shift raised savings allowing growth to occur.

The savings response was sluggish so that the real wage stagnated. Inequality and accumulation were connected because the wealthy saved so little—not because they saved so much. Rising productivity and population growth plus a sluggish supply of capital meant that Britain experienced the rising part of the Kuznets curve. Eventually enough capital was accumulated so that balanced growth proceeded with wages rising in step with productivity.