Engels’ Pause:A Pessimist’s Guide to the British

Industrial Revolution

Bob AllenDepartment of Economics

Oxford University2007

“Since the Reform Act of 1832 the most important social issue in England has been thecondition of the working classes, who form the vast majority of the English people...What isto become of these propertyless millions who own nothing and consume today what theyearned yesterday?...The English middle classes prefer to ignore the distress of the workersand this is particularly true of the industrialists, who grow rich on the misery of the mass ofwage earners.”

–Friedrich Engels, The Condition of the Working Class in England in 1844, pp. 25-6.

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 1860.

• 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!

Growth Accounting for Great Britain, 1760-1900

Growth of Due to growth in: Growth of

Y/L K/L T/L A real wage

1760-1800 .26% = .11 -.04 + .19 | .39%1800-1830 .63 = .13 -.19 + .69 | .00

1830-1860 1.12 = .37 -.19 + .94 | .861860-1900 1.03 = .30 -.16 + .89 | 1.61

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:

0

20

40

60

80

100

1760 1780 1800 1820 1840 1860 1880 1900 1920

historical GDP/workerhistorical real wage

< = Wages falling behind output growth Wages rising with output = >

Engels’Pause

Historical Factor Shares, 1770-1913

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

17701790181018301850187018901910

hist labour hist profit hist land

Historical Profit Rate, 1770-1913

0.05

0.1

0.15

0.2

0.25

1770 1800 1830 1860 1890

real profit rate nominal 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 1800.

– 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:

Y = f( AL,K,T) (1)

Kt = Kt-1 + It - Kt-1 (2)

I = sY (3)

Alternative, Kalecki or Kaldor savings function:

I = (sK K + sT T)Y (4)

Marginal products equal input prices, which are also related to shares:

w = L Y (5) L

r = K Y (6) K s = T Y (7) T

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

0.12

0.14

0.16

0.18

0.2

0.22

0.24

1760 1780 1800 1820 1840 1860

actual

Regression with data for 1760-1913 shows a slightly greater propensity to

save out of profits than rents:

I/Y = .138 φT + .196 φK

(.013) (.014)

This regression, slightly modified for 1760-80, was used in simulations.

Two production functions considered.Cobb-Douglas:

Y = A0(AL) K T (8)

The problem with the Cobb-Douglas is that it imposes constant shares.

So I use the translog:

LnY = 0 + K lnK + L ln(AL) + T LnT +

½ KK (lnK)2 + KL lnKln(AL) + KT lnKlnT +

½ LL (ln(AL))2 + LT ln(AL)lnT+ ½ TT (lnT)2 (9)

subject to the adding up conditions K + L + T = 1, KK + LK + TK =0, KL + LL + TL =0,and KT + LT + TT =0. When all of the ij = 0, the translog function reduces to the Cobb-Douglas.

Logarithmic differentiation gives the share equations:

sK = K + KK lnK + KL ln(AL) + KT lnT (10) sL = L + LK lnK + LL ln(AL) + LT lnT (11)

sT = T + TK lnK + TL ln(AL) + TT lnT (12)

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:– 1760-1800: .3% per year– 1800-1830: 1.5% per year– 1830-1860: 1.7% per year

• These values were used to calibrated the translog.

Calibrating the translog

sK 1 0 lnK lnL lnT 0 K

sL = 0 1 0 lnK-lnAL lnAL-lnT -lnAL-lnT L

sT - 1 -1 -1 0 0 lnK-lnAL lnT-lnAL KK

KL

KT

TT

sK 1 0 lnK lnL lnT 0 K

sL = 0 1 0 lnK-lnAL lnAL-lnT -lnAL-lnT L

sT - 1 -1 -1 0 0 lnK-lnAL lnT-lnAL KK

KL

KT

TT

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

Values of translog coefficients: 0 = 0.481081

K = 0.255594 L = 0.518544 T = 0.225862

KK = -1.58305 KL = 1.291068

KT = .291984

LL = -.99908

LT = -.29198

TT = 2.797242 x 10-16

Note: These coefficients were computed after rescaling thelabour and land indicesto equal 248 in 1760, the same value asthe capital stock in that year.

How well does the translog work?actual and simulated GDP

100

200

300

400

500

600

700 m

illio

ns o

f 1850s p

ounds

1761 1781 1801 1821 1841 1861

actual simulated

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

0.05

0.06

0.07

0.08

0.09

0.1

0.11

1770 1790 1810 1830 1850

actual simulated

The model simulates the two phase pattern of British industrialization:

0

20

40

60

80

100

1770 1790 1810 1830 1850 1870 1890 1910

simulated GDP/workersimulated real wage

historical GDP/workerhistorical real wage

The model does pretty well simulating factor shares:

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

1770 1800 1830 1860 1890

sim profit sim labour hist labour

hist profit hist land sim land

And the profit rate:

0.05

0.1

0.15

0.2

0.25

1770 1800 1830 1860 1890

real profit rate nominal profit rate

simulated profit rate

And the rent of land:

0

10

20

30

40

50

60 1850 s

hill

ings p

er

acre

1770 1800 1830 1860 1890

simulated actual

Why did inequality rise (1770-1850) and then stabilize 1860-1913?

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:

4600 4800 5000 5200 5400 5600 5800 6000 6200

labour

350 400 450 500 capital

translog Cobb-Douglas

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

25

30

35

40

45

50

55

60

65

Pounds p

er

work

er

(1850 p

rices)

1761177117811791180118111821183118411851

simulated actual I/Y=6%, historical productivity

prod =.3%, historical I/Yprod=.3%, I/Y=.06

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:

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

1761 1781 1801 1821 1841 1861

sim profit sim labour hist labour

hist profit hist land sim land

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:

0

20

40

60

80

1770 1790 1810 1830 1850

simulated GDP/workersimulated real wage

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

0

0.2

0.4

0.6

0.8

1761 1781 1801 1821 1841 1861

sim profit sim labour hist labour

hist profit hist land sim land

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.