Engels’ Pause:
A Pessimist’s Guide to the British
Industrial Revolution
Bob Allen
Department of Economics
Oxford University
2007
“Since the Reform Act of 1832 the most important social issue in England has been the
condition of the working classes, who form the vast majority of the English people...What is
to become of these propertyless millions who own nothing and consume today what they
earned yesterday?...The English middle classes prefer to ignore the distress of the workers
and this is particularly true of the industrialists, who grow rich on the misery of the mass of
wage 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 Ac count ing for Great Bri tain, 176 0-19 00
Gro wth of
Y/L
1760- 1800
1800- 1830
1830- 1860
1860- 1900
.26%
.63
1.12
1.03
Due to growth in:
K/L
T/L
=
=
=
=
.11
.13
.37
.30
-.04
-.19
-.19
-.16
+
+
+
+
A
.19
.69
.94
.89
Grow th of
real wage
| .39%
| .00
| .86
| 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:
100
80
Engels’
Pause
60
40
20
0
1760 1780 1800 1820 1840 1860 1880 1900 1920
< = Wages falling behind output growth
Wages rising with output = >
historical GDP/worker
historical real wage
Historical Factor Shares, 1770-1913
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
17701790181018301850187018901910
hist labour
hist profit
hist land
Historical Profit Rate, 1770-1913
0.25
0.2
0.15
0.1
0.05
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
L
(5)
r = K Y
K
(6)
s = T Y
T
(7)
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
0.24
0.22
0.2
0.18
0.16
0.14
0.12
1760
1780
1800
1820
actual
1840
1860
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 +
2
½
KK (lnK) + 
KL lnKln(AL) + 
KT lnKlnT +
2
2
½
LL (ln(AL)) + 
LT ln(AL)lnT+ ½ 
TT (lnT)
(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 CobbDouglas.
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
sL
sT - 1
1 0
= 0 1
-1 -1
lnK
0
0
lnL
lnT
0
lnK-lnAL lnAL-lnT -lnAL-lnT
0
lnK-lnAL lnT-lnAL

K

L

KK

KL

KT

TT
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:

0 = 0.481081

K = 0.255594

L = 0.518544

T = 0.225862

KK = -1.58305

KL = 1.291068

KT = .291984

LL = -.99908

LT = -.29198
-16

TT = 2.797242 x 10
Note: The se coeffi cien ts were compu ted after res cali ng the
labour and la nd in dice sto equal 248 in 1760, the same val ue as
the capit al stock in that year.
m illio n s o f 1 8 5 0 s p o u n d s
How well does the translog work?
actual and simulated GDP
700
600
500
400
300
200
100
1761
1781
1801
actual
1821
1841
simulated
1861
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
0.11
0.1
0.09
0.08
0.07
0.06
0.05
1770 1790 1810 1830 1850
actual
simulated
The model simulates the two phase
pattern of British industrialization:
100
80
60
40
20
0
1770 1790 1810 1830 1850 1870 1890 1910
simulated GDP/worker
simulated real wage
historical GDP/worker
historical real wage
The model does pretty well simulating
factor shares:
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1770
1800
1830
1860
1890
sim profit
sim labour
hist labour
hist profit
hist land
sim land
And the profit rate:
0.25
0.2
0.15
0.1
0.05
1770 1800 1830 1860 1890
real profit rate
simulated profit rate
nominal profit rate
1850 s hillings per ac re
And the rent of land:
60
50
40
30
20
10
0
1770
1800
1830
simulated
1860
actual
1890
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.
labour
Translog and Cobb-Douglas Isoquants in 1810
illustrate low elasticity of substitution:
6200
6000
5800
5600
5400
5200
5000
4800
4600
350
400
450
capital
translog
Cobb-Douglas
500
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.
P o u n d s p e r w o r k e r ( 1 8 5 0 p r ic
Alternative Growth Simulations
65
60
55
50
45
40
35
30
25
1761177117811791180118111821183118411851
sim ulated actual
I/Y=6%, historical productivity
prod =.3%, historical I/Y
prod=.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:
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
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:
80
60
40
20
0
1770
1790
1810
simulated GDP/worker
1830
1850
simulated real wage
With constant population, factor shares would
also have remained constant:
0.8
0.6
0.4
0.2
0
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.