When Did Growth Begin? New Estimates of Productivity Growth in England from 1250 to 1870
What this paper finds — and why it matters
Overview
Research Question. When did sustained productivity growth begin in England? This paper constructs new estimates of the evolution of productivity in England from 1250 to 1870, with the goal of both dating the onset of growth and using that dating to discriminate between competing theories of why growth began.
Methodological Innovation. The core challenge is that real wages over this period were heavily distorted by Malthusian population dynamics. Plague-induced population collapses (most dramatically the Black Death of 1348, which killed roughly 25% of England’s population) drove enormous swings in real wages that reflect movements along a stable labor demand curve, not changes in productivity. A naive regression of wages on labor supply is therefore inconsistent, because in a Malthusian world productivity growth induces population growth, making labor supply endogenous to productivity.
The authors address this by writing down and structurally estimating a full Malthusian model of the economy. Output is produced with fixed land and variable labor (and, in an extended model, capital) via a Cobb-Douglas production function. The labor demand curve equates the real wage to the marginal product of labor. Population growth is increasing in real per-capita income (the Malthus law of motion), capturing both preventive and positive checks. Productivity follows a random walk with drift, and the paper allows for two structural breaks in the average drift rate mu. Exogenous population shocks, modeled as infrequent, sizable plague draws from a beta distribution plus a Gaussian noise term, provide identification: plague shocks and productivity shocks generate observationally distinct dynamics – plague shocks cause an immediate population drop that gradually reverts, while productivity shocks cause an immediate wage jump followed by a slow population rise to a new steady state. The model is estimated via Bayesian Hamiltonian Monte Carlo (Stan), and structural break dates for mu are chosen by maximizing the Bayes factor (marginal likelihood) over the observed data on real wages, population, and days worked per worker.
Key Data. Real wages are from Clark (2010) unskilled building workers series. Post-1540 population is from Wrigley et al. (1997); pre-1540 population trends are from Clark (2007b) manorial records. Days worked per worker are from Humphries and Weisdorf (2019). All series are used as decadal averages.
Main Findings.
Onset of growth: 1600. Productivity growth was zero before 1600. The Bayes factor strongly favors a first structural break in mu at 1600; break dates before 1590 and after 1640 are clearly rejected.
Two-phase post-1600 growth. Between 1600 and 1810, average productivity growth was 4% per decade (posterior mean; 95% credible interval approximately 2%-6%). After 1810, productivity growth accelerated sharply to 18% per decade (95% CI approximately 12%-23%). The second break date is estimated to 1810 (the only alternative not clearly rejected is 1800).
Magnitude of productivity change. By the authors’ estimates, productivity in England was approximately 540% higher in 1850 than in 1500. This contrasts sharply with Clark’s (2010) dual-approach TFP series, which implies essentially no change over this period. The authors attribute the discrepancy to mismeasurement in Clark’s land rent series.
Productivity growth preceded the Glorious Revolution. Productivity rose by an estimated 48% between 1600 and 1680, well before the Glorious Revolution of 1688 and the English Civil War (1642-1651). This supports the view that economic change contributed to causing the bourgeois institutional reforms of the 17th century, consistent with the Marxist tradition (Hill, 1940, 1961), rather than that institutional change preceded and caused growth.
Weakness of Malthusian population force. The elasticity of population growth with respect to real income (gamma) is estimated at 0.09. Combined with a slope of the labor demand curve (alpha) of 0.53, this implies a half-life of plague-induced population dynamics of approximately 150 years. A doubling of real per-capita income stimulated population growth by only 6 percentage points per decade – indicating Malthusian forces were sufficiently weak to be overwhelmed by post-1800 productivity growth. The model implies that the post-1810 productivity growth rate would have produced a 28-fold long-run increase in steady-state real wages even without the Demographic Transition.
Capital extension. When capital is explicitly incorporated, using rates of return on agricultural land and rent charges to infer the capital stock, results are broadly similar: productivity growth from 1600-1810 is 3% per decade and post-1810 is 14% per decade. Capital’s production function exponent is estimated at 0.18, confirming that capital accumulation explains only a modest share of growth.
Scope Conditions. All estimates are for England specifically. The model assumes competitive factor markets, a Cobb-Douglas (or CES) production function, and a log-linear Malthusian population law of motion. Results are robust to alternative wage series (farm laborers, craftsmen, Allen’s series), alternative population sources (Broadberry et al., 2015), constant-days-worked assumption, and alternative prior distributions.
Q&A
Q1: Why can’t standard OLS regression of wages on labor supply recover productivity in this setting? In a Malthusian world, productivity growth causes population growth, which in turn raises labor supply. This means labor supply and productivity are positively correlated, biasing OLS estimates. The authors demonstrate this concretely: from 1300 to 1450 (plague era), wages and labor supply moved in opposite directions along a stable labor demand curve, while after 1630 the same data points begin shifting off that curve – a pattern that OLS would confound with changes in the slope rather than shifts in the intercept.
Q2: How do the authors distinguish empirically between a plague shock and a productivity shock? The two shocks generate fundamentally different dynamics. A plague shock causes an immediate, large drop in population and a corresponding spike in wages; over time, high wages induce population growth and both wages and population gradually return to their pre-plague levels. A permanent productivity shock, by contrast, causes an immediate rise in wages with no contemporaneous population change; population then slowly rises and wages partially revert until a new, higher steady-state population is reached. The model exploits these different impulse-response signatures in the joint data on wages and population to identify the two shocks separately.
Q3: What is the Bayes factor evidence for the 1600 break date? Figure 8 in the paper shows the Bayes factor for models with different first break dates (all holding the second break at 1810). The Bayes factor rises sharply from 1580 to 1600 and falls more gradually from 1600 to 1650. Break dates before 1590 and after 1640 are clearly rejected using the standard rule of thumb that a Bayes factor of 10 constitutes strong evidence. The 1600-1810 pair of break dates yields the highest marginal likelihood of any combination considered.
Q4: How does the paper’s productivity estimate compare to Clark’s (2010) dual-approach TFP series? Clark’s series implies productivity in England was essentially unchanged between the 15th and mid-19th centuries – a result the paper argues is implausible and inconsistent with Allen’s (2005) agricultural TFP estimates (which show a 162% increase in agricultural TFP between 1500 and 1850). The authors’ baseline estimate implies productivity was approximately 540% higher in 1850 than in 1500. The authors conjecture that a key driver of the difference is mismeasurement in Clark’s land rent series, which appears essentially flat from 1250 to 1600 despite enormous plague-induced swings in the land-labor ratio over this period.
Q5: What does the Malthusian model imply about “Engel’s Pause” – the apparent stagnation of real wages during early industrialization? Between 1730 and 1800, real wages fell slightly despite what the model estimates to be substantial productivity growth. The conventional explanation is that the gains from early industrialization accrued to capitalists rather than workers. The authors offer an alternative Malthusian explanation: England’s population grew rapidly over this period, and in the Malthusian model this population growth depressed wages relative to productivity. The authors do not reject the distributional explanation but show that Malthusian forces alone are sufficient to explain the wage-productivity divergence.
Q6: How quantitatively important are days worked (the Industrious Revolution) for the productivity estimates? The authors find that their productivity estimates are largely insensitive to whether the Humphries-Weisdorf (2019) days-worked series or a constant-days assumption is used. The qualitative pattern – zero growth before 1600, modest growth 1600-1810, rapid acceleration post-1810 – and the quantitative magnitudes remain similar. What does change is the estimated slope of the labor demand curve alpha: assuming constant days makes the labor demand curve steeper. This robustness is reassuring given that the Industrious Revolution is a contested empirical phenomenon.
Q7: What does the model imply about the speed of Malthusian population dynamics, and how does this compare to prior estimates? The estimated elasticity of population growth to real income gamma = 0.09, combined with alpha = 0.53, implies a half-life of population dynamics of approximately 150 years. This is consistent with but lies between prior structural estimates: Lee and Anderson (2002) find a half-life of 107 years, and Crafts and Mills (2009) find 431 years. All estimates agree that Malthusian dynamics in England were slow relative to the conceptual ideal of rapid subsistence convergence.
Q8: Can the model explain the post-1750 population explosion without invoking the Demographic Transition? Yes. The authors simulate predicted population paths from 1740 to 1860 taking real wages and days worked as given and using their estimated gamma and alpha. Despite the weak Malthusian population force, the model can explain the vast majority of the observed population growth from 6 million in 1740 to nearly 20 million in 1860 (10.4% per decade). The key mechanism is that days worked increased substantially over this period, raising per-capita income well above what real wages alone would suggest.
Q9: How does incorporating capital change the productivity estimates? In the capital-augmented model, the capital stock is inferred from rates of return on agricultural land and rent charges (Clark 2002, 2010). The capital exponent beta is estimated at 0.18, indicating a modest role for capital in pre-industrial England. Average productivity growth from 1600-1810 falls from 4% to 3% per decade, and post-1810 growth falls from 18% to 14% per decade. The authors conclude that the vast majority of growth from 1600 to 1870 cannot be attributed to capital accumulation. From 1600 to 1860, the estimated capital stock grew by a factor of five (8% per decade).
Q10: What theories of the onset of growth are consistent vs. inconsistent with the authors’ timing evidence? Inconsistent: The North-Weingast (1989) view that the Glorious Revolution of 1688 was the key institutional trigger, since productivity had already risen 48% between 1600 and 1680. Also inconsistent: gradual-growth theories (Kremer 1993, Galor-Weil 2000) in which there is no discrete acceleration. Consistent: Marxist accounts (Hill 1940, 1961) that economic change drove 17th-century institutional change; Acemoglu-Johnson-Robinson (2005) accounts linking Atlantic trade enrichment to the demand for secure property rights (timing broadly consistent, though growth rates do not visibly accelerate after the Civil War or Glorious Revolution); cultural-change accounts (Mokyr, McCloskey) tracing the onset of growth to the spread of literacy and scientific rationalism around 1600; Allen’s (2009a) directed-technical-change theory linking 17th-century wage growth to the later profitability of labor-saving innovation in the Industrial Revolution.
Q11: What does the model imply about the long-run real wage consequences of post-1810 productivity growth, even counterfactually assuming Malthusian forces persisted? The steady-state real wage in the Malthusian model is w-bar = mu/(alpha*gamma) minus subsistence-related terms. For mu = 0.018 (the post-1810 estimate), this formula implies a long-run real wage 28 times higher than the steady state under zero productivity growth. In other words, even if the Demographic Transition had not occurred and birth and death rates had remained sensitive to income, post-1810 productivity growth was fast enough relative to the weak Malthusian force to generate substantial sustained rises in living standards.
Key Concepts
Labor demand curve (in the paper’s sense). The equilibrium relationship between real wages and labor supply derived from competitive profit maximization by landowners facing a fixed land endowment: w_t = phi - alpha*l_t + a_t. Productivity is identified as shifts in this curve across time periods. The slope alpha is not simply the land share under a CES production function but equals one minus the labor share divided by the elasticity of substitution between labor and land.
Malthusian population force. The feedback mechanism by which higher real wages induce faster population growth, expanding labor supply and pushing wages back toward a steady state. Its speed is governed jointly by gamma (elasticity of population growth with respect to income) and alpha (slope of the labor demand curve); the half-life of wage/population dynamics after a shock equals log(0.5)/log(1 - alpha*gamma). In the paper’s estimates, this force was sufficiently weak (half-life approximately 150 years) that post-1800 productivity growth overwhelmed it.
Plague shock (xi_1t). An infrequent, large, exogenous negative population shock modeled as a draw from a beta distribution occurring with probability pi. Plagues are the primary source of identifying variation for the pre-1600 period: they generate movements along a stable labor demand curve and allow the slope alpha and the (lack of) productivity trend to be separately identified from labor demand shifts.
Structural break in average productivity growth (mu). The drift parameter in the random-walk model for the permanent component of productivity. The paper allows two breaks in mu, with break dates chosen to maximize the marginal likelihood (Bayes factor). The best-fitting breaks are at 1600 (zero to 4% per decade) and 1810 (4% to 18% per decade).
Permanent vs. transitory productivity component. Productivity is decomposed into a permanent component a-tilde_t (random walk with drift, sigma_epsilon1) and a transitory component epsilon_2t (iid noise, sigma_epsilon2). The paper reports and interprets the permanent component as the meaningful measure of underlying technological change; transitory shocks are treated as measurement error and short-run fluctuations.
Industrious Revolution. The hypothesized long-run increase in days worked per worker in England, associated with de Vries (1994, 2008). The paper uses Humphries-Weisdorf (2019) estimates showing a sharp drop after the Black Death followed by a sustained rise from 1350 onward. A key robustness result is that the paper’s productivity estimates are insensitive to whether this Industrious Revolution is assumed to have occurred.
Bayes factor (model selection). The ratio of marginal likelihoods p(y|M_t)/p(y|M_t’) for two competing models, used here to select structural break dates for mu. A factor of 10 is treated as strong evidence. The bridge sampling method of Gronau, Singmann, and Wagenmakers (2020) is used to compute marginal likelihoods.