Time Since Transition to Agriculture and Contemporary Development

We first document a negative relationship within the Western agricultural core area between time since transition to agriculture and contemporary levels of economic development. Table 1, Column (1) presents the country-level results, and Figure 3 Panel (a) shows the relationship between Log GDP per capita in 2005 and Average time since agricultural transition.^{Footnote 8} The base sample includes Western countries in Europe, Middle East, North Africa, and Southwestern Asia that belonged to the Western core of agricultural diffusion. Conley (Reference Conley1999) standard errors are included in all specifications to consider potential spatial correlations. The coefficient estimate is –0.492 and strongly significant. This means that a 1,000-year earlier transition to agriculture is associated with approximately a 39 percent lower GDP per capita. The numbers imply that if a country close to the mean time since transition such as Italy had experienced the transition to agriculture in 8,300 bp instead of in the actual year 7,300 bp, their GDP per capita in 2005 would have been 11,826 $US instead of 19,386 $US. The economic significance is thus also quite strong.

Table 1 BASELINE RESULT

Notes: The estimator is OLS, robust standard errors in parentheses. In calculating Conley standard errors (in square brackets), we assume that spatial autocorrelation exists among observations which are within ten degrees of each other. ***p < 0.01, **p < 0.05, *p < 0.1. The sample is all countries specified as Western in the text with available data.

Source: See Online Appendix B for data sources.

Notes: The figure shows the scatterplot and fitted line for the bivariate relationship between Log GDP per capita in 2005 and Average time since agricultural transition from the regression specification in Table 1.Source: Own map based on data from Eurostat and Pinhasi, Fort, and Ammerman (2005).

Figure 3 RELATIONSHIP BETWEEN LOG GDP PER CAPITA IN 2005 AND AVERAGE TIME SINCE AGRICULTURAL TRANSITION AMONG (A) 64 WESTERN COUNTRIES AND (B) 257 NUTS2-REGIONS IN EUROPE

Studies within the tradition of long-run development typically include geographical control variables together with their main variable of interest. However, no consensus has yet emerged on exactly what variables to include, and theory has not provided a definitive guide. For example, latitude may be strongly correlated with income today, but we do not find that controlling for other geographic correlates, there is basis for believing that a northern location per se should give an advantage for economic development. Table 2 presents a series of results showing that aside from the timing of transition, both log arable land area and log distance to coast and river remain consistently negative and statistically significant. These two geographic factors likely have direct impact on the outcome variable and remain important throughout different specifications, while other geographical controls, such as temperature, precipitation, area and altitude, roughness and terrain, and distance to Addis Abeba do not.Footnote ⁹ In the following specifications, we therefore include the two variables as controls for geography.

Table 2 BASELINE CROSS-COUNTRY RESULTS CONTROLLING FOR GEOGRAPHY

Notes: The estimator is OLS in all specifications. Robust standard errors are in parentheses. In calculating Conley standard errors (in square brackets), we assume that spatial autocorrelation exists among observations which are within ten degrees of each other. ***p < 0.01, **p < 0.05, *p < 0.1. The sample is all countries specified as Western in the text with available data.

Source: See Online Appendix B for data sources.

In Tables 3 and 4, we present further robustness checks on our cross-country results. First in Table 3, we vary the samples in our data to check whether the countries in the Fertile Crescent may be fundamentally different in some way and drive the results. In Column (1), we therefore include a Fertile Crescent-dummy and in Column (2) we exclude the Fertile Crescent countries altogether. The result of this exercise is that the estimate for Average time since agricultural transition becomes more negatively sloped and even more significant. In Column (3), we include two continental dummies for Europe and Southwest Asia. The Europe dummy is positive and significant, as one might expect. In Columns (4) and (5), we restrict the sample to only European and only former Roman countries, respectively. The latter countries arguably shared a similar institutional and cultural context during a very formative period of Western history. Even in these limited samples and when controlling for the standard geographical and historical variables, time since agricultural transition is still significant. In Column (6), we restrict the sample to only those countries with at least one Pinhasi site within their borders. The basic result stays the same.

Table 3 ROBUSTNESS OF CROSS-COUNTRY RESULTS TO SAMPLE VARIATION AND ALTERNATIVE INDICATORS OF TIME SINCE AGRICULTURAL TRANSITION

Notes: The estimator is OLS in all specifications. Robust standard errors are in parentheses. ***p < 0.01, **p < 0.05, *p < 0.1. The full sample of Western countries includes all countries specified as Western in the text. Geographical controls and a constant with unreported coefficients have been included in each regression. The set of geographical controls are Log arable land area and Log distance to coast or river.

Source: See Online Appendix B for data sources.

Table 4 CROSS-COUNTRY RESULTS CONTROLLING FOR VARIOUS HISTORICAL CHANNELS

Notes: The estimator is OLS in all specifications. Each row presents results from a specific regression with historical controls as specified. Robust standard errors have been used in all specifications and are shown for the point estimates of Average time since agricultural transition, but are not reported for the historical variables. ***p < 0.01, **p < 0.05, *p < 0.1. The sample is all countries specified as Western in the text with available data. Geographical controls and a constant with unreported coefficients have been included in each regression. The geographical controls are Log arable land area and Log distance to coast or river.

Source: See Online Appendix B for data sources.

Next, we replace Average time with three other measures: Predicted time since agricultural transition, Earliest date of transition, and Putterman’s Time since agricultural transition. The first measure is based on the location and dating of the 765 sites in the Pinhasi, Fort, and Ammerman (2005) sample. We exploit the observed pattern of a fairly stable speed of agricultural diffusion across space from the area of origin in the Fertile Crescent. That is, the predicted time is a linear function of the distance between the archaeological site Jericho, considered as the origin of agricultural diffusion, and the center of each region. This measure explicitly considers the timing of agricultural adoption as an outcome of the region’s location and its distance to Jericho, based on the demic diffusion theory. Earliest date uses information on the earliest incidence of agriculture within a country rather than the average date of transition.Footnote ¹⁰ Although the estimates in (8)–(10) are closer to zero, the negative slope coefficients are significant in both cases.

Given that the diffusion process spread to hunter-gathering societies in one direction, rather than what one may consider as a process of cultural exchange, in this article we essentially interpret the transition as an exogenous shock to the region. But what if there were pre-existing cultural differences that sometimes influenced the transition date? Acemoglu and Robinson (Reference Acemoglu and Robinson2012), for instance, suggest that the Natufians, who lived in the Middle East during the Mesolithic period, perhaps had adopted a sedentary lifestyle as a more or less random technological innovation that had not so much to do with how suitable the wild plants and animals in the neighborhood were for domestication. A similar line of reasoning is also found in Bowles and Choi (2013), who argue that an institutional innovation of private property in certain societies sometimes preceded transition to agriculture. Although we recognize this possibility, we find no reason to believe that such variations were systematically related to the distance to Jericho to bias our empirical results.

Similarly, a key identifying assumption in this setup is further that the income level did not in any way influence timing of agricultural adoption. Although local geographical and climatic conditions no doubt played a role in the diffusion of agriculture, we can control for a set of these exogenous factors. In doing so we think there are no good reasons to believe that current or historical levels of income per capita should have any plausible reverse causality on the date of agricultural transition.Footnote ¹¹ The main reason for this is the widespread archaeological and genetic support for the “Neolithic demic diffusion model,” arguing that agriculture mainly spread through physical migration by people from the original farming areas in the Fertile Crescent to areas in the periphery.Footnote ¹² Agriculture thus typically appeared in a region as an exogenous intervention and did not arise indigenously.

Finally in Table 4, we check the robustness of our main results to inclusion of a list of other historical variables that have been proposed as important in the literature, while also controlling for geography. The estimates of the historical variables are shown in the second column.Footnote ¹³ The first variable that we try is Ashraf and Galor (2013)’s Predicted genetic diversity and Predicted genetic diversity squared. For the world as a whole, this variable was shown to have an inverted u-shaped relationship with income in the original study. In our Western sample, the estimates have the wrong sign and are not significant. Ethnic fractionalization in Row (3) is negative and significant, but so is the coefficient estimate for Average time since agricultural transition.

Perhaps our main variable capturing time since the Neolithic just happens to be correlated with historical Atlantic trade, which is the true driving force behind the rise of Western Europe, as hypothesized by Acemoglu, Johnson, and Robinson (Reference Acemoglu, Johnson and Robinson2005)? In Row (4), we introduce an Atlantic dummy, which turns out to be strongly positive and significant. However, Average time since agricultural transition is still negative and significant. An indicator for the duration of state experience State history 1–1950 is entered in Row (5a), and the duration of state experience from 1–1500 is entered in Row (5b). Despite the strong link between time since the Neolithic and subsequent state history, up to and past European colonization, the control variables do not make the estimate of Average time since agricultural transition statistically insignificant. Hence, the long-term impact of agriculture does not appear to run solely through the timing of state formation.

In Row (6), we include a whole set of historical empire proxies capturing the proportion of the country controlled by Roman, Byzantine, Carolingian, and Ottoman rulers, as well as a dummy for whether the country was overrun by Mongols in 1300 ce.Footnote ¹⁴ Having been included in the Carolingian empire had a clear positive influence while Mongolian rule had a negative impact, but our main coefficient of interest is almost unaffected. Furthermore, the Legal Origin indicators in Row (7), often included as important determinants of economic performance (La Porta, Lopez‐De‐Silanes, and Shleifer Reference La Porta, Lopez‐De‐Silanes and Shleifer1999) are all significant, but do not seem to be very important mediator variables.

One potential mediator variable that may explain divergence of development in Europe especially between 1000 and 1500 ce may be the rise of Holy Land Crusades. Blaydes and Paik (Reference Blaydes and Paik2016), for example, document that the areas with larger numbers of crusaders subsequently witnessed increased political stability, urbanization, and institutional development. From their work, we use the number of Crusade location points in each country across the four waves of recruitment, with the First Crusades beginning in 1096 and the Fourth Crusades ending in 1204. These were the “largest and most significant of the Crusades. Indeed, out of 1,051 elite crusaders… 916 are categorized as participating in the first four waves” (Blaydes and Paik Reference Blaydes and Paik2016, pp. 566–67). Row (8) includes the number of Crusade recruitment locations from Blaydes and Paik (Reference Blaydes and Paik2016) as a proxy for Crusader presence. When we control for the Crusades (which appears to have a positive impact on the current income level), we still find the agricultural adoption variable to be statistically significant and negative.

Another related factor in our historical framework is religion. All the old areas of civilization are currently dominated by Muslims whereas Protestants are the majority in northern Europe. Furthermore, important scholarly works argue that certain institutional features of Islam were harmful to economic development whereas the Protestant emphasis on individualism has been discussed as a beneficial factor for economic development at least since Max Weber.Footnote ¹⁵ When we control for the Protestant population percentages in Row (9), the estimate for Average time since agricultural transition remains significant.

Finally, an additional historical shock which has been emphasized by many authors is the Black Death of 1347–1353 ce (Clark Reference Clark2008; Voigtländer and Voth Reference Voigtländer and Voth2013). Could it have been an extra high mortality in Black Death that “shocked” the north European countries and regions into a new equilibrium with higher wages and higher urbanization? Any such analysis is plagued by the fact that cross-country data on mortality from the Black Death are generally very unreliable. In Figure C1 of Online Appendix, we show the relationship between Average time since agricultural transition and Black Death mortality among 53 Western cities, using data from Christakos et al. (Reference Christakos, Olea, Serre, Yu and Yang2005). Interestingly, the relationship in the figure is positive, indicating that the cities with a long history of agriculture were actually worse hit by the Black Death on average. Although this evidence is far from conclusive, it does not seem to give support to a reversal happening because of a more adverse shock in north Europe.Footnote ¹⁶ In summary, we show that our main variable is robust to the inclusion of a range of historical variables suggested in the literature.

In addition to the series of robustness checks noted earlier, we evaluate whether our key findings are robust to changing the level of aggregation. Table 1, Column (2) shows the results for the cross-regional analysis, among the intrastate regions in 29 countries. Figure 3, Panel (b) shows an unconditional bivariate scatter plot for 257 NUTS2 intra-state regions with available data. The table again shows that the negative relationship persists at the finer regional level. The estimate for Average time since agricultural transition is negative and significant even when we control for country fixed effects and focus on within-country variations. Table 5 presents the results, in which the slope coefficient changes but retains its significance. With both geography and country fixed effects, R ² is 0.76 (Table 5, Column 4), which indicates that our specification explains a quite large proportion of the variation in regional income levels.

Table 5 CROSS-REGIONAL ANALYSIS AMONG 285 EUROPEAN NUTS2-REGIONS

Notes: The estimator is OLS. Columns (3) and (4) include country fixed effects. The sample is all Western regions with available data on NUTS2-level. Robust standard errors are in parentheses. ***p < 0.01, **p < 0.05, *p < 0.1. In calculating Conley standard errors (in square brackets) for the estimates of Average time since agricultural transition, we assume that spatial autocorrelation exists among observations which are within ten degrees of each other. The controls are fraction of land suitable for agriculture and log distance to coast or river.

Source: See Online Appendix B for data sources.

In order to zoom in even more closely on a micro level, we also use data for time since transition and average levels of GDP per capita that we have collected on the NUTS3-level of aggregation. Table 6 presents the results for five of the largest countries in the sample with many Pinhasi sites within their borders (Germany, France, Italy, Spain, and Turkey), in which we find that there remains the overall negative relationship within countries except in Germany where there is a positive relationship. In Figure 4a, we show the combined unconditional bivariate scatter plot between the income measure and average time since agricultural transition for 1,371 Western NUTS3 regions. Figure 4b shows separate unconditional regression lines for Germany, France, Italy, Spain, and Turkey. The estimated slope coefficients for the whole sample is –0.484, which is statistically significant at the 0.01 level. These results demonstrate a strong negative relationship between the timing of agricultural transition and GDP per capita both across and within most countries. The strong negative correlations at a disaggregated level within countries like Turkey, Spain, and Italy are particularly striking.^{Footnote 17}

Table 6 WITHIN-COUNTRY RELATIONSHIPS BETWEEN AVERAGE GDP PER CAPITA AND TIME SINCE AGRICULTURAL TRANSITION FOR NUTS3-REGIONS IN FIVE LARGE COUNTRIES

Notes: The table shows estimated coefficients for the within-country relationships between agricultural transition dates and log average GDP per capita 2005 for the five largest countries. The estimator is OLS in all specifications and each observation is a NUTS3-region. A constant with unreported coefficients has been included in all regressions. Robust standard errors are in ()-parentheses. Pinhasi sites refers to the number of archaeological sites in Pinhasi, Fort, and Ammerma (2005) within each country’s borders that are used to assess the date of transition for each region. ***p < 0.01, **p < 0.05, *p <0.1.

Source: See Online Appendix B for data sources.

Notes: The figure shows the scatter plot and fitted regression line for the bivariate relationship between Average Log GDP per capita 1997–2008 and Average time since agricultural transition (in k years) for 1,371 Western NUTS3-regions. It also shows the distinct scatter plots for Germany, France, Italy, Spain, and Turkey. German observations are hollow diamonds, French observations grey circles, Italian observations light triangles, Spanish observations squares, and Turkish observations black circles. All other region observations are black. More details for the within-country regressions are shown in Table 2. The estimated coefficients for region i in country j are (with robust standard errors in parenthesis): Average log GDP per capita 1997–2008 (ij) = 12.99 (0.147) – 0.484 (0.021) *Average time since agricultural transition(ij) + ε(ij).Source: Own map based on data from Eurostat and Pinhasi, Fort, and Ammerman (2005).

Figure 4a RELATIONSHIP BETWEEN AVERAGE LOG GDP PER CAPITA 1997–2008 AND AVERAGE TIME SINCE AGRICULTURAL TRANSITION AMONG 1,371 EUROPEAN NUTS3-REGIONS

Notes: The figures show the bivariate, unconditional relationships between average log GDP per capita in 2005 and average time since agricultural transition among NUTS3-regions within the five largest countries in the Western zone: Germany, France, Italy, Spain, and Turkey.Source: Own map based on data from Eurostat and Pinhasi, Fort, and Ammerman (2005).

Figure 4b BIVARIATE RELATIONSHIPS BETWEEN AVERAGE LOG GDP PER CAPITA 2005 AND AVERAGE TIME SINCE AGRICULTURAL TRANSITION AMONG THE SIX LARGEST COUNTRIES IN WESTERN ZONE

Timing of the Reversal

When did this reversal happen in the Western world? The Industrial Revolution, starting around 1800, contributed to the economic and technological dominance of Britain and other north European countries (Mokyr Reference Mokyr1990; Acemoglu and Robinson Reference Acemoglu and Robinson2012). Before the Revolution, the great divergence in the Western world after 1500 ce was due in part to the opening of the Atlantic trade and colonial ventures (Acemoglu, Johnson, and Robinson Reference Acemoglu, Johnson and Robinson2005). Some scholars trace the root of Western Europe’s rise to pre-1500 ce. Putnam, Leonardi, and Nanetti (1993), for example, trace the differences in current institutional performance in Italy back to 1100 ce’s governance structure and social networks. Voigtländer and Voth (Reference Voigtländer and Voth2013) discuss the Black Death of 1347 ce, which shocked many parts of Europe into a new pattern of rising wages and higher urbanization rates that further sped up susceptibility to plagues and a greater fiscal capacity. Bosker, Buringh, and Van Zanden (2013)’s city-level analysis of the Western zone shows that the faster growth of the European cities compared to Islamic cities during the Medieval period can be partly attributed to the more democratic and republican traditions in Europe, especially in Italy and Flanders. Blaydes and Chaney (Reference Blaydes and Chaney2013) focus on ruler duration and find that European durations were longer than in the Islamic world by 900 ce, due to the feudal system that decentralized power in Europe and gave rise to greater political stability and more beneficial economic development.

A key question in our analysis is whether the reversal since the Neolithic was visible already during the First Great Divergence, 1500–1800 ce. For the Malthusian era, it is widely accepted that population density is a better indicator than GDP per capita for the level of economic development in a country (Ashraf and Galor Reference Ashraf and Galor2011). In Table 7 Columns (1)–(3), we use logged population density in years 1, 1000, and 1500 ce as dependent variables. In 1 ce, the reversal does not seem to be in place since the estimate for Average time since agricultural transition is positive. In 1000 ce, the estimate is negative but insignificant. However, by 1500 ce, the reversal is evident; the time since agricultural transition in that year is both negative and significant. In Columns (4) and (5), we instead use Log GDP per capita from 1500 and 1820 ce as the dependent variables. The estimate for Average time since agricultural transition is negative in 1500 ce and becomes strongly significant as time passes. When we use income per capita data also for years 1000, 1600, 1700, 1913, 1980, and 2005 ce and run the same regressions as in Table 7, we can track more in detail how the regression coefficient of Average time since agricultural transition develops over time. Figure 5 shows the patterns, suggesting an increasingly strong tendency for a reversal over the course of the millennium.

Table 7 HISTORICAL EVOLUTION OF RELATIONSHIP

Notes: The estimator is OLS in all specifications. Average time since agricultural transition is measured as time since the transition at the corresponding date of the dependent variable (i.e., 1 ce, 1000 ce, etc.). Robust standard errors in parenthesis. ***p < 0.01, **p < 0.05, *p < 0.1. The sample is always all Western countries with available data. A constant with unreported coefficients have been included in each regression.

Source: See Online Appendix B for data sources.

Notes: The figure shows the regression coefficients from eight separate regressions for different time periods, exploring the bivariate, unconditional relationships between average log GDP per capita and average time since agricultural transition. The eight β₁-estimates from these regressions are shown as grey circles, and the dashed lines represent the associated 95-percent confidence intervals. The included years t (in the ce period with the number of Western country observations in parenthesis) are 1000 (20), 1500 (21), 1600 (19), 1700 (21), 1820 (28), 1913 (34), 1980 (43), and 2005 (64). Results from the regressions with controls for 1500 and 1820 are shown in Table 3 and for 2005 in Table 1. Results from the regressions for 1600, 1700, 1913, and 1980 are available upon request.Source: See Online Appendix B for data sources.

Figure 5 HISTORICAL EVOLUTION OF RELATIONSHIP BETWEEN LOG GDP PER CAPITA AND AVERAGE TIME SINCE AGRICULTURAL TRANSITION AMONG WESTERN COUNTRIES 1–2005 ce

We do not interpret these results as evidence against the critical roles played by other historical channels explored in the literature. Undoubtedly, these fundamental processes contributed importantly to the great divergence that made Britain and its northern followers much richer than the Mediterranean and Middle Eastern countries. What we do suggest, however, is that the process of reversing fortunes in the Western world seems to have followed an older trajectory, rooted in the transition to agriculture, which seems to have become manifested already by 1500 and has previously not been recognized.

Democracy as an Intermediate Channel

Do countries that made a late transition to agriculture over time develop more democratic institutions than early adopters? We find that agricultural adoption timing and indicators of inclusive, democratic institutions indeed have a strong association. In Table 8, we employ Democracy stock 1900–2000 from Gerring et al. (Reference Gerring, Philip Bond and Moreno2005). As described in Online Appendix B1, the authors use the sums of time-discounted individual country-year scores for the standard Polity2-variable over the 1900–2000 period, where Polity2 _i,s ranges in value from +10 (full democracy) to –10 (full autocracy) for country i and year s. The highest scorer in our Western sample is Switzerland at 637 (full democracy throughout the period) and the lowest is Saudi Arabia at –604.6. The variable might thus be said to measure an accumulated stock of democracy during the twentieth century. Our aim here is again not to establish a causal argument from institutions to economic performance, but to simply show that both of these endogenous outcomes are likely affected by our agricultural transition measure, and that the direction of effect on these two is the same.

Table 8 INCLUSIVE INSTITUTIONS

Notes: Robust standard errors in parentheses. ***p < 0.01, **p < 0.05, *p < 0.1. The estimator is OLS in all specifications. The sample is always all Western countries with available data. A constant with unreported coefficients have been included in each regression.

Source: See Online Appendix B for data sources.

Democracy stock 1900–2000 is the dependent variable in Column (1). We find that Average time since agricultural transition strongly predicts the level of the democracy stock such that countries with an early transition tended to be more autocratic during the twentieth century. The estimate is strongly significant both with and without geographical controls. It also implies that an earlier transition to agriculture by 1,000 years is associated with a 155.4 units lower democracy stock.

Column (2) presents a proxy for the level of executive constraints in 1500. The variable is mainly taken from Acemoglu, Johnson, and Robinson (Reference Acemoglu, Johnson and Robinson2005), but is complemented with information for the Ottoman countries during the period.A high score indicates stronger constraints against the executive (and hence more inclusive institutions). In line with our hypothesis, Column (2) confirms that there indeed appears to be a strong relationship between the timing of the agricultural transition and Executive constraints in 1500 such that countries that adopted agriculture early had less inclusive institutions already by 1500.

Key Assumptions

Our model is in many ways a standard micro-founded Malthusian growth model over the very long run. The fundamental novel assumption that we introduce is that the dynamics of long-run total factor productivity in each country, over several millennia, follows a logistic growth pattern, characterized by four basic stages; a pre-agricultural (hunter-gatherer) stage, an early take-off stage soon after the transition to agriculture, a maturity stage after the emergence of states where productivity shifts from increasing to decreasing growth, and a stagnation phase where productivity levels have converged to levels close to the long-run maximum productivity potential of country j.Footnote ¹⁸

There are two key premises that play a very important role for the pattern of productivity development: (i) The biogeographic potential of the natural environment for agriculture determines the timing of the adoption of Neolithic farming. The regions with the greatest potential will adopt sedentary agriculture first and enter an early take-off stage with rapid social development (Diamond Reference Diamond1997; Olsson and Hibbs 2005). (ii) The maximum productivity potential that is reached in the stagnation phase is lower in earlier adopting countries than in countries that adopt agriculture later. This implies that although late adopters will be far behind the productivity levels of early adopters early in history, the late adopters of agriculture and state organization will eventually overtake the early adopters when the latter have reached their lower stagnation phase (see a similar dynamics model in Lagerlöf (Reference Lagerlöf2016)). For this reason, the cross-country relationship between levels of development and time since transition to agriculture will be positive in early history and negative in later history.

We start by outlining the details of the model and then confront the assumptions and the predictions of the model with the results from our empirical section, as well as from existing research on long-run macro history in western Eurasia.

Utility and the Intertemporal Budget Constraint

Given the very long-run time frame considered in this research, the model is mainly intended to capture conditions during pre-industrial times when capital accumulation is relatively insignificant and when growth and income levels primarily depend on land, population levels, and total factor productivity.

A representative individual i with an infinite life receives utility from consumption C _it of food and other basic commodities at a level above minimum subsistence level $\bar c$:

$${U_i} = \sum\nolimits_{t = 0}^{\infty} {{{{u_i}\left( {{c_{it}} - \bar c} \right)} \over {{{\left( {1 + \rho } \right)}^{t}}}}},$$

where ρ > 0 is a standard time discount rate. For any level of consumption above subsistence level, we assume the usual properties of a concave utility function: ${u_i}^{'}\left( {{c_{it}} - \bar c} \right) \gt 0$ and ${u_i}^{''}\left( {{c_{it}} - \bar c} \right) < 0$. For all levels ${c_{it}} \le \bar c$, ${({{c_{it}} - \bar c}) = 0}$.

The individuals’ intertemporal budget restriction is given by

$${\sum\nolimits_{t = 0}^\infty {{{{c_{it}}} \over {{{( {1 + r} )}^t}}} \le } \sum\nolimits_{t = 0}^\infty {{{{y_{it}}} \over {{{( {1 + r} )}^t}}}}}$$ ,

where y _it is the level of individual output, which we assume is equal to output per capita in the population as a whole, and r > 0 are returns to savings from one period to the next. The standard Euler equation for an infinitely-lived individual that optimizes utility, given the intertemporal budget constraint, is

$${{{u_i}^{\rm{'}}\left( {{c_{it}} - \bar c} \right)} \over {{u_i}^{\rm{'}}\left( {{c_{it + 1}} - \bar c} \right)}} = {{1 + r} \over {1 + \rho }}.$$

In the long term, it is generally assumed that the time discount rate should be equal to the interest rate, that is, r = ρ. If that is the case, we should have perfect consumption smoothing so that the optimal level of consumption at each t is $c_t^* = c_{t + 1}^* = \ldots = {c^*}$.

Production

Let us describe the total output produced in some country or region j at time t as

$${Y_{jt}} = {A_{jt}}X_j^\alpha L_{jt}^{1 - \alpha ,}$$

where Y _jt is total output, A _jt is total factor productivity, X _j is the fixed amount of land, L _ij is the level of the population, and $\alpha \lt 1$ is the output elasticity of land. Output per capita is

$${y_{jt}} = {{{A_{jt}}X_j^\alpha L_{jt}^{1 - \alpha }} \over {{L_{jt}}}} = {{{A_{jt}}} \over {p_{jt}^\alpha }}$$ ,

where p _jt = L _jt/X _j is population density per unit of land.

Malthusian Population Density and Consumption

During most of the pre-industrial era, levels of population have adjusted to income per capita in a Malthusian fashion and grown such that income per capita has remained just above subsistence level $\bar y + \omega $ where $\bar y$ is the level of production associated with the minimum consumption level for survival $\bar c$ and $$\omega \gt 0$$ is a small number reflecting a certain precaution among households in their fertility choice. Hence, we can show that the equilibrium population density must be

$${p_{jt}^{\rm{*}} = {\left( {{{{A_{jt}}} \over {\bar y + \omega }}} \right)^\alpha }.}$$

Countries or regions will thus not differ in their levels of income per capita during these Malthusian times, but will have different levels of population density, depending on A _jt.

Inserting ${c_{it}} = {c^*}$, r = ρ and ${y_{jt}} = \bar y + \omega $ into the intertemporal budget restriction shows that

$$\mathop \sum \limits_{t = 0}^\infty {{{c^{\rm{*}}}} \over {{{\left( {1 + \rho } \right)}^t}}} = {{{c^{\rm{*}}}} \over \rho } = \mathop \sum \limits_{t = 0}^\infty {{{y_{it}}} \over {{{\left( {1 + \rho } \right)}^t}}} = {{\bar y + {\omega ^{\rm{*}}}} \over \rho },$$

implying the standard Malthusian result that

$${c^{\rm{*}}} = \bar y + \omega \gt \bar c.$$

Hence, during the Malthusian era, productivity increases led to a great increase in total production and in population density, whereas output and consumption per capita remained close to subsistence level.Footnote ¹⁹

Total Factor Productivity

So far, the model presented earlier has been a standard Malthusian growth model. We now introduce a novel modelling of long-term dynamics of total factor productivity (TFP). The account is a formalized version of the graphical analysis in Borcan, Olsson, and Putterman (Reference Borcan, Olsson and Putterman2018) where the key assumption is that total long-term TFP A _jt can be described as a logistic function, which we define mathematically here as:

(1) $${A_{jt}} = \left\{ {\matrix{ {{{{{\tilde A}_j}} \over {1 + \left( {{{{{\tilde A}_j} - {A_{j{\tau _j}}}} \over {{A_{j{\tau _j}}}}}} \right){e^{ - g\left( {t - {\tau _j}} \right)}}}}\,\,\,ift \ge {\tau _j}} \cr {1{\rm{ }}if\,\,t < {\tau _j}} \cr } } \right.$$

In this expression, ${\tilde A_j}$ is the long-run maximum productivity potential of country or region j, ${\tau _j} \in T$ is the date when the population in country j made the transition to Neolithic agriculture where T= {0,1,t….∞} is the set of all possible dates in time and g > 0 is a productivity growth rate parameter. At all dates before the transition to agriculture $t \lt {\tau _j}$, we assume a pre-agricultural (hunter-gatherer) level of productivity of A _jt = 1 for all j.

The growth of TFP in Equation (1) after the transition to agriculture is:

(2) $${{\partial {A_{jt}}} \over {\partial t}} = {\dot A_{jt}} = g{A_{jt}}\left( {1 - {{{A_{jt}}} \over {{{\tilde A}_j}}}} \right)$$

The dynamics of TFP is thus such that the effective growth rate is $g\left( {1 - {A_{jt}}/{{\tilde A}_j}} \right)$ right after the transition and then converges towards zero as t → ∞. It is also the case that the expression in Equation (2) will be convex in the segment A _jt< ${\tilde A_{j}/2}$ and concave thereafter, as the defining characteristic of a logistic function. More intuitively, the functional form implies that there is a period of rapid and increasing productivity growth in what we refer to as a “take-off” stage, soon after the transition, a “maturity stage” where productivity shifts from increasing to decreasing growth, and then a “stagnation phase” when the productivity level has almost converged to its maximum potential ${\tilde A_j}$.

Countries and regions make the transition to agriculture at different dates τ _j where the sequence is such that τ₁ < τ₂ < …τ _J, and where J is the last country in the (Western) geographical zone in the finite set of J existing countries. In line with Diamond (Reference Diamond1997), Olsson and Hibbs (Reference Olsson and Hibbs2005), and others, we make the assumption that τ ₁(F ₁), that is, the transition date of the origin region of agriculture in the zone, is a negative function of the quality of biogeographical conditions for agriculture F ₁ such that τ’ ₁(F ₁) < 0. This implies that the country with the best endowment for agriculture in a geographical zone, having a large number of suitable plants and animals for domestication (like Mesopotamia in the Western zone or China in East Asia), will make the transition first. Agriculture then spreads through migration to the neighboring countries and regions, which typically have similar biogeographies.

After the transition, the economy enters a take-off stage where the benefits of the technological paradigm shift become manifest. More and more domesticated plants and animals are brought under human control, people settle in villages near commonly-held fields, orchards, irrigation structures, public buildings, and defensive fortifications. The early farming villages soon develop into complex and stratified social units capable of providing large-scale public goods that further enhance productivity in food production (Scott Reference Scott2017). Eventually, centralized states with kings, soldiers, and bureaucrats emerge as the elites in the most powerful and well-organized farming villages extend their influence over their neighborhoods (Spencer Reference Spencer2010; Borcan, Olsson, and Putterman 2019). During early history, an earlier starting date for Neolithic agriculture (and hence a lower τ _j) will thus imply a relatively high level of productivity in Equation (1) since the productivity growth process has been progressing for a longer time.

However, a second crucial assumption in our model is that an early transition to agriculture also has an offsetting negative impact by lowering the maximum productivity potential ${\tilde A_j}$. More formally, we assume that ${\tilde A_j}\left( {{\tau _j}} \right)$ is a function such that $\tilde A_j^{'}\left( {{\tau _j}} \right) \gt 0$. Our argument for the different maximum productivity levels in this model rests on Lagerlöf (Reference Lagerlöf2016) who develops a theoretical mechanism through which it is shown that countries that made an earlier transition to states will have a lower productivity potential ${\tilde A_j}$ and income level Y _jt in the long run. As has been demonstrated in recent work (Borcan Olsson, and Putterman 2019), there is a tight, positive empirical relationship between the historical date of transition to agriculture and the subsequent transition to states. Hence, an early τ _j in our setting also means an early emergence of a state.

In Lagerlöf’s model, countries that transit into statehood early are always autocratic in the sense that a single dominant group has grabbed power and invests in extractive (taxing) capacity and in public goods, where only the latter advance economic development. In countries where states (and hence agriculture) emerged early, the government would over time build up substantially higher extractive capacity than in younger states. At a later date in history, democracy is introduced as an exogenous opportunity shock and government elites consider whether to adopt democracy, with an equal sharing of resources but with no costs of extractive capacity, or remain in autocracy. The large sunk investments under high extractive capacity in older states implies that elites in such countries are less prone to adopt democracy than in younger states, where the elites have less to lose. Hence, democracies tend to arise in younger states which are also able to reach a higher long-run level of public goods investment and income due to the absence of socially wasteful investments under unproductive extractive capacity.Footnote ²⁰

We propose that our assumption of $\tilde A_j^{'}\left( {{\tau _j}} \right) \gt 0$ should be primarily thought of as reflecting Lagerlöf’s mechanism via extractive capacity and the transition to democracy. If this mechanism is correct, we should not only find a negative long-run relationship between time since transition to agriculture and contemporary income levels, but also that a late transition to agriculture is positively associated with the adoption of democracy.

Numerical Simulation

Our theoretical framework can be used to make a comparative country (or regional) analysis where we analyze how the impact of time since transition to agriculture, t – τ _j, changes from having a positive effect on relative productivity levels early in history, to having a negative impact later in history when all countries approach their maximum long-run productivity potential. In Online Appendix D, we provide a mathematical analysis of these time-dependent effects.

In this section, we illustrate the dynamics of the logistic productivity function by performing a numerical simulation of the model. In the simulation, we assume t ∈ {1,2,…120} centennial periods where t = 1 might be thought of as 9900 bce and t = 120 as 2000 ce. We consider the dynamics of three example countries, A, B, and C, with agricultural transition dates τ _A = 15 (8500 bce), τ _B= 40 (6000 bce), and τ _C= 65 (3500 bce). We assume g = 0.13 and that maximum productivity potentials are ${\tilde A_A}$ = 100, ${\tilde A_B}$ = 130, and ${\tilde A_C}$ = 160.

The resulting dynamics of productivity are shown in Figure 6. At a very early date in history such as 4000 bce, Country A has already reached its maturity stage and has advanced way ahead of Country B, which is still in an early take-off stage. Country C is at this time still in a pre-agricultural stage.

Notes: The figures provide a simulation of the logistic productivity function for three example countries (A, B, C) with different dates of transition to agriculture and different maximum productivity potentials, as specified in the text. Panel (a) shows the level of productivity over time for the three example countries whereas Panel (b) shows the implied scatter plots with connected lines at three different dates; 2000 bce, 100 ce, and 2000 ce. A key insight from the figure is that the relationship between productivity levels and time since transition to agriculture changes from being positive to being negative over time.Source: Based on authors’ simulations, which are available upon request.

Figure 6 SIMULATION OF LOGISTIC PRODUCTIVITY FUNCTION AND ITS CHANGING IMPACT OVER TIME FOR THREE EXAMPLE COUNTRIES

The comparisons between productivity levels for the years 2000 bce, 100 ce, and 2000 ce are shown in Figure 6. In 2000 ce, Country C has now made a transition to agriculture, Country B has had a period of very rapid productivity growth, but is still behind Country A, which has reached its stagnation phase. Overall, there is at this time still a positive relationship between time since transition to agriculture and productivity levels. In 100 ce, Country B has overtaken Country A and Country C is in its most rapid development phase. By 2000 ce, Country C has overtaken both A and B and there is now a negative relationship between time since transition and levels of productivity.

Historical Records

These simulation results are consistent with the historical divergence between regions in the Western core that experienced early agricultural adoption (the Middle East) and those that experienced it late (Western Europe) even before the early modern period. The narratives on the early state formation in the Middle East (Wittfogel Reference Wittfogel1957; Carneiro Reference Carneiro1970; Kennedy 1981) indeed suggest that the earliest agricultural societies in the Middle East also witnessed the rise of civilizations first in the form of autocratic states, and that these differed from those that arose much later in Western Europe.

In our model, early adopters have lower maximum productivity potential due to higher extractive capacity built up in the long run under autocracy. This key assumption finds support in the historical comparative works looking at the societies of the Middle East and Western Europe. For example, in an overview of state building literature in the Middle East, Blaydes (Reference Blaydes2017) importantly makes the relevant connections between early agricultural adoption, rise of autocratic states, and institutional features that stagnated economic development in the Middle East in the long run. The author argues that the rulers in the Middle East long maintained strong grips on fiscal capacity and bureaucracy inherited down from one period to another, in part aided by constant threats of nomadic invasions from the desert peripheries.

Blaydes (Reference Blaydes2017) specifically identifies two institutional features across the polities in the Middle East that could develop because of the autocrats’ superior bureaucratic and financial position during the Islamic Golden Age: the use of foreign slave soldiers (i.e., mamluks) and state control over agricultural land (i.e., iqta). According to the author, the rulers bought military support rather than develop feudalism as in Europe, where kings conceded their land and political power to the local lords for military support. Agricultural land also belonged to the state; unlike Europe’s landed gentry, the military slaves who were assigned tax rights to the land in return for their service thus had no incentives to provide public goods or invest in the land. These institutional inheritances in history are aligned with autocrats’ incentives to keep both land and political power highly centralized, and are in line with our model.Footnote ²¹

Blaydes and Chaney (Reference Blaydes and Chaney2013) further attribute the divergence in political stability and representation in Western Europe vs. the Middle East to the rise of feudal institutions and their forms of executive constraint. The authors find that this unique institutional framework with checks on the sovereign was noticeably absent in the Middle East with important consequences on the region’s stagnation in the long run. Western Europe’s sustained economic development since the beginning of the early modern period and onwards, on the other hand, is well documented in the literature (Acemoglu, Johnson, and Robinson Reference Acemoglu, Johnson and Robinson2005; North and Weingast 1989). In Europe, political fragmentation and representative institutions found under weak rulers furthermore led to political innovations such as modern democracy (Cox Reference Cox2017; Stasavage Reference Stasavage2016). The case of Europe again fits the setting in our model; there is relatively little extractive capacity built and the elites find it less costly to switch from autocracy to democracy.