We now proceed to analyze the relationship between state history and different indicators for historical and contemporary levels of productivity. Our proxies for aggregate productivity will be an index of technology adoption, population density, rates of urbanization, and GDP per capita.

State history and pre-industrial economic development

State history and productivity in 1500 CE

We begin with the empirical question of the relationship between state history and productivity in the Malthusian era. The key predicted pattern in Fig. 1a was a hump-shaped relationship between our state history measure and aggregate productivity in a cross-section of countries, reflecting on the one hand that newer or more inexperienced states tend to be in the process of converging to their own maximum productivity potential, whereas more experienced states already have attained a relatively low maximum level. Was such a tendency in place already in 1500 CE?

As a starting point, we proxy historical productivity with the average index of technology adoption constructed by Comin et al. (2010). Using various data sources on the presence and complexity of various technologies, the country-level index captures advances in five sectors: agriculture, transportation, communications, writing, and military. The index is computed for 1500 CE and 2000 CE, using slightly different approaches, which we describe in some detail in online Appendix A.

In order to test this prediction, we set up the following model:

$$\begin{aligned} Technology1500 _{i}=\beta _{0}+\beta _{1}\cdot Statehist1500_{i}+\beta _{2}\cdot Statehist1500_{i}^{2}+\epsilon _{i} \end{aligned}$$ (4)

On the left hand-side of Eq. (4) we have the average technology adoption index in 1500 CE. On the right-hand side we include our main independent variable, Statehist (the cumulative index shown in Eq. (3) accumulated in 1500 CE), both linear and squared, to allow for a quadratic relationship. The Statehist index is normalized with respect to 3500 BCE–1500 CE and computed using a 1% discount rate per period. This equation captures the potentially hump-shaped relationship to Statehist across countries. We also consider variants of (4) that include additional controls, represented by:

$$\begin{aligned} Technology1500 _{i}=\beta _{0}+\beta _{1}\cdot Statehist1500_{i}+\beta _{2}\cdot Statehist1500_{i}^{2}+\beta _{j}^{\prime }\cdot Z_{i}+\beta _{k}^{\prime }\cdot X_{i}+\lambda _{c}+\epsilon _{i} \end{aligned}$$ (5)

\(Z_{i}\) is a vector of historical controls including: \(Agyears_{i}\), the time before present since the transition to agriculture in the country in question, a variable taken from Putterman and Trainor (2006); \( Origtime_{i}\)—the approximate time since the first settlement on the territory of the modern-day country by anatomically modern humans, a variable introduced by Ahlerup and Olsson (2012) as a determinant of the variation in levels of ethnic diversity across the world. In a more flexible specification, we include the square of \(Origtime_{i}\) in order to account for recent developments in the literature postulating that the patterns of human settlement in prehistory may have nonlinear effects on later economic development (Ashraf and Galor 2013). In the same specification we also include State age \(_{i}\) in 1500 CE (the time elapsed in 1500 CE from the date of state emergence). \(X_{i}\) is a vector containing geographic controls. These include: the absolute latitude of the centroid of the modern-day country i, whether the country is landlocked, its distance to coast or ocean-navigable river, average elevation, land suitability for agriculture, climatic variables for temperature and precipitation, and the risk of malaria.Footnote 36 \(\lambda _{c}\) is a vector of continent fixed effects. The results are displayed in Table 2. Columns (1) and (2) present linear and quadratic versions of Eq. (4), while columns (3)–(7) add further controls, as in Eq. (5).

Table 2 State history and average technology adoption in 1500 CE Full size table

In column (1) we display the simple association between technology adoption and Statehist, which is positive and significant. In column (2), where we add Statehist squared, our main coefficients of interest, \( \beta _{1}\) and \(\beta _{2},\) display a concave pattern: \(\beta _{1}\) is positive, while \(\beta _{2}\) is negative, both significant at 1%. In the online Appendix Table D1, we estimate this specification using Statehist discounted by alternative factors, 0.1% and 2%, which reveal the qualitatively identical result of significant concavity. As concavity does not imply non-monotonicity, to test for the latter, we run piece-wise estimations using the linear Statehist separately in countries below and above the technology-maximizing level of Statehist implied from Eq. (4) (which is 0.44, with only 9 countries recording a higher Statehist of 1500 CE).Footnote 37 The results reported for different Statehist discount rates in the online Appendix Table D2, including our main case 1% rate, show positive insignificant slopes above the maximizing Statehist. Therefore, we do not find an inverse-u shape in the case of technology adoption in 1500 CE.

In column (4) we add to the model the first historical control - Agyears (shown to be positively significantly correlated with the dependent variable in column 3, for comparison purposes). Its inclusion only slightly changes the signs and the magnitude of the coefficients of the Statehist terms. Moreover, the effect of the time from transition to agriculture is reduced relative to column (3). When we also add Origtime and geographical controls in column (5), the magnitude of the estimates changes slightly, but the relationship remains concave. The continent fixed effects in the last two columns reduce the squared term’s coefficient, which becomes insignificant.Footnote 38

State history, population and urbanization in 1500 CE

We now inquire whether this concave pattern is reflected in other commonly used indicators of historical productivity: population density (Table 3, panel A) and urbanization rate in 1500 CE (Table 3, panel B). All specifications are analogous to those in Table 2.

The extended Statehist is positively and significantly correlated with past population density and urbanization (column 1). Column 2 shows, however, that a quadratic relationship fits the data even better, with both linear and square terms obtaining highly significant estimated coefficients (the same holds when using discounts of 0.1% of 2%, as Appendix Table D3 shows). The population density maximizing level of Statehist is that of Greece (around 0.42). For population density, the below/above maximum regressions including only linear Statehist (Appendix Table D4) display negative slopes above the maximizing value of Statehist , significant when we use a 2% discount rate for Statehist. Hence, some evidence indicates an inverse-u shape already forming in 1500 CE (albeit not when we look at urbanization, which is maximized by a Statehist value of 0.64, which is above the range represented in the data). Both for population density and urbanization, quadratic yet monotonic patterns emerge in the specifications which introduce controls and continent fixed effects. In conclusion, while there are clear signs of diminishing benefits of additional state experience as of 1500 CE, there are few indications that added state experience was a net liability for more experienced states as of that year.Footnote 39

State history and current economic development

In our theoretical framework, the downward sloping portion of the cross-country Fig. 1a was assumed to result from less experienced states overtaking more experienced ones. The other portion may be explained by the many states in several parts of the world which emerged only in recent centuries. Thus, we expect contemporary levels of development to correlate in a non-monotonic fashion with accumulated Statehist. To investigate this, we estimate the model with technology adoption and GDP per capita in 2000 CE as a quadratic function of state history. The results are displayed in Tables 4, 5 and 6 below.

However, when analyzing the current levels of technological sophistication or output, using the raw Statehist data means that we only account for the history within the territories of present-day countries. This ignores the state history of other territories from which people migrated in recent centuries to settle in new territories. Population flows after 1500, when the era of colonization began, are instrumental in mapping the impact of historical events to today’s economic performance. This is because the ancestors of today’s population have evidently brought with them the history, the know-how and the experience with state institutions from their places of origin (Putterman and Weil 2010; Comin et al. 2010; Ashraf and Galor 2013).

Table 3 State history, log population density and urbanization in 1500 CE Full size table

Table 4 State history and average technology adoption 2000 CE Full size table

Table 5 Statehist versus Statehist 1–1950 CE and Log GDP pc 2000. Nonlinear relationship Full size table

Table 6 Adjusted Statehist and Log GDP pc 2000. Nonlinear relationship Full size table

We therefore also use an alternative measure of state history which is obtained by adjusting the 1500 CE Statehist index with the migration matrix developed by Putterman and Weil (2010). We then re-estimate our model using this new measure—the ancestry-adjusted Statehist—which, for each country, represents the average pre-industrial Statehist of its year 2000 population’s ancestors, with the weights for each source country being the share of then-living ancestors estimated to have lived on its present-day territory. These alternative results are displayed in Tables 4, panel B and 6.

Technology adoption in 2000 CE displays a similar concave relationship with year 2000 Statehist as did the technology index of year 1500 CE (Table 4, panel A). Furthermore, using the ancestry-adjusted Statehist in 1500 CE to explain the differences in average technology adoption in 2000 yields robustly significant estimates across all specifications, with larger magnitudes and higher R-squared statistics than when using the Statehist in 2000 CE. This result is consistent with our theoretical expectation that the relationship between technology and state experience was concave in the late Malthusian era, and that it was transmitted all the way into modern-day levels of technology adoption. The unconditional relationship shown in column (2) of Table 4, panel B, withstands using different discount rates for Statehist, and the relationship exhibits the downward sloping portion of an inverted-u shape in regressions with a linear Statehist above and below its implied maximizing value (panel B in Tables D5–D8).Footnote 40

Given the central role of aggregate productivity in the standard production functions for total output, we argue the hump-shape should also emerge when we look at GDP. Figure 4 illustrates the essence of our findings. On the Y-axis we have the logarithm of GDP per capita in 2000 and on the X-axis we have the extended Statehist (normalized with respect to 3500 BCE–2000 CE and computed using a 1% discount rate per period).

Fig. 4 Non-linear relationship between Log GDP per capita in 2000 and Statehist index. Note: The figure shows a fitted quadratic regression line corresponding to the estimates in Table 5, panel A, column 2, with 154 country observations distinguished by 3-letter country isocodes. On the Y-axis we have the logarithm of GDP per capita in 2000 and on the X-axis we have the extended Statehist (see Eq. (3) above). An increase in Statehist by 0.1 is interpreted approximately as an additional 300 years of effective fully autonomous statehood Full size image

The figure displays a scatter plot of all countries in the sample, while also allowing for a quadratic fit of the relationship between output and Statehist. The hump-shaped relationship emerges when using the extended Statehist. Footnote 41 In the online Appendix Figure C3, we show that the state history index based on 1–1950 CE data does not display the downward sloping portion seen in Fig. 4.

We estimate the quadratic relationship to the logarithm of GDP per capita in 2000 CE in Table 5, panel A. In panel B, the Statehist 1–1950 CE data are used for purposes of comparison. All specifications are analogous to the ones in the previous tables.

As before, the simple correlation between per capita income and Statehist (column 1) is positive and similar in magnitude across the two panels, but slightly less precisely estimated when the independent variable is the extended Statehist. In column (2) we add the squared Statehist, and the results mirror the pattern in Fig. 4: In panel A, both coefficients are significant at 1%, and their signs confirm the concave relationship between log per capita GDP and state history. By contrast, in panel B, the counterpart of this specification using Statehist 1–1950 CE displays coefficients with the same signs but much smaller and insignificant (the coefficient of the quadratic term becomes positive when controls are included).Footnote 42

While Agyears is significantly positively correlated with modern-day GDP (column 3), when we control for it alongside the linear and quadratic Statehist, its inclusion hardly changes the signs and the magnitudes of the coefficients of the Statehist terms. Moreover, the effect of the time from transition to agriculture is insignificant when the Statehist terms are added (column 4), indicating that although early states may only have arisen where agriculture had long been practiced, a country’s subsequent experience with states eclipses its experience of agriculture as a predictor of current productivity. As with technology, the concavity is robust to using alternative discount rates (0.1 and 2%) to calculate Statehist (Appendix Tables D5–D6). Moreover, separate linear estimates below and above the maximizing Statehist display a large, significant downward slope for countries in the upper range, consistent with Fig. 4 (Table D6, in the online Appendix).Footnote 43 \(^{,}\) Footnote 44 This confirms that a very limited or very extensive experience with state institutions can become a relative disadvantage across nations.

The concavity results are robust to the inclusion of Origtime, as well as geographical controls and continent fixed effects.Footnote 45 However, the coefficients on Statehist squared are smaller than the linear terms’ coefficients as more controls are introduced in columns (5)-(7). This implies that the optimum level of Statehist falls very close to, or outside the top of its range. Does this mean that the hump-shaped relationship between state history and income suggested by the earlier estimates (e.g., columns 2 and 4) is mistaken? We think not. Our framework posits such a relationship between state history and productivity as emerging across countries, whereas each individual country’s trajectory is described by a logistic curve, with no downward sloping portion (see the left side of Fig. 1a). As the number of factors controlled by our regressions grows, we may be approaching a situation in which the estimated coefficients on the focal Statehist variables will reflect only differences between otherwise nearly identical countries within a very narrow sub-region (countries not only in the same continent but sharing almost identical geographic coordinates, climate, etc.), as well as a very similar date of state origins, as indicated by the inclusion in column (7) of the variable state age. The resulting estimates of concavity without evidence of a downward sloped portion is consistent with the logistic curve pattern expected for any single country (left side of Fig. 1a) rather than the hump shape predicted for the full cross-section of countries over which state histories show wider variation.

Is our finding of concavity of per capita GDP with respect to state history in fact attributable to having included coding of state presence in the BCE era in our analysis, unlike previous studies? To see that this is the case, compare panel B of Table 5, which shows estimates of similar specifications but using the old state history variable covering years 1–1950 CE only. The main estimates are neither significant nor similar in terms of signs with the estimates in panel A.

Lastly, from column (2) in Table 5, based on the estimates of our coefficients of interest, we can infer that the predicted income-maximizing level of Statehist is reached at 0.355, which is very close to that of the United Kingdom and most countries in Western Europe.

The effects’ magnitudes are not straightforward to assess from the tables. However, some numerical examples may show more clearly how the impact upon per capita GDP of an increase in Statehist depends on the level of state experience at which the change occurs. Take for instance the case of Indonesia, which has 1350 years of state existence and a Statehist score of 0.254. If we could hypothetically increase the Statehist score by 0.1 (which is 58% of Statehist’s standard deviation, but enough to add 335 full-state years making it reach the level of the UK score), the implied approximate effect on per capita GDP in 2000 would be roughly a 20% increase, from USD 773 to USD 944 in 2000.Footnote 46 The opposite would happen if we were to increase the value of the Statehist score by 0.1 for China, which starts off with a value of 0.582 (a value exceeded by only five countries in the sample): the approximate effect would be a drop in per capita GDP in 2000 by 44.4%.

Taken together, our estimation results so far are consistent with our predicted pattern. Moreover, this becomes evident only when we employ the new extended Statehist index. Are the estimates improved by accounting for the state histories of the ancestors of present-day populations, instead of the state histories of places? To investigate this, we estimate the model for per capita GDP above using the ancestry-adjusted Statehist index. The results are displayed in Table 6, where we use the Statehist index in 1500 CE adjusted by the migration matrix (as in previous studies, but for the first time including full state history before 1 CE).Footnote 47

We find that the concave relationship between per capita income and the ancestry-adjusted Statehist is robust to all specifications and that the coefficients of interest are significant at 1% level in all columns in panel A. Moving from a linear (column 1) to a quadratic function (column 2) in Statehist as in all other tables, greatly improves the goodness of fit, strengthening the case for a nonlinear specification. Moreover, the explanatory power of the model (as measured by the regression R-squared) when we introduce only the ancestry-adjusted Statehist terms (column 2) is now 23.4% versus 5.2% for unadjusted Statehist.Footnote 48

In the online Appendix Table D12 we look at how sensitive the results from specifications where we include controls and county fixed effects are to excluding various countries from the sample. The estimates describing a concave function are significant when we exclude in turn the Middle-East and Sub-Saharan Africa, but the standard errors increase and the Statehist squared is insignificant when we exclude both these and North Africa (column 4). This is because this exclusion takes away a large part of the variation in Statehist that is due to very short and very long state age. Nevertheless, the signs and magnitudes of the coefficients point to the same concave relationship. There is no evidence of a concave relationship in the sample of European colonies, which are all very young and with little experience with home-based rule relative to the rest of the sample (median age 550 years and average 1180 years).Footnote 49

Statehist mechanisms

So far we have looked at the accumulated Statehist, which summarizes via their interaction (i) the variation in state age (the time elapsed since the first occurrence of \(z^1>0\)),Footnote 50 (ii) the degree to which the state was home-based (\(z^2\)), and (iii) the state’s territorial completeness and unity (\(z^3\)). In this sub-section, we briefly investigate the distinct effects of those three components and their respective contributions to the inverse-u shape. In Appendix Table D13, we estimate variants of columns (1), (2), (5) and (7) from Table 2, replacing Statehist with each of its components, in turn. Without controls (column 2), a quadratic relationship is found for each component (panels A–C), although for \(z^3\) (territorial completeness), the coefficients in quadratic specification (2) are not statistically significant, whereas when included alone, the level term attains a positive coefficient (in column 1) that is significant at the 5% level. When all three separate component terms are included simultaneously, in panel D, the results are similar. Two of the three components (state age, and territorial completeness/unity) also obtain highly significant positive coefficients in a strictly linear specification (column 1). Taken together, these results support that each component, not only state age, has some importance in its own right, a finding not explored in previous studies. When additional controls are added in column (3), and continent fixed effects as well in column (4), only the coefficient on level of \(z^2\) (home rule) remains statistically significant. Its positive sign suggests that having been independent rather than part of an externally based empire is most robustly and significantly associated with favorable outcomes, among the three components.Footnote 51

Borders endogeneity and spatial dependence

We now turn to the issue of whether endogeneity of borders raises concerns about the reliability of our findings. Throughout history, borders shifted as states consolidated or weakened their administrative or military capacities, or incurred political regime changes. For instance, Alesina and Spolaore (1997) showed that democratization can lead to secession, an example of which is the case of the Balkan countries. Gennaioli and Voth (2015) showed that the post-1500 military innovations in Europe led to more efficient warfare, stronger state capacity to finance warfare, and imminent territorial conquests or redistribution, which have redefined country borders. Their examples of Silesia, Alsace-Lorraine, and the Duchy of Milan are joined by numerous others, such as the regions split in the Peace of Westphalia in 1648 amongst Sweden, France, The Dutch Republic, Spain and the Holy Roman Empire. European colonisation is a leading example where late comers, having overtaken older states, proceeded to redraw the borders of these states in Latin America, North Africa, the Middle East and the Indian subcontinent. Against this backdrop, defining the state experience and economic indicators on the basis of present-day country borders may induce several risks.

First, there is a risk of retroactive measurement error, due to the fact that the current countries’ territories used to compute historical values of Statehist often bear little resemblance with the geopolitical logic in ancient times (with a few exceptions like Norway, Sweden, and Japan). We should note that our definition of Statehist requires keeping track of the changing boundaries of states-of-the-time within and across half-centuries, and the scores account for multiple polities, the internal or external basis of their rule and the percentage of territory they occupied within what may be thought of as an arbitrarily defined territory, from the standpoint of early periods. Although the state presence in some polities or sub-territories may be measured with error, if this error is random, at worst our estimates are biased towards zero. It would be more difficult to predict the bias if measurement error was correlated with the outcome variables, e.g. if borders shifted through conquest or colonization to include territories with more/less state history, productivity and technological sophistication, potentially also associated with the accuracy of data sources. Even so, the amalgamation of low information areas together into countries with better information and more state history is likely to lead to a reduction of error for the low Statehist parts of those countries, since the histories of such areas are typically better documented than are those of otherwise similar areas more distant from record-keeping societies. A second concern is that, as discussed earlier, productivity and technological sophistication sometimes drive conquest, moving borders and influencing state history. While we cannot fully dismiss the problem of endogenous borders, the issue of selection into state history is partly mitigated in cross-country regressions with contemporaneous economic development by the fact that whatever state-level polities existed at this and that period within the boundaries of what are today countries have changed their borders on many occasions and for a wide variety of reasons.

An alternative to using country borders could have been to divide the world randomly into equal-sized grid cells and then study the history of states and economic development in each such cell (e.g. Michalopoulos 2012). State history has been coded at the grid-cell level for sub-Saharan Africa after 1000 CE by Depetris-Chauvin (2014). For the present study, however, this would require constructing disaggregated data on a global scale for nearly six thousand years. The challenge with this approach, in addition to the sheer magnitude of the exercise, would be the precarious state history information for many grid cells. Average quality of data may well be higher with the countries-of-today approach than would be achievable with grid cells, unless a research effort several orders-of-magnitude larger were undertaken. With these caveats in mind, to the extent that researchers are interested in tracking the histories of countries in order to understand contemporary levels of development, the modern configuration of countries is still a natural point of departure.

A third concern, which is particularly salient in the context of jointly determined borders, is that the histories and outcomes of neighbouring countries transcend national boundaries. Countries in the same geographical or geopolitical regions tend to have correlated productivity levels and experience similar productivity shocks, for instance through contemporary diffusion of new technologies. In the presence of such spatial spillovers, the standard assumptions on the independence of observations are violated, and OLS regressions might yield biased and inefficient estimates. In this case, modelling spatial dependence is a more suitable approach. To account for potential spatial autocorrelation in the disturbances, we estimated alternative regressions using the Conley (1999) correction of the standard errors.Footnote 52 The results, displayed in Appendix Table D17 (panel A for Statehist and panel B for Ancestry-Adjusted Statehist) are very similar to the counterparts in Tables 5 (panel A) and 6, despite the fact that standard errors are, if anything, slightly larger than in the OLS regressions. We also estimate models where we allow the dependent variable to be a function of neighbouring countries’ outcomes (the spatial autoregressive model—SAR) and where we allow both the dependent variable and the errors terms to follow spatial autoregressive processes (SARAR).Footnote 53 In both models we input a matrix of weights given by the inverse great-circle distances between geodesic centroids.Footnote 54 Appendix Tables D18 and D19 show that the results with the Ancestry-Adjusted Statehist are robust across models, and that the SARAR results for Statehist generate qualitatively similar but insignificant results. We also report the SARAR estimates using a contiguity matrix defined not by geographical proximity, but by whether countries share the same legal origins (Appendix Table D20).Footnote 55 All results hold, with the linear and squared terms of both extended and Ancestry-Adjusted indices remaining significant. In sum, accounting for spatial spillovers does little to affect the results with extended state history and leaves the results with Ancestry-Adjusted indices unchanged.Footnote 56