The Expansive Corridor: Testing Acemoglu and Robinson (2019)

Abstract In The Narrow Corridor, Acemoglu and Robinson create a compelling narrative concerning the relationship between the power of states, the power of societies, and economic development, illustrated with a series of historical vignettes. Using a recently constructed historical dataset of state capacity, we provide a series of formal and informal tests of their hypothesis. We first visualise the historical paths of the strength of society and the strength of the state for each country so as to operationalise the claims of Acemoglu and Robinson. We then measure whether the balance of the strength of society and the strength of the state is predictive of improvements in both. We find very little evidence in favour of Acemoglu and Robinson.


Introduction
Social scientists have observed an interactive role between the strength of society and the strength of the state going back to at least de Tocqueville and Democracy in America. The relevance of strong, cohesive societies for institutional quality has since returned to the forefront of scientific research with the publication of Robert Putnam's Making Democracy Work (Putnam, Leonardi, & Nanetti, 1993) and later Bowling Alone (Putnam, 2000), with social capital and civil society organisations facilitating the functioning of democratic political institutions.
Acemoglu and Robinson (2019, see also Acemoglu & Robinson, 2022), using a lengthy series of historical vignettes, offer a different spin on this hypothesis. The strength of society and the strength of the state must be in balance with one another. When they balance one another, countries enter the titular 'narrow corridor' and societies are propelled forward, with the strength of society and state waxing (their 'Red Queen' effect, which leads to the 'Shackled Leviathan'), and economic performance following. When they do not, either the state will crush society ('Despotic Leviathan') or a society with strong norms and customs prevents the development of any effective coercive apparatus ('Absent Leviathan'). More formally, Acemoglu and Robinson (2017) model the narrow corridor as a saddle path that propels countries towards a strong state and strong civil society if they achieve a sufficient balance between the two forces. We will refer to the perspective presented by Acemoglu and Robinson (2019) as AR throughout the remainder of this paper.
AR convey this argument diagrammatically throughout the book (for example, Acemoglu & Robinson, 2019, p. 64, 268, 290), with the strength of society on the x-axis and the strength of the state on the y-axis. The corridor is denoted by an area falling between two positively-sloped lines emanating from the origin. The corridor is larger when both state and society are stronger. 1 While historical events may move countries into or out of the corridor, the crux of the model is that countries falling within the corridor will continue moving outwards within the corridor, while countries outside of it will collapse towards one of the axes.
Using a recent measure of state capacity with a lengthy time dimension (O'Reilly & Murphy, 2022), we will evaluate AR's hypothesis. First, we will visually examine the historical pathways countries have taken in their social and institutional development. That is to say, do countries in the narrow corridor stay within the corridor, and are they propelled forwards? And, do countries that start outside the narrow corridor fail to develop? Second, we assess econometrically whether the proximity of the power of society to the power of the state has any relationship with social and institutional development. Our quantification and operationalisation of the claims made by AR, interpreted in the most charitable way possible, at best weakly supports their model. The narrow corridor is not evident in most straightforward visualisations and simple regressions, where we would most expect to easily observe the hypothesis. On the other hand, we observe it in certain specifications and robustness checks, but we hardly believe it is appropriate to view these findings as supportive of AR on net.
Section 2 provides a review of previous literature. First, we discuss the strength of society, where for our purposes here that is to mean social capital, civil society, or social trust. Second, we discuss the strength of the state, where that is to mean formal institutional quality, especially as it pertains to state capacity. We will also explain our variables of interest. Section 3 creates a series of visualisations in an attempt to observe the patterns described by AR. Section 4 performs the more formal econometric analysis. Section 5 concludes.

Literature review and data description
AR is not the first attempt at creating a generalised visual model of institutional development. For instance, Williamson (2000, p. 597) sketches a hierarchical model of economic development and social causation, with the top of the hierarchy labelled as 'Embeddedness: informal institutions, customs, traditions, norms, religion' followed by 'Institutional Environment: formal rules of the gameesp. property rights (polity, judiciary, bureaucracy)', 'Governance: play of the gameeps. contract (aligning governance structures with transactions)', and 'Resource allocation and employment (prices and quantities; incentive alignment'. AR's model concerns the interaction of the first two levels of Williamson's hierarchy, with a notable difference being that Williamson's model sees an institution like the strength of the state built on top of a strong society (as they operate and change at different time scales), whereas in AR, their interaction is key.
This point is important because the specific emphasis placed on their posited interaction is what differentiates AR from previous literature. Following the work of Putnam, the literature on the strength of society and institutional quality was integrated into the new institutional economics by those such as Keefer and Knack (2005). A wide array of empirical literature has followed, including its basis in the promotion of property rights (Bjornskov & Meon, 2015;Bjornskov & Svendsen, 2013;McCannon, Tokar Asaad, & Wilson, 2018), the building of the welfare state (Bjornskov & Svendsen, 2013;Camussi, Mancini, & Tommasino, 2018), and economic liberalisation (Berggren & Bjornskov, 2017). Of the literature that considers an interactive effect between the strength of society and institutions, McCannon et al. (2018) find The expansive corridor 1061 complementarities between them, whereas Dearmon and Grier (2011) actually find that they may substitute for one another. Conversely, Nowrasteh and Forrester (2020) and Murphy (2021) offer reasons for some scepticism concerning any relationship between the strength of society and institutional quality at all.
In order to directly test the ideas that are specific to AR, we use two variables with long time dimensions. Descriptive statistics of these variables are found in the Appendix A. The measure of the strength of the state is a new measure of state capacity by O'Reilly and Murphy (2022). It uses up to six variables from the Varieties of Democracy (v-dem) dataset to construct a measure of state capacity that goes as far back in time as 1789. Further details on its contents are also found in the Appendix A. The measure we use is a broad measure of state capacity, which includes market-supporting institutions such as the provision of public goods and the rule of law, in addition to the coercive apparatus of the state. If the strength of the state in AR is read to only mean its coercive capacities, then one may question the appropriateness of the measure. However, we do not think that is inconsistent with what is meant by AR or with common treatments of state capacity.
First, much of the point of AR is that strong states out of balance with strong societies will crush society, and without the 'Red Queen' effect, the strength of the state will cease to grow. The presence of a very strong state requires a strong society to get there, and the strong society will use the coercive apparatus to serve society. Second, other standard models of state capacity, such as Besley and Persson (2009), perceive market-supporting institutions to be serving the same function as the coercive apparatus, which is to merely raise more resources to be made available for the executive. In either case, while pure coercive capabilities (here: the Weberian state and fiscal capacity) may be the starting point for building states, market-supporting institutions are implied by these models to follow. 2 To measure the strength of society, we use the civil society organisation (CSO) participatory environment index from Varieties of Democracy (see the Appendix A for more information). Descriptive statistics for standardised versions of the two measures of state capacity and the measure of civil society, as well as additional variables we will discuss below, are available in the Appendix A. The data are expressed as a panel of 10-year intervals from 1856 to 2015 (that is, 2015-2006; 2005-1996; [ … ], 1865-1856). Measures of civil society and state capacity are both available for 173 countries in 2015 and 40 countries in 1855.
The effect of strong societies on institutions has been considered at length in the empirical literature. What is novel in AR is the paths that countries take to achieve high quality institutions. While AR, in some instances, specified historical paths for various countries, they did not map their descriptions to quantitative assessments of the strength of states and the strength of societies. With the two aforementioned variables in hand, we are able to do so.
AR demarcate social and institutional development diagrammatically as movements towards the northeast in state capacity and civil society space, these movements representing stronger states and stronger societies (Acemoglu & Robinson, 2019, p. 64). When assessing whether the distance from the power of the state and the power of society results in development, we consider two primary measures which correspond directly to the Red Queen hypothesis, and then three additional measures of development which serve as robustness checks.
The first measure of development is defined as the sum of the state capacity and the civil society variables. Countries with high scores on both the index of state capacity and the CSO participatory environment index of civil society achieve the highest values of development by this measure. The second measure is constructed in terms of the distance to the development frontier, in the northeastern-most area of the narrow corridor. The frontier is defined as the maximum value for state capacity (2.15) and the maximum value for the CSO participatory environment (2.23) in the dataset. The frontier point (2.23, 2.15) is demarcated in red in Figure  S3 in the Supplementary Materials. We then calculate the Euclidian distance from each country to the frontier in state capacity and civil society space.
Subsequently, we consider three measures of development beyond the growth of the strength of the state and the strength of society. In their earlier work, Why Nations Fail, AR describe inclusive economic institutions and inclusive political institutions as the set of institutions that produces economic development (Acemoglu & Robinson, 2012). To measure inclusive institutions, we use the liberal components subindex from the v-dem dataset (see the Appendix A for more information).
As a second measure of development and inclusive institutions, we use the Status index from the Bertelsmann Stiftung Transformation Index (BTI) dataset. This index is the average of their political transformation index and their economic transformation index; it 'analyzes and compares transformation processes towards democracy and a market economy'. 3 The BTI index is available in two-year increments from 2006 to 2020. Finally, to measure a narrower conception of economic development, we use real GDP per capita from the Penn World Tables (Feenstra, Inklaar, & Timmer, 2015). Further robustness checks will be found in the Supplementary Materials. Again, descriptive statistics are presented in the Appendix A.

Visual analysis
With our methods of measuring the strength of the state and the strength of society in hand, we are able to operationalise the diagrammatic model of institutional development presented in Acemoglu and Robinson (2019, c.f. Acemoglu & Robinson, 2016 and in effect, to test it. AR argue that the source of societal and institutional development is the dynamic played out between the strength of the state and the strength of society. Countries that develop are in the 'narrow corridor' where society and the state, effectively balancing one another, grow in unison, leading to a 'Shackled Leviathan'. In two-dimensional space which maps the strength of the state against the strength of society, the Red Queen effect is represented visually by countries that fall within the narrow corridor moving towards the northeast corner, that is, stronger states and stronger societies. Figure 1 attempts to illustrate this relationship with data. On the x-axis, we use the CSO participatory environment index from Varieties of Democracy. On the y-axis, we use the c nar measure of state capacity, such that as many countries as possible appear on the chart. We include any country for which both c nar and the CSO participatory environment index are available in the year 1855. Both indexes are presented in a standardised form; the units and interpretation of each are therefore roughly comparable. On the chart, we plot each country's position in 1855 and 2015 and linearly interpolate the movement of the country in state capacity and civil society space to visualise the dynamics over the long run. To operationalise the widening corridor found in AR, we draw two dashed lines with a gap widening as both state capacity and civil society increase. A corridor that widens as both state capacity and civil society increase is consistent with figures are drawn throughout AR (Acemoglu & Robinson, 2019, p. 64, 268, 290). The boundaries of the corridor intersect when state capacity and civil society are two standard deviations below their mean value, and the corridor widens to two standard deviations in distance when the corridor is two standard deviations greater than the mean value of each variable. (This is by nature arbitrary but produces a visually acceptable result.) This plot is the first empirical representation of AR's narrow corridor, which uses data rather than simply historical narrative, over a period long enough to capture the model's long-term dynamics.
Should AR be correct, the only path to the northeast corner of the figure is by way of staying within the two lines, that is, the corridor. Falling outside the corridor should typically (and if the theory is to be taken literally, always) result in a collapse to either one axis or the other, and to either anarchy or totalitarian government. We should therefore only see countries observed to be either running northeast along the corridor, collapsing to the x-axis, or collapsing to the y-axis. Any other observations are problematic for AR.

The expansive corridor 1063
But what we observe is that nearly all countries have increased both their strength of society and their strength of the state over this period, regardless of their proximity in the corridor or their presence within it: we do not observe countries falling into one of three categories (Despotic Leviathan, Absent Leviathan, or Shackled Leviathan); rather, nearly all countries, over this time frame, appear to be in an expansive corridor of institutional development, with leviathans at various points in the process of being shackled. This result appears to be more consistent with modernisation theory than with AR.
Of course, there is significant heterogeneity across time in most of these countries, and the linear interpolation of their dynamics masks substantial variation over the 160 years. We provide a deeper breakdown by decade in Figure 2 for a few representative countries: The United States, Japan, Honduras, and Russia. Similar plots for the remaining 44 countries with data available starting in 1900 are shown in the Supplemental Materials. Though some countries like the United States start and remain in the corridor, we still do not observe the trifurcating process described by AR as a general rule. Using the reference lines to stand in for the theoretical corridor, six countries, including Japan, enter the corridor and then remain in the corridor thereafter, as the AR dynamics predict. In contrast, 31 countries exit the corridor after previously being in the corridor. Table 1 summarises these dynamics. Furthermore, several countries exhibit the dynamics predicted for countries that are 'in the corridor', even though they would not have been thought of as exemplars, from our reading of AR. By this we not only mean that they improved on both margins from 1855 to 2015, but have moved upwards and rightwards with some regularity over that period. These include countries such as Thailand, Morocco, and Nepal. Costa Rica behaves as AR expect it to, but Guatemala is measured to have a more powerful society than a powerful state, which is the opposite of what AR claim (Acemoglu & Robinson, 2019, pp. 291-303). This is also to say that the lack of trifurcation is not due to the selective sample of 48 countries. We also do not observe countries that 'should' be in the corridor behaving as expected. According to our measures, countries such as Austria, Denmark, Switzerland, and the United States have been roughly stagnant since 1950, even though AR's 'Red Queen' effect posits that these countries should be improving still further. Countries like those four have seen institutional development since then, but perhaps this development is better thought of as economic liberalisation than it is as either state or social capacity.
To provide an even more direct (if still informal) test of The Narrow Corridor, we place all countries (once per decade) in a grid and create a pseudo-transition probability matrix. We look to see, for example, the probability of a country which falls in the interval of [À0.2,0.2] in its power of society and [À0.2,0.2] in its state capacity will move northeast on the grid over the following decade. 4 If The Narrow Corridor is correct, countries that are balanced should have a higher probability of doing so. Specifically, we should observe a clustering of blue along the main diagonal of the matrix. We do not observe this dynamic in Figure 3. In the course of creating the figure, however, we found that the observed pattern is sensitive to small changes in how the data is discretised, which is to say that whatever pattern that you observe in this presentation of the data is not especially robust. (In the Supplementary Materials, we re-create the transition probability matrix with larger buckets.) Ultimately, although we are able operationalise AR's narrow corridor, the dynamic behaviour implied by AR is not borne out by data visualisations. We will now more formally test some of their claims econometrically. Notes: State capacity is measured by the standardised c nar and civil society is measured by the standardised CSO participatory environment index (10-year periods). Dashed lines represent a narrow corridor originating at (À2,À2) and widening to a width of one standard deviation in each direction at point (2,2).
The expansive corridor 1065

Formulating the hypothesis
Acemoglu and Robinson (2019) posit that countries with a balance between the strength of the of the state and the strength of civil society can spur the development of both forwards. To formally test this hypothesis, we define the distance from the narrow corridor as the natural log of the absolute difference between standardised state capacity, s it , and standardised civil society, c it , as described in Equation (1).
The distance, d it , is largest for countries with an imbalance between the strength of the state and the strength of civil society and is smallest for countries where the two are in balance and therefore closest to the narrow corridor. Figure 4 plots a histogram of the logged distance variable and the distance variable without the transformation.
To test the hypothesis that proximity to the narrow corridor is associated with development, I it , we estimate Equation (2) and Equation (3).  Table 2 presents a categorisation of countries based on how they move in state capacity and civil society space between 1855 and 2015. For the purpose here, the narrow corridor is defined as the area between the dashed lines in Figure 2. Specifically, the narrow corridor originates at (À2,À2) with a width of zero and widens to a width of one standard deviation in each direction at point (2,2). Myanmar begins in the corridor and then exits the corridor. Ecuador and El Salvador have entered the corridor in the most recent period. Missing values for South Korea make its dynamics difficult to categorise.
Equation (2) describes a cross-sectional regression estimating the effects of the initial distance from the corridor in period t À j on the change in development in country i from period t À j to period t: Equation (3) describes panel estimates of the effect of the distance, d itÀj , on the change in development over the non-overlapping 10-year periods. All panel estimates include period Notes: Probability that either state capacity or civil society scores increase in the next 10-year period. State capacity is measured by the standardised c nar and civil society is measured by the standardised CSO participatory environment index. Areas with fewer than 10 observations are omitted. Axes are labelled at the lower bound of each bin. The expansive corridor 1067 effects, s t : The most basic specifications are simple bivariate correlations. If omitted time-invariant country characteristics are important, a model with country fixed effects is appropriate (Angrist & Pischke, 2009, pp. 243-244). An alternative specification controls for the level of institutional development at the start of the period to account for mean reversion and institutional convergence to a steady state (that is, a dynamic panel model). The AR model predicts an ongoing development process, not a steady state. Therefore, the fixed effects estimates are our preferred model though we report both specifications. For completeness, we also include a specification that includes both fixed effects and the initial level of institutional development. 5

Estimation results
The first set of estimates use the sum of state capacity and civil society as the measure of development. An estimate of c, the coefficient on the distance from the corridor, less than zero is evidence in favour of the Red Queen hypothesis. First, we test the hypothesis using the two long cross-sections: 50 years and 100 years. Figure 5 shows a positive correlation between the change development and the distance from the narrow corridor in the 50-year cross-section. The first two columns of Table 2 present the results over the 50-year period from 1965 to 2015 using the comprehensive measure of state capacity. Counter to the predictions of AR, a greater distance from the narrow corridor is associated with an increase in institutional development in the bivariate specification, as well as in the specification controlling for the initial level of institutional development.
The results are similar if the frontier measure of development is used. Smaller values of the distance to the frontier measure indicate greater development; therefore, an estimate of c greater than zero is evidence in favour of the narrow corridor hypothesis. The negative coefficients in Columns 3 and 4 of Table 2 indicate that countries farther from the corridor are more likely to catch up to the frontier. To consider a longer cross-section of 53 countries (from 1915 to 2015) we use the narrow version of the state capacity index to improve data coverage. Figure 5. Correlation between distance from the corridor and the change in institutional quality (50-year change). Note: Institutional quality measured as the sum of state capacity and civil society.
Results using the narrow version are found in Columns 5 through 8. Once again, the bivariate results find evidence against the AR hypothesis, though the results are not significant once the initial level of development is controlled for.
Overall, the results from cross-sectional estimates are evidence against the Red Queen hypothesis. While descriptive and non-causal results do not typically serve much to falsify hypotheses, it is strongly implied in AR that the pathways they described were meant as literal pathways and not simple causal tendencies that would appear in a well-identified regression. If countries did not follow these pathways, either formally as found here, or visually as found in the previous section, it constitutes evidence against AR.
We now test AR using panel data at 10-year intervals from 1956 to 2015. Column 1 of Table  3 presents a simple regression of institutional and social development, measured as the sum of state capacity and civil society, on the distance from the narrow corridor. The effect of distance on development is positive, though insignificant. Our preferred specification in Column 2 includes country fixed effects, and the effect of distance is statistically insignificant. To control for the initial level of development, and to capture the effect of convergence towards a steady state level of societal and institutional development, we include the initial level of institutional development in Columns 3 and 4. These dynamic specifications imply an institutional steady state, which is not a part of AR's theoretical model. Nevertheless, if the initial level of development is controlled for, the effect of distance from the corridor is negative and statistically significant. The results in Column 4 include both fixed effects and the initial level of development. Once again, the effect of distance from the corridor is negative and statistically significant, as the AR model predicts. However, to reiterate, the dynamic models imply that there is a steady state, which contradicts the AR model. Estimates using the longer panel from 1856 to 2015 use the narrow index of state capacity, c nar : As shown in the first four columns of Table 4, the distance from the corridor measure is statistically insignificant in all specifications.
Estimates in Table 3 for the proximity to the frontier measure of development are similar. Panel estimates are insignificant in the bivariate specification and in the preferred fixed effects specification. But once again, the effect of distance from the corridor is significant in the dynamic panel specifications in Column 7 and Column 8. The results found in Columns 3, 4, 7, and 8 constitute the main results of this paper which support the hypothesis of AR. In other words, we find no evidence of the Red Queen effect in cross-section estimates or baseline panel fixed effects estimates. Dynamic panel specifications that control for initial level of development The expansive corridor 1069 Table 3. Panel estimates -institutional development  (1) (3)  The expansive corridor 1071 yield estimates consistent with the Red Queen effect but as noted earlier, are a problematic test of AR's theory. Once again, these estimates are not robust to using the longer panel from 1856 to 2015. If instead of using 10-year periods, estimation is conducted using a panel of 5-year periods, the effect of distance from the corridor is never significant with the expected sign. Therefore, we find the limited support for the AR hypotheses of societal development is not particularly compelling. Estimates using an alternative measure of the strength of civil society are presented in the Supplementary Materials. These estimates use the broader civil society participation index from the v-dem dataset to measure civil society. Estimates using this alternative measure are generally similar to those presented in the main text. An additional set of robustness checks presented in the Supplementary Materials replicate Table 3 and Table 4 using alternative measures of the distance from the corridor variable. First, distance is measured as the absolute difference between the state capacity score and the civil society score. Second, the corridor is defined as a dummy variable taking a value of one if a country falls within the corridor as defined in Figure 1. Also in found in the Supplementary Materials are robustness checks using measures of exclusion, log real GDP per capita as a measure of development, controls for initial levels of state capacity and civil society, and the interaction between state capacity and civil society.

Discussion and conclusion
Acemoglu and Robinson (2019) present a model in which societal and institutional development follows from a balance between the strength of the state and the strength of society. They provide several historical vignettes as evidence, but do not provide any statistical test of their hypothesis. This paper fills a gap in the literature by providing, to our knowledge, the first statistical test of the Acemoglu and Robinson's Red Queen effect.
Descriptive visualisations of how countries develop over time do not appear consistent with AR's prediction that countries in the narrow corridor will enjoy societal development whereas countries that lie outside of the corridor will fail to develop. Similarly, the transition probability matrix that we construct does not show any consistent pattern that countries with a balance of state capacity and civil society are more likely to be propelled through the narrow corridor.
We also run a series of regressions to test for the AR's Red Queen effect. In contrast to the predictions of AR, cross-sectional regressions over a 50-year period tend to find that countries further from the narrow corridor tend to experience development. Furthermore, we do not find evidence in support of AR's model in the preferred panel specifications that include country fixed effects. The strongest evidence in favour of the AR hypothesis is from dynamic panel estimates that show that countries closer to the narrow corridor tend to experience societal and institutional development (characterised by both a strong state and a strong society). However, these results are not robust to estimation using a longer panel or to fixed effects estimation. Dynamic panel estimation also implies a steady state institutional equilibrium which contradicts the broader theoretical framework of AR. Furthermore, we find no significant effect of proximity to the corridor if development is defined as the development of inclusive institutions or changes in output per capita.
The model developed by AR makes clear predictions about the pathways countries can take to societal and institutional development, that is, to a Shackled Leviathan, Absent Leviathan, or Despotic Leviathan. Several visualisations show evidence of only a consistent pathway in the direction of a Shackled Leviathan. Though we do find some very limited statistical evidence in support of their hypothesis, on net it does not support AR. Taken together, the evidence in this study does not validate AR's theory of development.
Notes 1. Reasons given as why the corridor widens as societies develop are somewhat sparse, but it is clearly the intention of the authors. Early on (Acemoglu & Robinson, 2019, p. 66), they state that the corridor at the origin does not exist because of the need for a bare minimum of state power and civil society power to get the process moving at all. There are later discussions on the causes of the shape of the corridor, with entrenched landed interests (Acemoglu & Robinson, 2019, pp. 401-402) and labour coercion (Acemoglu & Robinson, 2019, pp. 450-454) tightening the corridor, while participatory democratic institutions (Acemoglu & Robinson, 2019, pp. 483-488) widen it. As societies move within the corridor, these issues are worked out and democratic political institutions are strengthened, broadening it. 2. Besley, Persson, and Dann (2021) provide evidence that repressive forms of state power may be a dimension separable from the primary spectrum of state capacity and institutional development. It may ultimately be the case that these two dimensions should be kept distinct from one another. Nevertheless, they are conflated in Acemoglu and Robinson (2019). It is also unclear what we even be mean, empirically, were state capacity measures like the quality of the bureaucracy not to be used to assess medium levels of state power versus high levels of state power, as the coercive apparatus of the state (for example, a Weberian state and a military) is already more or less built out once a middling level of state power is achieved. 3. See https://www.bti-project.org/en/?&cb=00000 4. We define a movement to the northeast as either an increase in state capacity without a decrease in civil society, an increase in civil society without a decrease in state capacity, or an increase in both. 5. Including both fixed effects and a lagged dependent variable in the model risks introducing Nickell bias.

Disclosure statement
No potential conflict of interest was reported by the author(s).