LATE for history and other stories

By Alberto Bisin and Andrea Moro

Persistence studies in Historical Economics document the persistence of some historical phenomenon and often leverage this persistence to identify causal relationships of interest in the present. They constitute a sizeable component of Historical political economy and, more generally, of Historical economics: about 10%, according to Cioni et al. (2021)’s classification. The pioneering paper in the field, which we’ll use as a prototypical leading example in this post, is Acemoglu et al. (2001). It identifies the causal effects of quality of colonial institutions (executive power), instrumented by settlers’ mortality around 1800, on GDP per capita in 1995.

Generally, Persistence studies identify significant first-order causal effects, but tend to disregard the manifold historical mechanisms driving these effects (Voth, 2021). More specifically, several papers have expressed concerns about their causal identification strategy, combining quasi-experimental methods with historical data, where e.g., the impact of an instrument develops along history and the endogenous outcome variable is instead current (notably, and complementarily with the references in this post, the first issue of the Journal of Historical Political Economy is dedicated to theory and statistical methods in HPE, with prominent applications in Persistence studies). In this post we shall discuss three statistical issues which may arise in these contexts (more than in others): heterogeneous treatment effects, violation of exclusion restriction, spatial autocorrelation of the errors.

In the context of the effects of institutions on economic development, as in Acemoglu et al. (2001), heterogeneous treatment effects arise when the process of institutional change is exogenously affected by a valid instrumental variable but the “take up of new institutions” may be correlated with the returns of institutions in terms of economic development; e.g., countries with higher returns may be more likely to have adopted higher quality institutions. With treatment heterogeneity, the causal argument in the Instrumental Variable (IV) identification strategy remains generally unaffected but the interpretation of estimated coefficients may be incorrect: the research design identifies a Local Average Treatment Effect (LATE), rather than the Average (subject-level) Treatment Effect (ATE). In Bisin and Moro (2021) we discuss these issues in detail. We give an intuition in the following.

Consider the general representation of the statistical exercise in Peristence studies in Figure 1. In Acemoglu et al. (2001), for instance, the process {x_τ} represents the quality of institutions, from colonial times t − h to the present t. The instrument z_t−h is settler’s mortality: low settlers’ mortality facilitates the set-up of inclusive institutions by colonial powers, whereas high settlers’ mortality causes extractive institutions. The parameter β represents the returns to institutional quality in terms of economic development, measured by current per capita GDP.

Figure 1. Circles indicate variables observed by the investigator. Dashed circles indicate unobserved variables. Solid arrows indicate directions of causality. Double arrows indicate endogeneity or any other factor preventing the identification of a causal effect (omitted variables, selection bias, etc…). Dashed arrows indicate potential causal links. Highlighted in red are the relationships of interest.

For LATE effects to be distinct from ATE it is sufficient to hypothesize that that the benefits of “taking-up” high-quality institutions at t − h (or at least before the present time t) are correlated with the returns to institutional quality. To guide our interpretation of LATE effects it is therefore important to understand how the mechanism responsible for the persistence of treatment over time correlates with the values of treatment effects. Explicit models of these mechanisms, representing the outcome of political equilibrium processes, help to clarify the interpretation of the identified causal effects. For instance consider a “model” in which the cost for the colonial power to implement the inclusive institutions that reduce future expropriation risk is lower than the benefits for all countries except those with low returns to institutional quality and high settlers’ mortality. In this case the instrumental variable estimate would identify the low returns to institutional quality (LATE) rather than the average returns (ATE).

A more interesting “model” would introduce a process {s_τ}, capturing e.g., the dynamics of relevant cultural variables interacting with the dynamics of institutions (Bisin and Verdier (2017) model these interactions in related contexts). The validity of the instrument z_t−h, via the exclusion restrictions, is not hindered by the correlation of z_t−h with the cultural process {s_τ}, as long as culture does not have a direct effect on economic development, that is, as long as s_τ affects y_t only through {x_τ}. In this case, interpreting β as a measure of the returns of institutional quality effectively disregards the effect of the dynamics of cultural traits or social capital s_τ in the historical process of institutional change. The IV strategy identifies in this case the returns to the institutional quality of the countries whose cultural traits dynamics has favored “taking-up” high-quality institutions and whose returns to institutions might be different than the average.

To illustrate the role of the interaction between different processes in the course of history, consider the analysis of the economic development of the sample of countries colonized by European powers after 1500 in Acemoglu et al. (2002). This paper documents how i) colonial powers developed high-quality institutions disproportionally in initially poorer countries, (a “Reversal of Fortune”); ii) the inclusive institutions developed by colonial powers manifested their effects on economic development only after the Industrial Revolution in 1800-1900, and not before. Consider the two following possible interpretations of these results. One, assuming wealth in 1500 as exogenous with respect to economic development, is that historical poverty causes growth. Another interpretation, considering poverty in 1500 as an instrument for beneficial institutional change, is that inclusive institutions established by colonies cause economic growth. Both interpretations are valid in principle as long as they are qualified in terms of their effect being local. Poverty in 1500 acted locally, through institutional change in colonial times. But institutional change in colonial time acted locally on economic development through the Industrial Revolution. Both of these local effects in principle have selected a subset of Compliers whose effect the empirical analysis identifies and which depend on both institutional quality and the Industrial Revolution. More specifically, the heterogeneity of the effects could be intrinsic to the quality of institutions. But could also be due to the different nature of industrialization in time or place. Even if the mechanism generating development from good institutions had homogenous effect, heterogeneity could arise from different returns to industrialization.

A similar discussion could pertain, for instance, to the negative relationship between past slave exports and economic performance within Africa, uncovered by Nunn (2008), if this effect appears when the dependent variable, economic performance, is measured in 1980, but not when measured in 1960, as suggested by Bottero and Wallace (2013). This would indicate the interaction of the effects of slave trade with a more recent phenomenon, like e.g., de-colonization.

Figure 2. Circles indicate variables observed by the investigator. Dashed circles indicate unobserved variables. Solid arrows indicate directions of causality. Double arrows indicate endogeneity or any other factor preventing the identification of a causal effect (omitted variables, selection bias, etc…). Dashed arrows indicate potential causal links. Highlighted in red are the relationships of interest.

This analysis suggests that the interpretation of the causal effects in Persistence studies depends in a fundamental manner not only from the historical process of the treatment variable but also from any other intervening historical process correlated with treatment. While generally difficult, this calls for the importance of historical narratives to identify possibly important intervening processes.

In Figure 1 and in the related discussion we have assumed that the variable s_τ does not directly affect x_t. This is crucial for the the exclusion restriction, which is a necessary condition for the validity of the IV identification strategy, to be statisfied. In Figure 2 instead the distribution of the relevant cultural traits in the population along history directly affects current institutions. In this case, a valid IV strategy requires a joint empirical study of the relevant dimensions of the dynamics of culture and institutions over some relevant tract of history (Casey and Klemp, 2021). Indeed, Casey and Klemp (2021) develop a bias correction method along these lines and apply it to Acemoglu et al. (2001) data. Results are striking, the effect of “a change in constraints on executive power in 1800 from the lowest to the highest possible score [..] is about one-third as large as the coefficient generated by the conventional IV regression.”

Finally, the documented significant historical persistence of culture and institutions might reflect the structural dynamics of these processes along historical times, but it might also be a statistical artifact of spatial auto-correlation of the error in the regressions which characterize Persistence studies (Kelly, 2019). The intuition is simple, Consider a cross-country regression of a measure of quality of institutions – or a measure of socio-economic prosperity linked to quality of institutions – at the current time on some proxy of the quality of institutions at historical times. If spatially close countries are similar along several characteristics – say culture – for instance – then the correlation between the historical and the current measures will be strengthened simply because of the spatial proximity, the regression is mispecified and the significance of the persistence relationship will be overestimated. Various statistical procedures can be employed to identify and possibly correct this misspecification (Kelly, 2019) but of course no statistical procedure can substitute a careful modeling of the spatial correlation, e.g, modeling the cultural dynamics driving it. Indeed, whatever the postulated driving force of the spatial auto-correlation, it could be even be measured by some proxy and hence the postulated assumption can be tested with new data.

Research design methods identifying causal effects have produced fruitful research in historical economics. A careful counterfactual interpretation of these results needs to account for the potential heterogeneity of the uncovered effects. At the cost of assuming additional structure, modeling the mechanisms at play, and, if data allows, estimating or calibrating their parameters, can provide useful guidance over the implications of these results.

References

Acemoglu, Daron, Simon Johnson, and James A Robinson (2001) “The colonial origins of comparative development: An empirical investigation,” American Economic Review, Vol. 91, No. 5, pp. 1369–1401.

Acemoglu, Daron, Simon Johnson, and James A Robinson (2002) “Reversal of fortune: Geography and institutions in the making of the modern world income distribution,” The Quarterly journal of economics, Vol. 117, No. 4, pp. 1231–1294.

Bisin, Alberto and Andrea Moro (2021) “LATE for History,” in Bisin, Alberto and Giovanni Federico eds. Handbook of Historical Economics, Amsterdam: Elsevier North Holland.

Bisin, Alberto and Thierry Verdier (2017) “On the joint evolution of culture and institutions,” Working Paper 23375, National Bureau of Economic Research.

Bottero, Margherita and Björn Wallace (2013) “Is There a Long-Term Effect of Africa’s Slave Trades?” Economic History Working Paper 30, Bank of Italy.

Casey, Gregory and Marc Klemp (2021) “Historical instruments and contemporary endogenous regressors,” Journal of Development Economics, Vol. 149, p. 102586.

Cioni, M, G Federico, and M Vasta (2021) “The two Revolutions in Economic History,” in Bisin, Alberto and Giovanni Federico eds. Handbook of Historical Economics, Amsterdam: Elsevier North Holland.

Kelly, Morgan (2019) “The standard errors of persistence,” Working Paper DP13783, CEPR.

Nunn, Nathan (2008) “The long-term effects of Africa’s slave trades,” The Quarterly Journal of Economics, Vol. 123, No. 1, pp. 139–176.

Voth, Joaquim (2021) “Persistence – Myth and Mystery,” in Bisin, Alberto and Giovanni Federico eds. Handbook of Historical Economics, Amsterdam: Elsevier North Holland.