In this section, we develop a model where hereditary rule emerges as a political equilibrium in the spirit of Olson (1993) and induces better performance from leaders who care that their offspring will follow them in office. We show that this is valuable to whomever maintains the leader in power only if executive constraints are unable solve moral hazard problems in government.8

Time is infinite and each period is denoted by t. Citizens are infinitely lived and in period t have a payoff,, which depends two things (i) policywhereand (ii) the leader’s popularitywhere, i.e.The policy payoff depends on a binary policy choice. For the sake of concreteness, think of this as making a decision which affects the enforcement of property rights or a decision to invest in worthwhile infrastructure. In each period nature determines a “state of the world”,andif and only. We assume that both states are equally likely and that generating a payoffrequires a leader to incur a private cost of c.

The popularity component of citizens’ payoffs is a attached to a specific leader. Ex ante, we assume that a randomly selected leader is popular with probability \(\rho \). Let \({\bar{A}}\left( \rho \right) =\left[ 2\rho -1 \right] A\) be the expected popularity of a randomly chosen leader.

Leaders are drawn from a countably infinite pool of families denoted by \( f=1,\ldots \). Each leader lives for only one period and has a single offspring. To create a dynastic motive, we suppose that there is payoff of B if an incumbent’s offspring succeeds him/her. For simplicity, we suppose that this payoff is like a “warm-glow” bequest which is independent of the actual value of holding office. We also assume that \(B>c\), so that an incumbent leader would, in principle, be willing to generate a payoff of \(\Delta \) for the citizens if having his offspring succeed him is made conditional on this.

We consider two institutional possibilities. With strong executive constraints, we assume that \(e_{t}=s_{t}\) is ensured so that citizens always get \(\delta _{t}=\Delta \). We have in mind having an effective legislator which is able to “force” the leader to act in the interests of citizens. A perfect constraint is of course, the most extreme assumption, but having this happen probabilistically would yield broadly similar results. With weak executive constraints, the incumbent has full discretion over the choice \(e_{t}\). We expect \( e_{t}=s_{t}\) only if it is in the leader’s private interest to do so.

Retention and selection The retention of leaders lies in the hands of a sub-group of citizens (the selectorate). The term selectorate, coined by Bueno de Mesquita et al. (2003) could represent a variety of institutional settings. In democracies retention decisions rest with voters although party elites and insiders can also play an important role in who stands for office. In non-democracies the selectorate could comprise senior army officers in military dictatorships or influential aristocrats in monarchies. They could also be members of a party hierarchy as in a communist system like in China. Members of the selectorate decide whether to select the policy maker from the ruling family or to install a new ruling family. An hereditary dynasty is created when the selectorate chooses the offspring of the incumbent to take power. We suppose that the selectorate has a discount factor \(\beta <1\) and that they observe the popularity of the leader’s offspring before deciding whether to appoint him/her as leader.

Timing

The timing of the model with each period t is as follows:We will look for a stationary sub-game perfect equilibrium of the model where the selectorate and incumbents optimize in their policy and retention decisions.

3.1 Equilibrium

We first show what happens with strong executive constraints. The main analysis is for the case of at weak executive constraints where we focus on two possible equilibria. In the first of these, only popular incumbents are retained and incumbents never produce good policy. In the second, an hereditary dynasty emerges where the leader’s offspring is retained whether or not she is popular provided that her predecessor has generated \(\Delta \) while in office.

Strong executive constraints With strong executive constraints, \(e_{t}=s_{t}\) always by assumption. Then popularity is all that matters to the selectorate. Since this is observed before appointing the offspring then only popular offspring are appointed since \(A>{\bar{A}}\left( \rho \right) \). Thus, consistent with the data, hereditary rule is possible even with strong executive constraints. However, this will happen purely on the basis of popularity rather than performance in office. More generally, we expect hereditary leadership to emerge only if there is indeed an information advantage about popularity for dynasties.

Weak executive constraints We begin with the following benchmark result where hereditary succession plays no role. The following result is proven in the “Appendix”.

Proposition 1 There is always an equilibrium where only popular incumbents are retained and \(e_{t}

e s_{t}\) for all t.

The logic is straightforward. Since all incumbents set \(e_{t}

e s_{t}\), then only popularity matters to the selectorate. Hence if the leader’s offspring is popular, she will be chosen otherwise it is worthwhile picking a fresh family from the pool of potential rulers. Since incumbents believe that retention is only popularity-based, it is never worthwhile for the leader to set \(e_{t}=s_{t}\) since doing is costly.

This equilibrium is the mirror image of strong executive constraints case except for the policy performance of the leader. The frequency of incumbent turnover is driven purely by \(\rho \), the probability that an incumbent’s offspring is popular and we expect a dynastic leader to emerge with equal frequency in this equilibrium regardless of whether executive constraints are strong or weak. This equilibrium exists for all parameter values since it only relies on the the out of equilibrium belief that any leader who deviates to \(e_{t}=s_{t}\) will not thereby bequeath the leadership to their offspring.

We now consider a different equilibrium in which the offspring of all incumbents are retained under weak executive constraints regardless of their popularity as long as their predecessor has produced a good policy outcome for the citizens. The following Proposition, whose proof is in the “Appendix”, gives sufficient conditions for this to emerge:

Proposition 2 Suppose that \(\Delta \ge 2\rho \left[ 1-\rho \beta \right] A\) and \(\left( 1-\rho \right) B>c,\ \)then there is an equilibrium in which the offspring of all incumbents are retained and \(e_{t}=s_{t}\) in each period.

This kind of equilibrium can emerge as long as the incumbent believes that his offspring will be appointed as leader after she has paid c to generate \(\Delta \) for the citizens. This requires that A be small enough and/or \( \Delta \) is large enough so that the selectorate are willing to pick an unpopular leader when they believe that the dynastic equilibrium will break down if they fail to appoint the next member of the dynasty. This equilibrium also requires that the bequest motive be strong enough so make paying the cost c worthwhile. The condition for hereditary rule to be an equilibrium depends on \(\rho \). It is hardest to satisfy when \(\rho \) is close to one since it is highly likely that the unpopular offspring of a leader will be replaced by a popular leader if she is not allowed to succeed her parent.

This equilibrium can be thought of as a relational contract between the dynasty in power and the selectorate along the lines envisaged in the opening quote from Olson (1993). The hereditary dynasty delivers good policy outcomes in exchange for an assurance that unpopular members of the dynasty are selected to hold office conditional on their predecessor having set \(e_{t}=s_{t}\). This is supported by the belief that if the hereditary system were to break down (specifically if an unpopular member of the dynasty were removed) then a non-hereditary equilibrium would follow in which all subsequent incumbents perform poorly and only their popular offspring are retained. Thus, our equilibrium illustrates the idea that hereditary rule arises not out of intrinsic popularity but because incumbents who are part of the dynasty perform well.

Although we have applied this idea to a hereditary system, this could also be a model of a long-lived party system like the communist party in China where economic growth is “exchanged” for continuity in power regardless of whether leaders are intrinsically popular. This is a focal point of the system which creates political stability and good economic performance. Such systems only make sense in a setting of weak executive constraints, like China, where there are no direct means of enforcing good policy.

Predictions Proposition 2 gives conditions for there to be an equilibrium with good policy without strong executive constraints. Thus citizens can get good policy (\(e_{t}=s_{t}\)) in two cases: (i) if there are strong executive constraints and (ii) if there is a hereditary equilibrium under weak executive constraints. There will be bad policy outcomes (with \(e_{t}

e s_{t}\)) for citizens when then is no hereditary equilibrium with weak executive constraints.

Since there can be multiple equilibria, the model does not fully explain how some polities can coordinate on hereditary equilibria. For the core empirical results, we suppose that this coordination is uncorrelated with factors which shape economic performance. Neither does the model explain why all polities do not choose to have strong executive constraints, particularly those which cannot organize hereditary equilibria. This could be explained by adding additional features to the model by which bad policies generate rents for some agents who therefore have a vested interest in maintaining bad government.9

Comments on the model The model that we have presented is deliberately simple in order to focus on the nature of the exchange between the selectorate and the leaders. It could be complicated in a variety of ways which would make it more realistic while retaining the essence of the argument that we have developed for why hereditary rule can improve performance. For example, the assumption that strong executive constraints always improve performance is not needed for the broad thrust of the prediction to hold that strong executive constraints only improve things under weak executive constraints. To see this, suppose that under strong executive constraints, then \(e_{t}=s_{t}\) with probability \(\xi \). Then the expected policy payoff of voters is \(\xi \Delta \). It is still optimal in this world to select solely on the basis of popularity with strong constraints. The two equilibria described in Propositions 1 and 2 continue to exist. While the non-dynastic equilibrium of Proposition 1 is less good for voters than strong executive constraints, the dynastic equilibrium now out-performs strong executive constraints.10

We could also introduce an element of selection into the model whereby some leaders are more or less competent with growth providing a signal of competence. If competence is transmitted intergenerationally, this would provide an additional argument for hereditary selection.

The model has focused exclusively on an upside of dynastic rule. But dynastic rule could result in self-enrichment via violation of property rights. Absolutist monarchs in history were famous for seizing land and property. The scope for doing this without facing opposition would be larger if hereditary rules also generate other benefits of the kind highlighted in Proposition 2. The bequest motive, represented by B would likely be higher where rents accruing to leaders are larger as in the model of Myerson (2015). If rent extraction which creates these returns is also inefficient, this would weaken the value of hereditary rule. In the end, it will therefore be an empirical question whether such cases of hereditary rule are good or bad for growth.

The model has focused on hereditary rather than dynastic selection in general. However, similar theoretical forces could also explain how families/clans could develop reputations which would be relevant in periodic contests for power. This would depend on the selectorate using the history of all past members of a dynasty and factoring this into their decisions and could explain period re-emergence of members of dynasties.11

Growth implications We will apply the ideas above to aggregate measures of economic performance when specific leaders are in power. We shall suppose that the realization \( \Delta _{t}\) affects productivity so that aggregate output, \(Y_{t}\) , is given by the production function: $$\begin{aligned} Y_{t}=e^{\theta _{t}}\left[ K_{t}^{1-\alpha }L^{\alpha }\right] \end{aligned}$$ \(\theta _{t}=\left[ 1+\Delta _{t} \right] \theta _{t-1}\) and there is a fixed supply of labor, L. We shall suppose that aggregate capital \(K_{t}=sY_{t-1}\) where s is the savings propensity. This implies that growth is given by: $$\begin{aligned} g_{t}=\log \left( \frac{Y_{t}}{L}\right) -\log \left( \frac{Y_{t-1}}{L} \right) =\left[ 1+\Delta _{t}\right] \theta _{t-1}-\alpha \log \left( \frac{ Y_{t-1}}{L}\right) . \end{aligned}$$ We will apply the ideas above to aggregate measures of economic performance when specific leaders are in power. We shall suppose that the realizationaffects productivity so that aggregate output,, is given by the production function:where productivity depends on policy:and there is a fixed supply of labor, L. We shall suppose that aggregate capitalwhere s is the savings propensity. This implies that growth is given by:This forges a link between policy making as it is affected by institutions and behavior, and economic growth.

This very simple model, combined with the discussion of political equilibria, give us the following prediction about growth:

Core Growth Prediction Growth will be higher in a hereditary equilibrium only if executive constraints are weak.

\(\ell \) in country c who takes office in year t. Specifically, let \(g_{c\ell t}\) be the average growth rate during the leader spell. We then run regressions of the form: $$\begin{aligned} g_{\ell ct}=\alpha _{c}+\alpha _{t}+\lambda y_{\ell ct}+\beta _{1}\delta _{\ell ct}+\beta _{2}\sigma _{\ell ct}+\beta _{3}\left( \delta _{\ell ct}\times \sigma _{\ell ct}\right) +\varepsilon _{\ell ct} \end{aligned}$$ (1) \(\alpha _{c}\) are country dummies, \(\alpha _{t}\) are dummies for the years in which leaders take office, \(y_{\ell ct}\) is the level of income per capita in the year that leader \(\ell \) ’s spell in office begins, \(\delta _{\ell ct}\) is a dummy variable which is equal to one if leader \(\ell \) is a hereditary leader, and \(\sigma _{\ell ct}\) is a dummy variable which is equal to one if a country has strong executive constraints when the leader comes to power. We cluster the standard errors at the country level.12 We examine this prediction by looking at economic growth during the spell of leaderin country c who takes office in year t. Specifically, letbe the average growth rate during the leader spell. We then run regressions of the form:whereare country dummies,are dummies for the years in which leaders take office,is the level of income per capita in the year that leader’s spell in office begins,is a dummy variable which is equal to one if leaderis a hereditary leader, andis a dummy variable which is equal to one if a country has strong executive constraints when the leader comes to power. We cluster the standard errors at the country level.

According to the core prediction of the theory, we should expect \(\beta _{1}>0,\) \(\beta _{2}>0\) and \(\beta _{3}<0\) with a core implication of the theory being that \(\beta _{1}+\beta _{3}=0\), i.e. having a dynastic leader generates better performance only when executive constraints are weak.

The regression in (1) cannot be given a causal interpretation; our exercise is to study a specific and non-trivial prediction for the data motivated by theory. By including year and country fixed effects in each regression, the conditional correlation that we uncover controls for a range of country characteristics and general global trends which could confound the argument that the theory focuses on. And it is notable that we find that estimates of \(\beta _{2}\) in Eq. (1) are not significantly different from zero in all of our specifications after including country fixed effects. This does suggest that fixed country characteristics may be doing a decent job in conditioning out the relevant unobserved heterogeneity associated with institutional differences. But we caution against interpreting our results as causal effects.13