2.1 Institutional Economic Theory

In order to understand better the underlying thinking behind the relative rewards model developed in this paper it is useful to first present the Institutional Economic Theory upon which its principals are based (mostly developed by Douglas ^{North, 1990}; ¹⁹⁹⁶; ²⁰⁰⁵).

Institutional economic theory develops a very wide concept of ''institution''. ^{North (1990: 3)} proposes that ''institutions are the rules of the game in a society''. Institutions, according to this author, include any form of constraint that human beings devise to shape human interaction. Institutions can be either formal - such as political rules, economic rules and contracts - or informal - such as codes of conduct, attitudes, values, norms of behaviour, and conventions, or rather the culture of a certain society. ^{North (1990)} attempts to explain how institutions and institutional framework affect economic and social development. The main function of institutions in a society is to reduce uncertainty by establishing a stable structure for human interaction.

According to ^{North (1996)}, formal institutions are subordinate to informal ones in the sense that they are the deliberate means used to structure the interactions of a society in line with the norms and cultural guidelines that make up its informal institutions. Policy making that attempts to change the formal institutions of society will therefore have little success if it does not first adjust the informal institutions in a compatible way. The difficulty rises from the fact that, whereas a governing body can influence the evolution of a society's formal institutions in a rather direct way, informal institutions are much less tangible and usually fall outside the direct influence of public policy. They can be moulded, but tend to resist change and take time to evolve towards new social norms.

Together with the theoretical amplitude that the institutional economic theory offers, the historical perspective and institutional embeddedness argument which it offers are especially ideal for the study of entrepreneurial activity from a territorial point of view. This therefore forms the theoretical backbone guiding mechanics of the relative rewards model guiding the distribution of entrepreneurial talent developed in this paper.

2.2 Informal Institutions

The institutional evolution argument included within the economic institutional theory is especially important for the study of entrepreneurial activity since some of the main distinctions that separate territories across economies and territorial boundaries lies in the institutional history and entrepreneurial tradition, specific to every region. ^{North (1981}; ¹⁹⁹⁰⁾ explains using an institutional approach how there can exist 'radically differential' performance of economies over long periods of time. According to ^{North (1990)}, the interactions between institutions and organisations (economic, political, or social) shape the direction of institutional change. Institutions determine the opportunities of society and organisations are created to take advantage of these opportunities. As the organisations evolve, they alter the institutions. The resultant path of institutional change, according to this author, can, on the one hand, lead to a stagnant situation where institutions come to serve the sole purpose and interests of maintaining existing organisations, or on the other hand, can lead to a 'lock-in' that comes from the symbiotic relationship between institutions and evolving organisations as a consequence of the incentive structure provided by those institutions and the dynamic feedback process by which 'human beings perceive and react to changes in the opportunity set' (^{North 1990: 7}).

North followed-up his path dependency argument by describing the embedded character of informal institutions as a result of their cultural content. ^{Pilon and DeBresson (2003)} reinforced a similar argument in their study of innovative districts identifying local cultural 'anchoring' based on cultural similarities, cultural cohesiveness, and historical particularism and heritage, making certain geographical areas more conducive to innovative entrepreneurial activity.

The same argument holds within the theoretical framework established within the institutional economic theory and the relative reward model described below, which serves to explain the allocation of entrepreneurial and innovative abilities across economies.

3.1 - A Simple Model ¹

We assume that each agent has some talent that can be employed in two areas:

We will later add a third activity which will permit our subjects to choose to work for others (w). We include the imitator and the rent-seeker² under the proprietor category since, as the proprietor, both these groups do not contribute significantly to technological growth. The important aspect for us is that agents can choose the activity that maximises the returned 'value' on investment.

For now, we assume that the economy consists of a continuum of identical agents normalised to 1 (we will relax this assumption later). Each agent undertakes an ex-ante investment that will determine his/her total product. In the absence of constraints, this total product is equal to α k+x, where k ∈ (i, p) (innovator or proprietor) and where x is the amount of investment undertaken by the agent in question. This investment has to be chosen from the set (0.∞) and has cost Ik(x) with Ik'(·) and Ik''(·) > 0, limx 0 Ik'(x) = 0 and Ik(0) = 0. However, in the presence of constraints, the agent does not realise all the revenues he can potentially produce. The agent may face constraints which can either be formal institutionalised constraints such as taxes or capital constraints or they can be more informal in nature such as the presence of uncertainty, lack of information or knowledge. Of-course there is an almost infinite number of constraints which we will not go into at this point.³ Hence in the presence of constraints, the agent will lose a proportion (1 - qk) of his/her potential product. We assume that, qi ≤ qp, and consequently that (1 - qi) ≥ (1 - qp). This usually holds in reality since innovation decisions are relatively more sensitive to constraints.⁴ We illustrate the level of constraint as a proportion c. Therefore, the total net return to the agent is equal to

(1)

The potential revenue of the agent is (αk + x) and the agent gets all of this only to the proportion (1 - c) and only a proportion qk of it with probability c, while the cost of investment is always incurred.⁵ The investment level will be set to maximise this return which implies

(2)

where δk(·) is the inverse function of Ik'(·), and Ik''(·) > 0 implies that x(c) is everywhere decreasing in c. It can readily be seen from Eq. (2) that when c is positive, entrepreneurs will under-invest since they will not collect the full return that they potentially could generate.

The expected return to entrepreneurship can be formulated as

(3)

The first order condition for optimal investment can be seen as

(4)

Thus, both curves, for the innovator and the proprietor, are downward sloping and can have intersections (indifference points) depending on the relative positions of these curves.

Condition A. αi + x(0) - Ii(x(0)) > αp + x(0) - Ip(x(0)).

This states that when there are no constraints, the return to innovation is greater than simple proprietorship.

Condition B. Ǝc* such that (1 - c* +c*qi)(αi + x(c*)) - Ii(x(c*)) = (1 - c* +c*qp)(αp + x(c*)) - Ip(x(c*)).

This condition implies that at some level of constraint in the economy, simple proprietorship is equally profitable to innovation.

Proposition #1. Given that c* is not a tangency point of Yi and Yp, then at any level

ç < c* Yi, the entrepreneur will prefer to innovate,

ç = c* Intersection, the entrepreneur is indifferent towards innovation or proprietorship,

ç > c* Yp, the entrepreneur will prefer to be a simple proprietor.

Running a lagrangian function which maximises Yk, where k ∈ ( i, p), such that proposition one holds, we get a function Ye(c), which gives the entrepreneur's preferred choice of activity at any level of constraint. This is illustrated as the bold dashed line in Figure 1.

Figure 1: Entrepreneur's Preferred Activity According to Level of Constraint 

We will now add the third alternative opened to our agents, that of becoming a worker. We can write the expected returns to the worker as

(5)

where,

(6)

and although it does not affect our analysis we can intuitively deduce that

Condition C. Ye(x(0)) > w(0).

This states that when there are no constraints, the return to entrepreneurial activities are greater than the return to the worker⁶.

Condition D. Ǝc* such that Ye = (1 - c + cqw) w(c)

This condition implies that at some levels of constraint in the economy, being a worker offers a return equal to that of entrepreneurial activity. More than one such points are possible.

Proposition #2. Given that c* is not a tangency point of Ye and Yw, and j ∈ ( 1, 2) such that c*₁ < c*₂ where c*₂ may or may not exist, then at any level

ç < c*1 Ye, the agent will prefer to be an entrepreneur,

ç = c*j Intersection, the agent is indifferent towards being an entrepreneur or a worker,

c*₁ < ç < c*₂ Yw, the agent will prefer to be a worker,

ç > c*₂ Ye, the agent will prefer to be an entrepreneur.

Running a lagrangean function which maximises Yk, where k ∈ ( e, w), such that proposition two holds, we get a function Y*(c), which gives the agent's preferred choice of activity at any level of constraint. This is illustrated as the dashed bold line in Figure 2.

Figure 2: Agent's Preferred Activity, work or venture, According to Level of Constraint 

We must now relax our assumption of agent uniformity to allow for heterogeneity of innovative/entrepreneurial talents. To do this, we must adapt the returns on investments to bjx where bj is the type of the agent which has a distribution over ( 0, 1) given by G(b), so that Eqs. (4) & (5) can be transformed to

(7)

(8)

(9)

We could now rebuild our model using these adapted return-on-investment equations which allocate for heterogeneity in innovative/entrepreneurial talent and evaluate according to the marginal agent being indifferent between activity choices.

We can think of investments into innovative activities as creating positive externalities affecting the investment decision of other entrepreneurs⁷ (generating new technological opportunities, aggregate demand, reduced uncertainty, reduced constraints from the beaten path, or labour market externalities). On the other hand, investments into non-innovative proprietorships have mostly negative externalities affecting technological growth not just due to the resources which they orient away from innovative activities, but also for promoting a slowdown in rates of obsolescence which disfavour innovative behaviour (^{Gifford, 1992: 269})⁸.

Propositions #1 & #2 establishes that the allocation of talent is determined by the relative rewards created out of the institutional constraints of an economy, which permit the reward structure to vary considerably across amplitudes of constraints to innovation. Similar to ^{Baumol's (1996)} argument, 'that even though the supply of entrepreneurial talent is not sensitive to relative rewards, the allocation of this talent is'⁹. We are clearly demonstrating this with our model: the supply of talent is fixed but its distribution across activities crucially depends upon the relative rewards, which however, are also determined endogenously in our model.

3.2 - Dynamic Extension to the Model

Let us now consider a continuous time analogue of our model with overlapping periods. Leaving the worker out for the moment, each entrepreneur can potentially be infinitely active but faces an exit rate of B per period and also there are B new entrepreneurs who enter/initiate their investment at every instant, implying a constant population. Each entrepreneur has to make an irreversible investment choice at the start of each period, but can modify their choice from period to period. This is not too unrealistic since it can be imagined that an entrepreneur making an investment decision will be somewhat tied to this investment for a certain period before he can pull his resources out of this investment and reorient them towards a new activity. The per period returns are the same as given earlier with a discount rate adjusted for the probability of exit, denoted by r. This description implies that each entrepreneur, when initiating a new period, observes the level of constraints c, and anticipating the choice of future entrants due to the externalities which they bring, makes her own choice. Also, each entrepreneur chooses her investment level at each instant and this only influences her total product at that point. The investment level will therefore only depend on the current level of constraint in the economy, which we again write as x(c). The following value equations can therefore be written (dropping time arguments);

(10)

(11)

where the prime denotes a time-derivative. As return to innovation is given by Y_i and that to proprietorship by Y_p, innovation will be more attractive than proprietorship when Y_i > Y_p and new entrants would prefer entrepreneurship to proprietorship. Alternatively, we can define Y = Y_i - Y_p, and innovativeness will be more attractive than proprietorship when Y > 0. Subtracting (10) from (11), we obtain the law of motion of Y as

(12)

Let c*(t) be such that, Y(c*(t)) = 0. When c*(t) < c(t), entrepreneurs entering a new period would like to be innovators. However, as the investment choice is irreversible, c(t) is a predetermined variable and cannot jump to c*(t). Thus, when Y > 0, all entrepreneurs entering a new period would choose to invest in innovation and c would only fall due to the exit of existing proprietors. This change in c would take place at the rate Bc. Similarly when Y < 0, all entrepreneurs entering a new period would become proprietors but the increase in c will be equal to B(1 - c). These entrepreneurs would only have to choose when they would be indifferent between new investments alternatives, when Y = 0. Thus, the law of motion of c will be given by the following equation;

(14)

C' is then the representation of historical dependence in our model. Therefore, depending on where the economy starts, the long-run behaviour can be very different. In particular an economy which inherits an unfavourable allocation of entrepreneurial talent away from innovative activities, will have higher relative rewards for proprietorship activities and even-tually converges to a 'steady-state' with high proprietorship at the expense of innovativeness. Where an economy inherits higher relative rewards to innovation, momentum in the level of innovativeness will build with every new generation of investment and an innovative 'steady-state' will be established.

As observed by ^{Acemoglu (1995: 27)} for his similar model, the economic interest of the dynamic extension to our model is in the emphasis it places upon how fast allocations of talent influence future reward structures (Figure 3). If the majority of the investors in the current period choose to become proprietors, the return to innovation relative to that of proprietorship will be reduced in future periods and future generations of investors will be induced to choose proprietorship, thus giving us history dependence. Initial differences can have important long-run effects. Also, reversing the adverse effects on technological growth of a misallocation is difficult because such a misallocation also leads to an unfavourable future reward structure.

If we reincorporate the option for our agents to join the labour force, where

(15)

then Bc, when the relative rewards influence the allocation of talent towards the labour force, remains unknown and unpredictable. Also, beyond the scope of our model is determining the influence of the labour market on technological growth and innovativeness.

Figure 3: Dynamic Choice of Preferred Activity According to Constraints 

3.3 - Non-pecuniary rewards, social consensus, and historical dependence¹⁰

So far, our model has only dealt with the pecuniary (the money) aspects of the relative reward structure. But as we have mentioned in the sections of this paper that preceded our model, non-pecuniary rewards are also very important in the allocation of entrepreneurial talents within an economy. A great deal of non-pecuniary rewards is exogenously determined, and can only be captured by our model as adjustments up (positive rewards) and down (for negative rewards) of the different Yk curves. This would influence the relative rewards within our model in a static way, but would not collaborate our dynamic interpretation of it. But ^{Acemoglu (1995: 29)} identified a series of non-pecuniary rewards which did influence the allocation of talent in a dynamic and endogenous manner. The inclusion of these endogenously determined non-pecuniary rewards then strengthens the history dependence emphasised earlier.

Societies with high innovation levels will be less willing to constrain the entrepreneurs who innovate; therefore, innovation is more likely to persist. But this argument fits less well in the case where high levels of proprietorship exists. A proprietor will be relatively less eager to have new entrants investing in innovation, especially if the existing proprietors could choose a scheme which would not hurt themselves but make innovation (and entrepreneurship altogether) less attractive for new entrants. But it is generally difficult to 'create' a discriminating reward structure. Therefore, where there is a higher amount of proprietorship (it could also be argued that where there is a greater concentration of influence with proprietors), there may also be a weaker political will to improve the allocation of talent towards innovation.

But non-pecuniary aspects of the reward structure are not under the direct control of the government or any other group (^{North, 1990}). A society's attitude norms and value judgement can be much more powerful than political influence in determining the relative rewards of an economy. A society with high innovativeness will give relatively more respect to innovating entrepreneurs than a more stagnant society of proprietors (^{North, 2005}). There are many channels by which the social attitudes are influenced. Learning by new generations will start from the already established norms and role models (^{Lafuente & Vaillant, 2013}). This learning process will influence the views of the new generation as well as their stock of knowledge (^{Coleman, 1994}, as reported in ^{Acemoglu, 1995:30} ). This could mean that a social attitude such as social status may be determined both by external forces and through endogenous influence. Therefore, a social attitude such as the social status of a profession may depend on the choices that the rest of the society makes, and thus proprietorship may have less negative stigma when it is more 'wide-spread' (^{Vaillant and Lafuente, 2007}). Finally, a society's value judgement may conform to past practice or economic behaviour if individuals look for justification for their present place in society. Thus, entrepreneurs with innovative talents, who have placed their (irreversible) investments into proprietorship due to the relative reward structure, will gradually change their value judgements and will eventually pay more respect to being a proprietor (^{Bayon et al., 2016}). Therefore, there seems to exist a mechanism which makes the social consensus, and the non-pecuniary rewards, respond to the economic decisions of the agents.

An element of importance which we can extrapolate from this discussion is that the link between past allocation and non-pecuniary rewards implies that after a misallocation of talent, not only will pecuniary rewards favour non-innovative activities and investments, but the society may also lack the 'social/political will' to change the status quo (^{Driga et al., 2009}).

Our preceding model and the analysis which we have pulled from it suggests some important insight into the state of technological development in less developed regions (^{Vendrell-Herrero et al., 2020}). Many less competitive economies can be thought as being caught in a low reward, low innovation, low technological growth trap from which escape is not easy. The fact that domestic technological stagnation and dependence on borrowed technologies has become a part of the cultures of these societies coheres well with the above view (^{Findlay, 1978}). Entrepreneurially driven domestic technological development can therefore be a valid answer to technological growth in these societies (^{Yoruk & Jones, 2020}).