Big Push Model

The key to development lies in a big push. (a) Explain the role of coordination problems and externalities in producing development traps where some countries are unable to move from subsistence agriculture to an industrialised economy, (b) Evaluate the proposition that if the economy were open to trade such coordination problems might be resolved, (c) Discuss the Millennium Village projects in the context of the Big Push model.

A coordination problem is a situation where agents are unable to coordinate their behaviour, such that they end up in an equilibrium that leaves all agents worse off than in an alternative Pareto efficient equilibrium. This exists because complementarities between several conditions are necessary for successful development and the externalities arising from these complementarities are often not considered by decision making agents. Rosenstein-Rodan developed the big push theory which suggests that a government, or coalition of firms/organisations/individuals, needs to overcome these preconditions before growth can occur. Ellis describes this Big Push theory as a “minimum level of resources that must be devoted to… a development programme if it is to have any chance of success. Launching a country into self-sustaining growth is a little like getting an airplane off the ground. There is a critical ground speed which must be passed before the craft can become airborne….”.

For example, to move from a large unproductive agricultural sector to a productive agricultural economy fertiliser is necessary, amongst other things. This can either be produced domestically or imported from abroad. Either way certain pre-conditions are needed; if the fertiliser is to be produced domestically then infrastructure is needed to a fertiliser manufacturing sector can develop; if the fertiliser is to be imported then road and transport networks need to be built in addition to a port. In short, even the simplest activity requires a network of other activities which can’t be produced by an individual firm alone.

The coordination problem is seen as a trap, because even if some issues are overcome – for example education is improved – but other barriers remain – e.g. a lack of infrastructure – then it may still be the case that the economy is held back and can’t develop. In some cases, this piecemeal tackling of some issues is a complete waste in that it creates no economic growth (or very little, with the economy still remaining in a low-income trap), and overtime depreciation may render the individual funding worthless. Put simply, we can think of a situation where a country may spend a lot of money increasing the human capital of its people but then other development barriers mean that these individuals can’t find a job, and over time they will experience an atrophy of skills, such that the funding spent in educating them is completely wasted, with little to no benefit.

We can develop the intuition behind this big push theory into a model, making a number of assumptions. We start by assuming that labour is our only factor of production, we normalise traditional sector wages to 1, and hence the modern sector wage will be greater than one. We assume that there are constant returns to scale in the traditional sector, but increasing returns in the modern sector, and a fixed supply of labour F, is required before any output can begin, but after that the marginal product of labour is c: L = F + cQ. We ban savings from our model and assume that consumers spend an equal amount of their budget on each good, so demand for each good is Y/N where Y is GDP and N is the number of goods in the economy. To simplify matters we take a closed economy and assume perfect competition in the traditional sector, with free entry, and therefore have 0 supernormal profits. It also means that the price of a good from the traditional sector is 1 which equals the MPL. Our final assumption is that only one modern firm can enter each market and thus have a monopolist hold on this market; typically we would assume that they would want to raise their price above 1, but if they did this then they would lose all their business to the competing traditional sector firms, and as a result the price for this monopolist firm must be 1.

Now that we have stated our long list of assumptions we can begin our look at an economy which starts with just a traditional sector. A modern firm would only enter the market if it can produce more productively (i.e. benefit from economies of scale) than the traditional sector, and dependent on the wage rate. The traditional firm produces one unit of output for every good, and so, as we can see below, has a 45 degree production line, whereas the modern firm’s production line will have a slope of 1/c, so long as L>F. We have already stated that the price of the good must be 1, and hence the revenue can be read off the vertical axis; assuming that L/N units of labour are used a traditional firm will have revenues of Q1 whereas if all firms were modern then there would be higher revenues of Q2. This would imply that the economy would be better off with all modern firms, because we would then be able to produce greater output with the same quantity of labour. Yet, this socially optimal outcome may not be arrived at when we examine the costs. In this case the costs to the firms are the wages, and the wage line for the traditional sector is the same as the production function (i.e. a slope of 1). As expected this means that there will be no supernormal profit, as costs are Q1 (hence profit = revenue-costs = Q1-Q1 = 0). For the modern firm, the lower the wage, the higher the profits and the more likely a coordination failure won’t occur. A wage line which intersects the modern production function below A will mean that all firms will naturally modernise: there is a profit incentive to do so, even for traditional sector firms. A wage between A and B would mean that 2 equilibria exist: all firms become modern (which is a Pareto improvement) or no firm becomes modern. This is an example of a coordination failure, and shows how an economy can get stuck in a development trap, whereby the government may need to intervene in the market to reach the Pareto efficient point. It could do this by increasing the productivity of labour, so that c rises (i.e. the modern production function becomes steeper, and therefore profits rise and firms decide to become modern) or by reducing the equilibrium wage rate, perhaps through emancipation of women and encouragement of female participation in the labour market. A wage above 1 would mean there are no incentives to invest in modernisation at all.

In short, our simple model shows that there are cases when government needs to intervene, to provide services such as education, and infrastructure, and coordinate private efforts to advance the economy.

Another example of how the government can intervene in the economy to get a developed economy out of a low-income trap is by investing in linkage industries. These are certain firms which have either high backward linkages – which increase the demand for goods – or high forward linkages – which increase the supply of goods, and hence reduce the price. For example, the government could invest in a steel firm which has strong forward linkages; by subsidising the steel firm so it either sold goods at a loss, or had enough invested in it that it benefited from large economies of scale, it would be able to lower the price of steel which would then help many other industries which would have lower costs, and therefore higher profits and a greater incentive to invest and overcome coordination issues. This approach of building linkage firms has proved successful in the development of Taiwan, Singapore and South Korea.

Michael Kremer developed a slightly more advanced model, which explains a number of development phenomena, by designing what he calls an O-ring production function. He begins by breaking down a firm’s production process into a number of tasks, n, which can be carried out ordered by skill q which lies between 0 and 1. A higher skill means that the task will be completed successful, alternatively it could be considered as the percentage of final value that the product will retain (which means if the labour is of poor quality then the produced output will be poor and so will have to be sold at discount). He makes the assumption that each firm has two workers completing each task and gives the production function as BF = qiqj, where B depends on the characteristic of the firm and is usually larger with a larger firm. The most important assumptions here are that labour markets are competitive and workers supply labour inelastically (without regards to the wage – perhaps an unrealistic assumption in reality), plus it isn’t possible to substitute several low skill workers for one high skill worker. The given production function features positive assortative matching: workers with high skills work together as do those with low skills. This is because high skilled workers realise they can get paid more for partnering with people of equally high skills: consider an economy with 4 workers and an MPL of 3 and 3, and 4 and 4. Without matching we would have the sum of MPLs as 24, but with positive matching the sum would be 25, and would be hence higher. This demonstrates how it is possible for a country to fall into a trap of low skills and low productivity: if I am making a decision as to whether I should invest in my human capital, but everybody else is of lower skill than me then – in this model – it wouldn’t be beneficial for me to invest because my returns would be smaller than if there existed another person who would also invest in his human capital. Again, this shows that the government could intervene – provide education for everybody, to increase their human capital – and hence cause higher wages, higher productivity and greater output.

If we take away our current assumption that production occurs simultaneously, and look at what happens when production occurs sequentially Kremer finds that the highest skilled workers are allocated to the latter stages of production. This is because mistakes at the final stages of production destroy higher valued inputs than in earlier production stages. This provides the interesting empirical fact that poor countries have higher shares of primary production in GNP and workers are paid more in industries with high value inputs.

In short, the O-ring production function is empirically relevant, and one of its most important findings is that with imperfect matching there exists the possibility that there will be an underinvestment in skill which means there are strategic complementarities to investment. Summarising this, it is because it only makes sense to be a high skill worker if there are enough high skill co-workers to match with. Hence each worker has more incentive to choose a high level of education if other workers chose a high level of education. The policy implications of this is that an education subsidy can have a large multiplier effect in creating large differences in the skill level, thus boosting production and output.

Opening up the economy to trade is unlikely to solve the coordination problem. In our above model it may lead to greater marginal product of labour (so a steeper modern firm curve), caused by access to greater technology and production techniques, which could be helpful in causing firms to move to a higher equilibrium. But whilst it may make input goods cheaper, give greater access to technology and provide access to a large market, it doesn’t do a greater deal in helping overcome fundamental development problems. This can include a lack of education which makes absorption of technology difficult, a deficiency in infrastructure, poor health care contributing to a lack of human capital and a lack of foreign exchange to purchase physical capital with. Therefore, it is unlikely that trade would vastly benefit a developing country in our simple model, but equally there isn’t a mechanism for it to do harm.

The Millennium Village Project (MPV) is a programme, initiated by Jeffrey Sachs that takes 14 rural African villages, 500,000 Africans, and gives them $150m to help them reach the Millennium Development targets. Even though the MVP wasn’t explicitly designed to test any particular theory, authors such as Easterly have pointed out that its aims bear close resemblance to a big push. There was simultaneous intervention into 5 areas, which could be considered as development bottlenecks; agriculture, education, health, infrastructure and business development. Positive evidence from the project shows that there has been a 700% increase in the use of anti-malarial bed nets, a 350% increase in access to safer water and a 368% increase in primary-school meal programmes. However this doesn’t tell us what would have happened without the project: it may be the case that access to safer water would have improved even without the MVP funding. Therefore, we would need to use carefully selected randomised trials to measure the difference between changes in the MVP villages, and other villages with similar characteristics. Sachs however is highly critical of this method, claiming that it would be impossible to find such villages to make useful comparisons.

This acts as a major impediment to being able to evaluate the effects of trying to attain a big push. Without proper data, including data examining these villages a number of years after the funding (Clemens), we are unable to conclude whether the project was a success or not.

We might expect that if enough development barriers were overcome by this intervention that these micro-economies can overcome the development trap of coordination failure and produce at a higher equilibrium than previously. This will have obvious positive spill-over effects on the nearby economy, thus increasing economic growth in the country. However it is likely that growth in these small microcosms alone is enough to stimulate any significant development nationwide, let alone across the continent of Africa. But if it is successful then Sachs has proposed mechanisms for up-scaling his project to transcend national barriers to economic development. Unfortunately, we are unable to effectively conclude whether this has been a success due to the poor evaluation methods used in the project (McKenzie).

In conclusion, the theories and models we have proposed do seem to suggest that successful development requires a big push in a number of areas to overcome coordination failures and get the country out of a development trap. Unfortunately we don’t have substantial empirical evidence on whether a big push is necessary, even with recent studies of the Millennium Village project, as we are unable to effectively measure the progress of such a project. This thus makes the evaluation of the big push indeterminate, and we are left relying on our models. Finally, we point out that according to our models the government is able to overcome these coordination failures through a number of different mechanisms; investing in linkage firms, reducing wage costs, increasing the marginal productivity of labour, increasing the skill-set of the labour force and through reducing taxes to make projects more financially viable, to name a few such policies.

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