# Development Accounting

Explain in brief the use of development accounting. Discuss the implications for the productivity gap across countries, if any, taking into account:

• The high share of public sector investment in total investment in developing countries
• Rich countries have higher test scores

Development accounting is the manipulation of a production function to examine whether cross-country income differences arise from differences in total factor productivity (TFP), or due to factor accumulation. It is useful to find this information out so that we can correctly inform policy decisions and let developing countries know if they need to simply increase quantity of factors of production (i.e. promote higher fertility, immigration, labour market inclusion and capital appreciation), whether they need to increase the quality of the factors of production (better education and more efficient use of investment funds) or if they need to increase efficiency and technological adoption.

We follow Hall and Jones, taking our standard production function – with constant returns to scale – to be of the form:

Y = AKα(Lh)1-α   where Y is output, A is our TFP, K is physical capital, L is the number of employed, h is human capital and alpha is our capital-output share which we take as a constant 1/3.

This therefore tells us that total output can be increased either through increasing the factors of production of capital and labour (i.e. use more capital and labour), increasing the quality of human capital (h) so that effective labour increases, increasing the quality of capital or by increasing our TFP term. The TFP term incorporates technology and efficiency so would include institutions and how we organise our factors of production; because it is a residual it will include any other omitted factors also.

We can calculate K using the perpetual inventory equation, with a depreciation rate of 6% per year. Human capital is estimated using average years of schooling in the population for over 25 year olds with a weighting (see Psacharopoulos) to reflect that there are decreasing marginal returns to education (such that if schooling, s ≤4 our return would be 0.13, 4<s≤8 return would be 0.1 and 8<s return would be 0.07). Data for L and Y is easily available and the capital-output ratio is 1/3, based on fairly consistent US data. Therefore we can calculate our A term as a residual:

A = y/( kαh1-α) where we have divided our production function by L, to get in per worker terms, and re-arranged.

It is evident that we now have values for every variable in our production function – later we examine the correctness of these values – and we can use these to compare across countries to examine where income differences arise: how much of income variation is explained by variation in A compared with variation in the factors of production.

To do this we follow Caselli and assume that technology flows across borders such that each country has access to the same technology, we can then give our success ratio (which measures how much the difference in variance of income is explained by observed endowments) as:

Success = Var(log(yKH)) / Var(log(y))

Taking data from world incomes and factor use, we find that  = 0.5 and Var(log(y)) = 1.3, meaning our success ratio = 0.39. Thus, whilst this model isn’t perfect, as it is sensitive to outliers, only 39% of variance in world incomes is explained by observed endowments. This must mean that our TFP term has a variance not equal to 0 (as we previously assumed) which explains where the rest of income variance comes from. Weil takes the data for 2009 and finds slightly different values, such that productivity accounts for 53% of variation in income per capita whilst factor accumulation is responsible for 47%. Regardless of the exact numbers, it is evident that TFP is an important variable in explaining cross country income differences: even with the same factor levels as countries such as the US (same K, L and h) income would still be below US levels because the productivity gap accounts for a large portion of these income differences.

Before we can conclude that developing countries need to implement policies to increase this TFP variable – which could include measures such as disregarding patent laws, imitating foreign technology and indoctrinating workers to be more efficient – we need to see how reliable our method is. It may be the case that we are calculating Y, K and h incorrectly.

We eliminate the first potential error easily: it is unlikely that our values for Y should be incorrect as they are based on the Penn World tables in PPP dollars which accounts for exchange rate issues and should ameliorate against issues with GDP that are often downward biased with developing countries. We measure capital using the perpetual inventory equation with a fixed depreciation rate of 6%, if this were in fact higher then it would mean that countries which recently experience large investment rates over the sample period would have a relatively higher capital stock – ceteris paribus – than countries which did not. Caselli finds that the relative gain is so small that it has little effect on our calculation of A, meaning this can’t disprove our data on its own. Examining our initial guess for the capital stock at time 0 we find that for poorer countries our estimate of K is more sensitive to the initial guess. This is because our surviving portion of guess K0 as a fraction of final estimates of K is negatively correlated with per capita income (r = -0.24) which suggests that we overestimate K0 for poor countries. This would mean that we would also be overestimating our Kt for poor countries which would bias downwards our measured success of the factor only model. Simply put, if anything, incorrect overestimated estimates of initial capital stock would suggest that the productivity gap plays an even bigger role in explaining income differences than previously thought.

Moreover, evidence by Pritchett would suggest that K is considerably overestimated for poor countries, thereby increasing our calculated value for the productivity gap. He suggests that the capital stock in 1987 was actually only 57-75% of the officially measured capital stock. Pritchett points out that government investment efforts are much less productive than private ones. The first reason for this is that corrupt officials steal money from investment projects such that the amount of investment into a project doesn’t all go into the production of capital goods. Because we believe poor countries have worse institutions than developed countries this would mean that the capital stock for poor countries is heavily biased upwards. The second reason is that the government generally accounts for a larger share of investment projects in developing countries [often half or more], again biasing up the estimated capital stock for developing countries. This effect is exacerbated by the assumption made by economists that the government is less productive than the private sector; perhaps due to a lack of profit motive and the ability for rentiers to successfully lobby the government. Estimates of returns to public capital in Mexico are 5-7% compared to 14-18% for private capital [Shah 1992] showing that this is quite an appropriate assumption.

In short, Pritchett has shown that the capital stock for developing countries is heavily overstated, meaning our model would overstate the role that the productivity gap plays, compared to the situation in reality.

Turning to our measure of human capital, h, we have seen that we predicted it based on levels of schooling. Yet this doesn’t take into account the quality of schooling, nor other factors which may affect human capital. It simply assumes that more schooling is better, even with the assumption of diminishing marginal returns. In reality it may be the case that human capital is affected by other factors, such as overall education (which incorporates learning from family and friends, not simply formal schooling), health or experience. If we use standardised test scores to proxy for human capital then we find that this is biased against poor countries, which would understate their human capital levels and thus mean that the real productivity gap is smaller than our model predicts (i.e. TFP plays a smaller role than our results would lead us to believe). This is because developing countries tend to do poorly on test results, and as already stated, human capital is more than just education and should incorporate health and work experience. Weil incorporates health into human capital (proxied by the Adult Mortality Rate) and finds that this increases by a third the explanatory power of human capital differences in per capita income. Caselli confirms this in his model and finds that the factor only model success rate rises above 50% (from 39%). However if we instead use other proxies for health we find a trivial change, so more research is needed in this area.

Perhaps we have incorrectly calculated our capital-output share, Caselli finds that if this value were 0.6 (instead of 0.3) then the productivity gap falls to zero: all of our income variance is explained by variance in factor accumulation. But so long as α<4 most of the variation in income is still explained by TFP, and the capital-output share isn’t difficult to calculate, so our data shouldn’t be that incorrect. The bottom line of this means that it is unlikely incorrect estimates of the capital-output share are affecting our model.

In conclusion we have used development accounting to find that TFP accounts for over 50% of variation in income differences across the world, but that this figure depends on how we estimate our production function. Economic theory suggests that technology should flow across countries and hence TFP should account for a very small percentage of income variation. Yet this doesn’t appear to be the case at first glance, although improving our model by including variables such as health into human capital, evidence such as capital being over-estimated for poor countries and the quality of capital may well reduce the productivity gap. To do this we would need more data and more research to ensure that our calculations for the productivity gap are precise. Correctly calculating the productivity gap would allow policymakers to decide and implement policy to increase income and reduce income differences between countries.