per capita growth. However, finding valid instruments is difficult, see for example the discussion of Acemoglu and Johnson (2007) in Bloom et al. (2014).

Many have also argued that measurement error may plague the estimation results (Kruger and Lindhal, 2001). A recent contribution by Barro and Lee (2013) overcomes some of the limitations of the original perpetual inventory-based education dataset (Barro and Lee, 1993) and improves data accuracy by using information from consistent census data, disaggregated by age group, along with new estimates of mortality rates and completion rates by age and education level. A related question is whether using average years of schooling is the right measure for human capital. Recent work by Hanushek and Woessman (2015) shows that using school attainment as proxy for human capital fails to account for differences in quality of education across countries and thus is unlikely to provide a reasonable estimate of the role of human capital. They thus propose the use of scores from international tests of mathematics, science and reading achievement.<sup>5</sup> Based on an aggregate value of skills for about fifty countries, they concludes that it is learning – rather than schooling –that matters.

A further concern with cross country regressions is that causality might run both ways, from human capital to growth and back. Weil (2013) explicitly discusses this with reference to health and reviews different mechanisms through which income - or economic dynamics associated with income growth - might affect health. These include improved sanitation, which is associated with better health (though with a lag); and higher urbanization, which is often associated with a negative impact on health.

# **4.1.2 Development accounting**

Growth accounting - i.e. the decomposition of income growth rates into the contribution of different factors - was first applied to the growth time series of the US by Solow in the fifties. Later, a similar methodology has been applied on cross-sections of countries, leading to the _development accounting_ literature. This methodology decomposes income differences across countries into their measurable components: physical capital ( _K_ ), human capital ( _H_ ), and a residual which is interpreted as Total Factor Productivity ( _A_ or _TFP_ ). This work tries to answer the question: _What share of aggregate income differences can be attributed to variation in K and H and how much can be attributed to the efficiency with which these two factors are used (TFP)?_ Accurately measuring income and factors and properly choosing the production function’s functional form are the two key steps of development accounting. Efficiency is obtained as a residual. Traditionally, large part of this literature is dedicated to understanding this residual, which is often referred to as the “measure of our ignorance” [Abramovitz (1957), cited in Caselli (2005)].

> 5 Barro and Lee (2013) show a high correlation between their measure of school attainment and Hanushek and Woessman (2009)’s measure of human capital quality, though they note that human capital quality is quite diverse for countries with similar levels of educational attainment.

10