such as population growth and human capital accumulation. The next frontier is the inclusion of two additional variables: ideas and institutions [Jones and Romer (2010)].

A typical empirical contribution in this area estimates the correlation between different measures of human capital (such as years of schooling and life expectancy) and GDP per capita growth. The question they try to answer is: _If a country were to increase investment in a given human capital component, by how much would income growth change?_

**Early findings.** Barro and Sala-i-Martin’s book summarizes some of the key results of these estimations. They report that educational attainment is positively correlated with growth across countries: 1 standard deviation increase in male secondary schooling (equivalent to 0.68 years of schooling) is associated with an increase in the growth rate by 1.1 percentage points per year. When education is decomposed in primary, secondary and higher, it is secondary and higher education that are responsible for the positive impact on growth (Barro and Sala-i-Martin (1995), chapter 12, page 431.) Subsequent work has not always confirmed these results. For example, Pritchett (2001) uses data on 91 countries and does not find a significant association between a rise in educational attainment and the rate of growth of output per worker.

Increases in life expectancy are also found to be positively correlated with growth: 1 standard deviation increase in in life expectancy (13 years) is associated with an increase in the growth rate of GDP by 1.4 percentage points (Barro and Sala-i-Martin (1995), chapter 12, page 432). More recently, Barro (2015) reports that growth is positively associated with lower mortality rate, lower fertility and higher female relative to male school attainment for those aged 15+, while he finds that the impact of a general increase in attainment is not significantly different from zero. Zaman and Tiwari (2017) find that an increase in social protection spending is positively correlated with growth: Moving from 0 ‐ to 2% of GDP spending on SP increases growth by 0.1 0.4 percentage points.

**Identification, measurement, and reverse causation.** There are many interpretation on the estimates of a coefficient of GDP growth when regressed on the level of education and change in education. As discussed in Benhabib and Spiegel (1994) and Krueger and Lindhal (2001), level of schooling could be a proxy for steady state income, or could change the steady state growth rate by enabling the work force to develop and adopt new technologies (as in Nelson and Phelps, 1966 and Romer, 1990), or reflect an exogenous change in returns to education, or could reflect reverse causality of increased education in anticipation of future growth.

Importantly, a consensus around this literature is that obtaining unbiased estimated coefficients in cross-country setups has proven problematic due to potential omitted variables issues; reverse causality; heterogeneous effects, and measurement error. Acemoglu and Johnson (2007) use instrumental variables to address some of the identification problems in these types of regressions. They exploit international health improvements from the 1940s to estimate the effect of life expectancy on economic performance. They find that longer life expectancy increases population. It also increases GDP, but not enough to compensate the population effect so there is no impact on GDP 9