Download Measurement of Economic Progress Broadly defined, measurement

Measurement of Economic Progress
Broadly defined, measurement of economic progress focuses on quantitative analysis of the standard of living
or quality of life and their determinants. The analysis concerns many elements of the standard living such as its
material components, human capital, including education and health, inequality and other factors (see, among
others, Barro & Sala-i Martin, 2004, Howitt & Weil, 2008, Steckel, 2008, and references therein).
Theoretical foundation for empirical analysis of determinants of economic growth is provided by the Solow
growth model. The human capital-augmented version of the model with the Cobb-Douglas production function
(see Mankiw et al., 1992) assumes that, for country i at time t, the aggregate output Yi (t) satisfies Yi (t) =
Ki (t)α Hi (t)β (Ai (t)Li (t))1−α−β , where Ki (t) is physical capital, Hi (t) is human capital, Li (t) is labor supply and
Ai (t) is a productivity parameter (the efficiency level of each worker or the level of technology). The variables
L and A are assumed to obey Li (t) = Li (0)eni t and A(t) = A(0)egt , where ni and g are, respectively, the
population growth rate and the rate of technological progress. Physical and human capital are assumed to
follow continuous-time accumulation equations dKi (t)/dt = sK,i Yi (t) − δKi (t) and dHi (t)/dt = sH,i Yi (t) − δH(t)
with the depreciation rate δ and the savings rates sK,i and sH,i . Under the above assumptions, the growth model
leads to the regressions γi = a0 +a1 log yi (0)+a2 log(ni +g+δ)+a3 log sK,i +a4 log sH,i +²i , where γi = (log yi (t)−
log yi (0))/t is the growth rate of output per worker yi (t) = Yi (t)/Li (t) between time 0 and t (see, among others,
Barro & Sala-i Martin, 2004, Durlauf et al., 2005). Cross-country growth regressions typically include additional
regressors Zi and focus on estimating models in the form γi = aXi + bZi + ²i , where a = (a0 , a1 , ..., a4 ) ∈ R5 ,
b = (b1 , b2 , ..., bm ) ∈ Rm , the components of Xi = (1, log yi (0), log(ni + g + δ), log sK,i , log sH,i )0 are the growth
determinants in the Solow model and Zi ∈ Rm is the vector of growth determinants outside the Solow growth
theory.
The statistical analysis of economic progress and its determinants presents a number of challenges due to the
necessity of using proxy measures and corresponding weights for different components of the standard of living
and factors affecting it. The material standard of living is typically measured as per capita Gross Domestic
Product (GDP) adjusted for changes in price levels. Proxies for education and human capital used in growth
economics include school-enrollment rates at the secondary and primary levels, literacy rates, average years of
secondary and higher schooling and outcomes on internationally comparable examinations. Many works in the
literature have also used student-teacher ratios as a measure of quality of education. The two most widely
used measures of health are life expectancy at birth or age 1 and average height used as a proxy for nutritional
conditions during the growing years.
Barro (1991) and Barro & Sala-i Martin (2004) find that the growth rate of real per capita GDP is positively
related to initial human capital, including education and health, proxied by school-enrollment rates, upper-level
schooling and life expectancy and negatively related to the initial level of real per capita GDP. The results in
Barro (1991) also indicate statistically significant negative effects of political instability (measured using the
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number of revolutions and coups per year and the number of political assassinations per million population per
year) on growth. Other factors used in the analysis in Barro (1991) and Barro & Sala-i Martin (2004) include
fertility and the ratio of real government consumption to real GDP (with statistically significant negative effects
on growth), investment ratio, inflation rate as well as proxies for market distortions, maintenance of the rule of
law, measures for democracy, international openness, the terms of trade, indicators for economic systems and
countries in sub-Saharian Africa and Latin America and other variables.
A number of works in theoretical and empirical growth economics has focused on the development and
analysis of performance of models with endogenous technological progress. Many recent studies have also
studied the factors that lead to the observed differences in the determinants of economic growth in different
countries, including capital components, technology and efficiency. In particular, several works have emphasized
the role of geographical differences, cultural factors, economic policies and institutions as fundamental causes of
the differences in growth determinants (Howitt & Weil 2008).
Statistical study of economic growth determinants is complicated by relatively small samples of available
observations, measurement errors in key variables, such as GDP, heterogeneity in observations and estimated
parameters, dependence in data and large number of potential growth regressors under analysis. Related issues
in the analysis of economic growth concern difficulty of causal interpretation of estimation results, robustness
of the conclusions to alternative measures of variables in the analysis, and open-endedness of growth theories
that imply that several key factors matter for growth at the same time. Levine & Renelt (1992) focus on the
analysis of robustness of conclusions obtained using cross-country growth regressions. They propose assessing
the robustness of the variable Z of interest using the variation of the coefficient b in cross-country regressions
γi = aXi + bZi + cVi + ²i , where Xi is the vector of variables that always appear in the regressions (e.g., the
investment share of GDP, initial level of income, a proxy for the initial level of human capital such as the school
enrollment rate, and the rate of population growth in country i), and Vi is a vector of additional control variables
taken from the pool of variables available. Departing from the extreme bounds approach in Levine & Renelt
(1992) that requires the estimate of the coefficient of interest b to be statistically significant for any choice of
control variables V, several recent works (see Sala-i Martin et al., 2004, Ch. 12 in Barro & Sala-i Martin, and
references therein) propose alternative less stringent procedures to robustness analysis. Several recent works on
the analysis of economic growth and related areas emphasize importance of models incorporating disasters and
crises and probability distributions generating outliers and extreme observations, such as those with heavy-tailed
and power-law densities (see Barro, 1991, Gabaix, 2009 and Ibragimov, 2009).
References
Barro, R. J. (1991), ‘Economic growth in a cross section of coutries’, Quarterly Journal of Economics 106, 407–443.
Barro, R. J. & Sala-i Martin, X. (2004), Economic Growth, MIT Press, Cambridge, MA.
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Durlauf, S., Johnson, P. & Temple, J. (2005), Growth econometrics, in P. Aghion & S. Durlauf, eds, ‘Handbook of Economic Growth’,
North-Holland, Amsterdam.
Gabaix, X. (2009), ‘Power laws in economics and finance’, Annual Review of Economics 1, 255–293.
Howitt, P. & Weil, D. N. (2008), Economic growth, in S. N. Durlauf & L. E. Blume, eds, ‘New Palgrave Dictionary of Economics,
2nd Edition’, Palgrave Macmillan.
Ibragimov, R. (2009), Heavy tailed densities, in S. N. Durlauf & L. E. Blume, eds, ‘The New Palgrave Dictionary of Economics
Online’, Palgrave Macmillan.
URL: http://www.dictionaryofeconomics.com/article?id=pde2008 H000191
Levine, R. & Renelt, D. (1992), ‘A sensitivity analysis of cross-country growth regressions’, American Economic Review 82, 942–963.
Mankiw, N. G., Romer, D. & Wiel, D. N. (1992), ‘A contribution to the empirics of economic growth’, Quarterly Journal of Economics
42, 407–437.
Sala-i Martin, X., Doppelhofer, G. & Miller, R. I. (2004), ‘Determinants of long-term growth: A Bayesian averaging of classical
estimates (bace) approach’, American Economic Review 94.
Steckel, R. H. (2008), Standards of living (historical trends), in S. N. Durlauf & L. E. Blume, eds, ‘New Palgrave Dictionary of
Economics, 2nd Edition’, Palgrave Macmillan.
Marat Ibragimov, Department of Higher Mathematics, Tashkent State University of Economics,
[email protected]
Rustam Ibragimov, Department of Economics, Harvard University, [email protected]
Marat Ibragimov gratefully acknowledges support by a grant R08-1123 from the Economics Education and
Research Consortium (EERC), with funds provided by the Global Development Network and the Government of
Sweden. Rustam Ibragimov gratefully acknowledges partial support by the National Science Foundation grant
SES-0820124.
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