Reconciling conflicting evidence on the origins of comparative development: A finite mixture model approach

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1 Reconciling conflicting evidence on the origins of comparative development: A finite mixture model approach Thomas K.J. Grantham Research Institute on Climate Change and the Environment, London School of Economics CSAE, Oxford, 18 March 2013

2 The fundamental sources of development? 1. Geography Diamond (1997) Gallup et al. (1999) Masters & McMillan (2001) Sachs et al. (2001)

3 The fundamental sources of development? 1. Geography Diamond (1997) Gallup et al. (1999) Masters & McMillan (2001) Sachs et al. (2001) 2. Institutions Acemoglu, Johnson & Robinson (2001, 2003) Rodrik (1999) Easterly & Levine (2003)

4 The fundamental sources of development? Acemoglu, Johnson & Robinson (2001) - AJR Acemoglu (2008, p.162): there appears to be no causal effect of geography on prosperity today (though geography may have been important historically in shaping economic institutions)

5 The fundamental sources of development? In contrast, it has been shown that: The income-latitude correlation persists within countries (Parker, 2000) As does income-temperature correlation (Nordhaus, 2006; Dell et al., 2009) And that disease environment has a direct impact on income, even controlling for institutions (Sachs, 2003; Carstensen & Grundlach, 2006; Bhattacharyya, 2009b)

6 Why return to this question? Still being debated! e.g. Albouy s (AER, 2012) Comment and AJR s response Debate between Acemoglu & Robinson and Diamond over Why Nations Fail Policy relevance given concerns over climate change and development Increased computing power enables use of a more sophisticated estimation model

7 Specification vs Identification Most of the debate has focussed on issues of identification, e.g. concerns over data, sample, choice of variables, instrument quality etc. In contrast, my focus is on the appropriate specification of the empirical analysis (analogous to Cervellati & Sunde, 2011a,b) Both empirical and theoretical reasons to believe the standard linear estimation models are mis-specified

8 In theory... Growth as a dynamic, non-linear process (Unified Growth Theory, e.g. Galor & Weil, 2000) Effects of geography and institutions apparent at different stages of development (Bhattacharyya, 2009a) Expect this to be the case in particular for geography Developing countries more vulnerable to climate (World Bank, 2010) Shocks and natural disasters (e.g. Noy 2009, Dell et al. 2012) Nordhaus (2006): geography is an important source of income differences in Africa relative to high-income regions

9 Empirics... Bi-modality of global income (see Quah 1996, 1997) Result of two growth regimes - as predicted by poverty-trap models (see e.g. Azariadis & Stachurski, 2005) Determinants of income likely to have non-monotonic effects across regimes These may be obscured by application of linear regression model Conway & Deb (2005) - effect of prenatal care on birth weight Cervellati & Sunde (2011a,b) - effect of life expectancy on growth A finite mixture model may be a more appropriate estimation strategy

10 Bi-modality of global income Density Kernel density estimate GDP per capita (PPP, 1995) kernel = epanechnikov, bandwidth = 1.8e+03 Kernel density estimate Normal density

11 Related literature Bloom et al. (2003) use a finite mixture model to show that a poverty trap model is a better fit to the data than simple geographic determinism. Tol (2011) also uses FMM to test the demo-economic model of Strulik (2008)

12 Outline of remainder of presentation Data and sample issues Replication of AJR - testing robustness to sample composition Estimation using a finite mixture model Monte Carlo simulations Discussion and conclusions

13 Preview of results Confirm AJR results, but only for a sub-sample of countries Results are sensitive to sample composition AJR methods do not explain income variation across relatively poor countries or for the African sub-sample Geography may be significant for relatively poor countries - not a robust finding Monte Carlo simulations demonstrate importance of accounting for bi-modal income distribution

14 Data Data are taken directly from AJR (available online from Daron Acemoglu s webpage) Use AJR s base sample of 64 countries Dependent variable: log income per capita (1995, PPP) Independent variables: latitude and institutions (security of property rights) instrumental variable: settler mortality

15 List of countries included in AJR s base sample Angola Gabon Niger Venezuela Argentina Ghana Nigeria Vietnam Australia Guinea Nicaragua South Africa Burkina Faso Gambia, The New Zealand Congo, Dem. Rep. Bangladesh Guatemala Pakistan (formerly Zaire) Bahamas, The Guyana Panama Bolivia Hong Kong Peru Brazil Honduras Paraguay Canada Haiti Sudan Chile Indonesia Senegal Cote d Ivoire India Singapore Cameroon Jamaica Sierra Leone Congo, Rep. Kenya El Salvador Colombia Sri Lanka Togo Costa Rica Morocco Trinidad and Tobago Dominican Republic Madagascar Tunisia Algeria Mexico Tanzania Ecuador Mali Uganda Egypt Malta Uruguay Ethiopia Malaysia United States

16 Motivation Data Replication of AJR results Finite mixture model Monte Carlo simulations Discussion & Conclusions Countries included in AJR s base sample AJR base sample Other

17 The standard AJR result OLS vs IV Regressions of Log GDP per Capita, checking robustness OLS 2SLS (1) (2) Avg. protection 0.47*** 1.00*** against expropriation (0.06) (0.22) risk Latitude 1.58** (0.71) (1.34) Obs Standard errors in parentheses. p < 0.10, p < 0.05, p < 0.01.

18 Bootstrapping OLS vs IV Regressions of Log GDP per Capita, checking robustness OLS 2SLS 2SLS bootstrap s.e. (1) (2) (3) Avg. protection 0.47*** 1.00*** 1.00 against expropriation (0.06) (0.22) (3.50) risk Latitude 1.58** (0.71) (1.34) (4.83) Obs Standard errors in parentheses. p < 0.10, p < 0.05, p < 0.01.

19 Excluding influential observations OLS vs IV Regressions of Log GDP per Capita, checking robustness OLS 2SLS 2SLS 2SLS 2SLS bootstrap s.e. bootstrap s.e. 4 obs excl 6 obs excl (1) (2) (3) (4) (5) Avg. protection 0.47*** 1.00*** against expropriation (0.06) (0.22) (3.50) (12.88) (2.43) risk Latitude 1.58** (0.71) (1.34) (4.83) (53.40) (10.54) Obs Standard errors in parenthesis. p < 0.10, p < 0.05, p < 0.01.

20 A finite mixture model (FMM) approach Two regimes ( components ) - rich and poor Each regime is a linear model of the dependent var in its explanatory vars The two regimes are linked by a logit model Regime-sorting is endogenous - can specify vars FMM allows identification of heterogeneity, without having to assign observations into groups a priori.

21 The density function for global income (y) is C π j (z)f j (y x; β j ) (1) j=1 where x represents the explanatory variables (latitude and institutions) and π j is the probability of membership in regime j = rich, poor. It is assumed that 0 < π j < 1 and C j=1 π j = 1. Model estimated by maximum likelihood L = N ln (π j f j (y x; β j ) (2) i=1

22 FMM Results 2SLS vs FMM 2SLS FMM 2SLS FMM Comp. 1 Comp. 2 Comp. 1 Comp. 2 poor rich poor rich (1) (2) (3) (4) (5) (6) Bootstrap s.e. Bootstrap s.e. Bootstrap s.e. Avg. protection 1.00*** *** *** against exprop. (0.22) (0.07) (0.14) (3.50) (0.67) (0.29) risk Latitude *** (1.34) (0.45) (0.83) (4.83) (3.19) (2.10) Prob. of comp.1 (π 1 ) (0.04) (0.04) Obs Standard errors in parentheses. p < 0.10, p < 0.05, p < 0.01.

23 Monte Carlo Simulations - data construction Construct artificial income data using: parameter values from FMM regression actual data on latitude predicted values of institutions a random error term each observation randomly assigned to regime 1 or 2, according to specified probability OLS estimation on simulated data, repeated 2000 times vary probability of regime membership and repeat entire process

24 Simulation results Percentiles of estimated coefficient Power of test β 11 β 12 β 21 β 22 π 1 5th 50th 95th 10% 5%

25 Discussion of results Sensitivity to sample composition FMM results confirm AJR findings - but only for the rich regime AJR methods appear not to explain variation in income across poor countries and those in sub-saharan Africa Latitude is significant predictor of income in the poor regime - not robust Sample size? Lack of variation in latitude - sample predominantly tropical

26 Conclusions Results seem to support idea of non-monotonic effects across regimes AJR may have been premature in discounting the role of geography FMM and Monte Carlo results highlight importance of accounting for bi-modal distribution of income

27 Conclusions - Next steps Incorporation of more variables - esp geography Use of a bigger sample? Dynamic interaction of geography/climate with institutions and income