Causes of Cross-country Income Gaps

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1 Causes of Cross-country Income Gaps Prof. Lutz Hendricks Econ520 January 14, / 24

2 Objectives We start looking into the question: Why are some countries rich and others poor? We think about methods that could be used to answer such questions. 2 / 24

3 Why Are Some Countries Rich and Others Poor? Fact: Rich countries are 25 times richer than poor countries. What do poor countries lack? Some candidates... 3 / 24

4 Methods What methods could be used to answer questions such as: How important is capital for cross-country income differences? Regression analysis (we will look at this one next) Others? 4 / 24

5 Regression Analysis

6 GDP and Capital Stock: 1990 data Log K/L 12 NORCHE 11 SGP DEU AUT AUS FRA BEL FIN DNK ISL CAN JPN NLD ITA SWEUSA LUX ESP NZL GRC CYP ISR GBR HKG 10 BRB ARGHUN KOR PRT IRL ROMBRA VEN MEX GAB DZA 9 ECU IRNFJI CRI CHL MYS URY PERPAN NAM THA ZAF TTO MUS SYC TWN GUY JAM TUN COL BWA TUR 8 COGCPV DOM CHNBOL AGO COM CIV CMR GIN PNG ZWE PHL JOR MARPRY SYR LKA IDNGTM SLV HND EGY TZA ZMB 7 GNB BFA BEN GHA BGD LSO GNQ IND PAK NER NPL MRT KEN CAF SEN MWI MLI HTITGO GMB BDINGA ZAR MDG MOZ RWA SLE 6 ETH 5 UGA Log Y/L 6 / 24

7 Regression Analysis The figure above suggests that output and capital are related by a linear (straight line) relationship. We could postulate the (statistical) model: log(y i /L i ) = α + β log(k i /L i ) + ε i (1) i indexes the country The model "explains" the α + β log(k i /L i ) part of the variation in log(y i /L i ). ε i is the unexplained residual everything we have not modeled. 7 / 24

8 Ordinary Least Squares (OLS) OLS is a method for fitting a line through the data. OLS finds the coefficients (α,β) that minimize the sum of squared residuals. Formally, OLS solves: min α,β i (ε i ) 2 = min (log(y i /L i ) α β log(k i /L i )) 2 (2) i 8 / 24

9 OLS Illustration y x 9 / 24

10 Multiple regression Typically one would add covariates to a regression. The idea is to hold constant other things. The model log(y i /L i ) = α + β log(k i /L i ) + γ k X ik + ε i (3) k X ik is the value of regressor k for country i More compact: log(y/l) = Xβ + ε where Y/L and ε are N 1 vectors and X is an N K matrix Examples: 10 / 24

11 Example Hanushek and Woessmann: The Role of Cognitive Skills in Economic Development 639 Table 2 Education as Determinant of Growth of Income per Capita, Dependent variable: average annual growth rate in GDP per capita, (1) (2) (3) a (4) GDP per capita (4.24) (5.54) (4.43) (6.01) Years of schooling (3.23) (0.34) (0.64) (0.05) Test score (mean) (9.12) (4.96) (4.06) Openness (1.39) Protection against expropriation (2.29) Constant (7.41) (5.54) (3.32) (5.09) N R 2 (adj.) Notes: t-statistics in parentheses. a Regression includes five regional dummies. Source: Hanushek and Woessman (2008) growth in a specification that does not include the measure of cognitive skills, but the associ- America, Middle East and North Africa, Sub-Saharan Africa, and the industrial coun- 11 / 24

12 Reading a Regression Table A made-up example: Y = α + βx + ε (4) = (0.012) (0.45) X + ε (5) Point estimate ˆβ = 2.34: the estimated effect of the regressor on the dependent variable Standard error of ˆβ in parentheses (0.45) what does that mean? R 2 : measure of fit R 2 = 1 [residual sum of squares]/[total sum of squares] fraction of (squared) variation in Y that is explained by the regression 12 / 24

13 Application to capital and output The OLS estimate of β is about 0.5. Log K/L 12 NORCHE 11 SGP DEU AUT AUS FRA BEL FIN DNK ISL CAN JPN NLD ITA SWEUSA LUX ESP NZL GRC CYP ISR GBR HKG 10 BRB ARGHUN KOR PRT IRL ROMBRA VEN MEX GAB DZA 9 ECU IRNFJI CRI CHL MYS URY PERPAN NAM THA ZAF TTO MUS SYC TWN GUY JAM TUN COL BWA TUR 8 COGCPV DOM CHNBOL AGO COM CIV CMR GIN PNG ZWE PHL JOR MARPRY SYR LKA IDNGTM SLV HND EGY TZA ZMB 7 GNB BFA BEN GHA BGD LSO GNQ IND PAK NER NPL MRT KEN CAF SEN MWI MLI HTITGO GMB BDINGA ZAR MDG MOZ RWA SLE 6 ETH 5 UGA Log Y/L Just eyeballing the figure shows: variation in capital "explains" almost the entire variation in Y/L. Are we done? 13 / 24

14 Regression Analysis: Interpretation Issues

15 Interpreting Regression Results Suppose we regress ln(y/l) = α + β ln(k/l) + ε (6) and find β = 0.5 What does β = 0.5 mean in words? What do we learn about the question: By how much would Y/L rise, if we gave a country 10% more K/L? 15 / 24

16 Interpreting Regression Results Key point The OLS regression has nothing to say about this question. Is there an easy way to prove this? 16 / 24

17 Regressions Do Not Answer Causality Questions Proof: I can run the regression in reverse: log(k i /L i ) = ˆα + ˆβ log(y i /L i ) + ˆε i (7) I will get something close to ˆβ = 1/β = 2. Either regression is equally valid. This means the regression says nothing about whether K causes Y or the other way around (or neither). 17 / 24

18 Interpretation issues Fact OLS does nothing more than describe the data. OLS answers the question: If two observations differ by a given x, by how much do their y s differ on average? This has nothing to do with causality. We learn nothing about the question: If Greece increased its K/L by 10%, by how much would Y/L increase? 18 / 24

19 Interpretation Issues Fact No statistical method can answer cause-effect questions. 19 / 24

20 How Can We Answer Cause/Effect Questions? Possible methods: 1. controlled experiments almost never possible in economics 2. natural experiments (see below) these are rare 3. case studies subject to interpretation issues 4. quantitative models 20 / 24

21 Natural Experiments This is as close as we can get to experimental evidence in social sciences. The idea: By a fluke of nature, something varies at random across countries Examples? 21 / 24

22 Summary Statistical methods can describe data (useful). e.g.: capital and output are highly correlated across countries They cannot answer cause-effect questions e.g.: by how much would output rise, if we gave a country more capital? How can we answer cause-effect questions? natural experiments (rare) quantitative models 22 / 24

23 Reading A good reference for econometrics (practical issues and interpretation) is Kennedy (2008). 23 / 24

24 References I Hanushek, E. A. and L. Woessman (2008): The role of cognitive skills in economic development, Journal of Economic Literature, 46, Kennedy, P. (2008): A Guide to Econometrics. 6th edition, Wiley-Blackwell, 6 ed. 24 / 24

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