Advanced Econometrics and Statistics

Transcription

1 Advanced Econometrics and Statistics Bernd Süssmuth IEW Institute for Empirical Research in Economics University of Leipzig January 3, 2011 Bernd Süssmuth (University of Leipzig) Advanced Econometrics January 3, / 15

2 Outline II Macroeconometrics and Time Series Analysis II.2 Methods and Applications: Growth and Financial Markets II.2.1 Growth Accounting and Growth Regressions 1 Solow decomposition and growth accounting 2 Human capital extensions and convergence 3 Growth regressions and extreme bounds analysis (EBA) II.2.2 Productivity and Stochastic Frontier Models II.2.3 Cointegration and error correction models (ECM) Bernd Süssmuth (University of Leipzig) Advanced Econometrics January 3, / 15

3 Contents I 1 Growth Accounting and Growth Regressions The problem of model uncertainty Why an AI Regression usually is not the solution A solution: The Leamer-Levine/Renelt (LLR) EBA-Approach A re ned solution: The Sala-i-Martin (SiM) EBA-Approach Concluding remarks and some practical advise 2 Convergence, Productivity and Stochastic Frontier Models Concepts of classical convergence analysis Bernd Süssmuth (University of Leipzig) Advanced Econometrics January 3, / 15

4 The Problem Barro (1991) surveys substantial no. of potential growth factors Up to mid-1990s cross-country regressions dominate the scene Stylized methodology: γ = α + β 1 x 1 + β 2 x β n x n + ε, where (1) γ economic growth rates, x 1,..., x n vectors of explanatories varying across papers/researchers Problem: growth theories are not explicit enough about what variables x j belong in the true regression Habitually included as a sort of 1 st tier variables : initial level of income, investment rate, education & policy indicators Bernd Süssmuth (University of Leipzig) Advanced Econometrics January 3, / 15

5 Sometimes included sometimes not 2 nd tier variables : market distortions, distortionary taxes, maintenance of property rights, social trust, attitudes towards work, etc. Why no All-Inclusive (AI) -Solution? Ideal statistical world: As N-obs becomes larger ) all variables that do not belong in (1) will show coe s estimates converging to zero However: Sample size may not allow us to include all potential regressors ( AI Regression ) World has only 190 countries (U.S. 50, EU 30 states, etc.) If we consider di erences and levels, we readily go > 50 explanatories Example: Reed s (2009) study of U.S. state growth Bernd Süssmuth (University of Leipzig) Advanced Econometrics January 3, / 15

6 .. Source: Reed (EcInquiry, 2009) Bernd Süssmuth (University of Leipzig) Advanced Econometrics January 3, / 15

7 .. Two additional political controls (levels only): democratic/republican legistlature, democratic governor Bernd Süssmuth (University of Leipzig) Advanced Econometrics January 3, / 15

8 ) An AI-strategy would have to combine = 60 variables ) This makes 2 60 = possible models to check 6= feasible! 1,200,000 1,000, , , , , Variables Bernd Süssmuth (University of Leipzig) Advanced Econometrics January 3, / 15

9 An initial solution: The LLR-EBA-Approach Starting point: Variables z truely correlated w/ growth ( robust )? γ = α j + β yj y + β zj z + β xj x j + ε, where (2) y xed vector of regressors (always included) (L/R: initial income, investm-rate, secondary school enrollmt, pop growth) z variables of interest to be checked for robustness (in total: K such) x j vector consisting of 3 variables (Levine/Renelt) taken from K ) For each model j, we get: bβ zj and bσ b β zj ) How many possible models to check? J = K 3 = K! 3!(K 3)! Bernd Süssmuth (University of Leipzig) Advanced Econometrics January 3, / 15

10 There is an upper/lower EB for critical variable z for each model j bβ zj 2bσ b β zj. A variable is said to be robust in the sense of LLR if for all models J sign (EB L ) = b β zj 2bσ bβzj = sign (EB U ) = b β zj + 2bσ bβzj A variable is said to be fragile in the sense of LLR if sign (EB L ) = b β zj 2bσ bβzj < 0 < sign (EB U ) = b β zj + 2bσ bβzj ) Quite strong and hard to pass a requirement for a variable z ) Fit of models j 6= considered ) Granger/Uhlig: Reasonable EBA Bernd Süssmuth (University of Leipzig) Advanced Econometrics January 3, / 15

11 A re ned solution: The SiM-EBA-Approach Reasonable EBA only considers those models j for which R 2 (1 δ) R 2 max + δr 2 min; (problems: R 2 just one g-o-f measure; choice of δ? arbitrary) Sala-i-Martin considers 134 countries in a way similar to LLR: γ = β 1 x 1 + β 2 x 2 + β 3 x 3 + u, u s i.i.d. 0, σ 2 u x 1 2 X 1 robust variables (always included) (SiM: initial p.c. income, life expectancy, primary school enrollment) x 2 2 X 2 variables in question, x 3 2 X 3 noise variables ( combinors ) Bernd Süssmuth (University of Leipzig) Advanced Econometrics January 3, / 15

12 ) We want to know whether x 2 2 X 1 or x 2 2 X 3? ) Or in other words, whether x 2 is signal or noise? In SiM (AER, 1997): X 3 comprises K 3 = 58 variables, while vector x 3 allows for k 3 3 variables as in L/R out of these 58 However: di erent to LLR, SiM suggests to construct weighted con dence levels : eβ 2 = J j=1 w j bβ 2,j, where eσ b β 2 = J j=1 w j bσ b β 2,j J j=1 w j = 1 are relative likelihood values of models j Bernd Süssmuth (University of Leipzig) Advanced Econometrics January 3, / 15

13 Novel alternative: Bayesian Averaging of Classical Estimates (BACE) (Doppelhofer/Miller/SiM) BACE: no more set of xed var s, exibility in conditioning variables However: BACE needs to pre-specify the no. of explanatory variables likely to be optimal in an economic growth model (problematic!) (additionally, BACE works only for balanced data sets!) In practice I You might combine both approaches (Reed 2009) I Start with an X 1 -set that is as large as possible, and reduce it by throwing out those elements that in fact belong to the noise-set X 3 I Choose your x 2 s from X 1 do so until you checked all variables in X 1 and only robust variables remain in it I During algorithm: Drop unrobust variables altogether! I Remaining issue: initial choice of X 3 Bernd Süssmuth (University of Leipzig) Advanced Econometrics January 3, / 15

14 Convergence, Productivity and Stochastic Frontier Models Concepts of classical convergence analysis Contents I 1 Growth Accounting and Growth Regressions The problem of model uncertainty Why an AI Regression usually is not the solution A solution: The Leamer-Levine/Renelt (LLR) EBA-Approach A re ned solution: The Sala-i-Martin (SiM) EBA-Approach Concluding remarks and some practical advise 2 Convergence, Productivity and Stochastic Frontier Models Concepts of classical convergence analysis Bernd Süssmuth (University of Leipzig) Advanced Econometrics January 3, / 15

15 Convergence, Productivity and Stochastic Frontier Models Concepts of classical convergence analysis Beta-convergence Poor economies tend to grow faster than rich ones Sigma-onvergence Dispersion of cross-country distribution of world income shrinks over time Conditional Beta-onvergence Growth rate i = related to distance that separates it from its own St.St. Note: ln(tfp); Source: Bernard and Jones (REStat, 1996) o denotes U.S.; + denotes Japanese series Bernd Süssmuth (University of Leipzig) Advanced Econometrics January 3, / 15