CH2: Stochastic Trends and Production Parameters CH3: Factor Accumulation and Productivity Growth CH4: Investment and Productivity Determinants
A Comparative Analysis On the Determinants of Bolivia’s Economic Growth: Production Puzzles (Master Thesis’s Chapters 2,3,4)
Carlos A. Mendez Guerra https://sites.google.com/site/carlosmendez777
Graduate School of International Development Nagoya University
Novermber 8th, 2011
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CH2: Stochastic Trends and Production Parameters CH3: Factor Accumulation and Productivity Growth CH4: Investment and Productivity Determinants
Outline
1
Research Progress: What’s new?
2
Stochastic Trends and Production Parameters
3
Factor Accumulation and Productivity Growth
4
Investment and Productivity Determinants
5
Steps ahead
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CH2: Stochastic Trends and Production Parameters CH3: Factor Accumulation and Productivity Growth CH4: Investment and Productivity Determinants
Outline
1
Research Progress: What’s new?
2
Stochastic Trends and Production Parameters
3
Factor Accumulation and Productivity Growth
4
Investment and Productivity Determinants
5
Steps ahead
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CH2: Stochastic Trends and Production Parameters CH3: Factor Accumulation and Productivity Growth CH4: Investment and Productivity Determinants
Research Progress: What is new?
Results update based on new data sets: Extended Penn World Tables V.( 4.0) and Penn World Tables V.(7.0) New comparative analysis over time (46 years) and space (6 countries). New analytical chapters: Chapter 2: Stochastic Trends and Production Function Parameters Chapter 4: Investment and Productivity Determinants
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Motivation Analysis and Results Final Remarks
Outline
1
Research Progress: What’s new?
2
Stochastic Trends and Production Parameters
3
Factor Accumulation and Productivity Growth
4
Investment and Productivity Determinants
5
Steps ahead
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CH2: Stochastic Trends and Production Parameters CH3: Factor Accumulation and Productivity Growth CH4: Investment and Productivity Determinants
Motivation Analysis and Results Final Remarks
Fitting a Geometric Growth Process yt = y0 e gt ⇒ ln(yt ) = ln(y0 ) + gt + ǫ ln(BOLIVIA’s GDP per worker) ln(JAPAN’s GDP per worker) 8.8 8.9 9 9.1 9.5 10 10.5 11
JAPAN: g=2.6%*** R2=0.86;
1960
1970
BOLIVIA: g=−0.07% R2=0.01
1980
1990
2000
2010
Year 95% CI
Fitted values
ln( GDP per worker)
Source: Author’s calculations using data from Penn World Tables V. 7.0 Carlos Mendez (GSID)
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Motivation Analysis and Results Final Remarks
Stochastic Trends and Unit Roots Why a deterministic linear trend is not measurable in the growth process of Bolivia? Stochastic trends, structural breaks, steady state (poverty trap)?
If a stochastic trend is present, is it possible to indentify significant long term relations among macroeconomic variables? If macroeconomic variables like GDP or Investment have a stochastic trend, then shocks to these variables have permanent effects, whereas in traditional business cycle theory the effect of shocks on real GDP would usually be considered only temporary.
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Motivation Analysis and Results Final Remarks
Factor Shares and Production Function Parameters Economists have long studied labor and capital’s share of national income as indicators of income distribution. Data availability of labor’s share has also been seen as offering insights into the shape of the aggregate production function. Generally, studies of developed economies support the longstanding observation (Kaldor Fact) that factors’ shares of national income are relatively constant over time and across countries. However, looking at the data of developing countries, important differences are observable between the generalization of the Kaldor fact and the reported factor shares. Discrepancy: Data vs Common wisdom Carlos Mendez (GSID)
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Motivation Analysis and Results Final Remarks
Is it a ‘Naive’ Calculation of the Capital Share?
Capital Share in National Income Accounts .3 .4 .5 .6 .7 .8
Capital Share = 1 - Labor Share
1963
1973 Nat. Accounts (0.68) Kaldor Fact (1/3)
1983 year
1993
2003
Nat. Accounts HPtrend (0.68)
Source: Author’s calculations using data from the United Nations Data Base, Bolivia’s National Accounts Main Aggregates Carlos Mendez (GSID)
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Motivation Analysis and Results Final Remarks
Reseach Questions
1
Do the main production aggregates of the Bolivian economy contain stochastic trends? If so , is it possible to identify long term relationships among them ?
2
Considering the noticiable difference between the conventional wisdom and the ‘naive’ capital share , what other estimates of factor shares can be considered to understand the distribution of income between capital and labor in Bolivia?
3
How can the Bolivian economy be characterized in terms of returns to scale and the degree of substitution between capital and labor?
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Motivation Analysis and Results Final Remarks
A First Look at the Data
Levels
GDP (Output) Capital Stock Labor Output/Labor Capital/Labor Output/Capital Capital/Output Investment/Labor
Growth Rates
Mean
Std. Dev.
Min
Max
Mean
Std. Dev.
2.0E+10 1.9E+10 2.6.E+06 7,559 7,646 1.00 1.01 999
6.6E+09 4.8E+09 8.4.E+05 634 1,085 0.12 0.12 251
1.1E+10 1.2E+10 1.5.E+06 6,481 5,774 0.85 0.79 569
3.6E+10 3.0E+10 4.4.E+06 8,889 9,670 1.26 1.18 1,641
2.69 2.12 2.37 0.32 -0.24 0.57 -0.56 -0.19
3.96 3.30 0.38 3.93 3.33 4.31 4.30 20.42
Min
Max
-14.95 -4.95 0.83 -16.80 -7.47 -18.23 -8.54 -56.17
8.16 11.54 3.04 6.33 8.96 8.43 17.72 47.04
Source: Author’s calculations using data from Extended Penn World Tables V. 4.0
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Motivation Analysis and Results Final Remarks
23
log(GDP) 23.5 24
GDP growth rate −15 −10 −5 0 5 10
24.5
CH2: Stochastic Trends and Production Parameters CH3: Factor Accumulation and Productivity Growth CH4: Investment and Productivity Determinants
1963
1973
1983
1993
2003
1963
1973
1983
1993
2003
1993
2003
year
−5
Capital growth rate 0 5 10 15
log(Capital Stock) 23.223.423.623.8 24 24.2
year
1963
1973
1983
1993
2003
1963
1973
1983
year
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Motivation Analysis and Results Final Remarks
8.6
log(Capital/Labor) 8.8 9 9.2
Capital/Labor growth rate −10 −5 0 5 10
CH2: Stochastic Trends and Production Parameters CH3: Factor Accumulation and Productivity Growth CH4: Investment and Productivity Determinants
1963
1973
1983
1993
2003
1963
1973
1983
1993
2003
1993
2003
year
log(Output/Capital) −.2 −.1 0 .1 .2
Output/Capital growth rate −20 −10 0 10
year
1963
1973
1983
1993
2003
1963
1973
1983
year
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Motivation Analysis and Results Final Remarks
log(Capital/Output) −.2 −.1 0 .1 .2
Capital/Output growth rate −10 0 10 20
CH2: Stochastic Trends and Production Parameters CH3: Factor Accumulation and Productivity Growth CH4: Investment and Productivity Determinants
1963
1973
1983
1993
2003
1963
1973
1983
1973
1983
1993
2003
Investment/Labor growth rate −60 −40 −20 0 20 40
1963
1993
2003
1993
2003
year
log(Investment Labor) 6.4 6.6 6.8 7 7.2 7.4
year
1963
1973
1983
year
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Motivation Analysis and Results Final Remarks
Unit Root Tests ∆yt = α + βyt−1 + δt +
k X
ζj ∆yt−j + ǫt
j=1
Ho : There is a Stochastic Trend Ho*: There is not a Stochastic Trend Unit Root Tests GDP (Output) Capital Stock Labor Output/Labor Capital/Labor Output/Capital Capital /Output Investment/Labor
ADF Not Reject Not Reject Not Reject Not Reject Not Reject Not Reject Not Reject Not Reject
PP Not Reject Not Reject Not Reject Not Reject Not Reject Not Reject Not Reject Not Reject
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DF-GLS Not Reject Not Reject Not Reject Not Reject Not Reject Not Reject Not Reject Not Reject
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KPSS* Reject Ho* Reject Ho* Reject Ho* Reject Ho* Reject Ho* Reject Ho* Reject Ho* Reject Ho*
Not Not Not Not Not Not Not Not
ZA Reject Reject Reject Reject Reject Reject Reject Reject
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Motivation Analysis and Results Final Remarks
Cointegration Analysis Ho: The series are not cointegrated. H1: The series are cointegrated (Share the same stochastic trend). b ǫt = ln(
K Y ) − β1 ln( ) − β0 L L
∆b ǫt = γb ǫt−1 +
k X
ζj ∆b ǫt−j + vt
j=1
Engle-Granger 1st-step regression Dependent Variable: Ln(Output/Labor) t-stat
P-value
Ln(K/L) 0.32 0.07 4.35 Constant 6.10 0.65 9.38 Augmented Engle-Granger test for cointegration Number of lags = 5 Test 1% Critical Statistic Value
Coef.
Std. Err.
0.00 0.00
Z(t) -3.383 -3.585 Critical values from MacKinnon (1990, 2010)
5% Critical Value
95% CI 0.17 4.79
0.46 7.41
N (test) = 40 10%Critical Value
-2.928
-2.602
Reject Ho at 5% of significance ⇒ The series share the same stochastic trend Carlos Mendez (GSID)
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Motivation Analysis and Results Final Remarks
Cointegration Analysis Ho: The series are not cointegrated. H1: The series are cointegrated (Share the same stochastic trends). b ǫt = ln(Y ) − β1 ln(K ) − β2 ln(L) − β0 Johansen test for cointegration Trend: constant Sample: 1968-2008 Maximum Rank Parms LL Eigenvalue 0 39 361.39 . 1 44 373.67 0.45 2 47 380.48 0.28 3 48 381.53 0.05
Number of obs = 41 Lags = 5 Trace 5% Critical Statistic Value 40.27 29.68 15.71 15.41 2.09* 3.76
Reject Ho at 5% of significance ⇒ The series share the same stochastic trend. Carlos Mendez (GSID)
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CH2: Stochastic Trends and Production Parameters CH3: Factor Accumulation and Productivity Growth CH4: Investment and Productivity Determinants
Motivation Analysis and Results Final Remarks
Cobb-Douglas Production Function A Cobb-Douglass Production Function: Y = AK α L1−α ; ∀ 0 ≤ α ≤ 1 Linearization of Equation 1: Ln(Y ) = Ln(A) + αLn(K ) + (1 − α)L Econometric Model: Ln(Y ) = Ln(A) + αLn(K ) + (1 − α)L + ǫ Econometric Problems: 1
Spurious regression due to stochastic trends
2
Autocorrelation Carlos Mendez (GSID)
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Motivation Analysis and Results Final Remarks
Estimation of the Cobb-Douglas Function Dependent Variable: Ln GDP Initial Newey-West Base Stand. Err. (1) (2) Capital Share Labor Share Tech. Change Number of Observations Autocorrelation Analysis Durbin-Watson statistic Breusch-Godfrey statistic Breusch-Godfrey test (p-value) White noise test statistic White noise test (p-value) Number of Autocorrelations
First Differences (3)
PW-CO GLS (4)
0.5358*** (0.0917) 0.5410*** (0.0500) 0.0015 (0.0011) 46
0.5358*** (0.1256) 0.5410*** (0.0685) 0.0016 (0.0012) 46
0.3845** (0.1738 ) 1.1861 (1.5399) 0.0000 (0.0000) 45
0.4293*** (0.1545) 0.6229*** (0.1297) 0.0022 (0.0016) 46
0.3552 31.7260 0.0000 125.0869 0.0000 2.0000
0.3552 na. na.
1.82116 0.358 0.5498 19.0795 0.5167 0
1.674114 na na
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Motivation Analysis and Results Final Remarks
Hypothesis Testing under The Cobb-Douglas Production Function
Capital Share Labor Share Tech. Change Constant Number of Observations Hypothesis Testing Ho: Constant Returns to Scale Ho: Capital share =1/3 Ho: Capital share =0.68
Dependent Variable: Ln GDP Cointegration Newey-West PW-CO Engle-Granger Stand. Err. GLS (0) (2) (4) 0.3163*** 0.5358*** 0.4293*** (0.1131) (0.1256) (0.1545) 0.5410*** 0.6229*** (0.0685) (0.1297) 0.0016 0.0022 (0.0012) (0.0016) 6.1015*** (1.0096) 46 46 46 Not Applicable Not Rejected Rejected
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Not Rejected Not Rejected Not Rejected
Not Rejected Not Rejected Not Rejected
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Constrained ks + ls = 1 (5) 0.4611*** (0.0425) 0.5389*** (0.0425) 0.0024 (0.0001)
(6) 0.3163*** (0.0618) 0.6836*** (0.0618)
46
6.1014*** (0.5509) 46
Constrained Rejected Rejected
Constrained Not Rejected Rejected
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Motivation Analysis and Results Final Remarks
CES Production Function A Constant Elasticity of Substitution (CES) production function: y = γe λt [δK −ρ + (1 − δ)L−ρ ]
− νρ
Parameters: γ: Productivity λ: Technological Change δ: Capital Share ρ: Substituion ν: Returns to scale σ 1+ρ
: Elasticity of substitution
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Motivation Analysis and Results Final Remarks
Estimation of the CES Production Function As the CES function is non-linear in parameters and cannot be linearised analytically, it is not possible to estimate it with the usual linear estimation techniques. It can be estimated by non-linear least-squares using different optimization algorithms: Gradient-based optimisation Parameter γ λ δ ρ ν Elasticity Convergence
Global Op.
Constraint Parameters
LM
Conj.
Newton
BFGS
N-M
L-BFGS-B
PORT
0.0000 0.0106 0.8906 0.1349 0.7375 0.88 No
0.0000 0.0150 0.5000 0.2500 1.0000 0.80 Yes
475.6000 0.0033 0.2468 -0.1264 0.9721 1.15 No
0.00 -0.99 0.50 0.25 0.99 0.80 Yes
0.0400 -0.0850 0.5400 0.2900 1.0400 0.78 Yes
0.0000 -0.0960 0.5000 0.2503 1.0000 0.80 No
0.0000 -0.9850 0.4968 0.2530 0.9913 0.80 Yes
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A Summary of Factor Shares Estimates for Bolivia .32
Constrained Regression Estimation (No Trend)
.68 .33
Bernanke and Gurkaynak (2001)
.67 .33
Kaldor Fact
.67 .43
PW−CO GLS Regression Estimation
.62 .46
Constrained Regression Estimation (No Constant)
.54 .51 .49
CES Production Function Estimation
.54 .54
HAC Errors Regression Estimation
.68
National Accounts(Hptrend)
.32
0
.2
.4 Capital
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.6
.8 Labor
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Motivation Analysis and Results Final Remarks
The Capital Share: A Comparative View
Bolivia
N.Acc BG(2001) PW−CO
Chile
N.Acc BG(2001) PW−CO
Indonesia
N.Acc BG(2001) PW−CO
Japan
N.Acc BG(2001) PW−CO
Korea
N.Acc BG(2001) PW−CO
Peru
.68 .33 .39 .62 .41 .58
.43 .48 .32 .62 .6 .35 .56
N.Acc BG(2001) PW−CO
.69 .44 .55
0
.2
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.8 24/69
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Motivation Analysis and Results Final Remarks
Summary of Main Findings The main production aggregates of the Bolivian economy seem to contain stochastic trends. Therefore, shocks to these variables might have permanent effects. It is possible to identify a significant and not spurious relationship among GDP, capital and labor. Cointegration techniques are useful to understand the long term value of the capital share. They seem to support the Kaldor fact that around 1/3 of the national income correspond to capital gains. Labor share in national income increases drastically once the rents of the non-corporate and self-employed labor are accounted. The Bolivian economy might be characterized in terms of constant returns to scale in production, and low degree of substitution between capital and labor. Carlos Mendez (GSID)
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Motivation Analysis and Results Final Remarks
Outline
1
Research Progress: What’s new?
2
Stochastic Trends and Production Parameters
3
Factor Accumulation and Productivity Growth
4
Investment and Productivity Determinants
5
Steps ahead
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Motivation Analysis and Results Final Remarks
Ouput / Labor Ratio (GDP per worker ) 6500 7500 8500 9500
The Need of Growth Accounting Development Paradigm: Capitalism of State
1963
1968
1973
Neo−Liberalism
1978
1983
1988
1993
1998
Indigenous Socialism
2003
2008
(Ouput / Labor) Growth Rate −15 −10 −5 0 5
Period: I
II
III
National Revolution Sequel
Oil Boom and Debt Crisis
Washington Consensus
1963
1968
1973
1978
IV
Hyper−Inflation and
1983
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1993
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1998
Re− Distribution
2003
2008
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Motivation Analysis and Results Final Remarks
Reseach Questions
1
What is the relative contribution of capital stock, labor and productivity to GDP growth in Bolivia?
2
How is the behavior of Factor Accumulation (FA) and Total Factor Productivity (TFP) in each of the development paradigms and historical periods of Bolivia?
3
What is the contribution of Human Capital improvements in the process of economic growth in Bolivia?
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3.5
Evolution of GDP, Capital and Labor
Index 1963 =1 2 2.5
3
Period IV
Period III
Period II
1
1.5
Period I
1963
1968
1973
1978
1983
GDP Index Labor Stock Index Carlos Mendez (GSID)
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Capital Stock Index Productivity Puzzles
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The Growth Accounting Framework A Cobb-Douglass Production Function: Y = AK α L1−α ; ∀ 0 ≤ α ≤ 1
(1)
Linearization of Equation 1: Ln(Y ) = Ln(A) + αLn(K ) + (1 − α)L Differentiating the previous equation respect to time, we obtain a Growth Function in terms of the growth of inputs : dLn(Y ) dLn(A) dLn(K ) dLn(L) A˙ K˙ L˙ = +α +(1−α) = +α +(1−α) dt dt dt dt A K L Y˙ A˙ K˙ L˙ = + α + (1 − α) Y A K L Carlos Mendez (GSID)
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The Debate on the Capital Share
.32
Constrained Regression Estimation (No Trend)
.68 .33
Bernanke and Gurkaynak (2001)
.67 .33
Kaldor Fact
.67 .43
PW−CO GLS Regression Estimation
.62 .46
Constrained Regression Estimation (No Constant)
.54 .51 .49
CES Production Function Estimation
.54 .54
HAC Errors Regression Estimation
.68
National Accounts(Hptrend)
.32
0
.2
.4 Capital
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.8 Labor
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Motivation Analysis and Results Final Remarks
−15
−10
Growth Rate −5 0
5
10
Factor Accumulation Growth
1963
1973
1983 year
GDP Growth Rate FA2 (ks=0.33) FA4 (ks=0.43) FA6 (ks=0.51) Carlos Mendez (GSID)
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FA1 (ks=0.68) FA3 (ks=0.32) FA5 (ks=0.46) FA7 (ks=0.54) Productivity Puzzles
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Motivation Analysis and Results Final Remarks
−20
Growth Rate −10 0
10
Productivity Growth
1963
1973
1983 year
GDP Growth Rate TFP2 (ks=0.33) TFP4 (ks=0.43) TFP6 (ks=0.51) Carlos Mendez (GSID)
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TFP1 (ks=0.68) TFP3 (ks=0.32) TFP5 (ks=0.46) TFP7 (ks=0.54) Productivity Puzzles
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Motivation Analysis and Results Final Remarks
−4
−2
Growth Rate 0 2
4
6
Growth Determinants: Capital, Labor and Productivity
1963
1973
1983 year
GDP Growth trend, HP corrected LC3trend,(ks=0.32)
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6
FA
TFP
−4
−2
Growth Rate 0 2
GDP
4
Growth Trends: GDP, FA and TFP
1963
1973
1983 year
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Motivation Analysis and Results Final Remarks
.9 1.4 1.9 2.4 2.9 3.4 3.9 4.4
Growth Accounting (ks=0.32) 1.87
.46
.54
1.37
1.72
.43
1.88
1.61
1.5
1.01 .62
.69
.68
1985−2002
2003−2008
1963−2008
−.6 −.1 .4
.47
−.58
1963−1973
1974−1984 Capital
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TFP 36/69
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Motivation Analysis and Results Final Remarks
Growth Accounting ks=0.68 (1) GDP TFP K L
2.69 0.49 1.44 0.76
GDP TFP K L
2.96 0.18 2.14 0.65
GDP TFP K L
1.31 -0.40 1.01 0.71
ks=0.33 (2)
ks=0.32 ks=0.43 ks=0.46 ks=0.51 (3) (4) (5) (6) Total Sample: 1963-2008 2.69 2.69 2.69 2.69 2.69 0.40 0.43 0.43 0.43 0.45 0.70 0.68 0.91 0.98 1.08 1.59 1.61 1.35 1.28 1.16 PERIOD I : National Revolution Sequel (1963-1973) 2.96 2.96 2.96 2.96 2.96 0.57 0.46 0.46 0.43 0.37 1.04 1.01 1.35 1.45 1.61 1.35 1.37 1.15 1.09 0.99 PERIOD II : Oil Boom and Debt Crisis (1974-1984) 1.31 1.31 1.31 1.31 1.31 -0.66 -0.58 -0.58 -0.56 -0.52 0.49 0.47 0.64 0.68 0.76 1.48 1.50 1.26 1.19 1.08
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ks=0.54 (7) 2.69 0.45 1.15 1.09 2.96 0.33 1.70 0.93 1.31 -0.50 0.80 1.02
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Motivation Analysis and Results Final Remarks
Growth Accounting
GDP TFP K L GDP TFP K L
ks=0.68 ks=0.33 ks=0.32 ks=0.43 ks=0.46 ks=0.51 ks=0.54 (1) (2) (3) (4) (5) (6) (7) PERIOD III: Hyper-Inflation and Washington Consensus (1985-2002) 2.82 2.82 2.82 2.82 2.82 2.82 2.82 0.69 0.49 0.54 0.54 0.56 0.59 0.61 1.32 0.64 0.62 0.83 0.89 0.99 1.04 0.81 1.69 1.72 1.44 1.37 1.24 1.16 PERIOD IV : Social Revolution (2003-2008) 4.37 4.37 4.37 4.37 4.37 4.37 4.37 2.02 1.81 1.87 1.87 1.88 1.91 1.93 1.47 0.72 0.69 0.93 1.00 1.11 1.17 0.88 1.85 1.88 1.57 1.49 1.35 1.27
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Motivation Analysis and Results Final Remarks
10 8 6 4 2
Schooling, Secondary Complete, S>25
Index (1963=1) 0
Average Years of Schooling (Adult Population, S>25)
Human Capital Improvements
1963
1968
1973
1978
1983
1988
1993
1998
2003
2008
Source: Author’s calculations using data from Barro and Lee(2011) Carlos Mendez (GSID)
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Motivation Analysis and Results Final Remarks
Introducing Human Capital to the Growth Accounting Framework An extended Cobb-Douglass Production Function: Y = AK α (HL)1−α ; ∀ 0 ≤ α ≤ 1
(3)
Linearization of Equation 3: Ln(Y ) = Ln(A) + αLn(K ) + (1 − α)L + (1 − α)H Differentiating the previous equation respect to time, we obtain an extended Growth Function in terms of the growth of inputs : dLn(A) dLn(K ) dLn(L) dLn(H) dLn(Y ) = +α + (1 − α) + (1 − α) dt dt dt dt dt Y˙ A˙ K˙ L˙ H˙ = + α + (1 − α) + (1 − α) Y A K L H
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Motivation Analysis and Results Final Remarks
Growth Accounting with Human Capital (ks=0.32) 1.82
1.82
1.82
1.82
4
1.82
1.37
1.88
1.72
1.61
2
1.5
1.01 .69
.62
.68
0
.47
−.02
−1.23
−1.34
−2
−1.42
−2.48
1963−1973 Capital
1974−1984
1985−2002
2003−2008
Labor
Human Capital
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1963−2008 TFP
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Motivation Analysis and Results Final Remarks
Growth Accounting with Human Capital ks=0.68 (1) GDP TFP K L H
2.69 -0.37 1.44 0.76 0.86
GDP TFP K L H
2.96 -0.68 2.14 0.65 0.86
GDP TFP K L H
1.31 -1.26 1.01 0.71 0.86
ks=0.33 (2)
ks=0.32 ks=0.43 ks=0.46 ks=0.51 (3) (4) (5) (6) Total Sample: 1963-2008 2.69 2.69 2.69 2.69 2.69 -1.39 -1.42 -1.10 -1.01 -0.86 0.70 0.68 0.91 0.98 1.08 1.59 1.61 1.35 1.28 1.16 1.79 1.82 1.52 1.44 1.31 PERIOD I : National Revolution Sequel (1963-1973) 2.96 2.96 2.96 2.96 2.96 -1.22 -1.23 -1.06 -1.02 -0.94 1.04 1.01 1.35 1.45 1.61 1.35 1.37 1.15 1.09 0.99 1.79 1.82 1.52 1.44 1.31 PERIOD II : Oil Boom and Debt Crisis (1974-1984) 1.31 1.31 1.31 1.31 1.31 -2.45 -2.48 -2.11 -2.00 -1.83 0.49 0.47 0.64 0.68 0.76 1.48 1.50 1.26 1.19 1.08 1.79 1.82 1.52 1.44 1.31 Carlos Mendez (GSID)
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ks=0.54 (7) 2.69 -0.78 1.15 1.09 1.23 2.96 -0.89 1.70 0.93 1.23 1.31 -1.73 0.80 1.02 1.23 42/69
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Motivation Analysis and Results Final Remarks
Growth Accounting with Human Capital
GDP TFP K L H GDP TFP K L H
ks=0.68 ks=0.33 ks=0.32 ks=0.43 ks=0.46 ks=0.51 ks=0.54 (1) (2) (3) (4) (5) (6) (7) PERIOD III: Hyper-Inflation and Washington Consensus (1985-2002) 2.82 2.82 2.82 2.82 2.82 2.82 2.82 -0.16 -1.31 -1.34 -0.98 -0.88 -0.72 -0.62 1.32 0.64 0.62 0.83 0.89 0.99 1.04 0.81 1.69 1.72 1.44 1.37 1.24 1.16 0.86 1.79 1.82 1.52 1.44 1.31 1.23 PERIOD IV : Social Revolution (2003-2008) 4.37 4.37 4.37 4.37 4.37 4.37 4.37 1.16 0.02 -0.02 0.34 0.44 0.61 0.70 1.47 0.72 0.69 0.93 1.00 1.11 1.17 0.88 1.85 1.88 1.57 1.49 1.35 1.27 0.86 1.79 1.82 1.52 1.44 1.31 1.23
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Motivation Analysis and Results Final Remarks
Summary of Main Findings From 1963 to 2008 factor accumulation, specially physical capital, has been the main determinant of economic growth in Bolivia. The trend of TFP is extremely volatile across different measures of the capital share, and shows a clear cyclical behavior. The behavior of TPF and Factor Accumulation has been similar before the hyper-inflation period but not after it. The institutional reforms after the hyper-inflation period promoted capital accumulation but not TFP growth. Human Capital improvements (exponential growth) might account up to 52% of total growth. However, this value can be questionable if human capital improvements are measured in terms of outcomes rather than inputs. Carlos Mendez (GSID)
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Motivation Analysis and Results Final Remarks
Outline
1
Research Progress: What’s new?
2
Stochastic Trends and Production Parameters
3
Factor Accumulation and Productivity Growth
4
Investment and Productivity Determinants
5
Steps ahead
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Motivation Analysis and Results Final Remarks
−60
−40
Growth Rate −20 0
20
40
Capital is important, but what happened the K/L ratio?
1963
1973
1983 year
1993
2003
Investment per Worker Growth Rate Capital−Labor Ratio Growth Rate
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Motivation Analysis and Results Final Remarks
90
TFP Level(1963=100) 100 110
120
TFP behaviour in Bolivia
1963
1973
1983 year
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1993
Productivity Puzzles
2003
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Reseach Questions
1
Why investment does not seen to increase the capital-labor growth rate?
2
What factors can be indentified in order to explain the behavior of the TFP in Bolivia?
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Motivation Analysis and Results Final Remarks
22.5
Aggregate Investment
Period IV Period III Log (Investment) 21.5 22
Period II
21
Period I
1963
1968
1973
1978
1983
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1998
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2003
2008
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−5
0
GDP Share 5 10
15
20
Investment Share
Period I 1963
1968
Period III
Period II 1973
1978
1983
1988
1993
Period IV 1998
2003
2008
Investment Share FDI Share
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Motivation Analysis and Results Final Remarks
The Accelerator Model The ‘basic’ accelerator model: Kt∗ = µYt
(5)
Where Y is real GDP and µ is the fixed capital/output ratio. According to 5, not only does the optimal capital stock Kt∗ bear a fixed factor of proportionality to output, but the capital stock is always optimally adjusted in each time period, implying that Kt∗ = Kt and therefore that net investment Int equals: Int = Kt − Kt−1 = µ(Yt − Yt−1 )
(6)
Empirically equation 6 has not fared well do to the restrictive instantaneous adjustment assumption. Carlos Mendez (GSID)
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Motivation Analysis and Results Final Remarks
The Flexible Accelerator Model Relaxing the assumption of instantaneous adjustment, Koyck (1954) proposed a ‘flexible’ version of the accelerator model which emphasized the adjustment costs of investment: Int = λ(Kt∗ − Kt−1 ) = µ(Yt − Yt−1 )
(7)
where λ denotes the partial adjustment coefficient. Substituting equation 5 into equation 7 yields: Int = Kt − Kt−1 = λµYt − λKt−1
(8)
Kt = µλYt + (1 − λ)Kt−1
(9)
or
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Motivation Analysis and Results Final Remarks
Towards an Empirical Implementation of the Flexible Accelerator Model The investment equation 8 is in terms of net investment. Assuming a constant depreciation rate δ, one can add replacement investment δKt−1 to both sides of equation 8 and obtain the gross investment formulation: It = Kt − (1 − δ)Kt−1 = λµYt + (δ − λ)Kt−1
(10)
Econometric Models: It = α + λµYt + (δ − λ)Kt−1 + ǫt It = α +
m−1 X
βi Yt−i + βk Kt−1 + ǫt
(11) (12)
j=0 Carlos Mendez (GSID)
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CH2: Stochastic Trends and Production Parameters CH3: Factor Accumulation and Productivity Growth CH4: Investment and Productivity Determinants
Motivation Analysis and Results Final Remarks
Estimations of the Flexible Accelerator Model
Coefficients β0 = λµ βk = δ − λ
Dependent variable: Gross Investment Model (1) Newey-West PW-CO PW-CO Stand. Err. GLS GLS (2) (3) (4) 0.16*** 0.21*** 0.20* (0.04) (0.05) (0.11) -0.09 -0.16*** -0.17** (0.06) (0.07) (0.08) 0.02 (0.13)
Basic OLS (1) 0.16*** (0.03) -0.09** (0.05)
β1
Model (2) PW-CO GLS (5) 0.16 (0.12) -0.20** (0.10) -0.01 (0.14) 0.10 (0.14)
1.5e+09** (6.7e+08) 0.4 45
1.5e+09** (7.4e+08) 0.39 44
PW-CO GLS (6) 0.16 (0.13) -0.21** (0.10) -0.02 (0.15) 0.09 (0.15) 0.02 (0.14) 1.6e+09** (7.9e+08) 0.39 43
0.20* 0.28**
0.16 0.31**
0.16 0.32**
β2 β3 α R2 N
λβ0 λβk
1.1e+09*** (3.8e+08) 0.63 45
0.16*** 0.20**
1.1e+09*** (3.8e+08) na 45
1.4e+09** (6.4e+08) 0.42 45
Implied Ajustment µ = 1.01 δ = 0.11 0.16*** 0.21*** 0.20 0.27***
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CH2: Stochastic Trends and Production Parameters CH3: Factor Accumulation and Productivity Growth CH4: Investment and Productivity Determinants
Motivation Analysis and Results Final Remarks
The Accelerator Principle in the Harrod-Domar Model Set up of the Harrod-Domar Model: Y = cK dY dY Y MPK = =c⇒ = dK dK K f (0) = 0
(13) (14) (15)
I = S = sY
(16)
∆K = I − δK
(17)
Operationalization : Taking logarithm and differentiating equation 13 respect to time, we obtain: dLn(c) dLn(K ) dLn(Y ) = + dt dt dt ∆Y ∆K =0+ (18) Y K Equilibrium :Replacing equation 18 into 17 we obtain: Y ∆Y +δ =s = sMPK Y K Carlos Mendez (GSID)
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(19)
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Motivation Analysis and Results Final Remarks
Estimating the Harrod-Dommar model: Low Savings Rate ⇒ Low Growth Dependent Variable: GDP growth + Depreciation rate Basic Newey-West PW-CO Coefficients OLS Stand. Err. GLS (1) (2) (3) Savings Rate 13.81*** 13.81** 14.99*** (4.70) (5.44) (5.37) Constant -0.17 -0.17 -1.34 (4.73) (5.82) (5.41) R2 0.17 na. 0.16 N 44 44 44
Actual average Investment Share = 13.15% The actual investment (saving) rate is consistent with the Bolivian growth proces ⇒ An investment (saving) rate of 13% might no be enough to produce higher growth in the Bolivian case. Carlos Mendez (GSID)
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Motivation Analysis and Results Final Remarks
The Marginal Product of Capital (MPK)
Why the investment rate is low? Ho: Because the return of investment (MPK) is low Let’s go back again to the Harrod-Domar model: ∆Y Y + δ = s = sMPK Y K Low savings rate s ⇒ Low Growth
∆Y Y
Low return to investment (MPK) ⇒ Low Growth
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∆Y Y
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Motivation Analysis and Results Final Remarks
An attempt to estimate the MPK for Bolivia
∆Y Y + δ = s = sMPK Y K Dependent Variable: GDP growth + Depreciation rate Basic Newey-West PW-CO Coefficients OLS Stand. Err. GLS (1) (2) (3) MPK 0.08 0.08 0.06 (0.22) (0.27) (0.24) Constant -12.60*** -12.60*** -12.86*** (2.95) (3.99) (3.21)
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Understanding the MPK
A Cobb-Douglass Production Function: Y = AK α L1−α ; ∀ 0 ≤ α ≤ 1
(20)
One sector model: MPK = αAK α−1 L1−α = α Multisector model: MPK = α
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Y K
Py Y Pk K
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(21)
(22)
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Calculating the MPK for Bolivia Based on Caselli and Ferrer (2005) data: Initial Parameters Total Capital Share 0.33 Reproducible Capital Share 0.08 Py/Pk 0.60 Marginal Product of Capital (MPK) One Sector Multi Sector Total 0.31 0.08 Reproducible 0.19 0.05
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The Marginal Product of Capital (MPK) a Comparative View
Bolivia Chile Peru Singapore Botswana
αT 0.33 0.41 0.44 0.47 0.55
αR 0.08 0.16 0.22 0.38 0.33
Py/Pk 0.60 0.90 0.89 1.19 0.66
MPK(T1) 0.31 0.26 0.20 0.15 0.36
MPK(Tm) 0.19 0.24 0.18 0.18 0.24
MPK(R1) 0.08 0.10 0.10 0.12 0.22
MPK(Rm) 0.05 0.09 0.09 0.14 0.14
Source: Caselli and Freirer (2005)
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Motivation Analysis and Results Final Remarks
Determinants of Total Factor Productivity Analytical Famework: TFP=f(Cyclical variables, Policies, Institutions, Initial Conditions) Explanatory variables for TFP: 1
Terms of Trade (+ or -)
2
Real exchange rate appreciation (-)
3
Macroeconomic Instability (-)
4
Government Debt (-)
5
Civil liberties (+)
6
Democracy (+) Carlos Mendez (GSID)
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Motivation Analysis and Results Final Remarks
Variables for TFP analysis 1 .6 .4 .2 0
−100 1980 1990 2000 2010 .
1980 1990 2000 2010 .
Democracy Level
4
. 3.8
2.5
3.4
3
3.6
. 3.5
4
4.5
Civil Liberties 4.2
250 200 . 150 100 50
.
. 0 −50
0 −.2 1980 1990 2000 2010 .
Gov. Debt/GDP
1980 1990 2000 2010 .
Macro Instability .8
50
.6 .2 . .4
110 . 100 90 1980 1990 2000 2010 .
REER Apreciation 100
Terms of Trade (log) .8
120
TFP
1980 1990 2000 2010 .
Carlos Mendez (GSID)
1980 1990 2000 2010 .
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Motivation Analysis and Results Final Remarks
Econometric Implementation: ARDL Model Based on Fuentes, Larrain and Schmidt Hebbel (2006): ln(TFP)t = Ω(L)Xt + Θ(L)ln(TFP)t + ǫt
(23)
Where L is the lag operator, Ω(L) and Θ(L) are lag polynomials, and X is the vector of explanatory variables presented previously. The estimation strategy of equation 23 follows the general-to-particular approach (Hendry, 1995). Since the dynamic structure in the relation between TFP and the explanatory variables is unknown, the estimation uses contemporary and lagged values of the independent variables and lagged values of the dependent variable (the logarithm of the TFP index, ln(TFP)). Carlos Mendez (GSID)
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Motivation Analysis and Results Final Remarks
Estimation of the Determinants of TFP Dependendt Variable: Ln(TFP) with ks=0.32 Ln(TFP) with ks=0.68 (1) (2) (3) (4) (5) (6) Cyclical Variables Terms of Trade Terms of Trade (t-1) REER appreciation REER appreciation (t-1) Policies Macro.Instability (t-1) Government Debt Institutions Civil liberties (t-2)
0.1060*** (0.0335) -0.1072** (0.0447) -0.0001 (0.0004) -0.0002 (0.0003)
0.1060*** (0.0333) -0.1068** (0.0453) -0.0001 (0.0001) -0.0002 (0.0001)
0.1143*** (0.0356) -0.1059** (0.0436) -0.0001 (0.0001) -0.0002 (0.0001)
0.1251** (0.0582) -0.1433** (0.0657) -0.0003* (0.0004) -0.0002 (0.0004)
0.1259** (0.0595) -0.1408** (0.0671) -0.0002* (0.0001) -0.0002 (0.0002)
0.1342** (0.0619) -0.1420** (0.0679) -0.0002* (0.0001) -0.0002 (0.0002)
-0.0522* (0.0285) -0.00002 (0.0003)
-0.0532** (0.0195)
-0.0515*** (0.0175)
-0.0379 (0.0300) -0.00009 (0.0004)
-0.0430* (0.0234)
-0.0433* (0.0228)
0.0403*** (0.0131)
0.0400*** (0.0120)
0.0433* (0.0207)
0.0406* (0.0148)
Democracy (t-2) Initial Conditions TFP (t-1) Constant Adjusted R squared SER
0.0250*** (0.0056) 0.7922*** 0.7965*** (0.0766) (0.0575) 0.8121** 0.7918** (0.3734) (0.2856) 0.9493 0.9519 0.0054 0.0054 Carlos Mendez (GSID)
0.7852*** 0.7968** (0.0603) (0.0948) 0.9007*** 0.7906* (0.2811) (0.4202) 0.9590 0.9413 0.0046 0.0092 Productivity Puzzles
0.0216*** (0.0074) 0.8118*** (0.0613) 0.7245** (0.2851) 0.9437 0.0093
0.7943*** (0.0664) 0.8809*** (0.2972) 0.9456 0.0090 65/69
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Motivation Analysis and Results Final Remarks
Summary of Main Findings
Investment does not seen to increase the capital-labor growth rate because of the following reasons: 1 2 3 4
Investment is volatile and unstable. Adjustment costs are high. Investment rate is still low to sustain positive growth. Return to investment is low.
Productivity in Bolivia can be significantly explained by cyclical variables, stabilization policies, participatory institutions, and favorable initial conditions. Terms of trade improvements significantly affect productivity, but the direction of the total effect is not clear.
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Outline
1
Research Progress: What’s new?
2
Stochastic Trends and Production Parameters
3
Factor Accumulation and Productivity Growth
4
Investment and Productivity Determinants
5
Steps ahead
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Steps ahead
Review and adjust chapters 2, 3 and 4 based on comments of seminar members. Based on the main findings, incorporate further analysis regarding policy recomendations. Finish writing chapter 5: ‘Growth and Institutional Puzzles’ Finish the first draft of my Ph.D research proposal: ‘Productivity, Technology Adoption, and Structural Change under Globalization: A Comparative Analysis between Latin America and Asia’
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THANK YOU!
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