Download - On the Determinants of Bolivia's Economic Growth: Production Puzzles

CH2: Stochastic Trends and Production ParametersCH3: 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 Guerrahttps://sites.google.com/site/carlosmendez777

Graduate School of International DevelopmentNagoya University

Novermber 8th, 2011

Carlos Mendez (GSID) Productivity Puzzles 1/69



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




Outline





5 Steps ahead




Research Progress: What is new?

Results update based on new data sets: Extended Penn WorldTables V.( 4.0) and Penn World Tables V.(7.0)

New comparative analysis over time (46 years) and space (6countries).

New analytical chapters:

Chapter 2: Stochastic Trends and Production FunctionParametersChapter 4: Investment and Productivity Determinants




MotivationAnalysis and ResultsFinal Remarks

Outline





5 Steps ahead





Fitting a Geometric Growth Process

yt = y0egt ⇒ ln(yt) = ln(y0) + gt + ǫ

9.5

1010

.511

ln(J

AP

AN

’s G

DP

per

wor

ker)

JAPAN: g=2.6%*** R2=0.86; BOLIVIA: g=−0.07% R2=0.01 8.

88.

99

9.1

ln(B

OLI

VIA

’s G

DP

per

wor

ker)

1960 1970 1980 1990 2000 2010Year

95% CI Fitted values ln( GDP per worker)

Source: Author’s calculations using data from Penn World Tables V. 7.0





Stochastic Trends and Unit Roots

Why a deterministic linear trend is not measurable in thegrowth process of Bolivia?

Stochastic trends, structural breaks, steady state (povertytrap)?

If a stochastic trend is present, is it possible to indentifysignificant long term relations among macroeconomicvariables?

If macroeconomic variables like GDP or Investment have astochastic trend, then shocks to these variables havepermanent effects, whereas in traditional business cycle theorythe effect of shocks on real GDP would usually be consideredonly temporary.





Factor Shares and Production FunctionParameters

Economists have long studied labor and capital’s share ofnational income as indicators of income distribution.

Data availability of labor’s share has also been seen as offeringinsights into the shape of the aggregate production function.

Generally, studies of developed economies support the long-standing observation (Kaldor Fact) that factors’ shares ofnational income are relatively constant over time and acrosscountries.

However, looking at the data of developing countries,important differences are observable between thegeneralization of the Kaldor fact and the reported factorshares.

Discrepancy: Data vs Common wisdom





Is it a ‘Naive’ Calculation of the CapitalShare?

Capital Share = 1 - Labor Share.3

.4.5

.6.7

.8C

apita

l Sha

re in

Nat

iona

l Inc

ome

Acc

ount

s

1963 1973 1983 1993 2003year

Nat. Accounts (0.68) Nat. Accounts HPtrend (0.68)Kaldor Fact (1/3)

Source: Author’s calculations using data from the United Nations Data Base, Bolivia’s National Accounts MainAggregates





Reseach Questions

1 Do the main production aggregates of the Bolivian economycontain stochastic trends? If so , is it possible to identify longterm relationships among them ?

2 Considering the noticiable difference between the conventionalwisdom and the ‘naive’ capital share , what other estimates offactor shares can be considered to understand the distributionof income between capital and labor in Bolivia?

3 How can the Bolivian economy be characterized in terms ofreturns to scale and the degree of substitution between capitaland labor?





A First Look at the Data

Levels Growth Rates

Mean Std. Dev. Min Max Mean Std. Dev. Min Max

GDP (Output) 2.0E+10 6.6E+09 1.1E+10 3.6E+10 2.69 3.96 -14.95 8.16Capital Stock 1.9E+10 4.8E+09 1.2E+10 3.0E+10 2.12 3.30 -4.95 11.54Labor 2.6.E+06 8.4.E+05 1.5.E+06 4.4.E+06 2.37 0.38 0.83 3.04Output/Labor 7,559 634 6,481 8,889 0.32 3.93 -16.80 6.33Capital/Labor 7,646 1,085 5,774 9,670 -0.24 3.33 -7.47 8.96Output/Capital 1.00 0.12 0.85 1.26 0.57 4.31 -18.23 8.43Capital/Output 1.01 0.12 0.79 1.18 -0.56 4.30 -8.54 17.72Investment/Labor 999 251 569 1,641 -0.19 20.42 -56.17 47.04

Source: Author’s calculations using data from Extended Penn World Tables V. 4.0





2323

.524

24.5

log(

GD

P)

1963 1973 1983 1993 2003

year

−15

−10

−5

05

10

GD

P g

row

th r

ate

1963 1973 1983 1993 2003

year

23.2

23.4

23.6

23.8

2424

.2

log(

Cap

ital S

tock

)

1963 1973 1983 1993 2003

year

−5

05

1015

Cap

ital g

row

th r

ate

1963 1973 1983 1993 2003

year





8.6

8.8

99.

2

log(

Cap

ital/L

abor

)

1963 1973 1983 1993 2003

year

−10

−5

05

10

Cap

ital/L

abor

gro

wth

rat

e

1963 1973 1983 1993 2003

year

−.2

−.1

0.1

.2

log(

Out

put/C

apita

l)

1963 1973 1983 1993 2003

year

−20

−10

010

Out

put/C

apita

l gro

wth

rat

e

1963 1973 1983 1993 2003

year





−.2

−.1

0.1

.2

log(

Cap

ital/O

utpu

t)

1963 1973 1983 1993 2003

year

−10

010

20

Cap

ital/O

utpu

t gro

wth

rat

e

1963 1973 1983 1993 2003

year

6.4

6.6

6.8

77.

27.

4

log(

Inve

stm

ent L

abor

)

1963 1973 1983 1993 2003

year

−60

−40

−20

020

40

Inve

stm

ent/L

abor

gro

wth

rat

e

1963 1973 1983 1993 2003

year





Unit Root Tests

∆yt = α+ βyt−1 + δt +k∑

j=1

ζj∆yt−j + ǫt

Ho : There is a Stochastic TrendHo*: There is not a Stochastic Trend

Unit Root Tests

ADF PP DF-GLS KPSS* ZAGDP (Output) Not Reject Not Reject Not Reject Reject Ho* Not RejectCapital Stock Not Reject Not Reject Not Reject Reject Ho* Not RejectLabor Not Reject Not Reject Not Reject Reject Ho* Not RejectOutput/Labor Not Reject Not Reject Not Reject Reject Ho* Not RejectCapital/Labor Not Reject Not Reject Not Reject Reject Ho* Not RejectOutput/Capital Not Reject Not Reject Not Reject Reject Ho* Not RejectCapital /Output Not Reject Not Reject Not Reject Reject Ho* Not RejectInvestment/Labor Not Reject Not Reject Not Reject Reject Ho* Not Reject





Cointegration Analysis

Ho: The series are not cointegrated.H1: The series are cointegrated (Share the same stochastic trend).

ǫt = ln(Y

L)− β1ln(

K

L)− β0

∆ǫt = γǫt−1 +

k∑

j=1

ζj∆ǫt−j + vt

Engle-Granger 1st-step regressionDependent Variable: Ln(Output/Labor)

Coef. Std. Err. t-stat P-value 95% CI

Ln(K/L) 0.32 0.07 4.35 0.00 0.17 0.46Constant 6.10 0.65 9.38 0.00 4.79 7.41Augmented Engle-Granger test for cointegrationNumber of lags = 5 N (test) = 40

Test 1% Critical 5% Critical 10%CriticalStatistic Value Value Value

Z(t) -3.383 -3.585 -2.928 -2.602Critical values from MacKinnon (1990, 2010)

Reject Ho at 5% of significance ⇒ The series share the same stochastic trend





Cointegration Analysis

Ho: The series are not cointegrated.H1: The series are cointegrated (Share the same stochastic trends).

ǫt = ln(Y )− β1ln(K )− β2ln(L)− β0

Johansen test for cointegrationTrend: constant Number of obs = 41Sample: 1968-2008 Lags = 5Maximum Trace 5% Critical

Rank Parms LL Eigenvalue Statistic Value0 39 361.39 . 40.27 29.681 44 373.67 0.45 15.71 15.412 47 380.48 0.28 2.09* 3.763 48 381.53 0.05

Reject Ho at 5% of significance ⇒ The series share the samestochastic trend.





Cobb-Douglas Production Function

A Cobb-Douglass Production Function:

Y = AKαL1−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





Estimation of the Cobb-Douglas Function

Dependent Variable: Ln GDPInitial Newey-West First PW-COBase Stand. Err. Differences GLS(1) (2) (3) (4)

Capital Share 0.5358*** 0.5358*** 0.3845** 0.4293***(0.0917) (0.1256) (0.1738 ) (0.1545)

Labor Share 0.5410*** 0.5410*** 1.1861 0.6229***(0.0500) (0.0685) (1.5399) (0.1297)

Tech. Change 0.0015 0.0016 0.0000 0.0022(0.0011) (0.0012) (0.0000) (0.0016)

Number of Observations 46 46 45 46Autocorrelation AnalysisDurbin-Watson statistic 0.3552 0.3552 1.82116 1.674114Breusch-Godfrey statistic 31.7260 na. 0.358 naBreusch-Godfrey test (p-value) 0.0000 na. 0.5498 naWhite noise test statistic 125.0869 19.0795White noise test (p-value) 0.0000 0.5167Number of Autocorrelations 2.0000 0





Hypothesis Testing under The Cobb-DouglasProduction Function

Dependent Variable: Ln GDPCointegration Newey-West PW-CO ConstrainedEngle-Granger Stand. Err. GLS ks + ls = 1

(0) (2) (4) (5) (6)Capital Share 0.3163*** 0.5358*** 0.4293*** 0.4611*** 0.3163***

(0.1131) (0.1256) (0.1545) (0.0425) (0.0618)Labor Share 0.5410*** 0.6229*** 0.5389*** 0.6836***

(0.0685) (0.1297) (0.0425) (0.0618)Tech. Change 0.0016 0.0022 0.0024

(0.0012) (0.0016) (0.0001)Constant 6.1015*** 6.1014***

(1.0096) (0.5509)Number of Observations 46 46 46 46 46

Hypothesis TestingHo: Constant Returns to Scale Not Applicable Not Rejected Not Rejected Constrained Constrained

Ho: Capital share =1/3 Not Rejected Not Rejected Not Rejected Rejected Not RejectedHo: Capital share =0.68 Rejected Not Rejected Not Rejected Rejected Rejected





CES Production Function

A Constant Elasticity of Substitution (CES) production function:

y = γeλt [δK−ρ + (1− δ)L−ρ]−

νρ

Parameters:

γ: Productivity

λ: Technological Change

δ: Capital Share

ρ: Substituion

ν: Returns to scaleσ

1+ρ: Elasticity of substitution





Estimation of the CES Production Function

As the CES function is non-linear in parameters and cannotbe linearised analytically, it is not possible to estimate it withthe usual linear estimation techniques.

It can be estimated by non-linear least-squares using differentoptimization algorithms:

Gradient-based optimisation Global Op. Constraint Parameters

Parameter LM Conj. Newton BFGS N-M L-BFGS-B PORT

γ 0.0000 0.0000 475.6000 0.00 0.0400 0.0000 0.0000λ 0.0106 0.0150 0.0033 -0.99 -0.0850 -0.0960 -0.9850δ 0.8906 0.5000 0.2468 0.50 0.5400 0.5000 0.4968ρ 0.1349 0.2500 -0.1264 0.25 0.2900 0.2503 0.2530ν 0.7375 1.0000 0.9721 0.99 1.0400 1.0000 0.9913

Elasticity 0.88 0.80 1.15 0.80 0.78 0.80 0.80Convergence No Yes No Yes Yes No Yes





A Summary of Factor Shares Estimates forBolivia

.32.68

.54

.54

.49.51

.54.46

.62.43

.67.33

.67.33

.68.32

0 .2 .4 .6 .8

National Accounts(Hptrend)

HAC Errors Regression Estimation

CES Production Function Estimation

Constrained Regression Estimation (No Constant)

PW−CO GLS Regression Estimation

Kaldor Fact

Bernanke and Gurkaynak (2001)

Constrained Regression Estimation (No Trend)

Capital Labor





The Capital Share: A Comparative View

.55.44

.69

.56.35

.6

.62.32

.48

.43

.58.41

.62

.39.33

.68

0 .2 .4 .6 .8

Peru

Korea

Japan

Indonesia

Chile

Bolivia

PW−COBG(2001)

N.Acc

PW−COBG(2001)

N.Acc

PW−COBG(2001)

N.Acc

PW−COBG(2001)

N.Acc

PW−COBG(2001)

N.Acc

PW−COBG(2001)

N.Acc





Summary of Main Findings

The main production aggregates of the Bolivian economyseem to contain stochastic trends. Therefore, shocks to thesevariables might have permanent effects.It is possible to identify a significant and not spuriousrelationship among GDP, capital and labor.Cointegration techniques are useful to understand the longterm value of the capital share. They seem to support theKaldor fact that around 1/3 of the national incomecorrespond to capital gains.Labor share in national income increases drastically once therents of the non-corporate and self-employed labor areaccounted.The Bolivian economy might be characterized in terms ofconstant returns to scale in production, and low degree ofsubstitution between capital and labor.





Outline





5 Steps ahead





The Need of Growth Accounting

Capitalism of State Neo−Liberalism IndigenousSocialism

Development Paradigm:

6500

7500

8500

9500

Oup

ut /

Labo

r R

atio

(G

DP

per

wor

ker

)

1963 1968 1973 1978 1983 1988 1993 1998 2003 2008

I II III IV

NationalRevolution

Sequel

Oil Boom andDebt Crisis

Hyper−Inflation and

Washington ConsensusRe−

Distribution

−15

−10

−5

05

(Oup

ut /

Labo

r) G

row

th R

ate

1963 1968 1973 1978 1983 1988 1993 1998 2003 2008

Period:





Reseach Questions

1 What is the relative contribution of capital stock, labor andproductivity to GDP growth in Bolivia?

2 How is the behavior of Factor Accumulation (FA) and TotalFactor Productivity (TFP) in each of the developmentparadigms and historical periods of Bolivia?

3 What is the contribution of Human Capital improvements inthe process of economic growth in Bolivia?





Evolution of GDP, Capital and Labor

Period I

Period II

Period III

Period IV

11.

52

2.5

33.

5In

dex

1963

=1

1963 1968 1973 1978 1983 1988 1993 1998 2003 2008

GDP Index Capital Stock IndexLabor Stock Index





The Growth Accounting Framework


Y = AKαL1−α ; ∀ 0 ≤ α ≤ 1 (1)


Ln(Y ) = Ln(A) + αLn(K ) + (1− α)L

Differentiating the previous equation respect to time, we obtain aGrowth Function in terms of the growth of inputs :

dLn(Y )

dt=

dLn(A)

dt+α

dLn(K )

dt+(1−α)

dLn(L)

dt=

A

A+α

K

K+(1−α)

L

L

Y

Y=

A

A+ α

K

K+ (1− α)

L

L(2)





The Debate on the Capital Share

.32.68

.54

.54

.49.51

.54.46

.62.43

.67.33

.67.33

.68.32

0 .2 .4 .6 .8

National Accounts(Hptrend)

HAC Errors Regression Estimation

CES Production Function Estimation

Constrained Regression Estimation (No Constant)

PW−CO GLS Regression Estimation

Kaldor Fact

Bernanke and Gurkaynak (2001)

Constrained Regression Estimation (No Trend)

Capital Labor





Factor Accumulation Growth−

15−

10−

50

510

Gro

wth

Rat

e

1963 1973 1983 1993 2003year

GDP Growth Rate FA1 (ks=0.68)FA2 (ks=0.33) FA3 (ks=0.32)FA4 (ks=0.43) FA5 (ks=0.46)FA6 (ks=0.51) FA7 (ks=0.54)





Productivity Growth−

20−

100

10G

row

th R

ate

1963 1973 1983 1993 2003year

GDP Growth Rate TFP1 (ks=0.68)TFP2 (ks=0.33) TFP3 (ks=0.32)TFP4 (ks=0.43) TFP5 (ks=0.46)TFP6 (ks=0.51) TFP7 (ks=0.54)





Growth Determinants: Capital, Labor andProductivity

−4

−2

02

46

Gro

wth

Rat

e

1963 1973 1983 1993 2003year

GDP Growth trend, HP corrected KC3trend,(ks=0.32) LC3trend,(ks=0.32) TFP3trend,(ks=0.32)





Growth Trends: GDP, FA and TFP

GDP

FA

TFP

−4

−2

02

46

Gro

wth

Rat

e

1963 1973 1983 1993 2003year





Growth Accounting (ks=0.32)

1.01

1.37

.46

.47

1.5

−.58

.62

1.72

.54

.69

1.88

1.87

.68

1.61

.43

−.6

−.1

.4.9

1.4

1.9

2.4

2.9

3.4

3.9

4.4

1963−1973 1974−1984 1985−2002 2003−2008 1963−2008

Capital Labor TFP





Growth Accounting

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)

Total Sample: 1963-2008GDP 2.69 2.69 2.69 2.69 2.69 2.69 2.69TFP 0.49 0.40 0.43 0.43 0.43 0.45 0.45K 1.44 0.70 0.68 0.91 0.98 1.08 1.15L 0.76 1.59 1.61 1.35 1.28 1.16 1.09

PERIOD I : National Revolution Sequel (1963-1973)GDP 2.96 2.96 2.96 2.96 2.96 2.96 2.96TFP 0.18 0.57 0.46 0.46 0.43 0.37 0.33K 2.14 1.04 1.01 1.35 1.45 1.61 1.70L 0.65 1.35 1.37 1.15 1.09 0.99 0.93

PERIOD II : Oil Boom and Debt Crisis (1974-1984)GDP 1.31 1.31 1.31 1.31 1.31 1.31 1.31TFP -0.40 -0.66 -0.58 -0.58 -0.56 -0.52 -0.50K 1.01 0.49 0.47 0.64 0.68 0.76 0.80L 0.71 1.48 1.50 1.26 1.19 1.08 1.02





Growth Accounting

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)

GDP 2.82 2.82 2.82 2.82 2.82 2.82 2.82TFP 0.69 0.49 0.54 0.54 0.56 0.59 0.61

K 1.32 0.64 0.62 0.83 0.89 0.99 1.04L 0.81 1.69 1.72 1.44 1.37 1.24 1.16

PERIOD IV : Social Revolution (2003-2008)GDP 4.37 4.37 4.37 4.37 4.37 4.37 4.37TFP 2.02 1.81 1.87 1.87 1.88 1.91 1.93

K 1.47 0.72 0.69 0.93 1.00 1.11 1.17L 0.88 1.85 1.88 1.57 1.49 1.35 1.27





Human Capital Improvements

Index (1963=1)

Schooling, Secondary Complete, S>25

02

46

810

Ave

rage

Yea

rs o

f Sch

oolin

g (A

dult

Pop

ulat

ion,

S>

25)

1963 1968 1973 1978 1983 1988 1993 1998 2003 2008

Source: Author’s calculations using data from Barro and Lee(2011)





Introducing Human Capital to the GrowthAccounting Framework

An extended Cobb-Douglass Production Function:

Y = AKα(HL)1−α ; ∀ 0 ≤ α ≤ 1 (3)


Ln(Y ) = Ln(A) + αLn(K ) + (1− α)L+ (1− α)H

Differentiating the previous equation respect to time, we obtain an extendedGrowth Function in terms of the growth of inputs :

dLn(Y )

dt=

dLn(A)

dt+ α

dLn(K )

dt+ (1− α)

dLn(L)

dt+ (1− α)

dLn(H)

dt

Y

Y=

A

A+ α

K

K+ (1− α)

L

L+ (1− α)

H

H(4)





Growth Accounting with Human Capital(ks=0.32)

1.01

1.37

1.82

−1.23

.47

1.5

1.82

−2.48

.62

1.72

1.82

−1.34

.69

1.88

1.82

−.02

.68

1.61

1.82

−1.42

−2

02

4

1963−1973 1974−1984 1985−2002 2003−2008 1963−2008

Capital Labor Human Capital TFP





Growth Accounting with Human Capital

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)

Total Sample: 1963-2008GDP 2.69 2.69 2.69 2.69 2.69 2.69 2.69TFP -0.37 -1.39 -1.42 -1.10 -1.01 -0.86 -0.78K 1.44 0.70 0.68 0.91 0.98 1.08 1.15L 0.76 1.59 1.61 1.35 1.28 1.16 1.09H 0.86 1.79 1.82 1.52 1.44 1.31 1.23

PERIOD I : National Revolution Sequel (1963-1973)GDP 2.96 2.96 2.96 2.96 2.96 2.96 2.96TFP -0.68 -1.22 -1.23 -1.06 -1.02 -0.94 -0.89K 2.14 1.04 1.01 1.35 1.45 1.61 1.70L 0.65 1.35 1.37 1.15 1.09 0.99 0.93H 0.86 1.79 1.82 1.52 1.44 1.31 1.23

PERIOD II : Oil Boom and Debt Crisis (1974-1984)GDP 1.31 1.31 1.31 1.31 1.31 1.31 1.31TFP -1.26 -2.45 -2.48 -2.11 -2.00 -1.83 -1.73K 1.01 0.49 0.47 0.64 0.68 0.76 0.80L 0.71 1.48 1.50 1.26 1.19 1.08 1.02H 0.86 1.79 1.82 1.52 1.44 1.31 1.23





Growth Accounting with Human Capital

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)

GDP 2.82 2.82 2.82 2.82 2.82 2.82 2.82TFP -0.16 -1.31 -1.34 -0.98 -0.88 -0.72 -0.62K 1.32 0.64 0.62 0.83 0.89 0.99 1.04L 0.81 1.69 1.72 1.44 1.37 1.24 1.16H 0.86 1.79 1.82 1.52 1.44 1.31 1.23

PERIOD IV : Social Revolution (2003-2008)GDP 4.37 4.37 4.37 4.37 4.37 4.37 4.37TFP 1.16 0.02 -0.02 0.34 0.44 0.61 0.70K 1.47 0.72 0.69 0.93 1.00 1.11 1.17L 0.88 1.85 1.88 1.57 1.49 1.35 1.27H 0.86 1.79 1.82 1.52 1.44 1.31 1.23






From 1963 to 2008 factor accumulation, specially physicalcapital, has been the main determinant of economic growth inBolivia.

The trend of TFP is extremely volatile across differentmeasures of the capital share, and shows a clear cyclicalbehavior.

The behavior of TPF and Factor Accumulation has beensimilar before the hyper-inflation period but not after it.

The institutional reforms after the hyper-inflation periodpromoted capital accumulation but not TFP growth.

Human Capital improvements (exponential growth) mightaccount up to 52% of total growth. However, this value canbe questionable if human capital improvements are measuredin terms of outcomes rather than inputs.





Outline





5 Steps ahead





Capital is important, but what happened theK/L ratio?

−60

−40

−20

020

40G

row

th R

ate

1963 1973 1983 1993 2003year

Investment per Worker Growth RateCapital−Labor Ratio Growth Rate





TFP behaviour in Bolivia

9010

011

012

0T

FP

Lev

el(1

963=

100)

1963 1973 1983 1993 2003year





Reseach Questions

1 Why investment does not seen to increase the capital-laborgrowth rate?

2 What factors can be indentified in order to explain thebehavior of the TFP in Bolivia?





Aggregate Investment

Period I

Period IIPeriod III

Period IV

2121

.522

22.5

Log

(Inv

estm

ent)

1963 1968 1973 1978 1983 1988 1993 1998 2003 2008





Investment Share

Period I Period II Period III Period IV

−5

05

1015

20G

DP

Sha

re

1963 1968 1973 1978 1983 1988 1993 1998 2003 2008

Investment ShareFDI Share





The Accelerator Model

The ‘basic’ accelerator model:

K ∗

t = 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 K ∗

t bear afixed factor of proportionality to output, but the capital stock isalways optimally adjusted in each time period, implying thatK ∗

t = 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 restrictiveinstantaneous adjustment assumption.





The Flexible Accelerator Model

Relaxing the assumption of instantaneous adjustment, Koyck(1954) proposed a ‘flexible’ version of the accelerator model whichemphasized the adjustment costs of investment:

Int = λ(K ∗

t − Kt−1) = µ(Yt − Yt−1) (7)

where λ denotes the partial adjustment coefficient. Substitutingequation 5 into equation 7 yields:

Int = Kt − Kt−1 = λµYt − λKt−1 (8)

orKt = µλYt + (1− λ)Kt−1 (9)





Towards an Empirical Implementation of theFlexible Accelerator Model

The investment equation 8 is in terms of net investment.Assuming a constant depreciation rate δ, one can add replacementinvestment δKt−1 to both sides of equation 8 and obtain the grossinvestment formulation:

It = Kt − (1− δ)Kt−1 = λµYt + (δ − λ)Kt−1 (10)

Econometric Models:

It = α+ λµYt + (δ − λ)Kt−1 + ǫt (11)

It = α+

m−1∑

j=0

βiYt−i + βkKt−1 + ǫt (12)





Estimations of the Flexible AcceleratorModel

Dependent variable: Gross InvestmentModel (1) Model (2)

Basic Newey-West PW-CO PW-CO PW-CO PW-COCoefficients OLS Stand. Err. GLS GLS GLS GLS

(1) (2) (3) (4) (5) (6)β0 = λµ 0.16*** 0.16*** 0.21*** 0.20* 0.16 0.16

(0.03) (0.04) (0.05) (0.11) (0.12) (0.13)βk = δ − λ -0.09** -0.09 -0.16*** -0.17** -0.20** -0.21**

(0.05) (0.06) (0.07) (0.08) (0.10) (0.10)β1 0.02 -0.01 -0.02

(0.13) (0.14) (0.15)β2 0.10 0.09

(0.14) (0.15)β3 0.02

(0.14)α 1.1e+09*** 1.1e+09*** 1.4e+09** 1.5e+09** 1.5e+09** 1.6e+09**

(3.8e+08) (3.8e+08) (6.4e+08) (6.7e+08) (7.4e+08) (7.9e+08)R2 0.63 na 0.42 0.4 0.39 0.39N 45 45 45 45 44 43

Implied Ajustmentµ = 1.01

δ = 0.11λβ0 0.16*** 0.16*** 0.21*** 0.20* 0.16 0.16λβk 0.20** 0.20 0.27*** 0.28** 0.31** 0.32**





The Accelerator Principle in theHarrod-Domar Model

Set up of the Harrod-Domar Model:

Y = cK (13)

MPK =dY

dK= c ⇒

dY

dK=

Y

K(14)

f (0) = 0 (15)

I = S = sY (16)

∆K = I − δK (17)

Operationalization : Taking logarithm and differentiating equation 13 respect to time,we obtain:

dLn(Y )

dt=

dLn(c)

dt+

dLn(K)

dt

∆Y

Y= 0 +

∆K

K(18)

Equilibrium :Replacing equation 18 into 17 we obtain:

∆Y

Y+ δ = s

Y

K= sMPK (19)





Estimating the Harrod-Dommar model: LowSavings Rate ⇒ Low Growth

Dependent Variable: GDP growth + Depreciation rateBasic 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. 0.16N 44 44 44

Actual average Investment Share = 13.15%

The actual investment (saving) rate is consistent with theBolivian growth proces ⇒ An investment (saving) rate of 13%might no be enough to produce higher growth in the Boliviancase.





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

Y

K= sMPK

Low savings rate s ⇒ Low Growth ∆YY

Low return to investment (MPK) ⇒ Low Growth ∆YY





An attempt to estimate the MPK for Bolivia

∆Y

Y+ δ = s

Y

K= sMPK

Dependent Variable: GDP growth + Depreciation rateBasic 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)





Understanding the MPK


Y = AKαL1−α ; ∀ 0 ≤ α ≤ 1 (20)

One sector model:

MPK = αAKα−1L1−α = αY

K(21)

Multisector model:

MPK = αPyY

PkK(22)





Calculating the MPK for Bolivia

Based on Caselli and Ferrer (2005) data:

Initial Parameters

Total Capital Share 0.33Reproducible Capital Share 0.08Py/Pk 0.60

Marginal Product of Capital (MPK)

One Sector Multi Sector

Total 0.31 0.08Reproducible 0.19 0.05





The Marginal Product of Capital (MPK) aComparative View

αT αR Py/Pk MPK(T1) MPK(Tm) MPK(R1) MPK(Rm)Bolivia 0.33 0.08 0.60 0.31 0.19 0.08 0.05Chile 0.41 0.16 0.90 0.26 0.24 0.10 0.09Peru 0.44 0.22 0.89 0.20 0.18 0.10 0.09

Singapore 0.47 0.38 1.19 0.15 0.18 0.12 0.14Botswana 0.55 0.33 0.66 0.36 0.24 0.22 0.14

Source: Caselli and Freirer (2005)





Determinants of Total Factor Productivity

Analytical Famework:

TFP=f(Cyclical variables, Policies, Institutions, InitialConditions)

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 (+)





Variables for TFP analysis90

100

110

120

.

1980 1990 2000 2010.

TFP

−.2

0.2

.4.6

.8.

1980 1990 2000 2010.

Terms of Trade (log)

−10

0−

500

5010

0.

1980 1990 2000 2010.

REER Apreciation

0.2

.4.6

.81

.

1980 1990 2000 2010.

Macro Instability

5010

015

020

025

0.

1980 1990 2000 2010.

Gov. Debt/GDP

3.4

3.6

3.8

44.

2.

1980 1990 2000 2010.

Civil Liberties

2.5

33.

54

4.5

.

1980 1990 2000 2010.

Democracy Level





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 lagpolynomials, and X is the vector of explanatory variablespresented previously. The estimation strategy of equation 23follows the general-to-particular approach (Hendry, 1995).

Since the dynamic structure in the relation between TFP andthe explanatory variables is unknown, the estimation usescontemporary and lagged values of the independent variablesand lagged values of the dependent variable (the logarithm ofthe TFP index, ln(TFP)).





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 VariablesTerms of Trade 0.1060*** 0.1060*** 0.1143*** 0.1251** 0.1259** 0.1342**

(0.0335) (0.0333) (0.0356) (0.0582) (0.0595) (0.0619)Terms of Trade (t-1) -0.1072** -0.1068** -0.1059** -0.1433** -0.1408** -0.1420**

(0.0447) (0.0453) (0.0436) (0.0657) (0.0671) (0.0679)REER appreciation -0.0001 -0.0001 -0.0001 -0.0003* -0.0002* -0.0002*

(0.0004) (0.0001) (0.0001) (0.0004) (0.0001) (0.0001)REER appreciation (t-1) -0.0002 -0.0002 -0.0002 -0.0002 -0.0002 -0.0002

(0.0003) (0.0001) (0.0001) (0.0004) (0.0002) (0.0002)PoliciesMacro.Instability (t-1) -0.0522* -0.0532** -0.0515*** -0.0379 -0.0430* -0.0433*

(0.0285) (0.0195) (0.0175) (0.0300) (0.0234) (0.0228)Government Debt -0.00002 -0.00009

(0.0003) (0.0004)InstitutionsCivil liberties (t-2) 0.0403*** 0.0400*** 0.0433* 0.0406*

(0.0131) (0.0120) (0.0207) (0.0148)Democracy (t-2) 0.0250*** 0.0216***

(0.0056) (0.0074)Initial ConditionsTFP (t-1) 0.7922*** 0.7965*** 0.7852*** 0.7968** 0.8118*** 0.7943***

(0.0766) (0.0575) (0.0603) (0.0948) (0.0613) (0.0664)Constant 0.8121** 0.7918** 0.9007*** 0.7906* 0.7245** 0.8809***

(0.3734) (0.2856) (0.2811) (0.4202) (0.2851) (0.2972)Adjusted R squared 0.9493 0.9519 0.9590 0.9413 0.9437 0.9456SER 0.0054 0.0054 0.0046 0.0092 0.0093 0.0090Carlos Mendez (GSID) Productivity Puzzles 65/69





Investment does not seen to increase the capital-labor growthrate because of the following reasons:

1 Investment is volatile and unstable.2 Adjustment costs are high.3 Investment rate is still low to sustain positive growth.4 Return to investment is low.

Productivity in Bolivia can be significantly explained bycyclical variables, stabilization policies, participatoryinstitutions, and favorable initial conditions.

Terms of trade improvements significantly affect productivity,but the direction of the total effect is not clear.




Outline





5 Steps ahead




Steps ahead

Review and adjust chapters 2, 3 and 4 based on comments ofseminar members.

Based on the main findings, incorporate further analysisregarding 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 Changeunder Globalization: A Comparative Analysis between LatinAmerica and Asia’




THANK YOU!


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