Dynamic analysis of the constraints
to Growth: The Case of Brazil
By Cristina Vinyes, University of Minnesota
Advisor: Professor Terry L. Roe
12/14/09
1. Research problem
Real GDP percent growth, 1950-2005
Growth Diagnostic:
Hausman, Rodrik & Velasco (HRV)
1. Low Domestic Savings
High real interest rates
Real Interest Rates vs GDP per capita, 2005
High tax burden on capital
Growth Diagnostic continues

Low stock of Human Capital
Returns to education and years of schooling
(HRV)
Inadequate infrastructure:
Blyde et al.
Dynamics of a multisector Ramsey type model




Insight into the dynamics of an economy in transition to
long run equilibrium
Understand forces of economic growth on structural
transformation across multiple sectors.
Disaggregated model, fit to data and solves forward and
backward.
Need for an inter-temporal Ramsey model to measure
economy-wide impact of relaxing HRV’s constraints to
growth.
2. Model: the SAM
in 2001 millions USD
Behavior of households

Infinitely-lived Ramsey household

t[ 0 ,  )

u(qm , qa , qt , qs )e ( n )t dt
Intra-temporal problem:


  E pm , pa , pt , ps  q  min   p j q j | q  u(qm , qa , qt , qs )
qm , qa , qt , qs 

 j qm , qa , qt , qs

Budget constraint:
1
k  (wu lu  wsls  krk (1   )   a H a  E pm , pa , pt , ps  q)  k n     T
pk

Euler condition:

p
ˆ r k (1   )

    x  k
ˆ
pk
pk
Firms

Manufacture, transportation and service employ technology:

Min f j ( At luj , At lsj , k j ),  mjmj ,  ajaj ,  tjtj ,  sjsj

yˆ
yˆ
yˆ
yˆ

Total cost functions in units per effective worker:


ˆu , w
ˆ s , r k )    i  yˆ j
TC j   C j ( w

i m , a , t , s



j  m, t , s
j  m, t , s.
Agriculture technology

yˆ
yˆ
yˆ yˆ 
Min  f a ( At lua , At lsa , ka , Bt  ha ), ma , aa , ta , sa 
 ma  aa  ta  sa 


Value added function
 pva F a (lua , lsa , kˆa ; ha )  
 ( pva , wˆ u , wˆ s , r )ha  max 

k
a
ˆ
lua , l sa , k a w
ˆ
ˆ
 u lua  ws lsa  kr   ha 
a
k
At   e xt
Equilibrium Characterization
A competitive equilibrium is defined by the positive prices
{wˆ u , wˆ s , r k , pt , ps }t[0,) ,households consumption {qm , qa , qt , qs}t[ 0,)
and production plans





ˆm
ˆ a , y
ˆ t , y
ˆ s , kˆm
{y
,y
, kˆa , kˆt , kˆs , lum
, lua
, lut
,





lus
, l sm
, l sa
, l st
, l ss
, }t[ 0, )
given initial endowments kˆ(0), L (0), L (0), H such that,
 discounted present value of household utility is
maximized,
firms maximize profit subject to their technology at each
instant of time t,
markets clear for all inputs and outputs.
u
s
Inter-temporal equilibrium
We have three differential equations that are linear in the
dot variables,

Euler equation:

 ~
r ( pt , ps )
p 
E  pt , ps , p s   ˆ  ˆ k
     x  sk s 
ps 
 c  pm , p a , p s 

Budget Constraint:



1
~ u  p , p   w
~ s  p , p   
[w
t
s u
t
s
s
k
c  pm , pa , p s 
kˆ~r ( pt , ps )  ~ a  pt , ps  ha  E pm , pa , pt , ps  q]  kˆn    x 
~
K pt , ps , kˆ  kˆ 

Home good market clearing:


 ˆ ˆ

ps
j
a
sk
~
~
~
ˆ
ˆ  [ ys    sj y pt , ps , k   sa y  pt , ps   y  pt , ps  k  k x  n    ]
s
jm , t , s


Comparative statics


Stopler-Samuelson like effects
Rybcyznski-like effects
Sector factor Intensities
Industry Agriculture Transp.
Serv
K intensity
1,04
1,40
0,19
Lu intensity
0,73
0,07
0,41
0,03
2,42
0,65
0,53
0,15
0,36
Ls intensity
3. Validation
ex-post performance evaluations of applied general
equilibrium models are essential if policy makers are to
have confidence in the results produced by them (Kehoe 2003).
1,2
GDP
1,1
Value Added Relative to 2001

1
0,9
Data
0,8
Transportation with tao
0,7
0,6
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
4 Base Model Results


Basic forces of transition
Change in economy structure and resource allocation
Sector Share in GDP
Year
1991
2001
2011
2021
2031
2041
2051
Industry
Ag.
0,203
0,183
0,174
0,169
0,167
0,166
0,165
-
0,109
0,128
0,138
0,142
0,145
0,146
0,146
+
Unskilled Labor Share in
Transport Service Industry
0,020
0,021
0,021
0,021
0,021
0,021
0,021
=
0,676
0,668
0,664
0,663
0,662
0,662
0,661
-
0,205
0,194
0,188
0,185
0,184
0,183
0,183
-
Ag.
0,054
0,061
0,065
0,066
0,067
0,068
0,068
+
Transport Service
0,032
0,034
0,035
0,035
0,036
0,036
0,036
+
0,528
0,531
0,532
0,532
0,533
0,533
0,533
+
Skilled Labor Share in
Industry
Ag.
0,013
0,013
0,012
0,012
0,012
0,012
0,012
-
0,002
0,003
0,003
0,003
0,003
0,003
0,003
=
Capital Share in
Transport Service Industry
0,002
0,003
0,003
0,003
0,003
0,003
0,003
=
0,162
0,163
0,163
0,163
0,163
0,163
0,163
+
0,258
0,242
0,234
0,231
0,229
0,228
0,228
-
Ag.
0,111
0,126
0,133
0,136
0,138
0,139
0,139
+
Transport Service
0,007
0,008
0,008
0,008
0,008
0,008
0,008
=
0,624
0,625
0,625
0,625
0,625
0,625
0,625
=
5 Constraints to Growth

TAX
Reduce financial tax
Sector Share in GDP
Year Industry
2001
2011
2021
2031
2041
2051
1,001
0,937
0,902
0,883
0,874
0,869
-
Ag
T
1,000
1,080
1,118
1,136
1,144
1,149
+
0,933
0,940
0,943
0,945
0,946
0,946
+
Unskilled Labor Share in
Service Industry
1,002
0,996
0,993
0,992
0,991
0,991
-
1,000
0,966
0,948
0,939
0,934
0,932
-
Ag
T
1,000
1,066
1,097
1,112
1,120
1,123
+
0,970
0,997
1,010
1,016
1,019
1,020
+
Skilled Labor Share in
Service Industry
1,002
1,004
1,005
1,006
1,006
1,006
+
0,999
0,963
0,945
0,936
0,931
0,929
-
Ag
T
1,000
1,063
1,094
1,108
1,116
1,119
+
0,969
0,995
1,007
1,012
1,015
1,016
+
Capital Share in
Service Industry
1,001
1,002
1,002
1,003
1,003
1,003
+
0,999
0,962
0,943
0,934
0,929
0,927
-
Ag
T
Service
1,000
1,063
1,092
1,106
1,113
1,117
+
0,969
0,994
1,005
1,010
1,013
1,014
+
1,001
1,001
1,001
1,001
1,001
1,001
=
Constraints to Growth

Increase country’s productivity / skill labor
Compared to baseline results
skill/Base GDP
2001
2011
2021
2031
2041
2051
GDP growth Uwage payments Swage paymentsreturns to K
1,003
1,011
1,015
1,017
1,017
1,018
1,178
1,126
1,081
1,047
1,025
Sector Share in GDP
Year Industry
2001
2011
2021
2031
2041
2051
1,0329
1,0231
1,0178
1,0152
1,0139
1,0132
-
1,042
1,050
1,054
1,056
1,057
1,057
Ag
T
0,9568
0,9743
0,9820
0,9855
0,9872
0,9880
+
0,9907
0,9918
0,9923
0,9925
0,9926
0,9927
+
Unskilled Labor Share in
Service Industry
1,0206
1,0193
1,0187
1,0184
1,0182
1,0182
-
0,859
0,866
0,870
0,871
0,872
0,872
0,9923
0,9867
0,9838
0,9825
0,9818
0,9815
-
Ag
T
0,9372
0,9504
0,9563
0,9590
0,9604
0,9610
+
0,9732
0,9787
0,9812
0,9824
0,9830
0,9833
+
1,003
1,012
1,015
1,017
1,018
1,018
1,000
1,009
1,015
1,019
1,020
1,021
Skilled Labor Share in
Service Industry
0,9564
0,9569
0,9571
0,9572
0,9573
0,9573
+
land rents Expenditures
1,2033
1,1962
1,1926
1,1909
1,1900
1,1896
-
Ag
T
1,1366
1,1522
1,1592
1,1625
1,1641
1,1648
+
1,1801
1,1866
1,1895
1,1908
1,1915
1,1918
+
Capital Share in
Service Industry
1,1598
1,1601
1,1602
1,1603
1,1603
1,1603
+
1,000
1,007
1,012
1,015
1,016
1,017
1,0306
1,0244
1,0213
1,0197
1,0190
1,0186
-
Ag
T
Service
0,9735
0,9867
0,9927
0,9954
0,9967
0,9974
+
1,0108
1,0162
1,0186
1,0197
1,0202
1,0205
+
0,9933
0,9935
0,9935
0,9935
0,9935
0,9935
+
Constraints to Growth

Increase transport productivity
Sector Share in GDP
Year Industry
2001
2011
2021
2031
2041
2051
1,013
1,003
0,998
0,995
0,994
0,993
-
Ag
T
0,979
0,994
1,001
1,004
1,005
1,006
+
1,051
1,052
1,052
1,052
1,052
1,052
=
Unskilled Labor Share in
Service Industry
0,991
0,990
0,989
0,989
0,989
0,988
-
1,012
1,006
1,003
1,001
1,001
1,000
-
Ag
T
1,005
1,017
1,023
1,026
1,027
1,028
+
0,738
0,743
0,745
0,747
0,747
0,747
+
Skilled Labor Share in
Service Industry
1,012
1,013
1,013
1,013
1,013
1,013
=
1,004
0,998
0,994
0,993
0,992
0,992
-
Ag
T
0,997
1,009
1,015
1,017
1,019
1,019
+
0,732
0,737
0,739
0,740
0,741
0,741
+
Capital Share in
Service Industry
1,004
1,004
1,004
1,005
1,005
1,005
+
1,003
0,996
0,993
0,991
0,991
0,990
-
Ag
T
Service
0,996
1,008
1,013
1,016
1,017
1,018
+
0,732
0,736
0,738
0,739
0,740
0,740
+
1,003
1,003
1,003
1,003
1,003
1,003
=
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