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Growth Decomposition and
Productivity Trends
Leonardo Garrido and Elena Ianchovichina
PRMED
March 23, 2009
Possible growth decompositions



Contribution of demand components
Sectoral contribution to growth
Growth accounting
2
Contribution of Demand Components to
Growth (I)

What are the proximate drivers of growth in
aggregate demand?




Departs from fundamental equation Y=C+I+G+X-M
Aggregate supply = Y+M
Aggregate Demand = C+I+G+X
Steps:
1.
2.
3.
Calculate annual growth rate of each component of
aggregate demand
Calculate shares of each component of aggregate demand
Calculate the contribution to growth of each component
by multiplying growth rates of demand components
times share of component in aggregate demand
3
Contribution of Demand Components to
Growth (II): The Case of Egypt.
Growth Rates of Aggregate Demand / Supply by Demand Components. By Decades.
Imports of
Aggregate
Goods and
Supply / Demand
Services
1970s
5.6%
8.0%
6.5%
1980s
4.9%
-1.7%
2.7%
1990s
3.7%
2.8%
3.5%
2000s
4.0%
9.9%
5.5%
Source: Staff Calculations based on World Bank, WDI
Period
Real GDP
Private
Consumption
Government
Consumption
Gross Capital
Formation
4.5%
2.9%
3.5%
3.2%
3.7%
3.9%
3.8%
5.1%
14.4%
0.8%
3.3%
6.1%
Private
Consumption
Government
Consumption
Gross Capital
Formation
53.6%
50.1%
55.7%
52.2%
10.0%
8.9%
8.0%
7.8%
20.0%
25.6%
16.1%
17.5%
Exports of
Goods and
Services
5.5%
4.1%
3.5%
10.7%
Shares in Real Aggregate Supply of GDP and Demand Components
Imports of
Aggregate
Goods and
Supply / Demand
Services
1970s
61.7%
38.3%
100.0%
1980s
67.3%
32.7%
100.0%
1990s
75.6%
24.4%
100.0%
2000s
76.7%
23.3%
100.0%
Source: Staff Calculations based on World Bank, WDI
Period
Real GDP
Exports of
Goods and
Services
16.4%
15.4%
20.3%
22.7%
Contribution to Growth in Aggregate Demand / Supply by Demand Components. By Decades.
Imports of
Aggregate
Goods and
Supply / Demand
Services
1970s
3.4%
3.1%
6.5%
1980s
3.3%
-0.5%
2.7%
1990s
2.8%
0.7%
3.5%
2000s
3.1%
2.3%
5.5%
Source: Staff Calculations based on World Bank, WDI
Period
Real GDP
Private
Consumption
Government
Consumption
Gross Capital
Formation
4.5%
1.4%
2.0%
1.7%
3.7%
0.3%
0.3%
0.4%
14.4%
0.2%
0.5%
1.1%
Exports of
Goods and
Services
5.5%
0.6%
0.7%
2.4%
4
Sectoral Contribution to Growth

Similar approach to demand contribution to
growth


Uses GDP at factor costs (not at market prices)
which equals the sum of GDP of economic
activities
Imputed financial services not excluded from
each economic activity (assumption of financial
services proportion to sectoral GDP)
Growth Accounting (I)

With CRS Hicks Neutral Cobb Douglas
production function
Yt  At  Kt  Lt  Ht 


1
Taking logs and differentiating
 Yt
d ln 
 Lt

 Kt
    d ln 

 Lt

  1    d ln H t   d ln At

6
Growth Accounting (II)


GDP data in real terms. All series to be expressed in same currency unit
and base year
Factor shares: Obtained from National Accounts.  is the ratio of
compensation to capital (Net operating Surplus) to total GDP at factor
costs.



Assumption of CRS can be tested if times series of compensation to capital
and labor are available for the analyzed period.
The labor share b (=1- with CRS) can be calculated from National Accounts
as the ratio of remuneration to labor to GDP at factor costs
Capital services are assumed to growth at same rate as capital stock
(which implicitly says that no changes in capacity utilization occur during
the analyzed period)
7
Growth Accounting (III)

Capital stocks (K) estimated from perpetual inventory method, given the
depreciation rate (d) and the Investment flow (I):



Employment data expressed in number of workers per year


Kt = Kt-1*(1-dt) +It
Capital Stock data available from Nehru and Dhareshwar (1993)
If available, use number of hours worked by period
Human Capital accumulation proxy-ed by education attainment. With
different categories of education (primary, secondary, tertiary) a Human
Capital Index may be weighted by means of Returns to Education in each
category.

H t  H t prim 
ROEprimt
 H t sec
ROE sect
 H t high 
ROEhight

8
TFP as a proxy to returns to capital
accumulation

Problems with TFP (and growth accounting, in general)






TFP is a “measure of our ignorance”
Imperfect measures of factors of production
Natural resources not included
Factor shares as elasticities of output to changes in output constitutes
a strong assumption
Is Cobb-Douglas an adequate functional form?
Alternative measures for returns on capital accumulation

Ratio of Net operating Surplus (From National Stocks) to capital
stocks (estimated from perpetual inventory method)
9
Case example
10
Is the rate of return on economic activity
low?

Assess TFP growth using growth decomposition at
the aggregate level




Look at the TFP and factor accumulation trends
Look at the estimates in recent years and the final year
Conduct sensitivity analysis to see whether the finding are
sensitive to changes in the qualitative findings
The aggregate TFP growth estimates may be
misleading: it is important to look at sources of
growth
11
The case of Mongolia.
Efficiency has improved…
25.00%
20.00%
15.00%
10.00%
5.00%
0.00%
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
-5.00%
-10.00%
-15.00%
Output growth
TFP growth
Source: Ianchovichina and Gooptu (2007)
Factor growth
Linear (TFP growth)
12
Sensitivity analysis

Productivity growth was positive in 2004 under:


Different values for the parameters
Different functional forms
TFP growth estimates in 2004 (%)
(Cobb-Douglas)
α=0.3
α=0.4
γ=1 (CRTS)
5.8
5.2
γ=1.2 (IRTS)
5.0
4.2
γ=0.8 (DRTS)
6.7
6.2
TFP growth estimates in 2004 (%)
(CRTS CES)
σ=0.8
σ=1
α=0.5
7.1
4.5
Source: Staff estimates
α=0.5
4.5
3.4
5.7
σ=1.2
2.6
13
Sectoral decomposition
Not all sectors enjoyed high returns to capital


Returns to capital in manufacturing and transport were negative
Returns in agriculture were very volatile
Industries’ contribution to real growth in Mongolia (percentage points)
1996
1997
1998
1999
2000
2001
1.2
1.6
2.5
1.7
-6.2
-6.2
Agriculture
Industry
-1.7
-0.9
0.9
0.0
-0.2
3.7
Manufacturing
-2.4
-1.4
0.3
-0.5
-0.4
2.2
Mining
0.6
0.6
0.6
0.5
0.6
1.2
Construction
0.1
-0.1
0.0
0.0
-0.4
0.3
Services
1.6
3.2
-0.1
-0.1
3.4
1.5
Utilities
-0.8
-0.1
0.1
0.1
0.2
0.4
Transport
0.5
0.0
0.6
0.0
1.2
1.4
Trade
0.3
3.2
-1.2
-1.6
1.3
0.1
Other services
1.6
0.1
0.4
1.4
0.7
-0.3
Source: Staff estimates based on data from World Bank (LDB).
2002
-3.5
0.4
1.2
-1.2
0.4
6.0
0.2
2.0
2.7
1.1
2003
1.1
1.6
0.7
-0.3
1.2
3.1
0.0
1.5
1.4
0.2
2004
4.1
4.0
-0.1
4.1
0.0
1.5
0.1
1.8
-0.7
0.3
2005
1.9
-0.1
-2.2
1.7
0.4
4.3
0.1
-0.3
4.3
0.3
14
What do these results tell us?




Growth in Mongolia has been narrowly-based
Driven by the booming mining and real estate
sectors
Mongolia has remained vulnerable to terms-of-trade
changes
Large part of Mongolia’s labor force employed in
low-productivity activities
15
The case of Benin
Efficiency has declined…
12
y = -0.0884x + 0.9491
10
R2 = 0.0726
8
Annual % change
6
4
2
0
t
-2
-4
-6
-8
-10
72 974 976 978 980 982 984 986 988 990 992 994 996 998 000 002 004 006
19
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
Output
TFP
Factor growth
Linear (TFP)
Source: Ianchovichina (2008) based on the following assumptions:
Cobb-Douglas production function with CRTS and capital share α=0.4.
16
Sensitivity analysis


Result for 2006 is robust to changes in specifications
We rule out the possibility that this productivity deterioration was
due to negative TOT shocks as Benin’s TOT remained unchanged
in the period 2003-06
Sensitivity analysis of TFP growth in 2006
TFP growth estimates in 2006 (%)
(Cobb-Douglas)
α=0.3
α=0.4
γ=1 (CRTS)
-3.3
-3.6
γ=1.2 (IRTS)
-4.7
-5.1
γ=0.8 (DRTS)
-1.9
-2.1
TFP growth estimates in 2006 (%)
(CRTS CES)
σ=0.8
σ=1
α=0.5
-2.7
-3.9
α=0.5
-3.9
-5.5
-2.4
σ=1.2
-4.9
17
Need to rule out exogenous shocks
Terms of Trade (Export prices/ Import prices)
Index 2000 =100
110
100
90
80
70
91
9
1
93
9
1
95
9
1
97
9
1
99
9
1
01
0
2
03
0
2
Source: Ianchovichina (2008) and Benin CEM, Chapter 1
05
0
2
18
Over the years Benin grew primarily through expansion
of capacity, not more efficient use of existing capacity
Sources of growth
12
10
Annual % growth
8
6
4
2
0
-2
-4
1972-1979
GDP growth
1980-1989
Caital Storck Growth
1990-1999
Labor (quality adjusted Growth)
2000-2006
TFP Growth
Source: Ianchovichina (2008) and Benin CEM, Chapter 1
19
Industry has stagnated…
Key drivers of growth: agriculture and trade
Industries’ contribution to real growth in Benin (percentage points)
GDP
Agriculture
Industry
Manufacturing
Utilities
Mining
Construction
Services
Transport
Trade
Public
administration
Other services
1997
6.1
2.3
0.6
0.2
0.1
-0.2
0.5
3.3
0.5
1.5
0.5
1998
4.5
2.6
0.1
0.1
0.0
-0.1
0.1
1.9
0.4
0.5
0.4
1999
4.7
1.7
0.3
0.2
0.2
-0.5
0.4
2.7
0.5
1.3
0.3
2000
5.8
2.6
1.3
0.2
0.2
0.0
0.9
1.9
0.3
0.8
0.3
2001
5.0
1.2
1.4
0.2
0.2
0.0
0.9
2.4
0.4
0.9
0.3
2002
4.5
2.6
0.8
0.2
0.1
0.0
0.5
1.1
0.2
0.4
0.1
2003
3.9
0.6
0.3
0.2
0.2
-0.1
0.0
3.0
0.5
1.1
0.4
2004
3.1
1.5
-0.4
0.1
0.1
0.0
-0.6
2.0
0.4
0.8
0.1
2005
2.9
0.8
0.3
0.1
0.1
0.0
0.1
1.8
0.4
0.7
0.1
Average
4.5
1.8
0.5
0.2
0.1
-0.1
0.3
2.2
0.4
0.9
0.3
0.9
0.6
0.7
0.5
0.7
0.5
1.0
0.7
0.6
0.7
Source: Ianchovichina (2008) and Benin CEM, Chapter 1
20