Download Inclusive Growth Framework

Growth Decomposition and
Productivity Trends
Applied Inclusive Growth Analytics Course
June 30, 2009
Leonardo Garrido and Elena Ianchovichina
Presentation plan

Discuss different approaches for growth decomposition:





Introduce a simple Growth Accounting and Potential Growth
Model


Demand
Sectors of economic activity
Accounting
Shapley
Case example: Togo
Case examples: Mongolia and Benin
2
Contribution of Demand Components to
Growth
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.
Calculate annual growth rate of each component of aggregate demand;
y  e
  yT
 ln 
  y0

 T



 





1
2.
Calculate shares of each component of aggregate demand
3.
Calculate the contribution to growth of each component by multiplying growth
rates of demand components times share of component in aggregate demand
1.
(See excel file example)
3
Contribution of Demand Components to
Growth: A West African Economy.
Growth Rates of Aggregate Demand / Supply by Demand Components. By Decades.
Imports of
Aggregate
Goods and
Supply / Demand
Services
1970s
2.8%
10.9%
5.8%
1980s
1.1%
1.0%
1.0%
1990s
2.3%
-1.2%
0.9%
2000s
1.8%
4.0%
2.6%
Source: Staff Calculations based on World Bank, WDI
Period
Real GDP
Private
Consumption
Government
Consumption
Gross Capital
Formation
-1.1%
4.9%
4.1%
1.2%
9.8%
-2.3%
-0.5%
3.9%
11.9%
-0.2%
-4.8%
3.4%
Private
Consumption
Government
Consumption
Gross Capital
Formation
40.3%
45.8%
60.4%
60.5%
9.9%
8.9%
7.8%
7.2%
13.4%
9.9%
7.3%
7.7%
Exports of
Goods and
Services
8.5%
-1.0%
0.3%
5.6%
Shares in Real Aggregate Supply of GDP and Demand Components
Imports of
Aggregate
Goods and
Supply / Demand
Services
1970s
64.3%
35.7%
100.0%
1980s
58.5%
41.5%
100.0%
1990s
65.2%
34.8%
100.0%
2000s
65.0%
35.0%
100.0%
Source: Staff Calculations based on World Bank, WDI
Period
Real GDP
Exports of
Goods and
Services
25.4%
26.4%
22.8%
24.8%
Contribution to Growth in Aggregate Demand / Supply by Demand Components. By Decades.
Imports of
Aggregate
Goods and
Supply / Demand
Services
1970s
1.8%
3.9%
5.8%
1980s
0.6%
0.4%
1.0%
1990s
1.5%
-0.4%
0.9%
2000s
1.2%
1.4%
2.6%
Source: Staff Calculations based on World Bank, WDI
Period
Real GDP
Private
Consumption
Government
Consumption
Gross Capital
Formation
-0.4%
2.2%
2.5%
0.7%
1.0%
-0.2%
0.0%
0.3%
1.6%
0.0%
-0.4%
0.3%
Exports of
Goods and
Services
2.2%
-0.3%
0.1% 4
1.4%
Sector Contribution to GDP Growth.


Analogous to the demand contribution to growth

GDP at factor costs = Sum of GDP at factor costs by economic activity

GDP at market prices = GDP at factor costs plus net taxes

Net taxes = VAT plus Net import taxes and duties

Calculations of GDP by sectors of economic activity include the value of
banking services provided in the generation of output. Since Banking and
Insurance sector is also included in Sector GDP, one has to deduct those
services from total GDP at factor costs.
Always check for discrepancies in both, GDP demand versus
sum of components, and Sector GDP versus sum of GDP by
activities.
5
Sector Contribution to GDP Growth: A West
African Economy
GDP Values (Billions CFA of 2000)
Sectors of Economic activity
Primary
-Agriculture
Food crops
Cash crops
-Livestock, forestry, fishing
Secondary
-Mining
of which: Phosphate rock
-Manufacturing
-Construction
-Electricity, Water, Gas
Tertiary
-Merchant Services
Commerce
Transport and Communications
Banking and Insurance
Other services
-Nonmerchant Services
Imputed production of banking services
Imputed rent
Public services
Domestic services
2001
2006
Averages 2001-2006
GDP mkt Annual Growth
price Share
Rate
37.4
1.6
Contribution to
GDP growth
0.6
332.0
365.8
253.3
212.3
41.0
78.7
267.3
252.9
14.4
98.5
28.1
24.8
3.3
9.3
170.5
195.0
19.6
2.3
0.4
30.3
21.4
85.7
21.6
32.9
44.9
26.2
79.8
34.3
36.0
4.5
2.7
9.0
2.6
3.5
6.8
3.4
-1.2
8.0
1.5
0.3
0.1
-0.1
0.3
0.1
0.9
3.0
-16.0
3.8
0.2
0.7
-0.2
0.4
330.9
360.9
34.5
1.5
0.5
225.3
117.2
46.7
12.4
49.0
105.6
-10.7
20.9
94.5
0.9
247.2
132.9
65.6
8.3
40.4
113.7
-3.1
24.3
91.8
0.6
22.8
12.1
5.9
0.9
4.0
11.7
-0.7
2.4
9.9
0.1
1.6
2.1
5.8
-6.6
-3.1
1.2
-18.8
2.6
-0.5
-6.2
0.4
0.3
0.4
-0.1
-0.1
0.1
0.1
0.1
0.0
0.0
Total GDP at Factor Cost
Net Taxes
833.4
921.7
91.5
1.7
1.5
62.0
95.0
8.5
7.4
0.7
GDP at constant prices
895.4
1,016.7
100.0
2.1
2.1
Source: Staff Calculations, based on IMF, Central Bank of West African States data
6
Growth Accounting (I)

With CRS Hicks Neutral Cobb Douglas production function
Yt  At  Kt  Lt  Ht 


Dividing by L, taking logs and differentiating:
 Yt
d ln 
 Lt

1

 Kt
    d ln 

 Lt

  1    d ln H t   d ln At

Notice that the variable in parenthesis in the left hand side is
not GDP per capita, but average product of labor.


Growth Accounting decompositions normally use per capita GDP
When per capita GDP growth differs from the growth in per unit of
worker GDP, the difference will be accounted for in TFP

It may be an important source of error when countries are experience a
demographic transition
7
Growth Accounting. Nuts and Bolts (I)


GDP data in real terms. All series to be expressed in same currency 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.


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 assumed to growth at same rate as capital stock (which
implicitly says that no changes in capacity utilization occur during the
analyzed period)
8
Growth Accounting. Nuts and Bolts (II)


Capital Stock data available in sources such as Nehru and Dhareshwar
(1993) and Izyumov & Vahaly (2008)
Updates to capital stock obtained from perpetual inventory method,
given the depreciation rate (d) and the Investment flow (I):


Kt = Kt-1*(1-dt) +It
If no data available in capital stock, an estimate of initial capital stock (K0) can be
obtained using the depreciation rate dt as follows:
K 0  I 0 dt
9
Growth Accounting. Nuts and Bolts (III)

Non – parametric estimation of TFP (residual)


Requires assumptions on the production function specification, economies of scale,
knowledge of values of GDP, inputs and input shares.
TFP can also be computed econometrically by means of a times series regression
of the growth rate of GDP on capital and employment growth
Y Y  b 0  b1  K K   b 2  L L 




Intercept (b0) measures TFP
Coefficients (b1 ,b2)measure elasticity of output to changes in inputs (assumed to
equal factor shares under perfect competition)
CRS Assumption can be tested (Hypothesis b1 b2=1)
Dual approach to growth accounting: TFP (Solow Residual) calculated from
growth rates of factor prices, rather than factor quantities:
Y  R  K  w  L  Y Y  s  R R  K K  s  w w  L L
k

 TFP  Y Y  sk  K K   sL  L L   sk



 R R   s  w w
L
L
10
Growth Accounting. Nuts and Bolts (IV)


Growth accounting uses population (P) as proxy for individuals that generate
GDP (workers)
One can further decompose GDP per capita to capture demographic and
labor force dynamics:
 GDP   GDP   Wor ker s   LaborForce   WorkingAgePop  

  
  
 
 
  
Pop
Wor
ker
s
LaborForce
WorkingAge
Pop
Pop
t 
t 

t 
t 
t 




GDP/Workers = Average product of labor (Ypw)
Workers / Labor Force = Employment Rate (emp)
Labor Force / Working Age Pop. = Participation Rate (pr)
Working Age Pop. / Population is a proxy for age dependency ratio = padr=1/(adr+1)
where adr=(Pop under 15years of age + Pop over 64years of age ) / Pop aged 15.64
 GDP 

  Ypwt  empt  prt  padrt 
Pop

t
11
Growth Accounting. Nuts and Bolts (V)

Thus way, Human Capital accumulation can be modeled as:
H t  Popt  empt  prt  adrt  exp ROE Schooling
t




t
Where ROEt is a measure of returns to education and Schoolingt is a
proxy for the time a person invests building human capital (Average
years of schooling)
Returns to education normally calculated from Mincerian specifications
Traditionally, attainment data (Average Years of Schooling) has been
drawn from Barro and Lee (2000)
A new improved, richer dataset from Lutz. Et al (2007) available.

Lutz, Cuaresma and Sanderson (2008): The demography of Educational Attainment.
12
Problems with TFP (and with the growth
accounting decomposition, in general)

TFP: A “black box” or a “measure of our ignorance” which, as a
residual, picks up:



Imperfect measurement of factors of production
Omission of inputs in the production function (i.e. natural resources)
Possible incorrectness of assumptions:



Factor shares as output elasticity of factors reasonable only under perfect
competition
Functional form: Is Cobb-Douglas a reasonable specification? An
empirical question.
Alternative forms include CES (CRS or not), translogarithmic….
13
Problems with TFP…. (Cont’d)

To [partially] compensate for these shortcomings:

Further decomposition of GDP by economic activities and /or
employment by labor category:


Korea’s Growth Potential (Ianchovichina and Leipziger, 2008)
Alternative calculations for TFP: Micro level data.

TFP from ICA data: Escribano and Guasch (2004) : “Assessing the
Impact of the Investment Climate on Productivity Using Firm-Level
Data”
14
Growth Potential

Uses Extended Growth Accounting Framework (considering
population and labor dynamics)

Observe historical trends in variables of interest





Assumptions on future trends based on historical behavior
Use logistic specification when exponential growth is observed in historical
data
Make assumptions on the capital formation ratio to GDP and on
TFP growth.
Implicit assumptions on capacity utilization
Sensitivity analysis
15
Growth Accounting and Potential
example: The case of Togo

Excel based tool
16
Shapley decomposition

A tool for analyzing how employment generation and productivity growth
translates into poverty reduction




How is growth reflected in employment generation and in changes in output per
worker?
How is growth reflected in the sectoral pattern of growth and employment generation?
What are the sources of changes in output per worker?
Employment and Growth Analysis Tool: http://go.worldbank.org/461KJUVOX0
17
Shapley Decomposition
GDP growth
Employment Rate
Changes
Sectoral pattern
of employment
generation
Changes in
Aggregate Output
per Worker
Changes in the
demographic
structure of the
population
Changes within
sector
Employment
relocation effects
(Between effects)
Changes in
capital labor ratio
and TFP growth
The role of each
sector on
relocation effects
18
Putting everything together: Contribution of each component to total per capita output growth
Shapley Decomposition. The Case of
Tajikistan
Tajikistan: Decomposition of Changes in Per Capita GDP in components (Percent points
Per Year). 1997-2007
Contributions from changes in:
Sectoral
Output per
Level
composition of
worker Employment
employment
Change in Per Capita GDP:
Sectoral Contribution
7.2
-0.1
-1.0
-Primary
-Secondary
-Tertiary
2.2
3.7
1.4
0.2
-0.4
0.0
-0.2
-0.9
0.0
Participation rate
Pop1564/Population
Total
6.5
6.1
2.3
2.4
1.4
-0.6
0.9
Source: Staff Calculations.
19
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
20
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)
21
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
22
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
23
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
24
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.
25
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
26
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
27
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
28
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
29
The Case of Tajikistan: Efficiency Gains from
Increased Used of Existing Capacity
Real Per Capita GDP, and Growth rate of Total and Per Capita GDP
(LCU). 1986-2008
20%
400
0%
250
-10%
200
150
-20%
100
-30%
50
-40%
Real GDP growth rate (LCU)
Real GDP pc growth rate (LCU)
2008
2007
2006
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
1995
1994
1993
1992
1991
1990
1989
1988
1987
0
1986
% change per year
300
Real LCU per capita
350
10%
Real GDP per capita (LCU)
30