Post on 23-Dec-2015
Growth Decomposition and Growth Decomposition and Productivity TrendsProductivity Trends
Applied Inclusive Growth Analytics Course
June 30, 2009Leonardo Garrido and Elena Ianchovichina
Presentation plan Discuss different approaches for growth decomposition:
Demand Sectors of economic activity Accounting Shapley
Introduce a simple Growth Accounting and Potential Growth Model Case example: Togo
Case examples: Mongolia and Benin
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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;
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
1
0
ln
T
y
yT
ey
Contribution of Demand Components to Growth: A West African Economy.
4
Growth Rates of Aggregate Demand / Supply by Demand Components. By Decades.
Period Real GDPImports of
Goods and Services
Aggregate Supply / Demand
Private Consumption
Government Consumption
Gross Capital Formation
Exports of Goods and
Services1970s 2.8% 10.9% 5.8% -1.1% 9.8% 11.9% 8.5%1980s 1.1% 1.0% 1.0% 4.9% -2.3% -0.2% -1.0%1990s 2.3% -1.2% 0.9% 4.1% -0.5% -4.8% 0.3%2000s 1.8% 4.0% 2.6% 1.2% 3.9% 3.4% 5.6%Source: Staff Calculations based on World Bank, WDI
Shares in Real Aggregate Supply of GDP and Demand Components
Period Real GDPImports of
Goods and Services
Aggregate Supply / Demand
Private Consumption
Government Consumption
Gross Capital Formation
Exports of Goods and
Services1970s 64.3% 35.7% 100.0% 40.3% 9.9% 13.4% 25.4%1980s 58.5% 41.5% 100.0% 45.8% 8.9% 9.9% 26.4%1990s 65.2% 34.8% 100.0% 60.4% 7.8% 7.3% 22.8%2000s 65.0% 35.0% 100.0% 60.5% 7.2% 7.7% 24.8%Source: Staff Calculations based on World Bank, WDI
Contribution to Growth in Aggregate Demand / Supply by Demand Components. By Decades.
Period Real GDPImports of
Goods and Services
Aggregate Supply / Demand
Private Consumption
Government Consumption
Gross Capital Formation
Exports of Goods and
Services1970s 1.8% 3.9% 5.8% -0.4% 1.0% 1.6% 2.2%1980s 0.6% 0.4% 1.0% 2.2% -0.2% 0.0% -0.3%1990s 1.5% -0.4% 0.9% 2.5% 0.0% -0.4% 0.1%2000s 1.2% 1.4% 2.6% 0.7% 0.3% 0.3% 1.4%Source: Staff Calculations based on World Bank, WDI
5
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.
6
Sectors of Economic activity 2001 2006GDP mkt
price ShareAnnual Growth
RateContribution to
GDP growthPrimary 332.0 365.8 37.4 1.6 0.6
-Agriculture 253.3 267.3 28.1 0.9 0.2
Food crops 212.3 252.9 24.8 3.0 0.7
Cash crops 41.0 14.4 3.3 -16.0 -0.2
-Livestock, forestry, fishing 78.7 98.5 9.3 3.8 0.4
Secondary 170.5 195.0 19.6 2.3 0.4
-Mining 30.3 44.9 4.5 6.8 0.3
of which: Phosphate rock 21.4 26.2 2.7 3.4 0.1
-Manufacturing 85.7 79.8 9.0 -1.2 -0.1
-Construction 21.6 34.3 2.6 8.0 0.3
-Electricity, Water, Gas 32.9 36.0 3.5 1.5 0.1
Tertiary 330.9 360.9 34.5 1.5 0.5
-Merchant Services 225.3 247.2 22.8 1.6 0.4
Commerce 117.2 132.9 12.1 2.1 0.3
Transport and Communications 46.7 65.6 5.9 5.8 0.4
Banking and Insurance 12.4 8.3 0.9 -6.6 -0.1
Other services 49.0 40.4 4.0 -3.1 -0.1
-Nonmerchant Services 105.6 113.7 11.7 1.2 0.1
Imputed production of banking services -10.7 -3.1 -0.7 -18.8 0.1
Imputed rent 20.9 24.3 2.4 2.6 0.1
Public services 94.5 91.8 9.9 -0.5 0.0
Domestic services 0.9 0.6 0.1 -6.2 0.0
Total GDP at Factor Cost 833.4 921.7 91.5 1.7 1.5
Net Taxes 62.0 95.0 8.5 7.4 0.7
GDP at constant prices 895.4 1,016.7 100.0 2.1 2.1Source: Staff Calculations, based on IMF, Central Bank of West African States data
GDP Values (Billions CFA of 2000) Averages 2001-2006
Sector Contribution to GDP Growth: A West African Economy
Growth Accounting (I) With CRS Hicks Neutral Cobb Douglas production function
Dividing by L, taking logs and differentiating:
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 transition7
1ttttt HLKAY
ttt
t
t
t AdHdL
Kd
L
Yd lnln1lnln
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 (=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
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:
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Growth Accounting. Nuts and Bolts (II)
tdIK 00
10
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
Intercept (0) measures TFP
Coefficients (12)measure elasticity of output to changes in inputs (assumed to equal factor shares under perfect competition)
CRS Assumption can be tested (Hypothesis 12=1)
Dual approach to growth accounting: TFP (Solow Residual) calculated from growth rates of factor prices, rather than factor quantities:
LLwwsKKRRsYYLwKRY Lk
LLKKYY 210
wwsRRsLLsKKsYYPFT LkLk
11
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/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
Growth Accounting. Nuts and Bolts (IV)
tttttPop
PopWorkingAge
PopWorkingAge
LaborForce
LaborForce
sWor
sWor
GDP
Pop
GDP ker
ker
tttt
t
padrprempYpwPop
GDP
12
Thus way, Human Capital accumulation can be modeled as:
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.
Growth Accounting. Nuts and Bolts (V)
ttSchoolingROE
ttttt adrprempPopH exp
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
14
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”
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
18Putting everything together: Contribution of each component to total per capita output growth
Shapley Decomposition. The Case of Tajikistan
19
Output per worker
Level Employment
Sectoral composition of
employmentTotal
Change in Per Capita GDP: 6.5
Sectoral Contribution 7.2 -0.1 -1.0 6.1 -Primary 2.2 0.2 -0.2 2.3 -Secondary 3.7 -0.4 -0.9 2.4 -Tertiary 1.4 0.0 0.0 1.4
Participation rate -0.6
Pop1564/Population 0.9
Source: Staff Calculations.
Tajikistan: Decomposition of Changes in Per Capita GDP in components (Percent points Per Year). 1997-2007
Contributions from changes in:
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…
21
-15.00%
-10.00%
-5.00%
0.00%
5.00%
10.00%
15.00%
20.00%
25.00%
1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004
Output growth TFP growth Factor growth Linear (TFP growth)
Source: Ianchovichina and Gooptu (2007)
Sensitivity analysis Productivity growth was positive in 2004 under:
Different values for the parameters Different functional forms
22
TFP growth estimates in 2004 (%) (Cobb-Douglas)
α=0.3 α=0.4 α=0.5 γ=1 (CRTS) 5.8 5.2 4.5 γ=1.2 (IRTS) 5.0 4.2 3.4 γ=0.8 (DRTS) 6.7 6.2 5.7
TFP growth estimates in 2004 (%) (CRTS CES)
σ=0.8 σ=1 σ=1.2 α=0.5 7.1 4.5 2.6
Source: Staff estimates
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
23
Industries’ contribution to real growth in Mongolia (percentage points)
1996 1997 1998 1999 2000 2001 2002 2003 2004 2005
Agriculture 1.2 1.6 2.5 1.7 -6.2 -6.2 -3.5 1.1 4.1 1.9 Industry -1.7 -0.9 0.9 0.0 -0.2 3.7 0.4 1.6 4.0 -0.1 Manufacturing -2.4 -1.4 0.3 -0.5 -0.4 2.2 1.2 0.7 -0.1 -2.2 Mining 0.6 0.6 0.6 0.5 0.6 1.2 -1.2 -0.3 4.1 1.7 Construction 0.1 -0.1 0.0 0.0 -0.4 0.3 0.4 1.2 0.0 0.4 Services 1.6 3.2 -0.1 -0.1 3.4 1.5 6.0 3.1 1.5 4.3 Utilities -0.8 -0.1 0.1 0.1 0.2 0.4 0.2 0.0 0.1 0.1 Transport 0.5 0.0 0.6 0.0 1.2 1.4 2.0 1.5 1.8 -0.3 Trade 0.3 3.2 -1.2 -1.6 1.3 0.1 2.7 1.4 -0.7 4.3 Other services 1.6 0.1 0.4 1.4 0.7 -0.3 1.1 0.2 0.3 0.3
Source: Staff estimates based on data from World Bank (LDB).
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 BeninEfficiency has declined…
25
y = -0.0884x + 0.9491
R2 = 0.0726
-10
-8
-6
-4
-2
0
2
4
6
8
10
12
Ann
ual %
cha
nge
Output TFP Factor growth Linear (TFP)
t
Source: Ianchovichina (2008) based on the following assumptions: Cobb-Douglas production function with CRTS and capital share α=0.4.
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
26
Sensitivity analysis of TFP growth in 2006 TFP growth estimates in 2006 (%)
(Cobb-Douglas) α=0.3 α=0.4 α=0.5
γ=1 (CRTS) -3.3 -3.6 -3.9 γ=1.2 (IRTS) -4.7 -5.1 -5.5 γ=0.8 (DRTS) -1.9 -2.1 -2.4
TFP growth estimates in 2006 (%) (CRTS CES)
σ=0.8 σ=1 σ=1.2 α=0.5 -2.7 -3.9 -4.9
Need to rule out exogenous shocks
27
Terms of Trade (Export prices/ Import prices)
70
80
90
100
110
1991
1993
1995
1997
1999
2001
2003
2005
Ind
ex 2
000
=10
0
Source: Ianchovichina (2008) and Benin CEM, Chapter 1
Over the years Benin grew primarily through expansion of capacity, not more efficient use of existing capacity
28
Sources of growth
-4
-2
0
2
4
6
8
10
12
1972-1979 1980-1989 1990-1999 2000-2006
Ann
ual %
gro
wth
GDP growth Caital Storck Growth Labor (quality adjusted Growth) TFP Growth
Source: Ianchovichina (2008) and Benin CEM, Chapter 1
Industry has stagnated…Key drivers of growth: agriculture and trade
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Industries’ contribution to real growth in Benin (percentage points) 1997 1998 1999 2000 2001 2002 2003 2004 2005 Average
GDP 6.1 4.5 4.7 5.8 5.0 4.5 3.9 3.1 2.9 4.5 Agriculture 2.3 2.6 1.7 2.6 1.2 2.6 0.6 1.5 0.8 1.8 Industry 0.6 0.1 0.3 1.3 1.4 0.8 0.3 -0.4 0.3 0.5 Manufacturing 0.2 0.1 0.2 0.2 0.2 0.2 0.2 0.1 0.1 0.2 Utilities 0.1 0.0 0.2 0.2 0.2 0.1 0.2 0.1 0.1 0.1 Mining -0.2 -0.1 -0.5 0.0 0.0 0.0 -0.1 0.0 0.0 -0.1 Construction 0.5 0.1 0.4 0.9 0.9 0.5 0.0 -0.6 0.1 0.3 Services 3.3 1.9 2.7 1.9 2.4 1.1 3.0 2.0 1.8 2.2 Transport 0.5 0.4 0.5 0.3 0.4 0.2 0.5 0.4 0.4 0.4 Trade 1.5 0.5 1.3 0.8 0.9 0.4 1.1 0.8 0.7 0.9 Public administration
0.5 0.4 0.3 0.3 0.3 0.1 0.4 0.1 0.1 0.3
Other services 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
The Case of Tajikistan: Efficiency Gains from Increased Used of Existing Capacity
30
0
50
100
150
200
250
300
350
400
-40%
-30%
-20%
-10%
0%
10%
20%
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
Re
al L
CU
pe
r c
ap
ita
% c
ha
ng
e p
er
yea
r
Real Per Capita GDP, and Growth rate of Total and Per Capita GDP (LCU). 1986-2008
Real GDP growth rate (LCU) Real GDP pc growth rate (LCU) Real GDP per capita (LCU)