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

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;

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:

9

Growth Accounting. Nuts and Bolts (II)

tdIK 00

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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

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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

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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

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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

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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)