1. Growth Decomposition and Productivity Trends
Applied Inclusive Growth Analytics Course
June 30, 2009
Leonardo Garrido and Elena Ianchovichina
Round table presentation

2. 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

3. 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:
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
(See excel file example)

4. Contribution of Demand Components to Growth: A West African Economy.

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. Sector Contribution to GDP Growth: A West African Economy

7. 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 transition

8. 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. a is the ratio of compensation to capital (Net operating Surplus) to total GDP at factor costs.
The labor share b (=1-a 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)

9. 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: 9

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 (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:

11. 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/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

12. Growth Accounting. Nuts and Bolts (V)
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.

13. 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….

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”

15. 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

16. Growth Accounting and Potential example: The case of Togo
Excel based tool

17. 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:

18. Shapley Decomposition
GDP growth
Employment Rate Changes
Sectoral pattern of employment generation
Changes in Aggregate Output per Worker
Changes within sector
Changes in capital labor ratio and TFP growth
Employment relocation effects (Between effects)
The role of each sector on relocation effects
Changes in the demographic structure of the population
Putting everything together: Contribution of each component to total per capita output growth

19. Shapley Decomposition. The Case of Tajikistan

20. 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

21. The case of Mongolia. Efficiency has improved…
Source: Ianchovichina and Gooptu (2007)

22. Sensitivity analysis Productivity growth was positive in 2004 under:
Different values for the parameters
Different functional forms

23. 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

24. 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

25. The case of Benin Efficiency has declined…
Source: Ianchovichina (2008) based on the following assumptions:
Cobb-Douglas production function with CRTS and capital share α=0.4.

26. 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

27. Need to rule out exogenous shocks
Source: Ianchovichina (2008) and Benin CEM, Chapter 1

28. Over the years Benin grew primarily through expansion of capacity, not more efficient use of existing capacity
Source: Ianchovichina (2008) and Benin CEM, Chapter 1

29. Industry has stagnated… Key drivers of growth: agriculture and trade
Source: Ianchovichina (2008) and Benin CEM, Chapter 1

30. The Case of Tajikistan: Efficiency Gains from Increased Used of Existing Capacity