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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: Demand Sectors of economic activity Accounting Shapley

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Growth Decomposition and Productivity Trends

Applied Inclusive Growth Analytics Course

June 30, 2009

Leonardo Garrido and Elena Ianchovichina


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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:

    • 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)



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Sector Contribution to GDP Growth. Economy.

  • 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.



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Growth Accounting (I) Economy.

  • 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


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Growth Accounting. Nuts and Bolts (I) Economy.

  • 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)


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Growth Accounting. Nuts and Bolts (II) Economy.

  • 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


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    Growth Accounting. Nuts and Bolts (III) Economy.

    • 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:


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    Growth Accounting. Nuts and Bolts (IV) Economy.

    • 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


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    Growth Accounting. Nuts and Bolts (V) Economy.

    • 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.


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    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….


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    Problems with TFP…. (Cont’d) decomposition, in general)

    • 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”


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    Growth Potential decomposition, in general)

    • 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 decomposition, in general)

    • Excel based tool


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    Shapley decomposition decomposition, in general)

    • 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


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    Putting everything together: Contribution of each component to total per capita output growth

    Shapley Decomposition


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    Shapley Decomposition. The Case of Tajikistan to total per capita output growth


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    Is the rate of return on economic activity low? to total per capita output growth

    • 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. to total per capita output growthEfficiency has improved…

    Source: Ianchovichina and Gooptu (2007)


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    Sensitivity analysis to total per capita output growth

    • Productivity growth was positive in 2004 under:

      • Different values for the parameters

      • Different functional forms


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    Sectoral decomposition to total per capita output growthNot all sectors enjoyed high returns to capital

    • Returns to capital in manufacturing and transport were negative

    • Returns in agriculture were very volatile


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    What do these results tell us? to total per capita output growth

    • 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


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    The case of Benin to total per capita output growthEfficiency has declined…

    Source: Ianchovichina (2008) based on the following assumptions:

    Cobb-Douglas production function with CRTS and capital share α=0.4.


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    Sensitivity analysis to total per capita output growth

    • 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


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    Need to rule out exogenous shocks to total per capita output growth

    Source: Ianchovichina (2008) and Benin CEM, Chapter 1


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    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


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    Industry has stagnated… capacity, not more efficient use of existing capacityKey drivers of growth: agriculture and trade

    Source: Ianchovichina (2008) and Benin CEM, Chapter 1



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