Productivity Measures By Tarun Das

Official Economic Statistics by Tarun Das

Lectures on Productivity Measures _______________________________________________ _

Professor Tarun Das1

UN Statistical Institute for Asia and Pacific Chiba, Japan 20-24 August 2007

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Professor Tarun Das teaches Public Policy and Research Methodology to the MBA students at the Institute for Integrated Learning in Management (IILM), New Delhi. Presently, he is working at Ulaanbaatar, Mongolia as Glocom Inc. (USA) Expert on Strategic Planning under an ADB Project on Governance Reforms in the Ministry of Finance, Government of Mongolia. Earlier he worked as Economic Adviser in the Ministry of Finance and Planning Commission, Government of India. For any clarification, contact [email protected]/ [email protected]

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Official Economic Statistics by Tarun Das

ACKNOWLEDGEMENTS

Professor Tarun Das teaches Public Policy and Research Methodology to the MBA students at the Institute for Integrated Learning in Management (IILM), New Delhi. Presently, he is working at Ulaanbaatar, Mongolia as Glocom Inc. (USA) Expert on Strategic Planning under an ADB Project on Governance Reforms in the Ministry of Finance, Government of Mongolia. Earlier he worked as Economic Adviser in the Ministry of Finance and Planning Commission, Government of India. These lectures were prepared by the author at the IILM, New Delhi for the training of the Indian Statistical Service and Indian Economic Service. The lectures have been modified to some extent to suit the needs of statistical officers from various countries participating the training program at the UN Statistical Institute of Statistics for Asia and Pacific (SIAP), Chiba, Japan. The lectures are broadly based on various IMF publications and manuals on these topics. It is needless to indicate that these lectures express personal views of the author which may not necessarily reflect the views of the organisations he is associated with. The author is fully responsible for any omissions or errors in these lecture notes. Author would like to express his deepest gratitude to Ms. Davaasuren Chultemjamts, Director, UNSIAP and Dr. Kulshreshtha, Professor (Statistics), UNSIAP for providing an opportunity to deliver these lectures to the participants of the Third Group Training Course in Analysis, Interpretation and Dissemination of Official Economic Statistics during 20-24 August 2007 at UNSIAP, Chiba, Japan. Author is also grateful to the Ministry of Finance, Government of Mongolia, particularly to Mr. Batjargal, Director General, Fiscal Policy and Co-ordination Department for granting necessary permission to deliver these lectures.

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Official Economic Statistics by Tarun Das

Contents 1. Brief profile of the resource person 2. Productivity Analysis (pages 93-108) 6.1 Production Function 6.2 Equilibrium of the Firm 6.3 Cobb-Douglas Production Function 6.4 Total factor productivity 6.5 Growth accounting 6.6 Solow residual 6.7 Regression analysis and the Solow residual 6.8 Critique of the measurement in rapidly developing economies 6.9 Multifactor Productivity 6.10 Application of Index methods 6.11 Workout Session on Productivity in Japan

Answrs to Workout Sessions (pages 109-127) Selected References Lecture notes have been prepared mainly on the basis of the following IMF Publications and Manuals: Government Finance Statistics (GFS) 1986 Government Finance Statistics Manual (GFSM) 2001 Government Finance Statistics (GFS) Yearbook 2006 Monetary and Financial Statistics Manual (MFSM) 2007 Monetary and Financial Statistics (MFS): Compilation Guide 2007 International Financial Statistics (IFS) Balance of Payments Manual 2005 Balance of Payments Statistics Yearbook 2006

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Official Economic Statistics by Tarun Das Profile of the Resource Person Prof. Tarun Das • Professor Tarun Das teaches Public Policy and Research Methodology to the MBA students at the Institute of Integrated Learning in Management (IILM), 3 Lodhi Institutional Area, New Delhi-110003, India. • Presently, he is working at Ulaanbaatar, Mongolia as Glocom Inc. (USA) Expert on Strategic Planning under an ADB Project on Governance Reforms in the Ministry of Finance, Government of Mongolia. Earlier he worked as Economic Adviser in the Ministry of Finance and Planning Commission, Government of India. • Work Experience: 35 yrs as Development Economist in the government of India: Last assignments: Economic Advisor, Planning Commission (1986-1988) and Economic Adviser, Min of finance (1986-2006) • Country Co-coordinator for the IMF Govt Finance Statistics, Special Data Dissemination Standards, World Bank Global Development Finance (1990-2003), the Commonwealth Secretariat Debt Recording and Management System for India (1998-2003). • Worked as Consultant to the World Bank (Washington), ADB (Manila), UNDP (New York), UNESCAP (Bangkok), ILO (Geneva), UNCTAD (Geneva), UNITAR (Geneva), Global Development Network (GDN) (Washington), UN Commission for Africa (Addis Ababa). • Worked on Fiscal Management for the governments of Cambodia, Indonesia, Lao PDR, Mongolia, Nepal, Philippines and Samoa. • Member of Govt. Delegate to World Bank, ADB, IMF, UNCSD, WTO. • Research/Teaching Interest: Macro Econometric Modeling and Policy Planning, Research Methodology, Public Policy, Economic Reforms, Poverty, Inequality, Transport Modeling, Public Debt and External Debt. • Dr. Das is a widely traveled person and possesses diversity in skills in teaching, training, research, policy planning and modeling. He has published a number of books and papers on economic statistics, structural reforms, fiscal policies, management of public debt and external debt, transport modeling, poverty and inequality, foreign investment, technology transfer and privatisation strategy. • Qualifications: MA in Econ. (Gold Medalist), Calcutta University, 1969. Ph. D. in Econ, as Commonwealth Scholar, East Anglia Univ., England, 1977.

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Official Economic Statistics by Tarun Das Course Outline, Scope, Objectives and Pedagogy Background The consultant, an expert in the field of Economic, Financial and Government Statistics will cover select topics in Economic Statistics, namely: Government Finance Statistics (6 sessions), Monetary and Financial Statistics (4 sessions), BOP/Rest of the World Sector(6 sessions), and Productivity analysis (4 sessions) by conducting lecture and workshop sessions during 20-24 August 2007. These lectures form part of the wider Third Group Training Course in Analysis, Interpretation and Dissemination of Official Statistics, 2007 at U.N. Statistical Institute for Asia and the Pacific, Chiba.

Objectives The course aims to strengthen the capability of the national statistical services to take part in the process of improving their economic statistics and quality of analysis, interpretation and dissemination of official statistics. The consultant is expected to impart training to help participants understand select topics of the systems of economic accounts, specifically the system of Government Finance Statistics, Monetary and Financial Statistics, Balance of Payment Statistics, and Productivity analysis for their countries

Learning Outcome 1.

2. 3.

Develop a comprehensive understanding of the basic concepts, analytical framework, database, methodology, uses, applications and limitations of economic statistics. Develop skills and capabilities for analytical presentation, networking and teamwork through group workout sessions. More emphasis will be laid on understanding basic concepts, methodology, techniques, and their uses and limitations for various situations, rather than formal proofs and derivation of formula.

Pedagogy 1. Teaching techniques will consist of formal lectures, case studies, practical and workout sessions, and preparation and presentation of group project reports. 2. Selected case studies would be given so as to facilitate participants to relate to theoretical concepts with real life situations in economic analysis, policy formulation and planning. The students would present and discuss these case studies in the class. 3. Participants will be provided with complete course material well in advance. To make classroom presentations by the resource person more meaningful and effective, participants are required to come prepared and collect related information and data from journals, newspapers and websites, and participate actively in classroom sessions. 4. In order to develop teamwork and networking capabilities, students are encouraged to participate actively in group discussions and workout sessions.

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Official Economic Statistics by Tarun Das

Productivity Analysis Professor Tarun Das, IILM, New Delhi-110003, India

Introduction Productivity of an input or a factor of production means the contribution of the factor to overall production for which it is used. In general, productivities are measured by fitting production functions.

1) Production Function Production Function is a technical relation which connects factor inputs and outputs. It represents technology of a firm, industry or the economy, and includes all the technically efficient methods of production. a) Method of production means combination of inputs (factors) required to produce one unit of output. b) Technically efficient method of production: When there are two methods of production A and B, A is said to be more technically efficient than B, if A uses less of at least one factor and no more of other factors compared to B.

2)

Isoquant: Let us assume that a firm uses two factors Labor (L) and Capital (K) and produces a single Output (Q). Then the production function is given by Q = f (K, L) An isoquant is the locus of all feasible combinations of inputs (K, L) which produce the same level of output (Q°). Q° = f (K, L) a) Linear isoquant

Perfect Substitutability

Perfect complementarity of inputs

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Official Economic Statistics by Tarun Das

b) Smooth curve isoquant: Continuous substitutability of K and L over a certain range, beyond which factors cannot substitute each other

3) General form of a production function X = f (L, K, ν, γ) Where X= value added L= labour input K= capital input ν = Returns to scale parameter γ = efficiency parameter or total factor productivity (reflecting technological, entrepreneurial-organizational aspects, which are not due to productivities of inputs)

4) Important concepts involved in production functions There are two broad concepts of productivity – average product (AP) and marginal product (MP). Average product measures the output per unit of an input, whereas marginal product means rate of change in output due to change in input by one unit. i)

Average product of factors APL = Q / L,

ii)

APK = Q / K

Marginal product of factors MPL = ∂X/ ∂L,

MPK = ∂X/ ∂K

Average product is always positive. Theoretically, marginal product may be positive, zero or negative. However, production theory concentrates only on the efficient part of the production function (MPL>0 and MPK>0). Also, the production theory concentrates only on the diminishing (but positive) part of the marginal product. That is 7

Official Economic Statistics by Tarun Das

MPL>0 and ∂( MPL )/ ∂L=∂2X/ ∂L2 < 0 MPK>0 and ∂( MPK )/ ∂K=∂2X/ ∂K2 < 0 iii)

Marginal Rate of Substitution (MRS): The slope of the isoquant -∂K/ ∂L is called the MRS or the rate of technical substitution. It defines the degree of substitutability of factors. MRS = -∂K/ ∂L = (∂X/ ∂L) / (∂X/ ∂K) = MPL/ MPK

iv) Factor Intensity: Slope of the line joining origin to the isoquant gives the factor intensity. The lower part of the isoquant is more labour intensive while the upper part is more capital intensive.

v) Elasticity of substitution: MRS depends upon the units of measurement. Elasticity of substitution is a unit-free measure and is defined as follows

σ = [∂(K/L)/(K/L)] / [∂(MRS)/(MRS)] vi) Product Lines: A product line shows the physical movement from one isoquant to another, which is the same as the change in output from level to another, resulting from change in one or both of the factors of production. vii) Isocline: Isocline is the locus of points on different isoquants where the MRS is constant. For homogenous functions, the isoclines are straight lines passing through the origin and the K/L ratio (factor intensity) is constant along the isocline. However, in case of non-homogenous production functions, isoclines are not straight lines and the K/L ratio (factor intensity) is not constant along the isocline.

5)

Homogeneity and Returns to Scale

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Official Economic Statistics by Tarun Das Suppose the production function is X= f (L, K) and we increase the inputs λ times, then the new output is X* = f (λ L, λ K). If X*= f (λ L, λ K) = λ

β

. f (L,K) = λ

β

. X,

then the production function is said to be homogenous of degree β . It means that if both β the inputs increase λ times, then production rises λ times. There are three possible cases of a homogenous production functions. β =1; Constant returns to scale => Output increases in the same proportion as inputs. β <1; Decreasing returns to scale => Output increases less than proportionately with inputs β >1; Increasing returns to scale => Output increases more than proportionately with inputs Causes of Increasing Returns to Scale: Technical upgradation and economies of scale. Causes of Decreasing Returns to Scale: Managerial diseconomies at higher levels of output.

6) Law of Diminishing Returns If one of the factors of production (say capital) is fixed, the marginal product of the variable factor (labour) will diminish. If the production function is homogenous with constant or diminishing returns to scale, the productivity of variable factor will necessarily diminish. If the production function exhibits increasing returns to scale, the diminishing returns from decreasing marginal product of the variable factor may be offset, if the returns to scale are significantly large.

7)

Equilibrium of the Firm a)

Maximization of output subject to a cost constraint

Max X=f(L,K) subject to C = wL+rK where w is the wage rate and r the interest rate. Max φ = X+λ(C-wL-rK) where λ is the Lagrangian multiplier ∂φ / ∂K =∂X/ ∂K – λr = 0 => λ = 1/r. ∂X/ ∂K ∂φ / ∂L =∂X/ ∂L – λw = 0 => λ = 1/w. ∂X/ ∂L Equating the values of λ we get b)

[∂X/ ∂L]/[∂X/ ∂K] = MP / MP L

Minimization of cost subject to a output constraint 9

K

= w/r

Official Economic Statistics by Tarun Das

Min C = wL+rK subject to X=f(L,K) Minψ = wL+rK+λ(X-f(L,K))

[

] ∂ψ / ∂L =w-λ.∂X/ ∂L = 0 => λ = w/[∂X/ ∂L] Equating the values of λ we get [∂X/ ∂L]/[∂X/ ∂K] = MP / MP ∂ψ / ∂K =r-λ.∂X/ ∂K = 0 => λ = r/ ∂X/ ∂K .

L

K

= w/r

Therefore the conditions for equilibrium of the firm are i) ii)

8)

MPL/ MPK = w/r The isoquants are convex to the origin.

Choice of the optimal expansion path

The optimal expansion path in the long run is the locus of points of tangency of isocost lines and successive isoquants. If the production function is homogenous, the expansion path is a straight line passing through the origin with the slope being equal to the ratio of factor prices. In the short run, it is a straight line parallel to the axis of the variable factor 9) Cobb-Douglas Production Function2 In economics, the Cobb-Douglas functional form of production functions is widely used to represent the relationship of an output to inputs. It was proposed by Kunt Wicksell (1851-1926), and tested against statistical evidence by Paul Douglas and Charles Cobb in 1928. For production, the function is Y = ALαKβ, where: Y = output; L = labor input ; K = capital input and A, α and β are constants determined by technology. If α + β = 1, the production function has constant returns to scale If α + β < 1, returns to scale are decreasing, and If α + β > 1, returns to scale are increasing. Assuming perfect competition, α and β can be shown to be labour and capital's share of output. 2

Cobb C W and Douglas P H (1928) "A Theory of Production", American Economic Review, 18 (Supplement), 139-165.

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Official Economic Statistics by Tarun Das The exponents α and β are output elasticities with respect to labor and capital, respectively. Output elasticity measures the responsiveness of output to a change in levels of either labor or capital used in production, ceteris paribus. For example if α = 1.5, a 1% increase in labor would lead to approximitely a 1.5% increase in output. Cobb and Douglas,were influenced by statistical evidence that appeared to show that labour and capital shares of total output were constant over time in developed countries; they explained this by statistical fitting least-squares regression of their production function. There is now doubt over whether constancy over time exists. Various representations of the production function The Cobb-Douglas function form can be estimated as a linear relationship using the following expression: Log Y = log A + α log L + β log K

10) Total factor productivity Total-factor productivity (TFP) addresses any effects in total output not caused by inputs or productivity. For example, a year with unusually good weather will tend to have higher output, because bad weather hinders agricultural output. A variable like weather does not directly relate to unit inputs or productivity, so weather is considered a totalfactor productivity variable. The equation below (in Cobb-Douglas form ) represents total output (Y) as a function of total-factor productivity (A), capital input (K), labor input (L), and the two inputs' respective shares of output (α is the capital input share of contribution).

Technology Growth and Efficiency are regarded as two of the biggest sub-sections of Total Factor Productivity, the former possessing "special" inherent features such as positive externalities and non-rivalness which enhance its position as a driver of economic growth. Total Factor Productivity is often seen as the real driver of growth within an economy and studies reveal that whilst labour and investment are important contributors, Total Factor Productivity may account for up to 60% of growth within economies. Growth accounting exercises and Total Factor Productivity are open to the Cambridge Critique. Therefore, some economists believe that the method and its results are invalid. As a residual, TFP is also dependent on estimates of the other components. A 2005 study on human capital attempted to correct for weaknesses in estimations of the labour component of the equation, by refining estimates of the quality of labour. Specifically, 11

Official Economic Statistics by Tarun Das years of schooling is often taken as a proxy for the quality of labour (and stock of human capital), which does not account for differences in schooling between countries. Using these re-estimations, the contribution of TFP was substantially lower. 11) Growth accounting Growth accounting is a set of theories used in economics to explain economic growth. The total national income in an economy may be modeled as being explained by various factors. A basic function of these factors is of Cobb Douglas type; Q=ALxKy K: the total stock of capital (for example, buildings and machinery) available. L: the size of the labor force A: Known as the productivity available, and is computed from technology and efficiency. Here, an increase in national income is explained by an increase in the capital available (K), an increase in the labor force (L), or an improvement in the productivity used (A). The Production Function shows that there are two factors involved in economic growth viz. factor accumulation and improvements in efficiency. The levels of national income, the capital stock, and the size of the labor force can all be estimated through widely available economic statistics. A regression line can then be estimated to explain the level of national income in terms of labor, capital and a residual. A change in the residual, total factor productivity, represents the change in national income that is not explained by changes in the level of inputs (capital and labor) used. Total Factor Productivity can be measured by A=Q/(Lx Ky) This is normally taken as a measure of the level of technology employed. The annualized growth rate of A is called the "Solow residual." Over longer periods of time, it may be used as a measure of technological change. Over shorter periods of time, it could reflect the effect of the business cycle. 12) Solow residual The Solow residual is a number describing empirical productivity growth in an economy from year to year and decade to decade. Robert Solow defined rising productivity as rising output with constant capital and labour input. It is a "residual" because it is the part of growth that cannot be explained through capital accumulation. The Solow Residual is procyclical and is sometimes called the rate of growth of total factor productivity. Solow assumed a very basic model of annual aggregate output over a year (t). He said that the output quantity would be governed by the amount of capital (the infrastructure), the amount of labour (the number of people in the workforce), and the productivity of

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Official Economic Statistics by Tarun Das that labour. He thought that the productivity of labour was the factor driving long-run GDP increases. An example economic model of this form is given below :

Where: Y(t) represents the total production in an economy (the GDP) in some year, t. K(t) is capital in the productive economy - which might be measured through the combined value of all companies in a capitalist economy. L(t) is labour; this is simply the number of people in work, and since growth models are long run models they tend to ignore cyclical unemployment effects, assuming instead that the labour force is a constant fraction of an expanding population. A(t) represents multifactor productivity (often generalized as "technology"). The change in this figure from A(1960) to A(1980) is the key to estimating the growth in labour 'efficiency' and the Solow residual between 1960 and 1980, for instance. Different types of labor are reduced to a common unit, usually unskilled labor. In more complicated general equilibrium models, labor and capital are assumed to be heterogeneous and measured in physical units. In most versions of neoclassical growth theory (for example, in the Solow growth model), however, the function is assumed to apply to the entire economy. Then, the neoclassical theory of the distribution of income sketched above is assumed to apply: under perfect competition, the rate of return on capital goods (r) equals the marginal product of capital goods, while the wage rate (w) equals the marginal product of labor. To measure or predict the change in output within this model, the equation above is differentiated in time (t), giving a formula in partial derivatives of the relationships: labour-to-output, capital-to-output, and productivity-to-output, as shown:

Observe:

Similarly:

and

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Official Economic Statistics by Tarun Das

Therefore:

The growth factor in the economy is a proportion of the output last year, which is given (assuming small changes year-on-year) by dividing both sides of this equation by the output, Y:

The first two terms on the right hand side of this equation are the proportional changes in labour and capital year-on-year, and the left hand side is the proportional output change. The remaining term on the right, giving the effect of productivity improvements on GDP is defined as the Solow residual:

The residual, SR(t) is that part of growth not explicable by measurable changes in the amount of capital, K, and the number of workers, L. If output, capital, and labour all double every twenty years the residual will be zero, but in general it is higher than this: output goes up faster than growth in the input factors. The residual varies between periods and countries, but is almost always positive in peace-time capitalist countries. Some estimates of the post-war U.S. residual credited the country with a 3% productivity increase per-annum until the early 1970s when productivity growth appeared to stagnate. 13) Regression analysis and the Solow residual The above relation gives a very simplified picture of the economy in a single year; what growth theory econometrics does is to look at a sequence of years to find a statistically significant pattern in the changes of the variables, and perhaps identify the existence and value of the "Solow residual". The most basic technique for doing this is to assume constant rates of change in all the variables (obscured by noise), and regress on the data to find the best estimate of these rates in the historical data available (using an Ordinary least squares regression). Economists always do this by first taking the natural log of their equation; this produces a simple linear regression with an error term, ε : 14

Official Economic Statistics by Tarun Das

Ln (Y(t)) = α ln (K(t)) + (1 - α ) ln (L(t)) + (1 - α ) ln (A(t)) + ε : A constant growth factor implies exponential growth in the above variables, so differencing gives a linear relationship between the growth factors which can be deduced in a simple regression. Solow Growth Accounting B. Estimation The two methodologies used in most papers on productivity growth have been growth accounting and econometric estimation of production functions. We briefly review the two methods.

(i) Growth Accounting For empirical purposes, expression (4) poses a conceptual problem. Although it represents output per unit of joint inputs, its interpretation is much less straightforward than that of the partial productivity index, and its meaning, i.e., level of technology, is not clear in direct comparison among different economic units (see the discussion about Kim and Lau’s work [1994] in Section III). For this reason, it is usually expressed in growth rates, that is,

Where qt, lt, kt denote the growth rates of output, labor, and capital, respectively, and ϕt is the rate of total factor productivity growth. The expressions in front of the growth rates of the factors are the respective elasticities. How does neoclassical economics proceed empirically? By assuming perfect competition and profit maximization. Under such conditions, the price elasticity of demand is infinite, factor elasticities equal the factor shares in output, and thus the equation becomes

Where at and (1-at) are the labor and capital shares, respectively (this is the so-called Divisia Index weighing system). Since the national accounts and other statistics provide estimates of all the right-hand side variables, one can easily obtain the rate of productivity growth as a residual category. Expression (6) is the so-called “Solowresidual”, a procedure called growth accounting. The objective of this method is to determine how much economic growth is due to accumulation of inputs and how much can be attributed to technical progress; or, put in different terms, how much of growth can be explained by movements along a production function, and how much should be attributed to advances in technological and organizational competence, the shift in the production function (Nelson 1973). With discrete data, researchers use the so-called Tornqvist index. This views that expressions (5)-(6) are derived using differential calculus. In the discrete case it can be shown that Chambers 1988)

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Official Economic Statistics by Tarun Das

14) Why the productivity growth is attached to labour The Solow residual measures total factor productivity, but is normally attached to the labour variable in the macroeconomy because return on investment doesn't seem to change very much in time or between developing nations, and developed nations—not nearly as much as human productivity seems to change, anyway.

15) Critique of the measurement in rapidly developing economies Many economists observed that Solow’s model is a simplistic version of reality. There are many factors contributing to growth such as: (1) Increasing globalisation leading to trade liberalization (2) Impact of "learning by doing". (3) Growth of informations and communications technology (ICT) (4) Capital controversy over whether the level of capital in an economy can be measured even in theory; if not, neither can the Solow residual. (5) There could be impact of business cycles.

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Official Economic Statistics by Tarun Das (6) There could be switching and reswitching of production techniques due to significant changes in wages and inteest rates. (7) There is problems for aggregation of capital due to variations in vintages. (8) There is also problem of aggregation of labor due to differences in skill and experiences. 16) Multifactor Productivity Index (MFPI) Multifactor Productivity Index (MFPI) measure the changes in output per unit of combined inputs. Indexes of MFP are produced for the private business, private non-farm business, and manufacturing sectors of the economy. MFPI is also developed for 2-and 3digit Standard Industrial Classification (SIC) manufacturing industries, the railroad transportation industry, the air transportation industry, and the utility and gas industry. Whereas labor productivity measures the output per unit of labor input, multifactor productivity looks at a combination of production inputs (or factors): labor, materials, and capital. In theory, it’s a more comprehensive measure than labor productivity, but it’s also more difficult to calculate. (1) Labor Productivity (output per hour)=Output/Labor Inputs (2) Multifactor Productivity=Output/(KLEMS) Multi Factor Productivity is a measure of the physical output produced from the use of a given quantity of inputs by the firm. When having multiple outputs and multiple inputs, the ratio of the weighted sum of outputs with respect to the weighted sum of inputs is used to calculate the Multi Factor Productivity Index. In general, the weights are the cost share for inputs and the revenue shares for the outputs. Prices or cost shares and revenue shares may change between two periods. There are two alternatives in dealing with this problem which implies different calculations: the same weights may be used in both periods, or each period may use a different weight. Advantages of Index Methods: The approach only requires data on two observations, such as two firms or two time periods. Disadvantages of Index Methods: TFP cannot be decomposed into the different types of efficiencies (i.e. technical, allocative and economic, as mentioned earlier). Application of Index methods: An example of an analysis using the TFP index method in the water and sanitation sector is an assessment of the performance after privatization in England and Wales

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Official Economic Statistics by Tarun Das

17. Ranil Salgado (IMF) index for TFP TFP Growth = α GR(LP) +(1- α ) GR(KP) Where GR(LP) = Growth rate of Labor Productivity GR(KP) = Growth rate of Capital Productivity LP (Labor Productivity) = Output per employee KP (Capital Productivity) = Output per capital input α = the average shares of labor in output over the consecutive years t and t-1. α (Share of labor) = Ratio of compensation to employees in total output (GDP) Share of capital = 1 - α 18) OECD Methodology for Measuring Total Factor Productivity (a) Labor Productivity Labour productivity is defined as GDP per hour worked; where GDP for each country refers to its Gross Domestic Product, in national currency, at constant prices, OECD base year 2000, and output for country groups / zones GDP refers to the Gross Domestic Product, in US dollars, at constant prices, constant PPPs, OECD base year 2000. Labour input is defined as total hours worked of all persons employed. The data are derived as average hours worked from the OECD Employment Outlook, OECD Annual National Accounts, OECD Labour Force Statistics and national sources, multiplied by the corresponding and consistent measure of employment for each particular country. The measures of labour productivity are presented as indices and as rates of change. Source: OECD Employment Outlook, OECD Labour Force Statistics, OECD Annual National Accounts and OECD Quarterly National Accounts, and national sources. (b) Multi-factor Productivity The Multi-factor Productivity for the total economy is computed as the difference between the rate of change of output and the rate of change of total inputs, and presented as a rate of change. Price indices for information and communication technology assets are those published by the U.S. Bureau of Economic Analysis, corrected for overall inflation. The shares of compensation of labour input and of capital inputs in total costs are for the total economy. Shares are measured at current prices. Compensation of labour input corresponds to the compensation of employees and self-employed persons. Compensation of capital input is the value of capital services. Total inputs are volume indices of combined labour and capital inputs for the total economy. The indices have been constructed as weighted averages of the rate of change of total hours worked and the rate of change of capital services. Cost shares of inputs averaged over the two periods under consideration serve as weights (Törnqvist index). Price indices for information and communication technology assets are those published by the U.S. Bureau of Economic Analysis, corrected for overall inflation.

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Official Economic Statistics by Tarun Das

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Official Economic Statistics by Tarun Das

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Official Economic Statistics by Tarun Das

Workout Session on Productivity The following data relate to Japanese Economy. Estimate Total Factor Productivity for the Japanese Economy on the basis of a Cobb Douglas Production Function and Harrod neutrality. Year

GDP (billion Yen)

Plant-Machinery (billion Yen)

Employees (10 thosand)

Share of Labor in GDP

1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

313140 322328 331236 336575 347073 364712 375503 389753 416119 438136 460926 476369 481000 482191 487488 496922 513893 523421 517515 517811 532542 534852 532962 547133

132032 140342 150509 158437 166831 176575 183872 192547 203443 217987 234272 247563 258052 284149 272846 276844 283423 288788 288210 286603 285750 285966 284623 283782

3971 4039 4108 4176 4245 4313 4379 4428 4538 4679 4835 5002 5119 5202 5238 5283 5322 5391 5368 5331 5386 5389 5331 5344

0.770 0.768 0.765 0.765 0.767 0.767 0.765 0.779 0.773 0.782 0.771 0.752 0.723 0.722 0.731 0.735 0.731 0.725 0.715 0.715 0.707 0.725 0.736 0.724

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Official Economic Statistics by Tarun Das

Workout Session on Productivity Table-1 Year

1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002

GDP (bln Yen) 313140 322328 331236 336575 347073 364712 375503 389753 416119 438136 460926 476369 481000 482191 487488 496922 513893 523421 517515 517811 532542 534852 532962

Machinery (bln Yen)

Employees (10 thosand)

132032 140342 150509 158437 166831 176575 183872 192547 203443 217987 234272 247563 258052 284149 272846 276844 283423 288788 288210 286603 285750 285966 284623

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3971 4039 4108 4176 4245 4313 4379 4428 4538 4679 4835 5002 5119 5202 5238 5283 5322 5391 5368 5331 5386 5389 5331

Capital Share 0.23 0.23 0.24 0.24 0.23 0.23 0.23 0.22 0.23 0.22 0.23 0.25 0.28 0.28 0.27 0.26 0.27 0.27 0.29 0.29 0.29 0.27 0.26

Labor share 0.770 0.768 0.765 0.765 0.767 0.767 0.765 0.779 0.773 0.782 0.771 0.752 0.723 0.722 0.731 0.735 0.731 0.725 0.715 0.715 0.707 0.725 0.736

Official Economic Statistics by Tarun Das Table-2 Year

1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002

AP of Captal

AP of Labor

GR of AP(K)

GR of AP(L)

TFP Growth

2.37 2.30 2.20 2.12 2.08 2.07 2.04 2.02 2.05 2.01 1.97 1.92 1.86 1.70 1.79 1.79 1.81 1.81 1.80 1.81 1.86 1.87 1.87

78.86 79.80 80.64 80.59 81.77 84.56 85.75 88.02 91.70 93.64 95.33 95.24 93.96 92.69 93.07 94.06 96.56 97.09 96.41 97.13 98.88 99.25 99.97

-3.21 -4.27 -3.53 -2.09 -0.72 -1.13 -0.89 1.04 -1.75 -2.13 -2.22 -3.18 -9.39 5.15 0.46 1.01 -0.04 -0.93 0.62 3.10 0.36 0.12

1.18 1.05 -0.05 1.45 3.36 1.40 2.61 4.09 2.10 1.79 -0.10 -1.34 -1.36 0.40 1.06 2.62 0.55 -0.71 0.75 1.78 0.38 0.73

0.17 -0.19 -0.87 0.62 2.41 0.81 1.82 3.41 1.24 0.91 -0.61 -1.83 -3.59 1.70 0.90 2.19 0.39 -0.77 0.71 2.16 0.37 0.56

23

Official Economic Statistics by Tarun Das Table-3 1 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

LogY 2 12.65 12.68 12.71 12.73 12.76 12.81 12.84 12.87 12.94 12.99 13.04 13.07 13.08 13.09 13.10 13.12 13.15 13.17 13.16 13.16 13.19 13.19 13.19 13.21

LogK 3 11.79 11.85 11.92 11.97 12.02 12.08 12.12 12.17 12.22 12.29 12.36 12.42 12.46 12.56 12.52 12.53 12.55 12.57 12.57 12.57 12.56 12.56 12.56 12.56

LogL 4 8.29 8.30 8.32 8.34 8.35 8.37 8.38 8.40 8.42 8.45 8.48 8.52 8.54 8.56 8.56 8.57 8.58 8.59 8.59 8.58 8.59 8.59 8.58 8.58

24

GR(Y) 5

GR(K) 6

GR(L) 7

2.8919 2.7261 1.5990 3.0714 4.9573 2.9158 3.7247 6.5458 5.1558 5.0708 3.2955 0.9675 0.2473 1.0925 1.9167 3.3582 1.8371 -1.1348 0.0572 2.8051 0.4328 -0.3540 2.6242

6.1038 6.9941 5.1334 5.1624 5.6764 4.0494 4.6100 5.5046 6.9050 7.2047 5.5182 4.1496 9.6338 -4.0591 1.4547 2.3486 1.8752 -0.2003 -0.5591 -0.2981 0.0756 -0.4707 -0.2959

1.7078 1.6791 1.6514 1.6246 1.5986 1.5187 1.1128 2.4538 3.0598 3.2797 3.3957 2.3121 1.6084 0.6897 0.8554 0.7355 1.2882 -0.4275 -0.6917 1.0264 0.0557 -1.0821 0.2436

Official Economic Statistics by Tarun Das Table-4

1 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

Labor share (a) (%) 8 0.770 0.768 0.765 0.765 0.767 0.767 0.765 0.779 0.773 0.782 0.771 0.752 0.723 0.722 0.731 0.735 0.731 0.725 0.715 0.715 0.707 0.725 0.736 0.724

Contribution 0f labor to GDPGR 9

Contribution 0f capital to GDPGR 10

MFP Growth =5-9-10 11

1.31 1.29 1.26 1.24 1.23 1.16 0.86 1.91 2.38 2.55 2.58 1.70 1.16 0.50 0.63 0.54 0.94 -0.31 -0.49 0.73 0.04 -0.79 0.18

1.41 1.63 1.21 1.21 1.32 0.95 1.05 1.23 1.53 1.61 1.32 1.09 2.67 -1.11 0.39 0.63 0.51 -0.06 -0.16 -0.09 0.02 -0.13 -0.08

0.17 -0.19 -0.87 0.62 2.41 0.81 1.82 3.41 1.24 0.91 -0.61 -1.83 -3.59 1.70 0.90 2.19 0.39 -0.77 0.71 2.16 0.37 0.56 2.53

25

Official Economic Statistics by Tarun Das

TABLE-5

1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003

LogY 12.65 12.68 12.71 12.73 12.76 12.81 12.84 12.87 12.94 12.99 13.04 13.07 13.08 13.09 13.10 13.12 13.15 13.17 13.16 13.16 13.19 13.19 13.19 13.21

LogK 11.79 11.85 11.92 11.97 12.02 12.08 12.12 12.17 12.22 12.29 12.36 12.42 12.46 12.56 12.52 12.53 12.55 12.57 12.57 12.57 12.56 12.56 12.56 12.56

LogL 8.29 8.30 8.32 8.34 8.35 8.37 8.38 8.40 8.42 8.45 8.48 8.52 8.54 8.56 8.56 8.57 8.58 8.59 8.59 8.58 8.59 8.59 8.58 8.58

Regression Results: SUMMARY OUTPUT Regression Statistics Multiple R 0.99 R Square 0.98 Adjusted R Square 0.98 Standard Error 0.03 No of Observations 24 ANOVA

26

Regressn Residual Total

df 2 21 23

SS 0.80 0.01 0.82

MS 0.40 0.00

Intercept X1 Var-1 X2 Var-2

Coeffs. 1.232 0.318 0.924

Std. Error 1.48 0.18 0.43

t Stat 0.83 1.80 2.16

Official Economic Statistics by Tarun Das

TABLE-6 Observation 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Predicted Y 12.65 12.68 12.72 12.75 12.78 12.81 12.84 12.87 12.91 12.96 13.01 13.06 13.09 13.14 13.13 13.14 13.16 13.18 13.17 13.16 13.17 13.17 13.16 13.16

Residuals 0.01 0.00 -0.01 -0.02 -0.02 -0.01 -0.01 0.01 0.03 0.03 0.03 0.02 -0.01 -0.05 -0.04 -0.03 -0.01 -0.01 -0.02 -0.01 0.01 0.02 0.02 0.05

TFP 1.24 1.23 1.22 1.21 1.21 1.22 1.23 1.24 1.26 1.27 1.26 1.25 1.22 1.18 1.20 1.20 1.22 1.22 1.22 1.23 1.24 1.25 1.26 1.28

27

GR-TFP

Above Est

-0.51 -0.85 -1.28 -0.06 1.38 0.18 1.00 2.04 0.10 -0.20 -1.27 -2.00 -3.52 1.48 0.55 1.60 0.04 -0.55 0.72 1.59 0.29 0.64 1.98

0.17 -0.19 -0.87 0.62 2.41 0.81 1.82 3.41 1.24 0.91 -0.61 -1.83 -3.59 1.70 0.90 2.19 0.39 -0.77 0.71 2.16 0.37 0.56 2.53