1. Economics 216: The Macroeconomics of Development Lawrence J. Lau, Ph. D., D. Soc. Sc. (hon.) Kwoh-Ting Li Professor of Economic Development Department of Economics Stanford University Stanford, CA 94305-6072, U.S.A. Spring 2000-2001 Email: ljlau@stanford.edu; WebPages: http://www.stanford.edu/~ljlau

2. Lecture 3 Accounting for Economic Growth: Methodologies Lawrence J. Lau, Ph. D., D. Soc. Sc. (hon.) Kwoh-Ting Li Professor of Economic Development Department of Economics Stanford University Stanford, CA 94305-6072, U.S.A. Spring 2000-2001 Email: ljlau@stanford.edu; WebPages: http://www.stanford.edu/~ljlau

3. Lawrence J. Lau, Stanford University3 The Sources of Economic Growth u What are the sources of growth of real GNP over time? u The growth of measured inputs: tangible capital and labor u Technical progress, aka growth in total factor productivity, aka multifactor productivity, “the residual” or “a measure of our ignorance”--improvements in productive efficiency u Growth accounting is a methodology for decomposing the growth of output by its proximate sources u How much of the growth in real output is due to “working harder”? How much is due to “working smarter”?

4. Lawrence J. Lau, Stanford University4 Accounting for Economic Growth u S. Kuznets (1966) observed that "the direct contribution of man-hours and capital accumulation would hardly account for more than a tenth of the rate of growth in per capita product--and probably less." (p. 81) u M. Abramovitz (1956) and R. Solow (1957) similarly found that the growth of output cannot be adequately explained by the growth of inputs u Denison (1962), under the assumption that the degree of returns to scale is 1.1, found less technical progress

5. Lawrence J. Lau, Stanford University5 Accounting for Economic Growth u Griliches and Jorgenson (1966), Jorgenson, Gollop and Fraumeni (1987) and Jorgenson and his associates found even less technical progress by adjusting capital and labor inputs for quality improvements u Boskin and Lau (1990), using labor-hours and constant- dollar capital stocks, found that technical progress has been the most important source of growth for the developed countries in the postwar period

6. Lawrence J. Lau, Stanford University6 The Measurement of Technical Progress, aka the Growth of Total Factor Productivity u How much of the growth of output can be attributed to the growth of measured inputs, tangible capital and labor? and u How much of the growth of output can be attributed to technical progress (aka growth in total factor productivity), i.e. improvements in productive efficiency over time? u TECHNICAL PROGRESS (GROWTH IN TOTAL FACTOR PRODUCTIVITY) = GROWTH IN OUTPUT HOLDING ALL MEASURED INPUTS CONSTANT

7. Lawrence J. Lau, Stanford University7 Interpretation of Technical Progress (Growth of Total Factor Productivity) u Not “Manna from Heaven” u Growth in unmeasured Intangible Capital (Human Capital, R&D Capital, Goodwill (Advertising and Market Development), Information System, Software, etc.) u Growth in Other Omitted and Unmeasured Inputs (Land, Natural Resources, Water Resources, Environment, etc.) u The effects of improvements in technical and allocative efficiency over time, e.g., learning-by-doing u “Residual” or “Measure of Our Ignorance”

8. Lawrence J. Lau, Stanford University8 The Point of Departure: The Concept of a Production Function u Definition: u A production function is a rule which gives the quantity of output, Y, for a given vector of quantities of inputs, X, denoted:

9. Lawrence J. Lau, Stanford University9 The Single-Output, Single-Input Case

10. Lawrence J. Lau, Stanford University10 The Economist’s Concept of Technical Progress u A production function may change over time. Thus: u Y = F( X, t ) u Definition: u There is technical progress between period 0 and period 1 if given the same quantity of input, X 0, the quantity of output in period 1, Y 1, is greater than the quantity of output in period 0, Y 0, i.e., u TECHNICAL PROGRESS = THE GROWTH OF OUTPUT HOLDING MEASURED INPUTS CONSTANT

11. Lawrence J. Lau, Stanford University11 Technical Progress: The Single-Output, Single-Input Case

12. Lawrence J. Lau, Stanford University12 The Case of No Technical Progress

13. Lawrence J. Lau, Stanford University13 Under-Identification of Technical Progress from a Single Time-Series of Empirical Data no technical progress technical progress

14. Lawrence J. Lau, Stanford University14 The Inputs of Production u Measured Inputs u Tangible Capital u Labor u Land (possible) u Technical Progress or Growth in Total Factor Productivity u Intangible Capital (Human Capital, R&D Capital, Goodwill (Advertising and Market Development), Information System, Software, etc.) u Other Omitted and Unmeasured Inputs (Land, Natural Resources, Water Resources, Environment, etc.) u Improvements in Technical and Allocative Efficiency over time u Human Capital and R&D capital may be explicitly distinguished as measured inputs to the extent that they can be separately measured

15. Lawrence J. Lau, Stanford University15 The Question of Growth Accounting u What is the relative importance of the “measured inputs” versus “technical progress” or growth in total factor productivity (TFP) as sources of economic growth?

16. Lawrence J. Lau, Stanford University16 Decomposition of the Growth of Output u If the production function is known, the growth of output can be decomposed into: u (1) The growth of output due to the growth of measured inputs (movement along a production function) and u (2) Technical progress (shift in the production function) u The growth of output due to the growth of inputs can be further decomposed into the growth of output due to tangible capital, labor (and any other measured inputs)

17. Lawrence J. Lau, Stanford University17 Decomposition of the Growth of Output

18. Lawrence J. Lau, Stanford University18 Contribution of the Growth of Input u The rate of growth of output between period 0 and period 1 due to the growth of inputs can be estimated as: u or as: u The two are not the same except under neutrality of technical progress. u A natural estimate is the (geometric) mean of the two estimates (the geometric mean is defined as the the square root of the product of the two estimates)

19. Lawrence J. Lau, Stanford University19 Definition of Neutrality u Technical progress is said to be neutral if u F(X, t) = A(t) F(X), for all X, t

20. Lawrence J. Lau, Stanford University20 Contribution of Technical Progress u The growth of output due to technical progress can be estimated as: u or as: u The two are not the same except under neutrality of technical progress. u A natural estimate is again the (geometric) mean of the two estimates.

21. Lawrence J. Lau, Stanford University21 The Point of Departure: An Aggregate Production Function u Each country has an aggregate production function: Y it = F i (K it, L it, t), i = 1, …, n; t = 0, …, T u In general, F i (.) is not necessarily the same across countries, hence the subscript i

22. Lawrence J. Lau, Stanford University22 Decreasing, Constant or Increasing Returns to Scale? u Constant returns to scale is traditionally assumed at the aggregate level (except Denison, who assumes the degree of returns to scale is 1.1) u A problem of identification from a single time-series of empirical data u The confounding of economies of scale and technical progress for a growing economy u The higher the assumed degree of returns to scale, the lower the estimated technical progress (and vice versa)

23. Lawrence J. Lau, Stanford University23 Decreasing, Constant or Increasing Returns to Scale? u Theoretical arguments for Constant Returns at the aggregate level u Replicability u Theoretical arguments for Decreasing Returns u Omitted inputs--land, natural resources, human capital, R&D capital, other forms of intangible capital

24. Lawrence J. Lau, Stanford University24 Decreasing, Constant or Increasing Returns to Scale? u Theoretical arguments for Increasing Returns u Economies of scale at the microeconomic level (but replicability of efficient-scale units) u Increasing returns in the production of new knowledge--high fixed costs and low marginal costs (but diminishing returns of the utilization of knowledge to aggregate production) u Scale permits the full realization of the economies of specialization u Existence of coordination externalities (but likely to be a one- time rather than continuing effect) u Network externalities (offset by congestion costs, also replicability of efficient-scale networks)

25. Lawrence J. Lau, Stanford University25 Difficulties in the Measurement of Technical Progress (Total Factor Productivity) u (1) The confounding of economies of scale and technical progress u Solution: pooling time-series data across different countries--at any given time there are different scales in operation; the same scale can be observed at different times u (2) The under-identification of the biases of scale effects and technical progress u Bias in scale effects--as output is expanded under conditions of constant prices of inputs, the demands for different inputs are increased at differential rates u Bias in technical progress--over time, again under constant prices, the demands of different inputs per unit output decreases at different rates u Solution: econometric estimation with flexible functional forms

26. Lawrence J. Lau, Stanford University26 Original Observations

27. Lawrence J. Lau, Stanford University27 Constant Returns to Scale Assumed Result: No Technical Progress

28. Lawrence J. Lau, Stanford University28 Decreasing Returns Assumed Result: Technical Progress

29. Lawrence J. Lau, Stanford University29 Neutrality of Technical Progress Assumed: Uniform Shifts of the Production Function

30. Lawrence J. Lau, Stanford University30 Neutrality of Technical Progress Not Assumed: Non-Uniform Shifts of the Production Function

31. Lawrence J. Lau, Stanford University31 Neutrality of Technical Progress: Uniform Shift of the Isoquant

32. Lawrence J. Lau, Stanford University32 Identification of Scale Effects and Technical Progress through Pooling Across Countries Identification through Pooling

33. Lawrence J. Lau, Stanford University33 Two Leading Alternative Approaches to Growth Accounting u (1) Econometric Estimation of the Aggregate Production Function E.g., the Cobb-Douglas production function u (2) Traditional Growth-Accounting Formula u Are Differences in Empirical Results Due to Differences in Methodologies or Assumptions or Both?

34. Lawrence J. Lau, Stanford University34 Potential Problems of the Econometric Approach u Insufficient Quantity Variation u multicollinearity u restricted range of variation u approximate constancy of factor ratios u Insufficient Relative-Price Variation u Implications: u imprecision u unreliability u under-identification u restricted domain of applicability and confidence

35. Lawrence J. Lau, Stanford University35 Under-Identification from Insufficient Quantity Variation Under-Identification from Insufficient Quantity Variation

36. Lawrence J. Lau, Stanford University36 Under-Identification of Isoquant from Insufficient Relative-Price Variation Capital Labor Alternative isoquants that fit the same data equally well.

37. Lawrence J. Lau, Stanford University37 Solution: Pooling Across Countries The Effect of Pooling

38. Lawrence J. Lau, Stanford University38 Problems Arising from Pooling u Extensiveness of the Domain of the Variables u Solution: Use of a flexible functional form u The Assumption of Identical Production Functions u Solution: The meta-production function approach u Non-Comparability of Data u Solution: The meta-production function approach

39. Lawrence J. Lau, Stanford University39 Adequacy of Linear Representation

40. Lawrence J. Lau, Stanford University40 Inadequacy of Linear Representation

41. Lawrence J. Lau, Stanford University41 The Traditional Growth-Accounting Formula: The Concept of a Production Elasticity u The production elasticity of an input is the % increase in output in response to a 1% increase in the input, holding all other inputs constant. It typically lies between 0 and 1. u The % increase in output attributable to an increase in input is approximately equal to the product of the production elasticity and the actual % increase in the input.

42. Lawrence J. Lau, Stanford University42 Decomposition of the Change in Output

43. Lawrence J. Lau, Stanford University43 The Fundamental Equation of Traditional Growth Accounting Once More

44. Lawrence J. Lau, Stanford University44 The Maximum Contribution of Labor Input to Economic Growth u ANY TIME THE RATE OF GROWTH OF REAL GDP EXCEEDS 2% p.a. SIGNIFICANTLY, IT MUST BE DUE TO THE GROWTH IN TANGIBLE CAPITAL OR TECHNICAL PROGRESS!

45. Lawrence J. Lau, Stanford University45 Implementation of the Traditional Growth-Accounting Formula u The elasticities of output with respect to capital and labor must be separately estimated u The rate of technical progress depends on K t and L t as well as t u The elasticity of output with respect to labor is equal to the share of labor under instantaneous competitive profit maximization u The elasticity of output with respect to capital is equal to one minus the elasticity of labor under the further assumption of constant returns to scale

46. Lawrence J. Lau, Stanford University46 Implementation of the Traditional Growth-Accounting Formula Under the assumption of instantaneous profit maximization with competitive output and input markets, the value of the marginal product of labor is equal to the wage rate:. Multiplying both sides by L and dividing both sides by P.Y, we obtain:, or. In other words, the elasticity of output with respect to labor is equal to the share of labor in the value of total output.

47. Lawrence J. Lau, Stanford University47 Necessary Assumptions for the Application of the Growth-Accounting Formula u Instantaneous profit maximization under perfectly competitive output and input markets u equality between output elasticity of labor and the share of labor in output u Constant returns to scale u sum of output elasticities is equal to unity u Neutrality u the rates of technical progress can be directly cumulated over time without taking into account the changes in the vector of quantities of inputs

48. Lawrence J. Lau, Stanford University48 The Implication of Neutrality of Technical Progress u It may be tempting to estimate the technical progress over T periods by integration or summation with respect to time: u However, the integration or summation can be rigorously justified if and only if: u (1) Technical progress is Hicksian neutral (equivalently output- augmenting); or u (2) Capital and labor are constant over time

49. Lawrence J. Lau, Stanford University49 Necessary Data for the Measurement of Technical Progress u The Econometric Approach u Quantities of Output and Inputs u The Traditional Growth-Accounting Formula Approach u Quantities of Output and Inputs u Prices of Outputs and Inputs

50. Lawrence J. Lau, Stanford University50 Pitfalls of Traditional Growth Accounting (1) u (1) If returns to scale are increasing, technical progress is over-estimated and the contribution of the inputs is underestimated (and vice versa); u (2) Nonneutrality prevents simple cumulation over time; u (3) Constraints to instantaneous adjustments and/or monopolistic or monopsonistic influences may cause production elasticities to deviate from the factor shares, and hence the estimates of technical progress as well as the contributions of inputs using the factor shares may be biased;

51. Lawrence J. Lau, Stanford University51 Pitfalls of Traditional Growth Accounting (2) u (4) With more than two fixed or quasi-fixed inputs, their output elasticities cannot be identified even under constant returns

52. Lawrence J. Lau, Stanford University52 The Meta-Production Function Approach as an Alternative u Introduced by Hayami (1969) and Hayami & Ruttan (1970, 1985) u Haymai & Ruttan assume that F i (.) = F(.): u Y it = F (K it, L it, t), i = 1, …, n; t = 0, …, T u Which implies that all countries have identical production functions in terms of measured inputs u Thus pooling of data across multiple countries is justified

53. Lawrence J. Lau, Stanford University53 Extension by Boskin, Lau & Yotopoulos u Extended by Lau & Yotopoulos (1989) and Boskin & Lau (1990) to allow time-varying, country- and commodity- specific differences in efficiency u Applied by Boskin, Kim, Lau, & Park to the G-5 countries, G-7 countries, the East Asian Newly Industrialized Economies (NIEs) and developing economies in the Asia/Pacific region

54. Lawrence J. Lau, Stanford University54 The Extended Meta-Production Function Approach: The Basic Assumptions (1) (1) All countries have the same underlying aggregate production function F(.) in terms of standardized, or “efficiency-equivalent”, quantities of outputs and inputs, i.e. (1)Y* it = F(K* it,L* it ), i = 1,...,n.

55. Lawrence J. Lau, Stanford University55 The Extended Meta-Production Function Approach: The Basic Assumptions (2) (2) The measured quantities of outputs and inputs of the different countries may be converted into the unobservable standardized, or "efficiency-equivalent", units of outputs and inputs by multiplicative country- and output- and input-specific time-varying augmentation factors, A ij (t)'s, i = 1,...,n; j = output (0), capital (K), and labor (L): (2)Y* it = A i0 (t)Y it ; (3)K* it = A iK (t)K it ; (4)L* it = A iL (t)L it ; i = 1,..., n.

56. Lawrence J. Lau, Stanford University56 The Extended Meta-Production Function Approach: The Basic Assumptions (2) u In the empirical implementation, the commodity augmentation factors are assumed to have the constant geometric form with respect to time. Thus: (5)Y* it = A i0 (1+c i0 ) t Y it ; (6)K* it = A iK (1+c iK ) t K it ; (7)L* it = A iL (1+c iL ) t L it ; i = 1,...,n. A i0 's, A ij 's = augmentation level parameters c i0 's, c ij 's = augmentation rate parameters

57. Lawrence J. Lau, Stanford University57 The Extended Meta-Production Function Approach: The Basic Assumptions (2) u For at least one country, say the ith, the constants A i0 and A ij 's can be set identically at unity, reflecting the fact that "efficiency-equivalent" outputs and inputs can be measured only relative to some standard. u The A i0 and A ij 's for the U.S. Are taken to be identically unity. u Subject to such a normalization, the commodity augmentation level and rate parameters can be estimated simultaneously with the parameters of the aggregate production function.

58. Lawrence J. Lau, Stanford University58 The Commodity-Augmenting Representation of Technical Progress

59. Lawrence J. Lau, Stanford University59 The Meta-Production Function Approach u It is important to understand that the meta-production function approach assumes that the production function is identical for all countries only in terms of the efficiency- equivalent quantities of outputs and inputs; it is not identical in terms of measured quantities of outputs and inputs u A useful way to think about what is the same across countries is the following—the isoquants remain the same for all countries and over time with a suitable renumbering of the isoquants and a suitable re-scaling of the axes

60. Lawrence J. Lau, Stanford University60 The Extended Meta-Production Function Approach: The Basic Assumptions (3) (3) The aggregate meta-production function is assumed to have a flexible functional form, e.g. the transcendental logarithmic functional form of Christensen, Jorgenson & Lau (1973).

61. Lawrence J. Lau, Stanford University61 The Extended Meta-Production Function Approach: The Basic Assumptions (3) u The translog production function, in terms of “efficiency- equivalent” output and inputs, takes the form: (8)ln Y* it = lnY 0 + a K lnK* it + a L lnL* it + B KK (lnK* it ) 2 /2 + B LL (ln L* it ) 2 /2 + B KL (lnK* it ) (lnL* it ), i = 1,...,n. u By substituting equations (5) through (7) into equation (8), and simplifying, we obtain equation (9), which is written entirely in terms of observable variables:

62. Lawrence J. Lau, Stanford University62 The Estimating Equation (9)lnY it = lnY 0 + lnA* i0 + a* Ki lnK it + a* Li lnL it + c* i0 t +B KK (lnK it ) 2 /2 + B LL (ln L it ) 2 /2 + B KL (lnK it ) (lnL it )+(B KK ln(1+c iK )+ B KL ln(1+c iL ))(ln K it )t +(B KL ln(1+c iK )+ B LL ln(1+c iL ))(ln L it )t +(B KK (ln(1+c iK )) 2 + B LL (ln(1+c iL )) 2 +2B KL ln(1+c iK )ln(1+c iL ))t 2 /2, i = 1,...,n, where A* i0, a* Ki, a* Li, c* i0 and c ij 's, j = K, L are country-specific constants.

63. Lawrence J. Lau, Stanford University63 Tests of the Maintained Hypotheses of the Meta-Production Function Approach u The parameters B KK, B KL, and B LL are independent of i, i.e., of the particular individual country. This provides a basis for testing the maintained hypothesis that there is a single aggregate meta-production function for all the countries. u The parameter corresponding to the t 2 /2 term for each country is not independent but is completely determined given B KK, B KL, B LL, c iK, and c iL. This provides a basis for testing the hypothesis that technical progress may be represented in the constant geometric commodity- augmentation form.

64. Lawrence J. Lau, Stanford University64 The Labor Share Equation u In addition, we also consider the behavior of the share of labor costs in the value of output: (10) w it L it /p it Y it = a* Lii + B KLi (lnK it ) + B LLi (ln L it ) + B Lti t, i = 1,...,n.

65. Lawrence J. Lau, Stanford University65 Instantaneous Profit Maximization under Competitive Output and Input Markets u The share of labor costs in the value of output should be equal to the elasticity of output with respect to labor: (11) w it L it /p it Y it = a* Li + B KL (lnK it ) + B LL (ln L it ) +(B KL ln(1+c iK )+ B LL ln(1+c iL ))t, i = 1,...,n. u This provides a basis for testing the hypothesis of profit maximization with respect to labor.

66. Lawrence J. Lau, Stanford University66 Tests of the Maintained Hypotheses of Traditional Growth Accounting u Homogeneity B KK + B KL = 0; B KL + B LL = 0. u Constant returns to scale a* Ki + a* Li = 1. u Neutrality of technical progress c iK = 0; c iL = 0.

67. Lawrence J. Lau, Stanford University67 Homogeneity and Constant Returns to Scale

68. Lawrence J. Lau, Stanford University68 Isoquants of Homothetic and Non-Homothetic Production Functions

69. Lawrence J. Lau, Stanford University69 Rates of Growth on Inputs & Outputs of the East Asian NIEs and the G-5 Countries

70. Lawrence J. Lau, Stanford University70 Test Results: The Meta-Production Function Approach u The Maintained Hypotheses of the Meta-Production Function Approach u “Identical Meta-Production Functions” and u “Factor-Augmentation Representation of Technical Progress” u Cannot be rejected.

71. Lawrence J. Lau, Stanford University71 Tests of Hypotheses

72. Lawrence J. Lau, Stanford University72 The Maintained Hypotheses of Traditional Growth Accounting u The Maintained Hypotheses of Traditional Growth Accounting, viz.: u Constant Returns to Scale »Homogeneity of the production function is implied by constant returns to scale--a production function F(K, L) is homogeneous of degree k if: F(  K,  L) =  k F(K, L) »Constant returns to scale imply k=1; Increasing returns to scale imply k>1; decreasing returns to scale imply k<1 u Neutrality of Technical Progress u Instantaneous Profit Maximization under Competitive Output and Input Markets u Are all rejected.

73. Lawrence J. Lau, Stanford University73 The Different Kinds of Purely Commodity- Augmenting Technical Progress

74. Lawrence J. Lau, Stanford University74 Hypotheses on Augmentation Level and Rate Parameters u The hypothesis of “Identical Augmentation Level Parameters” A iK = A K ; A iL = A L cannot be rejected. u The hypothesis of Purely Output-Augmenting (Hicks-Neutral) Technical Progress c iK = 0; c iL = 0 can be rejected u The hypothesis of Purely Labor-Augmenting (Harrod-Neutral) Technical Progress c i0 = 0; c iK = 0 can be rejected u The hypothesis of Purely Capital-Augmenting (Solow-Neutral) Technical Progressc i0 = 0; c iL = 0 cannot be rejected

75. Lawrence J. Lau, Stanford University75 The Hypothesis of No Technical Progress u c i0 = 0; c iK = 0; c iL = 0 u This hypothesis is rejected for the Group-of-Five Countries. u This hypothesis cannot be rejected for the East Asian NIEs.

76. Lawrence J. Lau, Stanford University76 The Estimated Parameters of the Aggregate Meta-Production Function

77. Lawrence J. Lau, Stanford University77 The Findings of Kim & Lau (1992, 1994a, 1994b) using data from early 50s to late 80s u (1) No technical progress in the East Asian NIEs but significant technical progress in the industrialized economies (IEs) including Japan u (2) East Asian economic growth has been input-driven, with tangible capital accumulation as the most important source of economic growth (applying also to Japan) u Working harder as opposed to working smarter u (3) Technical progress is the most important source of economic growth for the IEs, followed by tangible capital, accounting for over 50% and 30% respectively, with the exception of Japan u NOTE THE UNIQUE POSITION OF JAPAN!

78. Lawrence J. Lau, Stanford University78 The Findings of Kim & Lau (1992, 1994a, 1994b) using data from early 50s to late 80s u (4) Despite their high rates of economic growth and rapid capital accumulation, the East Asian Newly Industrialized Economies actually experienced a significant decline in productive efficiency relative to the industrialized countries as a group u (5) Technical progress is purely tangible capital- augmenting and hence complementary to tangible capital u (6) Technical progress being purely tangible capital- augmenting implies that it is less likely to cause technological unemployment than if it were purely labor- augmenting

79. Lawrence J. Lau, Stanford University79 Purely Capital-Augmenting Technical Progress

80. Lawrence J. Lau, Stanford University80 Accounts of Growth: Kim & Lau (1992, 1994a, 1994b)

81. Lawrence J. Lau, Stanford University81 The Advantages of the Meta-Production Function Approach u Theoretical: u All producer units have potential access to the same technology but each may operate on a different part of it depending on specific circumstances u Empirical: u Identification of the rate of technical progress, the degree of economies of scale, as well as their biases u Identification of the relative efficiencies of the outputs and inputs and the technological levels u Econometric identification through pooling u Enlarged domain of applicability u Statistical verifiability of the maintained hypotheses

82. Lawrence J. Lau, Stanford University82 Applications of the Meta-Production Function Approach u Lau & Yotopoulos (1989) u Lau, Lieberman & Williams (1990) u Boskin & Lau (1990) u Kim & Lau (1992, 1994a, 1994b) u Kim & Lau (1995) u Kim & Lau (1996) u Boskin & Lau (2000)