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Measuring Productivity with Non-conventional Approach

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									Measuring Productivity
with Non-conventional
Approach
Comment by Harry X. Wu on papers by
#1) Cecilia Kwok-ying Lam
#5) Hideyuki Kamiryo
Session 6C
The Conventional Approach
(Solow-Jorgenson)
   An input-output approach
   Substitute the income share of factors in
    national accounts for the output elasticity of
    input factors to weight input (K, L, M) growth,
    then derive a “growth residual” that cannot
    be explained by the weighted input growth -
    TFP
   This assumes (strongly) that factors are
    paid their marginal social products, then
    profit-maximising agencies operate in a
    distortion-free market system with perfect
    competition
… methodologically

   Assume input homogeneity
   Impose CRS, (logically) assuming that the
    sum of factor incomes is equal to national
    income or GDP.
   Impose neutral technological progress
    restriction, assuming that the economy is
    operating on the frontier and hence no
    inefficient agency exists.
The question is…in reality

   What if
       Inefficient firms exist operating off the PPF?
       Market imperfection? – firms with market
        power
       Government intervention, hence price
        distortion?
       Some sectors (e.g. the government sector)
        are not subject to market principles?
Estimating Cross-country Technical
Efficiency, Economic Performance and
Institutions – A Stochastic Production Frontier
Approach


The 2006 Ruggles Travel Grant Paper

By Cecilia Kwok-ying Lam
The University of Birmingham
Theoretical Argument
   Following the institutional argument (North and
    Thomas 1973) that institutional arrangement
    shapes the efficiency of transactions, that is,
    given the same inputs, better institutions enable
    an economy produce more output (i.e. more
    efficient).
   Economic institutions include: Size of
    Government, Legal System, Regulatory
    Environment, Political Regime (Authoritarian
    vs Democracy), Political Rights, and
    Openness to Trade
Methodology
   Productivity measurement is a crucial measure of cross-
    country growth performance. However, measuring cross-
    sectional technical efficiency with standard growth
    accounting cannot serve the theoretical framework.
    Therefore, the stochastic production frontier (SPF)
    approach that measures technical efficiency is adopted.
   SPF (Fare, Grosskopf et al. 1994) decomposes
    productivity into changes in efficiency (catching up) and
    changes in technology (innovation). Each country is
    compared to a frontier.
        How much a country getting closer to the “world frontier”
         measures the “catching up” effect
        How much the world frontier shifts indicates “technical
         change” or “innovation” effect
   Following Aigner, Lovell et al. (1977) and Meeusen
    and Broeck (1977), the stochastic production frontier
    function (thereafter abbreviated as SPF) can be
    extended as: y  f x ;   exp( v  u )
                     i      i        i   i

   Assume v is a stochastic error independently distributed
    of u. It accounts for the measurement such as the effects
    of weather, strikes, luck etc, on the value of the output
    variable together with the combined effects of unspecified
    input variables.
   u is assumed to be a non-negative random variables
    associated with technical inefficiency of production and is
    independently distributed.
   if u=0, then sum of 2-sided errors (u+v) = v, the error term
    is symmetric, and the data do not support a technical
    inefficiency story. However, if u > 0, then v – u is
    negatively skewed, and there is evidence of technical
    inefficiency in the data.
 Specification

    Stochastic Production Frontier

ln Yit   0   i ln K it   2 ln Lit   3 africai   4 easiai   5 mideasti
  6 ecai   7 sasi   8 latini   9 timet  vit  u it



    Technical Inefficiency Model
     u it   1 gov   2 politic   3 openness  wit
Data (1) – Production
Function
   Y: Real GDP (PPP adjusted) (Penn World
    Table)
   K: Capital (from investment data)     (Penn
    World Table)
 L: Labour force (World Development Indicators)
 Year: 1980-2000; Countries: 80

 5-year average; 4 periods; 320 obs
Data (2) – The Role of the
State
   (Gwartnet, Lawson et al 2002)
   GOV – government consumption / total
    consumption
   TRS – Size of transfer and subsidies over
    GDP
   COURT – index of impartial court
   PROPR – index of intellectual property rights
   CREDIT – credit market regulation index
   LABOR – labour market regulation index
Data (3) – Political Institution
   POLITY IV database (2003)
 REGIME – regime type, from
  authoritative to democratic
 DURABLE – durability of the regime
  type
 XCONST – operational (de facto)
  independence of chief executive
 PR – political rights (Freedom House 2004)
Data (4) – International
Trade
   (Gwartnet, Lawson et al 2002)
 FOREIGN – free to own foreign
  currency bank account domestically
  and abroad
 TRADEB – regulatory trade barriers,
  hidden import barriers and cost of
  importing
 BLACK – black market exchange rate
  premium
Results (1a) – Production
Function (lnY)
       ind. var. coefficient (standard error)
       constant 3.6979*** (0.1799)
           lnK 0.6368*** (0.0133)
           lnL 0.3427*** (0.0152)
          time 0.0010    (0.0098)
         africa 0.0640   (0.0436)
          latin 0.0807** (0.0383)
         easia   0.0047      (0.0519)
           eca   -0.0216     (0.0550)
           sas   -0.1127     (0.0593)
       mideast   0.0360      (0.0507)
Results (1b) – Sources of
TE (u)
ind. var.           coefficient   (standard error)
               GOV 0.0231*** (0.0050)
               TRS -0.0456*** (0.0124)
             COURT -0.0411**      (0.0199)           σ2               0.0756*** (0.0115)
             PROPR 0.2386***      (0.0489)           γ                0.8260*** (0.0434)
COURT * PROPR -0.0192*** (0.0062)                    log (likelihood)           106.9769
       CREDIT -0.0261** (0.0121)
            LABOR -0.0171    (0.0146)
            DURAB -0.0068*** (0.0009)
             XCONT 0.0492*        (0.0299)
            REGIME -0.0050        (0.0142)
             PR 0.0517**          (0.0243)
        FOREIGN -0.0135           (0.0089)
            TRADEB -0.0680**      (0.0270)
             BLACK -0.0099        (0.0092)
         Results (2b) – TE by regions
                    TE (81-85)   TE (86-90)   TE (91-95)   TE (96-00)
All          mean      0.8144      0.8220        0.8374        0.8496
             s.d.      0.1470      0.1435        0.1407        0.1324
Industrial   mean      0.9194      0.9320        0.9500        0.9512
             s.d.      0.0438      0.0355        0.0263        0.0260
E. Asia      mean      0.7468      0.7473        0.7657        0.8024
             s.d.      0.1338      0.1227        0.1252        0.1143
ECA          mean      0.9230      0.9312        0.9472        0.9191
             s.d.      0.0375      0.0248        0.0054        0.0015
Middle E.    mean      0.8330      0.8309        0.8417        0.8710
             s.d.      0.1078      0.1059        0.0989        0.0748
Latin        mean      0.8237      0.8252        0.8337        0.8418
             s.d.      0.1086      0.1028        0.0950        0.1099
Africa       mean      0.6754      0.6885        0.7054        0.7211
             s.d.      0.1924      0.1888        0.1850        0.1692
 Results (3b)
   East Asia and Pacific
Period   Output   Capital   Labour    TFP       TE
         Growth   Growth    Growth   Growth   change
           (%)      (%)       (%)      (%)      (%)
81-85     5.19     9.05      2.67     -1.49     ..

86-90     7.02     6.45      2.49     2.06     0.07

91-95     7.00     8.46      2.30     0.82     2.42

96-00     4.00     6.67      2.11     -0.97    4.69

81-00     5.80     7.66      2.39     0.11     7.18
Main conclusion
   Economic performance as expressed in terms of
    technical efficiency (TE) is drastically different from
    that expressed in total factor productivity (TFP) growth.
   All three institutional aspects are important in
    explaining technical efficiency (TE) across countries.
   Domestic economic and political institutions account
    TE more than whether the country is openness to
    trade and capital flow. In other words, local
    governance matters more than whether an open
    economy strategy is adopted.
Questions

   It is difficult to accept that the measure of
    inefficiency of other countries with the US
    as the frontier. Given different factor
    endowments across countries, a country
    could be operating on its own frontier but
    still below the US benchmark.
   More explanation may be needed to discuss
    the results for the fast growing east Asia
    economies – least efficient after Africa?
   More detailed discussion of data
Productivity Comparisons by
Country: The Government Sector
vs the Private Sector

   By Hideyuki Kamiryo
   Hiroshima Shudo University
Problems with the
conventional approach
 The conventional growth accounting
  approach with aggregate production
  function assumes that the government
  sector (G) and the private sector (PRI)
  are subject to the same production
  function, which violates the
  competitive market assumption
 Studies at industry level (Jorgenson
  type) mainly focus on the business
  sector
Problems with the
conventional approach…
 Measuring capital and rents (the rate
  of return) for G is impossible; e.g. the
  Canberra Group may use (2008)
  expected rate of return which is not
  additive with the private sector
 However, the G sector has significant
  bearing on TFP measure, especially
  when the size of government is large
  and the budget deficit is large
The New Approach: Reformation of
SNA based on National Disposable
Income (NDI)
   Y=W+P=(WG+PG)+(WPRI+PPRI)
      where Y=YG+YPRI, P =Y − W, P G =YG − WG,
       and P PRI =YPRI − WPRI . Wages are those
      after being modified by consumption of NDI.
   NDI: after taxes and depreciation.
   National accounts are modified by NDI, hence
    they become consistent as a whole macro
    accounting system and satisfy the additivity
    requirement for sectors.
   Now, we can shift to the measurement of TFP
         Preliminary method for
         productivity comparison

   Measuring capital and rents (the rate of return)
    simultaneously by sector
   (1) 1-a=c/(rho/r) determined by national taste: (rho/r)=1
    for the government sector and (rho/r)≠1 for the private
    sector
   (2) k=(a/(1-a))/(r/w).
   As a result, the capital-output ratio and the rate of return
    (under marginal productivity) are derived.
        The structure of productivity
        (ALP, TFP, and ACP)

   In the transitional path (from DRS/IRS at the
    current situation to CRS at convergence), the
    bypass production function (using TFP as a
    residual in a narrow sense; see below)
    converges to the C-D production function
   ALP, TFP, and ACP, in the transitional path:
    ALP and ACP that are partly qualitative.
    TFP that is purely qualitative.
The structure of productivity
(ALP, TFP, and ACP)…
   TFP (in this study) is the product of the TFP
    as a residual (in a narrow sense) (TFPRESI)
    and the capital-output ratio with a power that
    controls the shift from DRS/IRS to CRS.

   The product of TFP and the capital-output
    ratio is 1.0 under convergence: 1.0=W*B*^(1-
    ) and 1.0=k^(a).
    TFP differs from the current year’.
    BTFP=TFP/k and B=(1- )/ .
                                   Figures:1-a=c/(rho/r),(r/w) to 1-a, and r(0) to 1-
                                   a
                               (rho/r )(c ) of three Clubs 30 countries 1995-2004                                                   (rho/r )(c ) of Club s that includes 8 countries 1995-2004
                                                                                                                      1.02
    1.2
                                                                                                                      1.01
    1.1                                                                                                               1.00
    1.0                                                                                                               0.99
                                                                                                                      0.98
    0.9




                                                                                                              rho/r
rho/r




                                                                                        2
                                                                           y = -1.0216x + 2.5726x - 0.4771            0.97
    0.8                                                                                                               0.96
                                                                                      R2 = 0.8771
    0.7                                                                                                               0.95
                                                                                                                      0.94                                                         y = -46.2x2 + 82.06x - 35.44
    0.6                                                                                                               0.93                                                                      R2 = 0.4643
    0.5                                                                                                               0.92
          0.40          0.50         0.60          0.70          0.80          0.90         1.00      1.10                   0.82         0.83         0.84     0.85     0.86     0.87           0.88     0.89      0.90
                                                           c                                                                                                            c=C/Y



                                r/w and 1-alpha : 30 countries in 1995-2004                                                         The rate of return, r (0), and the capital-output ratio, W (0):
  0.07                                                                                                       0.50                            Total economy of 30 countries 1995-2004
                                                                                                             0.45
  0.06
                                                                                                             0.40
  0.05                                                                                                       0.35
  0.04                                                                                                       0.30
                                                                                                                                                                                         r(0)
                                                                                                             0.25
  0.03
                                                                                                             0.20
  0.02                                                                                                       0.15
  0.01                                                                                                       0.10
                                                                                                             0.05
  0.00
                                                                                                             0.00
      0.78       0.80     0.82      0.84    0.86    0.88       0.90     0.92   0.94    0.96    0.98   1.00
                                                                                                                      0.0           0.5          1.0          1.5      2.0        2.5            3.0          3.5    4.0
                                                      1-alpha                                                                                             the capital-output ratio, W (0)
                     Tables: (1) The US, Russia, China, India, and Japan,
                     (2) The US versus Japan

           (0) The U S             (8) Russia                   (6) China                  (2) India                  (6) Japan
              G/*G    PRI/*PRI     G/*G     PRI/*PRI        G/*G    PRI/*PRI      G/*G     PRI/*PRI      G/*G    PRI/*PRI
    1996        0.867      1.080         0.722       1.283          1.138        1.054          1.284       1.169          0.928      1.229
    1997        1.081      1.082         0.868       1.324          1.121        1.074          1.139       1.199          0.945      1.180
    1998        1.202      1.080         1.769       1.087          1.116        1.090          1.102       1.222          0.695      1.290
    1999        1.141      1.090         0.985       1.001          1.090        1.098          1.067       1.224          0.968      1.328
    2000        1.243      1.071         1.291       1.232          1.083        1.111          1.470       1.193          1.121      1.304
    2001        1.041      1.102         1.379       1.203          1.049        1.136          0.645       1.181          3.496      1.362
    2002        1.033      1.166         1.485       1.100          1.144        1.118          2.160       1.167          5.159      1.359
    2003        0.951      1.138         1.622       1.087          1.219        1.108          0.885       1.166         (8.341)     1.269
    2004        0.748      1.118         2.566       1.083          1.187        1.107          1.059       1.155         (0.868)     1.234


         The US                                                              Japan
G sector ALP=y G        TFP G         kG          aG           1/ACPG=WG     ALP=y G        TFP G        kG             aG        1/ACPG=WG
   1995    19.88          26.13       24.69       (0.085)          1.242        5.68           4808      12374          (0.062)      4.616
   1996    21.59          25.05       26.22       (0.045)          1.215        5.16           4566      12947          (0.053)      4.696
   1997    24.64          21.28       27.46        0.044           1.115        5.72           3803      13638          (0.029)      4.729
   1998    26.86          20.11       28.99        0.086           1.079        5.88        41563714     13890          (1.079)      9.844
   1999    30.14          18.55       29.99        0.143           0.995        4.97          82051      13940          (0.384)      6.655
   2000    33.71          17.58       31.33        0.189           0.929        5.06          62111      13878          (0.353)      6.455
   2001    31.42          21.85       31.98        0.105           1.018        4.43         321700      13282          (0.544)      7.212
   2002    25.79          36.81       31.44       (0.103)          1.219        6.75        4415684      12861          (0.843)      8.461
   2003    24.17          52.69       31.78       (0.225)          1.315        8.55        3695951      12593          (0.827)      8.344
   2004    25.69          54.57       32.81       (0.216)          1.277       12.12        4796512      12435          (0.856)      8.298
                        Tables: (2) The US versus Japan

           The US                                                                 Japan
             Taxes/Y       (S-I )G /Y       C G /Y        S G /Y       Y G /Y       Taxes/Y       (S-I )G /Y     C G /Y       S G /Y      Y G /Y
1995            0.157         (0.022)         0.171        (0.013)      0.157          0.167        (0.056)        0.178       (0.010)     0.167
1996            0.159         (0.016)         0.166        (0.007)      0.159          0.171        (0.057)        0.180       (0.009)     0.171
1997            0.171         (0.000)         0.164         0.008       0.171          0.174        (0.046)        0.179       (0.005)     0.174
1998            0.176          0.007          0.161         0.015       0.176          0.089        (0.138)        0.185       (0.096)     0.089
1999            0.187          0.019          0.161         0.027       0.187          0.139        (0.093)        0.193       (0.053)     0.139
2000            0.198          0.029          0.161         0.037       0.198          0.148        (0.081)        0.200       (0.052)     0.148
2001            0.183          0.010          0.163         0.019       0.183          0.135        (0.080)        0.208       (0.073)     0.135
2002            0.155         (0.024)         0.171        (0.016)      0.155          0.117        (0.099)        0.215       (0.098)     0.117
2003            0.143         (0.040)         0.175        (0.032)      0.143          0.118        (0.092)        0.215       (0.097)     0.118
2004            0.144         (0.038)         0.175        (0.031)      0.144          0.115        (0.091)        0.214       (0.099)     0.115


        The US The G sector versus the total economy                              Japan        The G sector versus the total economy
       g A (FLOW)G      g A (TFP)G      g A (FLOW )   g A (TFP )     i=I/Y      g A (FLOW)G      g A (TFP)G  g A (FLOW )     g A (TFP )   i=I/Y
1996        0.089         (0.041)          0.046         0.045        0.096          0.031         (0.050)        0.011       (0.007)      0.126
1997        0.139         (0.151)          0.040         0.034        0.099          0.048         (0.167)        0.012        0.012       0.121
1998        0.086         (0.055)          0.039         0.045        0.106         (0.492)         10928        (0.027)      (0.006)      0.099
1999        0.117         (0.077)          0.048         0.052        0.111          0.483         (0.998)       (0.016)       0.020       0.091
2000        0.110         (0.053)          0.034         0.061        0.114          0.023         (0.243)       (0.000)       0.019       0.088
2001       (0.071)         0.243           0.029         0.017        0.104         (0.171)         4.179        (0.014)      (0.077)      0.075
2002       (0.185)         0.685           0.013        (0.008)       0.092         (0.203)        12.726        (0.004)       0.003       0.056
2003       (0.061)         0.432           0.034         0.033        0.092         (0.025)        (0.163)       (0.004)      (0.093)      0.052
2004        0.070          0.036           0.051         0.055        0.102         (0.018)         0.298         0.019       (0.048)      0.054
         Some questions to discuss
   How can we connect “operating surplus and
    wages/compensation in GDP” with “consumption and
    saving in NDI” after depreciation and tax redistribution?
   It is not very clear about the concept of the duality
    between the TFP that represents whole qualities (i.e.,
    TFP is not a residual but an essence of technology)
    and the capital and labor that represent whole
    quantities?
   What distinguishes the “qualitative” in the current
    investment and the “qualitative” in the level of
    technology accumulated in the past?
   Has the quality change of inputs been considered in line
    with the idea of “converting better to more” (Jorgenson)?

								
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