Download Measuring Productivity with Non

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 crosscountry growth performance. However, measuring crosssectional 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 africa i   4 easia i   5 mideast i
  6 ecai   7 sas i   8 latin i   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***
lnK 0.6368***
lnL 0.3427***
time 0.0010
africa 0.0640
latin 0.0807**
easia
eca
sas
mideast
0.0047
-0.0216
-0.1127
0.0360
(0.1799)
(0.0133)
(0.0152)
(0.0098)
(0.0436)
(0.0383)
(0.0519)
(0.0550)
(0.0593)
(0.0507)
Results (1b) – Sources of
TE (u)
ind. var.
coefficient
(standard error)
GOV
TRS
COURT
PROPR
COURT * PROPR
CREDIT
LABOR
DURAB
XCONT
REGIME
PR
FOREIGN
TRADEB
BLACK
0.0231***
-0.0456***
-0.0411**
0.2386***
-0.0192***
-0.0261**
-0.0171
-0.0068***
0.0492*
-0.0050
0.0517**
-0.0135
-0.0680**
-0.0099
(0.0050)
(0.0124)
(0.0199)
(0.0489)
(0.0062)
(0.0121)
(0.0146)
(0.0009)
(0.0299)
(0.0142)
(0.0243)
(0.0089)
(0.0270)
(0.0092)
σ2
0.0756*** (0.0115)
γ
0.8260*** (0.0434)
log (likelihood)
106.9769
Results (2b) – TE by regions
TE (81-85)
All
Industrial
E. Asia
ECA
Middle E.
Latin
Africa
TE (86-90)
TE (91-95)
TE (96-00)
mean
0.8144
0.8220
0.8374
0.8496
s.d.
0.1470
0.1435
0.1407
0.1324
mean
0.9194
0.9320
0.9500
0.9512
s.d.
0.0438
0.0355
0.0263
0.0260
mean
0.7468
0.7473
0.7657
0.8024
s.d.
0.1338
0.1227
0.1252
0.1143
mean
0.9230
0.9312
0.9472
0.9191
s.d.
0.0375
0.0248
0.0054
0.0015
mean
0.8330
0.8309
0.8417
0.8710
s.d.
0.1078
0.1059
0.0989
0.0748
mean
0.8237
0.8252
0.8337
0.8418
s.d.
0.1086
0.1028
0.0950
0.1099
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
Growth
(%)
Capital
Growth
(%)
Labour
Growth
(%)
TFP
Growth
(%)
TE
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, PG =YG − WG,
and PPRI =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 Club s that includes 8 countries 1995-2004
(rho/r )(c ) of three Clubs 30 countries 1995-2004
1.02
1.01
1.2
1.1
1.00
0.99
rho/r
0.9
2
y = -1.0216x + 2.5726x - 0.4771
0.8
rho/r
1.0
R2 = 0.8771
0.98
0.97
0.96
0.95
0.94
0.7
0.6
y = -46.2x2 + 82.06x - 35.44
R2 = 0.4643
0.93
0.92
0.5
0.40
0.50
0.60
0.70
0.80
0.90
1.00
0.82
1.10
0.83
0.84
0.85
c
0.87
0.88
0.89
0.90
c=C/Y
The rate of return, r (0), and the capital-output ratio, W (0):
Total economy of 30 countries 1995-2004
r/w and 1-alpha : 30 countries in 1995-2004
0.50
0.07
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
0.00
0.78
0.86
0.05
0.80
0.82
0.84
0.86
0.88
0.90
1-alpha
0.92
0.94
0.96
0.98
1.00
0.00
0.0
0.5
1.0
1.5
2.0
2.5
the capital-output ratio, W (0)
3.0
3.5
4.0
Tables: (1) The US, Russia, China, India, and Japan,
(2) The US versus Japan
1996
1997
1998
1999
2000
2001
2002
2003
2004
(0) The U S
(8) Russia
 G/*G
 PRI/*PRI
 G/*G
0.867
1.080
0.722
1.081
1.082
0.868
1.202
1.080
1.769
1.141
1.090
0.985
1.243
1.071
1.291
1.041
1.102
1.379
1.033
1.166
1.485
0.951
1.138
1.622
0.748
1.118
2.566
The US
G sector ALP=y G
1995
19.88
1996
21.59
1997
24.64
1998
26.86
1999
30.14
2000
33.71
2001
31.42
2002
25.79
2003
24.17
2004
25.69
 PRI/*PRI
1.283
1.324
1.087
1.001
1.232
1.203
1.100
1.087
1.083
(6) China
 G/*G
1.138
1.121
1.116
1.090
1.083
1.049
1.144
1.219
1.187
 PRI/*PRI
1.054
1.074
1.090
1.098
1.111
1.136
1.118
1.108
1.107
(2) India
 G/*G
1.284
1.139
1.102
1.067
1.470
0.645
2.160
0.885
1.059
 PRI/*PRI
1.169
1.199
1.222
1.224
1.193
1.181
1.167
1.166
1.155
(6) Japan
 G/*G
 PRI/*PRI
0.928
1.229
0.945
1.180
0.695
1.290
0.968
1.328
1.121
1.304
3.496
1.362
5.159
1.359
(8.341)
1.269
(0.868)
1.234
Japan
TFP G
26.13
25.05
21.28
20.11
18.55
17.58
21.85
36.81
52.69
54.57
kG
24.69
26.22
27.46
28.99
29.99
31.33
31.98
31.44
31.78
32.81
aG
(0.085)
(0.045)
0.044
0.086
0.143
0.189
0.105
(0.103)
(0.225)
(0.216)
1/ACPG=WG
1.242
1.215
1.115
1.079
0.995
0.929
1.018
1.219
1.315
1.277
ALP=y G
5.68
5.16
5.72
5.88
4.97
5.06
4.43
6.75
8.55
12.12
TFP G
4808
4566
3803
41563714
82051
62111
321700
4415684
3695951
4796512
kG
12374
12947
13638
13890
13940
13878
13282
12861
12593
12435
aG
(0.062)
(0.053)
(0.029)
(1.079)
(0.384)
(0.353)
(0.544)
(0.843)
(0.827)
(0.856)
1/ACPG=WG
4.616
4.696
4.729
9.844
6.655
6.455
7.212
8.461
8.344
8.298
Tables: (2) The US versus Japan
The US
Taxes/Y
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
0.157
0.159
0.171
0.176
0.187
0.198
0.183
0.155
0.143
0.144
Japan
(S-I )G /Y
(0.022)
(0.016)
(0.000)
0.007
0.019
0.029
0.010
(0.024)
(0.040)
(0.038)
C G /Y
0.171
0.166
0.164
0.161
0.161
0.161
0.163
0.171
0.175
0.175
S G /Y
(0.013)
(0.007)
0.008
0.015
0.027
0.037
0.019
(0.016)
(0.032)
(0.031)
Y G /Y
0.157
0.159
0.171
0.176
0.187
0.198
0.183
0.155
0.143
0.144
The US The G sector versus the total economy
g A (FLOW)G
1996
1997
1998
1999
2000
2001
2002
2003
2004
0.089
0.139
0.086
0.117
0.110
(0.071)
(0.185)
(0.061)
0.070
g A (TFP)G
(0.041)
(0.151)
(0.055)
(0.077)
(0.053)
0.243
0.685
0.432
0.036
g A (FLOW )
0.046
0.040
0.039
0.048
0.034
0.029
0.013
0.034
0.051
g A (TFP )
0.045
0.034
0.045
0.052
0.061
0.017
(0.008)
0.033
0.055
Taxes/Y
0.167
0.171
0.174
0.089
0.139
0.148
0.135
0.117
0.118
0.115
Japan
i=I/Y
0.096
0.099
0.106
0.111
0.114
0.104
0.092
0.092
0.102
g A (FLOW)G
0.031
0.048
(0.492)
0.483
0.023
(0.171)
(0.203)
(0.025)
(0.018)
(S-I )G /Y
(0.056)
(0.057)
(0.046)
(0.138)
(0.093)
(0.081)
(0.080)
(0.099)
(0.092)
(0.091)
C G /Y
0.178
0.180
0.179
0.185
0.193
0.200
0.208
0.215
0.215
0.214
S G /Y
(0.010)
(0.009)
(0.005)
(0.096)
(0.053)
(0.052)
(0.073)
(0.098)
(0.097)
(0.099)
The G sector versus the total economy
g A (TFP)G
g A (FLOW )
g A (TFP )
(0.050)
(0.167)
10928
(0.998)
(0.243)
4.179
12.726
(0.163)
0.298
0.011
0.012
(0.027)
(0.016)
(0.000)
(0.014)
(0.004)
(0.004)
0.019
(0.007)
0.012
(0.006)
0.020
0.019
(0.077)
0.003
(0.093)
(0.048)
Y G /Y
0.167
0.171
0.174
0.089
0.139
0.148
0.135
0.117
0.118
0.115
i=I/Y
0.126
0.121
0.099
0.091
0.088
0.075
0.056
0.052
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)?