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Searching for the Robust Method to Estimate Total Factor Productivity at Firm Level Yin Heng Li Shigang Liu Di SEBA Beijing Normal University Email:

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Searching for the Robust Method to Estimate Total Factor Productivity at Firm Level Yin Heng Li Shigang Liu Di. SEBA Beijing Normal University Email: [email protected] Motivation. Discuss the robust TFP estimation method at firm level, using competitive industry as an example. - PowerPoint PPT Presentation

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The Colonial Origins of Comparative Development: An Empirical InvestigationSearching for the Robust Method to Estimate Total Factor Productivity at Firm Level Yin Heng Li Shigang Liu Di
SEBA Beijing Normal University Email: [email protected]
Motivation
Discuss the robust TFP estimation method at firm level, using competitive industry as an example.
What does TFP measure?
Evaluate the input-output efficiency
Labor productivity cannot describe the true efficiency at firm level
The core of TFP estimation is dealing with the substitution among input factors
The importance of TFP estimation
Productivity is not everything, but approximates everything in the long run. Krugman1997
The factors affecting TFP
Misallocation of resources
with high TFP, and suppress or expel those
with low TFP?
The current situation of TFP estimation
Great differences exist even in researches appeared in the top journals
- Young (1995)’s estimation of the growth rate of TFP
in Hong Kong and Taiwan district in China is
between 2% and 3%, the growth rate of Korea is
1.7%
Structure
Value-added or gross output production function
Sample selection, function form and other robust test
summary
Panel construction
Problems :
Different firms may share the same code
Firms may change the code because of changing name or structure etc.
Idea :
Make sure that firms with the same code is the same one;
Match firms with the combination of relatively stable information, such as name, head, telephone, etc.;
Correct the wrong matching.
The measurement of output
The measurement of input
The measurement of data and variables
The measurement of capital
Estimate nominal investment from the found year with the data of original fixed capital
Deflate the nominal investment to get the real investment
Get the real capital with perpetual inventory method
The measurement of labor
The measurement of data and variables
The choice of industries
Two-digit industry 18: manufacture of clothing, shoes and hats; two-digit industry 19: manufacture of leather, fur and feather
Data clearing
Delete the sample with non-positive output, capital, labor and input
Delete the sample with less than 8 workers
Delete the sample with bigger value-added than output
Considering the heterogeneity of firms’ TFP
Get the TFP measurement from the input and output data with linear programming, treating the production process as a black box
It is a determinate method which can be sensitive to the random error or extreme values.
Index method
Without the consideration of random error
Based on the hypothesis that all inputs are static input without adjustment cost
Parametric method
Based on the set that all firms in the same industries have the same elasticity of output of capital, labor and input
Deal with random error
AB/BB
Firms’ decision and structure estimation
The more information of firm’s action and decision we use, the more robust and accurate result we can get.
Tradition methods neglect the information of firm’s action and decision structure.
Firms’ decision and structure estimation
Data generating process at firm level
Firms choose input and output to maximize the profit based on the observed productivity
Where is planed output, the real output is
Firms’ decision and structure estimation
The decision structure of firm’s factor input: dynamic and static
Two adjustment frictions make the firm’s input decision dynamic:
Adjustment cost, such as the cost of installment, test and dismantle
Adjustment lag, because the factor used now is decided at the former period
Firms’ decision and structure estimation
The decision structure of firm’s dynamic input: take capital as an example
Firms’ decision and structure estimation
The decision structure of firm’s static input : materials
Firms’ decision and structure estimation
The decision structure of firm’s labor input ( may change with industry)
Treated as dynamic if the adjustment cost cannot be neglected
Adjustment cost : training cost when employing new staff and the cost of layoff
Adjustment lag : new staff can only get to work after the training
Treated as static if the adjustment cost can be neglected
Firms’ decision and structure estimation
Model
Olley & Pakes1996
Get productivity from the investment function , and then take it into the production function
Step 1. get with nonparametric method, and then the productivity can be expressed as =
Step 2. let productivity follows the Markov process,get the estimation of with the moment condition
Firms’ decision and structure estimation
Levinsohn & Petrin (2003)
Use materials as proxy variables:
Firms’ decision and structure estimation
Bond & Söderbom (2005)and Ackerberg et al. (2006): Collinearity problem
Robinson (1988): “The variables in the parametric part cannot be predicted by those in the nonparametric part in the sense of OLS.”
Newey et al. (1999): There should exist no function between parametric part and nonparametric part in semi-parametric model.
Firms’ decision and structure estimation
Ackerberg et al.(2006)
Capital is decided before TFP
Labor decision is before materials
Firms’ decision and structure estimation
Step 1. the production function is , get with nonparametric method, and the productivity is
Step 2.the productivity follows Markov process, get the other parameters with the moment condition
Firms’ decision and structure estimation
The idea of the new structural estimation of TFP at firm level
Review the index method about estimating static input
Solow (1957)
Gandhi et al. (2011)
Firms’ decision and structure estimation
new structural estimation of TFP
Get the following formula according to the optimal condition of static input
the Hicks-neutral technique allows
Where is the share of materials to nominal output
Get with nonparametric regression, and in the situation of C-D production function, the mean of is
Firms’ decision and structure estimation
If labor is static input, then get with the method above, if not, get the estimation of at the next step
The productivity follows Markov process same as OP/LP/ACF, and get with the moment condition
Firms’ decision and structure estimation
New structural estimation of TFP
Step 1. estimate the parameter of static input following the idea of index method
Step 2. estimate the parameter of dynamic input following the idea of structural estimation
Avoid the assumptions in the proxy variables method such as the reversible proxy function and the measurement error
Make full use of firms’ decision
Solve the endogenous problem and the collinearity problem
Gross output (sales) is the real observable variable by firms who experience the production and management process, while value-added is just a statistical concept.
Value-added can be proper only if the theoretic definition is agreed with empirical measurement, which needs the following assumptions
Assumption 1. Labor and capital produce value-added following , and combine with materials according to to form output
The core in TFP estimation is to control the substitution among factors
Make the following choices to maximize profit
Labor intensive
Capital intensive

New endogenous problem appears because is put into the error term
TFP heterogeneity will be exaggerated because the heterogeneity coming from materials is put into TFP difference
Sample selection, function form and other robust test
Sample selection problem
There is a great number of entry and exit in the data, and we can only observe the existed ones
The structure estimation method don’t have to deal with sample selection problem because of the proxy of in the first step
Sample selection, function form and other robust test
We can only observe the existed samples with, and ,so there is endogenous problem in the second step
How to deal with it?
Rules of entry and exit
Conditional expectation
The probability that a firm i stay in period t
Get
Sample selection, function form and other robust test
Trans-log production function
Cobb-Douglas production function is a special situation of trans-log production function.
Summary
DEA method tries to measure TFP by construct a set of substitution of factors by linear programming, but determinate method cannot get the robust estimation with the data at firm level, because the measurement error cannot be neglected.
Summary
Index method is also not satisfactory because all the inputs are assumed to be static and the parameter of return to scale should be given.
Traditional methods, such as FE,IV and dynamic panel, will not get the robust result because the disturbance should be given before the estimation.
Summary
Structural estimation method, which is becoming the most potential approach, tries to open the black box of the firms’ production process by making full use of the information of their behavior and decision-making.
Olley and Pakes (1996), Levinsohn and Petrin (2003),Ackerberg et al.(2006) all face the “collineraity” problem.
The new structural estimation, which combines the structural estimation with the traditional index method, may get the most robust estimation of TFP at firm level.
Summary
The definition of variables affects the robustness of TFP estimation
-measuring firms’ output with value-added will
exaggerate TFP heterogeneity seriously
Sample selection and the production function form also affect the TFP estimation
Summary
The most robust estimation of TFP for clothing and leather industry in China
Summary
Unsolved problem:
The use of proxy variable in structural method and the index method need new foundation if firms have market power.
More information is needed to separate the effect of demand and price from TFP
Thank you!
1998 8795 29634.70 71628.43 4589.94 13460.20 331.38 787.72 19406.05 48162.89
1999 8482 31358.37 76530.40 4640.89 14266.12 331.24 638.53 20317.37 51764.68
2000 8872 33683.06 89291.19 4399.33 14301.95 332.19 663.23 21526.77 58845.14
2001 10269 33896.71 99122.08 4030.10 14122.47 320.76 616.40 21716.56 65105.94
2002 11488 34759.67 106787.20 3763.74 13890.40 315.26 592.85 22062.48 69204.64
2003 13219 37826.08 129803.20 3758.72 14743.61 321.98 642.17 23571.01 82674.73
2004 16210 36327.99 165626.10 3577.54 19389.14 316.30 616.25 21990.80 108535.00
2005 17549 43655.98 201137.20 3969.65 21885.35 319.08 657.42 26398.21 131528.40
2006 19260 47903.11 235153.90 4283.38 28367.65 313.16 676.45 28537.35 150848.60
2007 21314 52152.53 249305.10 4344.99 27960.65 301.58 671.94 30418.95 159284.20
Coef. Std. Coef. Std. Coef. Std.
98-02
k
l
m
03-07
k
l
m
- - - - 0.8158 0.0017 0.6969 0.0027 0.9518 0.0204
Year 98-02 03-07 98-02 03-07 98-02 03-07 98-02 03-07 98-02 03-07
Growth % 4.2136 6.8645 2.6128 3.2202 1.5407 2.7222 2.3363 4.2434 0.4844 0.1696
Ratio
(
)
(
)
(
)
(
)
OP LP ACF NEW-S1 NEW-S2
Coef. Std. Coef. Std. Coef. Std. Coef. Std. Coef. Std.
k
0.0459 0.0005 0.0084 0.0037 0.0115 0.0021 0.0537 0.0014 0.0621 0.0014
l
0.0936 0.0015 0.0773 0.0010 0.0501 0.0054 0.1358 0.0021 0.1090 0.0002
m
0.8309 0.0012 0.9144 0.0102 0.9372 0.0092 0.7302 0.0002 0.7302 0.0002
Year 98-02 03-07 98-02 03-07 98-02 03-07 98-02 03-07 98-02 03-07
Growth% 0.3810 0.5745 0.2169 0.1836 0.2574 0.3691 1.4941 3.9874 1.5763 4.0379
Ratio
90/10 1.0562 1.0514 1.1133 1.0822 1.1816 1.1270 1.4517 1.4990 1.4676 1.5141
95/5 1.0856 1.0809 1.2142 1.1271 1.3234 1.2080 1.6544 1.7231 1.6803 1.7427
Obs. 67483 97196 97196 97196 97196
Table 4Structural Estimation for Value -added
OP LP ACF NEW-S
k
l
Year 98-02 03-07 98-02 03-07 98-02 03-07 98-02 03-07
Growth% 0.9916 1.3299 4.4379 9.4516 5.8774 12.0461 11.4778 17.9319
Ratio
Obs. 67489 97196 97196 96920
Table 5Structural Estimation for Aggregate Output:
Sample Selection Considered
Coef. Std. Coef. Std. Coef. Std. Coef. Std. Coef. Std.
k
0.0457 0.0005 0.0259 0.0103 0.0304 0.0118 0.0343 0.0014 0.0341 0.0015
l
0.0936 0.0015 0.0773 0.0010 -0.0277 0.0380 0.1065 0.0028 0.1090 0.0002
m
0.8309 0.0012 0.7968 0.0783 0.8170 0.0665 0.7302 0.0002 0.7302 0.0002
Year 98-02 03-07 98-02 03-07 98-02 03-07 98-02 03-07 98-02 03-07
Growth% 0.3848 0.5796 0.9931 1.8084 1.4416 2.4926 1.7720 4.4306 1.7608 4.4184
Ratio
90/10 1.0562 1.0514 1.2926 1.3153 1.5180 1.5157 1.5034 1.5482 1.4996 1.5456
95/5 1.0858 1.0810 1.4062 1.4371 1.7527 1.7450 1.7337 1.7862 1.7296 1.7821
Obs. 67483 97196 97196 97196 97196
Table 6Sensitivity Analysis
Coef. Std. Coef. Std. Coef. Std. Coef. Std. Coef. Std.
k
0.0717 0.0054 0.0771 0.0047 0.0587 0.0088 0.0821 0.0043 0.0752 0.0062
l
0.2944 0.0113 0.2679 0.0000 0.2588 0.0120 0.2752 0.0086 0.1887 0.0094
m
0.3925 0.0010 0.3925 0.0010 0.4049 0.0010 0.3984 0.0013 0.4719 0.0013
kk
0.0089 0.0004 0.0091 0.0004 0.0104 0.0006 0.0080 0.0003 0.0075 0.0004
ll
0.0274 0.0012 0.0307 0.0000 0.0261 0.0011 0.0290 0.0010 0.0263 0.0008
mm
0.0392 0.0001 0.0392 0.0001 0.0390 0.0001 0.0387 0.0001 0.0426 0.0001
kl
0.0035 0.0010 0.0019 0.0000 0.0053 0.0012 0.0038 0.0008 0.0033 0.0009
lm
-0.0499 0.0002 -0.0499 0.0002 -0.0464 0.0002 -0.0494 0.0002 -0.0516 0.0002
mk
-0.0185 0.0001 -0.0185 0.0001 -0.0222 0.0001 -0.0182 0.0001 -0.0188 0.0001
t
- - - - - - 0.0342 0.0005
Year 98-02 03-07 98-02 03-07 98-02 03-07 98-02 03-07 98-02 03-07
Growth% 1.0973 3.3210 1.0765 3.3036 0.5199 2.3967 1.4325 2.6047 0.8027 2.5936
Ratio
90/10 1.4631 1.4616 1.4631 1.4616 1.4167 1.4232 1.6414 1.3594 1.4308 1.3966
95/5 1.6683 1.6467 1.6683 1.6467 1.5899 1.5791 1.9345 1.5050 1.6283 1.5619
Obs. 97196 97196 97196 97196 97196