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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: yheng@bnu.edu.cn. Motivation. Discuss the robust TFP estimation method at firm level, using competitive industry as an example. - PowerPoint PPT Presentation

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: yheng@bnu.edu.cn

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

Traditional methods

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

Traditional methods

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.

Traditional methods

Index method

Without the consideration of random error

Based on the hypothesis that all inputs are static input without adjustment cost

Traditional methods

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

The advantages

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 or Value-added?

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

Gross output or Value-added?

Gross output or Value-added?

The core in TFP estimation is to control the substitution among factors

Make the following choices to maximize profit

Labor intensive

Capital intensive

Gross output or Value-added?

Gross output or Value-added?

The result misusing value-added

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

The problems of tradition methods

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

Table 2Traditional Methods

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

SEBA Beijing Normal University Email: yheng@bnu.edu.cn

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

Traditional methods

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

Traditional methods

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.

Traditional methods

Index method

Without the consideration of random error

Based on the hypothesis that all inputs are static input without adjustment cost

Traditional methods

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

The advantages

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 or Value-added?

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

Gross output or Value-added?

Gross output or Value-added?

The core in TFP estimation is to control the substitution among factors

Make the following choices to maximize profit

Labor intensive

Capital intensive

Gross output or Value-added?

Gross output or Value-added?

The result misusing value-added

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

The problems of tradition methods

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

Table 2Traditional Methods

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