1. 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

2. Motivation Discuss the robust TFP estimation method at firm level, using competitive industry as an example.

3. 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

4. The importance of TFP estimation Productivity is not everything, but approximates everything in the long run. Krugman （ 1997 ） The factors affecting TFP – Is the TFP of firms improved? Misallocation of resources - Can the economic environment promotes firms with high TFP, and suppress or expel those with low TFP?

5. 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% - Hsieh (1999) got 3% more than Young’s.

6. Structure The measurement of data and variables Traditional methods Firms’ decision and structure estimation Value-added or gross output production function Sample selection, function form and other robust test summary

7. The measurement of data and variables Panel construction – Goal : identify firms across years – 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.

8. The measurement of data and variables The measurement of output – The real output – deflate gross output from three dimensions: time(year), space(province), industry(two-digit) The measurement of input – Construct the input deflator from time(year), space(province) and industry(two-digit), based on input-output table, like Brandt (2012).

9. 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 – Total average number of staff

10. 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

12. Traditional methods DEA (Data Envelopment Analysis) Index method Tradition parametric methods – OLS – FE – BB

13. Traditional methods DEA – 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.

14. Traditional methods

18. 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.

19. Firms’ decision and structure estimation

20. 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

21. Firms’ decision and structure estimation The decision structure of firm’s dynamic input: take capital as an example

22. Firms’ decision and structure estimation The decision structure of firm’s static input : materials

23. 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

24. Firms’ decision and structure estimation

26. Levinsohn & Petrin (2003) – A great loss of investment information – Use materials as proxy variables:

27. 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.

28. Firms’ decision and structure estimation Ackerberg et al.(2006) – Capital is decided before TFP – Labor decision is before materials

29. Firms’ decision and structure estimation

30. The idea of the new structural estimation of TFP at firm level – Review the index method about estimating static input Solow (1957) ； Caves et al. (1982) ； Hall (1989) – Separate the estimation of static input and dynamic input Gandhi et al. (2011)

31. Firms’ decision and structure estimation

33. 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

35. 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.

36. Gross output or Value-added?

37. The core in TFP estimation is to control the substitution among factors – Make the following choices to maximize profit Labor intensive Capital intensive Outsource and material intensive – Value-added production function only consider the substitution between labor and capital and neglect the efficiency from materials

38. Gross output or Value-added?

41. Sample selection, function form and other robust test

47. 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.

48. 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.

49. 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.

50. 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

51. Summary The most robust estimation of TFP for clothing and leather industry in China

52. 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

53. Thank you!