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Un-Incorporation and Conditional Misallocation: Firm-Level Evidence from Sri Lanka

  • Ranpati Dewage Thilini Sumudu Kumari ORCID logo , Shawn Xiaoguang Chen ORCID logo EMAIL logo and Sam Hak Kan Tang ORCID logo
Published/Copyright: August 4, 2023
The B.E. Journal of Macroeconomics
From the journal The B.E. Journal of Macroeconomics Volume 23 Issue 2

Abstract

Un-incorporated firms are usually found less productive than their incorporated counterparts. However, little is known about the misallocation conditional on firms’ incorporation status and their productivity. This paper investigates the resource misallocation across un-incorporated firms and gauges the consequent aggregate productivity loss in comparison with their incorporated counterparts. We examine the question by using firm-level survey data from Sri Lanka’s manufacturing sector for 2005–2017 that provide unique information about firms’ corporation status. Our findings suggest that misallocation is more severe in unincorporated firms than in incorporated ones, leading to extra 42 % aggregate TFP loss to the former. By comparing the sources of misallocation between the two types of firms, we find capital is more misallocated relative to output and there is a stronger positive correlation between firm-specific distortion and productivity across the unincorporated firms. Our findings suggest that the un-incorporated firms suffer additional productivity loss at the aggregate level due to misallocation.

Keywords: firm-level distortion; misallocation; Sri Lanka; total factor productivity; unincorporated firm
JEL Classification: O47; K22; H25
Corresponding author: Shawn Xiaoguang Chen, Business School, The University of Western Australia, Perth, Australia, E-mail:

Acknowledgments

The results and views enunciated in this paper are those of the authors alone and in no way represent those of the Central Bank of Sri Lanka. Authors acknowledge the support from The University of Western Australia, the Central Bank of Sri Lanka, and the Department of Census and Statistics of Sri Lanka. They appreciate the feedback from the participants in Australian Conference of Economists 2021 and in work-in-progress seminar series-2021 at The University of Western Australia. Authors also appreciate the insight given by Rodney Tyers, Kenneth Clements, Anu Rammohan, Missaka Warusawitharana and Nelson Perera. Authors are also grateful to the managing editor, Arpad Abraham, and two anonymous reviewers of this journal, for their constructive comments. Authors bear the responsibility for any remaining errors in the paper.

  1. Disclosure statement: No potential conflict of interest was reported by the authors.

Appendix A

A.1 Model Setup

The model of Hsieh and Klenow (2009) quantifies the magnitude of TFP losses due to misallocation and aggregate manufacturing TFP gains when misallocation is eliminated. The manufacturing sector is comprised of S industries, indexed by subscript s = 1, …, S. In the ASI from 2006 to 2018, s refers to the four-digit industry level. A single final good Y is produced using a Cobb–Douglas technology:

(A1) Y = ∏ s = 1 S Y s θ s , where ∑ s = 1 S θ s = 1 ,

and θ s is industry value-added share. At industry s level, the output Y s is a CES aggregate of M s differentiated products.

(A2) Y s = ∑ i = 1 M s Y s i σ − 1 σ σ σ − 1 ,

where σ is the elasticity of substitution across different inputs. Finally, the output of firm i in industry s is produced according to a Cobb–Douglas technology:

(A3) Y s i = A s i K s i α s L s i 1 − α s ,

where A si , K si and L si are firm-level TFP, physical capital and labour, respectively. Meanwhile, α s is industry-specific capital share. Each firm faces two types of firm-specific distortions in output τ Y s i and capital τ K s i .[23] The objective of firm si is profit maximisations by choosing P si and Y si while taking factor prices, distortions and the output demand curve as givens.

(A4) π s i = 1 − τ Y s i P s i Y s i − w L s i − ( 1 + τ K s i ) R K s i

where π si is profit, P si Y si is value-added, w is effective wage rate and R is the rental price of capital. Following Hsieh and Klenow (2009), we define firm’s revenue productivity TFP R s i as a measure of firm distortions, as Foster, Haltiwanger, and Syverson (2008) did:

(A5) TFP R s i = P s i A s i = P s i Y s i K s i α s L s i 1 − α s = σ σ − 1 R α s α s w 1 − α s 1 − α s 1 + τ K s i α s 1 − τ Y s i .

If there are no distortions (i.e. when τ K s i = τ Y s i = 0 ), there would be no variation in TFPR si within each industry. Following (A5), revenue productivity for industry s is:

(A6) TFP R s = P s Y s K s α s L s 1 − α s ,

where P s Y s = ∑ i P si Y si .

TFPR s can also be written as:

(A7) TFP R s = σ σ − 1 R α s ∑ i = 1 M s 1 − τ Y s i 1 + τ K s i P s i Y s i P s Y s α s × w 1 − α s ∑ i = 1 M s 1 − τ Y s i P s i Y s i P s Y s 1 − α s .

A.2 Measurement of Aggregate TFP Gains from Reallocation

We define industry s physical productivity as:

(A8) TF P s = Y s K s α s L s 1 − α s = ∑ i = 1 M s A s i TFP R s TFP R s i σ − 1 1 σ − 1 .

In the absence of distortions, efficient TFP in industry s is:

(A9) TFP s e = A s ̄ = ∑ i = 1 M s A s i σ − 1 1 σ − 1 .

The physical productivity for the entire manufacturing sector is aggregated as:

(A10) TFP = ∏ s = 1 S TFP s θ s .

Then, Cobb–Douglas aggregator obtains the ratio between actual and efficient output Y e in the aggregate manufacturing sector:

(A11) Y Y e = ∏ s = 1 S TF P s A s ̄ θ S = ∏ s = 1 S ∑ i = 1 M s A s i A s ̄ TFP R s TFP R s i σ − 1 θ s σ − 1 .

Finally, we calculate potential reallocation gains:

(A12) % TFP Gain  =   Y e Y − 1 × 100 .

A.3 Theoretical Framework for Regression Analysis

In Hsieh and Klenow (2009), firm size is determined by firm-level productivity and firm-level distortions. We derive the relationships among firm size, productivity and distortions as given below.

We have the following firm-level inverse demand curve:

(A13) P s i = P s Y s Y s i 1 / σ

From the firm’s profit maximisation problem in Eq. (A4) above, we have the following pricing equation:

(A14) P s i = σ σ − 1 1 A s i 1 − τ s i Y R 1 + τ s i K α s α s w 1 − α s 1 − α s ,

where σ σ − 1 is the mark-up, and the rest of the right-hand side is the marginal cost, which is jointly determined by the firm’s productivity, factor prices and distortions.

From Eq. (A13), we can get the demand function:

(A15) Y s i = P s i P s − σ Y s

From Eq. (A15), we can get the firm size, measured by firm-level value-added V A s i as below:

(A16) V A s i = P s i Y s i = P s i − ( σ − 1 ) P s σ Y s

Substituting Eq. (A14) into Eq. (A16), we can get:

(A17) V A s i = P s i Y s i = σ σ − 1 1 A s i 1 − τ s i Y R 1 + τ s i K α s α s w ( 1 − α s ) 1 − α s − ( σ − 1 ) P s σ Y s

Equation (A17) shows firm-level value-added is determined by firm-level productivity and firm-level distortions in output and in capital, as in Eqs. (A18) and (A19), respectively. Eq. (A19) also means that TFPR is a sufficient statistic for distortions in capital and output. Hence, we do not include firm size as a control variable in our regressions in Section 5.1.

(A18) Log V A s i ∝ Log A s i
(A19) Log V A s i ∝ Log TFP R s i ∝ Log 1 + τ s i K α s 1 1 − τ s i Y

where ∝ ′ ′ ′ ′ means ‘proportional to’.

Table A.1:

TFP and TFP Gains (%): 2005–2017, by ownership.

Year TFP TFP gains (%)
Sole Partnership Private Public Sole Partnership Private Public
2005 16.93 17.39 19.93 n/a 133 20 46 n/a
2006 16.42 17.32 18.99 19.32 81 63 96 50
2007 19.10 19.52 20.14 21.01 106 50 113 98
2008 18.83 19.91 21.09 21.45 83 63 108 56
2009 19.09 19.89 20.73 20.33 154 99 85 56
2010 19.78 19.36 20.73 19.75 134 77 118 65
2011 19.41 19.55 20.69 19.94 137 63 105 72
2014 17.50 16.84 21.81 19.10 182 376 84 96
2015 18.77 19.70 21.04 21.02 155 183 75 130
2016 20.73 20.77 21.54 20.43 69 70 69 133
2017 20.16 21.30 21.81 21.18 177 50 84 83
Average 18.79 19.23 20.77 20.35 128 101 89 84

  1. The entries are annual averages. TFP is the log of actual TFP. TFP gains = 100 × (efficient output/actual output − 1).

Table A.2:

Robustness results: TFP gains (%) by removing distortions.

Year Employees ≥ 10 Employees ≤ 1500 Sigma = 4 Wage/output = 0.35
Unincor. Incor. Unincor. Incor. Unincor. Incor. Unincor. Incor.
(1) (2) (3) (4)
2005 80 45 113 46 106 50 90 48
2006 81 88 144 84 115 89 92 64
2007 106 110 114 101 134 130 89 105
2008 92 105 90 96 109 132 75 108
2009 126 92 147 89 181 117 121 93
2010 119 104 132 115 171 144 123 116
2011 117 102 123 93 177 128 114 100
2014 214 84 223 78 257 102 184 87
2015 150 89 198 83 226 109 158 75
2016 91 76 97 71 123 96 101 82
2017 155 90 137 84 201 110 151 91
Average 121 90 138 85 163 110 118 88

  1. TFP gains = 100 × (efficient output/actual output − 1).

Panel (A)–(C) in Figure A.1 depicts the TFP gains for unincorporated and incorporated firms in Columns 1–4 in Table 3, respectively.

Figure A.1: Period average TFP gains (%) for 2005–2017 – sensitivity results. The entries are for period average TFP gains for 2005–2017. Period average TFP gains for unincorporated and incorporated firms, respectively, are: panel (A) 121 % and 90 %; panel (B) 138 % and 85 %; panel (C) 163 % and 110 %; and panel (D) 118 % and 88 %. TFP gains = 100 × (efficient output/actual output − 1).
Figure A.1:

Period average TFP gains (%) for 2005–2017 – sensitivity results. The entries are for period average TFP gains for 2005–2017. Period average TFP gains for unincorporated and incorporated firms, respectively, are: panel (A) 121 % and 90 %; panel (B) 138 % and 85 %; panel (C) 163 % and 110 %; and panel (D) 118 % and 88 %. TFP gains = 100 × (efficient output/actual output − 1).

Consistent with the baseline results in Figure 1, Figure A.1 shows that, under all alternative parameterisations, the potential TFP gains are higher within unincorporated firms than within incorporated firms.

Table A.3:

Summary statistics (2005–2017)a.

Variable (unit) Mean Std. Dev. Min. P1b P50b P99b Max.
Un-incorporated
Sole
Labour (number of persons) 35 63 5 5 13 331 609
Capital (LKR thousands) 18,700 40,400 25 54 4,710 226,000 317,000
Output (LKR thousands) 43,700 109,000 288 504 6,650 547,000 1,350,000
Value-added (LKR thousands) 19,400 48,400 109 239 3,120 271,000 477,000
Wage bill (LKR thousands) 13,100 32,800 86 151 1,990 164,000 404,000
Age (Years) 16 13 1 1 13 64 163
Partnership
Labour (number of persons) 61 90 5 5 31 511 758
Capital (LKR thousands) 27,400 44,600 68 142 9,740 220,000 337,000
Output (LKR thousands) 84,400 149,000 537 900 22,300 719,000 1,150,000
Value-added (LKR thousands) 32,800 57,600 273 438 9,440 298,000 487,000
Wage bill (LKR thousands) 25,300 44,800 161 270 6,700 216,000 346,000
Age (Years) 23 19 1 1 17 96 144
Incorporated
Private + public
Labour (persons) 260 352 8 11 117 1,656 2,419
Capital (LKR thousands) 179,000 324,000 200 530 63,500 1,820,000 2,880,000
Output (LKR thousands) 510,000 836,000 2000 3,980 196,000 3,900,000 10,400,000
Value-added (LKR thousands) 203,000 326,000 1050 2,120 78,000 1,710,000 2,710,000
Wage bill (LKR thousands) 153,000 251,000 600 1,200 58,800 1,170,000 3,120,000
Age (years) 24 24 1 1 16 120 189

  1. aSummary statistics are for the cleaned dataset. The sample size for sole is 4278, representing 52,584 firms. The sample size for partnership is 1117, representing 10,400 firms. Finally, the sample size for incorporated is 5323, representing 24,979 firms. bP1, P50 and P99 are the 1st, 50th (median) and 99th percentiles, respectively.

Table A.4:

TFP gain from removing misallocation between and within ownerships.

Year TFP gain (%)
Total Within ownerships Between ownerships
(1) (2) (3)
2005 89 45 30
2006 98 79 11
2007 114 108 3
2008 112 109 1
2009 112 105 4
2010 122 118 2
2011 126 114 6
2014 131 88 23
2015 135 103 16
2016 84 81 2
2017 99 98 0
Average 111 95 9

  1. aColumn (1) is calculated based on Eq. (21), where TFP Gain (Total) = 100 × (efficient output of all firms/actual output of all firms − 1) using all firms of both types of ownerships (unincorporated and incorporated). bColumn (2) is calculated based on Eq. (22), where TFP Gain (Within Ownerships) = 100 × (efficient output of unincorporated + efficient output of incorporated)/(actual output of unincorporated + actual output of incorporated) − 1). cColumn (3) is calculated based on Eq. (23), where TFP Gain (Between Ownerships) = 100 × [(Total TFP Gain/100 + 1)/(Within TFP Gain/100 + 1)].

Table A.5:

TFP, efficiency and TFP gains (%) (large 4-digit industries only).

Year TFP Efficiency (Y/Ye) TFP gains (%)
Unincorporated Incorporated Unincorporated Incorporated Unincorporated Incorporated
2005 17.09 19.08 0.521 0.629 92 59
2006 18.45 19.33 0.501 0.551 100 82
2007 19.96 20.42 0.492 0.480 103 108
2008 19.60 21.25 0.536 0.481 87 108
2009 19.55 20.83 0.412 0.507 143 97
2010 19.90 21.08 0.430 0.463 133 116
2011 19.79 20.97 0.415 0.506 141 97
2014 17.64 22.28 0.315 0.520 217 92
2015 19.63 21.75 0.328 0.523 204 91
2016 21.14 21.82 0.524 0.563 91 78
2017 20.38 22.51 0.372 0.522 169 92
Average 19.38 21.03 0.441 0.522 134 93

  1. Robustness check on Table 2 by dropping 4-digit industry-year cells that contain no more than five firms. Unincorporated = sole + partnership; incorporated = private + public. TFP is the log of actual TFP. Efficiency = actual output/efficient output. TFP gains = 100 × (efficient output/actual output − 1).

Table A.6:

TFP, efficiency and TFP gains (%) (Large 2-digit industries only).

Year TFP Efficiency (Y/Ye) TFP gains (%)
Unincorporated Incorporated Unincorporated Incorporated Unincorporated Incorporated
2005 17.59 19.59 0.407 0.637 146 57
2006 18.63 19.96 0.419 0.525 139 90
2007 20.18 20.90 0.414 0.422 141 137
2008 20.08 21.86 0.487 0.421 105 138
2009 19.86 21.54 0.383 0.411 161 144
2010 20.12 21.75 0.412 0.398 143 151
2011 20.76 21.74 0.415 0.442 141 126
2014 18.00 23.01 0.276 0.471 262 112
2015 20.65 21.45 0.353 0.514 184 95
2016 22.12 22.56 0.461 0.488 117 105
2017 22.39 23.27 0.362 0.478 177 109
Average 20.04 21.60 0.399 0.473 156 115
Average (Table A.5) 19.38 21.03 0.441 0.522 134 93
Average (Table 2) 19.34 20.99 0.443 0.533 132 90

  1. Robustness check on Table 2 with misallocation at the 2-digit industry level, by dropping 2-digit industry-year cells that contain no more than five firms. Unincorporated = sole + partnership; Incorporated = private + public. TFP is the log of actual TFP. Efficiency = actual output/efficient output. TFP gains = 100 × (efficient output/actual output − 1). The comparison of the average TFP in the last two rows with Table A.5 and Table 2 consistently suggest the TFP gain is bigger for the unincorporated firms, although the baseline results in Table 2 with misallocation at 4-digit industry level and with all industries include show a bit smaller TFP gain both for the incorporated and the unincorporated firms than those in Tables A.5 and A.6.

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Received: 2022-06-25
Accepted: 2023-06-27
Published Online: 2023-08-04

© 2023 Walter de Gruyter GmbH, Berlin/Boston

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Keywords for this article
firm-level distortion; misallocation; Sri Lanka; total factor productivity; unincorporated firm

Articles in the same Issue

  1. Frontmatter
  2. Advances
  3. The Macroeconomic Impact of the 1918–19 Influenza Pandemic in Sweden
  4. Aggregate Costs of a Gender Gap in the Access to Business Resources
  5. The Macroeconomic Effects of Shadow Banking Panics
  6. Wealth Inequality and the Exploration of Novel Technologies
  7. Contributions
  8. Learning, Central Bank Conservatism, and Stock Price Dynamics
  9. Progressive Taxation and Robust Monetary Policy
  10. The New Keynesian Phillips Curve and Imperfect Exchange Rate Pass-Through
  11. The Macroeconomic Impact of Social Unrest
  12. Interest Rates, Money, and Fed Monetary Policy in a Markov-Switching Bayesian VAR
  13. Un-Incorporation and Conditional Misallocation: Firm-Level Evidence from Sri Lanka
  14. Idiosyncratic Shocks, Lumpy Investment and the Monetary Transmission Mechanism
  15. Open Economy Neoclassical Growth Models and the Role of Life Expectancy
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