Journal of Productivity Analysis https://doi.org/10.1007/s11123-018-0530-1

Misallocation, productivity and fragmentation of production: the case of Latvia Konstantins Benkovskis1,2

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Abstract This paper evaluates misallocation of resources in Latvia during 2007–2014 using firm-level data. I find that misallocation of resources increased before 2010 and declined afterwards. Initially, output distortion was the major source of misallocation, while the importance of capital distortions increased after the financial crisis. Determinants of changes in allocation efficiency may include growing competition in domestic markets, tighter credit supply and legal issues. However, I show that fragmentation of production induces bias to the estimates of firm-specific distortions, leading to the overestimation of gains from reallocation. Thus, in the absence of inter-firm trade data, the conclusions on misallocation should be treated with caution. Keywords Misallocation Fragmentation Productivity Firm-level data Latvia ●

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JEL-codes D24 L11 O11 O41 O47 ●

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1 Introduction Latvia performed outstandingly in terms of productivity growth between 1995 and 2007: the average annual total factor productivity (TFP) growth amounted to 6.8% according to the AMECO database. The financial crisis and structural transformations led to a temporary drop in productivity, with TFP declining by 2.8% every year between 2007 and 2010. Afterwards, the TFP growth returned back on the positive track (close to 2–3%), yet far behind the precrisis numbers. The rapid growth of productivity in the 1990s and early 2000s was driven by unique factors: initial convergence due to transformation of the economy and credit boom led by foreign banks. As these factors are not likely to repeat in the foreseeable future, other ways to stimulate growth in Latvia are to be looked for.

* Konstantins Benkovskis [email protected] 1

Monetary Policy Department, Latvijas Banka, Kr. Valdemara iela 2A, Riga LV-1050, Latvia

2

Stockholm School of Economics in Riga, Strelnieku iela 4A, Riga LV-1010, Latvia

In this paper, I investigate the misallocation of resources in Latvia. The motivation for this study is twofold. First, I study how the changes in within-sector misallocation of resources affected Latvia’s TFP and output growth before and after the crisis. Second, I make an attempt to understand the driving forces behind the misallocation. The issue of resource allocation has a long-standing history in empirical economics, starting with the seminal work by Olley and Pakes (1996) who show how to evaluate the empirical effect of reallocation of capital towards more productive enterprises. The Olley–Pakes decomposition became increasingly popular and was applied to the analysis of resource allocation in various countries. For example, Bartelsman et al. (2009) perform decomposition for a wide range of countries and report that in the 1990s Latvia’s resources were allocated less efficiently compared with the old EU Member States. These results suggest that Latvia could increase its productivity and gross domestic product by reallocating resources from less productive to more productive firms. In this paper, I analyse the allocation of resources and potential TFP gains using the Hsieh and Klenow (2009) framework, namely, its modified version with intermediate inputs introduced by Dias et al. (2016b). This model is applied to Latvia’s firm-level data between 2007 and 2014 to assess how effective was the allocation of resources and what were the driving forces behind misallocation.

Journal of Productivity Analysis

The popularity of Hsieh and Klenow (2009) approach triggered a lot of attention to the underlying assumptions of the methodology, and raised discussions about potential biases. Foster et al. (2016) flag that caution is needed because of the assumption about constant returns to scale. Peters (2013) and Asker et al. (2014) emphasise the static nature of the methodology that does not account for entry decisions and capital adjustment costs. In this paper, apart from the evaluation of misallocations in Latvia, I contribute to the literature on misallocation by pointing to another potential bias due to production networks and fragmentation of production. The importance of production networks to misallocation is already highlighted by Jones (2011). However, I focus on the bias to the estimates of misallocation rather than amplification of misallocation across sectors. I argue that the firm-level data traditionally used in the analysis of misallocation lacks important component—the inter-firm trade—that becomes increasingly important due to outsourcing. A firm participating in value chains and outsourcing some stages of production either domestically or internationally tend to report higher share of intermediate input costs and lower shares of capital and labour costs. Researcher may treat this as a signal of misallocation if the information on inter-firm linkages is unknown. Although the inter-firm trade data are missing for Latvia, I prove the existence of the bias theoretically and support its existence by the industry-level indicators. The paper is structured as follows. Section 2 explains the main idea behind the misallocation modelling framework. Section 3 describes Latvia’s firm-level database; section 4 presents the level of misallocation for total economy and main macroeconomic sectors and checks the robustness of results. Section 5 discusses the effect of fragmentation and outsourcing for the evaluation of misallocation, while the final section concludes.

2 Theoretical framework 2.1 Firm-specific distortions and misallocation of resources Here I briefly describe the framework of Hsieh and Klenow (2009) modified by Dias et al. (2016b) that highlights the contribution of misallocation to aggregate productivity and output. This is a monopolistic competition model with firm heterogeneity a la Melitz (2003) where firms face distortions—drivers of misallocation. An assembly firm combines the output of different industries into a homogenous final good using a Cobb–Douglas production technology: Y¼

S Q s¼1

Ysθs ;

S P s¼1

θs ¼ 1;

s Ys ; θs ¼ PPY

where Y represents a homogenous final good, Ys denotes the output of industry s, Ps and P refer to the price of industry output and final good, respectively. There exist S industries, while the output of each industry is a constant elasticity of substitution aggregate of Ns differentiated products Ysi. Unlike Hsieh and Klenow (2009) or other empirical papers using this framework, I allow for industry-specific elasticity of substitution between products (σs), thus accounting for heterogeneous level of competition: s X σ σ1 σ s 1 s Ns σs Ys ¼ Y : i¼1 si

ð2Þ

Minimising the aggregate costs given the industry output Ys leads to the standard demand equation:  Psi ¼Ps

Ys Ysi

σ1

s

ð3Þ

;

where Psi denotes the output price of a firm i in industry s. I follow the approach of Dias et al. (2016b) and introduce intermediate inputs into the production function for a differentiated product: β

1αs βs

Ysi ¼Asi Ksiαs Lsis Msi

;

ð4Þ

where Asi represents firm-specific total factor productivity, Ksi stands for firm’s capital, Lsi—the number of employees and Msi—intermediate inputs. The coefficients of Cobb–Douglas production function can vary across industries, but not across firms within the same industry. Additional production factor, although making the theoretical framework more complex, provides useful insights about the misallocation of resources. As noticed by Dias et al. (2016b), three-factor model accounts for inefficient allocation of intermediate inputs, and allows evaluating labour and capital distortions separately. But this is not the only argument. The role of intermediate inputs is especially important in small and open countries like Latvia: according to the World Input-Output Database (WIOD),1 the share of intermediate inputs in Latvia’s gross output equals to 55.4% in 2014. Only few economies among those covered in WIOD have higher share of intermediate inputs: either very small countries (Malta, Luxembourg), or the countries integrated to the downstream of the global value chains (China, Czech Republic). Jones (2011, p. 477) particularly stresses the necessity of “redoing the Hsieh and Klenow (2009) analysis using gross output and intermediate goods within sectors”, suggesting that the impact of misallocation can be amplified,

ð1Þ 1

The 2016 release of the World Input-Output database available at http://www.wiod.org/database/wiots16.

Journal of Productivity Analysis

as the outputs of one firms serves as an intermediate inputs of other firms. Furthermore, the growing role of outsourcing and production fragmentation can be captured only by accounting for the role of intermediate inputs. Last but not least, three-factor modification helps solving the problem of enterprises with negative value added. The share of firms reporting negative value added raised to almost 20% after 2009 in Latvia: the exclusion of such firms may seriously affect conclusions about the misallocation of resources in two-factor framework. Adding intermediate inputs to the production function and defining Ysi as (always nonnegative) real output allows including all firms into the analysis. The framework includes three distortions: a capital distortion (τKsi), a labour distortion (τLsi) and an output distortion (τYsi). This leads to the following profit maximisation problem: πsi ¼ ð1  τYsi ÞPsi Ysi  ð1þτKsi ÞRs Ksi  ð1 þ τLsi Þws Lsi 

Lsi ;Ksi ;Msi PM s Msi !

Ysi / Lsi /

Aσsis ð1  τYsi Þσs

ð1þτKsi Þαs σ s ð1þτLsi Þβs σs

max; ð5Þ

where πsi represents firm’s profits, Rs, ws and denote industry-specific capital costs, wage and price of intermediate inputs, respectively. Equation (5) serves as a key element of the framework, accounting for the fact that firms may face different conditions on the labour, capital or product markets. For instance, τKsi is high when a firm has limited access to credit that will drive up the marginal product of capital. On the other hand, one can expect low capital distortions for foreign-owned firms, or firms receiving EU funds. Regarding labour distortions, being the subject to trade union activities may raise the marginal product of labour, reflected by higher τLsi. Another example is related with the shadow economy—some firms pay envelope wages, which corresponds to lower labour costs and negative labour distortions. As noticed by Dias et al. (2016b), capital and labour distortions also include any costs of the respective production factor beyond the market price (thus containing also frictions). The output distortion, τYsi, has equal effects on marginal products of capital, labour and intermediate inputs. This may happen due to legal restrictions on size, transportation costs, output taxes or subsidies. After solving the profit maximisation problem one could obtain the Eq. (6) that determines firm’s price as a markup over marginal costs:  α s  β s  1αs βs σs Rs ws PM ð1 þ τKsi Þαs ð1þτLsi Þβs s : σ s  1 αs βs 1  αs  β s Asi ð1  τYsi Þ

ð6Þ From the first order conditions it follows that output and allocation of resources are driven by distortions (see Eqs. (7)–(9)). In the ideal case of no distortions, the more

;

Aσsis ð1  τYsi Þσs

ð7Þ

ð1þτKsi Þαs ðσs 1Þ ð1þτLsi Þβs ðσ s 1Þþ1

Ksi /

PsM

Psi ¼

productive firms attract more resources and produce more output. However, any positive distortion reduces firm’s inputs and output. In other words, distortions create the misallocation of resources by shifting inputs away from their optimal levels. Distortions also drive the differences in the marginal revenue products. For example, positive capital distortion will slash the use of capital and labour; but the effect on capital will be larger, thus it is going to reduce the capital-to-labour ratio and increase the marginal revenue product of capital.

;

Aσsis ð1  τYsi Þσ s

ð1 þ τKsi Þαs ðσs 1Þþ1 ð1 þ τLsi Þβs ðσ s 1Þ

ð8Þ :

ð9Þ

Foster et al. (2008) emphasise the distinction between firm’s total factor quantity productivity (TFPQ) that equals to Asi, and total factor revenue productivity (TFPR) defined as

¼

si TFPRsi  Psi Asi ¼ αs βPs si Y1α β ¼ Ksi Lsi Msi s s  αs  βs  M 1αs βs αs

Rs αs

ws βs

Ps 1αs βs

ð1þτKsi Þ ð1þτLsi Þβs 1τYsi

:

ð10Þ

In the absence of distortions, the revenue productivity equals for all firms—higher productivity leads to higher output, but also lower prices. The presence of distortions creates the variation in firms’ TFPR. The higher revenue productivity serves as a sign of discrimination faced by the firm, since it reduces the use of production factors and pushes up the marginal products. The concept of TFPR allows deriving the efficient real output (Ysi*)—the real output when no firm is discriminated and distortions equal for all firms in the industry s. To put it differently, efficient real output corresponds to the ideal case with no misallocation of resources—TFPQ is the only driver of real inputs and outputs. The efficient real output of a firm i equals to   TFPRsi σ s Ysi ¼Ysi ; ð11Þ TFPRs where TFPRs* denotes the efficient level of TFPR in industry s given the absence of discrimination.2 Intuitively, Eq. (11) states that firms facing high distortions (and having high TFPR) underperform and their efficient real output would exceed the actual one in the absence of discrimination. 2

See equations (12)–(15) in Dias et al. (2016b) for technical details.

Journal of Productivity Analysis

Regarding the efficient level of TFPR, I follow Dias et al. (2016b) and define it as the industry level TFPR prevailing when all firms face the same average distortions.3 Replacing actual distortions in Eq. (10) by the industry average distortions leads to TFPRs 

α  β  α s  β s  1αs βs  1 þ τKs s 1 þ τLs s Rs ws PM s ; αs βs 1  αs  β s 1  τYs

ð12Þ where τ*Ks, τ*Ls and τ*Ys denote industry average distortions that do not alter the aggregate demand for production factors at the industry level. Such distortions are given by the following equations (see Dias et al. 2015; Appendix B2 for technical derivations): 1þ

τKs ¼

1þ

τLs

αs PM s Ms ; 1  αs  βs Rs Ks

ð13Þ

βs PM s Ms ¼ ; 1  αs  βs ws Ls

1  τYs ¼

ð14Þ

σs PM s Ms ; σ s  1 ð1  αs  βs ÞðPs Ys Þ

ð15Þ

where (PsYs)* stands for the industry efficient nominal output, Ks, Ls and Ms represent the aggregate actual levels of capital, labour and intermediate inputs, respectively. From Eqs. (10)–(12) it follows that !σ s       Ysi TFPRsi σs 1 þ τKsi αs 1 þ τLsi βs 1  τYs ¼ ¼ Ysi TFPRs 1 þ τKs 1 þ τLs 1  τYsi ð16Þ Namely, higher-than-average distortions reduce firm’s actual real output with respect to the efficient one. To see, how big is the contribution of misallocation to the aggregate industry output, one can calculate the gains from reallocation—compare the efficient aggregate output in the absence of discrimination (Ys*) with the actual real output. Using Eqs. (2), (4) and the definitions of TFPR and TFPQ, the ratio equals to P Ys Ys

Ns

ðYsi Þ i¼1

¼  P Ns

i¼1

σ s 1

Ysi σ s

¼

3

σ s 1 σs

s σ σ1 s

s σ σ1 s

1σ σ1 s s PNs σs 1 A C B ¼ @P  i¼1 si  σs 1 A Ns TFPRs 0

i¼1

 PNs

i¼1

ωsi



Asi TFPR

si

σs 1σ  s  σ s 1

TFPRs TFPRsi

ð17Þ

;

Although the definition of the efficient TFPR differs in Dias et al. (2016b) and Hsieh and Klenow (2009), both approaches lead to the same contribution of resource misallocation as proved by Dias et al. (2015) in Appendix B6.

where Aσs 1 ωsi ¼ PNs si σ s 1 : i¼1 Asi Equation (17) defines the contribution of misallocation as a weighted average of misallocations at the firm level, where the individual TFPQ serves as a weight. When variation of firms’ TFPR is high, the misallocation of resources drives the actual output far below the efficient one and gains from reallocation (defined as Y*s/Ys – 1) become substantial. Now it is straightforward to obtain the aggregated contribution of misallocation using Cobb–Douglas aggregator in Eq. (1): S XNs  TFPR σs 1 Y Y s ¼ ωsi i¼1 Y s¼1 TFPRsi

σ s θs !1σ

s

;

ð18Þ

where Y* denotes the efficient total aggregate output. I use the Eq. (18) to measure the total gains from reallocation in Latvia (more precisely, gains equal to Y*/Y – 1). Moreover, I will analyse gains by industry and year, as well as decompose those into the contributions attributed to output, capital and labour distortions.4 Like Dias et al. (2016b), I use the following formula to evaluate the contribution of reallocation to the aggregate value added: 

V  YY  q ¼ ; V 1q

ð19Þ

where V and V* represent the actual and efficient aggregate real value added, respectively, while q stands for the economy-wide share of intermediate inputs in gross output.

2.2 Identification of firm-specific distortions and productivity The framework above includes some unobservable firmlevel characteristics like TFPQ and distortions.5 Following the maximisation problem from Eqs. (1)–(3) and (5), the unobservable distortions can be expressed as a function of observable data on firm-level output, capital, labour and intermediate inputs. Although Eqs. (20)–(22) have the same intuition as in Hsieh and Klenow (2009), the form of 4

Contributions for individual distortions are estimated by eliminating variation in respective distortion and fixing the other inputs. See Dias et al. (2015) Appendix B5 for technical details and derivations. 5 Dias et al. (2016b) argue that the knowledge of firm-specific distortions is not necessary to evaluate the contribution of misallocation, since one can estimate TFPRsi from Eq. (10) and TFPRs* from Eqs. (12)–(15). However, in my view, the discussion about the evaluation of firm-specific distortions provides additional intuition to the reader.

Journal of Productivity Analysis

equations differs due to the additional production factor. Capital distortion faced by individual firm is proxied as 1 þ τKsi ¼

αs PM s Msi : 1  αs  βs Rs Ksi

ð20Þ

Low ratio of real capital to intermediate input costs serves as a sign of capital restrictions faced by a firm. Note that the assumption on industry average capital costs affects the absolute capital distortion τKsi, but not the relative distortion with respect to industry average (1 + τKsi)/(1 + τ*Ks). Thus, Rs does not alter the contribution of misallocation in Eqs. (16)–(18). Similar logic applies to (21), where the small ratio of employees to intermediate inputs implies high labour distortions: 1þτLsi ¼

βs PM s Msi : 1  αs  βs ws Lsi

ð21Þ

Like Hsieh and Klenow (2009), I use the firm’s wage bill rather than employment as a proxy to Lsi, which allows capturing the difference in human capital per worker and hours worked. The latter is of special importance for Latvia, since the share of part-time employment notably increased during the crisis period.6 As to the wage rate, I follow Dias et al. (2016a; 2016b) and normalise it to unity (ws = 1), since ws does not affect the relative labour distortion. The output distortion is detected as a case of abnormally low share of intermediate inputs in total output: 1  τYsi ¼

σs PM s Msi : σ s  1 ð1  αs  βs ÞPsi Ysi

ð22Þ

As stressed by Hsieh and Klenow (2009), Eq. (22) requires the assumption that observed nominal output does not contain any explicit output subsidies or taxes.7 The formula for the firm-specific TFPQ comes from Eqs. (3)–(4): σs

ðPsi Ysi Þσs 1

1

ðPs Ys Þ1σs Asi ¼ κs α β ð1α β Þ ; κs ¼ ; s s s s Ps K L M si

si

ð23Þ

si

where κs is an industry-specific constant. The advantage of Eq. (23) over the traditional Solow residual approach is due to the use of nominal output (PsiYsi) instead of typically unobservable real output (Ysi). Although κs remains unobservable, the contribution of misallocation is unaffected by 6 Braukša and Fadejeva (2016) analyse micro data from the Labour Force Survey (LFS) and conclude that part-time employment and temporary contracts were actively used in Latvia during 2009–2010. 7 Note that the same assumption is crucial while evaluating firmspecific TFPR in Eq. (10), or TFPQ in Eq. (23).

its absolute value (see the definition of ωsi in Eq. (17)) and the constant can be set to unity (κs = 1).

3 Data 3.1 Latvia’s firm-level database I use a firm-level database that contains information on a representative sample of Latvia’s enterprises in 2006–2014, with the number of firms in the data set varying between 61,159 in 2006 and 99,446 in 2014. The anonymised data set includes commercial enterprises in all areas of activities, excluding credit institutions and insurance companies.8 The data are provided by the Central Statistical Bureau of Latvia (CSB) and Latvijas Banka, and come from various sources. First, the anonymised data set contains detailed information on firms’ balance sheets, profit/loss statements, value added, number of employees, personnel costs, production value and intermediate inputs. Second, the anonymised data set includes information on firm-level external trade in goods provided by the CSB. Third, the data set on external trade in services is provided by Latvijas Banka. Finally, Latvijas Banka also collects information on external assets and liabilities of firms. The data set contains all necessary information for the empirical evaluation of the model described above. However, some important variables are missing for many firms due to non-reporting. All firms with missing/zero values for output, fixed capital, employment, intermediate inputs and wage bill are excluded from the data set for a particular year. Also, following the usual approach of resource allocation papers, I exclude outlying firms with too high or too low TFPQ, distortions of capital, labour and output.9 Finally, I exclude several 4-digit sectors of activities due to the small number of observations: the threshold was set to 100 observations during 2007–2014, after the exclusion of outliers. Table 1 compares the size distribution of firms in Latvia’s firm-level database after the exclusion of firms with missing data, sectors with small number of observations and outliers with the distribution from the Structural Business Indicators Statistics in 2014. 8

I exclude several sectors from the empirical analysis due to the lack of data or specific nature of the sector, namely: agriculture, forestry and fishing (A), financial and insurance activities (K), public administration and defence (O), education (P), health (Q), arts, entertainment and recreation (R), and other services activities (S). 9 Usually researchers trim observations below/above the 1st and 99th percentile (see e.g. Hsieh and Klenow, 2009; Dias et al. 2016b; GarciaSantana et al. 2016). I use a more conservative approach, trimming observations below Q1 − 1.5 IQR and above Q3 + 1.5 IQR, where Q1 and Q3 denote the 1st and 3rd quartiles, and IQR stands for the interquartile range. I check the role of alternative outlier detection procedures in the robustness section.

Journal of Productivity Analysis Table 1 Distribution of firms by size according to structural business indicators and firm-level database in 2014 No. of employed

Number of firms

Turnover

No.

% of total

Mio. of EUR

% of total

Mio. of EUR

% of total

Th. of pers.

% of total

31.8

Value added

Employed

(a) Structural business indicators 0–9

89,993

90.6

13,264.5

26.0

2049.2

20.3

196.1

10–19

4727

4.8

4846.4

9.5

832.2

8.3

63.1

10.2

20–49

2974

3.0

8324.3

16.3

1430.5

14.2

89.0

14.4

50–249

1486

1.5

13,185.3

25.8

2798.2

27.8

140.6

22.8

250+

202

0.2

11,450.8

22.4

2966.1

29.4

128.7

20.8

Total

99,382

100.0

51,071.2

100.0

10,076.2

100.0

617.5

100.0

(b) Sample of firm-level database (firms that satisfy minimum data requirement, excluding outliers) 0–9

23,940

81.5

9455.3

20.0

1349.9

14.9

79.7

22.5

10–19

2333

7.9

4644.2

9.8

749.6

8.3

31.6

8.9

20–49

1810

6.2

7778.0

16.5

1393.4

15.4

55.0

15.5

50–249

1141

3.9

16,039.6

33.9

3127.3

34.5

110.2

31.0

250+

150

0.5

9332.1

19.8

2434.5

26.9

78.5

22.1

Total

29,374

100.0

47,249.2

100.0

9054.8

100.0

355.0

100.0

Source: Central Statistical Bureau of Latvia, Latvia’s firm-level database, author’s calculations Includes data on commercial enterprises in NACE sections mining and quarrying (B), manufacturing (C), electricity and gas (D), water supply (E), construction (F), wholesale and retail trade (G), transportation and storage (H), accommodation and food service activities (I), information and communications (J), real estate activities (L), professional, scientific and technical activities (M), administrative and support service activities (N)

Overall, despite the substantial problem of missing observations, the sample remains representative with the coverage close to 30%. As expected, the problem of missing observations persists for small firms and is less relevant for large enterprises. Losses of information are not so large in terms of turnover or employment: the final sample covers 93% and 57% of initial full sample, respectively. Major variables used in the empirical analysis are firm’s industry (4-digit NACE), output,10 capital (average of the stock at the beginning and end of the year), number of employees (approximated by wage bill to account for differences in human capital and hours worked), and intermediate inputs. Industry wage rate is set to unity. I deflate intermediate inputs by industry-specific deflator for intermediate inputs reported by the CSB. Capital is deflated by an industry-specific investment deflator, which is constructed taking into account the composition of capital in each corresponding industry.11 Finally, nominal capital

costs are derived as the real interest rate plus depreciation rate, multiplied by the price of capital.12

3.2 Evaluation of industry-specific parameters Methodology described in Section 2 requires information on three industry-specific parameters: elasticity of substitution (σs) and two elasticities of output in the production function (αs and βs). Equations (13)–(15) can be rearranged to define the industry-specific parameters of interest:   ðPs Ys Þ 1  τYs σs ð24Þ ¼ ; σ s  1 Rs Ks ð1 þ τKs Þ þ ws Ls ð1 þ τLs Þ þ PM s Ms   Rs Ks 1 þ τKs σs ; αs ¼ σ s  1 ðPs Ys Þ ð1  τYs Þ

ð25Þ

  ws Ls 1 þ τLs σs : βs ¼ σ s  1 ðPs Ys Þ ð1  τYs Þ

ð26Þ

10

Defined as turnover net of change in stocks and purchases of goods and services for resale plus capitalised production and other operating income from the economic activity. 11 Fixed capital and investment deflators are split into four categories: intellectual capital, dwelling and other buildings, machinery and equipment, and other capital. Investment deflators are provided by the CSB (deflator for total investment used for other capital). Since deflators for dwelling and other buildings as well as total investment were highly volatile during 2007–2010, I filter them by the ChristianoFitzgerald filter (leaving oscillations above 2 years). This allows excluding the short-term (speculative) component of real estate prices.

Unfortunately, as noted by Dias et al. (2016b), it is not possible to identify the average industry distortions and industry-specific parameters simultaneously. 12

Industry-specific depreciation rate is set according to industry capital structure, assuming an 8% depreciation rate for intellectual capital, 5% for dwelling and other buildings, 13% for machinery and equipment, and 10% for other capital. Real interest rate is defined as the long-term credit rate minus change in the price of investment.

Journal of Productivity Analysis

Fig. 1 Elasticity of substitution between products by 4-digit NACE categories. Source: Latvia’s firm-level database, author’s calculations. Notes: Elasticities of substitution are evaluated using Eq. (24) for the period 2007–2014, assuming zero average industry distortions. 4-digit NACE categories are grouped into broad sections: mining and quarrying (B), manufacturing (C), electricity and gas (D), water supply (E),

construction (F), wholesale and retail trade (G), transportation and storage (H), accommodation and food service activities (I), information and communications (J), real estate activities (L), professional, scientific and technical activities (M), administrative and support service activities (N)

Empirical studies on misallocation usually assume equal elasticity of substitution between products for all industries (σ = 3).13 However, such assumption has serious drawbacks. First, it is not relevant to use the value of σ = 3 for the model with three production factors. Elasticity of substitution of 3 corresponds to a 50% mark-up, which realistically reflects profits over value added, but overestimates profits over turnover. Second, Broda and Weinstein (2006) demonstrate that elasticity of substitution between varieties of a product can vary over a very wide range; therefore, the assumption of equal elasticity is too restrictive. Regarding the parameters of Cobb–Douglas production function, Hsieh and Klenow (2009) determines those from the average factor share in the corresponding industry, implicitly assuming that industry average distortions are negligible in the US. However, not all countries enjoy environment with little average distortions: that is why Hsieh and Klenow (2009) use US factor shares for India and China; Bellone and Mallen-Pisano (2013), Calligaris (2015), Dias et al. (2016b), Garcia-Santana et al. (2016), and Inklaar et al. (2017) follow similar approach for France, Italy, Portugal, Spain and large sample of low- and middleincome countries, respectively. Using US factor shares may impose serious bias, however. Latvia’s industries use less advanced technologies,

have different structure and may participate in different stages of production. Jones (2011) acknowledges that assumption about validity of the US factor shares for other countries is certainly questionable. All in all, I argue that assuming no role for industry average distortions provides a better proxy for Latvia’s elasticities of output than the US benchmark. The high position of Latvia in various economic freedom indices supports my argument to some extent. For example, Latvia had high 24th rank in Doing Business 2014 report14 (US had 4th rank), being way ahead of China (96th) and India (134th), but also having higher position comparing with many EU countries like Portugal (31st), France (38th), Spain (52nd) and Italy (65th). Thus, I calibrate industry-specific parameters using Eqs. (24)–(26) and assuming (similar to Hsieh and Klenow 2009; as well as Libert 2016) that average industry distortions are negligible (τ* = 0).15,16 I will check the robustness of the results for alternative values of σs, αs and βs in the robustness section, though. According to Eq. (24), the elasticity of substitution is related to the mark-up level, which could be derived by comparing nominal output to nominal costs at the industry level. Figure 1 reports the evaluated elasticities of substitution by 4-digit NACE sectors.

13 See e.g., Hsieh and Klenow (2009), Bellone and Mallen-Pisano (2013), Calligaris (2015), Dias et al. (2016b), Garcia-Santana et al. (2016), Inklaar et al. (2017), or Libert (2016).

14 The report is available at http://www.doingbusiness.org/reports/ global-reports/doing-business-2014. 15 Note that in this case (PsYs)* = PsYs. 16 Alternatively, Gamberoni et al. (2016) estimates the production function following Wooldridge (2009) methodology. However, by doing so they also implicitly ignore average industry distortions.

Journal of Productivity Analysis

The elasticity of substitution for a typical Latvia’s industry is close to 6.5, which roughly corresponds to the 18% markup. The values vary significantly across industries, though, pointing to different market structures. The largest elasticities are observed in several sub-sectors of retail trade, as well as in the manufacture of furniture and products of wood, denoting a high degree of homogeneity for these services and products. In general, manufacturing industries tend to have higher elasticity of substitution and lower markups, although there are some notable exceptions, like manufacture of instruments and appliances for measuring, testing and navigation. The largest market power and the lowest σs is observed in wholesale of household goods, wholesale of information and communication equipment as well as telecommunications. I perform the evaluation of industry-specific production function parameters αs and βs in a similar way: the coefficient of respective input depends on industry-specific markup and the ratio of factor costs to output. Figure 2 shows that the majority of production costs are due to intermediate inputs (around 75%),17 which tend to be more important in manufacturing sector. The capital share is higher in manufacturing, although some services industries also require outstanding amount of capital in production. I observe a large share of labour inputs in employment activities, computer programming as well as postal and courier activities.

4 Misallocation of resources in Latvia 4.1 Total gains from reallocation I apply the methodology described in Section 2 to Latvia’s firm-level data, and find that potential gains from reallocation to aggregate gross output equal to 32%, while gains to aggregate value added: 72% in 2014 (see Fig. 3 and Table 2). Such sizeable gains are in line with results obtained for other countries using similar methodology (see Table 3).18 The closest comparison can be made to Dias et al. (2016b), who show that equalising TFPR within industries in Portugal would lead to a 28% gain in total output and a 79% gain in value added in 2011. Other papers use two-factor 17

This number significantly exceeds the share of intermediate inputs in gross output from the World Input-Output Database. On the one hand, this can be driven by the exclusion of sectors with low share of intermediate inputs: public administration and defence (O), education (P), health (Q) arts, entertainment and recreation (R) and other services activities (S). On the other hand, this may be due to positive industry average distortions that lead to underestimation of αs and βs. 18 The overview of results in Table 3 suffers from the fact that researchers use various strategies for parametrisation and outlier detection. Also, different time periods and sectoral focuses reduce the comparability.

model, which may lead to the underestimation of gains due to the absence of intermediate inputs’ misallocation. Nevertheless, comparison is still useful: for example, Calligaris (2015) reports that gains from reallocation to total value added equal to 80% for Italy in 2011, while GarciaSantana et al. (2016) find 49% gains to value added for Spain in 2007. Inklaar et al. (2017) provides some evidence on gains to manufacturing value added in Eastern Europe: 62% for Estonia and 88% for Slovenia in 2009. Gains from reallocation of resources contain two different tendencies during 2007–2014 in Latvia: growing misallocation of resources prior to and during the crisis (2007–2010) and declining misallocation after 2010. Thus, the misallocation of resources was not the major driver of economic dynamics during the crisis; however, it contributed to the economic growth in 2011–2014. One should be cautious about the interpretations of misallocation changes over time, though: Fig. 3 and Table 2 provide point estimates only, and changes may not be statistically significant. Among the empirical papers mentioned above, only few cover the period after the financial crisis; those provide mixed evidence. On the one hand, declining misallocation after the crisis in Latvia diverges from the findings of Dias et al. (2016b) for Portugal. On the other hand, Calligaris (2015) reports notable improvement in allocation between 2009 and 2011 for Italy, while Libert (2016)—the decline in variance of TFPR after 2009 for France. Positive impact of the crisis on allocation is to some extent supported by Gamberoni et al. (2016), who show that variance in marginal revenue product of labour dropped in 2009 in five big euro area countries. Figure 3 and Table 2 also highlight the relative importance of distortions for gains in aggregate output and value added. While the decomposition should be taken with a grain of salt due to a large contribution that cannot be attributed to any particular distortion, this exercise still provides some important insights. The largest contribution to potential gains comes from the output distortion. Moreover, the output distortion is the only one contributing to the decline of misallocation after the crisis. In order to get more insights, I check the relationship between relative output distortions and several firms’ characteristics: productivity, size, and the share of exports in turnover (see Fig. 6 in Appendix B). Figure 6a suggests that higher output distortions are associated with lower productivity of the firm.19 Dias et al. (2016a) assume that relationship between productivity and output distortions are driven by misreporting sales, which shows up as lower productivity and output “subsidy”; however, Latvia’s 19 This to some extent goes in line with Calligaris (2015), who finds the highest TFP gains for low-technology enterprises in Italy.

Journal of Productivity Analysis

Fig. 2 Production function coefficients by 4-digit NACE categories. Source: Latvia’s firm-level database, author’s calculations. Notes: Coefficients of production function are evaluated using Eqs. (25) and (26) for the period 2007–2014, assuming zero average industry distortions. 4-digit NACE categories are grouped into broad sections: mining and quarrying (B), manufacturing (C), electricity and gas (D),

Fig. 3 Gains from reallocation of resources within industries to aggregate gross output. Source: Latvia’s firm-level database, author’s calculations. Notes: Gains to total gross output are determined as 100 × (Y*/Y - 1). Contributions for output, capital and labour distortions are estimated by eliminating variation in respective distortion. The residual is attributed to interactions between various distortions

results contradict such explanation. Possibly, the observed negative correlation is driven by larger market power and higher markups of productive firms.20 20 See Peters (2013) for the model that studies the relationship between firm-specific markups and misallocation.

water supply (E), construction (F), wholesale and retail trade (G), transportation and storage (H), accommodation and food service activities (I), information and communications (J), real estate activities (L), professional, scientific and technical activities (M), administrative and support service activities (N)

According to Fig. 6b small enterprises face higher output distortions. The rationale for that could be found in Latvia’s legislation: the micro-enterprise tax was introduced since January 2011 to facilitate the creation of the new business. This is a single payment amounted to 9% of turnover, which replaces mandatory social security contributions, personal income tax and corporate income tax.21 On the one hand, very small firms with five or less employees reduce labour costs by abolishing personal income tax and social security payments, and do not pay corporate income tax. On the other hand, being eligible to the microenterprise tax implies a 9% tax on turnover, while other enterprises do not pay any taxes directly related with turnover—this increases the output distortion (τYsi) for micro-enterprises and may explain the pattern observed in Fig. 6b. The importance of output distortions in gains from reallocation may also come from another source. The 21

In 2011–2014, the right to pay this tax existed, if the following criteria were complied with: (a) turnover per calendar year did not exceed 99,600 euro, (b) number of employees at any time did not exceed five, and (c) income of a micro-enterprise employee did not exceed 711 euro per month. See the Law of Microenterprise Tax for more details at https://likumi.lv/ta/en/id/215302-micro-enterprise-taxlaw.

Journal of Productivity Analysis Table 2 Gains from reallocation of resources within industries to aggregate gross output and value added

Table 3 Comparison of estimated gains from reallocation for various countries

Year

Source

Total

Contributions of Output distortions

Capital distortions

Labour distortions

2.23

3.36

Country

Year Sector

Gains from reallocation Value added

Gross output

Gains to aggregate gross output 2007 31.73 11.23 2008 31.63 10.99

2.46

2.81

Current research (selected sectors)

Latvia

2014 Total

71.7

31.8

2014 Manufacturing

34.6

10.5

2014 Construction

63.7

16.4

2009 34.00 10.18

2.81

3.14

2010 38.90 10.87

3.17

3.86

2014 Trade

69.8

37.9

105.4

43.4

82.1

66.1

2011 31.79 9.83

3.30

4.21

2014 ICT

2012 32.94 10.86

3.39

4.36

2013 27.84 8.29

3.53

4.16

2014 Professional and admin. services

2014 31.82 10.76

3.68

3.85

Gains to aggregate value added 2007 70.84 25.07

4.99

7.51

2008 70.07 24.35

5.44

6.24

2009 74.80 22.39

6.19

6.90

2010 91.03 25.44

7.42

9.04

2011 74.23 22.94

7.72

9.84

2012 77.60 25.58

7.99

10.26

2013 64.92 19.33

8.23

9.71

2014 71.69 24.25

8.28

8.68

Source: Latvia’s firm-level database, author’s calculations Gains to total gross output are determined as 100 × (Y*/Y – 1), while gains to total value added are determined as 100 × (V*/V – 1). Contributions for output, capital and labour distortions are estimated by eliminating variation in respective distortion

framework of Hsieh and Klenow (2009) assumes a closed economy. In an open economy, however, local producers supply to domestic and foreign markets. Fadejeva and Krasnopjorovs (2015) show that firms’ perception about the competition level in Latvia and abroad differs substantially. Describing the degree of competition in 2013, the majority of manufacturing firms answer “moderate” about Latvia’s market and “severe”—about the foreign market. According to Eq. (22), tighter competition level (and higher elasticity of substitution) abroad corresponds to a higher output distortion for exporting enterprises due to more hurdles while expanding in a competitive environment.22 This drives up the dispersion of TFPR and justify the substantial contribution of the output distortion. Figure 6c supports the importance of the competition level to some extent— exporters tend to have higher output distortions (except for pure exporters, which can be driven by their high productivity level). Moreover, Fadejeva and Krasnopjorovs (2015) report that the gap between foreign and domestic Note that exporting firms also tend to be more productive. See Berthou et al. (2015) for the recent evidence for the euro area countries, or Benkovskis and Tkačevs (2016) for Latvia. 22

2014 Transportation

125.6

35.6

Hsieh and Klenow (2009)

China

2005 Manufacturing

86.6

—

India

1994 Manufacturing

127.5

—

US

1997 Manufacturing

42.9

—

Dias et al. (2016b)

Portugal 2011 Total 2011 Agriculture

79.0

28.0

81.8

31.3

2011 Manufacturing

53.5

13.7

2011 Services

91.5

38.4

Calligaris (2015)

Italy

2011 Total

80.2

—

Bellone and MallenPisano (2013)

France

2005 Manufacturing

30.5

—

2007 Total

49

—

Bulgaria 2007 Manufacturing

35

—

Brazil

2003 Manufacturing

62

—

China

2003 Manufacturing

70

—

Estonia

2009 Manufacturing

62

—

India

2002 Manufacturing

62

—

Slovenia 2009 Manufacturing

88

—

GarciaSpain Santana et al. (2016) Inklaar et al. (2017) (selected countries)

Source: Latvia’s firm-level database, author’s calculations, Hsieh and Klenow (2009), Dias et al. (2016b), Calligaris (2015), Bellone and Mallen-Pisano (2013), Garcia-Santana et al. (2016) and Inklaar et al. (2017)

competition narrowed in 2011–2013, as changes in the economic conditions induced growing severity of domestic competition. This finding coincides with reduced variance in output distortions and improved allocation of resources after 2010. Although the contribution of capital distortions was not amongst the most important drivers of misallocation in Latvia at the beginning of the sample period, it almost doubled after the crisis. This may be related with the tightening of the credit supply (Latvijas Banka 2015) and increase in the interest rate premia for riskier borrowers, which would push up the variance in TFPR. Finally, the

Journal of Productivity Analysis

contribution of misallocation due to labour distortion is relatively small and stable, in line with the conclusion about high flexibility of Latvia’s labour market by Braukša and Fadejeva (2016).

4.2 Misallocation by sectors Figure 4 shows potential gains from reallocation by major macroeconomic sectors in Latvia—the misallocation of

Fig. 4 Gains from reallocation of resources within industries to aggregate gross output of main macroeconomic sectors. Source: Latvia’s firm-level database, author’s calculations. Notes: Gains to total gross output are determined as 100 × (Y*/Y – 1). Contributions for

resources tends to be higher in services sectors. Dias et al. (2016a) discover similar trend in Portugal and explain it by higher level of informality and more rigid output prices in services comparing with manufacturing. Both explanations seem plausible also for Latvia: Putnins and Sauka (2011) report the smallest share of shadow economy for manufacturing in Latvia, while Benkovskis et al. (2012) provide evidence that consumer prices rigidity for services exceeds one for goods.

output, capital and labour distortions are estimated by eliminating variation in respective distortion. The residual is attributed to interactions between various distortions

Journal of Productivity Analysis

Output distortions provide the largest contribution to misallocation of resources for all macroeconomic sectors, but only two sectors—manufacturing and construction—see the decline of the contribution from output distortions (and the residual term) after the crisis. In the case of manufacturing, Fig. 4a reflects a steady decline: this can be justified by a gradually narrowing gap between the competition level in domestic and foreign markets. The contribution in construction, however, mainly declined in 2011. This may be attributed to a cleansing effect of crisis also related with competition: the demand for construction work dropped substantially in the post-crisis period, driving down the markups and reducing the variance in output distortions. The misallocation of capital keeps increasing in all sectors, reflecting the tightening of credit standards after the financial crisis. As to labour distortion, I observe the highest contribution in information and communication, as well as professional and administrative services. Similar to Dias et al. (2016a), I relate this to higher labour adjustment costs. Both abovementioned sectors require highly educated labour (IT specialists, lawyers, scientists etc.) that is scarce in Latvia.

4.3 Robustness check To perform the robustness check of abovementioned findings, I make six alternative calculations of gross output gains from reallocation. First, I follow the conventional approach and trim the 1% tails of TFPQ and distortions, being less strict in exclusion of outliers comparing with benchmark results. The results in Fig. 7a in Appendix B indicate that gains from reallocation are not robust to alternative outlier detection procedures: the contribution of misallocation increases to 60% in 2014. Results, although still containing two trends (downward before 2010 and upward afterwards), become more volatile. Nevertheless, the conclusions about contributions remain valid. The major contribution comes from the output distortion and the role of capital misallocation increases over time. The exclusion of firms reporting negative value added serves as the next robustness check. This brings us closer to the conventional approach of Hsieh and Klenow (2009) when such observations would be excluded by construction. According to Fig. 7b, this affects the results only marginally. In comparison with the benchmark approach, the gains from reallocation declined after 2008. Thus, firms with negative value added (and extremely low TFPQ) are responsible for some part of misallocation. The third robustness check limits the sample to firms that persisted during the whole period of 2007–2014. This modification moderately decreases potential gains from reallocation and induces a downward trend. This leads to the conclusion that persistent firms experience lower misallocation of resources, while growing misallocation during

2009–2010 was to some extent driven by firms that did not survive the crisis. Setting the elasticity of substitution between products to the same values for all industries changes the level of potential gains from reallocation, but does not alter major conclusions (see Fig. 7d and B2e). I also replicate the parametrisation strategy of Dias et al. (2016b) and apply US factor shares23 for the production function coefficients, simultaneously assuming that σ = 3 (see Fig. 7f). The two main trends (increase in misallocation prior to 2010 and decline afterwards) remain. However, the contribution of output distortion declines drastically, while the role of labour and capital distortions raises (capital misallocation continues increasing over time, signalling tighter credit supply). On the one hand, this may reflect the presence of sizeable industry average distortions in Latvia, which were ignored during the benchmark parametrisation. On the other hand, this can be related with the higher integration of Latvia into global value chains and lower capital intensity of domestic production.

4.4 Caveats of the methodology The approach of Hsieh and Klenow (2009) relies on several restrictive assumptions, therefore conclusions regarding the degree of misallocation should be taken with some caution. Foster et al. (2016) stresses the importance of the assumption on constant returns to scale that allows using costshares of respective production inputs as estimates of Cobb–Douglas production function parameters. But cost shares do not serve as a valid estimate if constant returns to scale do not hold. Moreover, the variation in TFPR is also affected by TFPQ and demand shocks in this case. Unfortunately, it is impossible to predict the size and the direction of the bias to estimated misallocation measures arising. Introducing intermediate inputs into the analysis does not solve the problem, since cost shares still provide biased estimates of output elasticities. It may reduce the severity of the bias, however: one can intuitively expect that constant returns to scale assumption is more reasonable for the gross output than for the value added. The static dispersion in TFPR can be largely explained by volatility of productivity using dynamic model with capital adjustment costs, as argued by Asker et al. (2014). As a result, gains from the reallocation of resources tend to be lower than ones suggested by the static model of Hsieh and Klenow (2009). Given that Asker et al. (2014) are able to explain 80–90% of variation in marginal revenue product of capital, it implies that gains from reallocation are overestimated when adjustment costs of inputs are not taken into 23 Using the data published by the Bureau of Economic Analysis for 2007–2014 and assuming the same production function for all 4-digit NACE sectors within respective 3-digit NAICS sectors.

Journal of Productivity Analysis

account. On the contrary, another dynamic framework by Peters (2013) suggests that gains from reallocation might be substantially larger if endogenous markups and entry decisions are included into the model.

TFPs can differ between the stages. The first stage can be labour-intensive (bookkeeping services), or capitalintensive (production of high-tech intermediate inputs). The production function is as follows: Ysi ¼

5 Fragmentation of production and misallocation A modern economy consists of linked web of producers rather than separate firms, which is not accounted by the original methodology of Hsieh and Klenow (2009). In this section, I argue that ignoring the fragmentation of production process may lead to serious bias while estimating gains from reallocation. The issue of production networks and misallocation is not new in the literature. Jones (2011) discusses how the effects from misallocation are amplified through the input–output structure of the economy. Fontange and Santoni (2015) test for the evidence of positive correlation in firm inefficiencies across sectors in France—they find positive cross-sectoral correlation of misallocation, which confirms that misallocation magnifies through input-output linkages. The abovementioned researches do not fully address the effect of production fragmentation on the estimates of misallocation at the firm level, however. Hsieh and Klenow (2009) assume homogeneity of intermediate inputs’ shares within sectors. Such an assumption is also traditional in the literature that studies the propagation of microeconomic shocks to aggregate fluctuations, as in Acemoglu et al. (2013), Di Giovanni et al. (2014), or Carvalho (2014)—it serves as a useful proxy in the absence of information on linkages between firms. But homogeneity of intermediate inputs across firms within each industry does not hold when some companies use outsourcing, i.e. early stages of production are performed by other domestic or foreign firms. In this case, the outsourcing firm will have notably higher share of intermediate input costs (and lower share of capital and labour costs) even if all firms use the same production technology. As I demonstrate below, the violation of the assumption on homogenous intermediate inputs within each industry seriously biases the estimates of firm-level distortions and gains from reallocation. Assume that production process in industry s consists of two stages now: production of intermediate inputs and final assembly.24 The second stage uses the output of the first stage as an intermediate input. Production functions and 24 This is the simplest possible value chain or production network —“vertical economy with a source and a sink” using the terminology of Carvalho (2014). While there exist more complicated networks with more firms involved (e.g. star economy with a central node), these can be viewed as specific cases when several firms provide intermediate inputs for a final good producer.

α

β

1α2;s β

α

β

2;s 2;s 2;s 2;s 2;s A2;si K2;si L2;si M2;si ¼A2;si K2;si L2;si   α1;s β1;s 1α1;s β1;s 1α2;s β2;s  A1;si K1;si L1;si M1;si ;

ð27Þ

where A1,si and A2,si denote firm-specific total factor productivity at first and second stage of production accordingly, K1,si and K2,si—firm’s capital, while L1,si and L2,si—number of employees used at respective production α1;s β1;s 1α1;s β1;s stage, M2;si ¼ A1;si K1;si L1;si M1;si stands for intermediate input of the second stage and M1,si—intermediate input of the first production stage. I assume that firm i faces the same capital and labour distortions and factor costs at both stages of production; in addition, there are no output distortions for the production at the first stage (e.g. transportation costs). After solving the profit maximisation problem subject to Eq. (27) and demand constraint in Eq. (3) one can express capital, labour and output distortions as a function of observable variables (see Appendix A1 for technical derivations):    PM 1;s M1;si α2;s þ α1;s 1  α2;s  β2;s    ; 1þτKsi ¼  1  α1;s  β1;s 1  α2;s  β2;s Rs K1;si þ K2;si

1þτLsi ¼ 

PM 1;s M1;si







ð28Þ

β2;s þ β1;s 1  α2;s  β2;s    : 1  α1;s  β1;s 1  α2;s  β2;s ws L1;si þ L2;si ð29Þ

1  τYsi ¼

PM M1;si σs  1;s  ; σ s  1 1  α1;s  β1;s 1  α2;s  β2;s Psi Ysi ð30Þ

The equations above are similar to Eqs. (20)–(22). Moreover, when firm i performs both production stages, Eqs. (28)–(30) are observationally equivalent to the singlestage production case with Msi ¼ M1;si , Ksi ¼ K1;si þ K2;si , and Lsi ¼ L1;si þ L2;si  , αs ¼ α2;s þ  α1;s 1  α2;s  β2;s βs ¼ β2;s þ β1;s 1  α2;s  β2;s . Now assume that a firm outsources the first stage to another enterprise, either in the same country (but most probably in another industry), or internationally, involving into global value chains. Such a decision can be motivated by several reasons. For example, own production costs can exceed the price of the outsourced intermediate inputs (PM2,s).25 This may happen due to better technology possessed by other firm, or some specific subsidy granted to 25

Namely,PM 2;s <

Rs K1;si ð1þτKsi Þþws L1;si ð1þτLsi ÞþPM s M1;si . M2;si

Journal of Productivity Analysis

other firm. Alternatively, this can be driven by legislation. The micro-enterprise tax introduced in Latvia since 2011 favours micro enterprises with a high share of labour costs, thus stimulating to form a separate enterprise providing services like legal and accounting.26 Instead of producing M2,si itself, firm i buys it at the price PM2,s. The production function transforms to:

The bias persists even when the share of outsourcing firms become substantial. In the absence of firm-to-firm trade data the researcher observes a weighted average of the industry elasticities of output: (1–w2,s)αs + w2,sα2,s > α2,s and (1–w2,s) βs + w2,s β2,s > β2,s, where w2,s stands for the share of outsourcing firms in the output of industry s. Thus, the bias persists as long as there exists a heterogeneity in terms of outsourcing degree within an industry,27 and the size of the 1α2;s β2;s α2;s β2;s ð31Þ Y′si ¼ A2;si K′2;si L′2;si M′2;si ; bias is an inverse U-shape function of the degree of outsourcing.28 ′ ′ ′ ′ where Y si, K 2,si, L 2,si and M 2,si denote the real output, Ignoring the fragmentation of production affects overall capital, labour and intermediate inputs in the case of conclusions, since some part of observed variance in TFP is outsourced first-stage. When data on firm-to-firm trade is due to outsourcing, not actual distortions. As a result, the unavailable and the vast majority of the firms in the industry gain from reallocation is overestimated. If we assume that still perform both stages of production, the researcher does outsourcing is still a rare occurrence, this bias should not observe α2,s and increase over time accounting for the growing role of outβ , but instead observe α ¼ α þ s 2;s 2,s    sourcing (see, e.g. Los et al. 2015; where the increasing α1;s 1  α2;s  β2;s and βs ¼ β2;s þ β1;s 1  α2;s  β2;s international fragmentation of production is stressed). from the data. This will lead to a substantial bias in However, industries that already use outsourcing intenevaluation of capital, labour and output distortions (see sively may see further decline of the bias. Appendix A2 for technical details): Ideally, one would need the data on transactions between !   α1;s 1  α2;s  β2;s 1 individual firms—the nice example is Norwegian   ð1þτKsi Þ; 1 þ τ′Ksi ¼ þ 1  α1;s  β1;s α2;s 1  α1;s  β1;s transaction-level custom data, which also identify buyers, used by Bernard et al. (2014). This will allow restoring the ð32Þ whole production chain, estimating capital and labour costs of production at all stages, and using the original Hsieh and  ! β1;s 1  α2;s  β2;s 1   ð1 þ τLsi Þ; Klenow (2009) methodology with two factors of producþ 1 þ τ′Lsi ¼ 1  α1;s  β1;s β2;s 1  α1;s  β1;s tion. Unfortunately, transaction-level data are still unavailable for Latvia. Thus, I rely on industry-level information to ð33Þ check for possible biases due to production fragmentation and outsourcing. Although it is hard to measure the popu1  τYsi larity of outsourcing strategy on the industry level, one 1  τ′Ysi ¼ ; ð34Þ 1  α1;s  β1;s indicator provides a useful proxy. I use information obtained from the firm-level trade database to evaluate the importance of re-exports. This is where τ′Ksi, τ′Lsi, and τ′Ysi are estimated capital, labour and done following the approach by Benkovskis et al. (2016), output distortions in the case of outsourced first stage of who (at least partially) capture re-exports flows when a production. It is easy to see that capital and labour particular firm exports and imports the same CN8 product distortions are overestimated (τ′Ksi >τKsi , τ′Lsi >τLsi ), while category within 12 months. Such operations are very size distortion are underestimated (τ′Ysi <τYsi ) when only few widespread in Latvia due to logistics reasons: Benkovskis firms in industry s outsource. Intuitively, in the absence of et al. (2016) point that re-exports equal to 32% of total information about the outsourcing of the first stage, one merchandise exports in 2013. The re-exporter can be treated interpret the firm’s lower share of capital and/or labour costs as a firm “outsourcing” the production of the good abroad, as a capital or labour distortion, but not a result of comparing with a usual exporter that inputs much more of outsourcing. Similarly, the larger share of expenses on its value added into the total output. According to the intermediate inputs are treated as a negative size distortion. analysis above, the higher share of re-exporting firms in an The size of the bias increases with the importance of the industry should be associated with higher capital and labour outsourced first stage of production (high α1,s, β1,s and low distortions, and lower output distortion, if we assume that α2,s, β2,s).

26 According to World Bank (2017), the largest number of microenterprise workers were employed in legal and accounting activities sector in 2015.

27 Note that if all firms within an industry outsource to the same degree, the researcher observes α2,s and β2,s, thus being able to use Eqs. (A10)–(A12) and estimate true capital, labour and output distortions. 28 Of course, more complicated functional forms are possible if there exist several ways of outsourcing.

Journal of Productivity Analysis

Fig. 5 Relationship between distortions and share of re-exporters at 4digit NACE industry level in 2014. Source: Latvia’s firm-level database, WIOD, author’s calculations. Notes: Re-exports is evaluated using Benkovskis et al. (2016) methodology. The average industry distortions are estimated using Eqs. (13)–(15). Higher value corresponds to the larger distortion relative to the industry average. Obtained by the kernel-weighted local polynomial smoothing

the share of outsourcing firms is relatively small. Indeed, Fig. 5 coincides with the predicted pattern (but it is not possible to check the hypothesis of non-linear relationship since none of Latvian industries has a very high share of reexporters). Thus, there is some empirical evidence in favour of outsourcing bias to misallocation estimates: fragmentation of production increases the heterogeneity of the intermediate inputs and leads to the overestimation of gains from reallocation.

6 Conclusions I apply Hsieh and Klenow (2009) framework modified a la Dias et al. (2016b) to Latvia’s firm-level data and find that potential output gains from reallocation equalled to 32% in 2014. However, these level estimates are not robust to outlier detection procedure, thus I focus on more robust results. The misallocation of resources in services

substantially exceeds the one in manufacturing, which may reflect higher informality and price stickiness in services sector. I observe growing gains from reallocation prior and during the financial crisis, and the decline in misallocation afterwards, although changes may not be statistically significant. The misallocation of resources was not the major driver of economic dynamics during the crisis; however, it contributed to the economic growth in 2011–2014. The output distortion serves as a major source of gains from reallocation, which can be partially explained by the different competition levels in domestic and foreign markets. Moreover, the gap between the competition level in Latvia’s market and foreign market narrowed after the crisis, as changes in the economic conditions induced growing severity of domestic competition—it contributed to the reduced misallocation of resources after 2010. Although misallocation of capital was small at the beginning of the sample, it increased over time and became an important source of misallocation in 2014, which may be related to the tightening of the credit supply. The approach I used to evaluate misallocations of resources in Latvia relies on several restrictive assumptions like constant returns to scale, absence of capital adjustment costs and exogenous markups, to name a few. These assumptions may lead to substantial biases, as was shown in the literature recently, thus empirical findings about misallocation should be taken with some caution. I contribute to the literature by pointing to the fact that the Hsieh and Klenow (2009) framework does not account for the possibility of fragmentation, i.e. split of production process between different firms. I prove that in the absence of network data of inter-firm trade the conventional methodology tends to overestimate capital and labour distortions, simultaneously underestimating output distortions of firms involved into outsourcing process. This induces an upward bias in the estimates of misallocation. Empirical data show that gains from reallocation tend to be larger for Latvia’s industries with positive (although not extremely high) share of re-exporters – enterprises that “outsource” most of their inputs abroad. While industry level data gives no clue about the size of the bias, it signals that strong conclusions regarding misallocation of resources and its driving forces should be treated with additional caution. Although the availability of data on transactions between different firms is still rare, this is one of the direction to proceed with the empirical analysis of misallocation. Network data will allow restoring the whole production chain, estimating direct and indirect capital and labour costs of production at all stages. The efforts in this area seem especially necessary given the ongoing process of increasing fragmentation.

Journal of Productivity Analysis

7 Disclaimer The views expressed in this paper are those of the author and do not necessarily reflect the stance of Latvijas Banka. The author assumes sole responsibility for any errors and omissions.

After re-arranging one can express capital, labour and output distortions as a function of observable variables:    PM 1;s M1;si α2;s þ α1;s 1  α2;s  β 2;s    ; 1 þ τKsi ¼  1  α1;s  β1;s 1  α2;s  β2;s Rs K1;si þ K2;si 

Acknowledgements This research was performed within the ESCB Competitiveness Research Network (CompNet). I am grateful to Richard Baldwin, Fabrizio Coricelli, Carlos Robalo Marques, Sašo Polanec and two referees for helpful comments.

1 þ τLsi ¼ 



PM 1;s M1;si β 2;s þ β1;s 1  α2;s  β2;s    : 1  α1;s  β1;s 1  α2;s  β2;s ws L1;si þ L2;si PM 1;s M1;si

σs    : σ s  1 1  α1;s  β1;s 1  α2;s  β2;s Psi Ysi

Conflict of interest The author declares that they have no conflict of interest.

8 Appendix A: Two-stage production framework A.1 Both stages of production performed in one firm Production process includes two stages and both stages occurs in one firm. The production function looks the following way: Ysi ¼

α

β

1α2;s β

α1;s β1;s 1α1;s β1;s M2;si ¼A1;si K1;si L1;si M1;si .

where tion problem evolves into πsi ¼

β

α

2;s 2;s 2;s 2;s 2;s A2;si K2;si L2;si M2;si ¼A2;si K2;si L2;si   α1;s β1;s 1α1;s β1;s 1α2;s β2;s  A1;si K1;si L1;si M1;si ;

ðA1Þ

L1;si ;L2;si ;K1;si ;K2;si ;M1;si

!

A.2 Outsourcing first stage of production Assume that output is still produced in two stages, but the first stage of production is outsourced to a different firm. Instead of producing M2,si itself, the firm i buys it at the price PM2,s. The production function transforms into:

max :

ð1 

α Y τYsi Þ σsσ1 Psi K2;s2;sisi s

ð1  τYsi Þ σsσ1 Psi s

P′si ¼Ps

Ys Y′si

ð1  τYsi Þ σsσ1 Psi s ð1  τYsi Þ σsσ1 Psi s

β2;s Ysi L2;si

¼ ð1 þ τKsi ÞRs

¼ ð1 þ τLsi Þws

M1;si

¼ PM 1;s

s

ðA8Þ

;

ðA3Þ

L′2;si ;K′2;si ;M′2;si

!

max : ðA9Þ

After solving the maximisation problem, the true capital, labour and output distortions should be derived as 1 þ τKsi ¼

PM α2;s 2;s M′2;si ; 1  α2;s  β2;s Rs K′2;si

ðA10Þ

1 þ τLsi ¼

PM β2;s 2;s M′2;si ; 1  α2;s  β2;s ws L′2;si

ðA11Þ

1  τYsi ¼

PM σs 2;s M′2;si   : σ s  1 1  α2;s  β2;s P′si Y′si

ðA12Þ

¼ ð1 þ τLsi Þws

ð1α1;s β1;s Þð1α2;s β2;s ÞYsi

σ1

ws L′2;si  PM 2;s M′2;si

¼ ð1 þ τKsi ÞRs

β1;s ð1α2;s β2;s ÞYsi L1;si

ðA7Þ

;

π′si ¼ ð1  τYsi ÞP′si Y′si  ð1 þ τKsi ÞRs K′2;si  ð1 þ τLsi Þ

Firm i maximises profits subject to production function and demand constraints given by Eqs. (A1) and (3). This leads to the following first order conditions: α1;s ð1α2;s β2;s ÞYsi K1;si

1α β2;s

where Y′si, K′2,si, L′2,si and M′2,si denote the real output, capital, labour and intermediate inputs in the case of outsourced first-stage. As before, the firm faces downward sloping demand:

ðA2Þ

ð1  τYsi Þ σsσ1 Psi s

β

α

2;s 2;s Y′si ¼ A2;si K′2;si L′2;si M′2;si 2;s

where P′si stands for the output price of the firm i under outsourcing. Profit maximisation problem is similar to Eq. (5):

  ð1  τYsi ÞPsi Ysi  ð1 þ τKsi ÞRs K1;si þ K2;si   ð1 þ τLsi Þws L1;si þ L2;si  PM 1;s M1;si

ðA6Þ



The profit maximisa-

ðA4Þ

ðA5Þ 1  τYsi ¼

Compliance with ethical standards



When data on firm-to-firm trade is unavailable and most of the firms in the industry still perform both stages of

Journal of Productivity Analysis

production, the researcher does not observe α2,s and β2,s. Instead, researcher observes  αs ¼ α2;s þ   α1;s 1  α2;s  β2;s and βs ¼ β2;s þ β1;s 1  α2;s  β2;s from the data. As a result, capital, labour and output distortions are going to be evaluated using Eqs. (A4)–(A6), creating a bias: PM M′2;si α2;s þα1;s ð1α2;s β2;s Þ PM 2;s M′2;si ¼ 1 þ τ′Ksi ¼ 1ααssβ R2;ss K′2;si ¼ 1α β 1α β s ð 1;s 1;s Þð 2;s 2;s Þ Rs K′2;si   α1;s ð1α2;s β Þ ¼ 1α1;s1β þ α 1α β2;s ð1 þ τKsi Þ; 1;s 2;s ð 1;s 1;s Þ

ðA13Þ PM M′2;si β þβ ð1α2;s β2;s Þ PM 2;s M′2;si ¼ 1 þ τ′Lsi ¼ 1αβssβ w2;ss L′2;si ¼ 1α2;s β1;s 1α β s ð 1;s 1;s Þð 2;s 2;s Þ ws L′2;si   β ð1α2;s β Þ ¼ 1α1;s1β þ β1;s 1α β2;s ð1 þ τLsi Þ; 1;s 1;s 2;s ð 1;s Þ

ðA14Þ

PM M′2;si

2;s s ¼ σsσ1 ð1αs β ÞP′si Y′si

1  τ′Ysi

s

¼

PM σs 2;s M′2;si σ s 1 ð1α1;s β1;s Þð1α2;s β2;s ÞP′si Y′si

¼

ðA15Þ

Ysi ¼ 1α1τ ; 1;s β 1;s

where τ′Ksi, τ′Lsi, and τ′Ysi are estimated capital, labour and output distortions in the case of outsourced first stage of production.

Journal of Productivity Analysis

9 Appendix B: Figures Figures 6 and 7.

Fig. 6 Relationship between relative output distortions (1 – τ*Ysi)/(1 – τYs) and several firms’ characteristics in 2014. Source: Latvia’s firmlevel database, author’s calculations. Notes: Firm-level output distortions are estimated using Eq. (22), while the average industry output

distortions—Eq. (15). Higher value corresponds to the larger output distortion relative to the industry average. Obtained by the kernelweighted local polynomial smoothing

Journal of Productivity Analysis

Fig. 7 Alternative estimates of gains from reallocation to aggregate gross output. Source: Latvia’s firm-level database, author’s calculations. Notes: Gains to total gross output are determined as 100 × (Y*/

Y – 1). Contributions for output, capital and labour distortions are estimated by eliminating variation in respective distortion. The residual is attributed to interactions between various distortions

Journal of Productivity Analysis

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