Munich Personal RePEc Archive

Increasing productivity dispersion:
Evidence from light manufacturing in
BrazilGonzales-Rocha, Erick and Mendez-Guerra, Carlos
Kwansei Gakuin University, Kyushu University

15 August 2018

Online at https://mpra.ub.uni-muenchen.de/88478/
MPRA Paper No. 88478, posted 19 Aug 2018 02:31 UTC

Increasing Productivity Dispersion: Evidence from
Light Manufacturing in Brazil
Erick Gonzales-Rocha
Kwansei Gakuin University

Carlos Mendez-Guerra
Kyushu University

August 15, 2018
Abstract
Large productivity dispersion within narrowly defined sectors is widely documented.
However, across studies, several statistics are used to assess dispersion and there is notenough discussion about differences among them. Using firm-level data for the textile and furniture sectors in Brazil over the 2003-2009 period, we estimated different
TFP measures according to four methods: Ordinary Least Squares (OLS for short),
the stochastic frontier model of Battese and Coelli (1988, 1992)(STCH for short), thecontrol function approach of Levinsohn and Petrin (2003) (LP for short), and the corrected control function approach of Ackerberg et al. (2015) (ACF for short). Next,
we calculated three dispersion statistics: Standard Deviation (SD); Coefficient of Variation (CV); and Interquartile Range (IQR). After confirming the existence of large
productivity dispersion within the studied sectors, we analyzed if the dispersion is increasing or decreasing over time. For both sectors, SD and CV convey an increasing
productivity dispersion message, but they do so at different rates (CV is seven times
higher than SD). On the contrary, IQR suggests less productivity dispersion over time
for textiles and mixed results for furnitures. Overall, in terms of characterizing theincreasing productivity dispersion, the CV statistic combined with the ACF method
define an upper bound while the IQR with LP method define a lower bound. Considering these results, the article underlines that there are non-trivial differences in the useof dispersion statistics. Thus, their use could not be interchangeable and should consider methodological issues, behavior in the tails of the firm productivity distribution,
sample sizes and scenarios of divergence/convergence, among others.

JEL Codes: D24, O47, O54,
Keywords: total factor productivity, dispersion, manufacturing firms, Brazil

1

Introduction

There is a growing consensus that Total Factor Productivity (TFP) explains most of thedifferences in income per capita across countries (Caselli 2005, Hsieh and Klenow 2010, andPages 2010), and its importance can be traced back at least to the seminal work of Solow(1957).1 More recently, the increasing availability of firm-level datasets has brought additional light to issues of selection, dispersion and allocative efficiency that occur at the microlevel and are shown to have aggregate effects (Bartelsman et al. 2010, Hsieh and Klenow
2009, and Restuccia, and Rogerson 2017). Among those, the existence of dispersion within
narrowly defined sectors is well documented (Syverson 2011). However, less attention has
been paid to the selection of statistics used to measure productivity dispersion. Across studies, the most commonly used measures are Standard Deviation (SD), Coefficient of Variation(CV) and Interquartile Range (IQR), with the latter having more prominence.2 These statistics have different methods of calculation, units of measurement and mathematical properties(Ram 2018). But, despite these differences, there is not enough discussion on whether suchdispersion statistics could be used interchangeably, convey the same message when applied
to the same sample, or have numerical differences in their values and rates of change.
In this context, our paper aims to study the behavior of productivity dispersion statistics
within two narrowly defined light manufacturing sectors in Brazil: textiles and furnitures.
We used panel data from the World Bank Enterprise Surveys to estimate TFP at the firmlevel under different estimation frameworks, including: Ordinary Least Squares (OLS for
short), the stochastic frontier model of Battese and Coelli (1988, 1992) (STCH for short),
the control function approach of Levinsohn and Petrin (2003) (LP for short), and the corrected control function approach of Ackerberg et al. (2015) (ACF for short). Estimatedresults—across all methods—suggest large productivity differences within each of the twostudied sectors. Nevertheless, determining if dispersion is increasing or decreasing over time
may vary depending on the used statistic. On the one hand, SD and CV unequivocallysuggest that dispersion has increased over time, even though CV does so at six to seventimes higher rates of change as compared to SD (CV with the ACF method set and upperbound for higher rates of change). On the other hand, IQR registers a reduction in dispersion
for the textile sector and a mixed (increase/decrease) message for the furniture sector (IQR
with the LP method set a lower bound for rates of change). We argue that these are nontrivial differences. The differences are based not only on how the statistics are constructed
but also on how dispersion occurs in the extremes of the productivity distribution, samples
sizes as well as scenarios of convergence or divergence. The rest of the paper is organized
as follows. Section 2 briefly describes the methods for estimating firm-level productivity,
dispersion statistics and the data source. Section 3 presents the results for each method andstatistic. Finally, Section 4 offers some concluding remarks.
1

It is argued that Tinberger (1942) introduced the concept in a study published in German which might
not have been translated to English until 1959 according to Chen (1997). Also, other researchers could havemeasured TFP before Solow (1957) but it is the latter who integrated the concept into economic theory
using calculus as noted by Griliches (1996).
2
See, for example, Cunningham, Foster, Grim, Haltiwanger, Pabilonia, Stewart and Wolf 2018, Bartelsman and Wolf 2017, Cette, Corde and Lecat 2018, Foster, Grim, Haltiwanger and Wolf 2018, 2017, 2016,
and Ito and Lechevalier 2009.

2
2.1

Methods and Data

Productivity Measurement

One common procedure for measuring Total Factor Productivity (TFP) relies on the econometric estimation of an aggregate production function.3 This function relates outputs to
inputs and a residual measure of efficiency. Within this framework, we measure productivity
at the two digit level ISIC code in order to have less heterogeneity across outputs and inputs
of different firms. In the database for Brazil, the sectors with the highest number of observations were textiles and furnitures.4 In addition, the textiles sector was selected given its
pivotal role in both providing employment for low skilled labor and creating dynamic effects
that foster industrialization (Adhikari and Yamamoto 2007, and Keane and te Velde 2008).
In this article, we calculated TFP applying different methods: Ordinary Least Squares(OLS); the stochastic frontier of Battese and Coelli (1988, 1992, STCH); the control function
approach of Levinsohn and Petrin (2003, LP); and the corrected control function approachof Ackerberg et al. (2015, ACF). Using a Cobb-Douglas production function, the equations
below describe the estimation of TFP in a setting where technology is Hicks neutral, capital(K) and labor (L) are paid the value of their marginal products, and production value added(V A) is the amount of sales (Y ) minus the cost of intermediate inputs (M ). Additionally,for presentation purposes, variables in logarithms are depicted by lower case letters.
Yit = Ait K βitk Lβitl Mit βm
VA=Y −M
vait = β0 + βk kit + βl lit + vit(1)

tf pit = vait − βˆk kit − β̂l lit(2)

The way in which the parameters for capital and labor are estimated in equation 1 varies
according to the estimation method.
The Stochastic Frontier Model of Battese and Coelli (1988, 1992, STCH)
Historically, several production functions assume producers to be successful optimizers. However, Kumbhakar and Lovell (2000) highlighted that not all producers use the minimum inputs under a given technology (technical efficiency), allocate inputs in a cost-effective manner
given input prices (cost efficiency), or allocate their outputs in a revenue-maximizing manner
given output prices (profit efficiency). Thus, there are several instances where cost is not
3

Another common method is the growth accounting approach. See, for instance, Stigler (1947),
Abramovitz (1956), Kendrick (1956, 1961) and Denison (1962, 1967, 1972, 1974). In this method, theelasticities of the inputs are typically calibrated to the national income shares.
4
Textile and clothing corresponds to ISIC 18 (manufacture of wearing apparel; dressing and dyeing offur) and furniture to ISIC 36 (manufacture of furniture; manufacturing n.e.c.).

minimized or profit is not maximized. In stochastic frontier models, the analysis is conducted relaxing the successful optimizers assumption and accounting for the differences offirms that operate at a production frontier (using inputs and outputs in the most efficientmanner) and those firms that do not. In the frontier approach, error terms are composed ofa traditional random noise component (as in various least squares techniques where errors
terms are assumed to be symmetrically distributed with zero means) and a new one-sided
inefficiency component that aims to capture the effects of inefficiency.5 The random variation in the operating environment generating inefficiencies that, in turn, create one-sided
variations make the production frontiers stochastic.
The specific model is is an extension of Battese and Coelli (1988) that can be applied topanel data. Battese and Coelli (1992) defined the model as:
Yit = f (xit ; β)exp(Vit − Uit )and
Uit = ηit Ui = {exp[−η(t − T )]} Ui , t∈ζ(i); i = 1, 2, ..., N ;where Yit is the production function for firm i in period t. Then, f (xit ; β) is an appropriate
function with vectors xit ; β of factor inputs and unknown parameters, respectively. The
measurement and specification of random errors Vit are assumed to be independently andidentically distributed N (0, σV2 ). While, one-sided inefficiencies Uit are independent andidentically distributed non-negative truncations of the N (µ, σ 2 ) distribution. An unknown
scalar parameter is represented byηit and ζ(i) represents a set of Ti time periods (out of a
T total period) for which there are observations for a firm i. The STCH model is suitablefor unbalanced panel datasets (Daude and Fernández-Arias 2010 and Ibarrarán, Maffioli andStucchi 2009).
The Control Function Approach of Levinsohn and Petrin (2003, LP)
The LP method is an extension of the method developed by Olley and Pakes (1996) (OPfor short) originally aimed at avoiding potential serial correlations between input levels andunobserved (but, potentially observable or predictable) firm-specific processes that affectthe production technology.6 OP used investment as a variable that could reveal and control for these unobserved shocks. Investment, however, is not easily found in firm level
datasets (several times is equal to zero), moreover it is prone to data quality problems andit is likely to be affected by unobservable shocks. Investment also requires the analysis ofa dynamic programming problem to verify the strict monotonicity assumption in terms of
marginal products of capital and productivity shocks. Hence, LP proposed a method thatuses intermediate inputs instead of investment to account for the unobserved shocks. Intermediate inputs are proposed because they are non-dynamic inputs (which makes it easier
to satisfy the strict monotonicity assumption), they affect current profits and do not rule5

The composed error terms are not symmetric and do not have zero means
In other words, factors or shocks hidden in the error term that might be affecting decisions about capitaland labor and, thus, make the estimated parameters inconsistent.
6

out shocks to the investment demand function (prices or other unobservables), and they are
more commonly available in firm level datasets.
The Corrected Control Function Approach of Ackerberg et al. (2015, ACF)
ACF suggested that the OP and LP methods suffer from functional dependence problems,particularly in their first stages, where the estimated coefficient of labor is correctly identified only under a few and specific instances (for instance, when shocks to the price of laboror output occur after levels of investment or intermediate inputs are defined, but before
decisions about labor are made).7 Therefore, ACF proposed a method that uses inverted
demand functions conditional on decisions about labor inputs avoiding the functional dependence problem and also relaxing other assumptions. Specifically, the ACF method allows
exogenous, serially correlated, unobserved shocks to the price and/or amount of labor while
also accommodating labor to have dynamic effects (such as hiring and firing costs). The basic
procedure, described by Ackerberg et al. (2015), uses the following value added production
function (ωit represent unobserved productivity shocks that are potentially observable orpredictable and εit represent shocks that are not observable):yit = β0 + βk kit + βl lit + ωit + εit
ACF requires a number of assumptions when intermediates inputs are used as a proxyfor unobserved shocks. The first assumption is concerned with the timing of decisions about
inputs and establishes the accumulation of capital under the function below (capital andinvestment are decided in period t − 1 while labor (lit ) can be decided in periods t, or t − b,with 0 < b ≤ 1):
kit = κ(kit−1 , iit−1 )The next assumptions are scalar unobservable and strict monotonicity (in ωit ) in thefollowing intermediate input demand function:
mit = fet (kit , lit , ωit )Subsequently, the above function is inverted ωit = fet−1 (kit , lit , mit ) and introduced into
the production function:e t (kit , lit , mit ) + εityit = β0 + βk kit + βl lit + fet−1 (kit , lit , mit ) + εit = ΦThen, using semiparametric methods, the first stage moment condition is defined asê t (kit , lit , mit ) is estimated, but βl is not):follows (Φhiê t (kit , lit , mit ) = 0
E [εit | Iit ] = E yit − ΦThe production function parameters (including βl ) are estimated in the second stage
moment condition:
7

ACF mentioned that in practice, the functional dependence problem would not be literally observed.

E [ξit + εit | Iit−1 ] = 0ihê t−1 (kit−1 , lit−1 , mit−1 ) − β0 − βk kit−1 − βl lit−1 | Iit−1 = 0
E yit − β0 − βk kit − βl lit − g Φ

Because the second moment requires the estimation of one additional parameter (βl ,besides β0 and βk ), one more unconditional moment needs to be defined:

E

"





ê t−1 (kit−1 , lit−1 , mit−1 ) − β0 − βk kit−1 − βl lit−1
yit − β0 − βk kit − βl lit − ρ Φ






1
kit

lit−1
ê t−1 (kit−1 , lit−1 , mit−1 )
Φ



#


 =0


In this way, the ACF method accounts for shocks related to kit and lit whereas LP allows
only shocks to kit and OP does not account for any of those. In any case, we used four
methods (OLS, STCH, LP and ACF) to calculate TFP and study the distribution dynamics.
2.2

Productivity Dispersion Measurement

Commonly used statistics to describe productivity dispersion are Standard Deviation (SD),
Coefficient of Variation (CV) and Interquartile Range (IQR) which are estimated using thefollowing well-known expressions.8
SDt = [(1/n − 1)

P

2 0.5
i (tf pit − tf pt ) ](3)

CVt = SDT F Pt /T F Pt

(4)

IQRt = Q3 − Q1

(5)where tf pit is logarithm of real TFP for firm i in time t, tf pt is the mean value of
logarithm of TFP, SDT F Pt is the standard deviation of TFP, T F Pt is the mean of real
TFP in year t and Q3 − Q1 is the difference between the third and the first quartile.
Subsequently, we estimated growth rates (GR) and rates of change (ROC)9 as
GRSD = (SDt+1 − SDt )/SDt
8(6)

The CV coefficient is based on real values as log-transformed data require a variation in the formula for
CV to be correctly estimated (Canchola et al., 2017).
9
By using rates of change we aim to analyze the behavior of dispersion statistics not only in terms of
their values but also in terms of their rates of change over time to see if there are different interpretations.

ROCsd = (sdt+1 − sdt )/((t + 1) − t)(7)where sd stands for logarithm of SD. GR and ROC can be calculated for CV and IQR in
a similar way (just replace sd for cv or iqr). Ram (2018) argued that methods of calculation,
units of measurement and mathematical properties among these measures are different.10 To
study the differences, a direct comparison of linear rates of change in the previous measurespresent problems because linear trends are unit dependent and the measurement units of SD,
CV and IQR are largely different. For that reason, logarithmic rates of change are estimatedso that comparisons can be made. Negative rates will indicate a reduction in productivity
dispersion (that is, convergence) while positive rates would suggest an increase in dispersion(that is, divergence).
Among the previous measures, IQR seems to be more used because it is easier to interpretand it would be more robust to outliers (see Cunningham et al. 2018, Bartelsman and Wolf
2017, or Foster et al. 2018). However, we argue that in narrowly defined sectors withinalready small sample sizes, IQR may leave aside valuable observations points. Moreover, it
is important to look at the entire distribution as there is considerable dispersion within theupper and lower tails.11
2.3

Data

Data comes from the World Bank’s Enterprise Surveys Project. This project is well known
for collecting firm-level data across countries using a common methodology, standardized
questionnaires and a stratified random sample that covers the non-agricultural economy ofmain cities and nearby business areas. In addition to adequately covering different cities,
sectors and firm sizes, the dataset also provides a wide arrange of variables that allow thecalculation of firm performance indicators such as productivity. One limitation, however, isthat the project only focuses on formal firms with more than 5 employees. Thus, consideringthat about 40 percent of the Brazilian economy is informal (Schneider et al. 2011), economywide generalizations should be taken with caution.
Using data for the years 2003 and 2009, a balanced panel dataset was constructed foreach sector. As expected, this construction implied a large reduction in the sample size.
After structuring the panel dataset, the data cleaning process included a post-estimationof outliers procedure for all main variables.12 Only 48 observations in textiles sector and62 observations in the furniture sector had the required variables to compute TFP in both
years. Table 1 summarizes the datasets that resulted from this construction and cleaning
process.
10Bartelsman and Wolf (2017) noted that dispersion calculated from value-added measures of production
tends to be higher when compared to gross output measures.
11
Cunningham et al. (2018) argued that the behavior between the tails could be different and noted theimportant implications of the dynamics of the most productive firms for the whole distribution.
12
We computed several residual statistics to identify outliers and conflicting observations.

Table 1: Summary Statistics - Textiles and Furnitures
TextilesVariable
Obs
Mean Std. Dev.
Min
Max
Sales 2003
48 11,400,000 35,700,000 150,847 181,000,000
Sales 200948 20,200,000 71,400,000
6,000 420,000,000
Labor 2003
48 2,117,498
7,368,616 65,918 41,500,000
Labor 2009
48 3,880,581 15,100,000
1,500 93,000,000
Capital 2003
48
895,799
2,850,071
1,285 16,000,000
Capital 2009
48 1,755,485
6,459,338
1,200 43,000,000
Int. Inputs 2003
48 5,404,904 18,300,000
3,131 98,300,000
Int. Inputs 2009
48 7,052,957 22,900,000
1,440 120,000,000
Electricity 2003
48
64,582
262,431571
1,821,798
Electricity 200948
176,889
732,14272
5,000,000

Furnitures
Obs
Mean Std. Dev.
Min
Max
62 11,300,000 28,000,000 151,062 160,000,000
62 13,900,000 33,300,000
2,400 212,000,000
62 1,605,594
4,093,550 48,065 27,400,000
62 1,807,292
4,449,864
1,200 29,000,000
62 1,649,194
5,261,774
2,087 39,100,000
62 2,160,630
6,698,165
220 50,000,000
62 4,862,486 10,700,000 15,654 59,600,000
62 6,631,881 15,100,000
900 82,000,000
62
104,235
234,240
14
1,598,513
62
145,859
380,13060
2,400,000

Notes: Monetary values are expressed in 2009 local currency units and were deflated using the National
Index of Consumer Prices (INPC in Portuguese) obtained from the Brazilian Institute of Geography andStatistics (IBGE in Portuguese). Statistics for balanced panel data only (firms with complete data for sales,
capital, labor, intermediate inputs and electricity for the years 2003 as well as 2009).
Source: Authors’ calculations using data from the World Bank’s Enterprise Surveys

3
3.1

Results
Productivity

Table 2 presents the results for the estimation of the production function. Overall, theestimated parameters are within similar ranges despite using different methods.13 The differences in the results for the method of ACF (columns 4 and 8) could be explained becauseof the strict use of balanced panel data.
It is worth noting that the estimated parameters in Table 2 will, in some instances,produce negative values of productivity which, according to Fernández-Arias and RodríguezApolinar (2016), are not uncommon to find in the LAC region. They also contested the
hypothesis about the existence of these negative values because of measurement errors in
the factor of labor (quality of education, specifically) and further showed that a possible
bias in human capital accumulation will actually strengthen the productivity shortfall in
the region. Using the results of the production function estimation, we calculated TFP.
Summary statistics for these values are presented in Tables 3 and 4. It can be observed that
the OLS and STCH methods consistently report similar values. ACF and LP provide TFPvalues in a different order of magnitude but with consistency within the methods.
Although these summary statistics are informative, they have limitations at the momentof understanding the behavior of TFP. In terms of central tendency indicators, medianvalues suggest the textiles sector is experiencing a productivity deterioration over time,
independently of the method used to calculate TFP. However, mean values for the same
sector suggest slight improvements overall. Meanwhile, for the furniture sector, both medianand mean values suggest improvements of TFP over time.
13

Estimations were also conducted for the case of OLS considering the information available for each year
(2003 and 2009) separately as well as including a year dummy variable. Results of the estimated coefficients
proved to be robust to these modifications and are not included for the sake of brevity. The methods of
ACF and LP require at least two points in time (panel data) to be executed, so no further explorations were
done. Additional results exploring other considerations are presented in Appendix A.

Table 2: Production Function Estimation

VARIABLES
CapitalLabor
Constant

Observations
R-squared
Number of panelid

Textiles
(1)
(2)
(3)
OLS
STCH
LP
0.147** 0.147*** 0.207*(0.0619) (0.0563) (0.119)
0.885*** 0.885*** 0.723***(0.0610) (0.0637) (0.103)
0.727
0.730
(0.534)(0.543)
96
0.866

96

Furnitures
(4)
(5)
(6)
(7)
ACF
OLS
STCH
LP
-0.0264 0.177*** 0.158*** 0.0749(0.213) (0.0484) (0.0409) (0.126)
1.079*** 0.876*** 0.886*** 0.768***(0.302) (0.0704) (0.0498) (0.103)
0.392
266.9***(0.556)(0.466)

96

48

124
0.895

48

124

124

(8)
ACF
-0.307(0.397)1.455***(0.506)62

62

Notes: Robust standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1. The coefficients were
estimated using the balanced panel data (only firms with complete data for sales, capital, labor, intermediate
inputs and electricity for the years 2003 as well as 2009). For the textiles sector, 48 firms comply with thiscondition and 62 firms for the furniture sector. Regarding the acronyms of the table, OLS stands for
Ordinary Least Squares estimation; STCH stands for the stochastic frontier model of Battese and Coelli(1988, 1992); LP stands for the control function approach of Levinsohn and Petrin (2003); and ACF stands
for the corrected control function approach of Ackerberg et al. (2015).
Source: Authors’ calculations using data from the World Bank’s Enterprise Surveys.

Table 3: Detailed TFP Summary Statistics - Textiles
ln TFP
stats

ols

stch

2003
2009
2003
2009
2003
Mean
0.7238 0.7302 0.7242 0.7307 2.1148
Min-0.4223 -0.4825 -0.4216 -0.4818 0.8579
Median0.7211 0.6063 0.7214 0.6071 2.1362
Max
2.3769 3.0903 2.3771 3.0909 3.7925
SD
0.6743 0.7249 0.6743 0.7249 0.7008
CV
0.9317 0.9927 0.9311 0.9921 0.3314
IQR
0.7748 0.5804 0.7747 0.5804 1.0232
Skewness 0.6038 1.6597 0.6039 1.6604 0.4584
Kurtosis 2.8994 5.9985 2.8999 6.0009 2.7735
N
48
48
48
48
48

lp

acf
2009
2003
2009
2.1067 0.2661 0.3248
0.3816 -1.0217 -0.7731
1.9652 0.2257 0.1420
4.5046 1.9961 2.9229
0.7584 0.6985 0.7748
0.3600 2.6248 2.3852
0.6220 0.9477 0.6892
1.0941 0.6042 1.7746
5.0508 3.0162 6.3930
48
48
48

OLS
2003
2.64540.65552.057110.77112.24500.84861.45902.1052
7.071148

2009
3.04420.6173
1.833721.98294.2587
1.39901.0473
3.527114.9573
48

TFP
STCH
LP
2003
2009
2003
2009
2.6464 3.0458 10.7674 11.9972
0.6560 0.6177 2.3581 1.4646
2.0577 1.8353 8.4687 7.1362
10.7740 21.9959 44.3692 90.4353
2.2459 4.2622 9.2640 15.9449
0.8487 1.3993 0.8604 1.3290
1.4593 1.0478 8.4587 4.5867
2.1056 3.5277 2.1716 3.6006
7.0722 14.9608 7.6344 16.2838
48
48
48
48

ACF
2003
2009
1.7075 2.1978
0.3600 0.4616
1.2533 1.1526
7.3606 18.5958
1.5281 3.5850
0.8949 1.6312
1.1192 0.8651
2.2062 3.8240
7.4955 17.0390
48
48

Notes: TFP values were calculated using the coefficients estimated for the balanced panel data (only firms
with complete data for sales, capital, labor, intermediate inputs and electricity for the years 2003 as well as2009). Variables in logarithms are represented by lowercase letters in the left side of the table. Regarding theacronyms of the table, OLS stands for Ordinary Least Squares estimation; STCH stands for the stochastic
frontier model of Battese and Coelli (1988, 1992); LP stands for the control function approach of Levinsohn
and Petrin (2003); and ACF stands for the corrected control function approach of Ackerberg et al. (2015).
Among the TFP summary statistics, SD stands for standard deviation, CV for coefficient of variation and
IQR for interquartile range (the rest are self-explanatory).
Source: Authors’ calculations using data from the World Bank’s Enterprise Surveys.

Table 4: Detailed TFP Summary Statistics - Furnitures
ln TFP
stats

ols

Mean
Min
Median
Max
SD
CV
IQR
Skewness
Kurtosis
N

stch

2003
2009
2003
0.3200 0.4634 0.4250-1.2502 -0.8941 -1.1492
0.2980 0.3492 0.4206
2.0427 2.8996 2.1796
0.6419 0.7236 0.6482
2.0057 1.5617 1.5252
0.9491 0.8654 0.9669
0.1879 1.0482 0.2255
3.2282 4.3489 3.2481
62
62
62

lp

acf

2009
2003
2009
0.5774 3.0057 3.1170-0.7938 1.3996 1.4350
0.4775 2.9523 3.1330
2.9628 4.8805 5.0867
0.7185 0.7942 0.8111
1.2445 0.2642 0.2602
0.8439 1.2456 1.0967
1.0508 0.2415 0.1895
4.3323 2.3608 2.6708
62
62
62

2003
-1.3122-3.0222-1.4033
1.71221.0100-0.7697
1.23910.81073.543062

2009-0.7700-2.2549-0.9338
3.88901.0236-1.3294
1.0401
1.83978.7438
62

TFP
STCH
LP
2003
2009
2003
2009
2003
2009
1.7022 2.2177 1.9019 2.4714 27.7540 31.4847
0.2865 0.4090 0.3169 0.4521
4.0536
4.1995
1.3472 1.4180 1.5229 1.6120 19.1596 22.9440
7.7112 18.1667 8.8430 19.3527 131.6947 161.8498
1.3017 2.6886 1.4897 2.9343 24.5432 29.5626
0.7647 1.2124 0.7833 1.1873
0.88430.93901.2858 1.2868 1.4729 1.3708 26.3602 26.0717
2.4574 3.9953 2.5198 3.8057
1.88102.231110.4709 21.9839 10.7788 19.9914 7.0615
8.6918
62
62
62
62
62
62
OLS

ACF
2003
2009
0.5086 1.4371
0.0487 0.1049
0.2459 0.3931
5.5411 48.8604
0.8743 6.1891
1.7189 4.3065
0.3190 0.4482
4.0584 7.4383
21.2710 57.4445
62
62

Notes: TFP values were calculated using the coefficients estimated for the balanced panel data (only firms
with complete data for sales, capital, labor, intermediate inputs and electricity for the years 2003 as well as2009). Variables in logarithms are represented by lowercase letters in the left side of the table. Regarding theacronyms of the table, OLS stands for Ordinary Least Squares estimation; STCH stands for the stochastic
frontier model of Battese and Coelli (1988, 1992); LP stands for the control function approach of Levinsohn
and Petrin (2003); and ACF stands for the corrected control function approach of Ackerberg et al. (2015).
Among the TFP summary statistics, SD stands for standard deviation, CV for coefficient of variation and
IQR for interquartile range (the rest are self-explanatory).
Source: Authors’ calculations using data from the World Bank’s Enterprise Surveys.

3.2

Productivity Dispersion

Dispersion indicators such as SD, CV or IQR suggest that there is indeed significant dispersion in productivity within relatively narrowly defined sectors (textiles and furnitures).
Taking advantage of our panel data, we also analyzed whether this dispersion is increasing(divergence) or decreasing (convergence) over time by calculating growth rates and rates ofchange for SD, CV and IQR.
The results in tables 5 and 6 suggest that while SD and CV unequivocally register increases in productivity dispersion for both sectors and across all methods, IQR indicatesdecreases in dispersion for textiles and mixed evidence for furnitures.14 For the increasing
productivity dispersion message of SD and CV, however, there are numerical differences,
CV registers higher (six to seven times) rates of change in dispersion as compared to SD.
Linking these two indicators to methods of productivity estimation, ACF yields the highest
dispersion. For the case of IQR, a decrease of dispersion in textiles could be explained by
the fact that IQR does not consider the dispersion in the tails of the distribution. We argue
that IQR is an indicator that should be used with caution, in particular with small sample
sizes because it might leave out valuable observations. For instance, we confirmed previous
findings of large dispersion within the tails of the productivity distribution. Within this large
dispersion in the tails, it is the most productive firms (fourth quartile) that have even muchhigher dispersion levels and rates as compared to the least productive firms (first quartile).15
As a matter of fact, in the tails, all dispersion statistics, including IQR, display positive rates
of change in dispersion overall (in particular for the fourth quartile and the method of ACF).
It could be said that in terms of measuring rates of change in productivity dispersion, we
find an upper bound set by the CV statistic and the ACF method and a lower bound set by
14
15

We focus on ROC because they have the same units and allow comparisons across dispersion statistics.
See Appendix B where we calculated dispersion statistics and rates of change for both tails.

IQR and the LP method.
Table 5: Growth Rates and Rates of Change - Textiles
Method
OLS
STCH
LP
ACF

Growth Rates (GR)GRSD GRCV GRIQR
0.0749 0.6485 -0.2822
0.0750 0.6489 -0.2820
0.0821 0.5447 -0.4577
0.1092 0.8227 -0.2270

Rates of Change (ROC)
ROCSD ROCCV ROCIQR
0.01200.0833-0.0553
0.01200.0833-0.0552
0.01320.0725-0.10200.01730.1001-0.0429

Exponential ROC
eROCSD eROCCV eROCIQR
0.01210.0869-0.0538
0.01210.0869-0.05370.01320.0752-0.09700.01740.1052-0.0420

Notes: The exponential Rate of Change responds to the following equation eROC = eROC − 1. For ROC
and eROC, SD stands for standard deviation, CV for coefficient of variation and IQR for interquartile range.
Regarding other acronyms in the table, OLS stands for Ordinary Least Squares estimation; STCH stands forthe stochastic frontier model of Battese and Coelli (1988, 1992); LP stands for the control function approachof Levinsohn and Petrin (2003); and ACF stands for the corrected control function approach of Ackerberg
et al. (2015).
Source: Authors’ calculations using data from the World Bank’s Enterprise Surveys.

Table 6: Growth Rates and Rates of Change - Furnitures
Method
OLS
STCH
LP
ACF

Growth Rates (GR)GRSD GRCV GRIQR
0.1274 0.5854 0.0008
0.1164 0.5158 -0.0693
0.0213 0.0618 -0.0109
0.0135 1.5053 0.4048

Rates of Change (ROC)
ROCSD ROCCV ROCIQR
0.02000.07680.00010.01840.0693-0.01200.00350.0100-0.0018
0.00220.1531
0.0566

Exponential ROC
eROCSD eROCCV eROCIQR
0.02020.07980.00010.01850.0718-0.01190.00350.0100-0.0018
0.00220.16540.0583

Notes: The exponential Rate of Change responds to the following equation eROC = eROC − 1. For ROC
and eROC, SD stands for standard deviation, CV for coefficient of variation and IQR for interquartile range.
Regarding other acronyms in the table, OLS stands for Ordinary Least Squares estimation; STCH stands forthe stochastic frontier model of Battese and Coelli (1988, 1992); LP stands for the control function approachof Levinsohn and Petrin (2003); and ACF stands for the corrected control function approach of Ackerberg
et al. (2015).
Source: Authors’ calculations using data from the World Bank’s Enterprise Surveys.

4

Concluding Remarks

While there is ample evidence about large productivity dispersion within narrowly defined
sectors, the discussion about the use of different statistics to document this dispersion is lessrobust. Across studies, three dispersion statistics are commonly applied: Standard Deviation (SD), Coefficient of Variation (CV) and Interquartile Range (IQR). Sometimes, thesestatistics are used individually, interchangeably or in parallel even though they have different
methods of calculation, units of measurement and mathematical properties. Therefore, weused Brazilian data for the textile and furniture sectors over the period 2003-2009 to estimate TFP using several estimation methods: Ordinary Least Squares (OLS for short), thestochastic frontier model of Battese and Coelli (1988, 1992)(STCH for short), the control

function approach of Levinsohn and Petrin (2003)(LP for short), and the corrected control
function approach of Ackerberg et al. (2015)(ACF for short). Then, we calculated their dispersion statistics and rates of change over time to allow comparison among them. Our goal
was to evaluate differences among dispersion statistics in terms of their use, numerical values and conclusions when they are applied to the same samples under different productivity
estimation methods.
Results suggest that there are non-trivial differences among statistics when it comes toevaluate productivity dispersion at the firm level. While SD and CV suggest an increaseof productivity dispersion over time for both sectors (with CV showing six to seven times
higher rates of change than SD), IQR suggests a reduction of dispersion in textiles andmixed findings for furnitures. IQR does not consider extremes values, but when studying
dispersion only within the tails of the productivity distribution, we found that all dispersion
statistics overwhelmingly suggest the existence of even higher levels and rates of dispersion.
This may suggest that the study of productivity dispersion should go beyond the analysis of
specific statistics at some points in time and into the analysis of the dynamics for the entire
distribution given the heterogeneous behavior of rims, complex patterns of convergence andthe possible formation of multiple convergence clubs.16 Overall, the CV statistics with the
ACF method set an upper bound and IQR with LP a lower bound in terms of registering
rates of change in productivity dispersion. If dispersion statistics are to be analyzed, they
are not interchangeable and its use ought to consider the behavior in the tails of the firm
productivity distribution (particularly with small samples sizes) and the methods of TFP
estimation. Future research could add to the analysis further differences under scenarios of
converge or divergence, non-manufacturing sectors, countries’ income levels and employment
weighted productivity dispersion statistics.
References
Abramovitz, M. (1956). Resource and output trends in the United States since 1870. The
American Economic Review, 46(2):5–23.
Ackerberg, D. A., Caves, K., and Frazer, G. (2015). Identification properties of recent
production function estimators. Econometrica, 83(6):2411–2451.
Adhikari, R. and Weeratunge, C. (2007). Textiles and clothing in South Asia: Current status
and future potential. South Asia Economic Journal, 8(2):171–203.
Bartelsman, E., Haltiwanger, J., and Scarpetta, S. (2010). Cross-country and within-country
differences in the business climate. International Journal of Industrial Organization,
28(4):368–371.
Bartelsman, E. J. and Wolf, Z. (2017). Measuring Productivity Dispersion. Tinbergen
Institute Discussion Papers 17-033/VI, Tinbergen Institute.
16

See, for example, Mendez-Guerra and Gonzales-Rocha (2018).

Battese, G. E. and Coelli, T. J. (1988). Prediction of firm-level technical efficiencies witha generalized frontier production function and panel data. Journal of Econometrics,
38(3):387 – 399.
Battese, G. E. and Coelli, T. J. (1992). Frontier production functions, technical efficiency
and panel data: With application to paddy farmers in India. Journal of Productivity
Analysis, 3(1):153–169.
Canchola, J., Tang, S., Hemyari, P., Paxinos, E., and Marins, E. (2017). Correct use ofpercent coefficient of variation (cv) formula for log-transformed data. MOJ Proteomics
Bioinform, 6(4).
Caselli, F. (2005). Chapter 9 accounting for cross-country income differences. volume 1 of
Handbook of Economic Growth, pages 679 – 741. Elsevier.
Cette, G., Corde, S., and Lecat, R. (2018). Firm-level productivity dispersion and convergence. Economics Letters, 166(C):76–78.
Chen, E. K. (1997). The total factor productivity debate: Determinants of economic growthin East Asia. Asian-Pacific Economic Literature, 11(1):18–38.
Cunningham, C., Foster, L., Grim, C., Haltiwanger, J., Pabilonia, S., Stewart, J., andWolf, Z. (2018). Dispersion in dispersion: Measuring establishment-level differences in
productivity. Working papers, U.S. Census Bureau, Center for Economic Studies.
Daude, C. and Fernández-Arias, E. (2010). On the role of productivity and factor accumulation in economic development in Latin America. IDB Working Paper Series 155,
Inter-American Development Bank.
Denison, E. F. (1962). The sources of economic growth in the United States and the alternatives before us. New York: Committee for Economic Development.
Denison, E. F. (1967). Sources of postwar growth in nine western countries. The American
Economic Review, 57(2):325–332.
Denison, E. F. (1972). Classification of sources of growth. Review of Income and Wealth,18(1):1–25.
Denison, E. F. (1974). Accounting for United States economic growth, 1929-1969. Washington
D.C.: Brookings Institution.
Fernández-Arias, E. and Rodríguez-Apolinar, S. (2016). The productivity gap in Latin
America: Lessons from 50 years of development. IDB Working Paper Series 692, InterAmerican Development Bank.
Foster, L., Grim, C., Haltiwanger, J., and Wolf, Z. (2016). Firm-level dispersion in productivity: Is the devil in the details? American Economic Review, 106(5):95–98.

Foster, L., Grim, C., Haltiwanger, J. C., and Wolf, Z. (2018). Innovation, productivity
dispersion, and productivity growth. Working Paper 24420, National Bureau of Economic
Research.
Foster, L. S., Grim, C. A., Haltiwanger, J., and Wolf, Z. (2017). Macro and micro dynamics
of productivity: From devilish details to insights. Working Paper 23666, National Bureau
of Economic Research.
Griliches, Z. (1996). The discovery of the residual: A historical note. Journal of Economic
Literature, 34(3):1324–1330.
Hsieh, C.-T. and Klenow, P. J. (2009). Misallocation and manufacturing tfp in China andIndia. The Quarterly Journal of Economics, 124(4):1403–1448.
Hsieh, C.-T. and Klenow, P. J. (2010). Development accounting. American Economic Journal: Macroeconomics, 2(1):207–23.
Ibarrarán, P., Maffioli, A., and Stucchi, R. (2009). Sme policy and firms productivity in
Latin America. IZA Discussion Papers 4486, Institute for the Study of Labor (IZA).
Ito, K. and Lechevalier, S. (2009). The evolution of the productivity dispersion of firms:
a reevaluation of its determinants in the case of Japan. Review of World Economics,
145(3):405–429.
Keane, J. and te Velde, D. W. (2008). The role of textile and clothing industries in growth anddevelopment strategies. Research reports and studies, Overseas Development Institute.
Kendrick, J. W. (1956). Productivity trends: Capital and labor. The Review of Economics
and Statistics, 38(3):248–257.
Kendrick, J. W. (1961). Productivity Trends in the United States. Princeton: Princeton
University Press.
Kumbhakar, S. C. and Lovell, C. K. (2000). Stochastic Frontier Analysis. Cambridge UK:
Cambridge University Press.
Levinsohn, J. and Petrin, A. (2003). Estimating production functions using inputs to control
for unobservables. The Review of Economic Studies, 70(2):317–341.
Mendez-Guerra, C. and Gonzales-Rocha, E. (2018). A comparison of TFP estimates via
distribution dynamics: Evidence from light manufacturing firms in Brazil. MPRA Paper
87723, University Library of Munich, Germany.
Olley, G. S. and Pakes, A. (1996). The dynamics of productivity in the telecommunications
equipment industry. Econometrica, 64(6):1263–1297.
Pages, C. (2010). The Age of Productivity. Palgrave Macmillan US.
Ram, R. (2018). Comparison of cross-country measures of sigma-convergence in per-capita
income 1960-2010. Applied Economics Letters, 25(14):1010–1014.

Restuccia, D. and Rogerson, R. (2017). The causes and costs of misallocation. Journal of
Economic Perspectives, 31(3):151–74.
Schneider, F., Buehn, A., and Montenegro, C. (2010). Shadow economies all over the world:
New estimates for 162 countries from 1999 to 2007. Policy Research Working Paper 5356,
The World Bank.
Solow, R. M. (1957). Technical change and the aggregate production function. The Review
of Economics and Statistics, 39(3):312–320.
Stigler, G. J. (1947). Trends in Output and Employment. New York: National Bureau of
Economic Research.
Syverson, C. (2011). What determines productivity?
49(2):326–65.

Journal of Economic Literature,Tinbergen, J. (1942). Zur theorie der langfirstigen wirtschaftsentwicklung. Weltwirts. Archiv,(1):511–49.

Appendix
A

Additional Results

Tables here present results when the coefficients for capital and labor were estimated using all
the information available for each sector (tables presented in the main text were estimatedusing only the balanced panel data: firms with information for all main variables in theyears 2003 and 2009). The balanced panel dataset is used in the main text because thestudy of distribution dynamics focuses solely on firms contained in it. Below, outputs forsummary statistics, the production function estimation and detailed TFP summary statistics
are reported.
Summary statistics suggest a substantial reduction in the number of observations for eachsector in the second round of the survey. In addition, a large number of observations is lost
because of missing data and firms that were not surveyed in both years. In the main text,
table 1 is equivalent.
Table 7: Summary Statistics (all data) - Textiles and Furnitures
TextilesVariable
Obs
Mean Std. Dev.
Min
Sales 2003
425 5,953,067 30,100,000 46,623
Sales 2009
153 11,200,000 50,600,000 1,200
Labor 2003
424 1,007,923
4,808,694 1,154
Labor 2009
140 2,302,671 12,000,000
500
Capital 2003
408
981,848 10,100,000164
Capital 2009122 1,713,296
9,966,734
80Int. Inputs 2003 391 2,456,418 11,500,000 3,131
Int. Inputs 2009 138 3,915,659 15,200,000
200Electricity 2003
415
68,227357,922
146
Electricity 2009
149
118,190
666,85350

Max494,000,000
420,000,000
80,200,000
95,500,000
200,000,000
101,000,000
172,000,000
120,000,000
4,772,132
6,374,000

Obs
305
161
305
152
291
126
303
142
302
152

Furnitures
Mean Std. Dev.
Min
Max
9,494,395 27,700,000 88,159 261,000,000
9,234,948 29,400,000 1,200 212,000,000
1,259,605
3,523,766 12,104 41,700,000
1,363,283
4,539,689
370 40,000,000
1,101,871
3,334,586 2,087 39,100,000
1,165,737
4,797,700
170 50,000,000
4,294,554 11,600,000 15,654 95,100,000
3,915,393 11,300,000
100 82,000,000
136,468
822,907
9 13,700,000
85,878272,09602,400,000

Notes: Monetary values are expressed in 2009 local currency units and were deflated using the National
Index of Consumer Prices (INPC in Portuguese) obtained from the Brazilian Institute of Geography andStatistics (IBGE in Portuguese).
Source: Authors’ elaboration.

For the production function estimation, the coefficients of capital and labor do not significantly change when using all the information available as shown in the table below (particularly for the furniture sector). Table 2 in the main text is equivalent.

Table 8: Production Function Estimation (all data)
TextilesFurnitures
(1)
(2)
(7)
(8)
(9)
(10)
(15)
(16)
OLS
STCH
LP
ACF
OLS
STCH
LP
ACF
0.158*** 0.160*** 0.279***-0.1170.216*** 0.209*** 0.0839-0.316(0.0293) (0.0253) (0.0952) (0.277) (0.0322) (0.0272) (0.109) (0.441)
0.872*** 0.869*** 0.758*** 1.252*** 0.802*** 0.804*** 0.727*** 1.467**(0.0346) (0.0314) (0.0469) (0.405) (0.0452) (0.0315) (0.0533) (0.572)
0.653**
0.803
0.898** 313.4***(0.320)(2.376)(0.384)(0.281)VARIABLES
CapitalLabor
Constant

Observations
R-squared
Number of panelid

498
0.793

498

490

56

445

411
0.849

56

411

404

349

67
67

Notes: Robust standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1. The coefficients were
estimated using all the information available for each sector. OLS stands for Ordinary Least Squares, STCH
for the non-parametric estimation, LP for Levinshon and Petrin and ACF for Ackerberg, Caves and Frazer.
Source: Authors’ elaboration.

Tables below show detailed TFP summary statistics only for firms with information inyears 2003 and 2009, calculated using coefficients of capital and labor estimated with all theinformation available. For the textiles sector, table 9 reports no major changes in the results
for the OLS and STCH methods as compared to results obtained using only the balanced
panel dataset. However, the LP and ACF methods register changes as reflected in central
tendency indicators. This may suggest they are more sensitive to extreme values or the
inclusion/elimination of firms, particularly in small samples. On the contrary, table 10forthe furniture sector indicates changes in central tendency indicators for the OLS and STCH
methods while the LP and ACF do not drastically change. These are also additinal reasonsfor using only the balanced panel dataset in the main text. Tables 3 and 4 are equivalent.
Table 9: Detailed TFP Summary Statistics (all data) - Textiles
log TFP
stats
2003
Mean
0.7475Min-1.065Median0.7634Max
2.7347SD
0.7994IQR
0.8496CV
1.0695Skewness 0.3002
Kurtosis 3.1481
N
53

ols

stch

lp

acf

2009
2003
2009
2003
2009
2003
0.7746 0.7648 0.7915 0.8092 0.7906 -0.936-0.4739 -1.0435 -0.4643 -0.814 -0.6283 -3.4071
0.6104 0.7844 0.6241 0.7812 0.6656 -0.9206
3.1118 2.7527 3.1251 2.8247 3.036
0.95380.728
0.7995 0.7281 0.8113 0.7478 0.8741
0.6218 0.8542 0.6099 1.0176 0.614
0.98470.9398 1.0453 0.9199 1.0026 0.9458 -0.9338
1.4853 0.3013 1.4799 0.4399 1.1353 -0.0307
5.3226
3.145
5.3078 2.8744 4.2028
3.443
53
53
53
53
53
53

2009
-0.8139-2.4534-1.0411
1.96180.85150.8264-1.0462
1.29255.143153

OLS
2003
2.95490.34472.145615.40462.92391.63810.98952.35868.856553

2009
3.14230.6226
1.841222.461
4.193
1.1686
1.3344
3.529115.4127
53

TFP
STCH
LP
2003
2009
2003
2009
3.007
3.1948 3.1965
3.151
0.3522 0.6286 0.4431 0.5335
2.1911 1.8666
2.184
1.945815.6856 22.7614 16.8552 20.8222
2.9763 4.2563 3.2394 3.7783
1.6782 1.1629 2.1582 1.1312
0.9898 1.3323 1.0134 1.1991
2.3601 3.5235 2.2953 3.0961
8.8671 15.3727 8.4984
12.91
53
53
53
53

ACF
2003
2009
0.5704 0.7415
0.0331 0.086
0.3983 0.3531
2.5956 7.1123
0.5704 1.2493
0.3796 0.3505
1
1.68492.078 4.0331
6.7708 19.2928
53
53

Notes: TFP values were calculated with the coefficients estimated using all the information available for eachsector. Variables in logarithms are represented by lowercase letters in the left side of the table. OLS stands
for Ordinary Least Squares, STCH for Stochastic, LP for Levinsohn and Petrin, and ACF for Ackerberg,
Caves and Frazer. Among the TFP summary statistics, Std. Dev. stands for standard deviation, IQR forinterquartile range and CV for coefficient of variation (the rest are self-explanatory).
Source: Authors’ elaboration.

Table 10: Detailed TFP Summary Statistics (all data) - Furnitureslog TFP
stats
Mean
Min
Median
Max
SD
IQR
CV
Skewness
Kurtosis
N

ols

stch

2003
2009
2003
0.8196 0.9164 0.8797-0.7473 -0.4544 -0.6888
0.8170 0.8217 0.8665
2.4680 3.2205 2.5399
0.6506 0.7326 0.6527
0.9463 0.8947 0.9650
0.7938 0.7994 0.7420
0.0279 0.8486 0.0389
2.9525 3.7169 2.9547
62
62
62

lp

2009
2003
2009
0.9792 3.4255 3.5145-0.3980 1.8181 1.6748
0.8894 3.3495 3.5562
3.2573 5.2802 5.5392
0.7307 0.8152 0.8489
0.8990 1.2939 1.1799
0.7462 0.2380 0.2415
0.8395 0.2196 0.0871
3.6777 2.2856 2.6391
62
62
62

acf
2003
-1.3597-3.0907-1.4497
1.69681.02031.2414-0.7504
0.80953.543562

2009-0.8096-2.3395-0.96373.90961.03531.0349-1.2789
1.8361
8.7633
62

TFP
STCH
LP
2003
2009
2003
2009
2003
2009
2.7973 3.4514 2.9762 3.6638 42.8212 47.8985
0.4736 0.6348 0.5022 0.6717
6.16005.33762.2640 2.2747 2.3787 2.4341 28.5120 35.0334
11.7988 25.0418 12.6788 25.9806 196.4058 254.4846
2.0205 3.8404 2.1658 4.0259 38.1145 45.7397
2.2415 2.1101 2.4135 2.2802 42.5022 39.9518
0.7223 1.1127 0.7277 1.0988
0.8901
0.95492.1143 3.5162 2.1373 3.4279
1.75112.24618.8733 18.0800 8.9944 17.2712 6.2442
9.0308
62
62
62
62
62
62
OLS

ACF
2003
2009
0.4918 1.4324
0.0455 0.0964
0.2347 0.3815
5.4565 49.8778
0.8579 6.3160
0.3051 0.4283
1.7443 4.4094
4.0893 7.4599
21.5625 57.6768
62
62

Notes: TFP values were calculated with the coefficients estimated using all the information available for eachsector. Variables in logarithms are represented by lowercase letters in the left side of the table. OLS stands
for Ordinary Least Squares, STCH for Stochastic, LP for Levinsohn and Petrin, and ACF for Ackerberg,
Caves and Frazer. Among the TFP summary statistics, Std. Dev. stands for standard deviation, IQR forinterquartile range and CV for coefficient of variation (the rest are self-explanatory).
Source: Authors’ elaboration.

B

Productivity Dispersion in the Distribution’s Tails

We estimated productivity dispersion statistics for the 25th (first quartile) and 75th (fourth
quartile) percentile of each distribution for all TFP estimation methods.
Table 11: Detailed TFP Summary Statistics for the Tails of the Distribution - Textiles
OLS
Stats
Mean
Min
Median
Max
SD
CV
IQR
skewnesskurtosis
N

STCH

LP

2003

2009

2003

2009

25th
75th
0.9594 5.6055
0.6555 2.7206
0.9340 4.7176
1.1765 10.7711
0.1610 2.7277
0.1678 0.4866
0.1971 4.3101-0.4284 0.6841
2.4166 2.1275
12
12

25th
75th
1.0885 7.4627
0.6173 2.4815
1.1175 3.7100
1.2911 21.9829
0.2022 6.9659
0.1857 0.9334
0.2702 6.9437-1.0138 1.3212
3.3688 3.1989
12
12

25th
75th
0.9597 5.6076
0.6560 2.7228
0.9342 4.7201
1.1768 10.7740
0.1610 2.7292
0.1678 0.4867
0.1974 4.3137-0.4276 0.6842
2.4141 2.1270
12
12

25th
75th
1.0890 7.4671
0.6177 2.4823
1.1183 3.7106
1.2921 21.9959
0.2022 6.9723
0.1857 0.9337
0.2704 6.9472-1.0147 1.3215
3.3703 3.1991
12
12

ACF
2003
2009
25th
75th
25th
75th
25th
75th
25th
75th
3.6868 22.7329 3.9198 29.1645 0.5915 3.7111 0.7091 5.7085
2.3581 13.3840 1.4646 9.9923 0.3600 1.8626 0.4616 1.8167
3.8838 15.8784 3.9569 15.4335 0.6399 3.1652 0.7291 2.3630
4.7388 44.3692 5.3108 90.4353 0.6973 7.3606 0.8588 18.5958
0.7154 11.3918 1.0282 25.3941 0.1066 1.8988 0.1399 6.0583
0.1940 0.5011 0.2623 0.8707 0.1802 0.5117 0.1972 1.0613
1.1599 15.4098 1.2577 22.5510 0.1581 3.1906 0.2617 4.5869-0.3438 0.9103 -0.9386 1.5195 -0.9645 0.7380 -0.3392 1.4909
2.0208 2.3458 3.8136 4.0038 2.7200 2.1524 1.6778 3.5873
12
12
12
12
12
12
12
12
2003

2009

Notes: TFP values were calculated using the coefficients estimated for the balanced panel data (only firms
with complete data for sales, capital, labor, intermediate inputs and electricity for the years 2003 as well as2009). The 25th indicates that data is provided only for the first quartile and 75th for the fourth quartile only.
Regarding the acronyms of the table, OLS stands for Ordinary Least Squares estimation; STCH stands forthe stochastic frontier model of Battese and Coelli (1988, 1992); LP stands for the control function approachof Levinsohn and Petrin (2003); and ACF stands for the corrected control function approach of Ackerberg
et al. (2015). Among the TFP summary statistics, SD stands for standard deviation, IQR for interquartile
range and CV for coefficient of variation (the rest are self-explanatory).
Source: Authors’ calculations using data from the World Bank’s Enterprise Surveys.

Table 12: Detailed TFP Summary Statistics for the Tails of the Distribution - Furnitures
Stats
Mean
Min
Median
Max
SD
CV
IQR
skewnesskurtosis
N

OLS
STCH
LP
2003
2009
2003
2009
2003
2009
25th
75th
25th
75th
25th
75th
25th
75th
25th
75th
25th
75th
0.6441 3.3353 0.7484 5.0597 0.7114 3.7601 0.8443 5.6088 8.1429 62.2579 8.9753 70.3704
0.2865 2.0979 0.4090 2.2220 0.3169 2.3766 0.4521 2.4049 4.0536 37.0110 4.1995 39.1444
0.6880 2.7051 0.7733 3.5288 0.7619 3.0679 0.8555 3.9041 8.3163 51.5461 9.4787 56.2534
0.8121 7.7112 0.9352 18.1667 0.9037 8.8430 1.0342 19.3527 10.6508 131.6947 13.0727 161.8498
0.1513 1.5761 0.1347 4.1454 0.1653 1.8310 0.1457 4.4853 2.0516 23.7691 2.7494 33.9243
0.2350 0.4725 0.1799 0.8193 0.2324 0.4869 0.1726 0.7997 0.2519
0.38180.30630.48210.1892 0.9286 0.1625 4.1296 0.1908 1.1156 0.1823 4.8444 3.0170 28.3175 3.3351 41.6356-1.1056 1.7331 -0.9411 2.1297 -1.1205 1.7227 -1.1762 1.9672 -0.5865
1.5951-0.3535
1.37093.2778 4.9089 3.6607 7.2871 3.3279 4.8899 4.3328 6.5130 2.3497
5.47382.20914.2414
16
16
16
16
16
16
16
16
16
16
16
16

ACF
2003
2009
25th
75th
25th
75th
0.0938 1.3997 0.1818 4.6208
0.0487 0.4491 0.1049 0.6931
0.0940 0.8369 0.1993 1.1868
0.1301 5.5411 0.2450 48.8604
0.0254 1.3896 0.0530 11.8801
0.2712 0.9928 0.2917 2.5710
0.0380 1.1145 0.0986 1.3454-0.3993 1.9813 -0.3389 3.5326
2.1238 6.1415 1.5056 13.6816
16
16
16
16

Notes: TFP values were calculated using the coefficients estimated for the balanced panel data (only firms
with complete data for sales, capital, labor, intermediate inputs and electricity for the years 2003 as well as2009). The 25th indicates that data is provided only for the first quartile and 75th for the fourth quartile only.
Regarding the acronyms of the table, OLS stands for Ordinary Least Squares estimation; STCH stands forthe stochastic frontier model of Battese and Coelli (1988, 1992); LP stands for the control function approachof Levinsohn and Petrin (2003); and ACF stands for the corrected control function approach of Ackerberg
et al. (2015). Among the TFP summary statistics, SD stands for standard deviation, IQR for interquartile
range and CV for coefficient of variation (the rest are self-explanatory).
Source: Authors’ calculations using data from the World Bank’s Enterprise Surveys.

Based on these results, the tables below present the growth rates and rates of change inproductivity dispersion statistics for both sectors.

Table 13: Growth Rates and Rates of Change for the Tails of the Distribution - Textiles
Growth Rates (GR)Method
OLS
STCH
LP
ACF

25th
GRSD GRCV
0.2560 0.1071
0.2557 0.1067
0.4373 0.3518
0.3123 0.0945

GRIQR
0.37090.36980.08430.6547

75th
GRSD GRCV
1.5537 0.9182
1.5547 0.9186
1.2292 0.7376
2.1905 1.0741

Rates of Change (ROC)
GRIQR
0.61100.61050.46340.4376

ROCSD
0.03800.03800.06050.045325th
ROCCV
0.01700.01690.05020.0151ROCIQR
0.0526
0.05240.01350.0839ROCSD
0.15630.15630.13360.045375th
ROCCV
0.1086
0.1086
0.09210.1216

Exponential ROC
ROCIQR
0.07950.07940.06350.0605eROCSD
0.03870.03870.06230.046325th
eROCCV
0.01710.01700.05150.0152

eROCIQR
0.05400.05380.01360.0876eROCSD
0.16910.16920.14290.046375th
eROCCV
0.11470.1147
0.09650.1293

eROCIQR
0.08270.08270.06550.0624

Notes: The exponential Rate of Change responds to the following equation eROC = eROC − 1. For ROC
and eROC, SD stands for standard deviation, CV for coefficient of variation and IQR for interquartile range.
Regarding other acronyms in the table, OLS stands for Ordinary Least Squares estimation; STCH stands forthe stochastic frontier model of Battese and Coelli (1988, 1992); LP stands for the control function approachof Levinsohn and Petrin (2003); and ACF stands for the corrected control function approach of Ackerberg
et al. (2015).
Source: Authors’ calculations using data from the World Bank’s Enterprise Surveys.

Table 14: Growth Rates and Rates of Change for the Tails of the Distribution - Furnitures
Method
OLS
STCH
LP
ACF

Growth Rates (GR)
25th
75th
GRSD GRCV GRIQR GRSD GRCV
-0.1102 -0.2343 -0.1412 1.6302 0.7338-0.1185 -0.2573 -0.0444 1.4497 0.6423
0.3401 0.2158 0.1054 0.4272 0.2627
1.0853 0.0753 1.5923 7.5493 1.5897

Rates of Change (ROC)
GRIQR
3.4472
3.34240.47030.2072

ROCSD-0.0195-0.02100.04880.122525th
ROCCV-0.0445-0.04960.03260.0121ROCIQR-0.0254-0.0076
0.01670.1588ROCSD
0.16120.14930.05930.122575th
ROCCV
0.09170.08270.03890.1586

Exponential ROC
ROCIQR
0.24870.24470.06420.0314eROCSD-0.0193-0.02080.05000.130325th
eROCCV-0.0435-0.0484
0.03310.0122

eROCIQR-0.0251-0.0075
0.01680.1721eROCSD
0.17490.1611
0.06110.130375th
eROCCV
0.09610.08620.03960.1719eROCIQR
0.28240.27730.06640.0319Notes: The exponential Rate of Change responds to the following equation eROC = eROC − 1. For ROC
and eROC, SD stands for standard deviation, CV for coefficient of variation and IQR for interquartile range.
Regarding other acronyms in the table, OLS stands for Ordinary Least Squares estimation; STCH stands forthe stochastic frontier model of Battese and Coelli (1988, 1992); LP stands for the control function approachof Levinsohn and Petrin (2003); and ACF stands for the corrected control function approach of Ackerberg
et al. (2015).
Source: Authors’ calculations using data from the World Bank’s Enterprise Surveys.