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Exporting and productivity as part of thegrowth process: Causal evidence from adata-driven structural VAR

Tommaso Ciarli aAlex Coad b
Alessio Moneta c
SPRU, University of Sussex, Brighton, UK.
CENTRUM Católica Graduate Business School (CCGBS) andPontificia Universidad Católica del Perú (PUCP), Lima, Perú.
cInstitute of Economics and Department EMbeDS, Scuola Superiore Sant’Anna, Pisa, Italy.
ab

2019/39

December 2019
ISSN(ONLINE) 2284-0400

Does Exporting Cause Productivity Growth?
Evidence from a Structural VAR Analysis∗
Tommaso Ciarli†Alex Coad‡

Alessio Moneta§

June 2022
Abstract
Does exporting more increase firm productivity? Or is it only firms that manage to increase productivity that increase their sales in the export market?
This paper provides new empirical evidence on the causal relation between
trade and productivity adopting a structural vector autoregressive analysis
combined with identification algorithms in the machine learning literature.
We focus on a well-studied country (Chile) and on already-exporting firms(intensive margin). We identify the contemporaneous and lagged causal
structure between firm productivity and export growth using two different
machine learning algorithms based on Independent Components Analysis(ICA), which exploit the non-Gaussian distribution of the data to recover the
independent structural shocks that drive the observed variables. Our findings
show that, for Chilean firms, productivity growth causes export growth in thesame year, but not the other way around. Export growth also has no causal
effect on TFP growth in subsequent years. To increase sales in the foreign
market, firms must first increase productivity. The increased presence in theforeign market does not contribute to such productivity growth.
JEL Classification: L21; D24; F14; C22
Keywords: Productivity; Exporting; Learning-by-exporting; Causality; Structural VAR; Independent Component Analysis∗

We are grateful to Sebastian Vergara for sharing with us his data and variable construction
pre-2003, and for helpful initial discussions on the construction of the 2001-2007 variables. We
thank Matté Hartog and Cristina Chaminade for insightful discussions that helped improving thepaper. We thank conference/seminar participants at Carnegie Mellon University, University ofJena, Queen Mary University of London, Free University of Berlin, University of Kassel, University of Rovira i Virgili, EMAEE 13 (Nice), and Globelics 15 (Havana) for useful comments.
Thanks also to Doris Entner for sharing the R code of the LiNG algorithm with us. The usual
caveat applies.
†
UNU-MERIT, Maastricht & SPRU, University of Sussex, ciarli@merit.unu.edu‡
Waseda University, Shinjuku, Tokyo, Japan, alex.coad@waseda.jp§
Corresponding Author. Institute of Economics and EMbeDS, Sant’Anna School of Advanced
Studies, Piazza Martiri della Libertà 33, 56127 Pisa, Italy. Email: a.moneta@santannapisa.it

11

Introduction

This paper investigates the still-unresolved causal relationship between exportingand productivity. Do firms learn from trade? Or is exporting a game that only
the best firms can play, and once they export there is little scope for productivity
growth? Since the 1990s economists have used micro data to study how firms takeadvantage from exporting, in both low income and high income countries (see e.g.
Cirera et al., 2012). The seminal work of Bernard and Jensen (1995) started a prolific field of enquiry, using firm and plant survey data from a large number of different countries. The results from this literature relatively unambiguously indicatethat exporting firms, on average, do better than non-exporting firms on different
performance measures.1 However, Bernard and Jensen (1999) subsequently highlighted that, in order to enter the global market, firms need to be more productive
than average. On the one hand, firms need to increase productivity before entering
the export market – because of trade costs, stronger competition, and investments
required to increase the scale. On the other hand, firms may increase productivity
while exporting – because of learning from foreign buyers, use of excess capacity,or stronger competition.2 Which comes first, the chicken (growth of exports) or
the egg (productivity growth)?
We focus on Chile, a small country, with a small domestic market, an open
economy, a well-tested firm survey, and a large literature on the relation between
exporting and productivity (e.g. Alvarez and Crespi, 2007; Alvarez and López,2005, 2008; López, 2009; Pavcnik, 2002).
Two contributions help to distinguish our work from previous attempts to disentangle the causal relations between firm productivity and exporting. First, weapply a class of methods for causal inference – linear non-Gaussian vector autoregression models – which bring together recent results from both the timeseries econometrics and machine learning literatures. Our methodology exploits
the non-Gaussian feature of the data to recover the set of independent structural
shocks that drive the movements of the observed variables. The identification of
the shocks, and the manner in which these are linearly mixed to form the observed variables, allow us to arrange the variables in a causal ordering. The causal
structure is identified through two different ICA-based3 algorithms, which are1

See for example surveys by Greenaway and Kneller (2007); International Study Group on
Exports and Productivity (2008); Wagner (2007).
2
Increases in exports may have implications for firm productivity through a number of mechanisms discussed in the literature: larger number of clients and/or markets from which the firm
could learn; increased technology/knowledge transfer from buyers; greater incentives to increase
productivity and compete in markets with higher quality; learning about new market opportunities; less vulnerability and dependence on a single market; having a larger scale of output; andimproved utilisation of existing production capacity.
3
Independent Component Analysis.

2based on different assumptions. The first is the LiNGAM (Linear Non-Gaussian
Acyclic Model) algorithm, which assumes acyclicity – i.e. that there are no causal
feedback loops that take place within the period of observation (e.g. within theyear), although lagged causal effects can go in both directions between variables.
The LiNGAM estimator has already been featured in previous econometric work
(e.g. Moneta et al., 2013; Brenner et al., 2018; Brancaccio et al., 2020). The second one is the LiNG algorithm (Lacerda et al., 2012), which – to our knowledge– has not yet been applied to economics research questions. The LiNG estimator relaxes LiNGAM’s acyclicity condition, and allows for simultaneous causal
feedback loops between variables even within the period of observation.
The second contribution is that we focus on the small number of firms (Bernard
et al., 2007) that have already accessed the export market (intensive margin), andwe analyse changes in export and productivity, rather than levels. Focusing on export growth rather than on entry, we can ignore the problem of self-selection into
exporting,4 and focus on the identification of whether (i) firms that export more
improve their productivity or (ii) the other way round: firms must improve theirproductivity in order to be able to export more.
Our main results show that, within a time period, export growth follows growth
in productivity, and not the other way round. There is no evidence of export
growth causing productivity growth. Export growth seems to be driven by anincrease in employment, which has a contemporaneous negative effect on productivity. This means that Chilean firms in the foreign market need to first improvetheir productivity (while also growing in size), in order to increase exports.
Over time, there is a weak positive impact of productivity growth on export
growth with one year lag, but the result is not robust, and is not significant whenusing the LiNG estimator that relaxes the acyclicity condition and allows for simultaneous causal feedback loops between variables.
Our result about the direction of the contemporaneous causal relationship between productivity growth and export growth is robust to a number of checks inwhich we vary indicators of productivity, sub-samples (looking at different sectors, following various criteria), and methods of estimation of the VAR model.
Our results are relevant for industrial and trade policy. They seem to suggestthat exporting firms in a small economy, which has been open for a few decades,
do not benefit a lot from increasing sales in the foreign market, at least within
two years. This might be because most of these firms operate in non-technology
intensive industries (e.g. Wang et al., 2021), where most competition is basedon price (Garcia-Marin and Voigtländer, 2019). Small changes in relative labourcosts can affect productivity (and firm size) and exporting. Whether these changes
4

As summarised by Park et al. (2010, p. 822): “conceptually, the fundamental problem is thatnonexporters are an inappropriate counterfactual for exporters.”3bring about a longer term effect on technological learning and upgrading is left for
future research.
Whether results depend or not on industry specialisation, they suggest thatpolicies that support firm productivity, are needed, because firms cannot rely
solely on learning from the foreign market to increase productivity and therefore
increase exports.
Our paper contributes to the literature attempting to identify the effect of firmchanges in exporting on changes in productivity. This is a large literature. For
example, Park et al. (2010) find that firm specific export shocks have a positiveeffect on productivity growth in China. To identify the effect of exports, they
instrument exporting growth with shocks in the currency exchange rate of thedestination country. Berman and Rebeyrol (2010), using data on French firms,
find that entry and persistence in the export market has no significant effect on
productivity, although they find positive effects of export growth on subsequent
productivity growth. More generally, we also contribute to the literature that has
focused on export intensity, rather than entry in the export markets (e.g. Castellani,
2002; Fernandes and Isgut, 2005; Antolín et al., 2013; De Loecker, 2013; Dalgiç
et al., 2021).
In the rest of the paper we first discuss the heterogeneous evidence on exporting and productivity (Section 2). Next, Section 3 discusses the methodologicalcontribution. Section 4 presents the dataset and discusses the measurement of
productivity in this paper. We then present and discuss the results in Section 5. In
Section 6 we discuss implications for policy and future research.

2

The mixed and heterogeneous relation between exporting and firm productivity

A large applied literature in trade has attempted to identify the direction of causality between exports and growth at the firm level. Wagner (2007) conducts a systematic literature review and shows that: (i) exporting firms are always more productive than non-exporters; (ii) exporters are often more productive even before
entering the export market; (iii) results on learning-by-exporting (LBE) are mixed,
and when matching estimators are used no significant effect of exporting emerges;and (iv) firms that exit the export market tend to reduce productivity. In a parallel review of empirical literature, Greenaway and Kneller (2007) also report that
results on LBE are not conclusive. Similar inconclusive results on LBE are foundwhen analysing the service sector (Wagner, 2012).
Mixed results are confirmed also by studies that make an attempt to better
control for causal relations using matching estimators. On the one hand, Girma4

et al. (2004) introduce matching estimators to this strand of literature and finda significant positive effect of exporting on productivity for UK manufacturingfirms. Tsou et al. (2008) analyze a census of Taiwanese firms repeated for threedifferent periods, and find that firms staying in the export market experience alarger increase in productivity than non-exporters. Similarly, Baldwin and Yan(2012) find that, following changes in the real exchange rate, firms that are alreadyin the export market experience a relatively larger gain in productivity than new
entrants. Manjón et al. (2013) find evidence of LBE for Spanish manufacturingfirms.
On the other hand, several studies do not find a significant positive effect ofexporting on productivity. No sustained effect of learning from exporting is observed by Mukim (2011) on Indian firms, by Arnold and Hussinger (2005) on
German firms, by Damijan and Kostevc (2006) on Slovenian firms, and by Eliasson et al. (2012) for small and medium firms. The International Study Group on
Exports and Productivity (2008) use panel data from 14 different countries, andfind no evidence of LBE.
Only a handful of studies investigate the exporting-productivity nexus using
growth rates rather than levels. Park et al. (2010) use exogenous shocks on the
demand for exporting firms (exchange rates shocks), and find evidence of LBE for
Chinese firms, especially when the destination is a high income country. Berman
and Rebeyrol (2010), using data on French firms, find that entry and persistencein the export market has no significant effect on productivity. In contrast, theyfind positive effects of export growth on subsequent productivity growth. They
explain this effect by referring to how exporting growth strengthens the incentives
for firms to innovate as well as by enhancing access to finance for investment.
Fernandes and Isgut (2005) focus on the level of exports (“export experience”),
rather than on export participation, finding a positive effect of LBE for Colombian
firms exporting to high income markets.
To explain such heterogeneity in findings, the literature has moved on to study
the heterogeneous conditions under which a firm’s exporting may positively affectits productivity.
One explanation focuses on export destination: firms may learn more fromexporting to more advanced countries. Wagner (2012) reports that the relation between exporting and productivity is influenced by export destination for a numberof papers included in his review. Similar results were documented by Fernandes and Isgut (2005) for Colombian exporting firms and by Dalgiç et al. (2021)
for Turkish firms. More relevant to our paper, Martins and Yang’s (2009) metaanalysis on LBE finds that, relative to industrialised countries, firms in developing
countries enjoy a stronger impact of exporting on productivity. Focusing on Chile,
a middle income country in the period of our analysis, we partially complement
existing research with valuable new evidence (we do not have information on ex5

port destination).
A second explanation focuses on firms’ ability to learn, by building complementary intangible assets. This literature suggests that specific investments may
be a necessary condition to benefit from exporting. Among others, decisions to export may complement decisions to innovate (Ito and Lechevalier, 2010; Aw et al.,2011). For instance, Dai and Yu (2013) find that firms with higher R&D investment enjoy significant improvements in productivity after exporting, contrary tofirms that do not invest before in R&D. Aw and Song (2013) finds that South Korean firms that only export, or only invest in R&D, do not experience the same
increase in productivity as firms that do both. Serrano and Myro (2019) documents a different mechanism for Spanish firms, more relevant to our paper: theytend to increase in firm size (in terms of sales and employees), and increase R&D
expenditure after they enter the export markets. An implication of these papers
for our results is that investments (e.g. in intangible complementary assets) may
be simultaneously driving productivity and exporting.
A third explanation, particularly relevant to our study, focuses on firm size.5(Damijan et al., 2010) find that larger firms benefit more from exporting. Firms
with a higher export intensity (with respect to domestic sales) also tend to profit
more from exporting (Girma et al., 2004).
A fourth explanation focuses on measure and methods. For instance, De Loecker(2013) proposes a method for computing productivity that includes exporting in
the firm decision (and therefore as a determinant of productivity) and finds significant LBE for Slovenian firms. Garcia-Marin and Voigtländer (2019) observe alack of growth of revenue productivity in the years after plants start to export, butshow that this can be decomposed into a decrease in marginal costs which occurs
alongside a commensurate decrease in prices. Hence, efficiency gains appear to betransmitted to consumers via lower prices, rather than leading to higher markups.
This reconciles the two suggestions that plants enjoy efficiency gains after starting
to export, but that these efficiency gains do not translate into productivity growthwhen this latter is measured in terms of revenue productivity.
The first three explanations consider time to be an important factor, as learning may take time, which may differ across sectors (Wang et al., 2021) and firms.
Using measures of learning, Crespi et al. (2008) find evidence of LBE with a lag.
However, Segarra-Blasco et al. (2020) find that only in more innovative countries firms benefit from a longer learning time, whereas firms in less innovative
countries learn more from their local peers.
To summarize, therefore, we highlight three points. First, firms tend to invest
in order to improve productivity before they increase their sales in a more com5

The literature has also investigated the role of firm age (Alvarez and López, 2005; Girma
et al., 2004; Fernandes and Isgut, 2005), although this dimension is not explored in our paper.

6

petitive foreign market. In this case, we should observe an increase in investment
and productivity that precedes growth in exports (or export intensity). Second,
while some mechanisms – such as market size, firm size, vulnerability, and useof existing capacity – may have an immediate effect on firm productivity, othermechanisms – such as learning from buyers, and from markets – may take one
or more years to have a visible effect on productivity growth. Third, considering that most existing studies use yearly data, we should acknowledge that within
the same year a firm takes many decisions. Firms may implement measures toincrease productivity and export simultaneously, as complementary activities.
Combining contemporaneous and lagged firm decisions in relation to employment, domestic sales, and exporting, our paper makes an important contribution
in determining the causal relation between growing exports and productivity in a
middle income country.

3

Econometric method

3.1

VAR and SVAR models

Consider the general structural vector autoregressive (SVAR) model
yit = Byit +pXΓ` yi,t−` + εit ,

(1)

`=1

in which yit is a vector of k variables, observed for firm i (i = 1, . . . , N ) in yeart (t = 1, . . . , T ); B and Γ` (` = 1,) are k × k matrices of structural coefficients;and εit is a vector of white-noise structural disturbances (shocks). The model inequation (1) generalises the standard SVAR model because it can be applied topanel data. However, differently from other formulations of panel VAR models(see, e.g., Breitung, 2005), in which both T and N are large, the matrices of coefficients do not contain the (firm) index i. In fact, since we deal with T relatively
small with respect to N , we assume that structural-causal relations are stable bothcross-sectionally (across firms) and over time.
A reduced-form VAR model is obtained by rearranging (1):
yit =

p
X
(I − B)−1 Γ` yi,t−` + (I − B)−1 εit ,

(2)

`=1

which can be rewritten as
yit =

p
X

A` yi,t−` + uit ,

`=1

7

(3)

where A` = (I − B)−1 Γ` (for ` = 1, . . . , p) and uit = (I − B)−1 εit . Differently from equation (1), equation (3) can be estimated without involving potential
problems of endogeneity. Notice, however, that the reduced-form VAR model in(3) does not allow estimating the matrix of instantaneous causal effects B, and— importantly — nor does it allow to properly estimate the matrices of lagged
causal effects Γ1 , . . . , Γp . But knowledge of the matrix B is sufficient to recoverΓ` , having estimated A` (for ` = 1, . . . , p) from equation (3) .
Let us call Γ0 = (I − B) and we assume it to be invertible. The matrix
Γ0 relates the k-dimensional vector of shocks εit to the k-dimensional vector of
reduced-form residuals uit . This why Γ0 is also known as the unmixing matrixand Γ−10 as the mixing matrix. We have
uit = Γ−10 εit .

(4)

Our approach to identify the structural model (1) is based on independent component analysis (ICA), which is a probabilistic method for finding linear combinations of the data that are maximally independent (Hyvärinen, 2013).
In our empirical analysis, yit will comprise four variables, and we will estimate
both one-lag and two-lag models. In keeping with previous applications of VARs
and SVARs on panel data of firm growth rates (e.g., Coad et al., 2011; Moneta
et al., 2013), we pool together observations under the assumption that there are no
significant firm-specific time-invariant component (‘fixed effects’) in the growth
rates of these series. This assumption that firms undergo similar structural patterns in their growth process seems plausible, because we are focusing on growth
rates rather than levels, and any firm-specific components affecting levels will already have been differenced out. As a consequence, we can simplify notation byomitting henceforth the subscript i.

3.2

Identification strategy

As in Moneta et al. (2013), our identification strategy is based on a method inwhich we first estimate the reduced-form VAR modelyt = A1 yt−1 + . . . + Ap yt−p + ut

(5)

and then we search for the ‘unmixing’ matrix Γ0 such that
Γ0 yt = Γ0 A1 yt−1 + . . . + Γ0 Ap yt−p + Γ0 ut(6)

In more compact form, we have:Γ0 yt = Γ1 yt−1 + . . . + Γp yt−p + εt ,8(7)where Γ` = Γ0 A` for ` = 1, . . . , p. Assuming that the k elements of εt are
mutually independent and (at least k − 1 of them) non-Gaussian, the method isable to identify Γ0 and, consequently, (having estimated all coefficient matrices
of equation 5) all the coefficient matrices of equation (7). The underlying idea is
to search for a mixture of the elements of ut such that the resulting components
are minimally dependent and maximally non-Gaussian (cfr. Hyvärinen and Oja,
2000; Hyvärinen et al., 2001). Since there are different measures of statisticaldependence and non-Gaussianity, and different optimization methods, there arecorrespondingly different ICA algorithms. In our application we use FastICA,
which is a fixed-point algorithm for maximum likelihood estimation and measures
non-Gaussianity with an approximation of negentropy (Hyvärinen and Oja, 2000).
Regardless which algorithm is used, ICA leaves undetermined the scale, sign,and order of the latent sources or structural shocks. In other words, Γ−10 is identified up to the post multiplication by CD, where C is a permutation matrix6 andD is a diagonal matrix with non-zero diagonal elements (Eriksson and Koivunen,
2004; Lanne et al., 2017; Gouriéroux et al., 2017). Further steps are needed to
fully identify Γ0 and εt . We adopt here two different ICA-based search methods
to identify the shocks and more generally the structural VAR model. The first was
proposed by Shimizu et al. (2006) and named LiNGAM (for linear, non-Gaussian,acyclic model), and when applied to VAR models, it is known as VAR-LiNGAM(Hyvärinen et al., 2008; Moneta et al., 2013; Coad et al., 2017). The second was
proposed by Lacerda et al. (2012) and was named LiNG (for linear, non-Gaussianmodel). To our knowledge, this is the first time that the LiNG algorithm has
been applied either in a VAR context (i.e. “VAR-LiNG”) or in the discipline of
economics. The algorithms VAR-LiNGAM and VAR-LiNG are described in theframes below.
Both algorithms, after having estimated the reduced-form VAR (step 1), run
an ICA algorithm (e.g., FastICA) on the estimated residuals obtaining a mixing
matrix P (≡ Γ−1
ICA ) which is able to generate a vector of independent components(step 2). But the order and scaling of these independent components is arbitrary.
Algorithm 1 (VAR-LiNGAM) solves the order indeterminacy by assumingthat the underlying causal structure among the contemporaneous variables contains no cycle (in other words can be represented by a directed acyclic graph).
This assumption, jointly with the fact that the diagonal elements of Γ0 must be
nonzero (and should be normalised to one), ensures that if we find an orderingof the components ε̂1t , . . . , ε̂kt (output of the ICA algorithm) that produces a correspondence with the data ε̂t = Γ̃0 ût such that Γ̃0 has non-zero elements in its
6

A permutation matrix is a square matrix in which exactly one entry in each row and column
is equal to 1 and all other entries are 0 (see, e.g., Horn and Johnson, 2012).

9main diagonal, this ordering must be the correct one.7 Exploiting this fact, step 3
is devoted to find the permutation of the matrix ΓICA generating the independent
components from ût which produces a correct matching between structural andreduced-form shocks. Step 4 solves the scale indeterminacy. This is simply done
by normalising the rows of Γ̃0 (the correctly row-permuted version of ΓICA ), sothat all diagonal elements equal unity. Let Γ̂0 denote this row normalised matrix
and B̂ = I − Γ̂0 (step 5). Since it is assumed that there are no causal loops or feedback, there is a permutation (applied equally to columns and rows) of Γ̂0 whichshould be lower triangular. The same can be said for Γ̂−10 and B̂. In practice,
however, even under the correct assumptions, these matrices are not exactly lower
triangular, because the ICA algorithm applied to finite data sets yields estimateswith errors. Therefore step 6 searches for an approximate lower triangularity.
This step is not essential for the sake of estimation of the structural model and is
run only for identifying the contemporaneous causal order. Step 7 estimates thematrices of the lagged coefficients of the structural model.
Algorithm 2 (VAR-LiNG) solves the order indeterminacy by simply exploiting the assumption that Γ0 has a zeroless diagonal, which is valid in the structural
VAR model by construction. Step 3 tests which entries of the ΓICA are significantly different from zero. This is done through the following bootstrap procedure: resampling ût and applying ICA to each s = 1, . . . , S bootstrap samples,(s)(s)
one obtains S unmixing matrices ΓICA . Each ΓICA is row-permuted (with a possiblee(s) to match ΓICA (the row-signed permutation
change of sign in each row) in a ΓICAe(s) − ΓICA ) is minimised). Hence, one
is chosen so that the Frobenius norm of (ΓICA
obtains an empirical distribution for each entry of ΓICA , and, therefore, a nonparametric quantile test to decide whether 0 is an outlier for each entry. Step 4 finds
the permutation of the matrix ΓICA which produces a matrix Γ̃0,j which has a zeroless diagonal. There might be several such matrices: we index each of themwith h = 1, . . . , m. Thus, the algorithm will output h possible causal structures.
However, some of them can be excluded a priori by excluding unstable contemporaneous causal structures, i.e. Γ̃0,h such that Γ̃−10,h has eigenvalues whose modulus
is greater than one, for some h between 1 and m. Step 5 and 6 solve the indeterminacy of scaling in the same way as algorithm 1. Step 7 is also analogous to step
7 in algorithm 1.
0
In other words, under acyclicity Γ0 and Γ−1
0 are essentially triangular (i.e. ZΓ0 Z is triangular−1
for some permutation matrix Z). ICA identifies Γ0 DC, where D is a diagonal matrix and C is
an arbitrary permutation matrix. Since Γ−1
0 is essentially triangular, any permutation C (different
from I) will yield a matrix Γ−1DCwithsome zeros on the main diagonal. To find out the correct00
permutation matrix C is sufficient to search for a permutation C 0 such that Γ−1
0 DCC has nozeros on the main diagonal. Notice that row-permuting Γ0 through C is equivalent to columnpermuting (in the same way) Γ−1
0 or row-permuting (in the inverse way) the rows of εt , since from0CΓ0 ut = εt it follows that ut = Γ−1
0 C εt .
7

10

To recapitulate, both algorithms are able to identify the structural model (ora class of possible structural models) from the estimated reduced form model.
The assumptions which permit such an inference are, for both algorithms, nonGaussianity and independence of the structural shocks. As regards the first algorithm, a further assumption is acyclicity, i.e. the assumption that there are no
feedbacks or loops. The second algorithm relaxes this assumption, but the class ofadmissible models is now broader, which leads us to assume stability to restrict the
number of causal structures. It should also be noted that an implicit assumptionof both algorithms is causal sufficiency, i.e. the assumption that all the causally
relevant variables have been modelled.
Algorithm 1: VAR-LiNGAM
1. Estimate the reduced form VAR model of equation (5), obtaining estimatesÂ` of the matrices A` for ` = 1, . . . , p. Denote by Û the k × T matrix of thecorresponding estimated VAR residuals (T is the number of observations),
that is each column of U is ût ≡ (û1t , . . . , ûkt )0 , (t = 1, . . . , T ). Check
whether ujt (for each row j = 1, . . . , k of U ) is indeed non-Gaussian, andproceed only if this is the case.
2. Use FastICA or any other applicable ICA algorithm (Hyvärinen et al., 2001)
to obtain a decomposition Û = P Ê, where P is k × k and Ê is k × T ,such that the rows of Ê are the estimated independent components of Û .
Then validate non-Gaussianity and (at least approximate) statistical independence of the estimated components before proceeding.
3. P
Let ΓICA = P −1 . Find Γ̃0 , the row-permuted version of ΓICA which minimizeskj=1 1/|Γ̃0jj | with respect to the permutation. Note that this is a linear
matching problem which can be easily solved even for high k (Shimizu et al.,2006).
4. Divide each row of Γ̃0 by its diagonal element, to obtain a matrix Γ̂0 with allones on the diagonal.
5. Let B̃ = I − Γ̂0 .
6. Find the permutation matrix Z which yields a matrix B̂ = Z B̃Z 0 which is
as close as possible to strictly lower triangular. This can be formalized asminimizing the sum of squares of the permuted upper-triangular elements,and minimized using a heuristic procedure (Shimizu et al., 2006). Set theupper elements of B̂ to zero.
7. Calculate estimates of Γ̂i for lagged effects using Γ̂` = (I − B̂)Â` , for ` =1, . . . , p.

11

Algorithm 2: VAR-LiNG
1. Same as step 1 in algorithm 1.
2. Same as step 2 in algorithm 1.
3. Let ΓICA = P −1 . Test which entries of ΓICA are zero. This is done using abootstrap procedure (see main text).
4. Find all admissible row-permuted matrices Γ̃0,1 , . . . , Γ̃0,m of ΓICA such thateach Γ̃0,h has zeroless diagonal for h = 1, . . . , m.
5. Divide each row of Γ̃0,h by its diagonal element, to obtain a matrix Γ̂0,h withall ones on the diagonal, for each h = 1, . . . , m.
6. Let B̃h = I − Γ̂0,h , for each h = 1, . . . , m.
7. Calculate estimates of Γ̂`,h for lagged effects using Γ̂`,h = (I − B̂h )Â` , for` = 1, . . . , p, for h = 1, . . . , m.

4

Data

We use the annual survey of manufacturing plants (Encuesta Nacional Industrial
Manufacturera – ENIA) collected by the Chilean Statistical Institute (Instituto
Nacional de Estadísticas – INE). The ENIA covers the universe of Chilean plants
in the manufacturing sector and has been widely used by researchers (see e.g.
Alvarez et al., 2016; Crespi et al., 2019). We use the database that covers theperiod from 2001 to 2007.8 The database includes all firms with more than 10
employees that have registered some activity for at least one semester during anyear, divided by manufacturing sector (ISIC version 3, at the 4-digit level). For
more information on the database see INE (2006, 2009a).
8

Data are available since 1979, but the INE changed the data collection and in particular theregistration of firms in 2001, which, at the time of our analysis, does not allow to correctly trackplants/firms across the pre- and post-2000 periods. Attempts to match the two periods and build alonger panel are part of future work.

12After some preliminary data cleaning,9 we create our SVAR variables. The
variables used for the SVAR are size, proxied by employment (empl); output,
which is proxied by total sales (output), and can be sub-divided into domestic
sales (domsales) and exports (exp); and also productivity. Sales, exports, andemployment are easily derived from the ENIA database, while the estimation of
productivity requires further discussion.
All variables in the ENIA are in nominal values. We thus deflate the variables
used in this paper to real values before computing the productivity. For output andmaterial inputs we use the deflators computed by the INE for each of the 4-digit(ISIC) sectors (INE, 2009b). Unfortunately the report includes deflators only until
2006. Although we could use deflators from other sources for 2007, we preferto drop the year 2007 from the data instead of having constant price variables
computed from different sources. Also, INE (2009b) does not include deflators
for a number of 4-digit sectors. We attempted some aggregations to avoid losing
firms in those sectors, but the differences among sectors were too large, leading
to an increase in the error of the computation of constant price variables, which
seems less desirable than dropping a few observations across the years.
The INE computes different deflators for the gross value of production, used
for total sales (output) and exports (exp), for overall input costs, used for variable
inputs (M aterial), i.e. excluding capital, and for material inputs not completelytransformed in the production process, used to compute beginning of the year andend of the year raw and input materials (respectively P rivap, P rivaf , M atvap
and M atvaf ). To compute value added at constant prices (V a) we use the generally preferred method of double deflation, and we remove initial inputs and add
left overs at the end of the year: V a = output−M aterial−(P rivap+M atvap)+(P rivaf + M atvaf ).
To compute the value of capital at constant prices we follow, in part, Crespi(2004) and use the implicit deflator for gross fixed capital formation released by
the Central Bank (Banco Central de Chile, 2004, 2006, 2009). For our purposes,
we did not consider estimating different deflators for different types of capital(machinery, buildings land and vehicles), because we could not find accounting
information available for vehicles and land.
Finally, we deflate the input variables used to compute productivity with thegross value of production (output): primary inputs, input materials purchased,primary and material inputs from other plants (of the same firm), office material– deflator for non-completely transformed inputs – and fuel – deflator for com9

We first check for inconsistencies in the data (Benavente and Ferrada, 2004) i.e. plants thatreport 0 days in operation, a negative gross value of production, 0 or negative number of employees, labour cost equal or less than 0, sales lower than exports, value added larger than sales and an
ISIC code lower than 1500. A non significant number of observations need to be dropped acrossthe 7 years.

13

pletely transformed inputs.
We then proceed to estimate total factor productivity (TFP) employing theLevinsohn and Petrin (2003) method (see also Petrin et al., 2004), and using thequantity of consumed electricity as an intermediate input. It is worth nothing that
estimations of the TFP using value added and the whole sample of firms is highly
correlated with labour productivity with a Spearman’s correlation index of 0.96.
However, for the sake of comparability with most other studies on the relation
between export and productivity we use TFP estimations.
Although differences are again quite small, we choose to estimate TFP using
output rather than value added. The main advantage of using output is that there
is a non-negligible number of firms that in some years have negative value added(at constant prices), requiring a further drop of observations.
Arguably, plants may differ quite substantially in their production technology.
It follows that using one single production function with labour and capital (andone intermediate input) may produce biased estimates. To overcome this problem
we attempt a large number of estimations, taking into account different combinations of the following dimensions: size, labour, and sector.
Using the ISIC Rev3 2-digit classification we create the following relatively
homogeneous sectors: (1) Manufacture of Food, Beverages and Tobacco; (2) Textile, Wearing Apparel and Leather Industries, traditional industries; (3) Manufacture of Wood and Wood Products, Including Furniture ; (4) Manufacture of Chemicals and Chemical, Petroleum, Coal, Rubber and Plastic Products; (5) Manufacture of other non-metallic mineral products and basic metals; (6) Manufacture offabricated metal products, except machinery and equipment; (7) Manufacture ofmachinery and equipment, office, accounting and computing machinery, electrical machinery and apparatus, radio, television and communication equipment andapparatus, medical, precision and optical instruments, watches and clocks, motor
vehicles, trailers and semi-trailers, and other transport equipment; (8) Publishing,printing and reproduction of recorded media; (9) Manufacture of paper and paper
products; and (10) Other manufacturing sectors.
We create sub-samples for different size categories, based on number of employees: small (< 50), medium (50 ≤ empl < 250) and large (≥ 250) firms.
Furthermore, we attempt different measures of labour skills as variable inputs inthe production function.
As expected, TFP estimations, as well as returns to scale, differ significantly
when computed for different sectors and plant sizes. The distinction between different types of workers also significantly affects TFP and returns to scale. We
leave the discussion on these significant differences for a different paper. For thispaper it suffices to say that we consider as our most reliable estimates those obtained separating the different sectors and including in the production function‘blue collars’, ‘white collars’, material inputs, and capital (tf p). However, in this14

paper we also attempt some robustness checks, using a TFP estimated with no distinction between different types of employment (tf p2), leading to no significant
differences in the relation between exporting and productivity.
Finally, we remove firms that we consider outliers. For each of the VAR series– growth of sales, employment, exports and productivity – we impose a threshold for outliers corresponding to tenfold growth/decline in the space of one year.
Observations beyond this threshold are dropped.
Table 1 summarises the variables used for the analysis.
Table 1: Summary statistics
Variable
gr_emplgr_expgr_tfpgr_tfp2
gr_domsales

Description
Obs Mean Std. Dev.
Employees
2303 0.027
0.284
Export sales
2303 -0.011
0.606
TFPb
2303 -0.011
0.266
c
TFP
2303 -0.015
0.270
Domestic market 2303 0.003
0.543
sales

Min
-2.223-2.256-1.507-1.793-4.196

Max
2.137
2.254
2.030
2.243
5.059

Notes: b Estimated for different sectors, and differentiating between blue white collars. c Estimated for different sectors, without differentiating between blue and white collars

Table 2: Correlation matrix.

gr_domsales
gr_emplgr_expgr_tfpgr_domsales
1
0.0924-0.07170.3327

gr_empl
0.13431
0.0915-0.2599

gr_exp-0.0132
0.14361
0.0836

gr_tfp0.4283-0.18810.16051

Notes: Lower triangle: Pearson correlation coefficients; upper triangle (and italics): Spearman’srank correlation coefficients. 4021 observations. All correlations significant at the 1% level, except
for the Spearman rank correlation between gr_domsales and gr_exp (ρ=-0.0132, p-value=0.4029)

5

Results

5.1

Preliminary evidence

In this section, we present the findings of our SVAR-based causal analysis. As
preliminary evidence, Table 2 shows the correlations (both Pearson and Spearman’s coefficients) between the variables of interest. Our four main variables are15

significantly correlated between them — although the magnitudes of the correlations are far below the typical values of around 70% that are associated withproblems of multicollinearity (e.g. Hair et al., 1998). The relationship between
growth of exporting and growth of TFP, which is the main object of our analysis,
displays a significantly positive correlation. The problem with correlation analysis, of course, is that it cuts off many possible channels of interactions among
variables, especially between lagged values, and that is silent about causal directions.
These aspects are accounted for in our SVAR analysis. As first step (corresponding to step 1 in both algorithm 1 and 2), we estimate a reduced-form VAR
model (equation 5). The coefficient matrices are estimated with median regression, also called least absolute deviation (LAD) regression. This is in line withsuggestions in Moneta et al. (2013) in the context of non-Gaussian data with the
motivation of improving the robustness to outliers. The VAR model is estimatedboth with one lag (p = 1) and two lags (p = 2). We will refer to these specifications as the 1-lag and the 2-lag model, respectively.10
We then investigate whether the assumption of non-Gaussian shocks is plausible (this task is also part of step 1 in both algorithms). Previous research has
shown that the distribution of firm growth rates is heavy-tailed and non-Gaussian(Bottazzi et al., 2002; Capasso et al., 2013). Although the assumption of nonGaussian shocks is not directly testable, it is possible to assess the departure fromnormality of the estimated reduced-form residuals, which are assumed to be linear
combinations of the independent shocks. In Figure 1, we graphically compare theempirical distribution of the estimated reduced-form residuals with a theoreticalnormal distribution with the same mean and variance. We do this by comparing the histograms with the theoretical normal density function (top panel). The
relative peakedness of the four residuals suggest the presence of leptokurtic (i.e.
supergaussian) distributions. We also plot (bottom panel) the quantiles of the empirical distribution of the reduced-form residuals against the quantiles of the theoretical normal distributions. These q-q plots, being far from straight lines, suggest
heavy departure from normality. This is also confirmed by a battery of tests, inwhich the common null hypothesis is normality of the reduced-form residuals: theShapiro-Wilk, the Shapiro-Francia, and the Jarque-Bera tests reject in all cases thenull hypothesis at the 0.01 level of significance.
The second step of both algorithms (VAR-LiNGAM and VAR-LiNG) aims atdelivering the mixing matrix linking structural shocks to reduce-form residuals.
Table 3 presents the mixing matrix (point estimate coefficients) P for both the10

According to different information criteria (Akaike, Hannan-Quinn, Schwarz), the 2-lagmodel is slightly preferable to the 1-lag model. We do not explore further lags since this would
reduce considerably our sample size.

16

Figure 1: Empirical distributions (top panel, red lines show the corresponding theoretical normal distribution) and quantile-quantile plots (bottom panel; quantilesof the empirical distribution vs. quantiles of the theoretical normal distribution) of
the reduced-form residuals (corresponding to the four variables in the following
order: growth of domestic sales, growth of employment, growth of exports, andgrowth of TFP), 2-lag model.

17

1-lag and the 2-lag model. This matrix is the output of the FastICA algorithm(Hyvärinen et al., 2001) applied to the reduced-form residuals. The matrix P is,in our sample, a (4 × 4) matrix such that Û = P Ê, where Û is the (4 × T ) matrixof the estimated reduced-form residuals and Ê is a (4 × T ) matrix of independent
components.11 We recall that the scale (sign) and order of these components,
and therefore of the columns of the matrix P , is undetermined. The columns of
P displayed in Table 3 are rescaled in order to produce components with unit
variance. Although the order of the columns is completely arbitrary, the orderof the rows is determined by the order of the variables entering in yt .12 We notethat some entries of this matrix are close to zero. For each column we can easily
identify a coefficient (in absolute value) that is maximally loading on a particularvariable. For example, looking at the fourth column of P for the 1-lag model (leftpart of the table) we see that there is an entry which has the highest value (among
the column-entries, in absolute value) for exporting growth (0.9466). Looking at
the third row, we also see that this is the maximum value (among the row-entries).
This means that the shock labelled as e4 (in the 1-lag model) is mostly loading onexporting growth. The same shock has a minimal impact on productivity growth(0.0017), which is the smallest entry both in the fourth column and in the fourthrow. If we look at the matrix P of the 2-lag model (right part of table 3), theimpact of the shock labelled as e3 has very similar characteristics (and almost
equal values) to the shock labelled as e4 in the 1-lag model. Taken together, thissuggests that the exporting growth shock does not transmit (within the one or two
years periods) to productivity growth. In other words, results suggest that there isno contemporaneous causal relationship from exporting to productivity growth.
Table 3: Mixing matrix
1-lag model
2-lag model
e1
e2
e3
e4
e1
e2
e3
e4
gr_domsales -0.1341 0.5872
0.0457 -0.0581 0.0357 -0.5783 -0.0518 -0.1561
gr_empl
-0.0058 0.0171
0.30610.00980.3036 -0.0164 0.0099 -0.0161
gr_exp-0.1063 -0.0124 0.0692
0.94660.04520.01010.9168 -0.1219
gr_tfp-0.2968 0.0472 -0.0887 0.0017 -0.0950 -0.0436 0.0023 -0.2723
Notes: Point estimates coefficients of the mixing matrix P as output of fastICA algorithm. This
corresponds to step 2 of both Algorithm 1 and 2. Left part: estimation from residuals of a 1-lag
VAR. Right part: estimation from residuals of a 2-lag VAR.

Steps 3-6 of the algorithms we use (VAR-LiNGAM and LiNG) aim at infer11

T = 2658 with one lag and is equal to 1667 with two lags.
In other words, each time we run fastICA we get a (randomly) column-permuted version of P
with, in addition, random changes of sign for each column. A part from column permutation andchanges of sign, all the entries of the output matrices from multiple (1000) realisations of fastICA
are identical, which confirms a stable convergence of the fastICA algorithm.
1218

ring the causal relationships, such as the one just elicited, in a more formal andrigorous way. As mentioned, VAR-LiNGAM assumes that there is a recursive
causal-structure. This means that the mixing matrix P contains at least k(k − 1)/2
entries (in our case 6 zeros since k = 4) that are (statistically close to) zero. Recursiveness also implies that if any entry (i, j) of P is (significantly) different
from zero, then the entry (j, i) must be (statistically close to) zero. In the VARLiNGAM setting this property is not tested empirically, but assumed a priori. In
order to overcome this limitation of the VAR-LiNGAM method, and improve theempirical reliability of our causal inference, we first identify the model through
VAR-LiNGAM, and then use a bootstrap procedure to check whether the causal
directions found are robust under resampling. It turns out that most of the causal
directions are robust, but some of them are reversed in artificial samples. We
finally apply VAR-LiNG, which does not assume recursiveness, to see whether
causal loops emerge. The causal relationship we are interested in, namely between productivity and export growth, emerges as robustly identified.

5.2

VAR-LiNGAM results

Table 4 shows the coefficients of structural VAR matrices (see equation 7) estimated through VAR-LiNGAM (algorithm 1 in section 3.2). The upper (lower)part of the table refers to the 1-lag (2-lag) model. The first block of 4 columns
corresponds to the estimated coefficients of matrix B (contemporaneous effects)(recall B = I − Γ0 ), the second block (columns 5-8) refers to the coefficients ofmatrix Γ1 (one-period-lag causal effects), while the third block (columns 9-12)
presents the estimated coefficients of Γ2 (two-period-lag causal effects).
As the literature on algorithmic causal inference has demonstrated (Spirtes
et al., 2000; Pearl, 2009; Peters et al., 2017), structural models can be represented
as directed graphs, and directed acyclic graphs (DAGs) in case of recursive structure. We thus represent the SVAR model, output of the VAR-LiNGAM algorithm,
as a DAG, in order to improve the causal interpretation of the model. The DAG is
built on the criterion that a non-zero entry in the (i, j) position of B corresponds
to a directed edge (i.e. arrow) from the j th to the ith variable in the sub-graphreferring to the contemporaneous values. Analogously, a (statistically significant)non-zero entry in the (i, j) position of the Γ1 corresponds to a directed edge (i.e.
arrow) from the j th variable at time t − 1 to the ith variable at time t.13 Figure 2
shows the resulting DAG for the 1-lag model.
13

Since the asymptotic distribution of the VAR-LiNGAM-estimated coefficients is unknown,
we cannot rely on a formal significance test. As rule of thumb, we do not represent a causal arrow
if the corresponding coefficient is significantly close to zero according to a standard t statistic,
where the standard errors are calculated following a bootstrap procedure. In Table 4 coefficientssignificantly different from zero are represented in bold.

19

20

gr_empl
0.4787
0.0619000.43690.0889-0.27120.02880.53230.0839000.43450.082-0.2466
0.0307

gr_exp-0.0871
0.012700
0
0
00-0.0897
0.0145000
0
00

gr_tfp0.83010.0773000.40230.0707000.94680.102
000.47430.081200l1_gr_domsales-0.22480.03840.00730.0068-0.01440.015700.0096-0.2182
0.04370.01450.00850.02370.021-0.00160.0119first lag
l1_gr_empl l1_gr_exp
0.1159-0.01480.033
0.008-0.02290.00870.02340.0041-0.0216-0.14420.03440.0392-0.0579
0.01210.01780.00440.0655-0.0047
0.038
0.0085-0.01960.00650.03090.0073-0.0421-0.1472
0.04770.0272-0.03590.01090.02110.0051l1_gr_tfp
0.29060.04720.01620.01220.10880.0442-0.2699
0.02
0.30250.06730.03210.01740.08860.067-0.2610.0375-0.06530.05420.00730.00870.02080.0205-0.02320.0108l2_gr_domsales

0.03550.03410.01220.02610.10270.04910.01240.02740.01390.01
0.00450.0064-0.09440.03
0.0001
0.006

second lag
l2_gr_empl l2_gr_exp

0.13170.03710.04980.01840.07430.051-0.0836
0.0238l2_gr_tfp

Notes: Structural coefficient matrices, output of the VAR-LiNGAM algorithm. Top part of the table: 1-lag model. Bottom part of the table: 2-lagmodel. Left block: contemporaneous effects matrices (B). Middle block: lagged effects matrix Γ1 . Right block: lagged effects matrix Γ2 . Standard
errors are obtained through bootstrap (1000 iterations). Bold coefficients refer to significant entries (95% confidence intervals).

gr_tfpgr_expgr_emplgr_domsales

gr_tfpgr_expgr_emplgr_domsales

gr_domsales
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

Table 4: VAR-LiNGAM estimates

Figure 2: Causal graph resulting from VAR-LiNGAM, 1-lag model'L L XXXX
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Blue edge = positive effect, red edge = negative effect.

Both the 1-lag and 2-lag models in Table 4 show that the primus motor is employment growth, which has large positive effects on growth of domestic sales andgrowth of exports. These can both be interpreted as firm strategic decisions: when
the firm intends to increases output, they first need to increase the scale. Notethat the sum of these two coefficients is close to unity (0.4787 + 0.4369 = 0.9156
in the 1-lag model; and 0.5323 + 0.4345 = 0.9668 in the 2-lag model), which
implies that the elasticity of employment growth to combined growth of outputs(i.e. domestic sales + exports) is close to unity when considering instantaneous
effects.
Another central result is that employment growth has a negative effect oncontemporaneous growth of TFP, presumably because efficiency increases whenfewer inputs (i.e. employees) are used to produce the same amount of output.
Downsizing firms achieve higher productivity in the same time year than firmsthat invest in recruiting and training new employees.
Growth of TFP has positive impacts on growth of domestic sales and, to alesser extent, growth of export. Firms that experience an increase in their productivity are therefore more likely to grow in terms of domestic and export sales.
This might suggest that firms would be better off pursuing productivity growth asa prerequisite for subsequent sales growth, instead of vice versa.
Growth of exporting has a negative impact on growth of domestic sales. This21

reflects the tension between domestic vs. exporting sales strategies, that was already visible in the negative correlations between these variables in Table 2. It
is interesting to observe that export seems to determine domestic sales rather
than vice versa. This could be because internationalized firms have already ‘conquered’ their home markets and become ‘outward-focused’ in the sense that they
pay more attention to how they fare in the more competitive export markets. But
as we discuss in Section 5.3 this result is not robust.
With regards to the causal link between TFP and export, our results suggestthat it is an increase in TFP that causes an increase in export in the same year,
rather than the other way around. Our VAR-LiNGAM estimates provide an interesting perspective on the export-productivity debate: not only firms need to be
more productive to enter the export market; once they export, they need to keepincreasing TFP to remain competitive. As noted, this comes hand in hand withan increase in size, measured as an increase in labour (which has a negative effect on TFP). Note, however, that export growth has a small positive impact on
TFP growth in the next year. The increased export partly contributes to increasing
productivity.
Very few coefficients are significant in the 2-lags model. TFP maintains its
positive impact on domestic sales, and interestingly pushes to a further increasein firm size through employment.

5.3

VAR-LiNGAM robustness analysis

We run a robustness analysis to check whether the causal links depicted in Figure
2 are stable over 1000 bootstrap samples, which were created by resampling withreplacement from the original data. We focus here only on the contemporaneous
causal structure. As Figure 3 shows, all the causal links found by VAR-LiNGAM
are very robust across bootstrap samples except the link between growth of domestic sales (DS in figure 3) and growth of exporting sales (EX in figure 3), which isreversed almost half of the times.

5.4

VAR-LiNG results

Table 5 reports the estimates of the application of algorithm 2 (VAR-LiNG, i.e. thealgorithm which allows the possibility of feedback loops in the contemporaneous
structure) for the model with one lag.14 Figure 4 depicts graphically the contemporaneous causal structure, while Figure 5 shows the lagged causal structure.
With respect to the VAR-LiNGAM algorithm, results mainly differ in relation
the contemporaneous structure, for which it is most difficult to estimate causal
14

The two-lag model produces very similar results.

22

Figure 3: Bootstrap robustness analysis on the contemporaneous causal structure. VAR-LiNGAM is applied to each bootstrap iteration. Numbers associatedto edges indicate the percentage each causal link is inferred out of 1000 bootstrap
iterations.
47%

DS



-

53%

EX

A@
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A@
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A
100%
100%

A @

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99% A
100%

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A 100%

A

A
A ?

P
Note: L= gr-empl, P=gr-tfp, EX= gr-exp, DS= gr-domsales.
Blue edge = positive effect, red edge = negative effect.

relations. The estimated contemporaneous causal structure shows a bi-directional
negative effect between growth of domestic sales and growth of exporting sales,
as suggested by the robustness results shown in Figure 3. This confirms the improvements in the causal estimations with the VAR-LiNG algorithm discussed in
Section 3.2
Feedback loops (positive) emerge also between growth of domestic sales andgrowth of productivity and between growth of domestic sales and growth of employment (positive) in the contemporaneous causal structure.
The main finding about the causal relation between productivity and exporting growth which resulted from the application of the first algorithm is confirmed:
there is no causal influence from exporting to productivity (growth) in the contemporaneous causal structure. But the viceversa holds: firms must keep increasing productivity to increase their presence in the foreign market. The coefficientwhich measures the instantaneous influence from productivity (growth) to exporting is very close to the coefficient obtained from the first algorithm: 0.3782 vs.
0.4023 (standard errors are also very similar: 0.0773 vs. 0.0707).
Results using the VAR-LiNG algorithm do not confirm the small positive
lagged impact of export growth on productivity growth that was found with the
VAR-LiNGAM algorithm (respectively Tables 5 and 4). These suggest that, notonly firms must improve TFP to increase their presence in the export market,
but there is also no causal evidence of “learning-by-exporting” that translates in23

Figure 4: Contemporaneous causal graph resulting from VAR-LiNG 1 lag

DS



EX

K@
A
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 

A A@ @@AA@
AA @ @
AA @ @
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AA
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Note: L= gr-empl, P=gr-tfp, EX= gr-exp, DS= gr-domsales.
Blue edge = positive effect, red edge = negative effect.

an increase in TFP in the year following an increase in exports. While the resultsfrom the VAR-LiNGAM algorithm showed a (weak) influence from lagged export
growth to current productivity growth, the results from the VAR-LiNG algorithm
show no such causal link (see Figure 5 for the one-year lagged effects).
Table 5: VAR - LiNG estimates
gr_domsales
gr_emplgr_expgr_tfpgr_domsales
000.02920.0083-0.06150.01990.09140.0234

gr_empl
0.29810.0478000.34490.0602-0.3058
0.0291

gr_exp-0.0653
0.01310.00000.0077000.00000.0077

gr_tfp0.46200.11150.00000.01220.37820.077300l_gr_domsales-0.22400.00620.01370.0062-0.0274
0.01700.02050.0111

l_gr_empl
0.09390.0197-0.0249
0.0197-0.0208
0.0462-0.06480.0200l_gr_exp-0.0066
0.00380.00850.0038-0.1426
0.03740.01160.0045l_gr_tfp
0.19250.01260.01410.0126
0.10800.0530-0.2757
0.0239Notes: Structural coefficient matrices, output of the VAR-LiNG algorithm, 1-lag model. Leftblock: contemporaneous effects matrices (B). Right block: lagged effects matrix Γ1 . Standard
errors are obtained through bootstrap (1000 iterations). Bold coefficients refer to significant entries(95% confidence intervals).

5.5

Further robustness checks

We performed several robustness studies to explore how stable our finding about
a contemporaneous causal effect from productivity growth to exports growth (anda lack of causal effect in the opposite direction) is, when we look at different
24Figure 5: Lagged causal structure resulting from VAR-LiNG 1 lag
L
L XXXX
Z
XXX
Z
XXX
Z
XXX
Z
XXX
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XXX
Z
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~
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P
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DS

Z
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EX
HH
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HHZ
jZ
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(t-1)

(t)

EX

DS

Note: L= gr-empl, P=gr-tfp, EX= gr-exp, DS= gr-domsales.
Blue edge = positive effect, red edge = negative effect.

variable measures, sub-samples, and methods of estimation. As mentioned, TFP
can be estimated without distinguishing between different types of employment.
This does not bring any difference to the VAR-LiNGAM estimate with respect tothe baseline results. However, the contemporaneous causal effect matrix resulting
from VAR-LiNG is not sparse enough to deliver an informative and reliable output. We also looked at different sub-samples guided by different criteria: sectors(following the taxonomy by Ferraz et al., 1996), size, and productivity. The VARLiNGAM results is remarkable stable in delivering a causal structure in which
productivity growth is always ordered before exporting growth. VAR-LiNG delivers in many cases a lack of causal influence from export growth to productivity
growth (in line with the baseline results). But in many other cases the output of
VAR-LING is not stable under variations of initial conditions, which we attributed
to a reduction of the sample size. We also considered the results from a VAR
model estimated by OLS rather than by LAD. In terms of causal structures, there
are no difference with the baseline results, both as regards VAR-LiNGAM and
VAR-LiNG. All these results are reported in Appendix (supplementary material).

25

6Discussion

In this paper we revisit a well-known debate, nurtured by growing but contradicting empirical evidence. Does exporting activity increase firm productivity or do
firms remain in the export market only if they managed to increase productivity?
To address this important question we choose a rather different strategy fromprevious papers, while exploring a relatively well-studied country. First, we focus on the intensive margin of exporting firms and compare firms that experience
different growth rates of exports (i.e. become more or less competitive in the international market). Second, we explicitly take into account the bi-directional causal
relation between productivity and export growth, including within the same year
and with up to two lags.
Applying VAR-LiNGAM and VAR-LiNG, a class of SVAR models that estimates causal networks, we find that export growth does not have a direct andinstantaneous causal impact on firm productivity growth within the same period.
Although results from the VAR-LiNGAM model show that with one year lag export growth does have a small causal effect on TFP growth, when we apply themore robust VAR-LING model, which allows to account for feedback loops inthe contemporaneous causal structure, this lagged causal effect vanishes. Instead,
we observe that TFP growth has a direct large contemporaneous causal effect onexport growth, which is robust to the application of both the VAR-LiNGAM and
VAR-LiNG algorithms, and to resampling robustness checks.
Our results are estimates of causal effects and therefore have interesting implications for policy. In particular, it appears that firms should focus on improving
their productivity in order to be able to increase their exports, because it is productivity growth that drives growth of exports, and not the other way round. While
there are certainly benefits from exporting, we do not find that firms in an emerging economy such as Chile can rely on exporting as a means to increase theirproductivity – and there remain competitive in the export market.
For example, firms should keep improving their productivity through e.g. redesigning their production routines, upgrading their capital and IT systems, andimproving management (Bloom et al., 2012) alongside appropriate organizationalinnovations (e.g. Cruz et al., 2018). As a result, they will be in a better position
to experience growth in their participation in global trade. There is instead nostrong influence of exporting on TFP growth – including with a lag. This effect isrelatively small and not robust to accounting for the possibility of feedback loops
in the contemporaneous structure between variables.
Our study is not without limitations. First, although we have no reason to expect that our data is unrepresentative, it is nevertheless not clear how our results
can be generalized to other countries and other periods. However, we are interested and curious to check how our method would change earlier LBE results in26

other countries where the hypothesis has been tested, using the same data.
Second, we focus on exporting undertaken by firms that have already taken
the binary decision of exporting, and succeeded. There may be differences inthe exporting-productivity relationship at the time when a firm enters the export
market and may have more to learn.
The application in this paper has allowed to shed new light on the long-lived
controversy of whether firms benefit from exporting, or need to boost productivity to be able to increase exporting. We have show that, in the case of Chilean
firms, between 2001-07, the contemporaneous causal direction runs from productivity growth to exporting. A one or two years lag does not show robust causal
evidence that an increase in export will lead to increased productivity after one or
two years. Future work could apply the family of techniques developed here to abroad range of controversial empirical evidence to produce new valuable evidence
for academics, practitioners and policymakers.
This paper has also shown how data-driven techniques for causal inference canbe introduced from the machine learning community into economics, and adapted
to time-series and VAR contexts, to provide new evidence on the causal relations
governing economic systems.

Appendix. Supplementary material
Supplementary material related to this article can be found online. The supplementary material contains impulse response function analysis and further robustness checks.

27

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