Over the ROC methodology: Productivity, economic size and firms’ export thresholds

• Author: Davide Zurlo,Stefano Costa,Federico Sallusti,Claudio Vicarelli
• Published date: 01 August 2019
• DOI: http://doi.org/10.1111/roie.12405
• Date: 01 August 2019

Rev Int Econ. 2019;27:955–980. wileyonlinelibrary.com/journal/roie © 2019 John Wiley & Sons Ltd

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INTRODUCTION

The recovery of international trade after a sharp drop in 2009 largely benefited those countries that were

ready to exploit the opportunities provided by the external demand, in a framework where domestic

demand was sluggish or decreasing. In this context, export activity stood out as a key factor for firm

survival. This was particularly relevant for Italy: especially during the “second dip” of the crisis (2011–

2014), the ability of Italian firms to operate in foreign markets was crucial to the evolution of the

business cycle (see, among others, Accetturo et al., 2013; Italian Institute of Statistics [ISTAT], 2017).

Received: 30 May 2018

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Revised: 11 March 2019

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Accepted: 12 April 2019

DOI: 10.1111/roie.12405

ORIGINAL ARTICLE

Over the ROC methodology: Productivity, economic

size and firms’ export thresholds

StefanoCosta

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FedericoSallusti

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ClaudioVicarelli

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DavideZurlo

ISTAT, Italian National Institute of

Statistics, Rome, Italy

Correspondence

Claudio Vicarelli, ISTAT, Italian National

Institute of Statistics, Via Cesare Balbo 16,

Rome 00184, Italy.

Email: cvicarelli@istat.it

Abstract

We identify the minimum combinations of productivity

and “economic size” that Italian manufacturing firms need

to achieve in order to access international markets. These

“export thresholds” are estimated by applying, for the first

time in economics, the ROC (receiver operating character-

istics) methodology. In this way, we detect a model‐based

(rather than a subjectively determined) cut‐off that allows

to identify exporters and nonexporters and provides a meas-

ure of each firm’s distance from the export threshold. This

methodology also paves the way to investigate other deter-

minants of thresholds, thus helping to design more effective

policy interventions to reduce barriers to trade.

KEYWORDS

ROC analysis, export threshold, intensive and extensive margin of exports

JEL CLASSIFICATION

F14; L60; L11

956

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COSTA eT Al.

Italy is characterized by a high number of exporting firms (more than 177,000 in 2014; in the EU

only Germany has more), which, however, represents only a small portion of the total number of enter-

prises (< 6%); moreover, the share of their exported turnover is particularly low (5.1% in median), so

that even exporting firms largely depend on domestic demand (ISTAT, 2017).

These characteristics of the Italian industrial system have fueled a debate about the identification

of the most appropriate policies to support and increase the internationalization of firms: is it more

effective to aim at boosting the export‐to‐turnover ratio (intensive margin) or at increasing the number

of exporters (extensive margin)? To answer this question, we need to know something more about the

necessary and sufficient conditions for export.

Along this line, the purpose of this work is to estimate for each industry an “export threshold”,

which is identified by the combination of productivity and “economic size” (defined over a set of

firm‐level size‐related variables) corresponding to the transition from nonexporter to exporter status.

To do so we apply, for the first time in economics, the receiver operating curve (ROC) analysis,

an approach already used in other disciplines, such as medicine (Kumar & Indrayan, 2011), machine

learning (Majnik & Bosnić, 2013), and natural science (Warnock & Peck, 2010). The main advantage

of applying ROC analysis is the possibility to obtain a model‐based, rather than a subjectively deter-

mined, cut‐off, allowing to discriminate between exporters and nonexporters, and to generate a map

of the distribution of firms across this threshold positioning every firm on the basis of its distance

from the minimum productivity–size combination, which corresponds to the access to international

trade. This is a novelty in comparison to standard models that estimate the probability to export

(see, e.g., Bernard & Jensen, 2004) or regression‐based methods that identify average export premia.

Furthermore, our approach could eventually provide a helpful knowledge tool for evidence‐based

policies aimed at promoting the internationalization of firms.

A large strand of literature, developed with the purpose of overcoming the limits of the “repre-

sentative firm” hypothesis, pointed out the role of heterogeneity, in terms of structural characteristics

(size, location, business sector exporting status), strategies (different forms of innovation, inter‐firm

relationships) and performance (revenues, profitability, productivity, innovation) in determining a

firm’s ability to export. Since the seminal work of Melitz (2003), the role of productivity emerged,

largely prevailing over other factors. Differences in productivity are at the heart of several subsequent

models (see Bernard, Redding, & Schott, 2011; Chaney, 2008; Melitz & Ottaviano, 2008), accord-

ing to which only more productive firms can cover the trade costs (sunk or entry costs) required to

profitably operate in international markets (see Redding, 2010 for a survey on theoretical literature).

There are two different kinds of trade costs: variable costs (e.g., tariffs) and fixed entry (e.g., invest-

ment related to regulation compliance, running distribution chain). A fall in variable costs induces an

endogenous shift in the productivity cut‐off for exporting. A reduction in the fixed export costs has the

same qualitative effect. This implies that reductions of both fixed and variable trade costs will cause

new firms that would not have exported under higher cost conditions to enter foreign markets.1

A fall

in variable costs induces an adjustment of the value of exports by firms that are already exporting

(intensive margin), and a rise in the number of exporters (extensive margin), while a fixed cost reduc-

tion only determines an adjustment of the extensive margin.2

In a Melitz model world, only firms above the export productivity level (a sort of “export thresh-

old”) sell both domestically and abroad. However, data also show that in many countries, firms’ pro-

ductivity distributions between exporters and nonexporters overlap (see Castellani and Zanfei (2007)

for Italy; see Schröder and Sørensen (2012) for a survey), implying that firms might not export even

though their productivity is above the threshold.

Schröder and Sørensen (2012) have shown that the mismatch between Melitz’s theory and empir-

ical evidence is only apparent, being mainly linked to the definition of productivity: empirical works