Tech on the ROC: export threshold and technology adoption interacted

These figures refer to the dataset defined in Sect. 2. For the definition of exporting firm and technology adoption, see Sects. 2 and 4, repectively.

See, among others, Castellani and Zanfei (2007) for the Italian case, Wagner (2007) and Schröder and Sørensen (2012) for two comprehensive surveys. Moreover, others (Geishecker et al., 2017; Schröder and Sørensen 2012) have shown that the mismatch between Melitz’s theory and empirical evidence is actually linked to the definition of productivity.

The exclusion of tobacco and refined petroleum products is due to the peculiar characteristics of these activities (regulation and monopoly). Maintenance and repair has been excluded because of its high content of services. Other manufacturing sector has been excluded because it includes miscellaneous activities (see NACE Rev. 2 Classification).

There is no universally agreed definition of “stable exporter” except that, for a firm to be defined as such, it has to be exporting on a regular basis over a specified (more than a year) period. This paper uses firm-year-level data; for this reason we are not able to identify one-off exports in the same way as in Geishecker et al. (2019) or temporary exports as in Bekes and Murakozy (2012). Moreover, we preferred the 2014–2016 time span because it is more homogeneous from a business cycle point of view, as it fully covers the Italian post-recession period.

The validity of a classifier can be measured based on two main metrics: sensitivity and specificity. Sensitivity represents the probability of detecting true positives. Specificity is the probability of detecting true negatives. This latter is usually considered in its reciprocal expression (1 - Specificity), which measures the probability of false positives.

Youden’s \(J\) identifies the observation that maximizes the vertical distance between ROC curve and the 45° line. It is the most commonly used criterion for detecting optimal cut-offs: \(Cut* = h(Sensitivity) - (1 - h)(1 - Specificity)\). Parameter \(h\) represents the relative weight to manage the trade-off between true and false positives. We set up \(h = 0.5\), thus opting for a “neutral” selection between false positive and false negative outcomes. Values of \(h > 0.5\) (i.e., finding true positives is more relevant than avoiding false positives) would correspond to a ‘liberal’ selection, which assigns positive classification even in the presence of weak evidence. Conversely, setting up \(h < 0.5\) (i.e., detecting true positives is less relevant than avoiding false positives) would correspond to a “conservative” selection, which assigns positive classifications only in presence of strong evidence. The best cut-off depends on whether one needs to maximize sensitivity at the expense of 1 - Specificity or vice-versa. This often happens in medicine. The first case leads to a test that is utterly sensitive (i.e., it correctly identifyies diseased people at the expense of a high number of false positives). The second case generates a test that is better at ruling out the disease. The Youden’s \(J\) allows to find the optimal combination of them.

In Costa et al. (2019), we tested two alternative models: a pure sales model (S-model, where \(X=Sales\)), in which the export threshold is defined over the value of firms’ turnover, and a pure productivity model (\(\pi\)-model, where \(X=Productivity\)), in which the export threshold is defined over the value of labor productivity (value added-per-worker). Both \(S\)-model and π-model have been proved to be consistent with Melitz’s theory (Geishecker et al., 2017). Fitting tests showed that the \(Z\)-model we used in this work outperforms the other two.

We refer to four geographical areas: North-West, North-East, Centre, South and Islands.

A first clue of this mismatch between firm export status and tecnology adoption (see the definition in following rows) emerges from our dataset. Even though in all sectors considered these two variables show a positive and significant relationship (see Table 7 in the Appendix), the same descriptive evidence show that in some industries, the relationship between exporting status and a condition of low-than-average technology adoption seems to leave space to possible mismatch.

This information is obtained from administrative sources and included in the aforementioned business register “Frame-Sbs”.

Please, note that the relative positioning of export threshold and technology line depicted in Fig. 1 is merely for illustrative purpose: in principle technology line can be steeper than export threshold, depending on the characteristics of the industry.

There are a number of possible reasons for this. For example, in terms of the model by Lileeva and Trefler (2010), such firms may be domestic units which have invested in technology and are expected to be shifting to exporter status (in our terms: crossing the export threshold). Moreover, they may also be units belonging to enterprises groups in which specific branches are in charge of exporting for the entire group. Furthermore, our Potential exporters may include suppliers of other exporting firms; in this case a possible high-technology exporting buyer could stimulate its intermediate goods suppliers to adopt an advanced technology, so that the (generally small-sized) suppliers would end up crossing the technology line without reaching the export threshold.