2. New Data on Services Policies

In November 2019, the World Bank and WTO released an update to their jointly managed I-TIP platform containing extensive data on national services policies. In its raw state, the dataset includes 68 countries, 25 sectors, and three modes of supply: cross-border trade in services (Mode 1 in WTO speak), Mode 3 (establishment of a commercial presence in a foreign country – essentially foreign direct investment in a services sector), and Mode 4 (temporary cross-border movement of services suppliers). The data exclude Mode 2, where trade occurs through movement of consumers to a foreign country (e.g., tourism) as this is generally unrestricted.

The dataset pertains to policies observed in 2016 that potentially affect services trade. It has nearly a quarter of a million observations (244,949), distinguishing up to 445 different measures, both sector specific and horizontal. If attention is restricted to countries and sectors for which information is reported fully at the level of these individual measures, the coverage falls to 68 countries and 24 sectors.Footnote ⁶ I-TIP data are freely downloadable from the WTO website. Borchert et al. (Reference Borchert, Gootiiz, Magdeleine, Marchetti and Mattoo2019) discuss database creation, including sourcing and access. The source for 45 of the 68 countries is the OECD STRI database, so that I-TIP adds information on 23 countries not covered by the OECD (Appendix Table 1 lists the countries). As with the 2008 iteration of the World Bank STRI, questionnaires administered to law firms in the countries of interest generated the raw data, treated by the World Bank and WTO team to ensure consistency and correctness. Table 2, taken directly from Borchert et al. (Reference Borchert, Gootiiz, Magdeleine, Marchetti and Mattoo2019), lists the general categories of measures included in the database.

Table 2. Classification of World Bank/WTO services policy data

Source: Borchert et al. (Reference Borchert, Gootiiz, Magdeleine, Marchetti and Mattoo2019).

3. Constructing an Index of Services Policies from I-TIP Data

There are two key analytical decisions in designing an STRI given the choice to collect data on particular measures: weighting the measures and aggregating them into an index. The first problem can be solved through application of purely statistical methods, such as factor analysis, or by using external expert judgment, as in the OECD STRI, which is based on a weighting and aggregation system driven by expert input (Grosso et al., Reference Gootiiz and Mattoo2015). Aggregation is then by weighted sum. The World Bank STRI, by contrast, appears to use the judgment of World Bank analysts to motivate the mapping of measures to quantitative scores. Then aggregation uses a constant elasticity of substitution function with parameters chosen again by the judgment of World Bank analysts.

As noted above, the selection of I-TIP data we use span 455 individual policy measures in 68 countries and 24 sectors. The challenge is to produce an overall index of services policy by sector using those data. We use the OECD index as our basis for this problem because it appears to us to represent the best currently available STRI.Footnote ⁷ It is quite possible that a superior index will be designed in the future, but, at the present time, we do not believe there is a better benchmark than the OECD STRI. There is an active research program based on it, showing that the index is robustly linked with trade in services (e.g., Nordås and Rouzet, Reference Nordås2017) and investigating questions such as the extent and effects of regulatory heterogeneity (Nordås, Reference Miroudot and Shepherd2016, Reference Nordås2018) and the services content of regional integration in the EU (Benz and Gonzalez, Reference Benz and Gonzales2019).Footnote ⁸ Moreover, we are interested in showing the potential for commonplace statistical techniques to extend coverage of an index to new countries as additional data become available.

The first problem we address in this paper is how to extend the OECD STRI to the countries included in I-TIP but not in the OECD database. The purpose of undertaking this exercise is to show that commonplace quantitative methodologies can reproduce the STRI very well, even without the detailed information contained in the aggregation algorithm, which has not been made public. Our analysis illustrates it is possible to obtain a comparable index across all 68 countries quickly and at very low cost, without the need to develop a new methodology.

Equivalently, our problem can be seen as one of dimensionality reduction. We start with up to 445 individual policy measures per country in I-TIP and attempt to reduce those measures to one score per country–sector pair. Our objective in reducing dimensionality is to reproduce the OECD STRI as closely as possible.

This class of problem is well suited to a basic machine learning application. We construct a dataset containing OECD STRIs by sector and all horizontal and sector specific policy measures from I-TIP for all 68 countries for which full data are available. For the analysis to be feasible, we limit consideration to those sectors that correspond well between the two databases, taking simple averages of measures where necessary. This approach is made necessary by the different levels of aggregation in the data: subsectors in I-TIP, and more aggregate sectors in the publicly available OECD data. The result is to reduce the number of sectors we can work with easily to eight: accounting, legal, commercial banking, insurance, air transport, road freight transport, distribution, and telecom. We believe these sectors represent a large share of services activity in most countries. Although we lose some of the nuance in the I-TIP data – which distinguishes sectors at a micro level, such as insurance versus reinsurance, or air passenger transport versus air cargo transport – we believe this approach is justifiable given our overall objectives as set out above.

We split the sample into three groups. We randomly assign 75% of observations for which there is an OECD STRI to a training subsample, with the remaining 25% assigned to a prediction subsample. Finally, those countries and sectors where no OECD STRI is available are assigned to an out of sample prediction subsample. The basic empirical strategy is to apply machine learning models to the training subsample only, with the aim of using the disaggregated policy data to predict an index score by sector, which can then be compared with the OECD STRI. By having the model produce indices for the prediction subsample, we can assess how it performs on data that were not used for training. Once an appropriate model has been selected, it can be used to make out of sample predictions for countries not in the OECD data.

3.1 Developing Services Policy Indices with Simple Machine Learning

Machine learning refers to a family of techniques commonly used in computer science and data science, whereby statistical algorithms are used to find patterns in data, and to make predictions based on those patterns. These types of approaches power many familiar consumer interfaces, such as movie suggestions on Netflix, or predictive text in Google searches or Gmail emails. To date, machine learning has been applied infrequently in economics, but Athey and Imbens (Reference Athey and Imbens2019) identify features of machine learning techniques that can potentially be of use to applied economists. An important example of such an approach is Athey et al. (Reference Athey, Bayati, Doudchenko, Imbens and Khosravi2017), who use machine learning to assist in developing a causal inference framework. The remainder of this section sets out our general approach. Readers who do not require the technical background can skip to the next section.

We apply a type of machine learning model called an elastic net as a prediction tool. The model itself can be understood as similar to the standard regression framework familiar to economists, with independent variables (inputs) and a dependent variable (output), with the relationship between the two summarized in a set of coefficients that are estimated by solving an optimization problem. In this case, the input is the set of policy measures from I-TIP, and the output is the OECD STRI. Model selection and performance assessment proceed by comparing the model's predictions of the STRI with what is observed. A good model is one that uses the inputs to reproduce the OECD's STRI to a high degree of accuracy, and which exhibits similar accuracy for the subsample of data used to train the model, and the remainder of the sample that was not used in training. A subsidiary consideration is model parsimony, namely the ability to achieve strong predictive performance while using a relatively small number of variables. The machine learning techniques we use automatically drop policy measures (inputs) with little explanatory power for the OECD STRI (the output) and identify a set of policy measures that have the greatest explanatory power, typically much smaller than the starting data set. We discuss the policy implications of this feature of the algorithms below.

In technical terms, the elastic net solves the following problem, where $\hat{\beta }$ is the vector of parameters of interest:

$$\hat{\beta } = {\rm argmi}{\rm n}_\beta \left\{{\displaystyle{1 \over {2n}}\mathop \sum \limits_{i = 1}^n {\lpar {y_i-x_i{\beta }^{\prime}} \rpar }^2 + \lambda \left[{\alpha \mathop \sum \limits_{\,j = 1}^p \vert {\beta_j} \vert + \displaystyle{{1-\alpha } \over 2}\mathop \sum \limits_{\,j = 1}^p \beta_j^2 } \right]} \right\}$$

The first term is the standard ordinary least squares (OLS) loss function. λ is a penalty term that shrinks parameter estimates towards zero in two ways, with a higher parameter resulting in greater shrinkage. The first term in square brackets penalizes coefficients that are large in absolute value, while the second performs shrinkage based on the square of the parameter value. With λ = 0, the elastic net collapses to standard OLS. With nonzero λ and α = 1, it is the least absolute shrinkage and selection operator (LASSO), while with α = 0, it is ridge regression. The essence of the procedure is that λ is iterated for given values of α, with zero coefficients dropped from the model progressively due to the shrinkage effect. Iteration continues until a model is selected based on its cross-validation performance, i.e. the ability of a model estimated on the training subsample only to produce close estimates of the values in the prediction subsample. By proceeding in this way, we can identify a subset of variables that have the best explanatory power in terms of the observed OECD STRI, and then use the estimated values from the elastic net regression to predict values out of sample, where no OECD STRI exists.

The elastic net is well suited to prediction problems with large numbers of potential predictors, even exceeding the number of observations, and deals well with situations where they are closely correlated. These characteristics are unlike OLS, where the number of potential predictors cannot be greater than the number of observations. More fundamentally, the objective of OLS is typically inference, whereas the objective of the elastic net is prediction. As a result, we do not report standard errors or statistical significance, which are typically important outputs of an OLS model. Instead, we report cross-validation performance, namely the ability of the model to make predictions that closely track observed values in the subsample not used to train the model in the first place.

To power the tool, we construct a set of explanatory variables that is all sectoral policy measures from I-TIP, all horizontal policy measures from I-TIP, and a set of sector dummies. We then also create interactions to allow for nonlinear effects and dependencies. Specifically, we interact all policy measures with all other policy measures, and we create a triple interaction between all horizontal policy measures, all sector specific policy measures, and the sectoral dummies. The I-TIP dataset contains missing entries for many response variables, presumably because they are believed to only be relevant to certain sectors. To facilitate the empirical analysis, we therefore code these missing values as zero, which means that they do not have any restrictive impact on trade in sectors where World Bank and WTO analysts have made an a priori determination of no effect.

Proceeding in this way gives a dataset of 544 observations, which is eight sectors for 68 countries. By interacting all the potential explanatory variables, as set out above, we have 16,974 variables. Many of those variables are constant within subsamples, often zero, and so are automatically dropped from the model. In practice, the elastic net works with a starting set of 1,606 variables. A standard regression technique like OLS cannot handle this problem given the number of observations, but the elastic net can, because the optimization problem has kinks due to the absolute value and square terms. Since OLS is unavailable we use two other dimension reduction techniques on the sectoral and horizontal measures to give a point of comparison but ignoring interaction terms: principal factor analysis and a simple mean. In both cases, we apply the relevant measures to the disaggregated policy data at the level of sectors, to produce a single index that summarizes, according to the assumptions of each, the variation in the disaggregated policies. As a robustness check on our machine learning models, we also set α = 1, which yields LASSO estimates, and α = 0, which yields ridge estimates.

Given that the problem in this case is prediction, not inference, we do not report coefficient estimates. For the training sample (272 observations), the elastic net retains 59 variables, a mix of measures in levels and interactions, and selects α = 0.25. The LASSO retains 55 variables, while the ridge estimator retains the full set of informative variables, namely 1,606. Table 3 summarizes the performance of the three machine learning methods, looking separately at the training and prediction subsamples.

Table 3. Output from Elastic Net, LASSO, and ridge applications to OECD STRIs using I-TIP data in levels and interactions

The three methods perform quite similarly on the training subsample: model fit is tight considering the relatively small amount of information used. The mean value of the OECD STRI is 0.279, so a mean squared error of only 0.005 using the elastic net indicates that model fit is good. Comparing the two parts of Table 3 shows that of the three machine learning methods, the elastic net has the best performance: R² is highest both on the training and prediction subsamples. We therefore prefer the elastic net's predictions, but we note that it is relatively close in performance to the other two models.

Table 4 reports the correlations at the sectoral level among the various measures computed as described above. The elastic net again is the strongest performer on this overall criterion, although the other two machine learning methods also perform well. The comparator indices, constructed using principal factor analysis and a simple mean, have a negative correlation with the OECD index, and thus represent a radically different way of summarizing the data. The evidence in Table 4 suggests that the OECD approach to weighting and aggregating measures results in an output that is substantially different from what can be obtained by naïve methods that focus only on the characteristics of the data, without using external knowledge on the effects of particular policies. It is an important finding that the OECD index, and by extension, ours, does not correlate strongly or even positively with naïve measures. But our three simple machine learning applications, using limited data, do a remarkable job of reproducing the OECD index. Moreover, our preferred method, the elastic net, produces predicted values that lie exclusively between zero and unity, as does the original OECD index. The alternative approaches do not have this property, nor would a simple OLS regression model. Given that the indices only have an ordinal interpretation, it is useful to investigate the rank correlation as well. We find that the OECD STRI and our SPI have a rank correlation coefficient of 0.788, which is again evidence of a strong correspondence between the two measures.

Table 4. Correlation between OECD STRI and alternative services policy index (SPI) estimates (common sample)

Figure 1 shows the correlation in a common sample of elastic net predictions for all countries in the I-TIP sample, i.e. those already covered by the OECD and those that are new, which we name the Services Policies Index (SPI), and the OECD STRI at the sector level. The association with the OECD index is not perfect, as would be expected with any statistical approach to reproduction of an existing index, but the figure shows that our SPI fits the original data well, which gives us confidence that out of sample estimates for the countries not in the OECD database should perform well, in particular given the similarity of the R² measures for the training and prediction sub-samples, as noted above. Summary statistics show that the new countries added to the sample are more restrictive than those in the original OECD sample, with an average STRI across sectors of 0.333 compared with 0.281; however, ranges in both cases are wide: the new countries have scores ranging from 0.096 to 0.872, compared with 0.157 to 0.960 for those in the OECD sample.

Figure 1. Correlation between the STRI and SPI, sector level (common sample)

To avoid terminological confusion in what follows we refer consistently to the OECD STRI as the STRI. Our constructed indices based on I-TIP data are referred to as Services Policy Indices (SPIs). The difference in terminology highlights that we are simply mimicking the OECD's original approach using a broader dataset. Ownership of the full methodology used to produce the OECD's indices lies with that organization, and we use a commonplace data-driven technique to extend database coverage.

4. Validating the SPI with Trade Data

We have already shown that our SPI closely mirrors the OECD's STRI, in our view currently the best available benchmark for measuring applied services policies. An important additional step in validating the SPIs is demonstrating their ability to act as statistically significant predictors of trade flows. Thus far, we have not used any information on trade flows to produce the SPI, but only the weights implied by the OECD's expert judgment system, which we have mimicked using machine learning. This second step is therefore quite independent of the first, and is designed to show that our index has explanatory power for bilateral trade, which we believe is an important criterion for any index that seeks to measure services trade policies.

We estimate a standard structural gravity model of services trade at the sectoral level in line with current best practice, as embodied by Anderson et al. (Reference Anderson, Larch and Yoto2018). Estimation is by Poisson Pseudo Maximum Likelihood (PPML), which means that estimates are robust to heteroskedasticity, take account of zero flows, and produce fixed effects (by exporter and by importer) that correspond exactly to the quantities prescribed by theory in Anderson and Van Wincoop (Reference Anderson and Van Wincoop2004)-type models (Fally, Reference Egger, Francois, Hoekman, Manchin, Francois and Hoekman2015).

The gravity model takes the following form, considering a single year and single sector cross-section only:

(1)$$X_{ij} = F_iF_jt_{ij}^{-\theta } e_{ij}\;$$

where: X_ij is exports from country i to country j; the F terms are exporter and importer fixed effects; t_ij is bilateral trade costs; θ is a parameter capturing the sensitivity of demand to cost; and e_ij is an error term satisfying standard assumptions.Footnote ⁹ Trade costs t are specified in the usual iceberg form. These costs are unobserved but can be specified in terms of observable proxies. For present purposes, we include standard gravity model controls based on geography and history, and an indicator of service sector restrictiveness (STRI for presentational purposes), as well as an interaction between the STRI and a dummy for countries that are members of an Economic Integration Agreement (EIA) under Article V of the GATS, the services equivalent of a PTA for goods. Formally:

(2)$$\eqalign{ -\theta logt_{ij} = & \,b_1STRI_j\ast intl_{ij} + b_2EIA_{ij} + b_3STRI_j \ast intl_{ij} \ast EIA_{ij} + b_4\log \lpar {distance_{ij}} \rpar + b_5contiguous_{ij} + \cr & b_6colony_{ij} + b_7common\;language_{ij} + b_8common\;colonizer_{ij} + b_9same\;country_{ij} + intl_{ij}} $$

Table 5 provides variable definitions and sources, along with those for equation (1). Apart from trade flows, the data sources are largely standard. Equation (1) should in principle cover all directions of trade, i.e. including trade from country i to country i, or intra-national trade. Inclusion of intra-national trade data is crucial for PPML to produce theory-consistent fixed effects estimates (Fally, Reference Egger, Francois, Hoekman, Manchin, Francois and Hoekman2015). International trade data do not include this term, so we use the Eora multi-region input–output table to do the job.Footnote ¹⁰ Eora covers 183 countries and 26 sectors through a single harmonized input–output table. We use data for 2015 only, the latest available year, corresponding most closely to the year of our SPI data (2016).

Table 5. Variables, definitions, and sources

In sector by sector regressions, the STRI is a country-specific variable and so is collinear with the importer fixed effects. To achieve identification, we follow Heid et al. (Reference Grosso, Gonzales, Miroudot, Nordås, Rouzet and Ueno2017) in interacting it with intl, a dummy equal to unity for trade between different countries, and zero for internal trade. The reason for this approach is that the STRI has a differential impact on domestic and foreign service providers, which is a key aspect of the rationale for the index in the first place. We divide the World Bank STRI by 100, so that it is on the same scale as the other policy indicators.

As noted above, our SPI data start from 24 sectors defined in the World Bank/WTO dataset, which we concord to eight sectors in the OECD STRI classification. We then further concord those data to four Eora sectors by taking simple averages of the relevant indices: distribution, finance and business services, telecom, and transport. It is not possible to estimate gravity models at a more detailed level as the Eora database in harmonized form is necessarily highly aggregated.

A second point that requires explanation is the interaction term between services policies and EIA membership. The services policies in I-TIP apply on a most favored nation (non-preferential) basis, which is why we map them to MFN policies from the OECD data. The OECD has collected preferential data for services trade within the EU, but there is no systematic dataset covering preferential services policies around the world. However, many countries are members of trade agreements that hope to boost exports between their members, relative to the MFN benchmark. By interacting MFN policies with a dummy for joint EIA membership, we seek to capture that effect. An EIA in this context is effectively a trade agreement for services, under Article V of the GATS. Our expectation is that the coefficient on MFN policies will be negative (trade reducing), while the coefficient on the interaction term will be positive (showing that trade reduction is attenuated by regional integration). Benz and Gonzalez (Reference Benz and Gonzales2019) show conclusively in the case of the EU that intra-bloc services policies are far more liberal than those pertaining to non-EU countries.

Table 6 reports gravity model regression results for the distribution sector. Column 1 includes the OECD STRI, and as expected, the policy variable has a negative coefficient, while the interaction term with EIA membership has a positive one, with both estimates statistically significant at the 10% level. The same is true for the World Bank STRI, which is included in column 7. The baseline data therefore support the view above that the measures captured by the STRI tend to restrict trade, in line with Nordås and Rouzet (Reference Nordås2017), with that effect attenuated by joint membership of a trade agreement covering services. The same patterns of signs and magnitudes applies for four SPIs, elastic net, LASSO, ridge, and principal factors. The simple mean has no statistically significant coefficients. We therefore conclude that the most naïve of our testbed of SPI measures does not have significant predictive value for trade, but that other measures that attempt to summarize the available data more systematically do have such power.

Table 6. Gravity models for distribution services using different measures of services policies

Note: All models are estimated by PPML Robust standard errors adjusted for clustering by country pair in parentheses below parameter estimates. Statistical significance is indicated as follows: * (10%), ** (5%), and *** (1%).

Table 7 repeats the exercise for financial and business services. Results are similar to those for distribution. The elastic net, LASSO, and ridge SPIs perform somewhat better than the OECD STRI and on par with the World Bank STRI, in that the levels term and the interaction term both have coefficients with the expected signs and magnitudes, and are statistically significant at the 5% level or better. This is largely due to increased sample size for the SPIs; additional results, available on request, show that results for the SPI are less precisely estimated on the smaller sample for which the OECD STRI and the SPI are both available. Column 1 contains data on 183 exporters and 45 importers, while the following five columns all use 183 exporters and 68 importers. The principal factors SPI does not have any statistically significant coefficients, while the simple mean SPI has a negative and 1% statistically significant coefficient in levels, but a statistically insignificant coefficient for the interaction term. The most naïve measures of services policies again have at best limited explanatory power, in contrast to more sophisticated measures like the STRI and the SPIs.

Table 7. Gravity models for finance and business services, STRI and SPIs

Note: All models are estimated by PPML. Robust standard errors adjusted for clustering by country pair are in parentheses below parameter estimates. Statistical significance: * (10%), ** (5%), and *** (1%).

Table 8 reports results for telecom services. The pattern of findings is again quite similar: the STRIs, as well as the elastic net, LASSO, and ridge SPIs, all have explanatory power for bilateral trade flows in this sector, although none of the interaction terms except for the LASSO model has a statistically significant coefficient, which suggests that regional integration may not be a strong force for global trade in this sector. By contrast, the principal factors and simple mean SPIs have positive and 1% statistically significant coefficients, which is contrary to expectations.

Table 8. Gravity models for telecom services using different measures of services policies

Note: All models are estimated by PPML. Robust standard errors adjusted for clustering by country pair in parentheses below parameter estimates. Statistical significance: * (10%), ** (5%), and *** (1%).

Finally, Table 9 presents results for the transport sector. Both STRIs, elastic net SPI, and ridge SPI all have 5% statistically significant coefficients or better in levels and on the interaction term. By contrast, the principal factors SPI and the simple mean SPI do not have any statistically significant coefficients. Results for this sector therefore accord well with those from the other sectors.

Table 9. Gravity models for transport services using different measures of services policies

Note: All models are estimated by PPML with importer and exporter fixed effects. Robust standard errors adjusted for clustering by country pair. Statistical significance: * (10%), ** (5%), and *** (1%).

As is typical for gravity models that include intranational trade data, there is evidence of home bias in all regressions: the intl dummy is consistently negative and statistically significative. Also of interest is the finding that, in some specifications, the effect of an EIA effectively neutralizes the negative trade impact of the SPI or STRI. While deserving of further research, this result suggests that some regional agreements do a good job of facilitating services trade beyond the level that would be expected based on MFN policy settings.

Taken together, these results indicate that the OECD STRI has much greater explanatory power for bilateral trade flows in services than naïve measures like a principal factor or simple mean. The same is true of the World Bank STRI, which is unsurprising given how closely correlated it is with the OECD index (rho = 0.8). Moreover, our three SPIs generally exhibit very similar performance to the OECD STRI, albeit with a substantially larger sample due to greater importer coverage. The difference in number of observations is just over 50%, so there are clear advantages to these extended measures based on data collected by the World Bank/WTO but aggregated into indices based on our machine learning-based reproduction of the OECD's approach. Given the strong and consistent explanatory power of the STRI and its derivative SPIs, the bar for producing a ‘better’ indicator of services trade restrictions is very high. In the absence of substantial additional benefits, it is far from obvious that further work in this area – in the sense of changing weights or adopting different aggregation schemes – passes a cost–benefit test, given the substantial time and resources that need to be devoted to dealing with the problems of weighting and aggregation discussed above.

To convert these results into more usable form, we reformulate the trade costs function to express the elastic net SPI in ad valorem equivalent (AVE) terms, following Benz (Reference Benz2017):

$$ AVE_j\equiv t_{ij}-1 = \exp \left( {\displaystyle{{-\beta SPI_j} \over \theta }} \right)-1 $$

Full results are presented in Appendix 2 (see on-line supplementary material). The advantage of presenting results in AVE terms is that it provides a simple number that can be compared across countries. It also shows that on a comparable standard, levels of restriction in services trade are typically higher than in goods. However, the AVE concept makes some significant simplifications, including by assuming that the bundle of regulatory measures captured by the SPI has economic effects like those of a tariff. While that may be true for some measures, it may not be for others, especially those that affect competitive conditions in the marketplace or influence the fixed costs of market entry. We therefore present AVEs subject to these caveats.

While any indicator of services trade restrictiveness should be a strong predictor of bilateral services trade, recent work has shown that because of the input–output relationships that exist between services and other sectors, it is also likely that services policies affect total trade (i.e., goods and services).Footnote ¹¹ We test this hypothesis and the predictive power of our SPIs compared with the STRI using aggregate Eora data summed across all 26 goods and services sectors in the database. The specification is the same as in the preceding tables, except that we use a dummy for PTA rather than EIA membership, to capture goods agreements as well as services agreements, and we include the log of the applied tariff rate as an additional explanatory variable. We aggregate the OECD STRI and our SPIs by taking simple averages across sectors, while the World Bank STRI is provided with a separate aggregate indicator.

Table 10 reports the results. We again use the full sample, but as tariff data are not available for all country pairs, sample size falls. Both STRIs, elastic net and ridge SPIs have the expected negative coefficients, and all four variables also have positive coefficients on the interaction term with the EIA variable, with all estimates statistically significant at the 1% level. The simple mean SPI also displays this pattern of coefficients, but the principal factor SPI has unexpected signs.

Table 10. Gravity models for total trade (goods and services), STRI and SPIs

Note: Robust s.e. adjusted for clustering by country pair. Statistical significance: * (10%), ** (5%), *** (1%).

The World Bank STRI performs similarly to the OECD index or our SPIs. The only result that is contrary to expectations is the negative sign on PTA, but this is likely due to the fact that there is also an interaction term with EIA – an element of the PTA variable – that creates a correlation between the two. A similar issue arises in relation to tariffs, which are negatively correlated with PTA membership. Other variables perform largely in accordance with expectations.

The conclusion we draw in this section is that the OECD STRI, and the extended version with 23 additional countries that we have termed the SPI, is a robust predictor of bilateral trade at the sectoral level for services, and also at the aggregate level for goods and services. We interpret this as showing that the indices capture important features of services trade policy.