METHODOLOGY FOR DERIVING THE STRI *

Transcription

1 OECD EXPERTS MEETING ON THE SERVICES TRADE RESTRICTIVENESS INDEX (STRI) Paris, 2-3 July 2009 METHODOLOGY FOR DERIVING THE STRI * * This paper summarises the methodology for the work of the OECD/TAD on services trade restrictiveness (STRI). The team responsible for the STRI project consists of: Massimo Geloso Grosso, Frederic Gonzales, Anna Jankowska, Rainer Lanz, Molly Lesher, Sébastien Miroudot, Hildegunn Kyvik Nordås (project leader) and Alexandros Ragoussis. Contact persons for this paper are Hildegunn Kyvik Nordås (Hildegunn.Nordås@oecd.org) and Alexandros Ragoussis (Alexandros.Ragoussis@oecd.org). The team would like to acknowledge the contribution of Dale Andrew and Douglas Lippoldt to the development of the STRI in general. The team would like to thank also Dale Honek, Markus Jelitto, Claudia Locatelli and Lee Tuthill of the WTO Secretariat for helping with the classification of measures. Finally, the team wishes to thank Ken Ash and Raed Safadi for useful comments and discussions on the STRI project.

2 TABLE OF CONTENTS METHODOLOGY FOR DERIVING THE STRI... 3 EXECUTIVE SUMMARY Introduction Relations to previous research Selection of indicators Alternative schemes for the calculation of the final index Robustness Checks and Relevance Summary and conclusions REFERENCES ANNEX 1. TRANSFORMATION INTO BINARY SCORES The regulatory database and the transformation ANNEX 2. MONTE CARLO SIMULATIONS Calculating the composite measure Tables Table 1. Weights per category for each sector Table 2. Spearman rank correlation by sector Table 3. Results gravity regressions by sector and mode Table A1. Types of measures in each sector Table A2. Thresholds used for the transformation into binary measure Figures Figure 1. Transformation from openness to a restrictiveness index Figure A1. Number of countries requiring visas to enter the country for tourism and/or business trips as a percentage of UN countries (WEF Visa DATA 2008) Figure A2. Duration of the university degree required to enter the profession: accountancy (OECD 2007)30 Figure A3. Local loop unbundling price (monthly) in USD Figure A2.1. Stability of Composite Scores Figure A2.2. Stability of Ranks

3 METHODOLOGY FOR DERIVING THE STRI EXECUTIVE SUMMARY The OECD Services Trade Restrictiveness Index (STRI) project was launched by the Trade Committee in June 2007 as a tool for quantifying barriers to trade in services at the sector level. This paper provides a detailed explanation for the methodology used for estimating the STRI. The process included the collection of data, selection of measures to include in the STRIs, scoring and weighting of measures as well as robustness and relevance checks. For each step in the process, the possible alternatives are presented along with their advantages and shortcomings providing the basis for the chosen methodology. Robustness checks are further applied to support major methodological choices. In translating qualitative information into numerical values the first step involved selecting a scoring strategy. Given the nature of the data of which 90% contain descriptive information regarding the presence of regulation, a binary approach was elected. Transforming all measures into binary presented challenges: when a rich variety of possible outcomes is reduced to a binary score, some variation is lost, while simplicity and tractability are gained. The challenge was addressed by using multiple binary variables for important continuous measures, minimising the variation loss from the aggregation. The selection of a weighting scheme requires a great deal of judgement. Although a vast body of empirical and theoretical research on trade and investment provides evidence on which policy measures restrict trade the most, trade and investment data are still not sufficiently detailed that elasticities can be estimated precisely. These would be the ideal basis for calculating weights. In the absence of precisely estimated elasticities, the paper argues that a combination of weights based on expert judgement applied to categories of measures and equal weights for individual measures within each category is the best choice. It is shown that the STRI for most sectors does not crucially rely on this choice as the indices are robust to all reasonable weighting schemes. An indicator of trade restrictiveness should be negatively correlated with trade and investment flows. The paper finally documents how the estimated STRI can be entered into standard gravity regressions for assessing their ability to measure trade restrictiveness. All the STRIs are statistically significantly and negatively correlated with at least one of the following variables: trade, FDI or FATS. It is therefore reasonable to conclude that the STRIs are robust and aptly capture trade restrictiveness. 3

4 1. Introduction 1. This paper presents the methodology for deriving the Services Trade Restrictiveness Index (STRI) using the bottom-up approach as outlined in TAD/TC(2007)4. The STRI is a composite index derived from a regulatory database compiled for the project, which covers potentially trade restricting regulation. The objective of the project is to develop indices that can serve as a tool for trade policy analysis comparing countries openness to trade within sectors, across time and across sectors. The STRI will be a useful tool for identifying areas for further trade liberalisation and for benchmarking best practices. 2. Four sectors have been included in the pilot phase of the project. These are computer services, construction, professional services (including accounting, architectural services, engineering services, legal services); and telecommunications. The STRI for these sectors are presented and documented in four separate papers. The objective of this paper is to explain the methodology for readers interested in the technical details. The structure of the paper follows closely the sector papers, explaining in more detail each step in the development of the index. 3. The paper starts with relating the methodology for calculating the STRI to other recent composite indices in Section two. Thereafter, it explains the steps taken to develop the index. The first step is to select indicators to be included in the index. This is done in two phases. First a database of possible trade restricting measures has been compiled; and from that database the measures to be included in the STRI have been selected using various methods. These are described in Section 3. The database contains qualitative information on potentially trade restricting regulation. Before indices can be calculated, these need to be transformed to numerical indicators. The possible ways of doing this and the choice of methodology are discussed in section 4.1. Having transformed a qualitative database to a quantitative one, each measure to be included in the STRI must be assigned a weight. Again there are several options, which are examined in Section 4.2. Finally the weighted scores are aggregated into a composite index. Most existing indicators are a weighted average of the indicators included. This is, however, not the only option and alternatives are discussed in Section Having calculated the STRI using the steps described above, its properties need to be analysed. The robustness to alternative weighting and scoring schemes has been checked and the extent to which the index actually measures what it is supposed to measure, namely trade restrictiveness is tested and explained in section 5, while Section 6 concludes and suggests areas for further development of the indicators. 2. Relations to previous research 5. Ideally, a trade restrictiveness index of a country should capture trade costs facing exporters to that country, relative to other countries. Such measures are well developed for trade in goods e.g. by the Overall Trade Restrictiveness Index (OTRI) estimated by the World Bank. OTRI is a measure of the uniform tariff equivalent of all tariffs and other observed trade restricting policies as developed by Anderson and Neary (1994; 2005). 6. Barriers to trade in services are not observable in the same way as tariffs and non-tariff measures for goods. Therefore, efforts to measure services trade restrictiveness have more in common with composite policy indicators than with OTRI, although previous OECD work has attempted to measure the tariff equivalent of services trade restrictiveness (Dihel and Shepherd, 2007). However, as acknowledged by the authors, more comprehensive services trade data than what is currently available is necessary for making robust estimates. In the mean time a composite index of services trade restrictiveness should have the following properties: 4

5 1. It should provide a tool for comparing countries within and across sectors as well as across time. This means that the indicator value should be independent of the sample over which it is calculated as far as possible, making it easy to extend the work to new countries without changing the indicator values for those already included. 2. The variation in the raw data should as far as possible be retained in the indices; 3. The indicator should be robust and the estimated values should be negatively correlated with observed trade and investment flows in services. 4. The indicator should be as simple as possible, given that it fulfils criteria The rest of this section compares and contrasts existing trade restrictiveness indicators and some well-known composite indicators with these criteria. 8. Work on services trade restrictiveness was pioneered by the Australian Productivity Commission (APC). APC compiled information on regulations that potentially restrict trade in services in the late 1990s, covering a wide range of sectors in both developed and developing countries in all regions of the world. Information on regulation was assigned scores and a weighted average was calculated using expert judgement for assigning weights. 1 The restrictiveness indices were, however, only calculated for one year. 9. The most recent contribution to research on services trade indices is the World Bank s indicators presented in the Global Monitoring Report These are estimated for 32 developing and 24 OECD countries in the following sectors: financial services, telecommunications, retail trade, transport and professional services. However, indices are published by country groups classified according to income level rather than individual countries. The indicators are based on a questionnaire filled in by law firms in each country. Each measure is allotted a score between 0 and 1 on a five-point scale, while weights are assigned by World Bank staff. 10. Aggregating a number of measures into a composite index has been applied to various other fields of interest. The OECD has previously engaged in that type of analysis when constructing the Product Market Regulation Indices (PMR), which has been estimated for 1999, 2003 and The Indices aim at reflecting in one index number the degree of government intervention in the OECD markets. Many of these measures are also relevant for trade, since they affect market entry and operations of local and foreign firms alike. 11. The scoring approach in the construction of the OECD PMR transforms all measures into a continuous scale [0, 6]. Continuous variables are re-scaled in that interval based on the minimum and maximum values. Binary variables are transformed using the extremes of the range. The first two PMR indicators (1999 and 2003) used principal component analysis for grouping measures into sub-indicators and for assigning weights to the measures. The 2007 indicators, however, used equal weights. 12. Other examples of well-known composite indices that are updated at regular intervals are The World Bank Knowledge Index; The World Bank s Worldwide Governance Indicators; The World Economic Forum Global Competitiveness Index and The UN Human Development Index. In the following each of these are briefly discussed, focusing on scoring and weighting schemes. 13. The approach for the construction of the World Bank Knowledge Index is to transform all values from different sources into a single scale [1, 10] based on countries ranking in each measure. The 1 See e.g. McGuire and Schuele (1999); Nguyen-Hong (2000); and Kalirajan, (2000). 5

6 aggregate index is then derived as the unweighted average of the transformed scores in each individual measure. 14. The World Bank s Worldwide Governance Indicators start with information on a large number of measures from different sources that are assumed to reflect the quality of governance and institutions. From this information the so-called unobserved components model is used for calculating the indices. In brief the observed measures are assumed to be imperfect signals of the true, but unobservable underlying quality of governance and institutions. Statistical methods are then used to combine the signals in a way that captures the underlying governance quality in the best possible way. In particular, the methodology extracts the minimum variance estimate of governance from the observed data, assuming that both the underlying true governance and the observed signals are normally distributed. 15. The World Economic Forum (WEF) Global Competitiveness Index have used the min-max scoring approach, where observations in each measure is re-scaled in the interval [0,1] based on the minimum and maximum values of the sample analysed. Further to that, principal component analysis is used for clustering of measures, while weights are assigned to measures according to their impact on the objective. 16. The scoring approach in the construction of the UN Human Development Index (HDI) is the same as the WEF Competitiveness Index. The weighting approach is however different as the HDI is calculated using a standard constant elasticity of substitution (CES) formula when aggregating the measures to the final index. That type of aggregation involves a penalty for deviations from the sample mean. Furthermore, CES aggregation implies complementarity among measures; the degree of which depends on the parameter values. Notice that the sample mean is country-specific, hence taken across measures, not across countries. Lessons from previous work 17. The underlying data for calculating indices typically have much more variation than the resulting index. This is inevitable, but it is nevertheless desirable that variation among countries is preserved as much as possible, such that policy differences can be identified making benchmarking easier. The crucial factor for preserving the variation is the scoring. When a rich variety of possible outcomes are reduced to a binary score, 0 or 1, some variation is lost, while simplicity and tractability are gained. 18. All measures that use a scoring system where scores relate to the sample mean, median or other sample-specific measures violate the first criteria above. Sample-based scoring makes the resulting indicator incomparable across samples. Extending the index to new countries would necessitate recalculation of the index for countries already included in the sample as well. Furthermore, sample-based scoring provides information on changes in the ranking of countries over time, but not changes in the absolute value of e.g. trade restrictiveness. This drawback applies to all the composite indicators discussed, but not to OTRI There are three points to retain from examples of similar work conducted from other international bodies. In particular that: Transformation of measure values into a unique scale is a standard practice. Transformation of continuous variables into ordinal scales through rankings is often used too. 2 When the indicator measures objectives for which no benchmark in an absolute sense can be identified (e.g. governance or human development), sample-based scoring is probably inevitable. 6

7 Comparability across different country and time samples, does not appear to be important in the existing practice. Sample-based methods for scoring and weighting are often used in the construction of composite indices. Well designed composite indicators can be a useful tool for policymakers and in policy analysis, comparing country performance and benchmarking purposes. The STRI project aims at developing such an indicator for services trade restrictiveness, building on best practice methodologies. The STRI can also be seen as a first step towards a trade restrictiveness index that reflects trade costs in a similar way as OTRI. 3. Selection of indicators 20. As opposed to barriers to trade in goods, barriers to services trade are mainly found behind the border. Selecting indicators to be included in the STRI is therefore not straight forward. A first step was to collect information on measures that satisfy one or more of the following criteria: Explicit barriers to trade and investment (i.e. restrictions on foreign ownership and other discriminatory measures); Barriers and regulations that are mentioned explicitly in the GATS; Barriers and regulations that are mentioned explicitly in regional trade agreements; Barriers and regulations that are related to future negotiations on rules in the WTO/GATS. 21. The sources of information on measures that satisfy these criteria are the following: The Product Market Regulation (PMR) survey undertaken by the OECD Economics Department. The 2007/2008 survey was augmented by questions on treatment of foreign parties for the STRI project; Surveys undertaken in relation to the Services Expert Meetings held in June and December 2008 for each of the pilot sectors; The International Telecommunications Union (ITU) regulatory database. The OECD Communications Outlook The OECD Employment Outlook The OECD Foreign Direct Investment (FDI) Restrictiveness Index (2006/7) The OECD Codes of Liberalisation and Capital Movement The Annual Report of the Autorité de Régulation des Communications Électroniques et des Postes (ARCEP) 2006 for France Government, Embassy, and Consulate websites The Henly Visa Restriction Index 2008 World Economic Forum (WEF) Visa Data The information from the above sources has been complemented by information from GATS schedules, and regional trade agreements. A final round of Members confirmation of the regulatory information was completed in April

8 23. Having selected information on a large number of regulatory variables, a set of measures was presented to services expert meetings held for each of the four pilot sectors. 3 Experts were asked to rank and score these measures according to their relative importance for trade. Experts also had the option to deem a measure not relevant and hence not to be included in the STRI and in addition they could add restrictions that they considered important, but not included in the set of variables presented to them. The set of measures were adjusted accordingly. 24. A final step in selecting variables for the index was to conduct statistical analysis of the measures assembled in the database. These included analysis of correlations as well as principal component analysis. Regulations that cover similar areas and are highly correlated are likely to capture slightly different aspects of the same regulation. Including several of these in the index could lead to double counting and should be avoided. 4 For practical reasons in such cases the variable with the best data coverage was chosen unless compelling reasons suggest otherwise. 3.1 Grouping measures into sub-measures 25. When taking the step from data gathering and scoring to grouping and weighting, the issue of subjective judgement inevitably arises. At this stage the purpose of the measures and the criteria for judging what is relatively more important need to be addressed. It should be noted at the outset that there is no such thing as a neutral and objective composite measure. There is no escape from making choices on what to include in the index and how to group measures, and grouping will have an impact on the weight that each measure is assigned, even when using equal weights. The issue is thus not whether to make judgements, but how to make the best and most transparent choices. 26. The appropriate grouping of measures depends on what the purpose of the index is. OECD Members have expressed the need for measures to help inform the GATS negotiations as well as regional agreements and domestic reforms. In order to design an index that can be used for multiple purposes, a multidimensional index is proposed. The measures are grouped in five different ways: Classification according to policy area ( categories in the sector papers). GATS framework Modes of supply Restrictions to firms establishment versus those affecting ongoing operations Discriminatory versus non-discriminatory measures 27. Market access and national treatment measures are classified together because they are often difficult to distinguish in practice. This grouping also allows making a distinction between restrictions subject to scheduling under the GATS, and consequently to negotiations for their removal; and other largely domestic regulatory measures which do not need to be scheduled and are often put in place to offset potential market failures and meet legitimate public policy objectives in services markets. 28. Establishment restrictions can generally be regarded as impediments to the movement of capital, while those applying to firms operations constrain service provision after establishment. Nondiscriminatory measures affect total demand whereas discriminatory ones typically only have a bearing on 3 4 Services expert meeting for computer services and professional services were held in June 2008 and expert meetings on construction and telecommunications in December This is in contrast to the Worldwide Governance Indicators where correlations among measures are seen as a sign of a good signal about the underlying true governance level. 8

9 import demand. Addition of the latter classification has been important since market access and national treatment measures have been grouped together. 29. The classification according to policy area is the classification on which the weighting schemes are based. There are seven policy areas as follows: Restrictions on foreign ownership and other market entry conditions Restrictions on the movement of people Discriminatory measures, standards and equivalence Public ownership, size and scope of public enterprises Price controls and regulations on market behaviour Barriers to competition Regulatory transparency and licensing/permit systems 4. Alternative schemes for the calculation of the final index 30. Scoring relates primarily to recording the presence of regulations. Weighting captures the relative importance of the measures. In order to calculate the final index one weight is used for each category (i.e. the seven policy areas), and then one weight for each measure within the heading. Their product forms a set of weights used for the aggregation of scores into a final index. Let be the score of country in measure ; w k the weight for measure k. Using the latter, the country STRI index value can be written as a function of both the scores and the weights for each measure The function f reflects the method of aggregation. In what follows we review a number of alternatives for scoring, weighting, and the final aggregation, before proceeding to their evaluation in terms of the objectives. 4.1 Scoring schemes 31. The scoring process involves assigning a numerical value to qualitative information on regulation. The score for measure k in country i is denoted. The raw data contains measures of different types and scales. Therefore the choice of a scoring scheme involves a decision on (i) a single type of value for all measures (binary, ordinal or continuous) and (ii) a unique scale. In order to ensure that all measures used are of a single type (for instance binary, or continuous) a choice has to be made among three alternatives: Transforming all scores into binary, all into continuous, or mixed-standardised scores Binary Scores for all measures 32. Transforming all variables into binary scores requires that continuous scores are transformed into by the use of a measure-specific threshold 33. The choice of the appropriate threshold should preferably be based on absolute values that are related to economic, legal or institutional factors. For example, when transforming foreign equity limits 9

10 is a natural choice based on the fact that 50% represents the majority control of a firm to the foreign investor. 34. The loss of information when transforming continuous data to binary could be reduced by the choice of multiple binary measures for each continuous variable transformed. Thus, in the example with equity limits two more thresholds and can be introduced, reflecting minority shares granting rights to block management decisions, the first by the foreign investor, the second by local owners. 35. Not all measures have natural thresholds, however. In such cases a threshold can be assessed in terms of deviation from the sample mean or median. Also in this case multiple thresholds can be introduced, e.g. additional thresholds of one standard deviation below and above the mean. If the distribution of the measure is strongly skewed, the median could be a preferred threshold. 36. Transforming all measures to binary scores ensures comparability across countries and measures and it is a simple and transparent methodology. The shortcomings are first, that a lot of variation in the raw data can be lost. Second, comparability across time depends on the choice of reference point for at least one of the binary scores. Both these problems can be mitigated, the first by introducing multiple thresholds and the second by choosing a time-invariant reference point, e.g. free trade Continuous scores for all measures 37. An alternative method to transforming all variables into binary is to transform continuous variables into a single continuous scale and express all binary variables onto that scale by using its extreme values. In particular, the method involves the choice of a single scale and transformation of all continuous scores into where can be either (a) the maximum value across the sample of countries analysed or (b) the maximum value the measure can take. For instance, when transforming foreign equity limits, the maximum could be 1, that is, 100%, independent of whether that value is observed in the sample or not. 38. When using that scheme, binary variables are transformed into a set of zeros and, which represents the maximum of the new scale. If moreover, then binary variables eventually are not transformed. 39. The advantage of using continuous scores for all measures is that there is no loss of information from aggregation of scores into values of 1 or 0, and hence no need for a choice of the appropriate threshold for assessing restrictiveness Mixed standardised scores. 40. An alternative scheme aiming to preserve information captured by the continuous variables, and at the same time incorporate information on similarity across the sample of countries analysed, involves standardising the pair of binary values observed in each measure (0 and 1) into a pair of binary values on a 10

11 continuous scale. A standardised score 5 allows comparison of observations from different normal distributions, which can be applied first to all continuous variables used. 41. In the binary case, the construction of these scores should be made appropriately. Assume a Bernoulli experiment of n trials,, with two possible outcomes, and a success ratio of p, where. The mean of a Bernoulli distribution is given by the success ratio p, and the standard deviation by. For the case of each binary measure used to construct the index, corresponds to the number of countries analysed; corresponds to the binary scores of the measure ; and the success ratio of p, to the ratio of countries where the restriction applies. The standard scores z, resulting from transformation of binary data can be written as The above formulas give end-points of the transformed scores. For binary measures the score remains binary, that is, it will be either or. 42. The standardisation procedure for continuous variables is based on the properties of the normal distribution, and the same procedure for binary variables based on the Bernoulli distribution. The transformed scores can be used in the construction of the aggregate index. They all express the previous scores in terms of the standard deviation distance to the average of the sample in each measure. 43. The advantage of this transformation lies in the fact that it takes into account the sample of observations in each measure. The higher the similarity of regulation to the rest of the world in some measure, the closer the binary transformed score will be to zero. A novelty in this approach is that low restrictiveness in one measure is expressed with negative values, therefore acts in reducing the value of the index. The aggregate index will be close to zero if restrictiveness in country is similar to the rest of the world. 44. Disadvantages of that scoring scheme rise from two sources. First, each measure is expressed in a different scale, since standardisation takes place within the sample of each variable. Second, the use of different distributions for normalisation requires caution when comparing the resulting scores across measures. Hence the objective of simplicity in presentations is not achieved, neither the objective of ensuring comparability across different samples, unless there is an adjustment of reference points. In particular, the index can be adjusted to take into account new countries and observations, by being expressed in terms of a standardised scale of some reference country and period. Such calculation could be performed specifically for the purposes of comparability across time Choice of a scoring scheme 45. To summarise, binary and continuous scoring are both simple and transparent, while mixed is not. Binary scoring can be made more easily comparable across samples and time, while continuous scoring preserves the variation in the raw data better. The regulatory database contains about 90% binary measures, (see Annex Table A1), which points to binary scoring. The variation in the continuous variables 5. also called z-values, z-scores: a dimensionless quantity derived by subtracting the population mean from an individual raw score and then dividing the difference by the population standard deviation. 11

12 that need to be transformed can be preserved by using multiple binary scores for the most important ones, in particular foreign ownership restrictions. The transformation is explained in detail in the Annex. 4.2 Weighting schemes 46. Weighting of individual measures involves judgement of what is relatively more important in terms of restrictiveness to trade. The weighting scheme can have a large impact on the final outcome of the index. The alternative weighting schemes most commonly found in the literature for composite indices are weights based on expert judgement, weights based on principal component analysis or factor analysis, unobserved component models, and weights based on impact The weighting schemes that have been explored for the STRI are expert judgment, principal component analysis (PCA) and the marginal effect on trade. Expert judgement is considered useful, since experts possess extensive knowledge and experience related to where the binding or most cumbersome restrictions on services trade are found. PCA, in contrast, explore the statistical properties of the underlying data, emphasising variety. 48. As mentioned above, the measures used for the construction of the STRI are grouped into categories according to common elements in the restrictions they represent. The classification used for weighing is that of policy areas, where two sets of weights were used. Each measure is assigned a weight within the category it belongs to, and each category was assigned a weight relative to other categories. The resulting weight for each measure in the overall sample was expressed as the product of both. The approach has two advantages. First, assessing the relative restrictiveness of broad categories of measures is manageable, while for individual measures this can be more difficult Second the approach results in an index which is independent of the number of measures inside each category Expert judgement 49. Expert judgement can be employed in several ways. For instance experts can be asked to allocate a budget of, say 100 points to the measures included in the indictor. Alternatively experts can be asked to rank the measures. The weights used in trade restrictiveness indices such as OTRI on the other hand are based on the marginal effect of the measure in question on trade flows. The STRI project took a new approach to expert judgement. In order to reduce the problem of subjectivity, which is often raised as a criticism of the method, a large group of experts was asked to agree (as opposed to compromise) on a ranking of categories of measures and scores on the individual measures within each category. The group discussions contributed to shedding light on a number of aspects of trade restrictiveness and consensus was reached for most groups in most sectors. The group assessment was expressed in terms of ranks of broad categories and grades on an integer scale for individual measures. The latter can be transformed into ranks before being used in the construction of weights See for instance OECD (2008) or Deardorff and Stern (2004) for a discussion. In particular, let be the grade reported during the expert meetings for measure belonging to category, where corresponds to maximum restrictiveness. The rank of measure inside the relevant category can be written as, where corresponds to maximum restrictiveness. 12

13 50. Let be the ranking of group, where corresponds to the category with minimum restrictiveness relative to the rest. Let also be the ranking of among measures of group, where corresponds to the measure with minimum restrictiveness inside. The resulting weight for measure can be written as the product of the weight for category, (the first fraction of the formula) and the weight for the measure inside the category, (second fraction): 51. Parameter reflects the importance assigned to categories ranked highly relative to the rest. In particular, for the resulting weights reduce to an equal-weighting scheme for categories ( where stands for the total number of categories). The larger parameter is, the higher the weight assigned to the most restrictive categories. For, the most restrictive category receives a weight of unity, and becomes the binding restriction rendering the others irrelevant. A very high value of a could be applied for instance in sectors where commercial presence is the only feasible mode of supply. In that case a foreign equity limit of 0% would render everything else irrelevant. Parameter reflects equivalently the importance assigned to more restrictive measures relative to the rest inside a category. For the resulting weights reduce to an equal-weighting scheme for measures inside each category ( where stands for the total number of measures inside category ). 52. The approach can be mixed according to the combination of values chosen for parameters and. For instance a choice can be made to assign a more than proportionally increasing weight to higher ranked categories (that is ), combined with equal weights for the measures inside each category ( ). 53. The advantage of the expert judgment weighting scheme lies in the sample-independent nature of the resulting weights. The weights can be used in any future revisions of the index without modification. Limitations lie primarily in the subjective nature of the assessment, although the consensus building exercise reduced that bias significantly Factor Analysis (Principal Components) 54. Factor analysis groups together individual indicators that are collinear. The method also evaluates measures by their contribution to the overall variance of the sample. The purpose of the use of this type analysis in the context of this study is to create weights based on each measure s contribution to the variance of the entire sample. The larger a factor s contribution to the variance in the data the larger is its weight. Principal component analysis (PCA) is one methodology within the family of factor analysis. 55. A principal component is an eigenvector in the correlation matrix of the variables included in a dataset. Eigenvectors are ranked according to their corresponding eigenvalues. Each component is defined as a set of coefficients, so-called loadings, measuring the correlation between the individual variables (measures or categories) and the latent component. The factors can be rotated with the purpose of having each measure loaded predominantly on just one of the factors. 56. PCA assumes that the variables are multivariate normally distributed, which is not the case for binary data. However this problem can be solved by using the tetrachoric correlation matrix 8 adjusted to 8. Tetrachoric correlations assume a latent bivariate normal distribution ( ) for each pair of variables ( ), with a threshold model for the observed values ( if and only if ). The means and 13

14 become positive definite, as the basis to extract the components, instead of Pearson s correlations. The factors are orthogonally rotated with the purpose of minimising the number of variables that have a high loading on the same factor. The approach followed here is to weight each variable according to the proportion of its variance that is explained by the component it is associated to (i.e. the normalised squared loading), while each component is weighted according to its contribution to the portion of the explained variance in the dataset (i.e. the normalised sum of squared loadings). 57. The regulatory database contains more variables than observations for most sectors. Having more variables than observations in a PCA is not advisable, and it was therefore necessary to run the PCA analysis in two steps. First the PCA is used to assign weights to each measure inside the categories of measures. Based on these weights, a sub-indicator is calculated (that is, the product of weights and scores) for each category, and a second, PCA is performed on the categories, assigning weights to them, or formally: 58. Let be the loading of measure at the PCA performed inside category on the respective component after rotation, and be the loading of category. Let also be the proportion of the variance of the entire sample explained by component in the PCA performed for measures inside categories, and be the same proportion in the PCA performed for categories. The resulting weight for measure can be written as the product of the weight for category (the first sum of the formula) and the weight for the measure inside the category (second sum): The resulting weight ensure that. is expressed on a scale from zero to one. The denominators of each fraction 59. The disadvantage of the use of such a methodology is that factor analysis assigns the largest weights to the measures that have the largest variation across countries, quite independently of their relative economic significance. It is hence based on the assumption that restrictiveness is more related to dissimilarity in regulation and market conditions than to the conditions as such. The methodology is also sensitive to modifications in the basic data. Data revisions and updates, involving additional observations such as the inclusion of new countries, may change the set of weights that are used to compute the aggregate index. The results are also likely to be sensitive to the presence of outliers Impact Analysis 60. An alternative method for weighting is based on estimating the direct impact of regulation and market conditions on trade in services. The assessment involves simple econometric modelling where the dependent variable is trade flows and the measures used for the construction of the index (or groups of them) are added as independent variables potentially explaining the flows. A simple cross-section setting with the addition of the relevant measures can be used to calculate the weights. variances of the latent variables are not identified, but the correlation,, of and can be estimated from the joint distribution of and and is called the tetrachoric correlation coefficient.. 14

15 61. Let stand for inward trade flows in country ; a regression constant; values of independent variables (unrelated to the measures) explaining inward flows; and scores of measures we are interested to estimate their impact. 62. A logarithmic model is used in order to abstract from measurement units of each explanatory variable, besides the estimated parameters are elasticities, which captures the desired marginal impact on trade. 9. The regression above will yield estimates of coefficients,, and. The estimates of reveal the impact of measures on trade flows in elasticity terms. A normalisation of these coefficients can then be used in calculating weights for each measure as 63. The disadvantage of such an approach is that the measures added in the regression are many and often highly correlated to each other. An important multicollinearity problem is hence introduced while reducing degrees of freedom in the regression with the addition of a large number of regressors. Notice that when the model is cross-sectional, the number of observations will not exceed 30, that is, the number of OECD members. 64. In order to overcome these problems two approaches can be followed. First, instead of regressing inward flows to all measures used for the construction of the index, only one measure can be introduced at a time. The estimation can be repeated for the number of measures used. Alternatively, the principal components scores of countries can be used as regressors. The latter approach is appealing since the independent variables added are not excessive in number and moreover uncorrelated. The estimates can then be used to construct weights for groups of measures each associated with one principal component. 65. The weight of each measure is calculated using the normalised squared factor loadings (that is the coefficients of correlation between measures and components) 66. The impact analysis scheme can be approached as a variant of the dual weighting scheme (one set of weights categories and another one for measures) used in previous methods. The previous approach would require one score for each category for the estimation of category weights, hence an aggregation of measures before the estimation of the model. The aggregation performed by PCA provides such scores to be used, except that they correspond to groupings of measures based on factor analysis instead of 9. Notice that a logarithmic model cannot be used if we use mixed scores (see scoring section) taking both positive and negative values. In the case of mixed scores we will need to standardise along with and proceed with a non-logarithmic model estimating standardised (or commonly known as beta-coefficients) later used to construct weights. Lastly for the case of binary scores we can used dummies instead of. 15

16 categories. PCA further ensures that the scores to be used are uncorrelated which is appropriate for the econometric models to be estimated. 67. This approach was explored for the STRI, but it turned out to be difficult to obtain consistent estimates of the elasticities due to insufficient data coverage Choice of a weighting scheme 68. From a theoretical point of view, the ideal weighing scheme would be based on impact analysis. The problem with such a choice lies in the unavailability of sufficiently reliable and complete services trade data for precise impact estimates to be made. Among the feasible weighting schemes, the most appropriate should come as close as possible to the ideal scheme. Expert judgement fits that criterion, as since experts discussed to what extent each of the broad categories of measures would deter trade. Expert judgment also ensures comparability across time. Nevertheless, although expert judgement is considered the best option for weighting categories of measures, the detailed information within categories does not lend itself easily to the same procedure. Therefore, it was decided to use equal weights for measures within categories. 69. In each of the sectoral papers, results are also presented for calculation using PCA weights as equal weights and random weights for robustness checks. Table 1 presents the estimated weights for each category and sector for equal weights, expert judgement and PCA. Table 1. Weights per category for each sector Restrictions on foreign ownership and other market entry conditions Construction Computer Professional Telecoms EJ EW PCA EJ EW PCA EJ EW PCA EJ EW PCA Restrictions to the movement of people Discriminatory measures, standards and equivalence Public ownership, size and scope of public enterprises Price controls and regulations on market behaviour Barriers to competition Regulatory transparency and licensing/permit systems Note: Abbreviations EJ, EW and PCA stand for expert judgment, equal weights and principal component analysis respectively. 16

17 4.3. Aggregation 70. Scores and weights are used to construct a final index using some aggregation method. Two options are considered: a linear and a geometric aggregation. The construction of the final index could also involve a mixed scheme, where, for instance, scores inside categories are aggregated geometrically and performance in different categories is aggregated linearly. In what follows, we describe how the two schemes operate Linear aggregation 71. A linear aggregation of measures involves summation of scores after weighting. The scores are summed inside categories using a set of measure-specific weights for each category. They are then aggregated over categories using a second set of weights. Both sets sum up to the value of one. That way, the final index values range from zero to one, independently of the number of measures treated. 72. Let be score of country in measure ; be the measure-specific weight measuring the relative importance of inside heading in terms of trade restrictiveness, and be the heading-specific weight. The overall weight for measure is given by the product. Using the latter the weighted average of scores, can be written as where. Both and, therefore. 73. Binary scores can act in a specific way during the arithmetic aggregation of data. In particular, since all scores can take either the value of zero or one, the outcome for a country corresponds to the sum of weights of measures for which restrictions apply Geometric aggregation 74. An alternative way for calculating the final index (often used in the trade literature for aggregation of transportation costs) would be to aggregate measures geometrically:. The approach requires however scores strictly above the value of zero for the index not to meaninglessly reduce to null. 75. For the case of binary data, the geometric aggregation should be adjusted accordingly. In particular, during the arithmetic aggregation of binary data, the outcome for each country corresponds to the sum of weights of measures for which restrictions apply. The equivalent approach in geometric terms would be to represent the index as the product of weights for measures where restrictions apply:. If, the weight for measure will be taken into account in the calculation of the index while for the weight will reduce to the value of 1 hence not taken into account for the aggregation. 76. The construction of weights plays an important role in the representation of the final index. If the aggregation to be applied is geometric then, contrary to the arithmetic approach, there is no need to express all raw weights relative to their sum, since it is not necessary for them to sum to the value of 1 to be used. Weights could instead be expressed in terms of the maximum value of restriction. It is important to notice that for values of the index will diminish when more restrictions are taken into account. Therefore the outcome should be approached as a trade openness instead of restrictiveness index. In that perspective, the product should diminish more, for more important restrictions on trade. A transformation of raw weights on a scale [0,1] with zero corresponding to the maximum raw weight value and 1 to irrelevant measures is appropriate. 17

18 77. Lastly we can transform the outcome of the aggregation into a restrictiveness instead of an openness index using the function to invert results. The STRI can be written as where parameter determines the marginal impact of additional restrictions once a number of them are in place. For values of the marginal contribution of additional restrictions will increase with the number of restrictions while for we will observe the opposite. Figure 1. Transformation from openness to a restrictiveness index 78. The properties of a geometric aggregation differ from those of the arithmetic approach without some specific advantage of the former over the latter. We cannot hence support one of the two as more appropriate for the STRI. We choose the arithmetic aggregation in order to minimize complication in calculations and the presentation of the final result. 5. Robustness Checks and Relevance 79. A number of robustness and relevance checks can be applied in order to test the sensitivity of results to the choices that have been made. The most sensitive issues regarding the calculation of the final index concern weighting and the relevance of measures that are being scored. 5.1 Equal and Random weights 80. PCA, equal weights and random weights are used to perform a sensitivity analysis on the resulting STRIs. A full equal-weighting scheme corresponds to the case where and, where stands for the number if measures inside category, and for the number of categories. Notice that equal weights for both categories and measures is equivalent to the mathematical scheme presented for the treatment of expert judgments, when. 81. Random weights on the other hand correspond to randomly chosen numbers applied to each measure where again. The calculation of the index is repeated 3,000 times using a different set of random weights. The upper limit, mean and lower limit of the index value is reported for 18