CALCULATION OF EXTERNAL TRADE INDICES BASED

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1 UNITED NATIONS DEPARTMENT OF ECONOMIC AND SOCIAL AFFAIRS STATISTICS DIVISION CALCULATION OF EXTERNAL TRADE INDICES BASED ON UNIT VALUES TRAINING MODULE DRAFT for use at the Workshop on Trade Indices, November 2009, Beirut Ronald Jansen Statistics Division/ DESA United Nations New York January

2 Table of Contents Preface... 3 Introduction... 4 Calculation of indices: Step by Step... 6 Step 1: Data preparation... 6 Source of data... 6 Level of transaction detail... 9 Data Quality Assurance Example: Basic Dataset Step 2: Identification of outliers Box-plot method for determining outliers Example: Detecting outliers in Basic Dataset Step 3: Separating homogenous from heterogeneous commodities Assessment of variability Assessment of multimodality Criteria for selection of homogeneous unit values Preparing the basic data set: a summary Example: Is the Basic Dataset homogeneous? Step 4: Calculating elementary trade indices Basic Formulas Laspeyres Paasche Comparison of Laspeyres and Paasche Volume indices Fisher Index Fixed-base versus chain indices Example: Calculating elementary indices for Basic Dataset Step 5: Determining the weights Weights and sources Structures of International Trade Indices Example: Determining weights for Basic Dataset Step 6: Calculating aggregated trade indices Higher-level price indices based on unit values Example: Calculating Export Price Indices for Basic Dataset Example: Export Price Index of Australia Annex 1: Basic Data Set Annex 2: An alternative outlier detection method Annex 3: Step-by-Step approach proposed by IMF working group Basic Steps in XMPI Development Step 1 Determining the objectives, scope, and conceptual basis of the index Step 2 Deciding on the index coverage and classification structure Step 3 Deriving the weighting pattern Step 4 Designing the sample Step 5 Collecting and editing the prices Step 6 Adjusting for changes in quality Step 7 Calculating the index Step 8 Disseminating the indices Step 9 Maintaining samples of businesses and commodity specifications Step 10 Reviewing and re-weighting the index

3 Preface At the request of national trade data compilers, who attended workshops on international merchandise trade statistics organized by the United Nations in Addis Ababa (2007) and in Cairo (2008) this guide was put together. They explicitly wanted a guide that explains in detail the steps needed for calculating an external trade index. Since most national offices still use merchandise trade statistics as basis for the trade index calculation, this guide tries to outline the steps necessary to decide if (1) basic unit values are good enough for index calculation and (2) how to actually arrive at the index. Calculation of External Trade Index numbers is not an easy task. In theory, there are many different ways of calculating price indices depending on its use or on assumptions regarding the purchaser or seller behavior. And in theory, we assume that price data are readily and accurately available. However, in practice, price data are not readily and accurately available. For import and export price indices there is the added complication that not only the prices of goods need to be known, but also the amounts in which they have been traded. In practice, the most difficult part of external trade index calculation is obtaining reliable price information and corresponding trade volumes. The manuals which are available at the international level to guide national data compilers are Guidelines on Price and Quantity Statistics (1977), Strategies for the Measurement of External Trade Indices (1981), and the draft Export and Import Price Index (XMPI) Manual, which can be viewed on the website of the IMF 1. The XMPI Manual explains very well all the theoretical intricacies of price indices in general, and import and export price indices in particular. However, it does not give cookbook recipes on how to actually do it. There is an attempt to do so in the last part of Chapter I, namely in Appendix 1.1: an Overview of the Steps Necessary for Developing XMPIs. To give the reader some more perspective, I reproduced those steps in Annex 3 of this guide. This guide is only meant as workshop material and should not be cited or further circulated. All comments are more than welcome. I further invite national data compilers to send me 2 examples of actual data sets, which can be used as practice material for a textbook compendium to this guide. The United Nations Statistics Division has set as a long-term goal to produce an internationally accepted compiler s guide for the production of external trade indices, and the current document is a very first step in that direction. 1 See 2 Please send to jansen1@un.org 3

4 Introduction Price indexes are designed to measure price change. Price is defined as the value placed on a product at the point of transaction. However, the buyer and seller may place a different value on the product, depending upon how indirect taxes, subsidies and transport charges are recorded. For example, the price a manufacturer receives for the direct retail sale of a product such as a motor vehicle is not the same price that a consumer would pay for the product because the consumer must pay goods and services tax (GST). The system of national accounts (SNA) refers to three special types of valuation bases: basic prices, producers' prices and purchasers prices. The basic price is the amount receivable by the producer from the purchaser for a unit of a good or service produced as output, minus any tax payable, plus any per unit subsidy receivable on that unit as a consequence of its production or sale. Both the import price index and the export price index are valued on a basic price basis, namely on a so-called free on board (FOB) valuation basis. The value of goods measured on an FOB basis includes all production and other costs incurred up until the goods are placed on board the international carrier for either export or import. Free on board values exclude international insurance and transport costs. They include the value of the outside packaging in which the product is wrapped, but do not include the value of the international freight containers used for transporting the goods. However, in practice, the imports price index may include insurance and freight costs as well (the so-called CIF basis), since the values of transactions on customs documents are often recorded on a CIF basis. Average unit values (or simply average prices) reflect multiple shipments of a given product within a consistently defined period, for which data are usually readily available. The advantage of average unit values is that they effectively increase the number of price observations used to calculate the index, thereby reducing sample variance. The reduction in variance is achieved because average unit values explicitly represent the entire population of transactions for a particular good or service, and so the concern when pricing a handful of single transactions does not apply. An average unit value should reflect prices in the current period, and the price should relate to homogeneous transactions. The import price index measures the changes in the prices of merchandise that is imported. A transaction is in scope of the import price index if the merchandise crosses the customs frontier during the reference quarter and is cleared and recorded by the Customs authorities. External Trade indices (also indicated as Export and Import Price Indices or XMPIs) are compiled using unit values collected and compiled for international merchandise trade statistics, prices collected with enterprise surveys or a combination of unit values and prices. This hybrid method seems the preferred way forward in this area. 4

5 Unit values The first method uses unit value indices compiled from detailed import and export merchandise trade data derived from administrative customs documents. Unit value indices are not price indices since their changes may be due to price and (compositional) quantity changes. However, they are used by many countries as surrogates for price indices. Unit value in the context of international trade is defined as the price actually paid for one unit (by quantity unit) of the given commodity when sold for exportation to the compiling country or purchased for importation from it. Price surveys The second method is to compile price indices using data from surveyed establishments on the prices of representative items exported and imported. The surveyed prices should be of items that are defined according to detailed specifications, so that the change in price of the same item specification can be measured over time. Hybrid method The third method is a hybrid approach that involves compiling establishment surveybased price indices for some product groups and customs-based unit value indices for others. Unit value indices are then used for relatively homogeneous product groups, whose composition of traded goods and services, in terms of the quality mix of items traded each period, is considered to be unlikely to change significantly; and price indices are used for specific high value items. In all practical cases, the hybrid approach seems the most realistic and most appropriate. In 1981, the United Nations published international guidelines on choosing among these alternatives methods A Strategy for Price and Quantity Measurement in External Trade and advised countries with less means to use more unit value indices than wellendowed countries. The preference for price survey indices was, for the large part, due to bias in unit value indices mainly attributed to changes in the mix of the heterogeneous items recorded in customs documents, but was also attributed to the often poor quality of recorded data on quantities. The former is particularly important in modern product markets. The latter, however, has become less important as a reason, since over the last decade, statistical offices working with customs authorities have made considerable improvements in the quality of international merchandise trade statistics, in particular also the quality of the quantity data. Moreover, commodity descriptions used by customs are kept up-to-date by periodically updating in response to changes in product markets. Finally, some trade may not be covered by customs controls, such as electricity, gas, and water, or be of unique goods, such as ships and large machinery. If these items are important for the trade of a country, then establishment price surveys should be carried out. 5

6 Unit value indices as measures of price changes of imported and exported goods serve economic analysis in many important ways. They are used as short-term indicators of inflation transmission, to measure changes in a country s terms of trade (effect), and as deflators of export and import values to yield measures of changes in export and import volumes. An issue of strategic concern is whether unit value bias could mislead economists in their analysis. As stated before, the hybrid approach seems the most realistic and most appropriate and it is therefore advised that countries in addition to unit value indices compile price indices for those items, which are not homogeneous, are high value and are traded in significant amounts by the compiling country. Calculation of indices: Step by Step The purpose of this guide is to help national compilers in the calculation of external trade indices, one step at a time. First, a basic data set needs to be prepared; then, unit values need to be calculated and outliers be eliminated; thereafter, a test for homogeneity will be done. At this point the basic unit value set is ready for index calculation. Hereafter, index numbers are generally calculated in three steps. First, there is the measurement of price changes of similar elementary items exported or imported by one particular trader or enterprise to or from a particular foreign importer or exporter by one particular means of transportation; these are the building blocks of price indices. The items should be as detailed as possible. National commodity classifications may be detailed enough for some fairly homogeneous items, but for certain important trading products a finer classification may have to be derived from the shipping details. Unit value indices derived in this way from international merchandise trade statistics or from more detailed customs documents are then compiled into so-called elementary indices. Data on weights (i.e. relative importance) are not available at this level of aggregation. At the next step weights are determined. The weights indicate the relative importance of the items in terms of their contribution to the imports or the exports value of the country. At the final step, weights are applied to the elementary indices to aggregate to higher levels, and weights are again applied to the resulting indices at higher stages of aggregation, until an overall index is derived. Standard index number theory applies to the issue of weighted formulas at the higher levels, irrespective of whether the elementary indices are compiled from unit values derived from customs data or price indices based on establishment surveys. Step 1: Data preparation Source of data Customs records are the basic source of data for international merchandise trade statistics and are, therefore, the major source of data for calculating unit values. The information 6

7 normally required in declaration forms and relevant for compilation of trade statistics (either for inclusion into statistics or for verification purposes) includes the following: Port of import/export: the port at which the goods actually enter or leave the customs territory of a country; Date of importation/exportation: for imports, the date on which the carrier transporting the goods arrives at the customs territory; for exports, the date of departure or date of clearance; Date of lodgement: the date on which the customs accepts the declarations submitted by importers, exporters or their agent; Importer/exporter: in general, refers to the party in the customs territory who signed the contract of purchase/sale and/or who is responsible for executing the contract (i.e., the agent responsible for effecting import into or export from a country). Each importer or exporter is usually assigned a unique identification number; 3 Nature of transaction (e.g., purchase/sale, barter, lease, gift.); Mode of transportation: the type of carrier which transports the goods into or out of the customs territory (e.g., sea and water, rail, road (truck), air, postal, other); 4 Carrier identification: the name and the voyage/flight/wagon/vehicle number of the carrier actually transporting the goods into or out of the customs territory; Bill of lading/airway bill: the importing or exporting carrier s bill of lading, airway bill number, rail receipt number, post office number; Consignee/consignor: the party to whom goods are consigned/the party who consigns the goods; Country of consignment: the country from which goods were dispatched to the importing country (to which goods were dispatched from the exporting country), 3 For example, China uses a 10-digit ID number structured where the first five digits give the location of the importer or exporter (city, province, special economic zone, bonded area, high-tech industrial development area etc.), the sixth digit gives category of importer or exporter (state-owned enterprise, Sinoforeign contractual joint venture, Sino-foreign equity joint venture, foreign-owned enterprise, collective enterprise, private enterprise, other), and the last four digits form a serial number. The ID number and name of the importer or exporter are required to be reported. 4 The Working Party on Facilitation of International Trade Procedures, a subsidiary body of ECE developed a one-digit numerical code to represent mode of transport and to specify categories of means of transport according to the mode for which they are intended. It also provides for the possibility of adding a second digit for any subdivision, as required. The definition of the codes (0 through 9) may be found on the Internet at 7

8 without any commercial transactions or other operations which change the legal status of the goods taking place in any intermediate country; Customs procedure (regime): the type of customs procedure under which imported or exported goods are cleared from customs; License number: validated import or export license number, for goods subject to import or export license; Related party transaction (i.e., one between parent company or sister company); 5 Location of domestic consumer/producer: Location of domestic consumer refers to the location in the customs territory for which imported goods are destined or where they will be ultimately consumed or utilized. Location of domestic producer refers to the location in the customs territory where the exported goods are produced, manufactured or from which the goods actually start their journey to the port of export, if the origin of production is unknown; Port of loading/destination: port of loading means the last foreign port where the imported goods were loaded on the carrier that brought them to the compiling country; port of destination means the ultimate foreign port to which the exported goods will be designated; Terms of delivery: the transaction terms of delivery is required to be reported, usually INCOTERMS 2000; Freight: the freight charges; Insurance: the insurance charges; Total value: the price actually paid for all units (by quantity unit) of the given commodity (multiply unit price by quantity), or the cost of the commodity if not sold or purchased; Customs value: the value of goods established in accordance with the customs law of a country; Type of financial transaction: an indication of payment method; Unit of account: the currency in which the transaction occurs is required to be reported; Statistical value: the value assigned to goods by a compiler of trade statistics, according to the rules adopted by the compiling country; 5 Many countries do not include this requirement; countries have different criteria for determining whether parties are related. 8

9 Number and kind of packages: the number and kinds of packages (bulk, boxes, barrels, baskets etc.); Marks: marks or other identification shown on the packages and the numbers and kinds of packages (boxes, barrels, baskets etc.); Commodity code: usually the HS-based code, where the first six digits are the HS codes and the others are national extensions; Commodity description and specification: a sufficient description of the commodity to permit verification of the classification code or the description and specification as shown on the validated import or export license; Gross weight (kg): the gross weight of shipments in kilograms, including the weight of moisture content, packing and containers (other than containers, such as cargo vans and similar substantial outer containers used for containerized cargo); Net weight (kg): the net shipping weight in kilograms, excluding the weight of packages or containers; Domestic or foreign goods: specification of whether the good is of domestic or foreign origin; Quantity and quantity unit: report the amount in terms of the unit(s) adopted by national legislation; in many cases, they are based on the standard units of quantity recommended by WCO. The unit of quantity specified in the transaction is also required to be reported if it is other than the customs standard units; Country of origin: as established in accordance with the country's rules of origin; Country of destination (also called country of final or ultimate destination): the country in which the merchandise is to be consumed, further processed or manufactured; the final country of destination as known to the exporter at the time of shipment; or the country of ultimate destination as shown on the validated export license. Two- or three-digit (alpha character) International Organization for Standardization (ISO) codes or other codes may also be used; Level of transaction detail Each of the above mentioned data elements could be taken into consideration in the calculation of the unit values. If any one of these elements (by itself or in combination with a specific commodity) is considered to significantly influence the variability of the data, it should be taken into consideration in unit value calculation. For instance mode of transportation and foreign destination could be important factors on the unit value. 9

10 In general, the following elements are recommended to be taken into account: (1) port of import or export; (2) mode of transportation, (3) country of origin or destination, and (4) customs procedure. Unit values should of course be compared using the same quantity unit. The commodity itself can be taken from the standard classification, but preferably is used in even finer detail. The purpose of the analysis and selection of unit values is to arrive at a unit value which for the reference period gives a good representation for the price of the traded good given its particular commodity description, port of import or export, mode of transportation, country of origin or destination and customs procedure. Data Quality Assurance Before going into the details of analyzing and selecting unit values, the quality of the data needs to be of high enough quality. In almost all countries both the Customs administration and the National Statistical Office make extensive use of computer equipment and applications. Practically all customs declarations are nowadays captured electronically. This implies that customs data are verified at the source, available in great detail and available to the statisticians in a very timely manner. Even in the least developed countries customs administrations are nowadays computerized due to the Automated System for Customs Data (ASYCUDA) project of United Nations Conference on Trade and Development (UNCTAD). ASYCUDA is operational in about 90 developing countries. That system verifies declaration entries at the time of transaction. Declarations need to be completely filled in order to receive customs clearance. This means among others that quantity information needs to be provided and will be verified. In addition, customs values are validated to avoid undervaluation for purposes of import duties using unit values on the declaration which are matched against a regularly updated list of commodity prices. Processing error in trade statistics involves errors in coverage, time of recording, commodity classification, valuation, quantity measurement and partner country. In the following paragraphs, some checking devices are proposed that should help reduce the number of processing errors (and also identify registration errors). Quality control by code validation A basic requirement in the processing of trade statistics is the validation of codes on the customs document against a standard code list. Automated systems for the entry of customs documents should have built-in standard code lists against which the entered information is checked. It is very important for such systems to ensure that the standard code lists at the various ports of entry/exit of a country are always aligned. In the case of frequently changing tariff line codes, additional effort should be made to keep code lists aligned and up-to-date. If possible, some cross-checking procedures for the validation of 10

11 codes should be implemented which can involve combinations of quantity units and commodities or a three-way combination of customs regime, partner country and port of entry. Quality control by validation of value and quantity A more difficult, but no less important validation of trade statistics is the checking of values and quantities. Customs procedures include a check on the reasonable value of the goods being imported (especially for trade between related enterprises). This means that lists of unit values for a large number of goods are available. Statisticians could do similar kind of checking and, in addition include some time-series trends on the unit value of the goods. Large deviations should then be traced back to the customs documents for correction. In addition to checking elements of the transactions (micro-level checks), macro-level checks can also be done. These involve checking growth rates and composition of aggregates for reasonableness, and checking against other available non-customs statistics for certain products, such as domestic production. Example: Basic Dataset Table 1: The basic data set Partner Trade Value Net Weight Unit Value Log (Unit Rank (FOB) (kg) Value) Yemen $220,226 84,417 $ Jamaica $299, ,967 $ Jordan $2,497, ,300 $ Rep. of Korea $7,884,633 2,755,607 $ Lebanon $1,134, ,787 $ Guyana $88,339 29,940 $ Saudi Arabia $5,148,588 1,713,378 $ The table above shows some entries of a fictitious dataset of Country Z for the exports of Cheese (HS-2002 commodity code 0406) in the period Jan-Dec 2004 where further the port of departure is always Sea-town and mode of transport always by Sea. In this example table there are only 7 transactions shown. In annex 1, the full data set of 100 transactions is given. The unit values of these export transactions of Cheese range from $2.61 per kilogram up to $7.38 per kilogram. The 25 th percentile equals $3.77 per kilogram, the median $4.09 and the 75 th percentile is $4.73. This means that 50% of the unit values are within the range of 1 dollar. Annex 1 also shows that the distribution of the unit values is somewhat skewed to the right with 50% of the data within a range of $1.50 below the median and 50% within a range of $3.50 above the median. In the following sections, we are looking into the variability of the unit values and pose the question if these are still acceptable, so that the median (or mean) could be taken as a good representation for the unit value of this set of goods transactions within this period. 11

12 Step 2: Identification of outliers Data points that seem to be inconsistent with the general characteristics of the sample are called outliers. Outliers may arise due to: Errors in data entry or processing. Atypical circumstances in the data generating process Intrinsic variability of the data generating process. Methods of outlier detection are useful for both conducting data quality checks and understanding the reliability and intrinsic characteristics of the data generating process. The method used in this step-by-step approach is Tukey s Box-plot, which in theory eliminates the outer 0.35% of either end of the distribution of data points under the assumption that the distribution is symmetrical. For many agricultural products, other raw materials and also minerals and chemicals, cost is a few dollars per kilogram. Obviously, cost per kilogram cannot get much cheaper in such cases, but they could at occasion be much more expensive. This implies (and is generally known) that unit value distributions are mostly asymmetrical with a long tail towards the higher unit values. After applying a logarithmic transformation to the unit value data a symmetrical distribution can be restored. Therefore, outlier detection and other tests on variability (see next section) are not done on the actual unit values but are done on the log-transformed data. For instance, whereas it was shown that the unit values in the basic dataset where skewed to the right, the log-transformed unit values are less skewed with a minimum of 0.416, a median of and a maximum of Box-plot method for determining outliers This guide advises to use the Box-Plot method of John Tukey to determine outliers (see for details). The picture below shows the reasoning behind the box-plot. Data points falling within the outermost 0.35% of the distribution are called outliers and will be eliminated from the dataset. This distribution does have to be approximately symmetrical in shape, which is why we advise to do a logtransformation first on the unit value data. On the log-transformed sample, the lower threshold is calculated by taking the 25 th percentile (Q1) and subtracting from it 1.5 times the width of the inter-quartile range, which the difference between Q3 (75 th percentile) and Q1. Similarly, the upper threshold is calculated by adding 1.5 times the inter-quartile range to Q3. Unit values outside of these thresholds are called outliers and are eliminated. Other outlier detection methods may be used, such as the Asymmetric Fence Method shown in annex 2, which is used by the Italian NSO. 12

13 Example: Detecting outliers in Basic Dataset For instance in the basic dataset of exports of Cheese by country Z, Q1 = $3.77 and Q3 = $4.73. On the log-transformed data Q1=0.577 and Q3= 0.675; this means that the lower threshold = Q1 (1.5*[Q3-Q1]) = = 0.430, which is 2.72 $/kg after retransformation to the actual unit value; and the upper threshold = Q3 + (1.5*[Q3-Q1]) = = 0.822, which is 6.64 dollar per kilogram in terms of actual unit value. So, any value lower than 2.72 or higher than 6.64 is an outlier and will be eliminated. In this case, the unit values of following transactions are considered outliers. The minimum unit value of $2.61 is smaller than the lower threshold and the two highest unit values of $7.37 and $7.38 are clearly higher than the upper limit. These transactions are therefore regarded as transactions which were generated under different conditions or with somewhat parameters and are thus eliminated. Figure 1: Lower and Upper acceptance limits in a normal data distribution 13

14 Step 3: Separating homogenous from heterogeneous commodities After elimination of outliers it still needs to be determined if the remaining sample of transactions can be considered homogeneous and suitable for calculation of trade indices, or not. The main criteria, which are recommended in this guide, are low variability and uni-modality of the data sample. Further, the sample needs to have a minimum of observations and the value and quantity of the eliminated outliers should be relatively small in comparison to the remaining value and quantity. Assessment of variability A measure of variability (or dispersion) recommended here is the relative inter-quartile range, which is a non-parametric measure of variability and is defined as RIQ ( Q Q ) 3 1 =, M where M represents the median and Q 1 and Q 3 the 25 th and 75 th percentiles of the unit value sample. In our data sample calculation of RIQ for exports of Cheese by Country Z (after elimination of outliers) gives the following. RIQ = ( ) / 4.09 = 0.23 Note that RIQ is calculated on the basis of the actual values, because M, the median, needs to have its actual magnitude in comparison to the inter-quartile range. Logtransformation would shrink the size of the median disproportionally. It should further be noted that any RIQ less than 1.0 indicates low variability in the data sample. Therefore, we recommend using a RIQ of 1.0 as the upper limit for selection of homogeneous data sets of a particular combination of commodity, port of import or export, mode of transportation, country of origin or destination and customs procedure. Assessment of multimodality Determining a single representative unit value can only be done if the data sample is unimodal. In other words, there should be one specific unit value for the particular combination of commodity, port of import or export, mode of transportation, country of origin or destination and customs procedure. For instance, if there are two varieties of Butter which are imported in about equal amounts, but have distinctly different prices, say $2 and $5 per kilogram respectively, the distribution of unit values will show two very distinct modes. In such case, it is advised to split the data set into the two sub-sets and perform further analysis on those sub-sets of data. 14

15 To assess the degree of multimodality in a sample of unit values, the following multimodality index (MMI) based on the histogram of the actual data is proposed: m + L + m MMI = ( ) 1 k 2 2 m 1 + L + m k 2, where k is the number of modes in the sample histogram and m j is the mass weight attached to its jth mode (i.e., the number of data points falling in jth mode s cell, divided by the total number of individual unit values used to construct the histogram). If there is only one mode (i.e., if k = 1), the multimodality index takes the value of one; if there are two equally relevant modes (i.e., if k = 2, with m 1 = m 2 ), the index is equal to two; etc. Note that mode in this case should be understood as a local high point. This means that the frequencies of data points in the interval immediately before and immediately after this particular interval are lower. Note further that subscript k in the formula above does not indicate the number of all intervals, but only the number of those intervals with a mode (a local high point). This guide recommends to split the range of data points into 10 equally spaced intervals by simply taking the difference between the minimum and maximum (after elimination of outliers) and dividing this by 10. This gives the width of each interval. For the basic data set the minimum after elimination of outliers is $2.73/kg and the maximum $5.95/kg. Ten equally spaced intervals would then run from 2.73 to 3.06; the first interval from to 0.470, the second from until 0.504; and so forth. Thereafter, the observed unit values are placed in one of the ten intervals and a histogram is drawn up of the number of observations per interval. Frequency of unit values equally-spaced Intervals Figure 2: Histogram of number of unit values per equally spaced interval 15

16 Figure 2 shows that whereas the distribution looks quite uni-modal with a real mode in the fourth interval, there are a number of small local modes, namely in the 1 st, 6 th and 10 th interval. Upon calculation MMI turns out to be Ideally, MMI is less than 1.5, but a MMI of less than 2.0 is still acceptable. However, if the variability of the data (the spread) is very low (small), then it becomes more likely to have a number of local high points in the dataset, and MMI may rise above 2. In other words, there is an inverse relation between RIQ and MMI. Low variability is highly desirable and is more important than a low MMI. Therefore, low variability is a must to ensure a homogeneous set of data. However, lack of apparent uni-modality can be compensated by a very low variability. In terms of criteria, the guide recommends a RIQ below 1.0 and a MMI below 2.0. If MMI is higher than 2, the dataset would still be acceptable if compensated by a very low RIQ. In particular, the multiplication of RIQ and MMI should remain below 1.0. Criteria for selection of homogeneous unit values In the previous section this guide recommended 2 criteria for selecting homogeneous unit values. Namely: 1. RIQ < 1 2. MMI < 2, or (RIQ*MMI) < 1 We want to add two practical criteria to support the reliability and validity of the data, namely: 3. There must be at least 30 observations in the sample 4. The trade value corresponding to outliers must be less than 5% of the total trade value Preparing the basic data set: a summary To summarize, the basic data set of unit values should be sufficiently detailed to make it plausible that the transactions could be called replications of each other. In practice this would mean that for any specific period transactions are selected from the same port of entry (or departure), same mode of transport, same destination country (or region), and same commodity description. If possible, choose also the same (or closely similar) customs procedure. If for certain products a specific company is the major exporter (or importer) then you may wish to pool data from only that company. Given that the data will be used for internal calculations only, confidentiality should not be an issue. 16

17 Note that it is possible to use different levels of detail for different commodities. In some cases you may need to choose very detailed commodities by exporter and country of destination, while for other cases broader categories among all exporters and by region of destination may be sufficient (because trade may be weak in those cases). However, you should use the same structure of data for each time period. If you use the Laspeyres formula to calculate the trade index, then the structure of data at time 0 is the structure, which should be used throughout; if you use Paasche, the structure of data at time t should be used throughout. Once you have established the basic data sets, each set goes through the screening and selection procedure. First, outliers are removed and then the above mentioned criteria are applied. To start the data processing, make sure that there are at least 30 transactions per data set. Then, rank the unit values from smallest to largest; create log-transformed unit values in a separate column, determine the 25 th and 75 th percentile and calculate the lower and upper acceptance limits. Determine which unit values are outside the boundaries and check if the corresponding transaction values are relatively low in comparison to overall trade value for that set of data. After removing the outliers, determine minimum, Q1, median, Q3 and maximum on the remaining unit values, thereafter calculate RIQ and MMI. Apply the selection criteria and conclude if data set is homogenous or not. As a brief overview the steps for data preparation are then as follows: 1. Determine structure of the basic transaction files and calculate the unit values and their corresponding log-transformations; 2. Make sure the files contain at least 30 transactions; 3. Rank the data by unit vale; 4. Determine Q1 and Q3; 5. Calculate lower and upper acceptance limits; 6. Remove outliers and calculate their total value; 7. Determine minimum, Q1, median, Q3 and maximum on remaining data; 8. Calculate RIQ and MMI; 9. Apply selection criteria; 10. Decide if the unit value data set is homogenous. Example: Is the Basic Dataset homogeneous? For our basic data set of exports of Cheese by Country Z for the period Jan-Dec 2004, there were 100 transactions. It was shown that the smallest and the two highest unit values were outliers. The total value of these transactions was $895,000, which is about 0.04% of the total value of all exports of Cheese by Country Z in 2004, which was 2.2 billion US dollars. On the remaining 97 transactions, minimum, Q1, median, Q3 and maximum were calculated to determine RIQ and MMI, which were 0.23 and 3.37 respectively. Whereas MMI could be considered too high, the very low spread compensates for this, since 17

18 RIQ*MMI = 0.8 which is lower than 1. Therefore, this unit value data set is considered to be homogeneous and valid for further calculation of the trade index. Step 4: Calculating elementary trade indices Elementary trade indices can be calculated on single commodities or on multiple refined commodities. For single commodities, the trade index is simply the price relative between time t and time 0. For multiple commmodities micro-index weights need to be available for use in Laspeyres or Paasche formulas. It is assumed that the unit values of any of these commodities are homogeneous and available in every quarter. As advised in this guide, the sample of unit values needs to satisfy the criteria mentioned in the previous section. Basic Formulas Laspeyres The formula for the Laspeyres price index, PL, is given above, where s i 0 denotes the share of the value of commodity i traded (as exports for an XPI and imports for an MPI) in period 0, that is, Paasche The formula for the Paasche index, P P, is shown above where s i t denotes the actual share of traded values of commodity i in period t, that is, 18

19 The Paasche index can also be expressed in two alternative ways: either as the ratio of two value aggregates or as a weighted average of the price relatives, the average being a harmonic average that uses the traded value shares of the later period t as weights. However, it follows from equation above that the Paasche index can also be expressed as a weighted arithmetic average of the price relatives using hybrid weights in which the quantities of t are valued at the prices of 0. Comparison of Laspeyres and Paasche If the objective is simply to measure the price change between the two periods considered in isolation, there is no reason to prefer the basket of the earlier period to that of the later period, or vice versa. Both baskets are equally relevant. Both indices are equally justifiable, or acceptable, from a conceptual point of view. In practice, however, XMPIs are calculated for a succession of time periods. Time series of monthly Laspeyres XMPIs based on period 0 benefit from requiring only a single set of nominal trade weights, those of period 0, so that only the prices have to be collected on a regular monthly basis. Time series of Paasche XMPIs, on the other hand, requires data on both prices and quantities (or nominal trade weights) in each successive period. Thus, it is much less costly, and time consuming, to calculate a time series of Laspeyres indices than a time series of Paasche indices. If detailed data on nominal trade flows are not timely, this is a decisive practical advantage of Laspeyres indices over Paasche indices and explains why Laspeyres indices are used much more extensively than Paasche indices. Monthly Laspeyres XMPIs can be published as soon as the price information has been collected and processed, since the base period weights are already available. Of course, weights should be updated regularly and Laspeyres indices with frequently updated weights, or annual chained Laspeyres indices, are a preferred option as discussed below. Volume indices Laspeyres and Paasche volume indices are defined in a similar way to the price indices, simply by interchanging the p s and q s in formulas shown above. They summarize changes over time in the flow of quantities of goods and services exported/imported. A Laspeyres volume index values the quantities at the fixed prices of the earlier period, while the Paasche volume index uses the prices of the later period. The ratio of the nominal (current price) traded values in two periods (V) reflects the combined effects of both price and quantity changes. When Laspeyres and Paasche indices are used, the value change exactly decomposes into a price index times a volume index only if the Laspeyres price (volume) index is matched with the Paasche volume (price) index. Suppose, for example, compilers want to deflate a time series of imports in the national accounts to measure changes in import volume supplied to the economy at constant 19

20 prices over time. To generate a series of import values at constant base period prices (whose movements are identical with those of the Laspeyres volume index), the imports at current prices must be deflated by a series of Paasche price indices. Laspeyres MPIs would not be appropriate for the purpose. If nominal values are available and deflated at a very low level of disaggregation, the resulting volume series for the detailed trade commodities can then be aggregated up using a say (chained) Laspeyres formula. It follows that volume series ca be defined as / L V P or / P V P. This division of a value change by price index to form a volume index is referred to as deflation. If a Paasche deflator is used for comparisons between say period 0 and successive periods this yields on deflation a Laspeyres volume series that measures quantities at a constant period 0 prices. Fisher Index When the base and current periods are far apart, the index number spread between the numerical values of a Laspeyres and a Paasche price index is liable to be quite large, especially if relative prices have changed a lot. Index number spread is a matter of concern to users because, conceptually, there is no good reason to prefer the weights of one period to those of the other. In these circumstances, it seems reasonable to take some kind of symmetric average of the two indices. More generally, it seems intuitive to prefer indices that treat both of the periods symmetrically instead of relying exclusively on the weights of only one of the periods. It will be shown later that this intuition can be backed up by theoretical arguments. There are many possible symmetric indices, but the best known is the Fisher price index, PF, defined as the geometric average of the Laspeyres and Paasche indices; that is, P F P L P P. Fixed-base versus chain indices When a time series of Laspeyres indices is calculated using a fixed set of quantities, the quantities become progressively out of date and increasingly irrelevant to the later periods whose prices are being compared. The base period whose quantities are used has to be updated sooner or later, and the new index series linked to the old. Linking is inevitable in the long run. In a chain index, each link consists of an index in which each period is compared with the preceding one, the weight and price reference periods being moved forward each period. Any index number formula can be used for the individual links in a chain index. A chain index between two periods has to be path dependent. It must depend on the prices and quantities in all the intervening periods between the first and last periods in the index series. Path dependency can be advantageous or disadvantageous. When there is a gradual economic transition from the first to the last period with smooth trends in relative 20

21 prices and quantities, chaining will tend to reduce the index number spreads among the Laspeyres, and Paasche indices, thereby making the movements in the index less dependent on the choice of index number formula. Example: Calculating elementary indices for Basic Dataset Basic Data Set concerned only data for commodity 0406, year 2004 and period January- December. To calculate trade indices, we need more periods and more commodities. Keeping all other variables equal we got additional data sets for commodities 0404 and 0405 for periods Jan-Dec 2004 and Jan-Mar Also for 0406 we obtained a data set for the period Jan-Mar The results of the data preparation for these data sets are given in the table below. It shows that all RIQ are lower than 1 and almost all (RIQ*MMI) are lower than 1 as well. The only exception here is for commodity 0405 in the period Jan-Dec In this case MMI > 2 and (RIQ*MMI)>1. Given our criteria we cannot accept 0405 in Note that all samples have more than 30 observations and that the value of the outliers is less than 0.05% in all cases. Table 2: The selection criteria calculated (RIQ*MMI Jan-Dec 2004 Q1 Median Q3 RIQ MMI ) 0404 (n=84) (n=100) (n= 100) Jan-Mar 2006 Q1 Median Q3 RIQ MMI 0404 (n=80) (n=100) (n=100) Given that Jan-Dec 2004 is our base period 0, the commodity 0405 needs to be dropped from the list of commodities for calculating the external trade index. If we take the median as the representative unit value for the period, then we find as price relatives for Jan-Mar for commodity 0404 and for commodity We disregard commodity 0405 since it did not meet our homogeneity criteria. Table 3: Price relatives HS Price relative In the following section we need to determine the micro-weights necessary to use in the Laspeyres or Paasche formula to calculate the aggregate trade index. 21

22 Step 5: Determining the weights Weights and sources The international trade price indexes are computed as averages of the price relatives of the many products for which prices or unit values are collected. For an input price index, the average is weighted to reflect the importance of each priced product in terms of its share of total purchases in the market. For an external trade price index, the average is weighted to reflect the importance of each priced commodity in terms of its share of total imports or exports. The international trade price indexes are ideally calculated from many prices collected from all types of establishments, covering the selected economic activities and products. In practice, often unit values are used instead of direct prices collected from customs documents. The collected prices or unit values are first combined to compile indexes for each individual product or commodity. For example, 40 prices or unit values for different types of transactions for a detailed type of product may be collected from a range of establishments or from a particular combination of port of entry (exit), mode of transport and destination (origin), and these prices/ unit values have to be combined in order to produce the trade index for the particular commodity. Once this has been done, the commodity price indexes are combined to produce the class, sub-group, group and subdivision indexes, and eventually the overall trade index. As some commodities have greater share in imports or exports than others, each commodity is given a weight to represent its importance in total trade (or expenditure, for an input index) during the base period for the weights. To arrive at the aggregate index figure the price relatives of the individual commodities are multiplied by these weights to derive a weighted average aggregate index. The weights are key elements in the construction of international trade price indices. They determine the impact that a particular price change will have on the overall index. For example, a 5% rise in the price of crude petroleum products has a much greater impact on the average rate of price change for imports than a 5% increase in the price of paper products, because the import value of crude petroleum products is generally much higher than that for paper. Without explicit weights, relative price changes for all commodities in the price basket would be given equal importance in calculating the index above. In discussing the importance of weights, it is necessary to refer to the structure of the international trade price indexes. At the top is the total value of commodities. This is progressively divided into finer product groupings, following the structure of the commodity classification until, at the lowest level, there are samples of prices for individual commodities. These highly detailed commodity samples are called elementary aggregates. 22

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