Aggregate and sector-specific exchange rate indexes for the Portuguese economy

In this paper, we compute and compare aggregate and sector-specific exchange rate indexes for the Portuguese economy. We find that alternative effective exchange rate indexes are very similar between them. We also find that sector-specific effective exchange rates are strongly correlated with aggregate indexes. Nevertheless, we show that sector-specific exchange rates are more informative than aggregate exchange rates in explaining changes in employment: whereas aggregate indexes are statistically insignificant in employment equations, regressions using sector-specific exchange rate indexes show a statistically significant and economically large effect of exchange rates on employment.

In this paper, we compute and compare aggregate and sector-specific exchange rate indexes for the Portuguese economy. We find that alternative effective exchange rate indexes are very similar between them. We also find that sector-specific effective exchange rates are strongly correlated with aggregate indexes. Nevertheless, we show that sector-specific exchange rates are more informative than aggregate exchange rates in explaining changes in employment: whereas aggregate indexes are statistically insignificant in employment equations, regressions using sector-specific exchange rate indexes show a statistically significant and economically large effect of exchange rates on employment.

resumo résumé / abstract
Portugal provides an example of a country that, in the 1970s and in the 1980s, actively tried to manage the exchange rate. Prior to the accession to the European Economic Community (EEC) in 1986, Portugal adopted a crawling peg in an effort not to lose competitiveness with regard to similar Spanish products. Joining the Exchange Rate Mechanism (ERM) in 1992, and then the European Monetary Union in 1999, therefore implied a drastic change in the behaviour of Portugal's effective exchange rate, not only because its nominal value with respect to other euro area countries could no longer be adjusted, but also because the evolution of the European Single Market, alongside the common currency, biased Portuguese trade towards European countries, especially Spain 1 .
This change in trade patterns in turn implies that effective exchange rates should be computed on the basis of time-varying weights -see, for example, Bayoumi et al. (2005). One difficulty with the computation of effective exchange rates is that the choice of the trade weights is not unique. In this paper we shall make use of the four basic sets of weights employed in the literature: bilateral export shares, bilateral import shares, bilateral trade shares (exports plus imports) and double-weighting schemes that account for competition from third countries. This and other issues in the computation of effective exchange rates have been the subject of a vast literaturesee, e.g., Turner and Van't dack (1993), Buldorini et al. (2002), Bennett and Zarnic (2008) and references therein. Another important issue is whether one can use an aggregate exchange rate index to discuss the economic performance, or whether one should use sectoral indexes. Several papers have shown that when the importance of the trading partners varies across sectors, sector-specific exchange rates may be more informative as indicators of industries' competitiveness than aggregate exchange rate indexes -see, among others, Campa and Goldberg (2001) and Gourinchas (1999).
aspects of competitiveness are certainly important, the real exchange rate is a leading candidate to take responsibility for, at least some of, this loss of competitiveness.
The purpose of this paper is therefore to compare the evolution and evaluate the usefulness of alternative effective exchange rate indexes for the Portuguese economy. In particular, we compute sector-specific effective exchange rates and compare their patterns over time with the aggregate effective real exchange rates 2 . In section 2 we describe the main features of Portuguese aggregate exchange rate indexes and international trade patterns in the period 1988-2006. In section 3 we present sector-specific effective exchange rate indexes and compare their behaviour with that of aggregate indexes. In section 4 we assess the informative content of sector-specific real exchange rate indexes, relative to aggregate indexes, by estimating their effect on employment. Section 5 concludes.
Aggregate exchange rate indexes synthesize information on bilateral exchange rates and, therefore, may be useful indicators of the competitiveness of domestic production in the international context. In this section, we present several aggregate effective exchange rate indexes for the Portuguese economy and discuss their behaviour.
Our data begins in 1988, two years after Portugal (and Spain) joined the EEC and four years before Portugal joined the ERM. We construct nominal and real effective exchange rates for Portugal until 2006. Real exchange rates are more informative than nominal exchange rates about trade competitiveness when inflation differentials between trading partners are significant, which was the case for the Portuguese economy in the period of our analysis. There are several measures of relative prices and costs that may be used to deflate nominal effective exchange rates. The relative export price is the most used measure of relative prices in the computation of real effective exchange rates (Turner and Van't dack, 1993). However, relative export prices have some drawbacks. In the first place, international competition tends to erode differences in export prices across countries. In the second place, the relative export price does not provide an accurate measure of a country's competitiveness as it focuses exclusively on the goods that are actually traded. Finally, export prices, which are not indexes, are inconsistent with the logic of double-weighting effective exchange rates. Industrial producer prices are also used as a measure of relative prices. However, they exclude important sectors, their construction differs across countries and their statistical quality is dubious. The consumer price index is another measure widely used to deflate exchange rates (Bennett and Zarnic, 2008). Consumer price indexes are based on similar baskets of goods, being comparable across countries. Additionally, consumer price indexes are available for a large number of countries and for a large time span. These are the reasons why we chose to use consumer price indexes in our computation of exchange rate indexes. However, consumer price indexes include goods and services that are not internationally tradable whereas capital goods, which are tradable, are excluded. In our analysis we do not consider cost indicators, such as labour unit costs, to construct real exchange rate indexes because they are available for a small number of countries and for a rather short period -for a description of cost indicators see, for example, Turner and Van't dack (1993).
Data for nominal exchange rates, defined as national currency per US dollar at the end of the period, and for the consumer price index are from the IMF International Financial Statistics database 3 . The country weights in the exchange rate indexes are based on data from OECD's STAN bilateral trade database (OECD, 2008) 4 .

Aggregate exchange rate indexes
We compute the effective exchange rate indexes as geometrically weighted averages of bilateral exchange rates 5 . The real effective exchange rate index at time t, I t , is given by the following formula: (1) where (2) is the bilateral real exchange rate between Portugal and country j, e j,t is the price of foreign currency j in terms of escudos 6 at time t, p t and p j,t are consumer price indexes for the Portuguese economy and for economy j, N(t) is the number of foreign currencies in the index at time t and w j,t is the weight of currency j in the index at time t, with ⌺ j w j,t = 1. An increase in the value of this index corresponds to a real depreciation of the Portuguese currency. The base of the index is the year 2000.
In the last two decades, Portuguese international trade patterns changed significantly, both in terms of export destinations and import origins. If the weights in the effective exchange rate formulas ideally should reflect the degree to which producers in the countries considered in the index compete with domestic producers, then the changes in the importance of trade partners described above should be taken into account in the computation of effective exchange rate indexes. In addition, although fairly similar in most cases, some countries' export and import shares are very different. For example, in 2006, exports to the US represented 4.3% of Portugal's exports, but imports from that country were only 1.5% of Portugal's imports. Therefore, the computation of the weights, w, associated with each bilateral exchange rate will yield different results according to whether one bases the computation on Aggregate and sector-specific exchange rate indexes for the Portuguese economy  export shares, on import shares, or on some combination of the two. In this paper we will present effective exchange rate indexes computed using export, import and "trade" weights, i.e., one effective exchange rate index will use weights based on export shares: (3) another index will use weights based on import shares: (4) and the trade-weighted index will employ the average of both shares: In the formulas, X j,t stands for Portuguese exports to country j and M j,t is imports from country j to Portugal (in year t). The indexes will be denoted FXExp, FXImp and FXTrade, respectively. Implicitly, these weights assume that exports from one country to another compete only with the importing country's production. By including additional information in the computation of the weights, it is possible to produce effective exchange rate indexes that attempt to take into account the effect of third-party competition. In order to account for such effects, we follow Turner and Van't dack (1993), who propose that the weight given to j's currency in the doubleweighted effective index be defined as: The factor w Xdw,j,t is given by: where X h j,t stands for the exports to country j from country h, with are total exports from country z (Portugal in the current analysis), and γ j is the domestic production of country j for its home market 8 . The exports from country z compete in foreign markets indexed by k, together with the domestic production and the exports from other foreign producers indexed  In Figure 1 we can see the evolution of selected bilateral exchange rate weights used in the computation of the FXTrade exchange rate index (the weights for the other indexes are similar). The four series depicted correspond to Portugal's main trade partners -compare Table 1. The evolution of the weights shows the importance of using time-varying data for currency weights in the construction of exchange rate indexes that aim at measuring the competitiveness of domestic firms in international trade. In fact, in Figure 1 it is clear that the weights can change substantially: we can see the significant and steady increase in the weight of the Spanish currency and the decrease in the weight of the English pound. The weights given to France and Germany have oscillated around a slightly declining trend. Figure 2 shows the behaviour of different measures of the aggregate effective real exchange rate described above, using all 52 trade partners for which there is data in STAN, and also FXTradeDW: the trade-weighted index using the group of 25 trade partners 9 and 27 third-market competing economies 10 . All four measures display a very similar evolution, suggesting that the choice of weights has little impact in the Portuguese case.  effective exchange rate were computed by us: FXTradeEA (using the thirteen countries first to join the euro), FXTradeB (using only the group of 30 countries with export or import shares larger than 0.5% in either 1988 or 2006 -recall Table 1) and FXTradeDW (using the group of 25 trade partners listed in Footnote 9 and 27 third-market competing economies listed in Footnote 10also shown in Figure 2).
The four measures computed by us (the three in Figure 3 and FXTrade, shown in Figure 2) present a broadly similar behaviour. Nevertheless, the global index (FXTrade) shows an overall smaller decline than the other indexes. The gap between this and the other two indexes was especially notorious in the early and mid 1990s: the sequence of exchange rate adjustments that followed the ERM crisis appears to have had less impact on the global index than on the indexes that depend more heavily on European countries.
12 In this work, as mentioned above, we use the STAN Bilateral Trade Database, which follows an industry classification based upon ISIC Rev. 3.
In Figure 4 we compare the evolution of the nominal (NFXTradeEA) and real (RFXTradeEA) aggregate effective exchange rates of the Portuguese currency against the currencies of the first thirteen countries to adopt the euro. Figure 4 shows that the nominal index has been more stable than the real index. It also shows that the nominal index may present a distorted picture of the evolution of competitiveness. In fact, despite the nominal depreciation before the birth of the euro, in real terms there was a large appreciation of the Portuguese currency. Most of the appreciation occurred between 1988 and 1992. This period was followed by small variations in the real exchange rate until the Portuguese escudo joined the euro. The period since then has again been characterized by a real appreciation, which amounted to approximately 7%. The inflation differential relative to the trade partners is thus an important feature of the Portuguese economy during this period.
Aggregate exchange rate indexes such as those analysed in the previous section may be useful summaries of the evolution of domestic firms' competitiveness. However, since the importance of trading partners varies across sectors, and the export destinations of an industry may be very different from the import origins of that same sector, sector-specific exchange rate indexes may be more informative than aggregate indexes concerning the evolution of industry competitiveness -see, e.g., Goldberg (2004).
In this section we present sector-specific exchange rates for 21 sectors, classified according to an industry classification based upon ISIC Rev. 3 12 . A complete list of the sectors may be found in Table 6 in the Appendix.    Table 2 shows the share of Portuguese exports (imports) that flow to (from) the countries indicated in the columns, for the most important sectors ranked by weight in total exports (imports) in 2006 13 . In 2006 Spain stands out as an important export destination for all sectors presented, with export shares varying between 8% for "Radio, television and communication equipment", and 25% for "Food products, beverages and tobacco". On the other hand, in 2006 Portugal bought from Spain 35% and 46% of its imports of "Textiles, textile products, leather and footwear" and "Food products, beverages and tobacco", respectively. In 2006 Germany was the most important destination of "Motor vehicles, trailers and semi-trailers", buying 31% of Portugal's exports of these goods. However, for "Food products, beverages and tobacco", Germany was only a residual destination with a 3% share of total exports. Table 2 also shows that the euro area's (13) share in "Radio, television and communication equipment" exports (46%) is much lower than its share in "Motor vehicles, trailers and semi-trailers" exports (79%). Another striking example of the difference in the weight of trade partners across sectors is given by the comparison between the OECD share in "Motor vehicles, trailers and semi-trailers" exports (95%) and its share in "Radio, television and communication equipment" exports (63%) -Singapore, in 2006, accounted for 25% of the exports of that sector. These differences imply that exchange rate movements will affect competitiveness differently in each sector and should, therefore, be weighted differently in the computation of sector-specific exchange rates, to which we now turn.

Sector-specific real exchange rates
Following the approach used in the computation of aggregate exchange rate indexes, we consider three sector-specific real exchange rate measures which differ in the weights given to bilateral exchange rates and sector-specific real exchange rate indexes based on doubleweighting schemes. The weights depend on the foreign countries' shares of Portugal's exports and imports for each of the 21 sectors considered in our analysis. The formulas used in computing effective exchange rates for sector i are: (1) export-weighted: where (9) (2) import-weighted (10) where (11) (3) trade-weighted (12) where (13) Dezembro '09 / (6/28) Aggregate and sector-specific exchange rate indexes for the Portuguese economy Fernando Alexandre/Pedro Bação/ João Cerejeira/Miguel Portela In the formulas above, rer j,t stands for the bilateral real exchange rates of each of Portugal's trading partner (indexed by j).
Additionally, we computed exchange rate weights in order to include information that would allow us to take into account sectoral third-party competition. As before, we followed Turner and Van't dack (1993) and defined the weight given to country j's currency in the double-weighted effective index as: where w Xdw,j,t (i) is defined as: Inflation differentials are accounted for by the consumer price index -see equation (2). It would seem more appropriate to use sectoral price indexes. However, we do not have access to that sort of data. As before, an increase in the value of these indexes implies a real depreciation of the Portuguese currency.
Although the weights of the different currencies vary significantly across sectors, the Portuguese industry-specific effective exchange rates are strongly correlated with aggregate exchange rate indexes. Table 3 shows ten sets of correlations of exchange rate indexes -see notes on Table 3 -and the number of sectors in the different levels of correlation. In fact, when using trade weights (that is, the average of export and import shares), Table 3 shows that in only 2 of the 21 sectors is the correlation between the industry-specific and the aggregate exchange rate index below 0.9 (column 3). This number increases to 4 (column 2) when imports are used as weights. The different industry indexes are also highly correlated between them. In 16 of the 21 sectors the correlation between the export-based and the import-based indexes is above 0.9 (column 8).  Given the evidence of high correlation presented above, it is not surprising that the change in the exchange rate indexes is broadly similar across industries. Table 4 shows the change in the exchange rate indexes for the 5 most important sectors ("Food products, beverages and tobacco", "Textiles, textile products, leather and footwear", "Chemicals excluding Pharmaceuticals", "Machinery and equipment, n.e.c.", and "Motor vehicles, trailers and semitrailers") and for the aggregate of 21 sectors. The same conclusion may also be drawn from the analysis of Figure 5 where sector-specific exchange rates show very similar patterns (for the graphs of the remaining sector-specific exchange rates see Figures 6, 7 and 8 in the Appendix).

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There is a growing literature on the impact of exchange rate movements on labour markets -see, e.g., Campa and Goldberg (2001) and the references therein. In particular, the wild swings of the US dollar in the 1980s have been a special focus of attention. Branson and Love (1988) estimate that the appreciation of the US dollar in the first half of the 1980s caused the loss of about 1 million jobs in US manufacturing. Using data for a sub-sample of manufacturing sectors over a similar time-period, Revenga (1992) found evidence that the appreciation of the US dollar had reduced employment in US manufacturing sectors by 4.5-7.5% on average, besides having reduced wages. Campa and Goldberg (2001) add data for the 1990s. They also find an effect of exchange rates on US manufacturing employment. However, their analysis shows that the exchange rate impact is less than previously estimated and that it is concentrated in low priceover-cost-markup industries and in industries with proportionally less college-educated workers. Similar studies have been conducted in other countries. An example already mentioned is that of Gourinchas (1999), who estimated that a 1% appreciation of the French franc decreases tradable employment growth by 0.9% in the following two years. Another recent study is that of Ekholm et al. (2008), who conclude that the sharp appreciation of the Norwegian krone in the early 2000s explains one seventh of the total decline in manufacturing employment in that period.

Aggregate versus sector-specific exchange rates indexes: an application to labour market demand
Here we will perform a similar analysis using Portuguese data. However, the goal here is not to conduct an exhaustive study of the impact of exchange rate movements on Portuguese manufacturing employment, but rather to compare the usefulness of the different exchange rate indexes discussed in the study of the issue. We use employment sector-level data, for the period 1988-2006, from the "Quadros de Pessoal" dataset provided by the Portuguese Ministry of Labour and Social Solidarity (Portugal, 2006). This dataset is based on a compulsory survey that matches all firms and establishments (with at least one employee) with their workers. In 1988, it included 122,774 firms and 1,996,933 workers, covering 43% of total employment. In 2006, it included 344,024 firms and 3,099,513 workers, covering 55% of total employment. We aggregated the firm-level data from "Quadros de Pessoal" to obtain sector-level data for 21 manufacturing sectors, which were selected to match the International Standard Industrial Classification of all economic activities, Revision 3 (ISIC Rev. 3), as they are more exposed to foreign trade. In the 21 sectors used in the previous section we did not include non-manufacturing sectors such as "Agriculture, hunting, forestry and fishing", "Mining and quarrying", "Electricity, gas and water supply", "Scrap metal", "Waste" and the residual sector "Other". We also excluded "Coke, refined petroleum products and nuclear fuel". For a list of the 21 sectors see Table 7 in the Appendix.
To evaluate at the sector-level the effect of real aggregate and sector-specific exchange rates on employment growth we use a model based on Gourinchas (1999), specified in first-differences, with the following form: The dependent variable, l it , is employment (in logs), measured as total workers observed for each sector i in year t. ExRate i,t-1 is either the lagged real effective aggregate exchange rate or sector i exchange rate (in logs), as defined in the previous section 14 . The exchange rate is smoothed by the Hodrick-Prescott filter, which filters out the transitory component of the exchange rate. In order to account for competition from non-OECD countries (in particular, from emerging countries), we include the variable ShareImp i,t-1 , which is the share of non-OECD countries in sector i OECD countries' imports. ∆ denotes the first difference of the variables. The model also includes a set of time dummies, λ t , in order to control for common aggregate time variant shocks, such as monetary policy shocks, and a set of sectoral dummies θ i . Since we specify a model in first-differences, these dummies account for sector-specific trends. Finally, ε it is a white noise error term. All variables are in real terms. The model is estimated by OLS, with robust standard errors allowing for within-sector correlation.
When the model is estimated using the aggregate real effective exchange rate we cannot control for aggregate shocks using time dummies. As such, we control for aggregate shocks that may affect input prices using changes in oil prices (∆RPOil t-1 ), changes in the long-term interest rate (∆LTIR t-1 ) and changes in unit labour costs (∆ULC t-1 ). Additionally, we also control for business cycle effects by including changes in the logarithm of real GDP in the European Union-15 (∆log(RGDP t-1 ):EU) or in the logarithm of real Portuguese GDP (∆log (RGDP t-1 ):PT). These control variables are included in vector Z t-1 and are lagged one year. Table 5 shows the results of the estimation of equation (16). Our results, using both EU-15 GDP and Portuguese GDP growth as control variables -columns (1) and (2) -, suggest that the aggregate exchange rate does not explain changes in employment. On the contrary, sector--specific exchange rates seem to have a significant role in the explanation of movements in employment -columns (3) to (6). Using the sector-specific exchange rate, and GDP growth for EU-15, column (3), the estimated employment-exchange rate elasticity is 0.989. Using the Portuguese GDP growth the elasticity is slightly smaller (0.889).
In column (5) we combine sector-specific exchange rates with time dummies to control for aggregate shocks. Time dummies are preferred to aggregate controls since we can control for any common aggregate shock which is correlated with changes in sector-specific exchange rates. In this case, there is both an increase in the employment-exchange rate elasticity and in its Dezembro '09 / (6/28) 20 21 significance: a 1% depreciation of the real exchange rate implies a 5.3% increase in sectoral employment. This result is robust to the inclusion of sector-specific trends -see column (6). In addition, it is important to note that the inclusion of sector-specific exchange rates increases the precision of the estimates.
Finally, it should be stressed that our results show a negative effect of non-OECD competition on employment, with an implied elasticity in the range 0.91-1.01.
The integration in the EEC, in 1986, implied structural changes in the behaviour of Portuguese real exchange rate indexes. On the one hand, changes in Portugal's international trade patterns have resulted in a significant variation in bilateral exchange rate weights in effective exchange rate indexes. On the other hand, the participation in the Exchange Rate Mechanism reduced the scope for changes in the nominal value of the escudo. However, even after the accession to the euro area, inflation differentials and fluctuations of the euro vis-à-vis other currencies still had an impact on real effective exchange rates.
These were the motivations for computing exchange rate indexes for the Portuguese economy. Exchange rate indexes depend on the group of trade-partner countries included in exchange rate indexes and on the bilateral exchange rate weights, which depend on whether we consider total trade, exports or imports. For example, between 1988 and 2006, the analysis of bilateral exchange rate weights shows an increasing weight of Spain and a decreasing weight of the United Kingdom in exchange rate indexes. After 1998, aggregate exchange rate indexes based on exports, imports and total trade exhibit very similar patterns.
Additionally, exchange rate indexes may be computed for the whole economy and for specific sectors of the economy, as the group of trade-partner countries varies between sectors. For this reason it has been argued that sector-specific exchange rates are more informative on the competitiveness of the economy. We computed exchange rate indexes for 21 sectors and concluded that Portuguese sector-specific effective exchange rates are strongly correlated between them and with aggregate exchange rate indexes.
Finally, following the literature on exchange rates and labour markets, we used employment sector-level data to evaluate the benefits of using sector-specific real exchange rates relative to aggregate exchange rate indexes. Our estimates suggest that sector-specific exchange rates are more informative than aggregate exchange rate indexes in explaining changes in manufacturing employment. We estimate that, at the sector-level, a 1% real appreciation decreases employment growth by 0.9-5.3%. Our results suggest that more effort should be devoted to the construction and analysis of sector-specific exchange rate indexes.       Aggregate and sector-specific exchange rate indexes for the Portuguese economy Fernando Alexandre/Pedro Bação/ João Cerejeira/Miguel Portela