Estimating the Elasticity of Consumer Prices to the Exchange Rate: An Accounting Approach

We analyse the elasticity of the household consumption expenditure (HCE) deflator to the exchange rate, using world input-output tables (WIOT) from 1995 to 2019. In line with the existing literature, we find a modest output-weighted elasticity of around 0.1. This elasticity is stable over time but heterogeneous across countries, ranging from 0.05 to 0.22. Such heterogeneity mainly reflects differences in foreign product content of consumption and intermediate products. Direct effects through imported consumption and intermediate products entering domestic production explain most of the transmission of an exchange rate appreciation to domestic prices. By contrast, indirect effects linked to participation in global value chains play a limited role. Our results are robust to using four different WIOT datasets. As WIOT are data-demanding and available with a lag of several years, we extrapolate a reliable estimate of the HCE deflator elasticity from 2015 onwards using trade data and GDP statistics.


Non-technical summary
Understanding the influence of exchange rate on inflation is critically important for setting monetary policy and measuring the extent of expenditure switching that follows exchange rate variations, which, in turn, has an impact on real activity.
In this paper, we analyse the impact of exchange rate variations on domestic consumer prices using several datasets covering most advanced and emerging economies, from 1995 to 2019. We perform an accounting exercise based on information contained in world input-output tables, by way of large matrices inversions. Our accounting approach helps identify which countries and sectors are under pressure to adjust their prices when subject to an exchange rate variation.
Our main findings are fourfold. First, we document the evolution over time of the impact of exchange rate variations on consumer prices. In line with the existing literature, we find that in response to a 1% appreciation of the domestic currency, domestic consumer prices decrease by arround 0.10% on average at the world level. The impact of exchange rate variations on consumer prices has remained broadly stable over the past two decades. This modest estimate is likely an upper bound. Indeed, we make two assumptions to simplify our computations.
We assume that exchange rate fluctuations completely pass-through to import prices. However, a large body of literature suggests that the pass-through is incomplete, even in the long run, as a result of slow nominal price adjustments or the pricing-to-market behaviour of firms (see Özyurt (2016) for a discussion of the literature). For example, the pass-through depends on the intensity of competition in domestic markets: while an exchange rate appreciation lowers the price of imported inputs, a firm with limited competitive pressure may avail of greater profit margins rather than reduce prices in an effort to maintain its market share. Hence, pricing-to-market strategies of exporters aiming to defend their market shares would imply a lower exchange rate pass-through.
In addition, we work under the producer pricing assumption. However, in large and attractive markets, competitive pressures may push producers to adopt local currency pricing strategies, where exporting firms adapt their mark-ups depending on the destination market to offset exchange rate movements. Under the local currency pricing paradigm, prices are thus sticky in the currency of the destination market. Hence, using alternative pricing assumptions would entail lower estimates of the percentage change in consumer prices in response to a 1% change in the exchange rate.

Introduction
This paper examines the elasticity of the household consumption expenditure (HCE hereafter) deflator to the exchange rate. We analyse the composition and determinants of the HCE deflator elasticity using world input-output tables (WIOT hereafter) covering twenty years of data, from 1995 to 2019. For the sake of robustness, we use several datasets (WIOD, two distinct releases of the OECD TiVA database and the MRIO database developed by the Asian Development Bank). We perform an accounting exercise based on information contained in WIOTs with large matrices inversion. We make two assumptions to simplify our computations. First, we assume a full exchange rate pass-through to import prices. Hence, we do not consider the fact that the pass-through might be incomplete, as suggested by a large body of literature (see for example Berman et al. (2012)). As a result, our estimates provide an upper bound of the HCE deflator elasticity. Using alternative pricing assumptions would entail lower values. Second, we suppose that all pricings occur using the currency of the producing country, despite the well-documented role of dominant-currency pricing (Gopinath et al. (2020)). As a consequence of these two assumptions, we also assume that the impact of the exchange rate fluctuation is proportional across sectors. Despite these simplifying assumptions, our estimates provide an accounting-based gauge of how large the elasticity of consumer prices to the exchange rate could be, considering direct and indirect import content in consumption and global value chain linkages.
This accounting approach helps identify which countries and sectors are under pressure to adjust their prices when subject to an exchange rate variation.
Our contribution to the literature is fourfold. First, we analyse the evolution of the elasticity of the HCE deflator to the exchange rate. We document differences across countries. We pay particular attention to the heteregeneity observed in the euro area, reflecting different degrees of openness to trade.
Second, building on sectoral data, we examine which sectors experience higher spillovers from an appreciation of the national currency. We focus on the main components of the HCE deflator, i.e. manufacturing goods, services, food and energy. We analyse the contribution of these different products to the HCE deflator elasticity and document cross-country heterogeneity in the elasticity.
Third, we look into the determinants of the HCE deflator elasticity and the role of global value chains in the transmission of an exchange rate appreciation. We identify four channels through ECB Working Paper Series No 2610 / October 2021 4 which the exchange rate impacts the HCE deflator when production processes are global: i) the prices of imported final goods sold directly to domestic consumers; ii) the prices of imported inputs entering domestic production; iii) the price of exported inputs feeding through imported foreign production; iv) changes in domestic and foreign production costs in turn pass through to the price of inputs for domestic and foreign goods, causing further changes in production costs through input-output linkages. We find that the first two channels explain three-quarters of the transmission of an exchange rate appreciation to domestic prices. By contrast, the last two channels, which reflect the impact of global value chains, play a more limited role, with marked cross-countries heterogeneity. Hence, only one-fourth of the elasticity of the HCE deflator to the exchange rate is attributable to participation in global value chains.
Fourth, we show that a precise assessment of the HCE deflator elasticity to the exchange rate can be estimated for recent years without resorting to WIOTs. The construction of World Input-Output tables is data-demanding and WIOTs are typically released with a lag of several years.
As a result, WIOTs are not available for the most recent years. For instance, the latest WIOD dataset dates back to 2014. Although the MRIO dataset covers most recent years, it suffers from data quality issues in 2018. To address the data gap in WIOTs, we extrapolate the HCE deflator elasticity from 2015 onwards using up-to-date GDP statistics and trade data on consumption and intermediates. We obtain a reliable estimate of the HCE deflator elasticity up to to 2019.
The rest of the paper is organised as follows. Section 1 reviews the related literature. Section 2 presents the methodology and the data sources. In section 3, we estimate the elasticity of the HCE deflator to the exchange rate up to 2019 and analyse its determinants. In section 4, we use up-to-date GDP and trade data to estimate the elasticity of the HCE deflator for the most recent years.

Related literature
Exchange rate pass-through to domestic prices A large body of literature documents the exchange rate pass-through (ERPT hereafter) to domestic prices. The pass-through depends, among other things, on trade openness, integration in international production chains, firms' pricing strategies and the currency of invoicing for trade.
In the euro area, Özyurt (2016) shows that the pass-through is partial and has declined in the 2000s. This decline coincided with the increasing share of emerging economies in world trade and ECB Working Paper Series No 2610 / October 2021 5 the accession of China to the WTO. The lowest degree of pass-through is found for Germany, most likely reflecting the large size of the country and the high share of local currency pricing.
By contrast, Ortega and Osbat (2020) find that the ERPT to euro area import and consumer prices has been stable since the 1990s.
The choice of invoicing currency determines the extent of the response of prices to an exchange rate movement. An exporter can price its products either in its own currency ('producer currency pricing' paradigm), in the destination's currency ('local currency pricing' paradigm), or in a third 'dominant' currency (see Ortega and Osbat (2020) for a discussion of the literature).
The invoicing decision is an active channel through which producers adjust their prices in relation to their own market power and to local competitive pressures. While prices fixed in the local currency are irresponsive to the bilateral exchange rate between the local currency and the currency of the producer, prices in the producer or dominant currency have a higher ERPT.
A large body of empirical literature suggests that the vast majority of trade is invoiced in a small number of 'dominant currencies,' with the U.S. dollar playing a major role. The 'dominant currency paradigm' (Gopinath et al. (2020)) implies that for non-U.S. countries, the exchange rate pass-through into import prices (in home currency) should be high and driven by the dollar exchange rate as opposed to the bilateral exchange rate, whereas for the U.S. the pass-through into import prices should be low.
The ERPT also depends on integration in global value chains. Based on Belgian firm-productlevel data, Amiti et al. (2012) find that import intensity and market share are key determinants of the ERPT to export prices. Although we do not estimate the ERPT (we rather assume a full exchange rate pass-through), our approach provides an accounting-based gauge of how large the exchange rate pass-through could be, considering direct and indirect import content in consumption. In this respect, the elasticity we compute can be regarded as an upper bound.
The Input-Output model applied to a change in production costs The Leontief's production model (or Input-Output model, I-O thereafter) analyses the impact of a demand shock in a closed economy (Leontief, 1951 Supply-driven price models have a number of well-documented limitations (Folloni and Miglierina, 1994) and rely on a number of simplifying assumptions. Firms' margins are assumed to be fixed. Prices only adjust to absorb cost changes. Production techniques are fixed during successive production cycles. Inputs substitution caused by change in relative prices (for instance, between countries producing the same goods) is not accounted for. Although global value chains are often internal to multinational firms, supply-driven price models assume a unique pricing system based on market prices and independent of firms' strategies. Despite these shortcomings, supply-driven price models provide a measure of the vulnerability of each sector to price or productivity shocks (Acemoglu et al., 2012;Carvalho, 2014 Traditionnaly, WIOTs are interpreted in a Leontief framework using Leontief production functions to analyse the evolution of quantities in the economy. Here, we assume a Cobb-Douglas production function: the technical coefficients correspond to the share of each input in total costs. We derive a price equation In each sector of each country, a representative firm uses domestic production factors (V ) and domestic and imported intermediates m according to a Cobb-Douglas technology: m n,n a n,n with γ n + n =N n =1 a n,n = 1 Where γ n is the share of domestic production factors, a n,n the share of output from (country,sector) n in the total production of (country,sector) n.
Assuming perfectly competitive firms and prices set at the marginal cost, standard cost minimisation for each country leads to the following pricing system: p a n,n n , ∀n With w n the unit income of domestic production factors and x n a constant depending only on parameters: a −a n,n n,n Using logs, we have: log(p n ) = log(x n ) + γ n log(w n ) + n =N n =1 a n,n .log(p n ), ∀n ECB Working Paper Series No 2610 / October 2021 8 Define P the vector of prices and Z a vector of log(x n )+γ n .log(w n ), both of dimension (1, N ) : Suppose an exogenous change in input prices defined in log points (i.e. approximating percentages for small changes). Define ∆ 0 log(P ) the vector of dimension (1, N ) computed as the difference between the original price vector log(P 0 ) and the new vector log(P 1 ). Then: with C the vector of dimension (1,N) that contains the direct effect of the change in prices expressed in log points.
C directly affects the HCE deflator. In addition, firms face a change in their costs, which affects their prices according to equation 1. Hence, the price change is transmitted to country-specific industries that are using domestic input through the change in input prices. The higher the country-specific industries' reliance on those inputs, the higher the change in their production prices.
In a first step, the impact of the change in input prices on each country-specific industry's output prices amounts to ∆ 1 log(P ) = CA.
In a second step, the impact of the change in input prices is passed on to all the country-specific industries using these inputs. For the k th step, the increase in production prices amounts to ∆ k log(P ) = CA k .
As the technical coefficients are smaller than 1, the effect of the change in input prices wears out as k increases. The overall effect of the change in input prices is equal to the sum of the initial change in prices and all the subsequent changes in each step. Let us call S the total effect of the change in input prices (in log points), a vector (1, N ) composed of the elements s ij measuring the total effect of the shock on the price of sector j in country i. We have: with (I − A) −1 the Leontieff inverse matrix. If the change in the input prices is small enough, the elements of S correspond to the elasticity of sectoral prices to a change in input prices. Using consumption shares to perform a weighted average of these elasticities yields the household consumption expenditure (HCE) deflator elasticity to a change in input prices 1 .

Data
WIOTs are an extension of the national input-output tables. National input-output tables measure the relationships between the producers of goods and services (including imports) within an economy and the users of these goods and services (including exports Aggregating national input-output tables into world input-output tables is challenging for a number of reasons. National input-output tables vary widely in terms of detail and scope, and are therefore not fully consistent. Furthermore, the availability of year-specific national input-output tables is limited, especially for developing economies. This paper uses several multi-year WIOTs for the sake of robustness: the World Input Output Database (WIOD), the multi-regional input-output tables ( Table 1) accounting for 85% of global GDP (see Table 1). It contains information for 56 industries (see Online Appendix A). It provides annual WIOTs expressed in U.S. dollars at basic prices. Market exchange rates were used for currency conversion (Timmer et al., 2015).
1 The HCE deflator covers more products and has different sectoral weights than the headline consumer price index (CPI) as the former also encompasses, for example, the rental equivalent of real estate expenditures.   Table   2). The industry list includes 34 sectors, among which 16 manufacturing and 14 services sectors.

ECB
It covers the period 1995-2011 and is based on the 1993 system of national accounts. The fourth revision, released in 2018, includes 65 economies (see Table 2 )). For example, all start with the construction of harmonised country-specific supply-use tables (SUTs) that are then transformed into world input-output tables. All databases use the "import proportionality assumption" to allocate specific bilateral imports to using industries. National input-output statistics provide how much of each product firms use for intermediary consumption and investment. However, the breakdown of these into domestic and imported product is not available. Hence, the construction of world input-output tables requires allocating imports to using industries. The import proportionality assumption assumes that the proportion of intermediates that an industry purchases from abroad is equal to the ratio of imports of intermediates to the total domestic demand of intermediates in that product. This assumption can be misleading. Feenstra and Jensen (2012) find that shares of imported materials differ substantially across U.S. industries. Based on Asian input-output tables, Puzzello (2012) finds that the proportionality assumption understates the use of foreign intermediate inputs. All databases, however, rely on the BEC (Broad Economic Categories) classification to map detailed six-digit products into intermediate use, final consumption and investment (Dietzenbacher et al., 2013).
One explicit difference between the databases is that WIOD and MRIO assume that the input mix is independent from the destination market. The TiVA databases do not rely on this assumption for two countries (Mexico and China). Instead, the TiVA databases use different input-output tables for the exporting, import processing and domestic-market oriented sectors of these countries (or at least two of those, depending on the country and the version of the TiVA database). Despite this difference, we obtain similar results with TiVA, WIOD and MRIO, which probably reflects the fact that we do not focus on Mexico and China.
Another difference relates to the method for harmonising national data and trade statistics.
WIOD and MRIO rely on the shares of imported inputs provided by national account, contrary to TiVA. As a result, TiVA is closer to international trade statistics than WIOD. This explains ECB Working Paper Series No 2610 / October 2021 12 why the share of imported inputs is smaller in TiVA for some countries (other than China and the USA). All computations in this paper have been conducted with the four databases. For ease of exposition, we use the WIOD as a baseline, since it covers the largest number of industries.

Accounting impact of an exchange rate variation on domestic prices
We are primarily interested in the impact of an exchange rate appreciation on consumer prices in the country whose currency's value is changing (country A by convention). We also estimate the inflationary impact on countries that directly and indirectly, through third countries linkages, consume inputs from country A. Hence, we will also analyse the impact of an appreciation of the US dollar. In both cases, implementing an exchange rate variation is more complex than implementing a change in production costs. The appreciation of the currency of country A leads to a fall in the national currency price of country A's imports, while the foreign-currency price of its exports increases.
Suppose a world with two countries A and B, each having its own national currency, and using a third currency for international transactions, the dollar. Following a 5% appreciation of the currency of country A against the two other currencies, the prices of country A expressed in dollars increase by 5% compared to those of country B expressed in dollars. Country B pays more for its imports of inputs, in dollars as well as in national currency, since its exchange rate against the dollar has not changed. Conversely, the price of imported inputs in country A remains constant in dollars, since the prices of country B have not changed, and declines once expressed in country A's national currency. This has an impact on consumer prices expressed in national currency in country A.
Note that, for the sake of simplicity, we make the strong assumption that producers completely pass the exchange rate appreciation on their production prices. We do not consider other relevant determinants of the exchange rate pass-through. For instance, pricing-to-market strategies of exporters aiming to defend their market shares would imply a lower exchange rate pass-through.
Similarly, settlement and invoicing of imports in the domestic currency is another factor likely to weaken the elasticity of domestic prices to exchange rate movements. Assuming that only 60% of invoices in the euro area goods trade are denominated in foreign currency (see Ortega and Osbat (2020)) would entail lower elasticity values. To anticipate on our results (see Figure   9), reducing the exchange rate pass-through on consumption goods would entail lower elasticity values than reducing the pass-through on inputs. Our estimates thus provide an upper bound of Back to our accounting approach, the change in the prices of imported goods is therefore transmitted to all domestic prices, both directly and through inter-industry linkages. These upward (downward) movements for country B (country A) affect all input prices in both countries.
The effects of the change in prices spread over multiple simultaneous production cycles. The overall impact of the exchange rate appreciation in dollar terms is equal, for the shocked country A, to the decline in consumer prices directly due to the exchange rate fluctuation, plus direct and indirect decreases (via inter-industry linkages in the country), in national currency and then converted back into dollar terms, in the prices of inputs imported from B and disseminated to all branches. The overall impact on prices in dollar terms in country A is therefore lower than the initial exchange rate variation, as national currency prices are also affected. For country B, the final impact is equal to the cumulative direct and indirect effects of the higher prices of imported inputs.
In a global economy composed of I countries, each with J sectors, 3 the appreciation of a country's currency i against all other currencies translates into a rise in country i's prices in dollars.
The dollar price of each sector will vary in percentage (approximated as log point assuming that the exchange rate variation is small enough) by: c i $ for sectors in the shock-stricken country i and 0 in other countries.
Hence, for each sector j in country i (see notation table): The appreciation affects producers through changes in relative prices between countries and, therefore, through changes in input prices traded between the shock-stricken country i and other countries.
Consider first the direct impact on other countries of the rise in imported input prices from shocked country i. For any sector l of a country k (k = i), the increase in producer prices 3 Online appendix D explores the two-country, one-sector case and contrasts the effect of an exchange rate variation and the effect of a price variation ECB Working Paper Series No 2610 / October 2021 14 depends directly on the quantity of inputs imported from the shock-stricken country i, weighted by the variation in level of the price of inputs in dollars (i. e. the exchange rate variation). If a kl,ij is the share of inputs from the country i's sector j needed in the production of country's k sector l, we have : For the shocked country, an appreciation of the currency has a disinflationary effect. In national currency, the prices of imported inputs fall in each sector by We approximate these changes by their log point equivalent 4 . This decline then spreads to all domestic-input using sectors. In sector j of the shocked country i, this fall amounts in national currency to: This change can be converted into dollars: This yields the first step impact of the exchange rate variation on all input prices of all countries.
To express this in matrix notation, we define two matrices that build on the world input-output matrix A defined in 2.1 : B i andB i . These two matrices retain only the first-step effects of the exchange rate variation on the price of goods and services imported by the shocked country i and 4 We could have used the log point approximation earlier and write that c i = −c i $ with nearly the same results for small exchange rate variations.

ECB Working Paper Series No 2610 / October 2021 15
the first-step effects of the exchange rate variation on the price of goods and services imported by the rest of the world from country i. Compared to A, we "close off" the links between a change in domestic input prices and the price of goods as well as the link between non-shocked input prices and the price of goods in a non-shocked country (see the notation table and infra) Let us first consider the impact of the exchange rate variation from the perspective of countries that import inputs from country i.
Let C i $ be the vector of log points changes in dollar prices following the appreciation of the currency of country i against all other currencies. Hence, where each a kl,ij element of the line block represents the technical coefficient related to imports of inputs by sector l in country k (with k = i) from sector j of country i.
Let us now consider the impact of the exchange rate fluctuation from the perspective of the shocked country i. Notation table • a kl,ij : the share of inputs from country i's sector j in the production of country's k sector l.
• A: Matrix of world input-output coefficients.
• B i : A including only the country blocks of each country's sectoral inputs imported from country i (excluding domestic inputs in i).
•B i : A including only the country blocks of the inputs imported by country i from other countries (excluding domestic inputs in i).
• c i $ : change in the exchange rate of the currency of country i in dollar. If it appreciates by 10%, c i $ = 0.1.
• c i : impact of the exchange rate variation on the price of non-i goods expressed in the • C i : vector of log point changes in prices everywhere expressed in country i's currency:  corresponds, in national currency, to C iBi with: where each a ij,kl element in the column block represents imports of inputs by sector j in country i from sector l of country k. We then convert the direct impact into dollars, by multiplying it by the new value of the national currency in dollars, 1 + c i $ . The direct impact of the appreciation of country i's currency on the price of its inputs corresponds, in dollars, toC i $B i with: The first-step effect on the world is therefore the sum of the vectors from equations 5 and 7, The change in input prices then spreads to all sectors in all countries via the global intersectoral exchanges transcribed by the matrix of technical coefficients of the large matrix A. This process will be simultaneously repeated several times, until the effects completely wear off. In the end, the total price effect of the exchange rate variation is equal to the sectoral shock itself, incremented by changes in input prices due to changes in imported input prices (both in the shocked country and in non-shocked countries), and by all changes in prices during the production processes: By contrast, we focus on the effect of an exchange rate variation on consumer prices. Hence, we are interested in the same impact expressed in national currency. To obtain the evolution of the sectoral prices of the shocked country in national currency, we remove the exchange rate variation in international currency, multiply the balance by the scalar of conversion equal to 1 1+c i $ and add the initial exchange rate variation in national currency.
Where hc i kj corresponds to household consumption in country i of goods and services produced by sector j from country k and hc i represents the total household consumption of country i. s i i,HC provides the elasticity of the HCE deflator of country i to its own exchange rate.
where s i kj is a coefficient of S i for country i.

Accounting impact of an exchange rate variation on consumer prices
We use the model presented in 2.3 to analyse the impact of an exchange rate variation on the household consumption expenditure (HCE) deflator. We assume that the variation in the nominal exchange rate is small enough to assimilate log and percentage points and hence consider s i i,HC as the HCE deflator elasticity to its own exchange rate. Following an appreciation of the national currency versus all other currencies, imported inputs and imported consumer goods become cheaper and domestic prices expressed in national currency decrease.

Heterogeneity across countries
Using the WIOD database, which covers a sample of 43 countries, we find that the HCE deflator elasticity ranges from 0.05 to 0.22 depending on the country (see Figure 1). This heterogeneity reflects different degrees of openness to trade and differences in foreign product content in domestic consumption. The elasticity is lower for large advanced and developing countries.

Impact of an appreciation of the US dollar
The model can also track the effect on the domestic economy of variations in the currency of foreign countries. As an example, we estimate the impact of an appreciation of the US dollar (USD) using WIOD. This exercise assumes that exports are always invoiced in the exporter's currency. We do not take into account the large role of the dollar in international trade invoicing.
The US example illustrates that countries are affected in proportion to their trading links with the country whose currency appreciates. We obtain the highest elasticities for the major trading partners of the US. The elasticity of the HCE deflator to the USD amounts to 0.12 for Canada and 0.09 for Mexico (see Figure 4). The elasticity is below 0.06 for most euro area countries.
Ireland stands out, with an elasticity of 0.09, i.e. close to that of Canada and Mexico. The U.S. Sources: WIOD and authors' calculations.

Evolution over time of the HCE deflator elasticity
The output-weighted elasticity of the HCE deflator to the exchange rate has remained broadly stable over the past two decades. Output-weighted elasticities are lower than arithmetic means, reflecting the fact that large countries are relatively closed compared to small economies. Using WIOD, we find that the mean output-weighted elasticity of the HCE deflator increased from 0.06 in 2000 to 0.08 in 2008 (see Figure 5). After peaking in 2008, the elasticity sharply declined in 2009. It has hovered around 0.08 in subsequent years. Our results concur with the literature.

Contributors to the HCE deflator elasticity
In this section, we analyse the contributions of each part of the consumption basket to the pass-through of exchange rate variations to consumer prices. We start with the contributions of domestic versus imported goods. We define Where:  Figure 6 shows that changes in the prices of imported final consumer goods and services contribute more to the total effect than changes in the prices of domestic final goods and services.

Sources: WIOD and authors' calculations
We also examine the contributions of each sectors to the HCE deflator elasticity. We regroup industries into four categories: manufacturing goods, services, food and energy. Figure 7 shows the impact of a change in the exchange rate on the main components of the HCE deflator.
Non-energy industrial goods explain the bulk of the total impact. However, services also play a significant role, especially in advanced economies. Although services are mainly produced domestically and do not rely much on imported inputs, they represent a substantial share of ECB Working Paper Series No 2610 / October 2021 28 total consumption: even small price changes have large impacts on the HCE deflator.
Finally, mixing both the industrial and origin analysis shows that domestic core inflation (i.e. all domestic products except food and energy) accounts for a significant share of the total impact In this section, we analyse the determinants of the HCE deflator elasticity. In particular, we assess the role of global value chains in the transmission of an exchange rate appreciation to the HCE deflator. We identify four channels through which an exchange rate appreciation impacts the HCE deflator when production processes are global: i) the prices of imported final goods sold directly to domestic consumers; ii) the prices of imported inputs entering domestic production; iii) the price of exported inputs feeding through imported foreign production; iv), changes in domestic and foreign production costs in turn passing through to the price of inputs for domestic and foreign goods and causing further changes in production costs through input-output linkages.
Defining HC i,dom and HC i,imp as the domestic and imported shares of HC i and adjusting the dimension of E1, E2 and E3, we have:  Overall, the first two channels explain three-quarters of the transmission of an exchange rate appreciation to domestic prices. By contrast, the last two channels, which reflect the impact of global value chains, play a more limited role, with marked across-countries heterogeneity.
Approximately one-fourth of the HCE deflator elasticity to the exchange rate is attributable to participation in global value chains.

Extrapolating the HCE deflator elasticity using GDP and trade statistics
In this section, we show that a precise assessment of the HCE deflator elasticity to the exchange rate can be estimated without resorting to WIOTs. The construction of World Input-Output 6 Although this functional form might seem counterintuitive (we expected the elasticity to be an affine function of openness as summarized by E1.HC), the analytical examination of the two-country, one-sector case shows that it is plausible (see Online Appendix E).

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tables is data-demanding and WIOTs are typically released with a lag of several years. As a result, world input-output matrices are not available for the most recent years. The latest years covered by WIOD and TiVA rev. 4 are, respectively, 2014 and 2015. While the MRIO database covers more recent years, it is fraught with data quality issues for 2018 (see Section 3.3 and Online Appendix F). Using WIOTs also involves cumbersome computations. Given these difficulties, we look for a simpler way to compute the elasticity of the HCE deflator to the exchange rate. We estimate the HCE deflator elasticity from 2015 onwards using GDP statistics and trade data on consumption and intermediates.
As a starting point, the sum of the share of imported goods in household consumption and the share of imported inputs in household consumption of domestic goods (E1.HC + E2.HC) is a good predictor of the impact of exchange rate fluctuations on household consumption prices.
However, these data (E1.HC and E2.HC) are not up-to-date for a large number of countries, as they are not routinely computed by national statistical institutes. We can rely on a proxy to identify consumption and intermediate goods imports using the CEPII BACI database and the BEC classification (Gaulier and Zignago, 2010) We perform an out-of-sample prediction for WIOD, 2014, using data for years 2000 to 2008.
The results are satisfactory, although the mean and median errors are larger than in Online 7 BACI provides disaggregated data on bilateral trade flows for more than 5000 products and 200 countries. The database is built from data directly reported by each country to the United Nations Statistical Division (Comtrade). Products are defined as items from the Harmonized System nomenclature, at the 6-digit level.

ECB Working Paper Series No 2610 / October 2021 37
Appendix C (see Figure 14). Our findings are robust to using other databases (results obtained with TiVA revisions 3 and 4 are available upon request). Using these equations, we can predict the HCE deflator elasticity from 2015 onwards. Figure   15 shows that the in-sample predictions are robust, giving confidence in the quality of the out-ofsample predictions. We also compare our predictions with the elaticity estimated using MRIO, which provides WIOTs up to 2019. Our predictions are in line with results from MRIO up to 2017. For the most recent years, there seem to be data issues in MRIO (see Online Appendix F), which the comparison helps to identify. We thus provide a simple accounting tool to estimate the percentage change in prices in response to exchange rate variations for the most recent years.

Conclusion
This paper studies the elasticity of the household consumption expenditure (HCE) deflator to the exchange rate. Our contribution to the literature is fourfold.
First, we analyse the composition and determinants of the HCE deflator elasticity using world input-output tables covering twenty-four years of data, from 1995 to 2019. We use several datasets to ensure the robustness of our results. In line with the existing literature, we find a rather modest output-weighted elasticity of the HCE deflator to the exchange rate of around 0.1 at the world level. The output-weighted elasticity has remained broadly stable over the past two decades. Aggregate figures mask substantial cross-country heterogeneity, reflecting different degrees of openness to trade and differences in foreign product content in domestic consumption.
The elasticity is larger for small open economies with higher import content of consumption.
Second, we examine which parts of the consumption basket contribute most to the elasticity of the HCE deflator to the exchange rate. Non-energy industrial goods explain the bulk of the total HCE deflator elasticity. Services also play a significant role, as they represent a substantial share

A01
Crop and animal production, hunting and related service activities A02 Forestry and logging A03 Fishing and aquaculture B Mining and quarrying C10-C12 Manufacture of food products, beverages and tobacco products C13-C15 Manufacture of textiles, wearing apparel and leather products C16 Manufacture of wood and of products of wood and cork, except furniture; articles of straw and plaiting materials C17 Manufacture of paper and paper products C18 Printing and reproduction of recorded media C19 Manufacture of coke and refined petroleum products C20 Manufacture of chemicals and chemical products C21 Manufacture of basic pharmaceutical products and pharmaceutical preparations C22 Manufacture of rubber and plastic products C23 Manufacture of other non-metallic mineral products C24 Manufacture of basic metals C25 Manufacture of fabricated metal products, except machinery and equipment C26 Manufacture of computer, electronic and optical products C27 Manufacture of electrical equipment C28 Manufacture of machinery and equipment n.e.c.

C29
Manufacture of motor vehicles, trailers and semi-trailers C30 Manufacture of other transport equipment C31-C32 Manufacture of furniture; other manufacturing C33 Repair and installation of machinery and equipment D35 Electricity, gas, steam and air conditioning supply E36 Water collection, treatment and supply E37-E39 Sewerage and other waste management services F Construction G45 Wholesale and retail trade and repair of motor vehicles and motorcycles G46 Wholesale trade, except of motor vehicles and motorcycles G47 Retail trade, except of motor vehicles and motorcycles H49 Land transport and transport via pipelines H50 Water transport H51 Air transport H52 Warehousing and support activities for transportation H53 Postal and courier activities I Accommodation and food service activities J58 Publishing activities J59-J60 Motion picture, video and television programme production; programming and broadcasting activities J61 Telecommunications J62-J63 Computer programming, consultancy; information service activities K64 Financial service activities, except insurance and pension funding K65 Insurance, reinsurance and pension funding, except compulsory social security K66 Activities auxiliary to financial services and insurance activities L68 Real estate activities M69-M70 Legal and accounting activities M71 Architectural and engineering activities; technical testing and analysis M72 Scientific research and development M73 Advertising and market research M74-M75 Other professional, scientific and technical activities; veterinary activities N Administrative and support service activities O84 Public administration and defence; compulsory social security P85 Education Q Human health and social work activities R-S Other service activities T Activities of households as employers; producing activities of households for own use U Activities of extraterritorial organizations and bodies  Appendix D: Comparing the impact of a change in prices with that of an exchange rate variation In this appendix, we use the two-country and one-good case to illustrate the difference between a change in prices and an exchange rate variation.

Effect of a change in prices based of value added contents
Using the notations of the paper, we have in the two-country and one-good case: When a change c occurs in the prices of country 2, we have the following initial vector: In the first instance, this has an impact on prices CA, and then CA 2 , etc. Hence, the total effect of the change in prices S is: To measure the impact on the household consumption expenditure deflator, we compute a weighted sum of these effects: (1 − f ) a 2,1 + f (1 − a 1,1 ) (1 − a 1,1 ) (1 − a 2,2 ) − a 2,1 a 1,2
Unexpectedly, E3.HC + E4.HC does not vary much with the openness rate of the economy (see Figure 12 of the main text).
Let us focus on the two-country, one-sector economy: We do not lose any generality by normalising the shock c to 1.

ECB Working Paper Series No 2610 / October 2021
To simplify, we assume that the ratio is equal to 0.5. a 1,1 + a 1,2 = a 2,1 + a 2,2 = 0.5 a 1,2 a 1,1 + a 1,2 = f a 2,1 = 0.48 a 2,2 = 0.02 In that case:s  Actual openness rates in the sample vary between 0.15 and 0.50. In that range, the relationship between the openness rate and the residual is not monotonous (see Figure 6).  Online Appendix F: MRIO data quality issues Figure 8 shows that the HCE deflator elasticity extrapolated from WIOD, World Bank and BACI data for the period 2015-2019 is close to the elasticity obtained with MRIO in 2016-2017. By contrast, the elasticity estimated using MRIO is much higher in 2018 and 2019. This discrepancy likely reflects data quality issues in MRIO. Figure 9 shows that the HCE deflator elasticity estimated using MRIO increased by more than 20% for India and China between 2017 and 2018. For China, the increase reaches 100%, which is not plausible. Such a sharp increase was not observed between 2016 and 2017. Computations with WIOD confirm that such sharp increases were not observed in the past and are thus unlikely (see Figure 10). Looking more closely at MRIO, we observe large shifts in the consumption of services in China in 2018.
Chinese households' consumption of Chinese education services increased by 43% between 2017 and 2018, whereas the consumption of Chinese transport services decreased by 43% over the same period. Such large and unlikely shifts suggest data quality issues in MRIO for 2018.