Poor households and the weight of inflation
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Schulz-Gebhard, Jan; Ipsen, Leonhard Working Paper Poor households and the weight of inflation BERG Working Paper Series, No. 205 Provided in Cooperation with: Bamberg Economic Research Group, Bamberg University Suggested Citation: Schulz-Gebhard, Jan; Ipsen, Leonhard (2025) : Poor households and the weight of inflation, BERG Working Paper Series, No. 205, Bamberg University, Bamberg Economic Research Group (BERG), Bamberg, https://doi.org/10.20378/irb-108327 This Version is available at: https://hdl.handle.net/10419/319883.2 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/
Poor Households and the Weight of Inflation Jan Schulz and Leonhard Ipsen Working Paper No. 205 April 2025 k* b 0 k B A M AMBERG CONOMIC ESEARCH ROUP B E R G Working Paper SeriesBERG Bamberg Economic Research Group Bamberg University Feldkirchenstraße 21 D-96052 Bamberg Telephone: (0951) 863 2687 [email protected] http://www.uni-bamberg.de/vwl/forschung/berg/ https://doi.org/10.20378/irb-108327
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Poor Households and the Weight of Inflation Jan Schulz1 Leonhard Ipsen1, 2 ja[email protected] [email protected] 1Economics Institute, University of Bamberg 2Bamberg Research Training Group on Bounded Rationality, Heterogeneity and Network Effects Abstract We argue that most of the existing literature on inflation inequality misses an essential source of disparity by focusing on differences in expenditures while ignoring the effect of a price change on the purchasing power of households’ incomes. As a remedy, we propose weighting price changes by income rather than by expenditure, as is commonly done. We theoretically derive why, under incomeweighting, lower-income households are disproportionately affected by any change in prices. This proposition is validated empirically for 21 EU countries using current sector-level input-output data. Our approach allows to reconcile the conflicting evidence in the literature on inflation inequality regarding structurally higher inflation perceptions and expectations of lower-income households. Ultimately, these findings call for a broad reassessment of current approaches to measuring inflation and income inequality. Keywords: Inflation, Inequality, Input-output Analysis, Europe JEL: E31, D31, C15, C67, D90 Acknowledgements: We thank Laura Egelmeers, Claudius Gräbner-Radkowitsch, Simon Grothe, Georg Maxton, Patrick Mokre, Calvin Röhl and Frank Westerhoff as well as the participants of the 2024 annual meeting of the Keynes Society in Bamberg, of the 36th EAEPE annual conference in Naples, the 2024 Young Economist Conference in Vienna, of the 2024 Workshop on Economics with Heterogeneous Interacting Agents in Bamberg and of the 5th Pluralumn* workshop in Duisburg for valuable comments at crucial junctions of this investigation. We also thank Luis Drechsel and Daniel Hilbinger for their excellent research assistance. Ipsen gratefully acknowledges funding by the HansBöckler-Foundation through grant PK045 and Schulz gratefully acknowledges funding by the German Federal Ministry of Education and Research through the grant DATIPilot for the project “elernen”.
�.Introduction We argue that most of the existing literature on in�ation inequality misses an essential source of disparity by focusing on di�erences in expenditures while ignoring the e�ect of a price change on the purchasing power of households’ incomes. In contrast, the incomeweighting of price changes o�ers a uni�ed explanation for two puzzles in the existing research on in�ation inequality: First, the apparent gap between perceived in�ation exposure of poorer households (Stantcheva ����) relative to the ambiguous results in empirical studies (Garcimartín, Astudillo, and Martínez ����). Second and relatedly, the structurally higher in�ation expectations and perceived exposure of lower-income households (D’Acunto, Malmendier, and Weber ����; Fofana, Patzelt, and Reis ����). These perceptions and beliefs are hard to rationalize, since relative exposure should depend on the type of good that is a�ected by a price shock and should disproportionately a�ect higher-income households whenever prices of luxury goods increase disproportionately. Empirical studies on in�ation inequality commonly weight price changes by households’ expenditure shares, re�ecting income-dependent di�erences in consumption baskets. Consequently, expenditure weights only capture the loss of purchasing power of the share of income allocated to expenditures. Yet, expenditure weighting is employed to construct real wages, even though wages as income streams represent both realized and potential uses of this income. In contrast, the income-weighting of price changes re�ects the loss of the purchasing power of a household’s total income. Technically, incomeweighting results from multiplying expenditure weights by the household’s propensity to consume. Since lower-income households consistently exhibit higher propensities to consume out of current income, poorer households experience a more signi�cant reduction in their potential uses of nominal income as consumption baskets become more expensive. Income-weighting thus rationalizes the structurally higher in�ation perceptions and expectations of lower-income households. We start by formally showing that, following a change in prices, the commonly applied expenditure-weighting only captures the loss of purchasing power of the share of income allocated to expenditures, while, contrastingly, income weights capture the purchasing power loss of a household’s entire income. A direct corollary of this argument is that constructing real wages by de�ating nominal wages with an expenditure-weighted price level — as is currently done — risks masking a substantial share of purchasing power loss (or gain), and thus obscuring realized income inequality. Technically, income-weighted in�ation rates result from scaling price changes by the households (income-dependent) propensity to consume. We make use of this relationship by estimating how in�ation rates vary along the income distribution for the expenditureand income-weighted case, respectively. In doing so, we are able to separate the e�ects of the decision what to consume from the e�ects of the decision how much to consume out of current income – �
addressing a major concern expressed in the literature about the use of income weights. The decomposition reveals that under income-weighting, lower-income households are disproportionally exposed to every change in prices. This is because the propensities to consume react much more strongly to income changes than the expenditure shares for speci�c products. We then empirically test our proposition, using a sector-level cost-push in�ation framework proposed in Ipsen and Schulz (����). Within this framework, we investigate the e�ects of income-weighted price shocks for a set of �� EU countries. While Ipsen and Schulz (����), based on expenditure-weights, �nd that the direction and magnitude of income-dependent in�ation inequality is conditional on the sectoral origins of price shocks, we �nd that under income-weighting, lower-income households are systematically overexposed to price shocks irrespective of their sectoral origin. Even an adverse shock to the price of a luxury good thus disproportionately a�ects poorer-income households. This result is in line with our theoretical propositions. Our �ndings help reconcile the con�icting evidence in the literature on in�ation inequality and call for a reassessment of previous �ndings in this area of research as well as the research on income inequality more generally. The remainder of this paper proceeds as follows: Section �outlines the related literature. Section �discusses the relation of expenditureversus income-weighted in�ation rates and introduces a novel elasticity decomposition for income-weighted price shocks. Section �describes the data and model used for the empirical analysis. Section �presents the results while Section �concludes with �nal remarks and perspectives for future research. �.Related Literature Our study connects to several strands of research. Most critically, it aims to explain two puzzles in the existing literature on in�ation inequality. That is �rst, the apparent gap between empirical �ndings on income-dependent in�ation exposure to the perception of poorer households feeling the most exposed to price increases: While some studies do suggest a disproportional exposure of lower-income households (Claeys and Guetta-Jeanrenaud ����; Gürer and Weichenrieder ����; Kaplan and Schulhofer-Wohl ����; Sologon et al. ����), others report pro-poor in�ation (Crawford and Old�eld ����), or relatively insigni�- cant di�erences on average (Hobijn and Lagakos ����; Ipsen and Schulz ����). The results in Ipsen and Schulz (����) suggest that the direction and magnitude of in�ation inequality dependents on the origin and propagation of a price shock. In line with these ambiguous results, some studies report a low persistence of income-dependent in�ation inequality (Hobijn and Lagakos ����; Strasser et al. ����). Disagreement can also be found on whether higher in�ation rates coincide with a wider dispersion of in�ation across income classes (Claeys and Guetta-Jeanrenaud ����; Crawford and Old�eld ����; Hobijn and �
Lagakos ����). Garcimartín, Astudillo, and Martínez (����) summarize the �ndings on income-dependent in�ation inequality as being inconclusive. This is in marked contrast to the strong perception of poorer households to be the most exposed to in�ation (Easterly and Fischer ����; Stantcheva ����). Second, we o�er an explanatory attempt for the structural di�erences in incomedependent in�ation expectations and perceived exposure (D’Acunto, Malmendier, and Weber ����). As pointed out by Fofana, Patzelt, and Reis (����) these di�erences cannot satisfactorily be explained by income-dependent di�erences in consumption baskets. Previous explanations considered the greater focus of low-income households on actual expenses and prices paid, shorter �nancial planning horizons, or lower �nancial literacy (Bruin et al. ����). However, the �ndings in Prati (����) reveal a robust connection between households’ in�ation perceptions and their material satisfaction, suggesting that persistently higher in�ation perceptions among lower-income households may indeed have an underlying economic rationale. We propose that the structural bias in in�ation perceptions and expectations can be explained by re�ecting the e�ect of a change in prices on the purchasing power of the total income rather than focusing solely on the share spent on expenditures. While expenditure-based approaches capture in�ation inequality arising from di�erences in consumption baskets (cf. Argente and Lee ����; Gürer and Weichenrieder ����; Hobijn and Lagakos ����; Kaplan and Schulhofer-Wohl ����, for example), they overlook that as consumption baskets become more expensive, poorer households experience a more signi�cant reduction in their potential uses of nominal income. As such expenditure-based approaches risk masking a substantial gap of realized in�ation inequality. As we show below, this gap can be closed by scaling expenditures by the households’ propensities to consume. The resulting income weights re�ect the total e�ect of a change in prices on the purchasing power of the households’ income. Since lower-income households devote larger fractions of their income to expenditures, i.e. are characterized by larger propensities to consume (cf. Schulz and Mayerho�er ����, for a review), income-weights capture the structurally greater loss of lower incomes’ purchasing power following a change in prices. The proposition of income-weighting relates to the logic of Engel’s Law (Engel ����), which holds that as income increases, the share of income spent on necessities – especially food – declines (even if the absolute amount rises). While earlier studies on Engel’s law are based on income weights (Engel and Kneip ����; Hamilton ����; Leser ����), current empirical work mostly relies on expenditure-based weights (cf. Lewbel and Houthakker ����, for a survey). This re�ects the concern that using income weights might confound the estimates of expenditure decisions for di�erent goods categories with the decision to spend or save at all (Barigozzi et al. ����). As we show below, we are able to address this �
caveat by introducing a novel elasticity decomposition for income-weighted price shocks. The following empirical analysis in this paper connects to recent attempts to explain cost-push in�ation dynamics and their distributional dimensions (Ferreira, Abreu, and Louçã ����). The foundational work of Weber et al. (����) and subsequent research of Ipsen, Aminian, and Schulz (����)�rst demonstrated that, for both the US and the EU, a small number of key sectors dominate price levels for consumers. Similar themes appear in Nikiforos, Grothe, and Weber (����) and Cucignatto, Garbellini, and Fora Alcalde (����), which highlight the sectoral and network e�ects for price shock transmission. Later, Ipsen and Schulz (����) suggested the pivotal role of sectorial asymmetries and propagation e�ects in production networks for modulating in�ation inequality. To account for this, we build on their cost-push in�ation framework to contrast the in�ation inequality arising from price shocks under expenditureversus income-weighting. We show, using more recent data than Ipsen and Schulz (����), that income-weighting shi�s the ambiguous, origin-of-shock-dependent in�ation exposure of households to a structural overexposure of lower-income households for any price change in the consumption baskets. By validating both structurally higher in�ation perceptions and expectations of lower-income households, income-weighting present a uni�ed explanation for the in�ation-inequality puzzles regarding income-dependent in�ation perceptions and expectations. �.Weights of In�ation We start this section by formally showing that the commonly applied expenditure-weighting only captures merely the loss of purchasing power of the share of income allocated to expenditures, while, income weights capture the loss of a household’s purchasing power concerning its whole (current) income. Let the absolute expenditures Cof a household be given by C=↵⋅Y,(�) with ↵ as its average and marginal propensity to consume and Yas its current income. Then, the expenditures for good iare given by Ci=✓i⋅C,(�) with ✓i as the expenditure share of good iin the households consumption basket. Assuming no change in consumption, the additional necessary expenditures in percentage terms faced by the household following a price change of good iin percentage terms ⇡i are given by %C=Ci⋅⇡i,(�) �
with ⇡i as a price shock to good i. Accordingly, the loss of purchasing power of the household’s income is then given by %PPY=%C Y (�) Substituting gives %PPY=✓i⋅↵⋅Y⋅⇡i Y=✓i⋅↵⋅⇡i.(�) Thus, the loss of purchasing power of the household’s income is proportional to its propensity to consume, as well as the price shock and the expenditure share in good i. Contrast this to the loss of purchasing power relative to total expenditures: %PPE=✓i⋅↵⋅Y⋅%Pi ↵⋅Y=✓i⋅C⋅%Pi C=✓i⋅⇡i (�) This case corresponds to the expenditure weighting used typically employed in studies of in�ation inequality but fails to consider the loss of purchasing power of a household’s total income. The quantities %PP Y and %PP E thus answer two di�erent questions: While the %PP Y indicates how much income would need to grow to cover the increased expenditures resulting from a price shock, %PP E shows how much expenditures would need to increase. Since expenditures and current income typically do not coincide, %PP Y≠ %PP E in general. Note that the assumption of a �xed ↵ and ✓i , i.e., no change of consumption behavior in response to the price shock, leads to upwards-biased estimates of the in�ationary impact (von Auer and Shumskikh ����). This is because Laspeyres indices use base-period weights and thus cannot take any kind of substitution into account. Since we are interested in in�ation inequality, this bias is unproblematic, though: As substitution possibilities are generally higher for richer households (Ipsen, Aminian, and Schulz ����), we understate in�ation inequality using base-period weights. Our estimates can thus be considered lower bounds for the actual impact on in�ation inequality. Equation �restates the above relationship for a single price shock to good ifor the overall price level. As in the previous case, let ✓i be a households expenditure weight on good i, that is its expenditures C i over the total expenditures C. The household’s income is given by Y, while ↵ describes its propensity to consume. ⇡i gives the growth rate of the price level of good iin a set of ngoods. It follows that ↵⇡e=↵ n � i=� ✓i⇡i=C Y⋅ n � i=� Ci C⇡i= n � i=� Ci Y⇡i=⇡y.(�) �
������ �. Elasticity estimates for expenditure-weighted (le�) and income-weighted price shocks for the sectoral categories in the FIGARO database for ���� based on regression equation �� with a country dummy. ��
plausibility of our approach, as the greatest exposure of lower-income households stems from the categories of necessities. At the same time, the highest elasticities can be found for luxury items. Furthermore, and in line with the results of (Ipsen and Schulz ����), we �nd the heterogeneity in the production network e�ect to be much smaller than for the direct e�ects. Technically, this implies that substantial in�ationary pressures propagate from sectors with larger income-dependent di�erences in consumption to sectors with smaller di�erences (cf. section �). As a consequence of this di�usion process, the possibilities of substituting away from sectors with price increases might be severely more limited than what one might initially expect looking only at di�erences in expenditure shares. The right-hand side of Figure �reports the corresponding elasticity estimates for the income-weighted speci�cation. It shows that, following a price shock, the purchasing power of lower incomes declines disproportionally no matter the sector of origin. The numbers suggest that elasticities are shi�ed towards a greater exposure of lower incomes by a constant factor. This is in line with our theoretical derivation in section �, where we suggested that the estimate ˆ y �≈+ , i.e., the estimated elasticity coe�cient can be additively decomposed into the income elasticity of the respective expenditure share and of the income elasticity of the propensity to consume . A negative ˆ y �< �for all sector classes implies that even for > �, < �and ��>> �� . Technically, lower incomes are disproportionally exposed under income weighting since the propensities to consume react much more strongly to income changes than the expenditure shares for speci�c products (even for luxury goods). To substantiate this claim and to examine whether there exists e.g. some unanticipated interaction between and , we estimate ˆ separately from the below equation to see, if the estimates indeed correspond to ˆ y �− ˆ e � , as the theory outlined in section �would suggest. The regression equation to be estimated by OLS for ˆ is given by log(↵c,q)=�+log(Yc,q)+c+✏c,q,(��) with cas the country and qas the quintile of the income distribution in cfor the APC ↵ and income Yand again using a country-dummy c for consistency with the basic regression equation (��). We estimate that ˆ ≈−�.����. The results are shown in Figure �. The estimate for ˆ is given as a line, while the di�erence in estimates for all sectors ˆ y �− ˆ e � is given as points. The theory aligns with the estimated di�erence remarkably well, with the highest downwards deviation being �.�� for For the income-weighted speci�cation, the relative importance of sectors remains asymmetric. However, for income-weighting, the average exposure of Q�households to any price shock is larger than the exposure faced by Q�, in line with our core argument. ��
������ �. Di�erences in elasticity estimates for expenditure and income weights (for the total e�ect) for each sector compared to the estimate for the income elasticity of the average propensity to consume ˆ ≈−�.����. ��
the elasticity di�erence for Postal and courier services and the highest upwards deviation of �.�� for the elasticity di�erence in Telecommunications. An immediate corollary to this is that the relative ranks of estimates based on income weights (almost fully) correspond to the relative ranks for estimates based on expenditure weights with e.g. the real estate sector having the most negative elasticity in both cases. Income-weighting is therefore consistent with both the notion that cost-push shocks a�ect the poor disproportionately in general and that this di�erential exposure is highest for necessities. Figure �indicates that it is indeed the higher income elasticity of the APC that drives pro-rich in�ation for income-weights. Neglecting the consumption and savings decisions of households might thus underestimate the extent to which poor households experience in�ation exposure. �.Conclusion The extant literature on income-dependent in�ation inequality provides two empirical puzzles: First, it continues to yield con�icting �ndings regarding its direction, magnitude, and persistence, while, at the same time, poorer households consistently perceive themselves as the most a�ected by rising prices. Second and relatedly, it fails to satisfactorily explain the consistently higher in�ation expectations of lower-income households. We argue that the income-weighting of price changes presents a uni�ed explanation for these puzzles. In contrast to the common expenditure-based approaches to in�ation inequality, income weighting re�ects the loss of purchasing power of a household’s total income as opposed to considering only the share of income allocated to expenditures. In this paper, we showed that income-weighting results from scaling expenditure weights by the household’s propensity to consume. We made use of this relationship to estimate how the impact of price shocks varies along the income distribution for the expenditure-weighted versus income-weighted case. In doing so, we were able to separate the e�ects of the decision on what to consume from the e�ects of the decision on how much to consume from current income. Since, empirically, the propensities to consume react much more strongly to income changes than the expenditure shares for speci�c products, the decomposition revealed that under income-weighting, lower-income households are disproportionally exposed to every cost-push price shock. Using a sector-level cost-push in�ation framework, we showed the empirical e�ects of income-weighting using recent data for �� EU countries. The analysis con�rmed our proposition of a systematic overexposure of lower incomes, reconciling con�icting results in the literature on income-dependent in�ation inequality. Our results validate the in�ation perception and expectation biases of lower-income households, casting doubt on explanatory approaches based merely on cognitive di�erences such as �nancial illiteracy or shorter �nancial planning horizons of poorer households. On the contrary, these results call for a reevaluation of previous empirical �ndings on in�ation and income inequality as well ��
as policies to address the distributional hardships in times of higher in�ation. Moreover, next to di�erences in the capacities to substitute, the propensities to consume constitute a second and o�en overlooked explanatory factor of in�ation exposure (see Sologon et al., ����, for a notable exception). Just as wealthier households are characterized by greater �exibility to switch to cheaper goods, they can decrease their in�ationary exposure by reducing their consumption propensity. Meanwhile, poorer households exhibit lower or even negative substitution, i.e. they are increasing their relative spending on a good as its price rises (Hobijn and Lagakos ����; Kaplan and Schulhofer-Wohl ����; Strasser et al. ����) and simultaneously have to dig into savings to meet their necessities (Bobasu, Charalampakis, and Kouvavas ����; Sologon et al. ����). This, in turn, increases their propensity to consume and thus their exposure to in�ationary shocks. Since we are using a Laspeyres index, our elasticity estimates thus constitute a lower bound, as we cannot account for these substitution responses in direct response to a price shock by construction that are more prevalent for richer households. This study comes with a set of limitations. One complicating factor in our empirical model is the assumption of a Leontief price model as in Weber et al. (����). The model presupposes a �:�pass-through of price shocks to customers, potentially overstating shock propagation if �rms adjust their margins or modify production processes (cf. Pichler et al. ����). Recent scholarship further indicates that within-industry consumption di�erences and substitution behavior can play a substantial role for in�ation asymmetries across households (Jaravel ����; Strasser et al. ����; Argente and Lee ����). At the industry level, ignoring substitution e�ects may not dramatically in�ate aggregate shock propagation (Duprez and Magerman ����), but it can mask important cross-sectoral heterogeneities. Future advances could draw on methods such as Pichler et al. (����), who incorporate modi�ed Leontief production functions to re�ect varying input dependencies. Moreover, our empirical analysis addresses only cost-push in�ation, thus neglecting other potential drivers, such as demand-led in�ation. A desirable path for future research would, therefore, be to address the e�ects of income-weighting for di�erent in�ationary dynamics. Finally, our analysis does not account for the wealth channel of in�ation (e.g., the e�ects on asset holdings), which can also contribute to unequal in�ation outcomes (Adam and Zhu ����; Bobasu, Di Nino, and Osbat ����; Doepke and Schneider ����). Despite these limitations, income weighting appears to be a promising explanation for the discrepancy between scholarship and public perceptions regarding in�ation inequality. Even more critically, income-weighting suggests that the current practice of constructing real wages by de�ating nominal wages with an expenditure-weighted price level risks masking a substantial share of purchasing power loss (or gain). Ultimately, this calls for a broad reassessment of current approaches to measuring in�ation and income inequality. ��
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Appendix A. Bridging Input-output and Consumption Data In this section, the process of mapping COICOP consumption by purpose data (Eurostat) to FIGARO Input-output data (Eurostat) is described. This process is based on bridging matrices provided by Cai and Vandyck (����). Using input data for the base year of ����, the authors construct bridging tables between �� consumption by purpose categories and �� products by activity (CPA) categories for �� European countries. � The �� CPA categories are fully aligned with the classi�cation of economic activities (NACE Rev. �) used in the FIGARO industry-by-industry Input-output tables (Eurostat n.d.). � Therefore, we can use these bridging matrices to integrate the consumption expenditure by income quintile based on COICOP categories with the FIGARO Input-output data (both Eurostat). The country speci�c bridging tables are structured as follows: Rows (��): CPA categories Columns (��): COICOP categories of consumption by purpose Cells: Final consumption expenditure of households by consumption purpose in million Euro, current prices In the �rst step, the three-digit level COICOP categories in the country-speci�c bridging tables were reduced to the two-digit level by summing over the columns belonging to a parent two-digit category. This was done to match the two-digit granularity of the incomedependent consumption data and reduces the initial ��x�� table to ��x��. In the next step, entries in the country-speci�c bridging tables were multiplied pairwise with the corresponding country-quintile-speci�c expenditure shares for each COICOP category taken from the Eurostat data on consumption expenditure by income quintiles. A�erward, row sums were taken, before normalizing these to one. This yielded a �x�� vector of sector-level country-quintile speci�c expenditure shares: ✓q,c,j . Each entry of this vector corresponds to the expenditure share of quintile qof country cin sector j. Now, to integrate these into the FIGARO Input-output data, we �rst computed countrysector-speci�c expenditure shares based on the demand vector in the FIGARO data. This gives ✓c,j,d : the share of total expenditures Cby households of country cin sector j of country d, relative to their total expenditures in all sectors j over all countries in the FIGARO data: � Due to missing data, the input data for Bulgaria and Ireland is based on the year of ����, while for Malta it is ����. � FIGARO Input-output data initially distinguishes �� categories. However, the product / industry category relating to extraterritorial organizations and bodies (Code U) usually contains no entries and is therefore of no relevance for this process. ��
✓c,j,d=Cc,j,d ∑n d=�Cc,j,d (A�) Finally, multiplying the sector-level country-quintile speci�c expenditure shares ✓q,c,j with the country-sector speci�c demand shares ✓c,j,d yields a demand vector containing the country-quintile speci�c expenditure share in sector jof country d:✓q,c,j,d. Note that a necessary assumption underlying this process is that income quintiles di�er in their relative consumption in sector j versus sector i, but do not di�er in their relative consumption in sector j of country dto sector j in country c. More speci�cally, in our model, asymmetries between income quintiles arise due to households consuming di�erently (e.g., having di�erent expenditure shares for food products), and not because of how much of the food products come from domestic versus foreign sectors of food production. For example, in our model, both lowand high-income households in Spain spend the same percentage of their expenditures on food in the French sector of manufacturing food products. However, since low-income households in Spain spend a greater share of their total expenditures on food products, their exposure to the French sector of manufacturing food products is greater (as is their exposure to the respective domestic sector). Thus, exposure to foreign versus domestic sectors might still di�er across income groups in our model. To see this, consider another example: Naturally, in the sector of real estate activities the share of domestic relative to foreign “consumption” by households is greater than for textile products. While lower-income households have a relatively higher expenditure share in the sector of real estate activities, higher-income households have a relatively higher expenditure share in textile products. Therefore, the exposure to (inter)national shocks in our model will still be asymmetric. ��
������ A�. Elasticity estimates for expenditure-weighted empirical price shocks for the sectoral categories in the FIGARO database for ���� based on regression equation �� with a country dummy. ��
E.�. Elasticity Estimates for Unit Shocks ������ A�. Elasticity estimates for expenditure-weighted unit price shocks for the sectoral categories in the FIGARO database for ���� based on regression equation �� with a country dummy. ��
������ A�. Elasticity estimates for income-weighted unit price shocks for the sectoral categories in the FIGARO database for ���� based on regression equation �� with a country dummy. ��
Appendix F. Average E�ects per Sector Class for Quintile �&� ������ A�. Average direct and indirect sector e�ects (%) for quintile �and �for the expenditure-weighted (le�) and income-weighted case (right). Averages are taken over �� EU countries. ��
Appendix G. Average E�ects per Sector Class for Quintile �&�– Expenditure Weights Sector Code Direct E�ect (Q�) Direct E�ect (Q�) Indirect E�ect (Q�) Indirect E�ect (Q�) Average Price Shock (%) A�� �.�×��−��.�×��−��.�×��−��.�×��−��.��� A�� ���.�×��−����.�×��−����.�×��−����.�×��−��.��� A�� ���.�×��−����.�×��−����.�×��−����.�×��−��.��� B�.�×��−����.�×��−��.�×��−��.�×��−��.��� C��T�� ��.�×��−���.�×��−��.�×��−��.�×��−��.��� C��T�� ���.�×��−��.�×��−����.�×��−����.�×��−��.��� C�� ���.�×��−����.�×��−����.�×��−����.�×��−��.��� C�� ��.�×��−����.�×��−����.�×��−����.�×��−��.��� C�� ��.�×��−���.�×��−����.�×��−����.�×��−��.��� C�� �.�×��−��.�×��−��.�×��−��.�×��−��.��� C�� ���.�×��−��.�×��−��.�×��−��.�×��−��.��� C�� ���.�×��−����.�×��−����.�×��−����.�×��−��.��� C�� ���.�×��−����.�×��−����.�×��−����.�×��−��.��� C�� ���.�×��−����.�×��−����.�×��−����.�×��−��.��� C�� �.�×��−��.�×��−��.�×��−��.�×��−��.��� C�� ��.�×��−����.�×��−����.�×��−����.�×��−��.��� C�� −��.�×��−�−���.�×��−�−���.�×��−�−���.�×��−��.��� C�� ��.�×��−����.�×��−����.�×��−����.�×��−��.��� C�� ��.�×��−���.�×��−����.�×��−����.�×��−��.��� C�� ���.�×��−��.�×��−����.�×��−����.�×��−��.��� C�� ��.�×��−����.�×��−���.�×��−����.�×��−��.��� C��_�� ���.�×��−����.�×��−����.�×��−����.�×��−��.��� C�� �.�×��−���.�×��−����.�×��−����.�×��−��.��� D�� ��.�×��−��.�×��−��.�×��−��.�×��−��.��� E�� �.�×��−��.�×��−����.�×��−����.�×��−��.��� E��T�� �.�×��−��.�×��−����.�×��−����.�×��−��.��� F���.�×��−����.�×��−��.�×��−��.�×��−��.��� G�� ���.�×��−����.�×��−����.�×��−����.�×��−��.��� G�� ���.�×��−����.�×��−��.�×��−��.�×��−��.��� G�� �.�×��−��.�×��−��.�×��−��.�×��−��.��� H�� ���.�×��−��.�×��−��.�×��−��.�×��−��.��� H�� ��.�×��−���.�×��−����.�×��−����.�×��−��.��� H�� ���.�×��−����.�×��−����.�×��−����.�×��−��.��� H�� ��.�×��−����.�×��−��.�×��−��.�×��−��.��� H�� ��.�×��−���.�×��−����.�×��−����.�×��−��.��� I�.�×��−��.�×��−����.�×��−����.�×��−��.��� J�� ��.�×��−���.�×��−���.�×��−���.�×��−��.��� J��_�� ��.�×��−���.�×��−����.�×��−����.�×��−��.��� J�� ���.�×��−����.�×��−�−��.�×��−�−��.�×��−��.��� J��_�� �.�×��−���.�×��−��.�×��−��.�×��−��.��� K�� ���.�×��−����.�×��−��.�×��−��.�×��−��.��� K�� ���.�×��−����.�×��−����.�×��−����.�×��−��.��� K�� ��.�×��−����.�×��−����.�×��−����.�×��−��.��� L��.�×��−���.�×��−��.�×��−��.�×��−��.��� ��
Sector Code Direct E�ect (Q�) Direct E�ect (Q�) Indirect E�ect (Q�) Indirect E�ect (Q�) Average Price Shock (%) M��_�� ��.�×��−����.�×��−��.�×��−��.�×��−��.��� M�� ��.�×��−���.�×��−����.�×��−����.�×��−��.��� M�� ���.�×��−����.�×��−���.�×��−���.�×��−��.��� M�� �.�×��−��.�×��−����.�×��−����.�×��−��.��� M��_�� ���.�×��−����.�×��−����.�×��−����.�×��−��.��� N�� ���.�×��−����.�×��−����.�×��−����.�×��−��.��� N�� �.�×��−���.�×��−����.�×��−����.�×��−��.��� N�� ���.�×��−����.�×��−����.�×��−����.�×��−��.��� N��T�� ���.�×��−����.�×��−��.�×��−��.�×��−��.��� O�� ���.�×��−����.�×��−����.�×��−����.�×��−��.��� P�� ��.�×��−����.�×��−����.�×��−����.�×��−��.��� Q�� ���.�×��−����.�×��−����.�×��−����.�×��−��.��� Q��_�� ���.�×��−����.�×��−���.�×��−���.�×��−��.��� R��T�� ���.�×��−����.�×��−���.�×��−���.�×��−��.��� R�� ���.�×��−����.�×��−���.�×��−���.�×��−��.��� S�� ��.�×��−���.�×��−����.�×��−����.�×��−��.��� S�� ��.�×��−���.�×��−���.�×��−���.�×��−��.��� S�� ���.�×��−����.�×��−���.�×��−���.�×��−��.��� T�.�×��−��.�×��−��.�×��−��.�×��−��.��� U� � � � �.��� ����� A�. Averages over all sector e�ects for a sector class for income quintile �and � based on expenditure weights (%). Last column gives average price shock of a sector class. ��
Appendix H. Average E�ects per Sector Class for Quintile �&�– Income Weights Sector Code Direct E�ect (Q�) Direct E�ect (Q�) Indirect E�ect (Q�) Indirect E�ect (Q�) Average Price Shock (%) A�� �.�×��−��.�×��−��.�×��−��.�×��−��.��� A�� ���.�×��−����.�×��−����.�×��−����.�×��−��.��� A�� ���.�×��−���.�×��−����.�×��−���.�×��−��.��� B�.�×��−����.�×��−��.�×��−��.�×��−��.��� C��T�� ��.�×��−��.�×��−��.�×��−��.�×��−��.��� C��T�� ���.�×��−����.�×��−����.�×��−����.�×��−��.��� C�� ���.�×��−���.�×��−����.�×��−����.�×��−��.��� C�� ���.�×��−���.�×��−����.�×��−����.�×��−��.��� C�� ��.�×��−���.�×��−����.�×��−���.�×��−��.��� C�� �.�×��−��.�×��−��.�×��−��.�×��−��.��� C�� ���.�×��−����.�×��−��.�×��−��.�×��−��.��� C�� ���.�×��−����.�×��−����.�×��−���.�×��−��.��� C�� ���.�×��−����.�×��−����.�×��−����.�×��−��.��� C�� ���.�×��−����.�×��−����.�×��−����.�×��−��.��� C�� �.�×��−��.�×��−��.�×��−����.�×��−��.��� C�� ���.�×��−���.�×��−��.�×��−����.�×��−��.��� C�� −���.�×��−�−��.�×��−�−���.�×��−�−��.�×��−��.��� C�� ���.�×��−���.�×��−����.�×��−����.�×��−��.��� C�� ��.�×��−���.�×��−����.�×��−����.�×��−��.��� C�� ���.�×��−����.�×��−����.�×��−����.�×��−��.��� C�� ��.�×��−���.�×��−����.�×��−���.�×��−��.��� C��_�� ���.�×��−����.�×��−����.�×��−����.�×��−��.��� C�� ��.�×��−��.�×��−����.�×��−����.�×��−��.��� D�� ��.�×��−��.�×��−��.�×��−��.�×��−��.��� E�� �.�×��−����.�×��−����.�×��−����.�×��−��.��� E��T�� �.�×��−����.�×��−����.�×��−����.�×��−��.��� F���.�×��−����.�×��−��.�×��−��.�×��−��.��� G�� ���.�×��−����.�×��−����.�×��−����.�×��−��.��� G�� ���.�×��−����.�×��−��.�×��−��.�×��−��.��� G�� �.�×��−��.�×��−��.�×��−����.�×��−��.��� H�� ���.�×��−����.�×��−��.�×��−��.�×��−��.��� H�� ��.�×��−���.�×��−����.�×��−����.�×��−��.��� H�� ���.�×��−����.�×��−����.�×��−����.�×��−��.��� H�� ��.�×��−����.�×��−��.�×��−��.�×��−��.��� H�� ��.�×��−���.�×��−����.�×��−����.�×��−��.��� I�.�×��−��.�×��−����.�×��−����.�×��−��.��� J�� ��.�×��−���.�×��−���.�×��−���.�×��−��.��� J��_�� ��.�×��−���.�×��−����.�×��−���.�×��−��.��� J�� ���.�×��−����.�×��−�−��.�×��−�−��.�×��−��.��� J��_�� ��.�×��−���.�×��−��.�×��−����.�×��−��.��� K�� ���.�×��−����.�×��−��.�×��−��.�×��−��.��� K�� ���.�×��−����.�×��−����.�×��−����.�×��−��.��� K�� ���.�×��−���.�×��−����.�×��−����.�×��−��.��� L��.�×��−���.�×��−��.�×��−��.�×��−��.��� ��
Sector Code Direct E�ect (Q�) Direct E�ect (Q�) Indirect E�ect (Q�) Indirect E�ect (Q�) Average Price Shock (%) M��_�� ���.�×��−���.�×��−��.�×��−��.�×��−��.��� M�� ��.�×��−���.�×��−����.�×��−����.�×��−��.��� M�� �.�×��−����.�×��−���.�×��−���.�×��−��.��� M�� �.�×��−��.�×��−����.�×��−����.�×��−��.��� M��_�� ���.�×��−���.�×��−����.�×��−����.�×��−��.��� N�� ���.�×��−����.�×��−����.�×��−����.�×��−��.��� N�� �.�×��−��.�×��−����.�×��−����.�×��−��.��� N�� ���.�×��−����.�×��−����.�×��−���.�×��−��.��� N��T�� ���.�×��−����.�×��−��.�×��−����.�×��−��.��� O�� ���.�×��−����.�×��−����.�×��−����.�×��−��.��� P�� ��.�×��−����.�×��−����.�×��−����.�×��−��.��� Q�� ���.�×��−����.�×��−����.�×��−���.�×��−��.��� Q��_�� ���.�×��−����.�×��−���.�×��−��.�×��−��.��� R��T�� ���.�×��−����.�×��−����.�×��−���.�×��−��.��� R�� ���.�×��−����.�×��−���.�×��−���.�×��−��.��� S�� ��.�×��−���.�×��−����.�×��−���.�×��−��.��� S�� ��.�×��−���.�×��−����.�×��−���.�×��−��.��� S�� ���.�×��−����.�×��−���.�×��−���.�×��−��.��� T�.�×��−��.�×��−��.�×��−����.�×��−�� �.��� U� � � � �.��� ����� A�. Averages over all sector e�ects for a sector class for income quintile �and � based on income weights (%). Last column gives average price shock of a sector class. See Appendix K for corresponding sector labels. ��
Appendix I. Elasticity Estimates of Expenditure-weighted In�ation Inequality Sector Code Direct Indirect Total Estimate ��% CI Estimate ��% CI Estimate ��% CI A�� -�.��� (�.���) -�.��� (�.���) -�.��� (�.���) A�� -�.��� (�.���)�.��� (�.���) -�.��� (�.���) A�� -�.��� (�.���) -�.��� (�.���) -�.��� (�.���) B -�.��� (�.���)�.��� (�.���)�.��� (�.���) C��T�� -�.��� (�.���)�.��� (�.���) -�.��� (�.���) C��T�� �.��� (�.���)�.��� (�.���)�.��� (�.���) C�� -�.��� (�.���)�.��� (�.���)�.��� (�.���) C�� �.��� (�.���)�.��� (�.���)�.��� (�.���) C�� �.��� (�.���)�.��� (�.���)�.��� (�.���) C�� �.��� (�.���)�.��� (�.���)�.��� (�.���) C�� �.��� (�.���)�.��� (�.���)�.��� (�.���) C�� -�.��� (�.���)�.��� (�.���) -�.��� (�.���) C�� �.��� (�.���)�.��� (�.���)�.��� (�.���) C�� �.��� (�.���) -�.��� (�.���)�.��� (�.���) C�� �.��� (�.���)�.��� (�.���)�.��� (�.���) C�� �.��� (�.���)�.��� (�.���)�.��� (�.���) C�� �.��� (�.���)�.��� (�.���)�.��� (�.���) C�� �.��� (�.���)�.��� (�.���)�.��� (�.���) C�� �.��� (�.���)�.��� (�.���)�.��� (�.���) C�� �.��� (�.���)�.��� (�.���)�.��� (�.���) C��_�� �.��� (�.���)�.��� (�.���)�.��� (�.���) C�� �.��� (�.���)�.��� (�.���)�.��� (�.���) D�� -�.��� (�.���)�.��� (�.���) -�.��� (�.���) E�� -�.��� (�.���) -�.��� (�.���) -�.��� (�.���) E��T�� -�.��� (�.���)�.��� (�.���) -�.��� (�.���) F -�.��� (�.���) -�.��� (�.���) -�.��� (�.���) G�� �.��� (�.���)�.��� (�.���)�.��� (�.���) G�� -�.��� (�.���)�.��� (�.���)�.��� (�.���) G�� -�.��� (�.���)�.��� (�.���)�.��� (�.���) H�� �.��� (�.���)�.��� (�.���)�.��� (�.���) H�� �.��� (�.���)�.��� (�.���)�.��� (�.���) H�� �.��� (�.���)�.��� (�.���)�.��� (�.���) H�� �.��� (�.���)�.��� (�.���)�.��� (�.���) H�� �.��� (�.���)�.��� (�.���)�.��� (�.���) I�.��� (�.���)�.��� (�.���)�.��� (�.���) J�� �.��� (�.���)�.��� (�.���)�.��� (�.���) J��_�� �.��� (�.���)�.��� (�.���)�.��� (�.���) J�� �.��� (�.���)�.��� (�.���)�.��� (�.���) J��_�� �.��� (�.���)�.��� (�.���)�.��� (�.���) K�� �.��� (�.���)�.��� (�.���)�.��� (�.���) K�� �.��� (�.���)�.��� (�.���)�.��� (�.���) K�� �.��� (�.���)�.��� (�.���)�.��� (�.���) L -�.��� (�.���)�.��� (�.���) -�.��� (�.���) M��_�� �.��� (�.���)�.��� (�.���)�.��� (�.���) M�� �.��� (�.���)�.��� (�.���)�.��� (�.���) ��
Sector Code Direct Indirect Total Estimate ��% CI Estimate ��% CI Estimate ��% CI M�� �.��� (�.���)�.��� (�.���)�.��� (�.���) M�� �.��� (�.���)�.��� (�.���)�.��� (�.���) M��_�� �.��� (�.���)�.��� (�.���)�.��� (�.���) N�� �.��� (�.���)�.��� (�.���)�.��� (�.���) N�� �.��� (�.���)�.��� (�.���)�.��� (�.���) N�� �.��� (�.���)�.��� (�.���)�.��� (�.���) N��T�� -�.��� (�.���)�.��� (�.���)�.��� (�.���) O�� �.��� (�.���)�.��� (�.���)�.��� (�.���) P�� �.��� (�.���)�.��� (�.���)�.��� (�.���) Q�� -�.��� (�.���)�.��� (�.���) -�.��� (�.���) Q��_�� �.��� (�.���)�.��� (�.���)�.��� (�.���) R��T�� �.��� (�.���)�.��� (�.���)�.��� (�.���) R�� �.��� (�.���)�.��� (�.���)�.��� (�.���) S�� �.��� (�.���)�.��� (�.���)�.��� (�.���) S�� �.��� (�.���)�.��� (�.���)�.��� (�.���) S�� �.��� (�.���)�.��� (�.���)�.��� (�.���) T�.��� (�.���)�.��� (�.���)�.��� (�.���) ����� A�. Elasticity estimates with ��% con�dence intervals for expenditure-weighted in�ation inequality. ��
