Poor households and the weight of inflation

Schulz-Gebhard, Jan; Ipsen, Leonhard Working Paper Poor households and the weight of inflation FMM Working Paper, No. 106 Provided in Cooperation with: Macroeconomic Policy Institute (IMK) at the Hans Boeckler Foundation Suggested Citation: Schulz-Gebhard, Jan; Ipsen, Leonhard (2024) : Poor households and the weight of inflation, FMM Working Paper, No. 106, Hans-Böckler-Stiftung, Macroeconomic Policy Institute (IMK), Forum for Macroeconomics and Macroeconomic Policies (FMM), Düsseldorf This Version is available at: https://hdl.handle.net/10419/324471 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. 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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/legalcode.de FMM WORKING PAPER No. 106 • August 2024 • Hans-Böckler-Stiftung POOR HOUSEHOLDS AND THE WEIGHT OF INFLATION Jan Schulz 1 , Leonhard Ipsen 2 ABSTRACT Public opinion and the perceptions of poorer households consistently indicate that the poor are most exposed to inflation. Meanwhile, the empirical literature on income-dependent inflation inequality remains ambiguous. In this paper, we explore two different explanations for this inflation-inequality puzzle. First, we examine the role of sectorial heterogeneity in modulating the impact of cost-push shocks on households. An Input-Output analysis for 21 EU countries within the global production network shows the income-dependent impact of a price shock to be highly contingent on the sector of origin. While these findings suggest a partial explanation for the ambiguous results on inflation inequality, they do not point to a consistent overexposure of lower-income households. As a second explanation, we propose the income-weighting of price shock effects as opposed to the conventional expenditureweighting. This approach considers the share of income allocated to consumption and thus directly affected by a change in prices. Using a utility framework, we demonstrate that under bounded rationality the decline in utility is indeed proportional to the average propensity to consume times the change in prices. Introducing these income-weights in our empirical analysis, we find lower-income households to be disproportionally affected by every sectorial price shock, fully explaining the inflation-inequality puzzle. ————————— 1 Economics Institute, University of Bamberg, [email protected] 2 Bamberg Research Training Group on Bounded Rationality, Heterogeneity and Network Effects, funded by the Hans Böckler Foundation, [email protected] Poor Households and the Weight of Inflation Jan Schulz1 Leonhard Ipsen1, 2 [email protected] [email protected] 1Economics Institute, University of Bamberg 2Bamberg Research Training Group on Bounded Rationality, Heterogeneity and Network Effects, funded by the Hans Böckler Foundation Abstract Public opinion and the perceptions of poorer households consistently indicate that the poor are most exposed to inflation. Meanwhile, the empirical literature on income-dependent inflation inequality remains ambiguous. In this paper, we explore two different explanations for this inflation-inequality puzzle. First, we examine the role of sectorial heterogeneity in modulating the impact of cost-push shocks on households. An Input-Output analysis for 21 EU countries within the global production network shows the income-dependent impact of a price shock to be highly contingent on the sector of origin. While these findings suggest a partial explanation for the ambiguous results on inflation inequality, they do not point to a consistent overexposure of lower-income households. As a second explanation, we propose the income-weighting of price shock effects as opposed to the conventional expenditure-weighting. This approach considers the share of income allocated to consumption and thus directly affected by a change in prices. Using a utility framework, we demonstrate that under bounded rationality the decline in utility is indeed proportional to the average propensity to consume times the change in prices. Introducing these income-weights in our empirical analysis, we find lowerincome households to be disproportionally affected by every sectorial price shock, fully explaining the inflation-inequality puzzle. Keywords: Inflation, Input-output Analysis, Europe, Inequality JEL: E31, D31, C15, C67, D90 Acknowledgements: We thank Frank Westerhoff, Georg Maxton, the participants of the meeting of the Keynes Society, and participants of the Workshop on Economics with Heterogeneous Interacting Agents for valuable comments at crucial junctions of this investigation. We thank Luis Drechsel for excellent research assistance. Funding by the Hans-Böckler-Foundation through grant PK045 is gratefully acknowledged. 1. Introduction Public opinion and the perceptions of poorer households consistently indicate that the poor are most exposed to inflation. Meanwhile, the empirical literature on the persistence, direction, and magnitude of income-dependent inflation inequality remains ambiguous. In this paper, we explore two different explanations for this inflation-inequality puzzle. First, we examine the role of sectorial heterogeneity in modulating the impact of cost-push shocks on households. An Input-Output analysis for 21 EU countries within the global production network shows the income-dependent impact of a price shock to be highly contingent on the sector of origin. While these findings suggest a partial explanation for the ambiguous results on inflation inequality, they only show lower-income households to be overexposed to inflationary pressure for some sectorial shocks. As a second explanation, we propose the incomeweighting of price shock effects as opposed to the conventional expenditureweighting. Since the poor consume a much larger share of their income than the rich, their exposure to the same shock on their consumption basket should thus also be higher. Following this argument, analyzing inflation inequality needs to consider the income-dependent propensities to consume. In a parsimonious utility framework, we demonstrate that under bounded rationality the decline in utility is indeed proportional to the average propensity to consume (APC) times the change in prices, while under rational expectations the APC does not affect the change in utility. In particular, if boundedly rational agents do not consider the effects of a shock to the 1 aggregate price level on their future consumption, the effect of a price level change on their utility will be weighted by their individual APC. Finally, introducing these income-weights in our empirical analysis, we find lowerincome households to be disproportionally affected by literally every sectorial price shock. Taken together, we suggest and empirically substantiate an explanation for the contesting results on inflation inequality and show why poorer households may indeed be overly exposed to inflation. The paper proceeds as follows: Section 2 outlines the related literature to our study. Section 3 describes the data and model used to conduct our empirical analysis. Section 4 presents the results. Section 5 discusses the role of the APC for inflation inequality based on a utility framework. Section 6 presents the results of our empirical analysis, this time considering the income-weighting argument. Section 7 concludes with a final discussion and perspectives for further research. 2. Related Literature Our study connects to different strands of existing literature. Most importantly, it aims to provide a partial explanation for what can be called the inflationinequality puzzle. While unequal inflation exposure can manifest along a multitude of dimensions such as wealth (Doepke and Schneider, 2006), age (Adam and Zhu, 2016), idiosyncratic consumption or price differences (Kaplan and Schulhofer-Wohl, 2017; Strasser et al., 2023), or race (Hobijn and Lagakos, 2005), we focus on income-dependent inflation inequality of 2 households. The existing literature on this provides inconclusive results on the existence and direction, depending on the observational period and area (Garcimartín et al., 2021). It furthermore reports low persistency of asymmetric exposure across time (Hobijn and Lagakos, 2005; Strasser et al., 2023), while again providing inconclusive results on whether or not higher inflation rates also lead to higher inflation inequality (Claeys and Guetta- Jeanrenaud, 2022; Crawford and Oldfield, 2002; Hobijn and Lagakos, 2005). Meanwhile, the perceptions of poorer households consistently indicate that the poor are most exposed to inflation (Easterly and Fischer, 2001; Stantcheva, 2024). We propose two explanations for this apparent mismatch: sectorial asymmetries in price shock propagation and the consideration of affected income shares, as opposed to focusing only on expenditure shares. The first claim is motivated by foundational research from Weber et al. (2024). As their study showed for the US and subsequently was confirmed in a similar study by Ipsen et al. (2023) for the EU, a class of few sectors dominates the overall price level for consumers. The latter also provide suggestive evidence that poorer EU countries face greater exposure to volatile and rising prices, calling for a more thorough investigation of this channel. Both studies emphasize that the size of a sector or its share in final consumption may be an insufficient predictor of its actual importance in determining the price level. Often overlooked, a sector's role in the production network constitutes another key 3 variable, as it modulates the propagation of shocks. In their letter, Ipsen and 1 Schulz (2024) build on a similar Leontief Input-Output model to uncover these production network effects for inflation inequality. They show for the same set of countries as in our study that the global production network dampens asymmetries in inflation exposure between lower- and higher-income households. Yet, in most cases, this happens at the expense of poorer households. In the present, related study, we pick up upon their work to further explore the role of sectorial asymmetries for inflation inequality, going beyond their focus on production networks. Nikiforos et al. (2024) also build upon the aforementioned Input-Output model of Weber et al. (2024) to analyze the impact of price shocks on the functional distribution of income, namely profit versus wage shares. Our study now provides the other side of this coin by showing that price shocks also asymmetrically affect households dependent on their personal income. Some parallels to our work can also be found in the analysis provided by Cucignatto et al. (2023), who try to decompose the shock propagation of the latest energy price shock for three European countries, also considering the underlying production network. Our work goes beyond this in several aspects. First, we consider shocks propagating in the global production network. Second, we analyze the relevant importance of all sector classes, not only the energy sectors. Most importantly, we focus on distributional consequences along the income distribution for a much larger set of 21 EU countries. The shortage of semi-conductors is an illustrative example, that cost a multitude worth of 1 production relative to its input price. 4 Concerning our second proposition, the role of the APC in inflation inequality, related literature is somewhat scarce. Auclert (2019) addresses the importance of differences in the propensity to consume, however, focusing on monetary policy transmission. Analysing inflation inequality in the euro area, Strasser et al. (2023) mention the propensity to consume as one aspect of consumption heterogeneity but do not explore this aspect further. Commonly, empirical analyses of inflation inequality are based on expenditure shares (see, for example, Argente and Lee, 2021; Gürer and Weichenrieder, 2020; Hobijn and Lagakos, 2005; Kaplan and Schulhofer-Wohl, 2017). While these expenditure shares capture heterogeneities in spending patterns, they do not consider the share of income used for expenditures. As poorer households consistently spend larger shares of their available income for consumption purposes, i.e. have a higher APC (Fisher et al., 2016; Eurostat, 2021a), focusing solely on expenditure shares might mask a substantial source of realized inflation inequality. This argument relates to a strand of literature that is concerned with the nexus of households’ expenditure shares and income, dating back at least to Engel (1857). By now known as Engel’s Law, it establishes that with increasing income, the relative income share spent on food decreases, albeit a larger absolute amount is spent. Similarly to our approach, parts of this literature indeed appear to use food’s income share in several prominent papers (Engel and Kneip, 1996; Hamilton, 2001; Leser, 1963), although using food’s expenditure share is still much more common (cf. Lewbel and Houthakker, 2008 for a survey). While theoretical models of Engel’s law indeed suggest income-weighting (Hamilton, 2001), empirical papers typically 5 build on expenditure shares to not confound their estimates of expenditure decisions for different goods’ categories with the decision to spend or save at all (Barigozzi et al., 2012). In our parsimonious utility framework, we build on a Cobb-Douglas functional form for savings decisions, implying that optimal savings decisions are independent of the price level to address this issue. This framework allows us to interpret the expenditure- and income-weighting cases as pertaining to the utility effects of price shocks for full and boundedly rational decision-making without any confounding effect of the savings decision. We are, to the best of our knowledge, the first to provide a systematic analysis of the importance of income-dependent asymmetries in the propensity to consume for realized inflation inequality as an aggregate phenomenon not constrained to specific goods categories. 3. Empirical Strategy In this section, we will discuss the data and model used for our empirical analysis. Our global production network, the shares of final demand of a 2 countryc in sectori of countrya, as well as the sector-specific price shocks are based on the World Input Output Database (WIOD). It provides annual panel Input-Output data for the years 2000 to 2014 for 43 countries with 56 sectors each and covers economic activity that accounts for more than 85 percent of world GDP (Timmer et al., 2015). To be able to analyze income-dependent inflation, we offset the final demand data of the WIOD with sector-level data on consumption by purpose Data and code are available under https://github.com/ip5490/Inflation-Inequality. 2 6 In Figure 5 we map sectors on a four-quadrant chart. Sector classifications can be found in Appendix C. The vertical axis corresponds to the total effect estimate of a sector, indicating whether a price shock to this sector is equalizing (increasing exposure with income) or disequalizing (decreasing exposure with income). The horizontal axis shows whether the production network amplifies or dampens inflation inequality. We compute this mediating effect for each sector as . If this difference is positive (negative), the production network dampens (amplifies) inflation inequality relative to the direct effect of a price shock. In other words, if positive, the production network pushes the estimate closer to the zero line – the neutral effect benchmark – relative to the direct effect. The opposite is true for a negative mediating effect. While Figures 2 - 4 already point to significant asymmetries in the effects of price shocks, Figure 5 shows that the role of the production network in distributing these shocks is far from uniform either. In sum, our results suggest that the income-dependent inflation inequality arising from a price shock is highly contingent on the sector of origin. Thus, from a sectorial perspective, ambiguous results on inflation inequality for different periods and places are not surprising but to be expected. Mediating!Effect =|Dir.!Effect!Estimate|−|Ind.!Effect!Estimate| 13 (3) What does this mean for the actual inflation rates and inequalities at the household level? Are lower- or higher-income households more affected? Figure 6 provides an aggregate answer for our 21 countries under consideration. It shows the average mean effect of a sector in percentage points. Red (inequality enhancing) and blue (inequality reducing) contrast 10 the distributive effect of a price shock to a given sector. The darker (lighter) coloring shows the average relative effect size of the direct (indirect) effect of a price shock to a given sector. The ratio of the total effect of inequality reducing prices to inequality enhancing prices suggests an approximately equal exposure across incomes (51:49), underlining the systemic importance of a set of few sectors for the overall price level (Weber et al., 2024). Ipsen and Schulz (2024) provide a more detailed decomposition of the income- We first compute the average effect of a sector class considering sectors from all supply- 10 countries (i.e. globally) for each income quintile of each of the 21 demand-countries. We then compute the mean of these for each sector class. 14 Fig. 5. Each quadrant delimits a distinct effect of a sectorial price shock on inflation inequality. The vertical axis reports the total effect estimates, where negative (positive) values indicate that a price shock is inequality enhancing (reducing). The horizontal axis reports the sum of , where negative (positive) values indicate that the production network amplifies (dampens) inflation inequality. Sectors are labeled according to ISIC Rev. 4 classification. See Appendix C for a table with sector descriptions. |Total Effect Estimate| −|Indirect Effect Estimate| dependent effect sizes, finding the total exposure to price shocks to even tilt slightly against lower-income households. 15 Fig. 6. Average mean direct (darker) and indirect (lighter) effect of each sector in percentage points. Red marks sectors whose total effect is inequality enhancing, blue marks inequality reducing sectors. Sectors with insignificant effect are marked in gray. Total effect ratio of Inequality Reducing Prices to Inequality Enhancing Prices suggests an approximately equal exposure across incomes (51:49). All in all, a sectorial perspective on inflation inequality uncovers considerable heterogeneity in income-dependent inflation exposure, providing a promising explanation for ambiguous results in previous studies. It is not able, however, to substantiate the perceptions of poorer households that they are consistently most exposed to inflation. We discuss a second explanation for this mismatch in the following. 5. The Role of Income-weights for Inflation Inequality Empirical studies on inflation inequality commonly base their analysis on differences in expenditures. While this approach is able to capture incomedependent heterogeneity in the consumption basket, it fails to consider the actual income that is allocated to consumption and is thus directly affected by a price change in this basket. As the propensities to consume from available income vary substantially along wealth- and income-levels, focusing solely on differences in expenditures might mask a substantial source of realized inflation inequality. In this section, we use a straightforward utility framework to show how under bounded rationality the marginal growth rate of utility is proportional to the price change times the average propensity to consume. We assume a Cobb-Douglas type utility function with and reflecting the weights on current and expected future consumption to capture intertemporal motives, i.e., the utility function is given by α (1 −α) U 16 with as the average propensity to consume, as available current income, and as the price level. Here, only enters the current consumption term (left). As a consequence, agents consider the effect of the price level for their current consumption, while only considering the nominal income for the utility they gain out of their savings. This implies that agents act boundedly rational, since the price level will also affect their future consumption and hence, should affect the utility gained out of their savings. Indeed, a recent euro area survey data provides some evidence for this behavior, as the most common reaction to the recent inflationary surge was to modify consumption behavior, while not even half of the respondents reported adjusting their savings (Bobasu et al., 2024). By the FOC, the optimal propensity to consume is given by, which implies the canonical result that expenditures are a constant fraction of income. Optimizing gives the utility function for U(γ;Y,α,p) = (γ⋅Y p)α ⋅((1 −γ)Y)1−α γ Y p p Y γ* ∂U ∂γ ! = 0 ⇒γ* = α, γ* U*(Y,α,p) = (αY p)α ⋅((1 −α)Y)1−α. 17 (4) (5) (6) Taking the logarithmic derivative and approximating by the discrete growth rate in utility over the discrete growth rate in the price level yields For our application case, all initial price levels are normalized to unity. This implies that we can express the marginal growth rate of utility in response to a price shock as Thus, if agents solely focus on the consumption effect of a change in prices, the marginal growth rate of utility is indeed proportional to the price change times the average propensity to consume. The above equation (8) nests the usual use case of expenditure weights for . This case corresponds to a situation, where agents do not gain any utility out of savings and thus, intertemporal motives do not matter. Within the same framework, Appendix D shows that under a full rationality assumption, the propensity to consume does not affect the reaction in utility. Empirically, as Table 1 shows, a significant share of households report APCs well over 90 percent of available income. For income-quintile one, only Cyprus reports an APC of below 100 percent. Arguably, these cashconstrained households will only be concerned with present consumption and dlog U* dlog p=−α p≈Δu*/u* Δp/p. Δp Δu*/u Δp=−α⇔ − Δu* u=α⋅ Δp. α= 1 18 (7) (8) cannot consider the effect of a change in prices on their savings. Since we are interested in why poorer households are indicated to be disproportionally affected by inflation, considering the APC seems to be well-grounded. 6. Empirical Results for Income-weighted Inflation Inequality To empirically investigate the impact of APCs on the realization of incomedependent inflation inequality, we rerun our Input-Output analysis, this time using income-weighted expenditure shares. Therefore, we compute the share of expenditure in a given sector as a ratio of the total income as opposed to the total expenditures. We compute these for every country-income pair as with as the average expenditures of income quintileq of countryc on goods produced in sectorj and as the mean disposable income of quintileq of countryc (see Appendix A for the country specific APCs and Eurostat (2021a) for information on the data collection. We can now replace the expenditure shares of our initial Input-Output setup with these incomeweighted shares. exj,c,q×APCc,q=exj,c,q n ∑ j=1 exj,c,q × n ∑ j=1 exj,c,q Incomec,q =exj,c,q Incomec,q , exj,c,q Incomec,q 19 (9) Figures 7 - 9 report the estimates (points) and 95 percent confidence intervals (whiskers) for the direct, indirect, and total effect, respectively. It shows that if we are to consider the differences in the APCs for inflation inequality, every sectorial price shock disproportionally affects lower-income households. The massive differences in the APCs between income groups even outweigh differences in expenditure patterns in the other direction. These findings are consistent with the indication that poorer households are consistently overexposed to inflation. 20 Fig. 7. Estimates of income-dependent inflation exposure for the effect of a price shock to the final goods produced by a sector (direct effect). Whiskers give the 95 percent confidence interval. Estimates below zero are Inequality Enhancing Prices, as the inflation exposure of households towards these sectors is reduced with increasing income. Positive estimates accordingly show Inequality Reducing Prices, as exposure rises with increasing income. Based on income-weighted expenditure shares. 21 Fig. 8. Estimates and 95 percent confidence interval of income-dependent inflation exposure for the effect of a price shock to the intermediate goods produced by a sector (indirect effect). Based on income-weighted expenditure shares. Fig. 9. Estimates and 95 percent confidence interval of income-dependent inflation exposure for the effect of a price shock to all goods produced by a sector (total effect). Based on income-weighted expenditure shares. 7. Conclusion The empirical literature on income-dependent inflation inequality provides contesting results about its direction, magnitude, and persistence. Meanwhile, the perceptions of poorer households consistently indicate that they are most exposed to inflation. We propose and empirically substantiate two possible explanations for this inflation-inequality puzzle. First, we show for a set of 21 EU countries embedded in the global production network, that the incomedependent impact of a price shock is highly contingent on the sector of origin. This sectorial perspective poses a promising contester for explaining ambiguous results on inflation inequality. Conditional on the availability of data, future research could test the explanatory power of our sector-level estimates for the realized inflation-inequality in previous studies. Our results directly imply the testable hypothesis that poor households' perceptions of inflation should react the strongest, whenever inflationary pressures originate in sectors like housing and agricultural products. Monitoring sectorial prices could give policy-makers a head start in mitigating inflation and especially in preventing unnecessary hard-ship for lower-income households. Second, we propose that income-dependent differences in the propensities to consume matter for realized inflation inequality. Focusing solely on differences in expenditures fails to consider the actual income that is allocated to consumption and thus directly affected by a price change in the consumption basket. Using a utility framework, we show that for agents who focus their concern on the consumption effect of a change in prices, the 22 Appendix A: Average Propensity to Consume 29 GEO Q1 (%) Q2 (%) Q3 (%) Q4 (%) Q5 (%) Austria 129.8 97.9 85 75.9 59.4 Belgium 118.9 92.1 73.8 63.3 50 Bulgaria 113.9 89.6 75 62.2 44.1 Croatia 121 107.7 88.4 80 63 Cyprus 89.3 87 86.5 82.6 65.2 Denmark 117.5 85.6 74.8 62.3 46.5 Estonia 108.3 81.9 69.9 54 45.3 France 114.1 84.9 78.7 72 55.3 Germany 143.4 91.6 84.4 77.5 63.4 Greece 168 110.4 101.5 88.6 72 Hungary 113.4 94.8 83.3 74.8 66.2 Latvia 114 88.7 78 72.4 56.9 Lithuania 110.7 82.1 69.5 51.8 39.4 Luxembourg 112.9 86.8 80.4 63.8 52.8 Malta 136.2 94.6 87.6 74.4 53.9 Netherlands 148.2 104.3 83.6 68.3 52.9 Poland 104.1 60.6 53.5 47.2 38.8 Romania 195.4 126.6 104.1 86 65.6 Slovakia 103 89.2 79.6 71.3 55 Slovenia 116.5 95.7 87 78.2 64.3 Spain 129.3 90.6 76 65.8 50.6 Mean 124.2 92.5 81.0 70.1 55.3 Table 1: Average Propensity to Consume for each income quintile in 21 EU countries for the year 2020. Based on Eurostat (2021a). Appendix B: Leontief Price Model Derivation We base this section on the Leontief price models used in Ipsen and Schulz (2024), Valadkhani and Mitchell (2002) and Weber et al. (2024). Equation (i) shows the model’s principle case of the price of being a linear function of the prices of inputs times the technical coefficients plus the value added . Since our data comprises global trade data, we need no additional import and export variables. The technical coefficients are computed as the ratio of value of inputs from to the overall value of output. With normalizing the output of , (i) gives the price per unit of output. A change in prices is thus to be interpreted as percentage changes. For sectors, this becomes a system of linear equations. Since we want to simulate the down-stream propagation of shocks, we need to take the transpose of the technical coefficient matrix . In matrix notation, this gives Pj sectorj Pi≠j aij Vj aij sectori sectorj sectorj Pj=a1jP1+ . . . + aij Pi+ . . . + anj Pn+Vj n P1 P2 ⋮ Pn = a11a21 ⋯an1 a12a22 ⋯an2 ⋮ ⋮ ⋱ ⋮ a1na2n⋯ann P1 P2 ⋮ Pn + v1 v2 ⋮ vn A 30 (i) (ii) As a next step, we single out the sector which we want to expose to an exogenous price shock. This splits (iii) into 11 with the price vector of the shocked sector and as the price vectors of the remaining endogenous sectors. Since is determined by our exogenous shock, we are only interested in captures how the prices in the endogenous sectors depend on the price of the exogenous sector. captures how the prices in the endogenous sectors depend on each other. If we solve for , we get Assuming no substitution, the quantity of inputs remains unchanged following a change in prices. Thus, following a change in prices in the exogenous sector , the price change in the remaining sectors, , is given by P=A′ P+v. [PX PE]=[A′ XXA′ EX A′ XEA′ EE][PX PE]+[vX vE] PX PE PX PE=A′ XE PX+A′ EE PE+vE. A′ XE PX A′ EE PE PE PE= (I−A′ EE)−1A′ XE PX+ (I−A′ EE)−1vE. ΔPx ΔPE ΔPE= (I−A′ EE)−1A′ XEΔPX. Recall that we compute the price shock to as its average percentage change over our 11 period of observation. sectorj 31 (iii) (iv) (v) (vi) (vii) At this point, we introduce the expenditure shares. represents the expenditure share of of in the exogenous . represents the expenditure share of of in the endogenous sector . We are now able to decompose the effect of a price shock to the final goods produced by a sector into and the effect of a price shock to the intermediate goods produced by a sector into The total effect of a price shock to a sector is then given by These direct, indirect and total price shock effects to a sector are used as the dependent variable to compute the elasticity estimates according to equation (2) in Section 3. esx,q,i quintileq countryi sectorx ese,q,i quintileq countryi e≠x Δπdirect q,i,x=esx,q,iΔPx Δπindirect q,i,x=∑ e≠x ese,q,iΔPe. Δπtotal q,i,x=esx,q,iΔPx+∑ b≠x ese,q,iΔPe. 32 (viii) (ix) (x) Appendix C: Sector Classifications 33 Table 2 Sector Label Description Sector Label Description A01 Crop and animal production, hunting and related service activities C25 Manufacture of fabricated metal products, except machinery and equipment A02 Forestry and logging C26 Manufacture of computer, electronic and optical products A03 Fishing and aquaculture C27 Manufacture of electrical equipment B Mining and quarrying C28 Manufacture of machinery and equipment n.e.c. C10-C12 Manufacture of food products, beverages and tobacco products C29 Manufacture of motor vehicles, trailers and semi-trailers C13-C15 Manufacture of textiles, wearing apparel and leather products C30 Manufacture of other transport equipment C16 Manufacture of wood and of products of wood and cork, except furniture; manufacture of articles of straw and plaiting materials C31/C32 Manufacture of furniture; other manufacturing C17 Manufacture of paper and paper products C33 Repair and installation of machinery and equipment C18 Printing and reproduction of recorded media D35 Electricity, gas, steam and air conditioning supply C19 Manufacture of coke and refined petroleum products E36 Water collection, treatment and supply C20 Manufacture of chemicals and chemical products E37-E39 Sewerage; waste collection, treatment and disposal activities; materials recovery; remediation activities and other waste management services C21 Manufacture of basic pharmaceutical products and pharmaceutical preparations F Construction C22 Manufacture of rubber and plastic products G45 Wholesale and retail trade and repair of motor vehicles and motorcycles C23 Manufacture of other nonmetallic mineral products G46 Wholesale trade, except of motor vehicles and motorcycles C24 Manufacture of basic metals G47 Retail trade, except of motor vehicles and motorcycles 34 Sector Label Description Sector Label Description H49 Land transport and transport via pipelines L68 Real estate activities H50 Water transport M69/ M70 Legal and accounting activities; activities of head offices; management consultancy activities H51 Air transport M71 Architectural and engineering activities; technical testing and analysis H52 Warehousing and support activities for transportation M72 Scientific research and development H53 Postal and courier activities M73 Advertising and market research I Accommodation and food service activities M74/ M75 Other professional, scientific and technical activities; veterinary activities J58 Publishing activities N Administrative and support service activities J59/J60 Motion picture, video and television programme production, sound recording and music publishing activities; programming and broadcasting activities O84 Public administration and defence; compulsory social security J61 Telecommunications P85 Education J62/J63 Computer programming, consultancy and related activities; information service activities Q Human health and social work activities K64 Financial service activities, except insurance and pension funding R/S Other service activities K65 Insurance, reinsurance and pension funding, except compulsory social security T Activities of households as employers; undifferentiated goods- and services-producing activities of households for own use K66 Activities auxiliary to financial services and insurance activities U Activities of extraterritorial organizations and bodies Appendix D: Utility Maximization under Full Rationality The utility function is given by with as the average propensity to consume, as available current income, and as the price level. In this version, enters both the term relating to current consumption (left) and in the savings (right). Thus, in this setup, agents correctly anticipate both the consumption as well as wealth effect of a change in . By the FOC, we can derive the optimal average propensity to consume Optimizing gives the utility function for Taking the logarithmic derivative and approximating by the discrete growth rate in utility over the discrete growth rate in the price level yields U U(γ;Y,α,p) = (γ⋅Y p)α ⋅((1 −γ)Y p)1−α , γ Y p p p γ* ∂U ∂γ ! = 0 ⇒γ* = α. γ* U*(Y,α,p) = (αY p)α ⋅((1 −α)Y p)1−α . 35 (i) (ii) (iii) Assumeíng that the initial price level is , than the marginal growth rate of utility is given by In this case, the model suggests that if agents correctly anticipate the effect of a change in prices on their consumption and savings behavior, then the effect of a price shock on utility is not mediated by the average propensity to consume. dlog U* dlog p=−1 p≈Δu*/u* Δp/p. p= 1 Δu*/u Δp=−1⇔ − Δu* u=Δp. 36 (iv) (v) Imprint Publisher Macroeconomic Policy Institute (IMK) of Hans-Böckler-Foundation, Georg-Glock-Str. 18, 40474 Düsseldorf, Contact: [email protected], https://www.fmm-macro.net FMM Working Paper is an irregular online publication series available at: https://www.boeckler.de/de/fmm-working-paper-22457.htm The views expressed in this paper do not necessarily reflect those of the IMK or the Hans-Böckler-Foundation. 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