Low pass-through from inflation expectations to income growth expectations: Why people dislike inflation

Hajdini, Ina et al. Working Paper Low pass-through from inflation expectations to income growth expectations: Why people dislike inflation IDB Working Paper Series, No. IDB-WP-1672 Provided in Cooperation with: Inter-American Development Bank (IDB), Washington, DC Suggested Citation: Hajdini, Ina et al. (2025) : Low pass-through from inflation expectations to income growth expectations: Why people dislike inflation, IDB Working Paper Series, No. IDBWP-1672, Inter-American Development Bank (IDB), Washington, DC, https://doi.org/10.18235/0013365 This Version is available at: https://hdl.handle.net/10419/309192 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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Knotek II John Leer Mathieu Pedemonte Robert Rich Raphael Schoenle WORKING PAPER No IDB-WP-1672 InterA merican Development Bank Department of Research and Chief Economist January 2025 * Federal Reserve Bank of Cleveland ** Morning Consult *** Inter-American Development Bank **** Brandeis University Low Pass-through from Inflation Expectations to Income Growth Expectations: Why People Dislike Inflation Ina Hajdini* Edward S. Knotek II* John Leer** Mathieu Pedemonte*** Robert Rich* Raphael Schoenle**** Inter-American Development Bank Department of Research and Chief Economist Januar y 2025 Cataloging-in-Publication data provided by the Inter-American Development Bank Felipe Herrera Library Low pass-through from inflation expectations to income growth expectations: why people dislike inflation / Ina Hajdini, Edward S. Knotek II, John Leer, Mathieu Pedemonte, Robert Rich, Raphael Schoenle. p. cm. — (IDB Working Paper Series ; 1672) Includes bibliographical references. 1. Inflation (Finance)-United States. 2. Income distribution-Effect of inflation on-United States. 3. Income distribution-Mathematical models-United States. I. Hajdini, Ina. II. Knotek, Edward S. III. Leer, John. IV. Pedemonte, Mathieu. V. Rich, Robert. VI. Schoenle, Raphael. VII. Inter-American Development Bank. Department of Research and Chief Economist. VIII. Series. IDB-WP-1672 http://www.iadb.org Copyright © 2025 Inter-American Development Bank ("IDB"). This work is subject to a Creative Commons license CC BY 3.0 IGO (https://creativecommons.org/licenses/by/3.0/igo/legalcode). The terms and conditions indicated in the URL link must be met and the respective recognition must be granted to the IDB. Further to section 8 of the above license, any mediation relating to disputes arising under such license shall be conducted in accordance with the WIPO Mediation Rules. 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Abstract Using a large, nationally representative survey of US consumers, we estimate a causal 20 percent pass-through from inflation expectations to income growth expectations for the average consumer, with considerable heterogeneity in pass-through associated with sociodemographic factors. The results also indicate that higher inflation expectations cause an increase in consumers’ likelihood to search for higher-paying jobs but do not change the likelihood of asking for a raise, suggesting that consumers recognize significant wage rigidity with their current employer. In a calibrated search-and-matching model, we find that demand and supply shocks combined with incomplete pass-through produce a strong negative relationship between expected inflation and expected utility. Taken together, the survey results and model analysis provide a labor market account of why people dislike inflation. JEL classifications: E31, E24, E71, C83 Keywords: Inflation, Wage-price spiral, Expectations, Randomized controlled trial The randomized controlled trial is registered at the AER RCT Registry (#AEARCTR-0009062). The views expressed here are solely those of the authors and do not necessarily reflect the views of the Federal Reserve Bank of Cleveland or the Federal Reserve System. We thank Oscar Arce, Alex Bick (discussant), Mark Bils, Olivier Coibion, Julia Coronado, Jon Faust, Juan Herreño, Olena Kostyshyna, Emiliano Luttini (discussant), Ay¸segül ¸Sahin, Maarten van Rooij (discussant), Michael Weber and seminar participants at various institutions for valuable comments and discussions. We thank Caroline Smith from Morning Consult for her work fielding the experiments. 1 Introduction The rapid economic recovery in the United States from the COVID-19-induced recession was characterized by the highest inflation rates seen in the last forty years. These high inflation readings were accompanied by increases in inflation expectations and strong wage gains in tight labor markets, raising concerns about potential feedback into expectations of other macroeconomic aggregates, in particular in the labor market (e.g., Curtin (2022); Blanchard (1986)).1However, disentangling the causal effect of inflation expectations on income growth expectations is challenging because these concepts should be related in general equilibrium.2More generally, while the literature on expectations formation has made progress in examining how expectations respond to information treatments, it has made less progress in understanding how individuals perceive the relationship between different expected variables. This paper sheds new light on these issues by investigating the causal relationship between inflation expectations and income growth expectations, and how those expectations affect labor market decisions, in the context of a randomized controlled trial (RCT) for a large, nationally representative survey of the US population. Three findings emerge. First, inflation expectations causally affect income growth expectations but pass-through from the former to the latter is far less than one-for-one, on the order of 20 percent. Second, higher inflation expectations increase the probability that consumers will search for a new job that pays more but do not affect the likelihood that they will negotiate for a higher wage with their current employer. This finding is consistent with consumers’ recognition of substantial nominal wage rigidity with their current employer.3Third, a canonical search-and-matching model calibrated to fit our empirical findings shows that low passthrough from expected inflation to expected income growth is consistent with consumers’ beliefs that higher future inflation will reduce their expected utility. Taken together, the survey results and model analysis formalize a labor market channel underlying consumers’ aversion to inflation. Our empirical findings primarily come from a survey experiment fielded by the decision intelligence company Morning Consult in March 2022, at a time when inflation expectations and inflation concerns were starting to rise to notable levels, and before inflation had clearly begun 1See Lorenzoni and Werning (2023) for a theoretical analysis on the wage-price spiral in the context of a New Keynesian model. 2See, for example, Werning (2022) for a discussion on the challenges related to pinning down the pass-through from inflation expectations to current inflation. 3The recent finding of Jäger et al. (2023) that workers wrongly anchor their beliefs about outside options on their current wage speaks to the role that perceived nominal wage rigidity plays for workers’ income growth expectations. 1 to turn back down.4The embedded experimental module consisted of four parts. The first part elicited inflation expectations and income growth expectations over the next 12 months prior to any experimental treatments.5The second part consisted of an RCT that allowed us to provide information to respondents on two key objects, inflation or income growth, to determine the causal relationship between inflation expectations and income growth expectations. In particular, we randomly assigned information treatments to six groups: one control group; one placebo group; three groups that received different information on inflation; and one group that received information on wage growth, which is the primary source of income growth for most consumers. Following the treatments, the third part of the experiment re-elicited inflation expectations and income growth expectations. This experimental step allows us to measure how consumers’ posterior expectations of inflation and income growth react to information treatments while conditioning on their prior expectations. Specifically, the resulting exogenous, experimentally induced variation in posterior inflation expectations then allows us to estimate the causal impact on income growth expectations. This pass-through estimate is causal as it considers exogenous variation of inflation or income, while allowing respondents to form their own mental models about the precise transmission mechanism as highlighted in (Andre et al.,2022a). We find that a 1.0 percentage point increase in inflation expectations increases income growth expectations, but only by 0.2 percentage point—implying an expected decrease in real income growth of 0.8 percentage point. There is, however, considerable variation in pass-through associated with socio-demographic characteristics. While the extent of pass-through is high and statistically significant for higherincome respondents, it is low and statistically insignificant for lower-income respondents. This finding is consistent with the former group believing it is better protected from increases in expected inflation than the latter group. We also find a larger pass-through point estimate for male respondents than for female respondents. This result is consistent with evidence that highlights different characteristics in the labor market for women and men. For instance, Biasi and Sarsons (2022) find that in the United States, women engage less frequently in pay negotiations, whereas Card, Cardoso, and Kline (2016) find that, in Portugal, women are less likely to work at firms where workers have high bargaining power. It is important to note, however, that pass-through remains incomplete and is well below one-for-one in all cases. 4We also performed a pilot in January 2022 as well as a follow-up exercise in September 2022 that confirms the March results. 5We ran robustness exercises with different prior question wordings to mitigate any concern about particular wording, finding no statistical difference depending on the specific prior. This exercise includes using the point estimate question of the NY Fed Survey of Consumer Expectations instead of the question fielded by Morning Consult. 2 Finally, the fourth part of our survey asks respondents about the likelihood of pursuing different labor market actions over the following year to increase their incomes and potentially offset the effects of inflation. Exploiting the exogenous variation in beliefs once again for estimation purposes, we find that higher inflation expectations moderately increase the perceived likelihood that an individual applies for another job paying a higher wage.6However, higher inflation expectations do not increase the perceived likelihood of two other labor market actions: working longer hours or asking for a raise from a current employer. These results suggest that consumers’ mental models (see, for example, Andre et al. (2022a) for a general study of subjective models) incorporate the belief that there is a high degree of nominal wage rigidity associated with their current employer. Interpreting our findings structurally, through a model, can provide further economic insight, which, in particular, can help understand why people may dislike inflation. We show how this conclusion can arise by adapting a relatively standard New Keynesian model with search-andmatching in labor markets as in Mortensen and Pissarides (1994), tracing out the expected utility implications of demand and supply shocks. A central finding from this model setup is that wage rigidity stands out in capturing a labor market channel explanation why people dislike inflation. While current work by Afrouzi et al. (2024) and Guerreiro et al. (2024) provides further microfounded modeling advances in this context, our modeling exercise also simply gauges the extent to which a canonical model can fit our empirical facts. The model features several frictions. Motivated by the observation that the provision of publicly available information moves consumers’ expectations which contrasts with a full-information rational expectations view of the world, we allow for sticky information in the inflation expectations formation process, similar to Mankiw and Reis (2002). In a novel interpretation of how information stickiness can play out, we calibrate the degree of information stickiness to be consistent with the estimated effect that new information from treatments has on our respondents’ inflation expectations.7In addition, matching our survey findings requires sluggish wage adjustment. We model wage rigidity as infrequent nominal wage renegotiation in a Calvo (1983) fashion, calibrated to match our estimate of empirical pass-through as a moment.8Finally, to capture the impact of inflation expectations on labor market actions, we assume that workers who cannot renego6Pilossoph and Ryngaert (2022) find that higher inflation expectations are correlated with the likelihood that workers will search for other jobs in the short term. 7We find that the degree of information stickiness is about 0.28. 8We would note that, in contrast to the experiment in our survey, it is impossible within the model setting to isolate the causal effect of inflation expectations on income growth expectations. 3 tiate their wages and who apply for other jobs due to higher inflation expectations generate an outside contract with certainty. This wage-push factor puts upward pressure on their nominal wage with the current employer, with an elasticity that we calibrate to match our empirical findings. Given this setup, our model analysis then highlights the responses of key macroeconomic variables to a positive demand shock and a positive (adverse) supply shock that are meant to broadly capture the prevailing inflationary disturbances in the US economy at the time of our survey in early 2022. A central finding that emerges is that nominal wage rigidity plays a crucial role in driving the dynamics of macroeconomic variables within the model. When we subject the model to an inflationary demand shock, this rigidity causes a decline in real wages relative to a counterfactual of full pass-through from inflation expectations to expected nominal wage growth. When we subject the model to an inflationary supply shock, sticky wages temper the movements in real wages compared to the counterfactual of full pass-through. In both cases, the responses of real wages under imperfect pass-through help to amplify the fluctuations in output and consumption, generating additional volatility in the wake of the original shock. Moreover, the model predicts that greater wage rigidity produces a stronger negative relationship between inflation expectations and expected utility regardless of whether we look at supply or demand shocks. This latter result is particularly important because it identifies a labor market channel that can explain why consumers dislike inflation.9 The rest of the paper is organized as follows. Section 2discusses work related to our paper. Sections 3and 4provide a detailed description of our experiment and its implementation, respectively. Section 5explains our identification strategy and presents the main empirical findings. Section 6gives a brief overview of the model, our calibration strategy, and the macroeconomic implications of the model. Section 7concludes. 2 Literature Review Our paper is most related to a series of papers that study the issue of public attitudes about inflation, specifically why consumers and firms associate higher inflation expectations with lower output and well-being. For example, Shiller (1997) and Candia, Coibion, and Gorodnichenko (2020) provide evidence consistent with our results, though that evidence is non-causal. Other studies, such as Savignac et al. (2021), look at the relationship between firms’ inflation expecta9Following a one-time exogenous shock occurring in the present period, realized inflation hperiods ahead co-moves with current expectations about inflation hperiods ahead, in the presence of information stickiness. Therefore, within the context of the model, we refer to the two variables interchangeably. 4 Respondents then select from three options, filling in the percentages if they select (1) or (3), while (2) is coded as zero: 1. Increase by %; 2. Stay about the same; and 3. Decrease by %. Our posterior inflation expectations question uses the following wording: “In the next year, do you think prices in general will increase, decrease, or stay about the same?” If respondents’ answers indicated an expected increase or decrease, then they were subsequently asked to provide a quantitative percentage response. As noted in the above design description, this question is purposely slightly different from the prior inflation expectations question, by asking directly about prices and by its focus on prices in general rather than the prices to which consumers are exposed. We expect that answers to this question will not be identical to the indirect measure of inflation expectations. Nevertheless, responses should be strongly positively correlated, which allows us to capture the (potential change in) posterior beliefs after an information treatment. In terms of the interpretation of the results in the rest of the paper, all exercises in terms of inflation will consider this question as the posterior. While the ICIE question is used to measure respondents’ priors, it is the systematic deviation between the treated groups and the control group in terms of this aggregate inflation question that is our main outcome of interest. The prior only serves as a control variable to measure the information set of the respondents. In fact, as shown in Appendix E, our results are not affected if we select the canonical NY Fed inflation expectations question to elicit the prior inflation expectations. Our second prior question elicits income growth expectations. The second question is the following: “Do you expect your income to increase, decrease, or stay about the same over the next 12 months?” The question comes with the same options as in the previously described posterior question. If respondents indicated they expect their income to increase or decrease, then they were subsequently asked to provide a quantitative percentage response. Our posterior income growth expectations question uses the following wording: “Between December 2022 and December 2023, do you expect your income to increase, decrease, or stay about the same over the next 12 months?” Compared to the prior question on income growth expectations, this question mainly differs 11 in its reference to a fixed time period. This period partially overlaps with the previous income growth question, so we expected a positive correlation with the previous question given the overlap as well as the fact that many wages are adjusted infrequently and at a particular time of the year. In Section 6, we consider these periods to model and evaluate our results. Questions about labor market decisions follow the elicitation of all these posterior expectations, asking consumers: “How likely are you to do the following to increase your income over the next three months?” We asked respondents to provide answers for three actions, choosing from the response set very likely,somewhat likely,somewhat unlikely,very unlikely, or they do not know. The actions we asked for are: • Apply for a job(s) that pays more • Work longer hours • Ask for a raise In addition to these actions, an open-ended answer option records any further possibilities that survey respondents might offer. 5 Empirical Analysis This section uses the expectations elicited through the RCT to estimate the causal impact of inflation expectations on income growth expectations as well as on the short-term plans around labor market decisions. Three main findings emerge. First, the pass-through of inflation expectations to income growth expectations is positive and statistically significant but less than unity. Second, estimated pass-through varies across respondent demographic characteristics, with some evidence of statistically significant differences. Third, while higher inflation expectations cause consumers to report a moderately higher probability that they will search for a higher-paying job, they do not increase the perceived probability of working more hours or asking for a raise from a current employer. 5.1 Inflation Expectations and Income Growth Expectations The analysis takes three steps. First, we verify that our “posterior” questions capture information similar to that of the baseline prior questions. This finding validates the choices of question wording against the backdrop of the design considerations outlined above in the experimental 12 description. Second, we establish which treatments affect the posterior beliefs. Last, we use the results from the treatments to infer the causal effect of inflation expectations on income growth expectations, which yields our main findings. In the first step, we estimate two specifications that relate prior beliefs to posterior beliefs. For inflation expectations, we estimate the following specification: EihπPosterior pi=α+βEihπPrior pi+εi(1) where EihπPrior pidenotes respondent i’s prior inflation expectations from the ICIE question and EihπPosterior pidenotes the posterior general price growth expectations in the next year. For income growth expectations, we estimate the following specification: EihπPosterior yi=α+βEihπPrior yi+εi(2) where EihπPosterior yidenotes the posterior expectations of income growth between December 2022 and December 2023 and EihπPrior yidenotes the prior income growth expectations over the next 12 months. When we estimate regressions in (1) and (2) for the full sample of respondents and the control group (after winsorizing 2.5 percent of the highest and lowest responses to remove extreme outliers), we find that the responses to our posterior questions are systematically related to the responses to the prior questions. Table 1reports the estimation results. As columns (1) and (4) in Table 1show, we find positive and statistically significant correlations between the prior and posterior beliefs for both inflation expectations and income growth expectations for the full sample. This finding in particular validates the choices of question wording against the backdrop of the design considerations outlined above in the experimental description. Our second step investigates the properties of our treatments and their effect on the posterior inflation expectations and posterior income growth expectations. In the case of inflation expectations, we estimate the following specification: 13 EihπPosterior pi=α+βEihπPrior pi+ 6 ∑ j=2 γj p×Tj i+ 6 ∑ j=2 θi p×Tj i×EihπPrior pi+εi(3) We estimate a similar regression for income growth expectations: EihπPosterior yi=α+βEihπPrior yi+ 6 ∑ j=2 γj y×Tj i+ 6 ∑ j=2 θj y×Tj i×EihπPrior yi+εi(4) where Tj iis a dummy variable that is equal to 1 if respondent ireceived treatment jand 0 otherwise. The control group j=1 is the reference group. Regression specifications (3) and (4) relate the posterior belief to the prior belief and each of the treatments. Ideally, if the treatment represents new information to the respondent, then providing that information will elicit a response and move the posterior away from the prior. If treatment jis effective, then we should expect a negative coefficient for θj pand θj yas the prior will have a reduced role in explaining the posterior for the treated group compared to the control group. To estimate specifications (3) and (4), we run two types of regressions. First, we conduct Huberrobust regressions, and second, we run trimmed regressions, with the latter dropping 5 percent of the biggest changes between individuals’ prior and posterior beliefs. Both types of regressions aim to remove the influence of outliers, especially those that display extreme revisions. Drawing upon the common practice in survey analysis (for example, Coibion, Gorodnichenko, and Ropele (2020b)), we view the Huber-robust regressions as our preferred specification, with the trimmed regressions serving mainly as a robustness check.13 The estimation of (3) and (4)—reported in columns 2-3 and 5-6, respectively, in Table 1—shows three results.14 First, there is a high correlation of the posteriors with the priors as in the above first step, even after controlling for outliers. For inflation expectations, we find that a 1 percentage point increase in the prior beliefs of the control group increases the posterior beliefs by around 0.51 percentage point. This correlation between prior and posterior for the control group is similar to the one found in other similar household experiments, such as Coibion et al. (2019) or Coibion, 13Appendix Bimplements a third quantile regression approach, with results reported in Table 9. 14Figure 6in Appendix Cshows the distribution of the prior and posterior and Figure 7in Appendix Cshows the distribution of the posterior for each treatment group. We observe rounding (see Binder (2017)) in particular at zero as in other surveys (43 percent for the prior, 32 percent for the posterior; see Andrade, Gautier, and Mengus (2023) for properties of zero answers). Hajdini et al. (2024) describe in more detail the distribution of the prior. 14 Gorodnichenko, and Weber (2022), who find a correlation of 0.54 and 0.66 using a distributional question as prior. This result confirms that the ICIE measure is a good prior for aggregate inflation expectations. In the case of income growth expectations, the correlation is even higher and associates the same 1 percentage point increase in prior beliefs with an increase in the posterior beliefs of between 0.78 and 0.96 percentage points. Second, in terms of the effect of the treatments, our results show that all of the treatments for inflation expectations have a statistically significant effect on the posterior except for the placebo, as column 2 indicates. Moreover, the estimated coefficients on the interacted treatment and prior are negative, indicating that consumers who receive one of the treatments place less weight on their prior beliefs. Column 3 shows similar results when we explicitly drop respondents who make extreme changes between their prior and posterior beliefs (over 50 percentage points). The magnitude of the estimated effects varies across treatments. In particular, while the prior interacted with the treatment about the Federal Reserve’s inflation target is negative and statistically significant, the coefficient is an order of magnitude smaller compared to those reported for the prior interacted with treatments 3-5. As previously noted, the prior interacted with the placebo does not generate a meaningful effect on the posterior beliefs compared to the control group. These results are not driven by outliers.15 Third, in contrast to inflation expectations, the regression results show that the treatments have little effect on the posterior beliefs of income growth expectations. That is, there is a high correlation between the prior and posterior beliefs, meaning that most respondents do not revise their answers. As a result, the Huber-robust regressions fail to run with the standard tuning factor due to the small number of outliers that can be dropped. When we use the minimum tuning value to achieve convergence, the results in column 5 indicate that the treatments generally exert little influence on the posterior beliefs. However, the same conclusion arises for the trimmed regressions in which we eliminate respondents who reported extreme absolute changes between their prior and their posterior beliefs at or above the 95th percentile (10 percentage points). As shown in column 6, we find little effect from the information treatments, other than the wage inflation treatment, on respondents’ posterior beliefs for income growth expectations. Overall, the results in Table 1suggest that the information treatments have a greater effect on 15As a robustness check using other techniques, Table 9in Appendix Bconfirms these results using quantile regressions. Figures 8and 9in Appendix Cplot the distribution of priors and posteriors and their relationship with the control group. We observe big differences between the control group and treatments 3, 4, and 5. The change in the slope is smaller but statistically significant for treatment 2. The control group and the placebo have a very similar distribution, with small differences that are irrelevant in terms of the magnitude and the distribution of the responses. 15 inflation expectations than on income growth expectations. The evidence of strong priors for income growth expectations is consistent with the view that consumers are very attentive to their income trajectories, which, as in Weber et al. (2023), makes their forecasts less responsive to information treatments about aggregate variables. In the case of inflation expectations, however, the findings suggest that respondents are subject to some type of information frictions as all treatments contain public information. In fact, even though inflation was high at the time of the experiment and salient because of elevated news coverage and the notable impact of inflation on consumers’ budgets, the results suggest that consumers were not fully informed about price developments. While a detailed investigation into information frictions is beyond the scope of this paper, the observed treatment effects offer some insights into how these frictions manifest in consumers’ inflation expectations. From our treatment about the Fed’s inflation target, we see uncertainty about the Fed’s objectives, a point studied in Coibion et al. (2020a). From the SPF treatment, we see that there is uncertainty about the inflation outlook. Moreover, the fact that consumers continue to put some weight on their priors, even after the receipt of this information, suggests that they face sluggish or costly inflation expectations formation, as in Coibion and Gorodnichenko (2015). Finally, while past inflation can affect expectations in many ways, the fact that it affects expectations over 12 months indicates over-extrapolation, as in Angeletos, Huo, and Sastry (2021). 16 Table 1: Effects of Treatments on Expectations (1) (2) (3) (4) (5) (6) EihπPosterior piEihπPosterior piEihπPosterior piEihπPosterior yiEihπPosterior yiEihπPosterior yi EihπPrior pi0.262*** 0.506*** 0.490*** (0.026) (0.006) (0.020) EihπPrior yi0.775*** 0.775*** 0.960*** (0.048) (0.056) (0.010) T2: Target 0.126 -0.382 -0.292 -0.081 (0.138) (0.395) (0.296) (0.104) T3: Wages 0.771*** -0.540 -0.445* 0.146 (0.153) (0.385) (0.256) (0.108) T4: CPI 0.586*** -0.547 -0.271 -0.048 (0.150) (0.395) (0.277) (0.112) T5: SPF 0.720*** -0.429 -0.147 -0.049 (0.149) (0.409) (0.338) (0.106) T6: Placebo 0.498*** 0.482 -0.439 -0.182* (0.148) (0.403) (0.274) (0.106) T2 x Prior -0.023*** -0.053* -0.116 -0.003 (0.008) (0.028) (0.081) (0.015) T3 x Prior -0.213*** -0.036 -0.037 -0.029* (0.013) (0.028) (0.087) (0.017) T4 x Prior -0.258*** -0.065** -0.171* 0.013 (0.011) (0.027) (0.092) (0.013) T5 x Prior -0.281*** -0.084*** -0.061 0.005 (0.011) (0.030) (0.085) (0.016) T6 x Prior -0.008 -0.026 -0.103 0.006 (0.008) (0.026) (0.085) (0.015) Constant 5.667*** 1.343*** 4.223*** 0.925*** 0.925*** 0.274*** (0.337) (0.098) (0.291) (0.185) (0.217) (0.075) Regression OLS Huber Trimmed OLS Huber Trimmed Observations 1,072 5,892 6,373 1,074 6,622 6,335 R-squared 0.236 0.786 0.432 0.604 0.555 0.922 Notes: The table shows estimates of equations 1and 2that relate priors and posteriors, as well as estimates of equations 3 and 4that gauge the effect of treatments and their interaction with prior beliefs. In the third and final step, our analysis uses information from the effective treatments in Table 1to derive an instrument that can be used to infer the causal effect of inflation expectations on income growth expectations. Specifically, we construct the instrument for expected inflation, \ EihπPosterior pi, using the following specification: 17 \ EihπPosterior pi=     ∑j=2,4,5 γj p×Tj i+∑j=2,4,5 θj p×Tj i×EihπPrior pii f Ti=2,4,5 0i f Ti=1,6 (5) where we exclude the treatment providing information on wage inflation (T3) because the reported results indicate it directly affects income growth expectations. Based on the estimation results from the Huber regression and the trimmed regression, we then apply the relevant coefficients in column 2 and column 3 to form an instrument for each regression model. This approach is similar in spirit to the one in Coibion et al. (2019) that uses the prior as an instrument. In this case, it only uses the variation for the treated group. Any concern about the effect of the prior, such as priming because of the question, on the pass-through is shared by both treated and control groups. Because multiple treatments are available to us, we weigh them according to their importance in affecting the posterior.16 This identification strategy is validated by a combination of factors related to our survey design and the estimated effects of information treatments on expectations. First, the assignment of information treatments to the respondents in the survey is random. Second, we only use targeted, carefully worded treatments containing information about inflation to form the instrument for inflation expectations. Third, and in line with the findings of other RCT work on inflation expectations, we find that providing people with publicly available information treatments—even at a time when inflation was particularly salient—tends to move their beliefs, thus invalidating full-information rational expectations. Fourth, the results in Table 1demonstrate that the inflation treatments in the first stage only change the posterior beliefs of inflation expectations but do not have an effect on income growth expectations, which serves as a test of exclusion restrictions in the instrumentation. Moreover, our finding that inflation-related information treatments only affect inflation expectations is consistent with the theoretical findings in Angeletos and Lian (2023) that information frictions attenuate general equilibrium inference. In terms of income growth expectations, we consider both OLS and instrumental-variable (IV) regressions of the posterior belief of income growth expectations on the prior belief of income growth expectations and the posterior belief of inflation expectations, where the instrument is defined by equation (5). As previously discussed, the instrument captures the exogenously induced 16Coibion, Gorodnichenko, and Ropele (2020b) use the past inflation treatment as an instrument. Unfortunately, we do not have the time series dimension that they have to generate enough predictive power for the instrument. 18 variation in expected inflation generated from the assigned information treatment(s).17 Because only three of the treatments are used in constructing the instrument, the sample size for the regressions is smaller compared to those in Table 1. Table 2: Effect of Inflation Expectations on Income Growth Expectations (1) (2) (3) EihπPosterior yiEihπPosterior yiEihπPosterior yi EihπPosterior pi0.085*** 0.203*** 0.168*** (0.014) (0.069) (0.045) EihπPrior yi0.674*** 0.636*** 0.624*** (0.025) (0.033) (0.033) Constant 0.109 -0.805 -0.563* (0.101) (0.521) (0.332) Regression OLS IV IV Sample All Huber Trimmed F-test 120.584 572.491 Observations 5,525 5,525 5,322 R-squared 0.558 0.539 0.538 Notes: This table shows results from OLS and IV regressions of the posterior of income growth expectations on the prior of income growth expectations and the posterior of inflation expectations. Columns (2) and (3) use IV, instrumenting with \ EiπPosterior p. Column (2) uses the instrument constructed from the regression in (1) with Huber weights, whereas column (3) uses the instrument constructed from the trimmed regression in (1). The estimates of γj pand θj p, where j={2,4,5}, for both Huber and trimmed regressions are reported in Table 1. Robust standard errors are in parentheses. Table 2reports the results and highlights a key empirical finding of our paper. Specifically, we document a moderate positive causal relationship from inflation expectations to income growth expectations that reflects only partial pass-through. As shown in column 1, the OLS regression indicates that inflation expectations exhibit a very low correlation with income growth expectations. However, as shown in column 2, the Huber IV regression yields a notably higher coefficient. In particular, the estimate implies that a 1 percentage point increase in inflation expectations increases expected income growth by 0.2 percentage point.18 The trimmed IV regression in column 3 shows a slightly lower pass-through estimate of 0.17, but it is within one standard deviation of 17As a robustness check, we have also constructed instruments by demographic groups, such as by gender, allowing for coefficient heterogeneity in the γi pand θi p. We find that subsequent results are not affected. 18This pass-through differs markedly from a correlation of 0.37 in the raw data, as shown in Table 8in Appendix B. This difference highlights the importance of estimating a causal relationship as we do based on our RCT. 19 the estimate in column 2. Moreover, the instrument displays a relatively high F-test statistic. Looking more closely at the Huber IV regression, which is our preferred specification, the results suggest that pass-through is considerably lower than one-to-one.19 Viewed differently, the same 1 percentage point increase in inflation expectations implies a 0.8 percentage point reduction in expected real income growth. A key takeaway from this finding is that it suggests consumers associate increases in expected inflation with a marked decline in expected real income growth and offers one reason for an aversion to inflation. Our subsequent analysis will explore how the effect of expected inflation on real income may influence the labor market actions of consumers and further shape their attitudes toward inflation. Finally, we show that distinct demographic characteristics are associated with different degrees of pass-through from inflation expectations to income growth expectations. To do so, we separate our sample based on the gender of survey respondents and their self-reported annual income (less than $50,000, between $50,000 and $100,000, and more than $100,000). We report OLS and IV regression results in Table 3. 19In Table 17 in Appendix D, we calculate the pass-through for each of the treatments individually, rather than combining them as in Table 2. Each of the inflation treatments produces very similar estimates, pointing to incomplete pass-through in each treatment, with the magnitudes similar to the main result of 0.2. 20 for higher degrees of nominal wage rigidity. Second, the mechanism we propose to capture the relationship between inflation expectations and labor market actions has a negligible effect on the macroeconomic dynamics of the model; on average, consumers’ efforts to increase their wages due to higher inflation expectations do not improve their utility, real wage, or consumption. Overall, we view the lessons coming from this modeling exercise as helping us further understand why consumers dislike current and future inflation. 6.1 A Search-and-Matching Model We employ a New Keynesian model featuring a Mortensen and Pissarides (1994) type of searchand-matching frictions in labor markets. We further incorporate a right-to-manage feature as developed in Trigari (2006), where firms and workers bargain over nominal wages and then workers guarantee to supply the labor hours demanded by firms at the bargained wage.23 A matched firm-worker pair negotiates wages infrequently in a Calvo fashion. Finally, as in Christoffel and Kuester (2008), we account for firms’ fixed costs of maintaining a job.24 The economy in the model is composed of representative families that make optimal decisions on behalf of their members with respect to consumption and one-period riskless bond holdings. There are three types of firms: labor goods firms produce a homogeneous labor intermediate good; wholesalers use the labor good as an intermediate to produce differentiated goods and face Calvo price rigidity; and retailers bundle the differentiated goods into a homogeneous consumption basket sold to households and the government. Monetary policy sets the nominal interest rate following a Taylor rule, and government spending is exogenous. Because these parts of the model are standard in the literature and are not central to our paper, we describe them in more detail in Appendix F. We now lay out some key features of the labor market because they directly connect the model with our empirical findings presented in Section 5. The matching process between workers and 23For our purposes, the right-to-manage (RTM) framework differs from, for instance, “efficient bargaining" (EB), where labor supply always equals labor demand. The advantage of the RTM over EB is that it generates more realistic movements in inflation dynamics, which facilitates matching the model-implied pass-through with the empirical estimates. On the other hand, RTM can trigger fluctuations in labor hours that are larger than what is observed in the data. The increased variability in labor hours is a particularly important limitation that we return to below, especially because our empirical results suggest that consumers do not expect to increase their hours when they raise their inflation expectations. See de Walque et al. (2009) for an instructive review of such tensions in this group of models. 24The RTM framework can counterfactually dampen the response of employment in the extensive margin, and, as shown in Christoffel and Kuester (2008), the presence of a fixed cost amplifies the response of unemployment over the business cycle. 27 labor firms is governed by a Cobb-Douglas function: mt=σmuξ tv1−ξ t(7) where mtare matches formed in period t;utis unemployment; vtare vacancies; ξ∈[0,1]is the elasticity of matching with respect to unemployment; and σm>0 is matching efficiency. Matches become productive in the following period, so employment in the extensive margin evolves according to nt= (1−µ)nt−1+mt−1(8) where µ∈[0,1]is the employment separation rate. Labor market tightness is defined as: θt=vt ut (9) Then, the probabilities that a vacancy is filled and that an unemployed worker matches with a firm are, respectively, qt=mt vt ,st=mt ut (10) To match our findings in Table 1that providing an individual a treatment consisting of publicly available information at time thas an effect on our respondents’ inflation expectations, we assume that inflation expectations are subject to sticky information, such that: e Etˆ πt+h= (1−λ)Etˆ πt+h+λe Et−1ˆ πt+h, for any h≥1 (11) where Etis the full-information rational expectations operator, λ∈[0,1]denotes the probability that our agents do not update their information set in period t, and ˆ πtis inflation in log-linear deviation from its steady-state value. To match Fact 1, we assume that agents in the economy face nominal wage rigidities. If a worker is not separated from employment, she can bargain her nominal wage to W∗ t+1in period (t+1)with probability (1−γ)∈[0,1]. In contrast, the nominal wage of the γshare of workers who cannot bargain partially adjusts for past inflation such that Wt+1=Wt(ew tπζw t¯ π1−ζw), where ζw∈[0,1]denotes time-varying wage indexation to past inflation and ew tis a newly introduced wage-push factor explained further in the subsequent paragraph. In our setup, different combinations of the nominal wage stickiness parameter, γ, generate different levels of model-implied 28 pass-through from inflation expectations to nominal wage growth expectations. This model feature allows us to study the macro implications of Fact 2 and of a counterfactual scenario of unit pass-through. Finally, to match Fact 3 one would ideally want to incorporate on-the-job search, which is affected primarily by inflation expectations. However, for simplicity purposes, we abstract from formally modeling that channel in the present paper. Instead, we introduce a wage-push factor, ew t. The wage-push factor affects the nominal wage only if the worker cannot bargain her wage to W∗ t+1and it captures the following idea: in the case of no bargaining, we assume that, due to higher inflation expectations, the worker applies for another job with some probability and is able to generate an outside contract with certainty, which is used to put upward pressure on the nominal wage with her current employer.25 The wage-push factor is assumed to be persistent and to be affected by inflation expectations as follows ˆ ew t=ρwˆ ew t−1+¯ eπEtˆ πt+1(12) where ˆ ew tis the wage-push factor in log deviations from its steady-state value; ¯ eπis the elasticity between inflation expectations and the wage-push factor; and ρw∈[0,1)is the persistence in the wage-push factor. For workers who bargain in a given period, the nominal wage is set according to Nash bargaining, W∗ t=argmaxWt(VE t− VU t)ηt(Jt)1−ηt(13) where VE tand VU tdenote, respectively, the value of employment and unemployment for a worker; Jtis the market value of a labor firm matched to a worker; and ηtis the time-varying bargaining power of workers.26 6.2 Calibration Our calibration of the model aims to capture US labor market trends around the time of our survey in early 2022 while also matching our three empirical findings. In terms of steady-state values, we 25The wage-push factor plays a role similar to having within-quarter job-to-job transitions with a time-varying transition probability that is only affected by inflation expectations. Within-period job-to-job transitions with constant probability have been incorporated in Krusell et al. (2017). Another interpretation would be to have a non-bargaining worker’s nominal wage indexed to a base, fixed real wage growth that is greater than 1, along with indexation to past inflation. Time variation in this case would only be induced by inflation expectations. 26Under EB, optimal nominal wages satisfy ηtJt= (1−ηt)(VE t− VU t). In our case of an RTM framework, the optimal nominal wage condition is ηtδW tJt= (1−ηt)δF t(VE t− VU t), where δW tand δF tdenote, respectively, the net marginal benefits from an increase in the wage to the worker and the firm. See Christoffel and Kuester (2008) for more details. 29 set the unemployment and vacancy rates to their respective quarterly realizations in 2021:IV of 4.2 percent and 7 percent. The separation rate in the steady state is set to 4.1 percent, matching the quarterly separation rate in 2021:IV. Table 5summarizes these choices. Due to high labor market tightness these choices imply that in the steady state the probability of finding a job is very high (s = 93.52 percent), whereas the likelihood that a firm finds a worker is very low (q = 0.27 percent). Table 5: Parameters Variable Value Description u4.2 percent Unemployment rate; US quarterly unemployment rate in 2021:IV v7 percent Vacancy rate; US quarterly vacancy rate in 2021:IV µ4.1 percent Quarterly separation rate; US data in 2021:IV s0.9352 Probability of finding a job (implied by the steady-state model equilibrium) q0.0027 Probability of finding a worker (implied by the steady-state model equilibrium) ξ0.6 Elasticity of matches w.r.t. unemployment; see Petrongolo and Pissarides (2001) η0.5 Bargaining power of workers; conventional value σm0.0037 Efficiency of matching; reconciles mwith u=4.2 percent and v=7 percent ρw0.9 Persistence of the wage-push factor ¯ eπ0.0228 Wage-push elasticity w.r.t. inflation expectations across all respondents; Tables 2,4 ¯ eπ0.114 Wage-push elasticity w.r.t. inflation expectations in counterfactual analysis; Table 4 γ0.875 Nominal wage stickiness; pass-through across all respondents in Table 2 γ0.65 Nominal wage stickiness; unit pass-through for counterfactual analysis ζw0.675 Wage indexation; pass-through across all respondents in Table 2 ζw0.306 Wage indexation; pass-through for counterfactual analysis λ0.285 Information stickiness; Table 6 In terms of labor market parameters, as shown in Table 5, we parameterize the model as follows: the elasticity of matches with respect to unemployment, ζ, is set to 0.6, consistent with Petrongolo and Pissarides (2001). Wage bargaining power is set to its conventional value in the literature, i.e., η=0.5. The implied efficiency of matching, σm, is set to 0.0037 to be consistent with the steady-state values of the unemployment and vacancy rates, and matching. We assume the wage-push factor process is persistent with an autocorrelation coefficient of 0.9. A few more parameters remain to be calibrated in a way that is directly related to our empirical results. First, to calibrate λ, we investigate how our respondents react to new information.27 27As shown by Coibion and Gorodnichenko (2015), in a setting with information stickiness similar to ours, the frequency of updating the information set (1−λ)is all one needs to pin down the response of expectations to new information at the time of forecast. 30 Specifically, we rearrange equation (11) to read as: e Etπt+h−e Et−1πt+h | {z } (posterior - prior) = (1−λ)Etπt+h−e Et−1πt+h | {z } new info in period t with (1−λ)capturing the effect of new information made available in period ton inflation expectations. To discipline λconsistently with our experiment, we use the estimates from the following regression: EihπPosterior pi−EihπPrior pi=α+βTihIij −EihπPrior pii+εi(14) where Tiis an indicator that takes value 1 if individual ireceives treatments 2, 4, or 5 (and possibly 3, depending on the specification), and takes a value of zero if the individual iis in the control or placebo group. hIij −EihπPrior piicaptures new information due to information treatment j.Iij is the numerical information contained in treatments 2, 3, 4, or 5. In this specification, β= (1−λ). Table 6presents the estimates of β. As our benchmark calibration, we use the estimate of β=0.715, or equivalently, λ=0.285, as reported in column (4) of Table 6, where we account for the control, placebo, and wage treated groups.28 Table 6: Effect of New Information on Inflation Expectations (1) (2) (3) (4) New information 0.742*** 0.711*** 0.742*** 0.715*** (0.014) (0.014) (0.012) (0.012) Constant 1.581*** -0.678*** 1.702*** -0.251 (0.163) (0.208) (0.139) (0.181) Wage Treatment No No Yes Yes Control and Placebo No Yes No Yes Observations 3,338 5,528 4,430 6,620 R-squared 0.730 0.432 0.735 0.483 Notes: The table shows estimates of equation (14). Column (1) only contains information for treatments 2, 4 and 5. Column (2) includes the placebo and control groups. Column (3) is (1) plus treatment 3 and column (4) contains all treated and control groups. We use robust standard errors. Second, we calibrate nominal wage stickiness, γ, and wage indexation to past inflation, ζw, to 28Coibion, Gorodnichenko, and Weber (2022) argue that the inclusion of the control group is important since the prior and posterior questions about inflation expectations are worded differently. Our results remain qualitatively similar if we calibrate λto a lower value of about 0.26. 31 match Fact 1 and Fact 2 quantitatively along the IRFs of nominal wage growth to various shocks. Solving the model under rational expectations, one can show under general assumptions (see details in Appendix G) that the response of nominal wage growth expectations to a change in inflation expectations is given by: ∂e Et(ˆ Wt+7−ˆ Wt+3) ∂e Etˆ πt+4 =a1−a2 1−λ+1+a3(15) where the elements a1,a2, and a3are convoluted functions of the many structural parameters of the model.29,30 However, wage indexation to past inflation, and especially nominal wage stickiness, γ, are key parameters in these functions, and it is possible to calibrate them such that we are able to match Fact 1 and Fact 2 quantitatively. In particular, we can match the inflation expectations pass-through to nominal wage growth across our respondents by choosing a wage contract duration of about 8 quarters (γ=0.875) with indexation to past inflation of 0.675.31 To construct a counterfactual scenario of unit pass-through from inflation expectations to nominal wage growth expectations, we set γ=0.65, which implies an average wage contract duration of about 3 quarters. The wage indexation to past inflation in this case is set to ζw=0.306. Note that while many choices of time horizons exist for computing moments, we choose the time horizons in equation (15) to align with those in the survey. Second, to match Fact 3, we set the elasticity of the wage-push factor with respect to inflation expectations so that we match the evidence shown in Tables 2-4. Parameter ¯ eπis the elasticity between inflation and nominal wage growth expectations conditional on having applied for another job due to higher inflation expectations. Hence, we parameterize ¯ eπas follows: ¯ eπ=pass-through | {z } Tables 2,3 ×elasticity of job applications w.r.t. inflation expectations | {z } =0.114, Table 4 (16) 6.3 Impulse Response Functions: Lessons Next, we analyze the dynamics of our model subject to a positive demand shock and a positive (adverse) cost-push shock, the two predominant disturbances that we judge were affecting the US 29While there are many parameter combinations that can match the model-implied pass-through in (15) with the empirical one, we interpret a less than unit pass-through as evidence of significant nominal wage rigidity and thus remain focused on calibrating this parameter together with the wage indexation to past inflation. 30Recall that our posterior question about income growth expectations infers e Et(ˆ Wt+7−ˆ Wt+3). 31Duration of a wage contract is given by 1/(1−γ). 32 economy around our survey period. Two lessons emerge that help us understand the mechanism behind households’ association of higher inflation with worse economic outcomes, consistent with our empirical findings and the work of Shiller (1997) and Candia, Coibion, and Gorodnichenko (2020). Lesson 1: Negative or dampened responses of real wages to shocks due to nominal wage rigidity translate into greater fluctuations and volatility in output and consumption. Regardless of whether the model is subjected to a demandor supply-side inflationary disturbance, an economy calibrated to quantitatively match our empirical pass-through of inflation expectations to income growth expectations has large ramifications for real wage dynamics relative to a counterfactual scenario of a unit pass-through. As we subsequently explain, severe nominal wage rigidity is the driving source for consumers’ dislike of inflation in the model. Figure 2: Response to a Positive Demand Shock Notes: In black: calibration matching our empirical pass-through from inflation to nominal wage growth expectations (γ=0.875,ζw=0.675)according to Equation (15). In dashed gray: calibration matching counterfactual of unit pass-through from inflation to nominal wage growth expectations (γ=0.65,ζw=0.306). In red: x axis. 33 Consider Figure 2, where the economy is subject to a one standard deviation positive demand shock.32 Relative to the counterfactual of unit pass-through, real wages decline, which results in a larger increase in labor hours that amplifies the responses of output and consumption.33 The dynamics of real wage and inflation are such that the nominal wage growth, which is defined as the sum of real wage growth and inflation, increases in both cases. Consumers’ utility is affected by two opposing forces: it declines in response to working more along both the extensive and the intensive margins, but it increases in response to higher consumption.34 The former channel is considerably larger in the case of 20 percent pass-through compared with full pass-through, yielding a larger decline in utility even though inflation has risen by less. 32The standard deviation of the demand shock is set equal to 1. 33On impact, the real wage is given by ˆ wt= (1−γ)ˆ w∗ t−γˆ πt, where ˆ w∗ tis the fully flexible real wage. In contrast to the case of incomplete pass-through, under unit pass-through, real wages are sufficiently flexible to respond positively to a positive demand shock. 34It is worth noting that hours in the model fluctuate in response to both the demand and the supply shocks that drive inflation up, while the survey respondents indicated that they did not expect to change their hours in response to higher inflation, indicating some tension between the theoretical model and the empirical data. We leave the resolution of this conundrum for future work. 34 Figure 3: Response to a Positive Cost-Push Shock Notes: In black: calibration matching our empirical pass-through from inflation to nominal wage growth expectations (γ=0.875,ζw=0.675)according to Equation (15). In dashed gray: calibration matching counterfactual of unit pass-through from inflation to nominal wage growth expectations (γ=0.65,ζw=0.306). In red: x axis. Figure 3considers the case where the economy is shocked by a one standard deviation costpush supply disturbance.35 Relative to the counterfactual of a unit pass-through economy, the decline in real wages is smaller, putting more downward pressure on labor hours. Since wages are more flexible in the counterfactual scenario of a unit pass-through, they decrease more and faster compared to the incomplete pass-through case, resulting in a decline in the nominal wage growth. The large decline in hours worked translates into large declines in output and consumption. Under a supply shock, greater nominal wage frictions cause larger increases in inflation and larger decreases in consumption/output, strengthening consumers’ negative association between the two. As was the case for a positive demand shock, a positive cost-push supply shock initially causes an increase in utility, followed by a decline a few periods later, and then a subsequent increase as consumers receive higher utility from working less and enjoying more leisure.36 35The standard deviation of the cost-push shock is set equal to 1. 36As with the demand shock, we note that the fluctuations along the hours margin run counter to our survey results in which respondents believe they will not adjust their hours worked in response to a change in expected inflation, 35 The comparative analysis pertaining to Figures 2and 3is similar when the model is calibrated to match the pass-through from inflation expectations to income growth expectations associated with highversus low-income respondents. To avoid repetition, we report those IRFs in Appendix I. We next show how the correlation between expected period utility and inflation expectations varies with the degree of nominal wage stickiness and wage indexation to past inflation. A representative family’s period utility in deviation from its steady-state value is given by: Ut=(c(1−ϱ))1−σ(ˆ ct−ϱˆ ct−1)−κhnh1+φ 1+φˆ nt+ (1+φ)ˆ ht(17) where ˆ ctand ˆ htdenote consumption and labor hours, respectively, in deviation from their steadystate values; ϱis the degree of external habit in consumption; φis the inverse of labor supply elasticity; and κhis a scaling factor to labor disutility.37 We simulate 50 periods of expected period utility and inflation expectations data when shocking the model with demand and cost-push innovations, for a given pair jof (γ,ζw), and consider the following regression of simulated data:38 EtUj,t+1=αj+γt+βe Etˆ πt+1+θγj×e Etˆ πt+1+ϕζw,j×e Etˆ πt+1+εj,t(18) where αjis an IRF fixed effect, with an IRF being the series of expected period utility and expected inflation for a given combination of γand ζw; and γt+1is a fixed effect of every period after the shock. 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Trigari, Antonella. 2006. “The Role of Search Frictions and Bargaining for Inflation Dynamics.” Working Paper 304, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University. DOI https://ideas.repec.org/p/igi/igierp/304.html. Weber, Michael, Bernardo Candia, Tiziano Ropele, Rodrigo Lluberas, Serafin Frache, Brent H. Meyer, Saten Kumar, Yuriy Gorodnichenko, Dimitris Georgarakos, Olivier Coibion et al. 2023. “Tell me something I don’t already know: Learning in low and high-inflation settings.” Tech. rep., National Bureau of Economic Research. DOI https://doi.org/10.3386/w31485. Werning, Iván. 2022. “Expectations and the Rate of Inflation.” DOI https://economics.mit.edu/ sites/default/files/publications/expectation-passthrough.pdf. 45 Appendix (For Online Publication) A Survey Details and Questions The experiment was put into the field by Morning Consult during the first week of March 2022. The goal was to sample a total of 6,600 adult respondents. The number of collected responses was 6,629. The survey starts with demographic questions. These are the ones we include in the paper: • What is your five-digit ZIP Code? • What is your gender? –Male –Female • What is your age? –18-34 –35-44 –45-64 –65+ • Which category represents the total combined income of all members of your HOUSEHOLD during the past 12 months? This includes money from jobs, net income from business, farm or rent, pensions, dividends, interest, Social Security payments and any other money income received by members of your family who are 15 years of age or older. –Under 50k –50k-100k –100k+ Then, we have the prior questions for the experiment: • Next we are asking you to think about changes in prices during the next 12 months in relation to your income. Given your expectations about developments in prices of goods and services during the next 12 months, how would your income have to change to make you equally well-off relative to your current situation, such that you can buy the same amount of goods and services as today? (For example, if you consider prices will fall by 2% over the next 12 months, you may still be able to buy the same goods and services if your income also decreases by 2%.) To make me equally well off, my income would have to 46 –Increase by __%; –Stay about the same; and –Decrease by __%. • Do you expect your income to increase, decrease, or stay about the same over the next 12 months? –Increase by __%; –Stay about the same; and –Decrease by __%. At this point, respondents were randomly assigned to receive either a single treatment or to be part of the control group of respondents (with the number of respondents in parentheses): • Control (N=1,075) • The Federal Reserve targets an inflation rate of 2% per year in the long run. (1,155) • A recent survey from the Conference Board found that wages were expected to rise 3.9% in 2022. (1,093) • Between January 2021 and January 2022, the Consumer Price Index (CPI), which measures the average change in prices over time that consumers pay for goods and services, showed the inflation rate in the US was 7.5%. (1,112) • According to the Survey of Professional Forecasters, the Consumer Price Index (CPI), which measures the average change in prices over time that consumers pay for goods and services, showed the inflation rate will be 3.7% by the end of 2022. (1,074) • According to the US Census Bureau, the United States population was 332,402,978 as of December 31, 2021. (1,120) After being assigned to the control group or receiving a treatment, we asked everybody for their posteriors in the following questions: • In the next year, do you think prices in general will increase, decrease, or stay about the same? –Increase by __%; –Stay about the same; and –Decrease by __%. • Between December 2022 and December 2023, do you expect your income to increase, decrease, or stay about the same over the next 12 months? 47 –Increase by __%; –Stay about the same; and –Decrease by __%. After the posteriors, individuals were asked about their likely labor market actions to increase their income over the next three months. • How likely are you to do the following to increase your income over the next three months? –Apply for a job(s) that pays more *Very likely *Somewhat likely *Somewhat unlikely *Very unlikely *Don’t know / No opinion –Work longer hours *Very likely *Somewhat likely *Somewhat unlikely *Very unlikely *Don’t know / No opinion –Ask for a raise *Very likely *Somewhat likely *Somewhat unlikely *Very unlikely *Don’t know / No opinion –Other (in this case, respondents are asked to provide a description of labor market actions) 48 B Additional Tables Table 8: Summary Statistics and Relationship between Price and Wage Inflation Panel A Panel B Inflation Exp Nominal Income Real Income Nominal Income Growth Exp Growth Exp Growth Exp 1st percentile -2 -12 -100 Inflation Exp 0.365*** First quartile 0 0 -7 (0.012) Median 0 0 0 Constant 0.891*** Third quartile 10 2 0 (0.104) 99th percentile 100 100 50 Mean 12.692 5.523 -7.169 Standard deviation 24.536 18.822 22.735 Observations 20,550 20,550 20,550 20,550 Notes: This table shows summary statistics for expectations of inflation and nominal income growth. We also report a measure of expected real income growth derived as the difference between expected nominal income growth and expected inflation at the individual level. The right part of the table shows a regression of expected nominal income growth on expected inflation. Huber-robust standard errors are in parentheses. *** denotes statistical significance at the 1 percent level. 49 Table 9: Robustness First Stage Exercise with Trimmed and Quantile Regressions (1) (2) (3) (4) EihπPosterior piEihπPosterior piEihπPosterior yiEihπPosterior yi EihπPrior pi0.262*** 0.467*** (0.026) (0.016) EihπPrior yi0.775*** 1.000 (0.048) - T2: Target -0.627 0.558 -0.203 - (0.460) (0.248) (0.104) - T3: Wages -0.695 1.333** -0.208 - (0.450) (0.592) (0.230) - T4: CPI -0.825* 0.533 -0.109 - (0.456) (0.587) (0.254) - T5: SPF -0.749 1.556*** -0.100 - (0.465) (0.596) (0.247) - T6: Placebo 0.133 1.333** -0.373 - (0.465) (0.590) (0.248) - T2 x prior -0.002 -0.079*** -0.127* - (0.036) (0.022) (0.072) - T3 x prior -0.003 -0.107*** -0.047 - (0.035) (0.022) (0.071) - T4 x prior -0.015 -0.107*** -0.114 - (0.035) (0.022) (0.074) - T5 x prior -0.025 -0.189*** -0.039 - (0.036) (0.023) (0.071) - T6 x prior 0.047 0.013 -0.078 - (0.035) (0.022) (0.074) - Constant 5.667*** 0.667 0.925*** - (0.337) (0.419) (0.185) - Sample OLS Quantile OLS Quantile Observations 6,620 6,620 6,622 6,622 R-squared 0.261 0.559 Notes: The table shows estimates of equations 3and 4that gauge the effect of treatments and their interaction with prior beliefs. Columns (1) and (3) show results that exclude responses in the tails of the distribution (less than the 5th percentile or greater than the 95th percentile) of changes between priors and posteriors, using robust standard errors. Columns (2) and (4) use quantile regressions at the median. 50 Table 10: Effect of Inflation Expectations on Wage Increase Actions, Trimmed Sample Apply for a job(s) Work longer hours Ask for a raise (1) (2) (3) (4) (5) (6) EihπPosterior pi0.005*** 0.018*** 0.004** 0.008** -0.002 0.004 (0.002) (0.004) (0.002) (0.004) (0.002) (0.004) Constant 2.212*** 2.103*** 2.263*** 2.225*** 2.110*** 2.063*** (0.023) (0.039) (0.022) (0.039) (0.022) (0.041) Regression OLS IV OLS IV OLS IV F Test 423.226 447.834 388.324 dy dx ¯ x ¯ y0.019 0.067 0.014 0.031 -0.008 0.015 Observations 4,471 4,471 4,406 4,406 4,256 4,256 R-squared 0.002 -0.013 0.001 -0.001 0.000 -0.003 Notes: This table shows OLS and IV regressions from equation 6.ℓj iis a value that ranges from 1 to 4, where 1 is “Very unlikely, ” 2 is “Somewhat unlikely,” 3 is “Somewhat likely” and 4 is “Very likely.” For columns (1) and (2) ℓj iis the answer to the question about “apply for a job(s) that pays more,” columns (3) and (4) are the answers to the question about “work longer hours,” and columns (5) and (6) are the answers about “ask for a raise.” We use as an instrument the values generated from column (3) in Table 1Robust standard errors are in parentheses. Table 11: Effect of Inflation Expectations on Apply for a Job(s) by Demographics Apply for a Job(s) That Pays More All Male Female <50k 50k-100k 100k+ (1) (2) (3) (4) (5) (6) EihπPosterior pi0.029*** 0.021*** 0.042*** 0.019** 0.048*** 0.025*** (0.006) (0.007) (0.010) (0.010) (0.011) (0.007) Constant 2.015*** 2.172*** 1.802*** 2.173*** 1.801*** 2.033*** (0.054) (0.060) (0.102) (0.095) (0.096) (0.074) Regression IV IV IV IV IV IV F-Test 143.328 82.591 59.017 59.277 36.924 137.812 dy dx ¯ x ¯ y0.114 0.072 0.184 0.076 0.182 0.094 Observations 4,651 2,371 2,280 1,984 1,662 1,005 Notes: This table shows IV regressions from equation 6.ℓj iis a value that ranges from 1 to 4, where 1 is “Very unlikely, ” 2 is “Somewhat unlikely,” 3 is “Somewhat likely” and 4 is “Very likely.” ℓj iis the answer to the question “apply for a job(s) that pays more.” Column (1) is for the full sample, column (2) only for male respondents, column (3) for female respondents, column (4) for respondents who have an income lower than 50k, column (5) for respondents with income between 50k and 100k, and column (6) for respondents with income higher than 100k. We use as an instrument the values generated from column (3) in Table 1. Robust standard errors are in parentheses. 51 Table 12: Effect of Inflation Expectations on Work Longer Hours by Demographics Work Longer Hours All Male Female <50k 50k-100k 100k+ (1) (2) (3) (4) (5) (6) EihπPosterior pi0.009 0.004 0.018** 0.001 0.024** 0.012 (0.005) (0.007) (0.009) (0.009) (0.011) (0.008) Constant 2.219*** 2.372*** 2.008*** 2.263*** 2.067*** 2.296*** (0.051) (0.060) (0.091) (0.088) (0.093) (0.078) Regression IV IV IV IV IV IV F-Test 149.752 88.642 60.033 61.735 39.939 138.630 dy dx ¯ x ¯ y0.034 0.014 0.080 0.003 0.088 0.043 Observations 4,573 2,339 2,234 1,942 1,630 1,001 Notes: This table shows IV regressions from equation 6.ℓj iis a value that ranges from 1 to 4, where 1 is “Very unlikely, ” 2 is “Somewhat unlikely,” 3 is “Somewhat likely” and 4 is “Very likely.” ℓj iis the answer to the question “work longer hours.” Column (1) is for the full sample, column (2) only for male respondents, column (3) for female respondents, column (4) for respondents who have an income lower than 50k, column (5) for respondents with income between 50k and 100k, and column (6) for respondents with income higher than 100k. We use as an instrument the values generated from column (3) in Table 1. Robust standard errors are in parentheses. 52 ments to instrument for inflation expectations. By contrast, columns (5) to (8) show that the information treatments do not seem to affect consumers’ posterior income growth expectations, conditional on the prior, meaning that the treated and control groups are effectively the same, and preventing us from doing the same to instrument for income growth expectations. As a result, we run \ EihπPosterior pi=     ∑j=2,4,5 γj p×Tj it +∑j=2,4,5 θj p×Tj it ×EihπPrior pii f Tit =Target,CPI,SPF 0i f Tit =Control,Placebo where we use the numerical information provided within each treatment Tj it that varies over time as above. Table 15 shows the results for the average and by demographics Table 15: Pass-through from Inflation Expectations to Income Growth Expectations, by Demographics Follow-up EihπPosterior yi All Male Female <50k 50k-100k >100k EihπPosterior pi0.174*** 0.243*** 0.135** 0.148*** 0.210** 0.253** (0.043) (0.068) (0.056) (0.056) (0.087) (0.107) EihπPrior yi0.594*** 0.597*** 0.582*** 0.597*** 0.567*** 0.603*** (0.019) (0.030) (0.026) (0.025) (0.037) (0.062) Time FE Yes Yes Yes Yes Yes Yes F-test 314.429 123.973 185.655 185.638 76.927 61.875 Observations 12,882 6,039 6,843 6,029 4,452 2,401 R-squared 0.486 0.541 0.441 0.477 0.459 0.559 Notes: This table shows results from IV regressions from different demographics. The regression used is the same as in column (2) in Table 2. Regressions have robust standard errors. We see a pattern similar to the one in the baseline exercise. The estimated pass-through is a little bit smaller, but still close to 20 percent. We find the same pattern for the results by demographics as before. Finally, we run the regressions on the labor market actions using the same strategies, meaning that we use the same controls and time fixed effects. The results are presented in Table 16. 59 Table 16: Effect of Inflation Expectations on Wage Increase Actions, Follow-up Apply for a job(s) Work longer hours Ask for a raise that pays more (1) (2) (3) (4) (5) (6) EEihπPosterior pi0.006*** 0.036*** 0.005*** 0.015*** -0.002 0.002 (0.001) (0.004) (0.001) (0.004) (0.001) (0.004) Time FE Yes Yes Yes Yes Yes Yes Regression OLS IV OLS IV OLS IV F-Test 372.1 377.8 359.9 dy dx ¯ x ¯ y0.020 0.121 0.016 0.049 -0.007 0.007 Observations 4,651 4,651 4,573 4,573 4,409 4,409 Notes: This table shows OLS and IV regressions from equation 6.ℓj iis a value that ranges from 1 to 4, where 1 is “Very unlikely,” 2 is “Somewhat unlikely,” 3 is “Somewhat likely” and 4 is “Very likely.” For columns (1) and (2) ℓj iis the answer to the question about “apply for a job that pays more,” columns (3) and (4) are the answers to the question about “work longer hours,” and columns (5) and (6) are the answers about “ask for a raise.” Regressions have robust standard errors. We find very similar results in terms of point estimates and elasticities. Overall, the follow-up exercise confirms the robustness of the baseline results, suggesting that they are not driven solely by a particular time period in early 2022. In addition, it is worth noting that this exercise from September 2022 shows that our baseline results are robust to varying the precise time frame used in the priors and posteriors. In particular, in this exercise we used a time frame for the posterior income growth expectations question that had greater temporal overlap with the prior than was the case in our baseline exercise conducted in March 2022. Given that our results are essentially unchanged, we are comfortable that different timing assumptions were not driving the results documented in the body of the paper.39 In addition to this exercise, we use the variation on the same information treatment to learn about the effect of each treatment on the pass-through result. In order to do so, we use the “control” groups (placebo and control) and only one treatment group individually at a time. Table 17 describes the results for each treatment group. 39As a reminder, in the baseline survey results from March 2022, the inflation prior asked about income needed to offset price changes “over the next 12 months,” while the inflation posterior asked about the growth in prices “in the next year.” Meanwhile, the income growth prior asked about expected income changes “over the next 12 months” while the income growth posterior asked about expected income growth “between December 2022 and December 2023.” In the survey results from September 2022, the wording of the prior and posterior questions was unchanged, meaning that there was now more overlap in the time frames for the income prior and posterior questions, whereas there had been little overlap in the March wave. The fact that our results are essentially the same implies that the lack of overlap in the baseline results was not important for our findings. 60 Table 17: IV Results for Each Individual Treatment EihπPosterior yi (1) (2) (3) (4) EihπPosterior pi0.174*** 0.151* 0.148* 0.207** (0.043) (0.078) (0.079) (0.090) EihπPrior yi0.594*** 0.598*** 0.602*** 0.606*** (0.019) (0.028) (0.028) (0.030) Time FE Yes Yes Yes Yes Treatment All Target CPI SPF F-Test 314.429 86.127 96.273 82.905 Observations 12,882 7,792 7,735 7,673 R-squared 0.486 0.494 0.478 0.491 Notes: This table shows results from IV regressions one treatment at a time. The regression used is the same as in column (2) in Table 2. Regressions have robust standard errors. Table 17 shows that the effect changes slightly depending on the treatment. The estimated pass-through is slightly stronger when consumers are treated with information about future inflation, and slightly lower for the other treatments, but they are all comparable. The table shows that our main findings are highly robust: pass-through is on the order of roughly 20 percent. Because each inflation treatment is generating a similar pass-through estimate, we do not believe that the imbalance of having three inflation treatments and one wage treatment is a primary driver of our main result. E Robustness of Experiment to Prior on Inflation Expectations Here, we show that our novel indirect measure of inflation expectations, used to capture respondents’ prior inflation expectations in the experiment, does not bias the effect of inflation expectations on income growth expectations or labor market actions. In Hajdini et al. (2022a), we describe our novel measure of inflation expectations in detail. In particular, we show that it has properties similar to other measures of inflation expectations such as those of the Federal Reserve Bank of New York’s Survey of Consumer Expectations (SCE) or the Surveys of Consumers by the University of Michigan. We use the ICIE as the main variable on this paper because its good properties and because it allows us to obtain a larger amount of observations for the experiment, as it is part of the main product of the survey. Regardless of such evidence, we chose to perform a complementary RCT experiment in June 2023 to explore whether relying on our novel indirect 61 measure of inflation expectations biases the effect of inflation expectations on income growth expectations or labor market actions. We find that the choice of the prior question does not yield any significant differences in our main results. Specifically, a sample of around 4,400 respondents entered our RCT experiment in June 2023. Respondents were randomly assigned to two groups: one group was asked our novel ICIE question and the other group was asked the conventional inflation expectations question from the Federal Reserve Bank of New York’s Survey of Consumer Expectations. In particular, the latter question asks consumers the following: “In the next year, do you think that there will be inflation or deflation? (Note: deflation is the opposite of inflation).” Respondents were then provided with the following options: “1. Inflation (%); 2. Deflation (%); 3. Neither inflation nor deflation.” Then, all respondents were asked the same question about income growth expectations, as in the regular exercise in the main text: “Do you expect your income to increase, decrease, or stay about the same over the next 12 months?” Subsequently, half of each group (randomly assigned) received a treatment related to inflation: “According to the Survey of Professional Forecasters, the Consumer Price Index (CPI), which measures the average change in prices over time that consumers pay for goods and services, showed the inflation rate will be 3.4% by the end of 2023.” The rest of the respondents received no treatment. Finally, all respondents were asked about their posterior inflation expectations and income growth expectations, respectively, relying on the following two questions: “In the next year, do you think prices in general will increase, decrease, or stay about the same?” “Between December 2023 and December 2024, do you expect your income to increase, decrease, or stay about the same?” Last, we ask respondents the labor market action questions in the same way as in the main RCT experiment. The ultimate goal of this exercise is to understand whether the estimated pass-through from inflation expectations to income growth expectations depends on the question used to elicit prior inflation expectations. Our strategy is to first evaluate the effect of the prior and treatment on posterior inflation expectations, running regressions similar to (1) and (3). We do so for the two distinct priors separately as well as jointly, with results shown in Table 18. 62 Table 18: Effects of Treatments on Expectations: Different Priors (1) (2) (3) EihπPosterior piEihπPosterior piEihπPosterior pi EihπPrior pi0.491*** 0.218*** 0.399*** (0.003) (0.006) (0.063) T1: SPF 0.580*** 0.130 0.239*** (0.064) (0.095) (0.005) T1 x Prior -0.446*** -0.057*** -0.192*** (0.005) (0.010) (0.005) Constant 0.164*** 0.830*** 0.645*** (0.035) (0.066) (0.041) Sample ICIE NYFED Pooled Observations 1,813 1,974 3,846 R-squared 0.880 0.576 0.525 Notes: The table shows estimates of equation (1) that relate priors and posteriors, as well as estimates of equation (3) that gauge the effect of treatments and their interaction with prior beliefs. In column (1), EihπPrior pi refers to prior inflation expectations elicited using the ICIE question, whereas in column (2), EihπPrior pidenotes prior inflation expectations inferred from the NY Fed question. In column (3), both priors are pooled so EihπPrior pidenotes prior inflation expectations inferred from both the ICIE and the NY Fed question. We then take advantage of the exogenous variation in inflation expectations induced by our information treatment to construct our instrument for inflation expectations, similar to the main RCT experiment. We construct the instrumental variable in two ways: i) using the pooled first-stage regression, thereby assuming the same coefficient for both priors, and ii) allowing for prior-specific coefficients. Specifically, Ei \ hπPosterior pi=     γpTi+θpTi×EihπPrior pi if treated group 0 if control group where Ti=1 if individual iis treated with the inflation information and 0 otherwise; for the first variant of constructing the instrumental variable we rely on estimates of γpand θpreported in column (3) in Table 18, whereas for the second variant we use estimates of γpand θpreported in column 1 for the respondents who are asked the ICIE question and estimates shown in column (2) for those who are asked the Federal Reserve Bank of New York’s SCE question. 63 We then estimate, analogously to our previous instrumented regression setup, the following regression EihπPosterior yi=α0+α1×NYFed +β0EihπPosterior pi+β1EihπPosterior pi]×NYFed+ψEihπPrior yi+εi (E.1) where NYFed is a dummy variable taking value 1 if prior inflation expectations are elicited using the Federal Reserve Bank of New York’s SCE question and 0 otherwise. We note that, differently from the analysis in the main text, our regression above includes the dummy variable NYFed as well as its interaction with the prior in order to test whether the effects of the choice of prior are significantly different or not. We instrument EihπPosterior piusing Ei \ hπPosterior pi. Similarly, we run the following regression of the reported likelihood of undertaking labor market action ℓj ion expected inflation, to assess the extent to which inflation expectations drive labor market decisions: ℓj i=α0+α1×NYFed +β0EihπPosterior pi+β1EihπPosterior pi×NYFed+εi(E.2) where ℓj iis a value that ranges from 1 to 4, where 1 is “Very unlikely, ” 2 is “Somewhat unlikely,” 3 is “Somewhat likely” and 4 is “Very likely” for three labor market actions: i) apply for a job(s) that pays more, ii) work longer hours, and iii) ask for a raise. As in (E.1), we control for the dummy variable NYFed and its interaction with the prior to test whether the choice of prior has significantly different effects on the estimated pass-through from inflation expectations to labor market actions. Table 19 shows the pass-through results and Table 20 shows the findings in terms of labor market actions. 64 Table 19: Pass-through Estimates for Different Inflation Expectations Priors (1) (2) (3) (3) EihπPosterior yiEihπPosterior yiEihπPosterior yiEihπPosterior yi EihπPosterior pi0.178*** 0.106 0.178*** 0.104 (0.039) (0.131) (0.039) (0.131) EihπPosterior pi×NYFed(= 1)-0.060 -0.120 -0.060 -0.119 (0.048) (0.141) (0.048) (0.141) EihπPrior yi0.531*** 0.558*** 0.531*** 0.558*** (0.029) (0.034) (0.029) (0.034) NYFed(= 1)-0.311 0.098 -0.311 0.092 (0.233) (0.684) (0.233) (0.681) Constant 0.488*** 0.753 0.488*** 0.761 (0.157) (0.574) (0.157) (0.571) Sample Separated Separated Pooled Pooled Regression OLS IV OLS IV F-Test 17.489 17.803 Observations 4,405 4,405 4,405 4,405 R-squared 0.423 0.409 0.423 0.409 Notes: This table shows results from OLS and IV regressions in (E.1). Columns (1) and (2) are the results of regressing the posterior of income growth expectations on the prior of income growth expectations and the posterior of inflation expectations using the IV constructed separately for both priors. In column (2) we use IV, instrumenting with Ei \ πPosterior p. Columns (3) and (4) are the results of regressing the posterior of inflation expectations on the prior of inflation expectations and the posterior of income growth expectations using the pooled estimation for the IV. In column (4) we use IV, instrumenting with Ei \ πPosterior p.NYFed(= 1)is a variable that takes a value of 1 if the prior is the NY Fed question. Robust standard errors are in parentheses. 65 Table 20: Effect of Inflation Expectations on Labor Market Actions Apply for a job(s) Work longer hours Ask for a raise (1) (2) (3) (4) (5) (6) EihπPosterior pi0.049*** 0.049*** 0.005 0.005 -0.008 -0.008 (0.015) (0.015) (0.014) (0.014) (0.014) (0.014) EihπPosterior pix NYFed(= 1)-0.025 -0.025 0.012 0.012 0.003 0.003 (0.018) (0.018) (0.016) (0.016) (0.016) (0.016) NYFed(= 1)0.049 0.049 -0.146 -0.146 -0.052 -0.053 (0.098) (0.098) (0.093) (0.093) (0.089) (0.089) Constant 1.688*** 1.689*** 1.949*** 1.949*** 1.770*** 1.770*** (0.076) (0.076) (0.072) (0.071) (0.072) (0.071) Sample Separated Pooled Separated Pooled Separated Pooled F-test 21.521 21.274 21.521 21.274 21.521 21.274 Observations 4,405 4,405 4,405 4,405 4,405 4,405 Notes: This table shows IV regressions from equation (E.2). Columns (1) and (2) report the estimated pass-through from inflation expectations to labor market action “apply for a job(s) that pays more,” columns (3) and (4) report the estimated pass-through from inflation expectations to labor market action “work longer hours,” and columns (5) and (6) provide the estimated pass-through from inflation expectations to labor market action “ask for a raise.” NYFed(= 1)is a variable that takes a value of 1 if the prior is the NY Fed question. Sample separated means that the instrument is built separately for each prior and pooled means that it is built jointly for both priors, as explained in the text. Robust standard errors are in parentheses. The following results arise. First, the choice of wording for the inflation expectations question that forms the prior—ICIE or based on the SCE—makes no statistically significant difference in our pass-through regressions. The coefficients on the NY Fed SCE dummy and the interacted prior with the NY Fed SCE dummy are all statistically insignificant. Second, the levels of the pass-through estimates are somewhat lower than in our main exercise. This result indicates that consumers may not be strongly affected by the wording of the question, because in this period, independently of the prior, they expect a low pass-through. Third, we also find similar results in terms of labor market actions, which confirms the results of the main exercise in the paper and reinforces the main result of the robustness exercise—for a different outcome variable—that results are independent of the choice of prior. F Model The model has been largely adapted from Christoffel and Kuester (2008) and Christoffel, Kuester, and Lizert (2009). 66 Households. There are a large number of identical families with unit measure. Each family consists of a measure ntof employed members and ut=1−ntof unemployed members. Each family member has the following utility function: e E0 ∞ ∑ t=0 βt (cit −ϱct−1)1−σ 1−σ−κh h1+φ it 1+φ!(F.1) where cit denotes the consumption of consumer i;ct−1is the family’s aggregate real consumption in period (t−1);hit is the working hours of employed consumer i;κh>0 is a parameter of work disutility; and ϱ∈[0,1)captures the degree of external habit in consumption. Each family faces the following constraint: ct+τt+κtvt=Z1−ut 0withitdi +utb+ed tdt−1 Rt−1 πt −dt+Ψt+ntΦK(F.2) where e Eis a generic expectations operator; τtis lump-sum taxes per capita in real terms; κtdenotes real cost per vacancy posting vt;wit is the real wage of employed consumer i;dtdenotes the risk-free one-period real bond holdings with return ed tRtand ed tbeing a shock to the risk premium; and bis real unemployment benefits. Variable Ψtdenotes the real dividends of the family from firms in the economy, such that Ψt=ΨC t+R1−ut 0Ψh itdi, where ΨC tand Ψh it are dividends arising from the differentiated goods and labor goods firms, respectively, to be described in what follows. The model does not account for capital income, so we assume that the family receives a fixed share ntΦK,ΦK≥0, out of current revenue of labor firms as “capital income.” The family makes optimal decisions on behalf of its members by maximizing the aggregate utility function in (F.1) with respect to consumption and real bond holdings, subject to the budget constraint in (F.2). Firms. There are three types of firms: i) firms that produce a homogeneous intermediate good, “labor good”; ii) wholesale firms that purchase labor goods in a perfectly competitive market, and use them as inputs to produce differentiated goods; and iii) retail firms that purchase differentiated goods from the wholesalers and bundle those goods into a homogeneous consumption basket sold to consumers and the government. Retailers’ demand for differentiated good jis given by: yjt =Pjt Pt−ε yt(F.3) where Pjt is the jth good price; ε>1 is the own-price elasticity of demand; Ptis the aggregate price 67 level; and ytdenotes the final good/economy’s aggregate output. The wholesale sector has a unit mass with firms indexed by j∈[0,1]. Each firm produces variety jaccording to yjt =ld jt, where ld jt denotes firm j’s demand for the intermediate labor good, which it can acquire in a perfectly competitive market at real price xh t. Wholesalers face Calvotype price stickiness such that in every period, a fraction ω∈(0,1)of them cannot reset the price. Similar to Christiano, Eichenbaum, and Evans (2005), we assume that the firms that cannot reoptimize can adjust prices by the index factor πζp t−1¯ π1−ζp, where ζp∈[0,1]denotes the degree of inflation indexation. The problem of wholesalers is then expressed as follows: max Pjt e Et ∞ ∑ h=0 ωhΓt,t+h Pjtπζp t−1,t−1+h(¯ π1−ζp)h Pt+h −mct+h yj,t+h (F.4) where Γt,t+h=βhλt+h λt, with λtbeing households’ marginal utility of consumption; πt−1,t−1+h= Pt−1+h/Pt−1; and mct=xh teC tis the marginal cost, with eC tbeing a cost-push shock. Total profits of the wholesale sector in period tare given by ΨC t=Z1 j=0Pjt Pt −mctyjtdj (F.5) Finally, the labor good firms are homogeneous and they need exactly one worker to operate. So, there is a mass of nt= (1−ut)of such firms at any given time. Match ican produce lit labor good units via lit =zthα it, where ztis a productivity shock and α∈(0,1). Labor markets. The matching process between workers and labor firms is governed by a Cobb-Douglas function, mt=σmuξ tv1−ξ t(F.6) where mtis matches formed in period t;utis unemployment; vtis vacancies; ξ∈[0,1]is the elasticity of matching with respect to unemployment; and σm>0 is a scaling factor. Labor market tightness is defined as: θt=vt ut (F.7) Then, the probabilities that a vacancy is filled and that an unemployed worker matches with a firm are, respectively, qt=mt vt ,st=mt ut (F.8) 68 Figure 12: Response to a Positive Demand Shock Notes: In dotted red: calibration matching our empirical pass-through from inflation to nominal wage growth expectations for high-income consumers (γ=0.8515,ζw=0.35). In dashed blue: calibration matching our empirical pass-through from inflation to nominal wage growth expectations for low-income consumers (γ=0.895,ζw=0.6). In black: x axis. 75 Figure 13: Response to a Positive Cost-Push Shock Notes: In dotted red: calibration matching our empirical pass-through from inflation to nominal wage growth expectations for high-income consumers (γ=0.8515,ζw=0.35). In dashed blue: calibration matching our empirical pass-through from inflation to nominal wage growth expectations for low-income consumers (γ=0.895,ζw=0.6). In black: x axis. 76