Christopher Roth
email: roth@wiso.uni-koeln.de

Mirko Wiederholt
email: mirko.wiederholt@gmail.com

Johannes Wohlfart
email: johannes.wohlfart@econ.ku.dk.

Laura Gati

Yuriy Gorodnichenko

Peter Maxted

Kris Nimark

Gianluca Violante

The Effects of Monetary Policy: Theory with Measured Expectations *

Keywords: JEL Classification: D12, D14, D83, D84, E32, G11 Monetary Policy, Expectation Formation, Aggregate Consumption

We study the effects of monetary policy on aggregate consumption with a general equilibrium model but without making assumptions about expectation formation. The key idea is to express consumption of non-hand-to-mouth households as a function of expectations only and to elicit all expectations appearing in the consumption functions for alternative policy scenarios with a tailored survey. We illustrate this approach by computing aggregate consumption for alternative policies before the March 2021 and March 2022 FOMC meetings. We find that a modest forward guidance statement in the March 2021 FOMC meeting would have reduced aggregate consumption by 0.17% on impact and an interest rate hike of 50 basis points in the March 2022 FOMC meeting would have reduced aggregate consumption by 0.15% on impact.

Introduction

Understanding the effects of monetary policy is essential for the successful conduct of monetary policy. According to different macroeconomic theories, expectations play a central role in shaping the effects of both conventional and unconventional monetary policy on aggregate consumption.

Expectations are important for the effects of unconventional monetary policies such as forward guidance, since these policies operate by changing private-sector expectations [START_REF] Eggertsson | The Zero Bound on Interest Rates and Optimal Monetary Policy. Comments and Discussion[END_REF]. Current state of the art models make particular theoretical assumptions about the expectation formation process of households to study the effects of forward guidance on consumption. For example, papers have proposed anticipated future credit constraints [START_REF] Mckay | The Power of Forward Guidance Revisited[END_REF], a lack of common knowledge [START_REF] Angeletos | Forward Guidance Without Common Knowledge[END_REF], level-k thinking [START_REF] Farhi | Monetary Policy, Bounded Rationality, and Incomplete Markets[END_REF], finite reflection (García-Schmidt and Woodford, 2019), myopia [START_REF] Gabaix | A Behavioral New-Keynesian Model[END_REF], or inattention [START_REF] Wiederholt | Empirical Properties of Inflation Expectations and the Zero Lower Bound[END_REF] as reasons for more muted effects of forward guidance than suggested by standard models. Modelling expectation formation in response to forward guidance is challenging, especially in a setting with heterogeneous agents with limited cognitive abilities, which may in addition disagree about the response of the economy to policy shocks (Andre et al., 2022a).

Expectations are also important for the effects of conventional monetary policy. In a heterogeneous agent New Keynesian model with the current nominal interest rate as the primary monetary policy instrument [START_REF] Kaplan | Monetary policy according to HANK[END_REF], consumption of a non-handto-mouth household depends on the expected paths of interest rates, inflation, and own after-tax income. The most common set of assumptions about expectation formation in this literature is: agents have full information about the policy and rational expectations about the effects of the policy.

In this paper, we propose an approach to identify the effects of monetary policy that feeds in experimental estimates of the expectation adjustments in response to policy announcements into a model, and thus remains agnostic about the way expectations are formed. 1 To capture respondents' subjective beliefs about the effects of monetary policy in a clean way, we employ hypothetical vignettes with different policy scenarios for current or future interest rates.

The main idea of this paper can be illustrated with a simple example. Many macroeconomic models imply equations of the form:

Y = γE [X (Z)] , (1)
where Y is an outcome variable (e.g. consumption), X is an endogenous variable (e.g. permanent income), and Z is a structural shock (e.g. a policy shock). Furthermore, γ is a coefficient and E is the subjective expectation of the agent. The marginal effect of the structural shock on the outcome variable is

∂Y ∂Z = γ ∂E [X (Z)] ∂Z .
To compute the derivative

∂E[X(Z)] ∂Z

, one usually makes assumptions about expectation formation. The most common assumption is that the agent has full information rational expectations (i.e. the agent knows the realization of the shock Z and is right about the effect of Z on X). The alternative is to assume that the agent has incomplete information about the realization of Z (e.g. due to inattention) or distorted beliefs about the effect of Z on X (e.g. due to level-k thinking or some other deviation from rational expectations).

In this paper, we take a different route. We elicit directly the expectation E [X (Z)] for alternative policies and can thereby compute the effect of the shock Z on the outcome variable Y without making assumptions about expectation formation.

The specific macroeconomic model that we build on is a New Keynesian model with heterogeneous agents. The assumptions about preferences, budget constraints, asset structure and borrowing constraints are similar to the assumptions in [START_REF] Mckay | The Power of Forward Guidance Revisited[END_REF]. The expectation side of the model is new. Rather than making theoretical assumptions about expectation formation, we feed experimentally estimated adjustments of all those expectations appearing in the consumption functions into the model. For example, consider a household who is currently not borrowing constrained and holds the belief that it will not be borrowing constrained in the future. The log-linearized consumption function of this type of household has the following form. Current consumption is a linear function of three terms: the expectation of the discounted sum of current and future real income, the expectation of the discounted sum of current and future real interest rates, and the expectation of end-of-previous-period real bond holdings [START_REF] Angeletos | Forward Guidance Without Common Knowledge[END_REF]). This is an example of equation ( 1) but with multiple terms on the right-hand side of the equation. In the survey, we elicit all expectations that appear on the right-hand side of this consumption function for a baseline policy and an alternative policy. Substituting the difference in expectations across policies into the consumption function we can assess the effect on consumption of implementing one policy instead of another policy. As part of the survey, we also elicit a household's subjective probability of being borrowing constrained in the future and whether the household is currently borrowing constrained. This allows us to substitute the expectation difference into the consumption function that is adequate for this type of household. Aggregating across households yields the aggregate consumption response on impact of the announcement of the policy change.

This approach can be used to study the effects of conventional and unconventional monetary policy. To illustrate this point, we elicited the expectations that appear in the consumption functions for alternative forward guidance statements in March 2021 and for alternative interest rate decisions in March 2022. The elicitation was done in the days before the FOMC meeting to capture the expectation adjustment in the relevant context.

In March 2021 we studied the effects of unconventional monetary policy, since there appeared to be broad agreement at the Federal Reserve to keep the current interest rate near zero. In March 2022, we investigated the effects of conventional monetary policy, because FOMC members were publicly debating the timing and the size of an interest rate increase. We highlight our approach in detail for the forward guidance survey conducted announcement. The effect peaks at 0.19 percentage points for the rate in 2023 and then reverts back to close to zero in 2026 and 2030, consistent with the Fed's long-term projections remaining unchanged. The increase by 0.19 percentage points corresponds to approximately 50 percent of the difference in Fed projections across scenarios. This in turn suggests that respondents attach positive probability to a state where the Fed will ex-post not increase the future federal funds rate as projected. Second, we document downward adjustments of inflation expectations in response to the increase in the projected federal funds rate in 2023. Expectations decrease by 0.25 percentage points for inflation in 2021, on impact of the announcement, and less strongly for later time periods. Third, there is a muted average response of nominal income expectations over all relevant time horizons. Together, the significant effects on inflation expectations and the muted response of nominal income expectations imply that the Fed announcement increases respondents'

expected real income. Finally, using an additional experiment, we show that neither expectations about future credit constraints nor expectations about the nominal value of respondents' home change in response to the change in the Fed projection.

In our survey, participants are randomly assigned into groups to which the policy change is described as (i) endogenous to current economics conditions, (ii) exogenous to current conditions, or (iii) exogenous to current conditions and also reflected in stock market movements, or (iv) to which no reason for the change in the projections in provided. Our respondents' expectation adjustment does not vary systematically across these treatment arms. This highlights the robustness of our main findings and showcases that households do not form their expectations as posited by a large class of theoretical models, which would predict sharp differences in expectation adjustment depending on whether a policy change is endogenous or exogenous.

Both the result that households do not adjust their nominal income expectations and the finding that expectation adjustments do not depend on the reason for the policy change highlight the value of an approach that feeds measured expectations into models and makes no theoretical assumptions about the expectation formation process.

Finally, we turn to the model-based aggregate consumption responses to the change in the Fed's projections. We obtain these responses from directly feeding the estimated expectation adjustments of the relevant behavioral types into the theoretical model. Thus, we calculate the effects of adjustments in the Fed's projection on aggregate consumption based on how non-hand-to-mouth households actually adjust their expectations in response to changes in the Fed's projection. Assuming an intertemporal elasticity of substitution of 1 2 , our estimates imply a consumption decrease among non-hand-to-mouth households who are certain that they will not be credit constrained in the future (48 percent of our sample) by 0.51 percentage points. This overall effect masks opposing effects working through intertemporal substitution, lowering consumption by 0.7 percentage points, and higher expected real income, somewhat increasing consumption by approximately 0.19 percentage points. We also study the consumption response among nonhand-to-mouth households attaching positive probability to future credit constraints (25 percent of our sample) focusing on two corner cases -i) that they behave as if they expected no constraints, and ii) that they behave as if they were certain to be constrained in the next period. While in case i) their consumption would somewhat increase by 0.3 percent, in case ii) their consumption would be unchanged. Focusing on case ii) for this group of households, we calculate a direct effect of the change in the Fed's projection due to expectation adjustment on overall consumption in the economy of -0.24 percent.

When we assume that households who report to usually be inattentive to Fed announcements do not change their spending, the effect declines to -0.17 percent. Any additional effect on consumption depends on assumptions about how quickly the reduction in consumption due to the expectation adjustment is reflected in changes in income.

In our March 2022 survey on the effects of conventional monetary policy, respondents are presented with a baseline scenario in which the Fed keeps the current federal funds rate at 0.1 percent, and an alternative scenario in which the federal funds rate is increased to 0.5 percent. Respondents increase their inflation expectations in response to the policy change, in line with respondents interpreting the interest rate hike as a signal about the Fed's private information of future inflationary pressures. Similarly as in our forward guidance survey, respondents do not update their expectations about their nominal household income. Feeding those expectation adjustments into our model, we obtain a reduction of aggregate consumption by 0.45 percent if all non-hand-to-mouth households are are attentive to the Fed announcement. If we assume that only those who report to usually hear about Fed announcements within seven days are attentive, aggregate consumption falls by 0.15 percent in response to the interest rate hike. Taken together, this suggests a relatively muted response of aggregate consumption to conventional monetary policy.

We contribute to a literature assessing the effects of forward guidance [START_REF] Eggertsson | The Zero Bound on Interest Rates and Optimal Monetary Policy. Comments and Discussion[END_REF], as well as a series of papers analyzing potential mechanisms that could explain small effects of forward guidance (Del [START_REF] Negro | The Forward Guidance Puzzle[END_REF]. [START_REF] Mckay | The Power of Forward Guidance Revisited[END_REF] provide a theoretical framework highlighting that anticipated future credit constraints imply a more muted consumption response to changes in forward guidance. [START_REF] Angeletos | Forward Guidance Without Common Knowledge[END_REF] show that without the common knowledge assumption, forward guidance has less powerful effects than in standard theories. Gabaix (2020) models agents' partial myopia toward distant atypical events using a new microfounded "cognitive discounting" parameter, which substantially limits the effectiveness of forward guidance. [START_REF] Wiederholt | Empirical Properties of Inflation Expectations and the Zero Lower Bound[END_REF] studies the effects of forward guidance when expectations adjust sluggishly and are dispersed. We offer a new approach to assess the effectiveness of forward guidance that combines a parsimonious model with survey-based estimates of expectation adjustments, while making no theoretical assumptions on the way expectations are formed. Our findings suggest that changes in forward guidance lead to changes in expected inflation with flat nominal income expectations, which may result in a more muted consumption response than implied by canonical models [START_REF] Eggertsson | The Zero Bound on Interest Rates and Optimal Monetary Policy. Comments and Discussion[END_REF] due to opposing effects working through intertemporal substitution and changes in expected real income. In addition, the inflation expectation adjustments we measure in our survey are smaller than those in canonical models.

Our approach has a range of desirable features. First, surveys of this type can be flexibly tailored to different kinds of relevant policy counterfactuals, including new policy measures, for which no historical data are available. Together with the ex-ante nature of our approach, this opens a possibility for policymakers to use our method to predict effects of different policy options on aggregate outcomes before committee meetings. Second, a key advantage of our approach compared to models calibrated based on historical data is that it captures rich state-dependence in the consumption response to policy changes. Specifically, it predicts the effects of policy changes based on current expectation adjustments, current hand to mouth-status, current perceived probability of becoming credit constrained in the future and current attention to monetary policy across the population. Third, our approach makes it unnecessary to elicit beliefs for cases in which there is room for misunderstanding whether respondents should account for general equilibrium feedback effects or not, such as about their consumption responses to policy changes. In particular, making sure that respondents understand whether they should "hold fixed" the behavior of other agents or allow for changes in other agents' decisions would be difficult, and the resulting data potentially difficult to interpret. In our approach, we elicit respondents' immediate expectation adjustments that should directly shape their consumption responses to the policy change. General equilibrium effects are then fully determined through the workings of the model. Fourth, by measuring hypothetical fullinformation expectation adjustments for each respondent, policymakers can vary other model inputs, such as the fraction of the population that is assumed to be attentive to the policy change, and examine how this affects aggregate responses to the policy.

We also contribute to a literature that empirically studies households' expectation formation in the context of monetary policy (Coibion et used by households to predict the effects of different macroeconomic shocks, including changes in policy rates. Our paper differs from the existing literature in three main ways: first, our measurement of expectations and behavioral types is directly guided by the insights of a macroeconomic model. Second, we use our estimated elasticities of expectations as inputs in our model to quantify the impact of monetary policy on consumption.

Third, different to experiments providing actual pieces of information on monetary policy, our approach based on hypothetical policy changes can be used to predict the effects of specific future policy options ex-ante.

Our paper proceeds as follows. Section 2 presents a model of consumption responses to monetary policy announcements. Section 3 provides an overview of our design for the March 2021 forward guidance survey. In Section 4 we discuss reduced-form evidence from our forward guidance experiment. In Section 5 we present the model-implied consumption responses to the forward guidance announcement. Section 6 presents results from our March 2022 experiment on conventional monetary policy. Section 7 concludes.

Theoretical framework

This section presents a model of how households adjust their consumption in response to policy announcements on future interest rates. The assumptions about preferences, budget constraints and borrowing constraints are similar to the assumptions in [START_REF] Mckay | The Power of Forward Guidance Revisited[END_REF]. In Section 5, we use this model together with our experimentally estimated expectation adjustments to predict consumption responses to forward guidance. In Section 6, we use the same approach to predict consumption responses to conventional monetary policy announcements (i.e., announcements about the target for the current short-term interest rate).

Assumptions

The economy is populated by a unit continuum of households, indexed by i ∈ [0, 1], with preferences given by

E i,t ∞ ∑ s=t β s-t C 1-γ i,s 1 -γ -v i (N i,s ) , (2)
where C i,s is consumption of household i at time s and N i,s is labor supply of household For now, we assume that R t = R debt t . There are firms in the economy that generate profit. Households therefore have dividend income. For now, we assume that households cannot trade their stakes in the firms.

The flow budget constraint of household i in period t reads

P t C i,t + B i,t = R t-1 B i,t-1 + W i,t N i,t + D i,t -T i,t , (3)
where P t C i,t is the consumption expenditure of household i in period t, P t is the consumer price index in period t, and B i,t are the household's holdings of the liquid asset between periods t and t + 1. Turning to the right-hand side of the flow budget constraint, W i,t N i,t is labor income, D i,t is dividend income, and T i,t are tax payments of household i in period t. The wage rate and the dividend income may differ across households. The tax payment can be any function of income and wealth, so long as it does not affect the consumption Euler equation.

The borrowing constraint of household i in period t reads

B i,t ≥ -L i,t (4)
where the borrowing limit L i,t may differ across households, can depend on the entire history of the economy, and is taken as given by household i. A special case is a borrowing limit of zero in every period and every state of the world.

The expectation operator in equation ( 2) is assumed to satisfy linearity and the law of iterated expectations. Formally, for any two random variables X and Y,

E i,t [X + Y] = E i,t [X] + E i,t [Y] , (5)
and

∀s > t : E i,t [E i,s [X]] = E i,t [X] . (6)
Furthermore, we assume that for any binary random variable

Z E i,t [X] = θ i,t E i,t [X|Z = 1] + (1 -θ i,t )E i,t [X|Z = 0], (7)
where θ i,t denotes household i's period-t subjective probability of the event Z = 1. We make no other assumptions about the expectation operator.

We assume that in period t, each household chooses consumption C i,t so as to maximize its objective (2) subject to its budget constraint (3) and its borrowing constraint (4),

given its subjective beliefs about the future paths of all relevant variables.

Terminology

Note that in period t, each household belongs to exactly one of the following three groups:

• Group 1: The household's borrowing constraint is binding in period t.

• Group 2: The household's borrowing constraint is not binding in period t, and the household believes that the borrowing constraint will not be binding in the future.

• Group 3: The household's borrowing constraint is not binding in period t, and the household believes that the borrowing constraint is binding in the future with strictly positive probability.

Following the literature, we will refer to households in group 1 as "hand-to-mouth" households. We distinguish between these three groups because households in different groups have different consumption functions, which we turn to next.

Consumption functions

The consumption of a household in group 1 (i.e., the consumption of a hand-to-mouth household) is given by the flow budget constraint and the binding borrowing constraint

C i,t = 1 P t (R t-1 B i,t-1 + W i,t N i,t + D i,t -T i,t + L i,t ) . (8)
The household consumes all liquid wealth, all after-tax income, as well as all available credit.

The consumption function of a household in group 2 can be derived from the present value budget constraint in real terms

∞ ∑ s=t Q t,s C i,s = R t-1 Π t Bi,t-1 + ∞ ∑ s=t Q t,
= E i,t E i,s β R s Π s+1 C -γ i,s+1
.

Log-linearizing the last three equations around the steady state of the non-stochastic version of the economy (where households may be ex-ante different and therefore may have different initial wealth levels Bi , different labor income Wi N i , different dividend income Di , and different tax payments Ti ) and rearranging yields

c i,t = 1 C i Ỹi (1 -β) E i,t ∑ ∞ s=t β s-t ỹi,s + 1 β -1 Bi Ỹi 1 C i Ỹi -1 γ βE i,t ∑ ∞ s=t β s-t (r s -π s+1 ) + 1 β -1 Bi Ỹi 1 C i Ỹi E i,t r t-1 -π t + bi,t-1 . (9)
Here Ỹi,t denotes real labor income plus real dividend income minus real tax payments Ỹi,t ≡ Wi,t N i,t + Di,t -Ti,t , and lower-case letters denote log-deviations from the steady state of the non-stochastic version of the economy (e.g., c i,t = ln (C i,t )ln (C i ) and ỹi,t = ln Ỹi,tln Ỹi ). 5 Consumption of a household who is not borrowing constrained in period t and does not expect to be borrowing constrained in the future depends on three expectations: permanent non-interest income (the first term in equation ( 9)), the income and substitution effect linked to expected real interest rates (the second term in equation ( 9)), and the perceived beginning-of-period real liquid wealth (the third term in equation ( 9)).

Combining the two interest income terms and the non-interest income term yields

c i,t = 1 C i Ỹi (1 -β) E i,t ∑ ∞ s=t β s-t 1 β Bi Ỹi (r s-1 -π s ) + ỹi,s -1 γ βE i,t ∑ ∞ s=t β s-t (r s -π s+1 ) + 1 C i Ỹi (1 -β) 1 β Bi Ỹi E i,t bi,t-1 . (10)
The consumption of a household who is not borrowing constrained in period t and does not expect to be borrowing constrained in the future depends on permanent income, the intertemporal substitution term, and the perceived end-of-previous-period real liquid wealth.

Turning to the effect of policy announcements on consumption, let

c i,t = c Policy1 i,t - c Policy2 i,t
denote the difference between consumption under policy announcement 1 and consumption under policy announcement 2 and let E

i,t [X] = E Policy1 i,t [X] -E Policy2 i,t [X]
denote the difference between the expectation of variable X under policy announcement 1 and the expectation of the same variable under policy announcement 2. Equation (10) implies that

c i,t = 1 C i Ỹi (1 -β) E i,t ∑ ∞ s=t β s-t 1 β Bi Ỹi (r s-1 -π s ) + ỹi,s -1 γ β E i,t ∑ ∞ s=t β s-t (r s -π s+1 ) + 1 C i Ỹi (1 -β) 1 β Bi Ỹi E i,t bi,t-1 . (11)
For a household in group 2, differences in consumption across policy announcements are determined by differences in expectations across policy announcements. The key idea of this paper is to elicit these differences in expectations with a survey and to compute the effect of policy announcements on consumption from equation (11).

The consumption function of a household in group 3 looks different because of the positive subjective probability of being borrowing constrained in the future. Since the borrowing constraint of a household in group 3 is not binding in period t, the household's consumption Euler equation holds with equality in period t

C -γ i,t = E i,t β R t Π t+1 C -γ i,t+1 .
Let θ i,t denote household i's subjective probability in period t of being borrowing constrained in period t + 1. Using this notation, one can write the consumption Euler equation in period t as

C -γ i,t = θ i,t E b i,t β R t Π t+1 C -γ i,t+1 + (1 -θ i,t ) E n i,t β R t Π t+1 C -γ i,t+1
, where E b i,t denotes the expectation conditioning on a binding borrowing constraint in period t + 1, while E n i,t denotes the expectation conditioning on a non-binding borrowing constraint in period t + 1.

Consumption in the case of a binding borrowing constraint in period t + 1 is given by the flow budget constraint and the consumption function of a group 1 household

C i,t+1 = R t Π t+1 R t-1 Π t Bi,t-1 + Ỹi,t -C i,t + Ỹi,t+1 + Li,t+1 .
See equations (3) and (8). Log-linearizing the last two equations around the steady state of the non-stochastic version of the economy and combining these two equations yields

c i,t = - 1 γ E i,t [r t -π t+1 ] + θ i,t E b i,t x i,t+1 - 1 β c i,t + (1 -θ i,t ) E n i,t [c i,t+1 ] , with x i,t+1 ≡ Bi C i β 2 r t -π t+1 + r t-1 -π t + bi,t-1 + Ỹi -C i C i β (r t -π t+1 ) + Ỹi C i 1 β ỹi,t + ỹi,t+1 + Li C i li,t+1 .
To illustrate the implications of beliefs about future binding borrowing constraints for current consumption, consider the limit as θ i,t converges to one, that is, the household believes that the borrowing constraint (4) will very likely be binding in the next period.

The last two equations then imply

c i,t = 1 C i Ỹi 1 1+β E i,t ∑ t+1 s=t β s-t 1 β Bi Ỹi (r s-1 -π s ) + ỹi,s -1 γ β 1+β E i,t [r t -π t+1 ] + 1 C i Ỹi 1 1+β E i,t 1 β Bi Ỹi bi,t-1 + β Li Ỹi li,t+1 . (12)
Comparing equation (12) to equation (10) shows that the anticipation of a binding borrowing constraint in the next period has several implications. First, the relevant definition of "permanent" income becomes the expected average income up to and including the period in which the borrowing constraint becomes binding. Second, the intertemporal substitution term depends only on the expected real interest rate up to the period in which the borrowing constraint becomes binding. Third, the expectation of the future real value of the borrowing limit affects current consumption.

The effect of the policy announcement on consumption then equals

c i,t = 1 C i Ỹi 1 1+β E i,t ∑ t+1 s=t β s-t 1 β Bi Ỹi (r s-1 -π s ) + ỹi,s -1 γ β 1+β E i,t [r t -π t+1 ] + 1 C i Ỹi 1 1+β E i,t 1 β Bi Ỹi bi,t-1 + β Li Ỹi li,t+1 , (13)
where c i,t is the difference between consumption under policy announcement 1 and consumption under policy announcement 2 and E i,t [X] is the difference between the expectation of variable X under policy announcement 1 and the expectation of the same variable under policy announcement 2.

For households in group 2 and households in group 3, differences in consumption across policy announcements are determined by differences in expectations across policy announcements. However, the consumption function of a household in group 2 differs from the consumption function of a household in group 3. The key idea of the paper is to elicit differences in expectations across policy announcements for an individual household with a survey and to compute the effect of the policy announcement on the consumption of the household from the consumption function of this type of household.

Experimental design and data

In this section we present our main experimental design and our data. The full experimental instructions are provided in Appendix B.1.

Samples

For our main survey we collect a sample of 2,218 respondents that is representative of the US population in terms of education, gender, age, region, and household net income.

The survey was conducted as an online survey shortly before the regular FOMC meeting on March 16/17 2021 in collaboration with the panel data provider Luc.id, which is commonly used in economic research [START_REF] Haaland | Designing Information Provision Experiments[END_REF].

Experimental design: Main survey

Combining theory and empirics

According to our model, expectations about the federal funds rate, the inflation rate, and household income are the key expectations that should shape the consumption response to changes in Fed projections. In our survey, we elicit the response of exactly these expectations over different relevant forecast horizons. Moreover, we include tailored questions to measure current hand-to-mouth status, attention to Fed announcements, and the perceived probability of becoming credit constrained, which all matter for households'

spending responses in the model.

Survey modules

Demographics, definitions and introduction

In the beginning of our survey, we elicit a basic set of demographic characteristics. Then, we provide our respondents with basic definitions of the inflation rate as well as the federal funds rate. In particular, we explain to our respondents that the Federal Reserve (Fed) controls the federal funds rate and that besides choosing the current rate, the Fed publishes projections of where this interest rate will be in the coming years. We then fix beliefs about the current level of the federal funds rate (0.1 percent) as well as the projection by the Fed according to which the rate will still be 0.1 percent at the end of 2023.

Baseline scenario Respondents are then asked to imagine the following hypothetical scenario:

Please imagine that at the next meeting of the Fed on March 16/17 2021, the Fed announces that the current federal funds rate will remain unchanged at 0.1 percent. Moreover, the Fed announces that its projection about the future federal funds rate at the end of 2023 remains unchanged at 0.1 percent. Note:

Further imagine, that the Fed's projection of the federal funds rate at the end of 2030 remains unchanged at 2.5 percent.

We then elicit the respondents' own expectations under this hypothetical scenario, such

as their expectations about the future federal funds rate at the end of the years 2021, 2022, 2023, 2026 and 2030, and their expectations about annual inflation in 2021, 2022 and 2023, as well as their average expected inflation rate for the years 2024-2026. We also elicit our respondents' expectations about their average annual household income in nominal dollar terms in 2021, 2022-2023, as well as 2024-2026. To make it clear to respondents that we are interested in their expectations conditional on learning about the Fed announcement we explicitly ask them about their expectations "if they learned about the Fed's announcement".

Alternative scenario Respondents are then asked to imagine an alternative scenario about the Fed's projections. Specifically, respondents receive the following instructions:

We will now ask you to consider the following alternative hypothetical scenario. Please imagine that at their next meeting on March 16/17 2021, the Fed announces that the current federal funds rate will remain unchanged at 0.1 percent. However, the Fed announces that its projection about the future federal funds rate at the end of 2023 increases from 0.1 percent to 0.5 percent.

Note: Further imagine, that the Fed's projection of the federal funds rate at the end of 2030 remains unchanged at 2.5 percent.

We then re-elicit respondents' own expectations regarding the federal funds rate, the inflation rate, and their net household income under this alternative hypothetical scenario using the same time horizons as in the baseline scenario.

Beliefs about the source of the change in projections

To probe the robustness of our findings, we cross-randomize respondents into four different groups receiving different messages on the source of the change in the Fed projection: In the "no-reason" group, respondents are not provided with a reason for why the projection changes. In the "endogenous" group, respondents are told that the change in the projection is due to a change in the Fed's outlook on the broader development of the economy. In the "exogenous" group, participants are told that the change in the Fed's projection occurred because the composition of the committee changed before the meeting. In addition, respondents in this group are told that the change in the projection is not due to a change in the Fed's outlook on the broader development of the economy. In the "exogenous-stock" group, respondents receive the same instructions as respondents in the "exogenous" group, but are additionally told that in response to the Fed announcement, the S&P 500 stock market index falls by one percent. This last treatment arm allows us to study whether our findings differ when we provide additional information that might be important for households' learning about Fed announcements in the real world.

Measuring inattention

A key variable in the consumption response to Fed announcements is the fraction of households that are inattentive to such announcements, and may therefore not adjust their consumption in response to such events. To quantify the fraction of inattentive households, we ask our respondents to think of announcements by the Federal Reserve in general. We then ask them how long it would typically take until they hear of a Fed announcement on a scale ranging from "less than seven days" to "typically I would never hear of such an announcement".

Identifying hand-to-mouth consumers In our model, only non-hand-to-mouth households will adjust their consumption in response to changes in expectations. Therefore, it is critical for us to identify hand-to-mouth consumers. Following the approach in Kaplan et al. ( 2014), we use a series of questions on balance sheet variables to identify liquidity constraints. Specifically, we ask respondents about their household's liquid wealth in the last days before the main earner's last income receipt as well as their total revolving credit card debt and overall combined credit limit for all credit cards owned by the household.

Anticipated credit constraints

Another key variable in our model is households' perceived likelihood of becoming credit constrained in the future (McKay et al., 2016). To measure anticipated credit constraints we ask our respondents about the probability that their household will be in a situation where it would like to borrow more money on its credit cards, but would be unable to do so. We elicit the perceived probabilities of being credit constrained at some point until the end of 2021, at some point until the end of 2022, and at some point until the end of 2026.

Additional characteristics Finally, we elicit an additional set of characteristics, including respondents' numeracy, their risk and time preferences, their perceived exposure to macroeconomic fluctuations as well as their household's savings rate in 2020.

Discussion of the design

Within-design Our design leverages differences in predictions across two alternative hypothetical scenarios -i.e. within-subject variation -to identify the effects of changes in projections of the federal funds rate. We believe that within-subject variation is particularly suited for our purposes for several reasons: First, our within-design helps us to control for individual-level fixed effects, and thus strengthens our statistical power and deals with individual-specific measurement error. Second, in our within-design it is salient to respondents that there is a change in the Fed's projections. Since in our model we are interested in expectation formation among households if they are attentive to Fed announcements, our design matches the theory closely.

Full-information expectation adjustments

Our design provides us with estimates of how individuals would adjust their expectations if they heard about the change in the Fed's projections, regardless of whether they are usually attentive to Fed announcements.

Setting equal to zero the consumption responses of households that self-report to be usually inattentive to Fed announcements, we obtain an estimate of the consumption stimulus due to forward guidance when only attentive households adjust their expectations.

Moreover, eliciting expectation adjustments also among those households who report to be less attentive, one can examine how the degree of attention shapes the impact of the policy.

Model-implied consumption responses

One alternative approach to study the consumption response to Fed announcements would be to elicit respondents' beliefs about their household spending under both the baseline and the alternative scenario. Compared to our approach of measuring expectation adjustments and feeding those into a model, this alternative approach has several disadvantages. First, if one elicits directly respondents' beliefs about their household spending under the baseline and the alternative policy scenario, it will be difficult to interpret the responses since it is not clear what the respondents "hold fixed". Would the responses reflect how much their con-sumption would change if monetary policy was the only thing that changed? Or would the responses reflect how much their consumption would change after everybody else had also changed their consumption, leading to a change in output, income and inflation in the economy? By instead eliciting respondents' beliefs about the effects of the policy on aggregate outcomes such as inflation and individual outcomes such as their after-tax income we circumvent this problem.

Moreover, according to standard theory, the consumption of group 2 and group 3

households not only depends on the beliefs measured in our survey, but it depends on nothing else than these beliefs. That is, the expectations changes in equations ( 11) and

(13) are sufficient statistics for the consumption changes in equations ( 11) and ( 13). This also means that all general equilibrium effects on the consumption of group 2 and group 3 households operate through these expectations.

Over time agents might receive additional information and change their consumption because they revise these beliefs, so what we measure is the response of consumption to the policy announcement on impact of the announcement.

Second, self-reported data on household spending is known to be subject to a high level of measurement error, even for recall of past spending levels ( Third, another advantage of measuring expectation adjustments as an input for modelimplied consumption changes is that we can vary other inputs, such as the degree of attention to Fed announcements or the degree of liquidity constraints, and examine how such changes affect predicted consumption responses.

Sample restrictions and summary statistics 3.3.1 Sample restrictions

We drop respondents in the top and bottom percentiles of response time, as very short or very long response times may indicate inattention to our survey, reducing the sample size from 2,218 to 2,175 for the main survey.

Point forecasts of macroeconomic variables elicited in household surveys are known to include extreme outliers, which may reflect typos or inattention to the survey questions.

Even if extreme responses reflect true beliefs, they could be driving predicted consumption responses according to our model, which features averages taken over individual survey responses, which are sensitive to outliers. We deal with this concern by excluding outliers in elicited point forecasts.

Since our model is calibrated using individual-level data (see Section 5), we require a sample for which all relevant expectations variables are available. Specifically, we exclude responses predicting a federal funds rate higher than 20 percent for any horizon (corresponding to the 98th or 99th percentile in the main survey depending on the horizon), responses predicting an inflation rate higher than 20 percent for any horizon (98th or 99th percentile), and responses predicting cumulative income growth of less than -70 percent or higher than 200 percent for any horizon (first and 98th or 99th percentile). In addition, we set to missing those who predict extreme differences in beliefs across the two hypothetical scenarios, as such extreme differences likely indicate typos. Specifically, we set to missing those predicting absolute effects on the federal funds rate and on the inflation rate of more than 5 percentage points or absolute effects on cumulative income growth of more than 50 percentage points. Again, these cutoffs mostly correspond to the bottom first or second or top 98th or 99th percentiles across variables and horizons.

Even though these steps are not restrictive individually, and even though there is strong overlap of groups containing outliers across survey questions, our focus on a common sample implies that these procedures result in dropping 13.6 percent of responses in the main survey. None of our reduced-form results and our model-based estimates are sensitive to the exact cutoffs used, and our reduced-form results are very similar if we use all available non-outlier observations for each forecast and horizon instead of focusing on the smaller common sample. Throughout, we obtain similar results if we winsorize outliers instead. 4 Reduced-form evidence

Summary statistics

Descriptive results

We first provide descriptive evidence on the distributions of hand-to-mouth status, anticipated probabilities of becoming credit constrained, and attention to Fed announcements in our sample.

Hand-to-mouth status

We classify hand-to-mouth households using a similar procedure as Kaplan et al. (2014). Among those who report to have carried over positive credit card debt from the last billing cycle (27.3 percent), we classify those as hand-to-mouth who carried over credit card debt of more than 80 percent of their combined limit on all cards (8.5 percent of the full sample). Among those who report not to have carried over any credit card debt, we classify those as hand-to-mouth who report liquid wealth holdings before the last income receipt of the main earner of less than their monthly household net income (18.4 percent). Together, this procedure yields a fraction of 26.9 percent handto-mouth households, which is very close to previous findings (Kaplan et al., 2014).6

Anticipated credit constraints

The anticipated probability of becoming credit constrained plays a key role for the consumption response to Fed announcements among non-handto-mouth households according to our model. dents report that it typically takes at most seven days until they learn about Fed announcements. The fraction is somewhat higher (62 percent) for the self-reported time until respondents hear of stock market movements in response to Fed announcements, in line with the idea that households may be more attentive to stock market movements than to Fed announcements, e.g. due to higher news coverage. Finally, Table A.2 provides an overview of the numbers of respondents in different cells according to their hand-tomouth status, their perceived chance of becoming credit constrained and their attention to Fed announcements. Attention to Fed announcements is substantially higher among non-hand-to-mouth households, in line with the idea that these households' decisions depend on their expectations about the future, such as the expected real interest rate.

Reduced-form results from the vignettes

According to our model, the consumption of hand-to-mouth households does not depend on their expectations, for given labor income and given hand-to-mouth status. Only the expectation adjustment of non-hand-to-mouth households should matter for the direct consumption effects of forward guidance. Therefore, we focus on the expectation adjustments of the 1,375 households that are classified as non-hand-to-mouth (73.1% of our final sample). Our results for expectations are qualitatively similar if we instead use the full sample. We measure the effect of the change in the Fed's projections on a respondent's expectations as the difference between a respondent's reported expectations under the "rise" and under the "baseline" scenario. This in turn suggests that respondents attach positive probability to a state where the Fed will ex-post not increase the future federal funds rate as projected. 7

Columns 1-4 of Table 2 highlight downward adjustments in average inflation expectations in response to the increase in the projected federal funds rate in 2023. Inflation expectations decrease by 0.25 percentage points for 2021 (p < 0.01), by 0.17 percentage points for 2022 (p < 0.01), and somewhat less strongly for the later time periods. The size of the adjustment of inflation expectations is substantial compared to the first-stage adjustment of expectations about the federal funds rate. These findings highlight that households expect most of the changes in inflation to occur early on after the announce- 7 Another potential reason for the less than one-to-one pass-through of projections to expectations is that a fraction of respondents may be inattentive to our survey and just quickly click through the questions.

ment, while effects are less pronounced for 2023, when the effect on the federal funds rate expectations is highest. The size of the adjustment of inflation expectations is somewhat smaller than implied by benchmark models. Overall, the effects on federal funds rate and inflation expectations suggest an important role of the intertemporal substitution mechanism in households' consumption responses.

Columns 5-7 of Table 2 display results on nominal income expectations. The table reveals a muted average response of income expectations over all relevant time horizons.

These effects are very precisely estimated and the minimum detectable effect sizes for a power of 80% and a significance threshold of 5% are below 1 percentage point. This suggests a limited relevance of adjustments of nominal income expectations in response to the change in Fed projections.

Table 3 displays results on real income expectations. Consistent with the fall in inflation expectations and the muted response of nominal income expectations, we observe a significant increase in real income expectations for some horizons. Expectations about cumulative real income growth increase by 0.48 percentage points for the years 2022-2023 (p < 0.01), and by 0.53 percentage points for the years 2024-2026 (p < 0.05). These reduced-form results already suggest that reductions in consumption due to intertemporal substitution may be partially offset by positive effects on real income expectations.

Robustness to different beliefs about the shocks

To probe the robustness of our findings, we varied the source of the change in the Fed's increased projection for the year 2023 that is provided to respondents. Panel B of Tables 1-3 highlight that households' expectation adjustment does not systematically vary depending on whether the source of the change is described to be (i) endogenous to current economic conditions, (ii) exogenous to current conditions, or (iii) exogenous to current conditions and also reflected in stock market movements, or whether (iv) no reason for the change is given. The lack of differences across the different sources of the shock underscores the robustness of our main findings.

Robustness to sample definition

In some of our projections of consumption responses in Section 5 we assume that only households that report to typically hear about Fed announcements within seven days adjust their consumption. Appendix Tables A.4-A.6 display reduced-form results on expectation adjustments restricting the sample to non-handto-mouth households who are attentive to Fed announcements. Although there are some small quantitative differences compared to the baseline results focusing on all non-handto-mouth households, the patterns are overall very similar.

Robustness experiment

We conducted an additional robustness experiment (n=392) in March 2021 in collaboration with Luc.id with a sample representative of the US population in terms of education, gender, age, region, and household net income. 8 Our design is identical to our main experiment except that we elicit different expectations in the hypothetical scenarios. In the robustness experiment, we elicit expectations about the future federal funds rate, the probability that the household will be borrowing-constrained in the future, and the value of the household's main residence under the baseline scenario of a constant Fed projection and under the alternative scenario of a rise in the projected Fed funds rate. 9 We use our robustness experiment to examine whether non-hand-to-mouth households update their expectations about future credit constraints and the value of their main residence in response to changes in Fed projections. These expectations play an important role in the effects of forward guidance according to influential models (Kaplan et al.,

2018; McKay et al., 2016). Table A.3 in the online appendix shows similar first-stage effects

on expectations about the federal fund rate in the robustness experiment as in the main survey. Table 4 shows that neither respondents' perceived likelihood of becoming credit constrained nor their home price expectations change in response to the change in the Fed projection. The estimated effects are close to zero, and relatively precisely estimated given the high statistical power in our within-design.

Consumption counterfactuals with measured expectations

In this Section, we feed the measured expectation adjustments from Section 4 into our model outlined in Section 2, and discuss the implied consumption changes in response to the Fed announcement.

Expected path of federal funds rate, inflation and income

The survey elicits each household's expected path for the federal funds rate, the inflation rate, and own income under the baseline policy announcement and under the alternative policy announcement.

Let E i,t [r s ] denote household i's expectation in period t of the federal funds rate in period s.

Let E i,t [r s ] = E a i,t [r s ] -E b i,t [r s ]
denote the difference between the expectation under the alternative policy announcement and the expectation under the baseline policy announcement. The survey elicits each household's expectation in quarter t=2021:Q1 of the federal funds rate at the end of five years (2021, 2022, 2023, 2026, and 2030) under the two policy announcements. Hence, from the survey, one can directly compute E i,t r 2021:Q4 , E i,t r 2022:Q4 , E i,t r 2023:Q4 , E i,t r 2026:Q4 , and E i,t r 2030:Q4 . We interpolate the answers for those quarters s that we do not ask about with the following formula:

E i,t [r s ] =                                    0 E i,t
s ≥ t + 39 . ( 14
)
This formula contains two assumptions. First, the difference in the expectation under the two policy announcements starts in the quarter for which it is expressed for the first time. Second, the effect of the announcement in 2021:Q1 on the expected federal funds rate in quarter s converges to zero at rate ρ from quarter 2030:Q4 onwards.

Turning to inflation, let E i,t [π s ] denote household i's expectation in period t of the inflation rate in period s.

Let E i,t [π s ] = E a i,t [π s ] -E b i,t [π s ]
denote the difference between the expectation under the alternative policy announcement and the expectation under the baseline policy announcement. The survey elicits each household's expectation in quarter t=2021:Q1 of the annual inflation rate over the year 2021, over the year 2022, over the year 2023, and over the period 2024-2026. We compute the expected quarterly inflation rates with the following formula:

E i,t [π s ] =                            1 4 E i,t [π 2021 ] 1 4 E i,t [π 2022 ] 1 4 E i,t [π 2023 ] 1 4 E i,t [ π2024-2026 ] ρ s-(t+23) 1 4 E i,
] = E i,t [Y i,s ]-Y i,t-1 Y i,t-1 . Let E i,t [y i,s ] = E a i,t [y i,s ] - E b i,t [y i,s
] denote the difference between the expectation under the alternative policy an- nouncement and the expectation under the baseline policy announcement. The survey elicits each household's expectation in quarter t=2021:Q1 of own nominal income in the year 2021, average own nominal income in the years 2022-2023, and average own income in the years 2024-2026 under the two policy announcements. Hence, from the survey, one

can directly compute E i,t [y i,2021 ] = E i,t [Y i,2021 ] Y i,2020 , E i,t [ ȳi,2022-2023 ] = E i,t [ Ȳi,2022-2023 ] Y i,2020
, and

E i,t [ ȳi,2024-2026 ] = E i,t [ Ȳi,2024-2026 ] Y i,2020
. To arrive at expectations of quarterly own nominal income, we use the following formula:

E i,t [y i,s ] =                    E i,
This formula contains two assumptions. First, if the household expects annual nominal income in 2021 to be x% higher in the year 2021 than in the year 2020, then the household expects quarterly nominal income to be x% higher in each quarter of the year. Second, the effect of the policy announcement in quarter t=2021:Q1 on the expected own nominal income in quarter s converges to zero at rate ρ from quarter 2026:Q4 onwards.

Finally, the expectation of own real income is determined by the expectation of own nominal income and the expectation of the rate of inflation

E i,t [ ỹi,s ] = E i,t [y i,s ] - s ∑ k=t E i,t [π k ] ,
where E i,t [ ỹi,s ] is the expectation of household i in period t=2021:Q1 of the percentage difference between own real income in quarter s and own real income per quarter in 2020. The last equation implies

E i,t [ ỹi,s ] = E i,t [y i,s ] - s ∑ k=t E i,t [π k ] , (17)
where E i,t [ ỹi,s ] is the difference between the real income expectation under the alter- native policy announcement and the real income expectation under the baseline policy announcement.

Consumption response of non-hand-to-mouth anticipating no constraints

For a nonhand-to-mouth, attentive household who does not expect to be borrowing constrained in the future, the impact of the policy announcement on consumption then equals

c i,t = 1 C i Ỹi (1 -β) ∑ ∞ s=t β s-t E i,t [ ỹi,s ] -1 γ β ∑ ∞ s=t β s-t ( E i,t [r s ] -E i,t [π s+1 ]) + 1 C i Ỹi (1 -β) 1 β Bi Ỹi E i,t bi,t-1 , (18)
if the household has positive liquid wealth ( Bj > 0), and

c i,t = 1 C i Ỹi (1 -β) ∑ ∞ s=t β s-t E i,t [ ỹi,s ] -1 γ β ∑ ∞ s=t β s-t ( E i,t [r s ] -E i,t [π s+1 ]) + 1 C i Ỹi (1 -β) 1 β Bi Ỹi E i,t bi,t-1 + ∑ ∞ s=t β s-t ( E i,t [r s-1 ] -E i,t [π s ]) , (19)
if the household has negative liquid wealth ( Bj < 0). The difference between these two equations is due to the fact that expected interest income is part of expected income for a household with positive liquid wealth, while expected interest payments are part of expected expenditure for a household with negative liquid wealth.

Table 5 shows the cross-sectional distribution of c i,t computed from the survey answers, assuming a quarterly discount rate of β = 0.99, an intertemporal elasticity of substitution of 1 γ = 1 2 , and no effect of the policy announcement on the expectation of past real liquid wealth and of the past policy rate, E i,t bi,t-1 = 0 and E i,t [r t-1 ] = 0. We assume that expectation adjustments beyond the measured horizons go to zero at rate ρ = 0.9. Moreover, we weight each respondent's consumption growth by the respondent's overall household spending in 2020.

Panel A of Table 5 shows the consumption response among non-hand-to-mouth households attaching a zero probability to becoming credit constrained at any point until the end of 2022, assuming that all of these households react to the Fed announcement. On average, our model calibrated using the survey-based expectation adjustments predicts a reduction of consumption by 0.51 percent (p < 0.01) in response to the hypothetical increase in the projected federal funds rate in 2023 from 0.1 to 0.5 percent. This average effect shrouds opposing effects of intertemporal substitution and changes in expected real income. While the intertemporal substitution mechanism lowers consumption by 0.7 percentage points (p < 0.01), the income effect channel somewhat increases consumption by approximately 0.19 percentage points (p = 0.5), and effects working through higher expected real interest payments reduce consumption by 0.001 percentage points (p = 0.12). Panel B of Table 5 reports the average expectation adjustment assuming that the subset of respondents that self-report that they usually learn about Fed announcements only after seven days or later (or never) would not adjust their expectations and spending at all. Under this assumption, consumption on average decreases by 0.35 percent (p < 0.05).

While the intertemporal substitution mechanism lowers consumption by 0.46 percentage points (p < 0.01), the income effect channel insignificantly increases consumption by approximately 0.11 percentage points (p = 0.64) and effects working through real interest rate payments lead to a decrease by 0.001 percentage points (p = 0.12). Thus, consistent with inattentive respondents not reacting to the announcement, both the income and intertemporal substitution mechanisms as well as the overall spending response are smaller in absolute magnitude in Panel B.

Table 6 highlights that our findings on the consumption adjustment of non-hand-tomouth households attaching a zero probability to becoming credit constrained remain similar if we vary the rate ρ at which we assume expectation adjustments beyond the measured horizons to go to zero.

Consumption response of non-hand-to-mouth anticipating constraints

For a non-handto-mouth, attentive household who expects to be borrowing constrained with probability one in the next period, the impact of the policy announcement on consumption equals

c i,t = 1 C i Ỹi 1 1+β ( E i,t [ ỹi,t ] + β E i,t [ ỹi,t+1 ]) -1 γ β 1+β ( E i,t [r t ] -E i,t [π t+1 ]) + 1 C i Ỹi β 1+β Li Ỹi ( E i,t [l i,t+1 ] -E i,t [π t+1 ]) + 1 C i Ỹi 1 1+β 1 β Bi Ỹi E i,t bi,t-1 , (20)
if the household has positive liquid wealth ( Bj > 0), and

c i,t = 1 C i Ỹi 1 1+β ( E i,t [ ỹi,t ] + β E i,t [ ỹi,t+1 ]) -1 γ β 1+β ( E i,t [r t ] -E i,t [π t+1 ]) + 1 C i Ỹi β 1+β Li Ỹi ( E i,t [l i,t+1 ] -E i,t [π t+1 ]) + 1 C i Ỹi 1 1+β 1 β Bi Ỹi E i,t bi,t-1 + ∑ t+1 s=t β s-t ( E i,t [r s-1 ] -E i,t [π s ]) , (21)
if the household has negative liquid wealth ( Bj < 0). The only difference between these two equations is a small difference in the last term and is due to the fact that expected interest income is part of expected income for a household with positive liquid wealth, while expected interest payments are part of expected expenditure for a household with negative liquid wealth.

Table 7 shows the cross-sectional distribution of c i,t computed from the survey answers, assuming a quarterly discount rate of β = 0.99, an intertemporal elasticity of substitution of 1 γ = 1 2 , and no effect of the policy announcement on the expectation of past real liquid wealth and of the past policy rate, E i,t bi,t-1 = 0 and E i,t [r t-1 ] = 0. In addition, we assume no differential effect of the two policy announcements on the expectation of the nominal borrowing limit, E i,t [l i,t+1 ] = 0, implying that deflationary expectations raise the expectation of the real value of the borrowing limit. We again weight each respondent's consumption growth by the respondent's overall household spending in 2020.

The table shows the consumption responses of non-hand-to-mouth households attaching a positive probability to becoming credit constrained until the end of 2022 for two corner cases. Panel A shows the consumption responses of these households if they behaved as if the probability of becoming credit constrained was zero. Panel B shows the consumption responses if they behaved as if the probability of becoming constrained was 100% already in t + 1 (using the derivations above). These two can be thought of as corner cases that should give a broad idea about what the overall consumption response of these households might be. Both panels assume that all households in this group adjust their expectations and consumption.

Panel A shows that if these households behaved as if they perceived a zero percent chance of being constrained, they would increase consumption by 0.3 percent (p = 0.3).

The positive overall response is the net effect of large expected real income effects of 1.46 percent (p < 0.01) and somewhat smaller intertemporal substitution effects of -1.16 percent (p < 0.01). Panel B highlights that if these households behaved as if they knew with certainty that they will become credit constrained in the next period, they would increase consumption by an insignificant 0.02 percent. The muted overall response masks intertemporal substitution effects of -0.03 percent (p < 0.01), insignificant real income effects of -0.11 percent (p = 0.71), and effects working through higher expected interest payments on debt of -0.01 percent (p < 0.05), which are balanced by positive effects working through a higher expected real credit limit of 0.17 percent (p < 0.01).

Table A.7 highlights insignificant overall consumption increases by 0.07 percent or by 0.02 percent for the two corner cases if we assume that among the group of non-hand-tomouth households anticipating credit constraints only those who report to typically learn about Fed announcements within seven days or less react.

Overall direct consumption effects from expectation adjustments

We can use the estimates for the groups of non-hand-to-mouth households attaching a zero probability to future credit constraints (48 percent of the sample) and of non-hand-to-mouth households perceiving a strictly positive probability of such constraints (25 percent of the sample) to obtain an estimate of the overall direct consumption effects from expectation adjustments in response to the policy announcement. For this exercise we assume that those predicting a positive probability of constraints behave as if they faced a 100 percent chance of constraints in the next period. The overall consumption response is given by the following If only those non-hand-to-mouth households who typically learn about Fed announcements within seven days react, the overall consumption response is given by: ct = 0.27 × 0 (24) + 0.48 × (-0.354) + 0.25 × (0.018) = -0.17

Thus the overall average consumption response due to the expectation adjustment in response to the increase in the projection about the 2023 federal funds rate will be -0.24 percent if all non-hand-to-mouth households react, and -0.17 if only those who are attentive to Fed announcements react.

Further discussion

In addition to these effects working through expectation adjustments, there could be additional effects if households' incomes decrease in response to lower consumption due to the expectation adjustments. Such effects could affect the consumption response of non-hand-to-mouth households, and also lead to an additional consumption response among hand-to-mouth households. However, if the reduced consumption is mostly reflected in an increase in inventories and lower capacity utilization of capital and labor, such income effects will be small. Moreover, there could be additional adjustments in expectations, which have further effects on non-hand-to-mouth households' consumption. However, given that in the short-term no new data (e.g. on GDP)

will become available, such additional expectation adjustments should only matter in the medium-term and not on impact.

The effects of conventional monetary policy

In this section, we apply our approach to assess the effects of conventional monetary policy on aggregate consumption. We describe the results of an additional experiment that we conducted shortly before the March 2022 meeting of the Federal Reserve.

Sample We recruit a sample broadly representative of the US population using Prolific, a commonly used online labor market for research studies. We apply the same sample restrictions with respect to extreme response times and outliers in expectations using the same cutoff values as in the main survey, which reduces the initial sample size of 838 observations to 692 observations. Again, none of our results are sensitive to the exact sample restrictions we apply.

Design

The design of this survey closely resembles the design of the March 2021 experiment (described in Section 3.2.1). Specifically, we elicit expectations about the federal funds rate, inflation and household income under two different policy scenarios. In the baseline scenario, the Fed announces at their meeting in March that it keeps the federal funds rate unchanged. Subsequently, respondents are presented a rise scenario, in which the Fed announces at their meeting that it increases the federal funds rate by 50 basis points. In both scenarios we fix beliefs about the Fed's projection of the federal funds rate in 2031 (2.5 percent). As in the March 2021 survey, we also collect rich data on attention to Fed announcements, whether respondents are hand-to-mouth consumers and anticipated credit constraints. Following the core idea of our approach, we design the survey such that we can use the elicited expectation adjustments together with our model to calculate the implied impact of the policy announcement on aggregate consumption.

Reduced-form results

We start by presenting the reduced-form effects of the policy announcement on respondents' expectations. Table A.8 presents the differences in respondents' expectations about the federal fund rate between the rise and the no-change scenario, respectively. In the rise scenario, participants increase their federal funds rate A key strength of our approach is that it flexibly accounts for such state-dependence in expectations adjustments.

Columns 5-7 of Table A.9 presents the reduced-form differences in respondents' nominal income expectations between the rise and the no-change scenario. The table reveals muted and statistically insignificant adjustments of cumulative nominal income expectations. These effects are very precisely estimated and the minimum detectable effect sizes for a power of 80% and a significance threshold of 5% are close to 1 percentage point. Consistent with our main evidence presented in Section 4, this suggests a limited relevance of adjustments of nominal income expectations in response monetary policy announcements.

Consumption counterfactuals with measured expectations

We next feed the measured expectation adjustments into our model outlined in Section 2, and present the implied aggregate consumption counterfactual.

Table A.10 presents the model-implied consumption responses for group 2 house-holds (reporting a zero percent chance of becoming credit constrained until the end of 2023). Tables A.11 and A.12 present the consumption responses for group 3 households (reporting a positive chance of becoming constrained until 2023) under the assumption that all households react and under the assumption that only attentive households react, respectively.

Taken together, assuming that all non-hand to mouth households react to the announcement, while hand-to-mouth households do not react, our model implies an aggregate consumption response of:

ct = 0.33 × 0 (25)
+ 0.25 × (-1.407)

+ 0.42 × (-0.232) = -0.45
If only those non-hand-to-mouth households who report to typically hear about Fed announcements within seven days are assumed to react to the announcement, the overall consumption response to the policy announcement is smaller:

ct = 0.33 × 0 (26)
+ 0.25 × (-0.364)

+ 0.42 × (-0.139) = -0.15
Taken together, our model-based estimates imply a relatively moderate immediate response of aggregate consumption to the interest rate hike, even under the assumption of full attention to the announcement.

Conclusion

We study the effects of both unconventional and conventional monetary policy combin- The sample is restricted to non-hand-to-mouth households. Notes: This table shows the effect of the hypothetical increase in the Fed's projection of the future federal funds rate at the end of 2023 from 0.1 to 0.5 percent on respondent's own expectations about the federal funds rate at different horizons. Panel A shows results pooling across the four arms. Panel B shows results separately for each of the four arms providing respondents with different reasons for the change in the Fed's projections. Arm "Change endogenous" attributes the change in the Fed's projections to a change in the Fed's broader economic outlook. Arm "Change no explanation" does not give an explanation for the change in projections. Arm "Change exogenous" attributes the change in the Fed's projections to a change in the composition of the Fed's committee before the next meeting. Arm "Change exogenous stocks" features the same explanation as "Change exogenous" and in addition explains that the stock market drops by 1 percent in response to the Fed's projections. The sample is restricted to non-hand-to-mouth households. Robust standard errors are in parentheses. * denotes significance at 10 pct., ** at 5 pct., and *** at 1 pct. level. table shows the effect of the hypothetical increase in the Fed's projection of the future federal funds rate at the end of 2023 from 0.1 to 0.5 percent on respondent's expectations about inflation and the cumulative growth of nominal household net income compared to 2020 at different horizons. Panel A shows results pooling across the four arms. Panel B shows results separately for each of the four arms providing respondents with different reasons for the change in the Fed's projections. Arm "Change endogenous" attributes the change in the Fed's projections to a change in the Fed's broader economic outlook. Arm "Change no explanation" does not give an explanation for the change in projections. Arm "Change exogenous" attributes the change in the Fed's projections to a change in the composition of the Fed's committee before the next meeting. Arm "Change exogenous stocks" features the same explanation as "Change exogenous" and in addition explains that the stock market drops by 1 percent in response to the Fed's projections. The sample is restricted to non-hand-to-mouth households. Robust standard errors are in parentheses. * denotes significance at 10 pct., ** at 5 pct., and *** at 1 pct. level. Notes: This table shows the effect of the hypothetical increase in the Fed's projection of the future federal funds rate at the end of 2023 from 0.1 to 0.5 percent on respondent's expectations about the cumulative growth of real household net income compared to 2020 at different horizons. Expected real income growth is constructed from the respondents' expectations about nominal income growth and about inflation. Panel A shows results pooling across the four arms. Panel B shows results separately for each of the four arms providing respondents with different reasons for the change in the Fed's projections. Arm "Change endogenous" attributes the change in the Fed's projections to a change in the Fed's broader economic outlook. Arm "Change no explanation" does not give an explanation for the change in projections. Arm "Change exogenous" attributes the change in the Fed's projections to a change in the composition of the Fed's committee before the next meeting. Arm "Change exogenous stocks" features the same explanation as "Change exogenous" and in addition explains that the stock market drops by 1 percent in response to the Fed's projections. The sample is restricted to non-hand-to-mouth households. Robust standard errors are in parentheses. * denotes significance at 10 pct., ** at 5 pct., and *** at 1 pct. level. Notes: This table shows the effect of the hypothetical increase in the Fed's projection of the future federal funds rate at the end of 2023 from 0.1 to 0.5 percent on respondent's expectations about the cumulative growth of the nominal value of their main residence until 2023 compared to 2020 and the probability of becoming credit constrained over different horizons. Panel A shows results pooling across the four arms. Panel B shows results separately for each of the four arms providing respondents with different reasons for the change in the Fed's projections. Arm "Change endogenous" attributes the change in the Fed's projections to a change in the Fed's broader economic outlook. Arm "Change no explanation" does not give an explanation for the change in projections. Arm "Change exogenous" attributes the change in the Fed's projections to a change in the composition of the Fed's committee before the next meeting. Arm "Change exogenous stocks" features the same explanation as "Change exogenous" and in addition explains that the stock market drops by 1 percent in response to the Fed's projections. The sample is restricted to non-handto-mouth households in the robustness experiment. Robust standard errors are in parentheses. * denotes significance at 10 pct., ** at 5 pct., and *** at 1 pct. level. -0.001 0.00 0.01 0.00 0.00 0.00 0.00 902 (0.000) Notes: This table shows the immediate consumption responses to the hypothetical increase in the Fed's projection of the future federal funds rate at the end of 2023 from 0.1 to 0.5 percent according to the model, which is calibrated using the survey-based changes in expectations. The table focuses on consumption responses of non-hand-to-mouth households with a zero perceived probability of being credit constrained at some point until the end of 2022. We assume effects on expectations to converge to zero at a quarterly rate ρ = 0.9 for horizons beyond those measured in the survey. In Panel A all of the included households are assumed to react. In Panel B only those included households who report that they typically learn about Fed announcements within seven days (68 percent) are assumed to react, while the consumption response is set to zero among those included households that report that it typically takes longer than seven days or that they typically never hear about Fed announcements (32 percent). Each of the three terms of the consumption response is winsorized at -15 percent and 15 percent. The overall consumption response is the sum of the winsorized individual terms. All statistics are weighted by the respondents' total household spending in 2020. Robust standard errors are in parentheses. * denotes significance at 10 pct., ** at 5 pct., and *** at 1 pct. level. table shows the immediate consumption responses to the hypothetical increase in the Fed's projection of the future federal funds rate at the end of 2023 from 0.1 to 0.5 percent according to the model, which is calibrated using the survey-based changes in expectations. The table focuses on consumption responses of non-hand-to-mouth households with a zero perceived probability of being credit constrained at some point until the end of 2022. The table varies the quarterly rate ρ at which we assume effects on expectations to converge to zero for horizons beyond those measured in the survey. Throughout, all of the included households are assumed to react. Each of the three terms of the consumption response is winsorized at -15 percent and 15 percent. The overall consumption response is the sum of the winsorized individual terms. All statistics are weighted by the respondents' total household spending in 2020. Robust standard errors are in parentheses. * denotes significance at 10 pct., ** at 5 pct., and *** at 1 pct. level. Notes: This table shows the effect of the hypothetical increase in the Fed's projection of the future federal funds rate at the end of 2023 from 0.1 to 0.5 percent on respondent's own expectations about the federal funds rate at different horizons. Panel A shows results pooling across the four arms. Panel B shows results separately for each of the four arms providing respondents with different reasons for the change in the Fed's projections. Arm "Change endogenous" attributes the change in the Fed's projections to a change in the Fed's broader economic outlook. Arm "Change no explanation" does not give an explanation for the change in projections. Arm "Change exogenous" attributes the change in the Fed's projections to a change in the composition of the Fed's committee before the next meeting. Arm "Change exogenous stocks" features the same explanation as "Change exogenous" and in addition explains that the stock market drops by 1 percent in response to the Fed's projections. The sample is restricted to non-hand-to-mouth households in the robustness experiment. Robust standard errors are in parentheses. * denotes significance at 10 pct., ** at 5 pct., and *** at 1 pct. level. Notes: This table shows the effect of the hypothetical increase in the Fed's projection of the future federal funds rate at the end of 2023 from 0.1 to 0.5 percent on respondent's own expectations about the federal funds rate at different horizons. Panel A shows results pooling across the four arms. Panel B shows results separately for each of the four arms providing respondents with different reasons for the change in the Fed's projections. Arm "Change endogenous" attributes the change in the Fed's projections to a change in the Fed's broader economic outlook. Arm "Change no explanation" does not give an explanation for the change in projections. Arm "Change exogenous" attributes the change in the Fed's projections to a change in the composition of the Fed's committee before the next meeting. Arm "Change exogenous stocks" features the same explanation as "Change exogenous" and in addition explains that the stock market drops by 1 percent in response to the Fed's projections. The sample is restricted to non-hand-to-mouth households who report that they typically learn about Fed announcements within seven days or less. Robust standard errors are in parentheses. * denotes significance at 10 pct., ** at 5 pct., and *** at 1 pct. level. table shows the effect of the hypothetical increase in the Fed's projection of the future federal funds rate at the end of 2023 from 0.1 to 0.5 percent on respondent's expectations about inflation and the cumulative growth of nominal household net income compared to 2020 at different horizons. Panel A shows results pooling across the four arms. Panel B shows results separately for each of the four arms providing respondents with different reasons for the change in the Fed's projections. Arm "Change endogenous" attributes the change in the Fed's projections to a change in the Fed's broader economic outlook. Arm "Change no explanation" does not give an explanation for the change in projections. Arm "Change exogenous" attributes the change in the Fed's projections to a change in the composition of the Fed's committee before the next meeting. Arm "Change exogenous stocks" features the same explanation as "Change exogenous" and in addition explains that the stock market drops by 1 percent in response to the Fed's projections. The sample is restricted to non-hand-to -mouth households who report that they typically learn about Fed announcements within seven days or less. Robust standard errors are in parentheses. * denotes significance at 10 pct., ** at 5 pct., and *** at 1 pct. level. Notes: This table shows the effect of the hypothetical increase in the Fed's projection of the future federal funds rate at the end of 2023 from 0.1 to 0.5 percent on respondent's expectations about the cumulative growth of real household net income compared to 2020 at different horizons. Expected real income growth is constructed from the respondents' expectations about nominal income growth and about inflation. Panel A shows results pooling across the four arms. Panel B shows results separately for each of the four arms providing respondents with different reasons for the change in the Fed's projections. Arm "Change endogenous" attributes the change in the Fed's projections to a change in the Fed's broader economic outlook. Arm "Change no explanation" does not give an explanation for the change in projections. Arm "Change exogenous" attributes the change in the Fed's projections to a change in the composition of the Fed's committee before the next meeting. Arm "Change exogenous stocks" features the same explanation as "Change exogenous" and in addition explains that the stock market drops by 1 percent in response to the Fed's projections. The sample is restricted to non-hand-to-mouth households who report that they typically learn about Fed announcements within seven days or less. Robust standard errors are in parentheses. * denotes significance at 10 pct., ** at 5 pct., and *** at 1 pct. level. -0.007 * * * 0.00 0.04 -0.05 0.00 0.00 0.00 473 (0.002) -Effects from real credit limit 0.080 * 0.00 0.84 0.00 0.00 0.00 0.09 473 (0.043) -Effects from interest payments -0.003 0.00 0.05 0.00 0.00 0.00 0.00 473 (0.002) Notes: This table shows the immediate consumption responses to the hypothetical increase in the Fed's projection of the future federal funds rate at the end of 2023 from 0.1 to 0.5 percent according to the model, which is calibrated using the survey-based changes in expectations. The table focuses on consumption responses of non-hand-to-mouth households with a positive perceived probability of being credit constrained at some point until the end of 2022. We assume effects on expectations to converge to zero at a quarterly rate ρ = 0.9 for horizons beyond those measured in the survey. Panel A shows model-based predicted consumption responses if these households never expected to become credit constrained. Panel B shows model-based predicted consumption responses if these households perceived a 100% chance of becoming credit constrained in period t+1 (i.e. one quarter after the survey). In both panels, only those included households who report that they typically learn about Fed announcements within seven days (46 percent) are assumed to react, while the consumption response is set to zero among those included households that report that it typically takes longer than seven days or that they typically never hear about Fed announcements (54 percent). Each of the three terms of the consumption response (four terms in Panel B) is winsorized at -15 percent and 15 percent. The overall consumption response is the sum of the winsorized individual terms. All statistics are weighted by the respondents' total household spending in 2020. Robust standard errors are in parentheses. * denotes significance at 10 pct., ** at 5 pct., and *** at 1 pct. level. -0.000 0.00 0.00 0.00 0.00 0.00 0.00 172 (0.000) Notes: This table shows the immediate consumption responses to the hypothetical increase in the future federal funds rate in March 2022 from 0.1 to 0.5 percent according to the model, which is calibrated using the survey-based changes in expectations. The table focuses on consumption responses of non-hand-tomouth households with a zero perceived probability of being credit constrained at any point until the end of 2023. We assume effects on expectations to converge to zero at a quarterly rate ρ = 0.9 for horizons beyond those measured in the survey. In Panel A all of the included households are assumed to react. In Panel B only those included households who report that they typically learn about Fed announcements within one weeks (41 percent) are assumed to react, while the consumption response is set to zero among those included households that report that it typically takes longer than one week or that they typically never hear about Fed announcements (59 percent). Each of the three terms of the consumption response is winsorized at -15 percent and 15 percent. The overall consumption response is the sum of the winsorized individual terms. All statistics are weighted by the respondents' total household spending in 2021. Robust standard errors are in parentheses. * denotes significance at 10 pct., ** at 5 pct., and *** at 1 pct. level.

ing

Main figures

Main tables

A Additional tables

  al., 2020b; D'Acunto et al., 2021; Link et al., 2020). 3 For instance, Coibion et al. (2019) and Coibion et al. (2020a) conduct information provision experiments to study how households' inflation expectations respond to different real-world pieces of communication about future inflation or policy rates. 4 Andre et al. (2022a) characterize a large degree of heterogeneity in the subjective models 3 This literature belongs to a broader research effort to better understand how households form macroeconomic expectations (Andre et al., 2022b; Armona et al., 2019; Bachmann et al., 2015; Bailey et al., 2018; Cavallo et al., 2017; Coibion et al., 2018; Fuster et al., 2020; Kuchler and Zafar, 2019; Roth and Wohlfart, 2020; Roth et al., 2021). 4 For a review of the broader literature on information provision experiments, see Haaland et al. (2021).

Figure 1

 1 displays the distributions of the perceived percent chance of becoming credit constrained over different horizons among non-hand-to-mouth households in our sample. The figure highlights that a majority (60 percent) attach zero probability to becoming credit constrained at any point until the end of 2026. Inattention to Fed announcements Figure 2 provides histograms of non-hand-to-mouth respondents' self-reported time until they typically hear about Fed announcements (Panel A) or the stock market reaction to such announcements (Panel B). 54 percent of respon-

  expectations by approximately 0.2 points for 2022, 2023 and 2024 (p < 0.01) compared to the baseline scenario. For 2027, the expectation adjustment declines somewhat to 0.15 percentage points (p < 0.01), and for 2031 expectations differences revert back close to zero (p = 0.25). The increases for the federal funds rate in the initial years correspond to approximately 50 percent of the difference in Fed projections across scenarios. This likely reflects that also under the baseline scenario respondents expect increases in the federal funds rate in later meetings in 2022.Columns 1-4 of TableA.9 present the reduced-form differences in respondents' inflation expectations between the rise and the no-change scenario. It shows that households increase their inflation expectations by 0.16 percentage points for 2022 (p < 0.01), by 0.19 percentage points for 2023 (p < 0.01), by 0.29 percentage points for 2024 (p < 0.01) and by 0.21 percentage points for 2025-2017 (p < 0.01). These findings highlight that households expect the strongest changes in inflation to occur a few years after the announcement. The increase in inflation expectations suggests that respondents interpret the policy announcement as a signal about the Fed's private information of increased inflationary pressures. Thus, adjustments of inflation expectations differ from the adjustments we measured for the hypothetical forward guidance announcement in our March 2021 survey. Given the very different macroeconomic environment in March 2022, e.g. given the war in Ukraine, this suggests an important role for state-dependence in the effects of monetary policy announcements on inflation expectations.

Figure 1 :

 1 Figure 1: Perceived probability of being credit constrained

Figure 2 :

 2 Figure 2: Time until learned about Fed announcements or stock market reaction

  from 0.1 to 0.5 percent on respondent's expectations about inflation and the cumulative growth of nominal household net income compared to 2021 at different horizons. The sample is restricted to non-hand-tomouth households. Robust standard errors are in parentheses. * denotes significance at 10 pct., ** at 5 pct., and *** at 1 pct. level.

  i at time s. The disutility of labor function v i : R + → R is twice continuously differen-

	tiable, strictly increasing, and convex, and may differ across households. The preference
	parameters satisfy β ∈ (0, 1) and γ > 0.
	Households can save, or borrow up to a borrowing limit. Households can save by
	holding a positive amount of a liquid asset (e.g., a nominal government bond) with gross
	nominal interest rate R t between periods t and t + 1. Households can borrow by holding a
	negative amount of the liquid asset with gross nominal interest rate R debt t	between periods
	t and t + 1.

Table A .

 A 1 Panel A shows summary statistics of the remaining sample of 1,880 respondents for the main survey, including benchmarks from the 2019 American Community Survey.

Our sample closely resembles the population according to the targeted variables gender, age, education, income and region even after our sample restrictions. Moreover, our sample is broadly balanced across the survey arms providing different explanations for the hypothetical change in the Fed's projections.

Table 1

 1

illustrates the results for the first stage. It confirms that respondents substantially update their federal funds rate expectations when going from the baseline to the rise scenario. While the average federal funds rate expectations increase by 0.05 percentage points for 2021 (p < 0.01) and by 0.08 percentage points for 2022 (p < 0.01), the effect peaks for 2023 with an increase by 0.19 percentage points (p < 0.01), and then reverts back to close to zero in 2026 and 2030, consistent with the fact that the Fed's longer-run projection is constant across the scenarios. The increase by 0.19 percentage points corresponds to approximately 50 percent of the difference in Fed projections across scenarios.

  = t, t + 1, t + 2 s = t + 3, . . . , t + 6 s = t + 7, . . . , t + 10 s = t + 11, . . . , t + 22 s = t + 23, . . . , t + 38

	r 2021:Q4
	E i,t r 2022:Q4
	E i,t r 2023:Q4
	E i,t r 2026:Q4
	ρ s-(t+39) E i,t r 2030:Q4

s

  expectation in period t of the percentage difference between own nominal income in period s and own nominal income in period t -1. Assuming that households know their own past nominal income, we have E i,t [y i,s

	to grow at a constant rate within a year and within the period 2024-2026. The expected
	quarterly inflation rate thus equals (1/4) times the expected annual inflation rate. Second,
	the effect of the policy announcement in quarter t=2021:Q1 on the expected inflation rate
	in quarter s converges to zero at rate ρ from quarter 2026:Q4 onwards.
	Turning to own nominal income, let E i,t [y i,s ] = E i,t	Y i,s -Y i,t-1 Y i,t-1	denote household i's
		s = t + 8, . . . , t + 11	.	(15)
		s = t + 12, . . . , t + 23
		s ≥ t + 24
	This formula also contains two assumptions. First, the household expects the price level

t [ π2024-2026 ] s = t, . . . , t + 3 s = t + 4, . . . , t + 7

  a model with experimentally estimated adjustments of expectations. Informed by the model, we conduct experiments with representative samples of the US population to study how households adjust their expectations in response to changes in the Fed's projections about future interest rates or changes in current interest rates. Feeding those experimentally measured expectation adjustments into our model, we find that a modest forward guidance statement in the March 2021 FOMC meeting would have reduced aggregate consumption by 0.17% on impact and an interest rate hike of 50 basis points in the March 2022 FOMC meeting would have reduced aggregate consumption by 0.15% on impact.

Table 1 :

 1 Reduced-form results: Adjustment of expectations about federal funds rate

			∆ Expected federal funds rate
			(percentage points)
		(1)	(2)	(3)	(4)	(5)
		2021	2022	2023	2026	2030
	Panel A: Pooled
	Mean expectation adjustment 0.052 * * * 0.075 * * * 0.190 * * * 0.030	0.001
		(0.013)	(0.014)	(0.019) (0.024) (0.028)
	Panel B: By arm
	Change endogenous (a)	0.055 * * 0.092 * * * 0.174 * * * 0.069	0.034
		(0.025)	(0.026)	(0.030) (0.043) (0.051)
	Change no explanation (b)	0.013	0.023	0.155 * * * -0.014 -0.005
		(0.024)	(0.028)	(0.038) (0.044) (0.052)
	Change exogenous (c)	0.070 (0.023)	(0.030)	(0.041) (0.050) (0.058)
	Change exogenous stocks (d) 0.070 * * 0.080 * * 0.203 * * * -0.025 -0.117 *
		(0.029)	(0.031)	(0.042) (0.052) (0.061)
	p-value(a=b)	0.220	0.067	0.686	0.186	0.592
	p-value(b=c)	0.090	0.047	0.179	0.106	0.166
	p-value(a=c)	0.676	0.770	0.276	0.697	0.376
	p-value(c=d)	0.988	0.585	0.643	0.100	0.009
	R-squared	0.01	0.02	0.07	0.00	0.01
	Observations	1,375	1,375	1,375	1,375	1,375

* * * 0.104 * * * 0.230 * * * 0.094 * 0.103 *

Table 2 :

 2 Reduced-form results: Adjustment of expectations about inflation and nominal income growth

						∆ Expected cumulative
		∆ Expected inflation rate	income growth
			(percentage points)		(percentage points)
		(1)	(2)	(3)	(4)	(5)	(6)	(7)
		2021	2022	2023	2024-26	2021	2022-23 2024-26
	Panel A: Pooled
	Mean expectation adjustment -0.250 * * * -0.167 * * * -0.039 -0.133 * * *	-0.071	0.044	-0.188
		(0.025)	(0.029) (0.036) (0.040)	(0.161)	(0.172)	(0.197)
	Panel B: By arm
	Change endogenous (a)	-0.193 * * * -0.141 * * * -0.038	-0.096	0.271	0.413	0.284
		(0.044)	(0.053) (0.072) (0.077)	(0.316)	(0.366)	(0.433)
	Change no explanation (b)	-0.334 * * * -0.230 * * * -0.103 -0.169 * * -0.777 * * * -0.808 * * -1.017 * * *
		(0.051)	(0.057) (0.071) (0.080)	(0.299)	(0.315)	(0.387)
	Change exogenous (c)	-0.222 * * * -0.106 *	-0.021 -0.169 * *	0.472	0.652 *	0.144
		(0.047)	(0.060) (0.077) (0.083)	(0.349)	(0.340)	(0.398)
	Change exogenous stocks (d) -0.255 * * * -0.188 * * * 0.002	-0.107	-0.247	-0.086	-0.206
		(0.053)	(0.059) (0.069) (0.077)	(0.320)	(0.338)	(0.347)
	p-value(a=b)	0.037	0.260	0.522	0.516	0.016	0.012	0.025
	p-value(b=c)	0.108	0.135	0.437	0.999	0.007	0.002	0.037
	p-value(a=c)	0.649	0.657	0.875	0.522	0.671	0.632	0.813
	p-value(c=d)	0.642	0.327	0.824	0.586	0.129	0.124	0.508
	R-squared	0.07	0.03	0.00	0.01	0.01	0.01	0.01
	Observations	1,375	1,375	1,375	1,375	1,375	1,375	1,375
	Notes: This

Table 3 :

 3 Reduced-form results: Adjustment of expectations about real income growth

	∆ Expected cumulative
	real income growth
	(percentage points)
	(1)	(2)	(3)
	2021	2022-23 2024-26

Table 4 :

 4 Robustness experiment: Adjustment of expectations about nominal home value growth and probability of being credit constrained

		∆ Expected probability	∆ Expected cumulative
		credit constrained	home value growth
		(percentage points)	(percentage points)
		(1)	(2)	(3)	(4)
		2021 2021-22 2021-26	2023
	Panel A: Pooled
	Mean expectation adjustment 0.025	0.516	0.240	0.284
		(0.659) (0.811) (0.527)	(1.217)
	Panel B: By arm
	Change endogenous (a)	-0.372	0.006	-0.018	-0.958
		(0.746) (1.005) (0.568)	(2.342)
	Change no explanation (b)	0.811	2.711	0.735	2.559
		(1.579) (2.132) (1.731)	(2.713)
	Change exogenous (c)	-1.289	-1.094	-0.432	1.220
		(1.557) (1.910) (0.849)	(2.401)
	Change exogenous stocks (d)	1.299	1.065	0.867	-1.561
		(1.097) (1.065) (0.997)	(2.292)
	p-value(a=b)	0.499	0.252	0.680	0.327
	p-value(b=c)	0.344	0.185	0.545	0.712
	p-value(a=c)	0.596	0.611	0.686	0.517
	p-value(c=d)	0.175	0.324	0.322	0.403
	R-squared	0.01	0.01	0.00	0.01
	Observations	298	298	298	298

Table 5 :

 5 Model-based results: Predicted consumption response to interest rate announcement among non-hand-to-mouth households with zero perceived chance of credit constraints

		Predicted consumption response (percent)
	Mean	Median SD p10 p25 p75 p90	N

Only attentive non-HTM react:

	Overall response among non-HTM	-0.354 * *	0.00	3.77 -4.46 -1.59 0.50 4.15 902
		(0.161)
	-Real income effects	0.108	0.00	5.61 -5.88 -1.36 0.79 6.73 902
		(0.231)
	-Intertemporal substitution effects	-0.462 * * *	0.00	3.29 -4.63 -1.04 0.16 2.48 902
		(0.132)
	-Effects from interest payments

Table 6 :

 6 Model-based results: Predicted consumption response to interest rate announcement among non-hand-to-mouth households with zero perceived chance of credit constraints: Different values of ρ

		Predicted consumption response (percent)
	Mean	Median SD p10 p25 p75 p90	N

  This table shows summary statistics for the main experiment (Panel A) and for the robustness experiment (Panel B). The p-value in Column 9 refers to the null hypothesis that the means across the fours arms in Columns 5-8 are equal.

	Table A.1: Summary statistics and balance check
		ACS				Online Sample
		(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)
		2019	Full Sample	Full Sample	Full Sample	Change endo-genous	Change no expla-nation	Change exo-genous	Change exog. stocks	p-value (5) = (6) =
		Mean	Mean	Median	SD	Mean	Mean	Mean	Mean	(7) = (8)
	Panel A: Main experiment
	Female	0.51	0.50	1.00	0.50	0.48	0.54	0.50	0.50	0.351
	Age	47.78	52.50	60.00	15.23	51.24	52.47	53.89	52.53	0.070
	At least bachelor's degree	0.31	0.41	0.00	0.49	0.40	0.41	0.40	0.42	0.847
	Log(Household net income)	11.06	11.06	11.13	0.81	11.13	11.03	11.00	11.09	0.259
	Northeast	0.17	0.19	0.00	0.39	0.22	0.19	0.19	0.17	0.251
	Midwest	0.21	0.27	0.00	0.45	0.24	0.30	0.29	0.28	0.180
	South	0.38	0.31	0.00	0.46	0.31	0.31	0.29	0.34	0.348
	West	0.24	0.22	0.00	0.41	0.23	0.20	0.24	0.21	0.573
	Main earner employed		0.63	1.00	0.48	0.65	0.63	0.60	0.62	0.397
	Log(Household liquid wealth)		9.60	9.77	2.85	9.59	9.52	9.67	9.63	0.870
	Log(Household credit card debt)		2.15	0.00	3.63	2.14	2.16	2.10	2.19	0.984
	Prob. credit constrained 2021-22		15.84	0.00	29.78	16.57	16.21	15.97	14.67	0.769
	Observations		1,880	1,880	1,880	495	449	443	493
	Panel B: Robustness experiment
	Female	0.51	0.52	1.00	0.50	0.58	0.44	0.46	0.59	0.071
	Age	47.78	51.60	50.00	15.79	50.98	52.56	51.47	51.54	0.927
	At least bachelor's degree	0.31	0.31	0.00	0.47	0.33	0.32	0.34	0.26	0.585
	Log(Household net income)	11.06	10.77	10.98	1.41	10.84	10.85	10.90	10.92	0.455
	Northeast	0.17	0.20	0.00	0.40	0.16	0.21	0.23	0.19	0.603
	Midwest	0.21	0.20	0.00	0.40	0.16	0.21	0.19	0.24	0.514
	South	0.38	0.40	0.00	0.49	0.45	0.41	0.34	0.43	0.341
	West	0.24	0.20	0.00	0.40	0.23	0.17	0.25	0.14	0.169
	Main earner employed		0.56	1.00	0.50	0.61	0.54	0.55	0.54	0.707
	Log(Household liquid wealth)		9.26	9.77	2.89	9.15	9.22	9.45	9.20	0.881
	Log(Household credit card debt)		2.46	0.00	3.69	2.69	2.34	2.20	2.64	0.742
	Observations		392	392	392	95	84	113	100
	Notes:

Table A .

 A 2: Numbers of respondents in different groups This table shows the numbers of respondents in different groups according to hand-to-mouth-status, the perceived probability of being credit constrained at some point until the end of 2022, and the time it typically takes until the respondent learns about Fed announcements.

		Number of respondents
		Learn ≤7 days	Learn >7 days	Learn never All
	HTM at credit limit	57	58	44	159
	HTM at zero kink	128	157	61	346
	Non-HTM 0% chance constrained	614	177	111	902
	Non-HTM > 0% chance constrained	219	216	38	473
	All	1,018	608	254	1,880

Notes:

Table A .

 A 3: Robustness experiment: Adjustment of expectations about federal funds rate

			∆ Expected federal funds rate
			(percentage points)
		(1)	(2)	(3)	(4)	(5)
		2021	2022	2023	2026	2030
	Panel A: Pooled
	Mean expectation adjustment 0.064 * *	0.066 * 0.176 * * * 0.022 -0.024
		(0.027)	(0.033)	(0.037) (0.049) (0.059)
	Panel B: By arm
	Change endogenous (a)	0.103	0.101	0.263 * *	0.188 0.231 *
		(0.091)	(0.112)	(0.103) (0.123) (0.135)
	Change no explanation (b)	0.032	0.004	0.134 * * * -0.041 -0.056
		(0.032)	(0.035)	(0.040) (0.085) (0.095)
	Change exogenous (c)	0.052	0.039	0.092	-0.017 -0.066
		(0.044)	(0.051)	(0.068) (0.093) (0.102)
	Change exogenous stocks (d) 0.069 * * * 0.115 * * * 0.226 * * * -0.037 -0.189
		(0.022)	(0.044)	(0.062) (0.082) (0.127)
	p-value(a=b)	0.461	0.410	0.247	0.126	0.083
	p-value(b=c)	0.700	0.572	0.594	0.846	0.943
	p-value(a=c)	0.618	0.616	0.168	0.184	0.080
	p-value(c=d)	0.732	0.260	0.147	0.871	0.452
	R-squared	0.02	0.02	0.08	0.01	0.02
	Observations	298	298	298	298	298

Table A .

 A 4: Reduced-form results among respondents that are attentive to Fed announcements: Adjustment of expectations about federal funds rate

			∆ Expected federal funds rate
			(percentage points)
		(1)	(2)	(3)	(4)	(5)
		2021	2022	2023	2026	2030
	Panel A: Pooled
	Mean expectation adjustment 0.053 * * * 0.074 * * * 0.195 * * * 0.034	0.017
		(0.013)	(0.016)	(0.021) (0.026) (0.030)
	Panel B: By arm
	Change endogenous (a)	0.032	0.089 * * * 0.156 * * * 0.043	0.054
		(0.028)	(0.030)	(0.036) (0.051) (0.057)
	Change no explanation (b)	0.008	0.007	0.153 * * * -0.011	0.012
		(0.024)	(0.029)	(0.042) (0.048) (0.060)
	Change exogenous (c)	0.077 * * * 0.108 * * * 0.242 * * * 0.106 * * 0.101 *
		(0.024)	(0.032)	(0.046) (0.053) (0.059)
	Change exogenous stocks (d) 0.094 * * * 0.087 * * 0.227 * * * 0.004	-0.087
		(0.029)	(0.034)	(0.046) (0.055) (0.065)
	p-value(a=b)	0.511	0.046	0.957	0.434	0.611
	p-value(b=c)	0.041	0.019	0.151	0.104	0.292
	p-value(a=c)	0.219	0.676	0.139	0.397	0.572
	p-value(c=d)	0.643	0.666	0.823	0.182	0.032
	R-squared	0.02	0.02	0.07	0.00	0.01
	Observations	1,114	1,114	1,114	1,114	1,114

Table A .

 A 5: Reduced-form results among respondents that are attentive to Fed announcements: Adjustment of expectations about inflation and nominal income growth

						∆ Expected cumulative
		∆ Expected inflation rate		income growth
			(percentage points)		(percentage points)
		(1)	(2)	(3)	(4)	(5)	(6)	(7)
		2021	2022	2023 2024-26	2021	2022-23 2024-26
	Panel A: Pooled
	Mean expectation adjustment -0.208 * * * -0.121 * * * 0.018 -0.078 * -0.031	0.099	-0.127
		(0.027)	(0.032) (0.040) (0.043) (0.188) (0.195) (0.221)
	Panel B: By arm
	Change endogenous (a)	-0.127 * * *	-0.068	0.062	-0.008	0.228	0.359	0.407
		(0.049)	(0.059) (0.083) (0.085) (0.390) (0.445) (0.492)
	Change no explanation (b)	-0.321 * * * -0.202 * * * -0.068	-0.119 -0.629 * -0.697 * * -0.740 *
		(0.058)	(0.065) (0.077) (0.090) (0.336) (0.340) (0.436)
	Change exogenous (c)	-0.179 * * *	-0.059	0.031	-0.114	0.567	0.890 * *	0.189
		(0.051)	(0.065) (0.082) (0.086) (0.412) (0.390) (0.464)
	Change exogenous stocks (d) -0.212 * * * -0.155 * *	0.042	-0.079	-0.268	-0.134	-0.370
		(0.056)	(0.064) (0.075) (0.083) (0.361) (0.368) (0.375)
	p-value(a=b)	0.010	0.125	0.250	0.369	0.096	0.060	0.081
	p-value(b=c)	0.066	0.116	0.382	0.969	0.025	0.002	0.145
	p-value(a=c)	0.461	0.913	0.786	0.380	0.551	0.369	0.747
	p-value(c=d)	0.669	0.291	0.920	0.771	0.128	0.056	0.350
	R-squared	0.06	0.02	0.00	0.00	0.01	0.01	0.00
	Observations	1,114	1,114	1,114	1,114	1,114	1,114	1,114
	Notes: This

Table A .

 A 6: Reduced-form results among respondents that are attentive to Fed announcements: Adjustment of expectations about real income growth

		∆ Cumulative real
		income growth
		(percentage points)
		(1)	(2)	(3)
		2021	2022-23 2024-26
	Panel A: Pooled
	Mean expectation adjustment 0.178	0.420 * *	0.340
		(0.191) (0.206)	(0.273)
	Panel B: By arm
	Change endogenous (a)	0.355	0.523	0.555
		(0.392) (0.459)	(0.565)
	Change no explanation (b)	-0.308	-0.139	0.089
		(0.345) (0.367)	(0.579)
	Change exogenous (c)	0.746 * 1.113 * * *	0.623
		(0.418) (0.430)	(0.562)
	Change exogenous stocks (d) -0.056	0.212	0.113
		(0.366) (0.381)	(0.488)
	p-value(a=b)	0.204	0.261	0.564
	p-value(b=c)	0.052	0.027	0.508
	p-value(a=c)	0.495	0.349	0.932
	p-value(c=d)	0.149	0.117	0.493
	R-squared	0.00	0.01	0.00
	Observations	1114	1114	1114

Table A .

 A 7: Model-based results: Predicted consumption response to interest rate announcement among non-hand-to-mouth households with positive perceived chance of credit constraints (corner cases): Only attentive households

		Predicted consumption response (percent)
		Mean	Median SD p10 p25 p75 p90 N
	Panel A: Assume 0% ever constrained:
	Overall response	0.066	0.00	3.36 -3.15 0.00 0.00 3.98 473
		(0.175)
	-Real income effects	0.329	0.00	4.92 -3.36 0.00 0.00 5.76 473
		(0.249)
	-Intertemporal substitution effects	-0.263 *	0.00	3.04 -3.65 0.00 0.00 1.68 473
		(0.153)
	-Effects from interest payments	0.000	0.00	0.03 0.00 0.00 0.00 0.00 473
		(0.001)
	Panel B:

Assume 100% constrained in t+1:

	Overall response	0.018	0.00	2.88 -0.44 0.00 0.00 0.78 473
		(0.147)
	-Real income effects	-0.051	0.00	2.72 -0.24 0.00 0.00 0.69 473
		(0.140)
	-Intertemporal substitution effects

Table A .

 A 8: Reduced-form results (March 2022 survey): Adjustment of expectations about federal funds rate This table shows the effect of the hypothetical increase in the future federal funds rate in March 2022 from 0.1 to 0.5 percent on respondent's own expectations about the federal funds rate at different horizons. The sample is restricted to non-hand-to-mouth households. Robust standard errors are in parentheses. * denotes significance at 10 pct., ** at 5 pct., and *** at 1 pct. level. Table A.9: Reduced-form results (March 2022 survey): Adjustment of expectations about inflation and nominal income growth This table shows the effect of the hypothetical increase in the future federal funds rate in March 2022

				∆ Expected federal funds rate
				(percentage points)
			(1)	(2)	(3)	(4)	(5)
			2022	2023	2024	2027	2031
	Mean expectation adjustment 0.226 * * * 0.227 * * * 0.197 * * * 0.145 * * * 0.040
			(0.021)	(0.024)	(0.028)	(0.031) (0.034)
	SD expectation adjustment	0.45	0.53	0.59	0.67	0.74
	Observations		462	462	462	462	462
						∆ Expected cumulative
		∆ Expected inflation rate	income growth
			(percentage points)		(percentage points)
		(1)	(2)	(3)	(4)	(5)	(6)	(7)
		2022	2023	2024	2025-27	2022 2023-24 2025-27
	Mean expectation adjustment 0.155 * * * 0.193 * * * 0.293 * * * 0.214 * * * -0.242	0.297	-0.430
		(0.051)	(0.058)	(0.062)	(0.066) (0.335) (0.368) (0.450)
	SD expectation adjustment	1.10	1.24	1.34	1.41	7.20	7.91	9.68
	Observations	462	462	462	462	462	462	462
	Notes:

Notes:

Table A .

 A 10: Model-based results (March 2022 survey): Predicted consumption response to interest rate announcement among non-hand-to-mouth households with zero perceived chance of credit constraints

		Predicted consumption response (percent)
		Mean	Median SD	p10	p25 p75 p90 N
	Panel A: All non-HTM react:
	Overall response among non-HTM	-1.407 * * *	-1.19	4.70 -7.70 -3.62 1.25 4.17 172
		(0.429)
	-Real income effects	-0.913	-0.47	6.91 -10.46 -4.27 2.21 9.45 172
		(0.626)
	-Intertemporal substitution effects	-0.494	-0.49	3.83 -4.99 -1.87 1.09 3.18 172
		(0.334)
	-Effects from interest payments	-0.000	0.00	0.01 0.00	0.00 0.00 0.00 172
		(0.001)
	Panel B:

Only attentive non-HTM react:

	Overall response among non-HTM	-0.364	0.00	3.12 -3.88 -0.73 0.00 3.38 172
		(0.289)
	-Real income effects	0.016	0.00	4.76 -4.07 -0.10 0.00 5.00 172
		(0.446)
	-Intertemporal substitution effects	-0.380	0.00	2.87 -2.39 -0.51 0.00 1.53 172
		(0.264)
	-Effects from interest payments

In a recent commentary, Monika Piazzesi calls for the use of subjective beliefs measured in surveys as an input in theoretical models(Brunnermeier et al.,

2021). For an introduction to this "temporary equilibrium with measured expectations" approach see[START_REF] Piazzesi | Housing and Macroeconomics[END_REF]. Applications include[START_REF] Landvoigt | The Housing Market(s) of San Diego[END_REF] and[START_REF] Leombroni | Inflation and the Price of Real Assets[END_REF].

By contrast, expectation adjustments around Fed announcements as measured in observational data are more difficult to interpret, as households' information sets are typically unobserved. Most importantly, it is unclear what fraction of households have heard at all of a Fed announcement.

The definition of the variable bi,t-1 is bi,t-1 = ln Bi,t-1ln Bi if Bi > 0, bi,t-1 = ln Bi,t-1ln Bi if Bi < 0, and bi,t-1 = 0 if Bi = 0.

In the model only households with a binding borrowing constraint are "hand-to-mouth", but in the empirical implementation we also assume that households at the zero kink are "hand-to-mouth" and thus do not respond to expectations.

We apply the same sample restrictions as in the main survey to our initial sample of 478 respondents in the robustness survey. This results in dropping 8 respondents in the top and bottom percentiles of response time, and dropping 78 respondents providing outlier responses. We define outliers according to respondents' predicted federal funds rate as in the main survey (described in Section 3.3.1), and according to whether they predict home price growth less than -90 or greater than

percent, or absolute differences in expected home price growth across scenarios of more than 150 percent. See TableA.1 Panel B for summary statistics and tests of balance across arms for the robustness survey.9 In Appendix B.2, we provide the full set of experimental instructions.

B.1.6 Between-subject variation in sources of change in the Fed Projection

Exogenous

Exogenous with stocks

We thank the Fritz-Thyssen Foundation for financial support. Roth: Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy -EXC 2126/1-390838866. We received ethics approval from the University of Warwick (HSSREC 90/20-21). The activities of CEBI are financed by the Danish National Research Foundation, Grant DNRF134. Support from the Danish Finance Institute is gratefully acknowledged.

in March 2021, and afterwards briefly discuss our results for the interest rate survey in March 2022.

 tableshows the immediate consumption responses to the hypothetical increase in the Fed's projection of the future federal funds rate at the end of 2023 from 0.1 to 0.5 percent according to the model, which is calibrated using the survey-based changes in expectations. The table focuses on consumption responses of non-hand-to-mouth households with a positive perceived probability of being credit constrained at some point until the end of 2022. We assume effects on expectations to converge to zero at a quarterly rate ρ = 0.9 for horizons beyond those measured in the survey. Panel A shows model-based predicted consumption responses if these households never expected to become credit constrained. Panel B shows model-based predicted consumption responses if these households perceived a 100% chance of becoming credit constrained in period t+1 (i.e. one quarter after the survey). In both panels, all of the included households are assumed to react, independently of their self-reported attention to Fed announcements. Each of the three terms of the consumption response (four terms in Panel B) is winsorized at -15 percent and 15 percent. The overall consumption response is the sum of the winsorized individual terms. All statistics are weighted by the respondents' total household spending in 2020. Robust standard errors are in parentheses. * denotes significance at 10 pct., ** at 5 pct., and *** at 1 pct. level. This table shows the immediate consumption responses to the hypothetical increase in the future federal funds rate in March 2022 from 0.1 to 0.5 percent according to the model, which is calibrated using the survey-based changes in expectations. The table focuses on consumption responses of non-hand-tomouth households with a positive perceived probability of being credit constrained at some point until the end of 2023. We assume effects on expectations to converge to zero at a quarterly rate ρ = 0.9 for horizons beyond those measured in the survey. Panel A shows model-based predicted consumption responses if these households never expected to become credit constrained. Panel B shows model-based predicted consumption responses if these households perceived a 100% chance of becoming credit constrained in period t+1 (i.e. one quarter after the survey). In both panels, all of the included households are assumed to react, independently of their self-reported attention to Fed announcements. Each of the three terms of the consumption response (four terms in Panel B) is winsorized at -15 percent and 15 percent. The overall consumption response is the sum of the winsorized individual terms. All statistics are weighted by the respondents' total household spending in 2021. Robust standard errors are in parentheses. * denotes significance at 10 pct., ** at 5 pct., and *** at 1 pct. level. 11 Table A.12: Model-based results (March 2022 survey): Predicted consumption response to interest rate announcement among non-hand-to-mouth households with positive perceived chance of credit constraints (corner cases): Only attentive households Predicted consumption response (percent)

Mean

Median SD p10 p25 p75 p90 N Panel A: Assume 0% ever constrained:

Overall response -0.473 -0.009 * * * 0.00 0.04 -0.03 -0.03 0.00 0.00 290 (0.003) -Effects from real credit limit 0.008 0.00 0.16 -0.01 0.00 0.00 0.00 290 (0.008) -Effects from interest payments -0.002 0.00 0.06 0.00 0.00 0.00 0.00 290 (0.003) Notes: This table shows the immediate consumption responses to the hypothetical increase in the future federal funds rate in March 2022 from 0.1 to 0.5 percent according to the model, which is calibrated using the survey-based changes in expectations. The table focuses on consumption responses of non-hand-tomouth households with a positive perceived probability of being credit constrained at some point until the end of 2023. We assume effects on expectations to converge to zero at a quarterly rate ρ = 0.9 for horizons beyond those measured in the survey. Panel A shows model-based predicted consumption responses if these households never expected to become credit constrained. Panel B shows model-based predicted consumption responses if these households perceived a 100% chance of becoming credit constrained in period t+1 (i.e. one quarter after the survey). In both panels, only those included households who report that they typically learn about Fed announcements within seven days (39 percent) are assumed to react, while the consumption response is set to zero among those included households that report that it typically takes longer than seven days or that they typically never hear about Fed announcements (61 percent). Each of the three terms of the consumption response (four terms in Panel B) is winsorized at -15 percent and 15 percent. The overall consumption response is the sum of the winsorized individual terms. All statistics are weighted by the respondents' total household spending in 2021. Robust standard errors are in parentheses. * denotes significance at 10 pct., ** at 5 pct., and *** at 1 pct. level.

B Experimental instructions