Supply chain networks and the macroeconomic expectations of firms

Hajdini, Ina; Kumar, Saten; Malik, Samreen; Norris, Jordan J.; Pedemonte, Mathieu Working Paper Supply chain networks and the macroeconomic expectations of firms IDB Working Paper Series, No. IDB-WP-1721 Provided in Cooperation with: Inter-American Development Bank (IDB), Washington, DC Suggested Citation: Hajdini, Ina; Kumar, Saten; Malik, Samreen; Norris, Jordan J.; Pedemonte, Mathieu (2025) : Supply chain networks and the macroeconomic expectations of firms, IDB Working Paper Series, No. IDB-WP-1721, Inter-American Development Bank (IDB), Washington, DC, https://doi.org/10.18235/0013598 This Version is available at: https://hdl.handle.net/10419/324838 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/3.0/igo/ Supply Chain Networks and the Macroeconomic Expectations of Firms Ina Hajdini Saten Kumar Samreen Malik Jordan J. Norris Mathieu Pedemonte WORKING PAPER No IDB-WP-1721 InterA merican Development Bank Department of Research and Chief Economist July 2025 * Federal Reserve Bank of Cleveland ** Auckland University of Technology *** NYU Abu Dhabi **** Inter-American Development Bank Supply Chain Networks and the Macroeconomic Expectations of Firms Ina Hajdini* Saten Kumar** Samreen Malik*** Jordan J. Norris*** Mathieu Pedemonte**** InterA merican Development Bank Department of Research and Chief Economist July 2025 Cataloging-in-Publication data provided by the Inter-American Development Bank Felipe Herrera Library Supply chain networks and the macroeconomic expectations of firms / Ina Hajdini, Saten Kumar, Samreen Malik, Jordan J. Norris, Mathieu Pedemonte. p. cm. — (IDB Working Paper Series; 1721) Includes bibliographical references. 1. Business logistics-New Zealand. 2. Business enterprises-New Zealand. 3. Business communication-New Zealand. 4. Macroeconomics. I. Hajdini, Ina. II. Kumar, Saten. III. Malik, Samreen. IV. Norris, Jordan J. V. Pedemonte, Mathieu. VI. Inter-American Development Bank. Department of Research and Chief Economist. VII. Series. IDB-WP-1721 http://www.iadb.org Copyright © 2025 Inter-American Development Bank ("IDB"). This work is subject to a Creative Commons license CC BY 3.0 IGO (https://creativecommons.org/licenses/by/3.0/igo/legalcode). The terms and conditions indicated in the URL link must be met and the respective recognition must be granted to the IDB. Further to section 8 of the above license, any mediation relating to disputes arising under such license shall be conducted in accordance with the WIPO Mediation Rules. Any dispute related to the use of the works of the IDB that cannot be settled amicably shall be submitted to arbitration pursuant to the United Nations Commission on International Trade Law (UNCITRAL) rules. The use of the IDB's name for any purpose other than for attribution, and the use of IDB's logo shall be subject to a separate written license agreement between the IDB and the user and is not authorized as part of this license. Note that the URL link includes terms and conditions that are an integral part of this license. The opinions expressed in this work are those of the authors and do not necessarily reflect the views of the Inter-American Development Bank, its Board of Directors, or the countries they represent. Abstract Using a randomized control trial of approximately 1,000 firm pairs in New Zealand that have a customer-supplier relationship, we provide an information treatment to analyze both the direct effects on expectations and actions of firms receiving this information and the spillover effects on connected firms that did not directly receive information. In a follow-up three months later, we find direct and spillover effects on expectations and actions that are both significant and of comparable magnitude. An increase in expected GDP growth increases prices and employment; an increase in expected GDP uncertainty reduces prices, investment, and employment. We provide evidence that it is communication between the firms, as opposed to observable actions, driving the spillover effect on the expectations of connected firms. This is consequential as we find communication to be symmetric upstream vs downstream, while propagation via actions is asymmetric. We embed firm-to-firm communication along the supply chain in a New Keynesian pricing problem and discuss its implications for the transmission of aggregate uncertainty to firms’ pricing decisions and aggregate inflation. JEL classifications: D8, E3, E4, E5, L14 Keywords: Communication, Firms, Macroeconomic expectations, Networks, Spillovers *This study has been approved by the Aotearoa Research Ethics Committee, New Zealand (AREC 24 20), Auckland University of Technology Ethics Committee (24/306) and New York University Abu Dhabi’s Ethics Board (HRPP-2024-110). We thank Olivier Coibion, Yuriy Gorodnichenko, Juan Herre˜ no, Zhen Huo, Hiroshi Toma, Michael Weber, seminar participants at Universit´ e Laval, the Federal Reserve Bank of Cleveland, and the IADB for their helpful comments and suggestions. The views expressed here are solely those of the authors and do not necessarily reflect the views of the IADB, the Federal Reserve Bank of Cleveland or the Federal Reserve System. Samreen Malik and Jordan Norris acknowledge the support by Tamkeen under the NYU Abu Dhabi Research Institute Award for the Center for Behavioral Institutional Design CG005. (ADHPG-CG005). The usual disclaimer applies. Emails: [email protected], [email protected], samr[email protected], [email protected], [email protected]. 1 Introduction Macroeconomic expectations are a key driver of aggregate dynamics (Beaudry and Portier, 2006,2007;Jaimovich and Rebelo,2009). Empirical research over the past decade has intensified the analysis of uncovering how these expectations are formed (Coibion and Gorodnichenko,2015;Coibion et al.,2018a), and what their effect is on individual decisionmaking (Coibion et al.,2020b;Georgarakos et al.,2024). Special interest has been placed on firms’ decision-making given their price-setting power (Coibion et al.,2018b,2020a), and the influence of aggregate uncertainty in shaping these decisions (Bloom et al.,2007; Bloom,2009;Coibion et al.,2024;Kumar et al.,2023). The interdependence of beliefs between firms is thought to play a key role, for example, being at the foundation of sentiment-driven business cycles (Angeletos and La’O, 2013;Gaballo,2018). Motivated by supply chain interactions being fundamental to shock propagation and amplification (Acemoglu et al.,2012,2016;Carvalho et al.,2021;Ozdagli and Weber,2023;Pasten et al.,2020), we investigate how a firm’s supply chain shapes its macroeconomic expectations, and the consequences for its decision-making. We provide experimental evidence on the presence and relevance of information diffusion between firms, and reveal direct communication to be a central, yet unexplored, mechanism. Unlike standard shock propagation via prices or output being asymmetric upstream vs downstream (Acemoglu et al.,2016;Carvalho and Tahbaz-Salehi,2019), we find communication to be symmetric. This potentially reconfigures our understanding of how shocks propagate through supply chains, and we embed communication into a macroeconomic model to explore its aggregate consequences. To proceed, we surveyed approximately 1,000 firm-firm pairs in New Zealand, with one firm being the primary supplier of the other. We incorporated a randomized controlled trial (RCT) using an information-based treatment of official forecasts of GDP growth. We had two treatment groups, one receiving the mean of the forecasts and the other receiving the range across forecasts, in order to assess the impact of uncertainty. Importantly, in each treated pair, only one firm receives the information (either the supplier or the customer in the relationship, chosen at random). This design therefore allows us to identify 1 both the direct effect of receiving macroeconomic information on the “main” firm that the treatment was applied to, and the spillover effect on the “connected” firm in the same pair that did not directly receive the treatment. The survey consists of two waves (baseline and follow-up), and information is provided at the end of the baseline. The follow-up takes place three months later, allowing us to identify the diffusion of macroeconomic information between a firm and its supplier or customer, and to measure the effects on real decisions. The provision of information caused both the main and the connected firms to update their expectations. The direct effect on the main firms corroborates findings in the literature (Coibion et al.,2018b;Kumar et al.,2023).1The spillover effects on the connected firms, however, are new. As expected, the connected firms’ expectations show a change only in the follow-up period, not in the baseline period, consistent with it taking time for the information to diffuse. Interestingly, the spillover effects are large, with their magnitude being comparable to that of the direct effects, implying that the information diffusion is strong. Analyzing the impact of our information treatment on firms’ decisions (actions)— prices, investment, employment, and wages—we find significant effects in the follow-up of the directly treated and connected firms, both with similar magnitudes. Using variation induced by the treatment to instrument firms’ GDP growth expectations, we find that a 1 percentage point increase in expected GDP growth increases firms’ prices by 0.28 percentage points and employment by 0.92 percentage points, compared to their plan three months ago. We find that a 1 percentage point increase in uncertainty, measured as the distance between the most and least likely GDP growth scenario, decreases prices by 0.31 percentage points, investment by 0.63 percentage points, and employment by 0.79 percentage points, compared to their plans three months ago. We find no effect on wages from either the mean or the uncertainty treatments. 1Despite the official forecasts being public information, the inattention of firms with respect to this information is well-established, both in our setting (see Coibion et al.,2018b) and more generally (Candia et al., 2024;Song and Stern,2024). For theoretical mechanisms rationalizing this inattention, see, for instance, Afrouzi and Yang (2018); Gabaix (2020); Sims (2003). 2 The significant shift in expectations and decisions of connected firms suggests that the supply chain network is a highly relevant source of information for macroeconomic expectations and decisions, with meaningful interactions and information spillovers between connected firms. Next, we assess the potential mechanisms underlying this information diffusion. Specifically, we want to disentangle whether communication between firms, or inference from changes in observable actions of the other firm, can explain the learning we find. We offer a number of pieces of evidence suggesting that communication is important. First, we decompose the spillover effect on a connected firm’s posterior beliefs into the impact coming from the main firm’s posterior beliefs as opposed to the main firm’s actions. We find only the former to be significant, suggesting that connected firms form their beliefs by directly learning the main firm’s beliefs, conceivably through communication. Second, in the survey, we asked the firms directly about their GDP communication within the pair. We find a large and statistically significant effect: 85% (73%) of mean (uncertainty) treated firms reported communicating, compared to only 35% of control firms. Third, we show that the spillover effects are symmetric whether flowing upstream or downstream (the main firm is a customer or supplier in the pair, respectively). If learning were mediated exclusively through observing the actions of the main firms, one would expect asymmetric treatment effects, as the literature has documented that shocks tend to propagate via prices or output more in one direction (Acemoglu et al.,2016;Carvalho and Tahbaz-Salehi,2019). Conversely, using our survey question on GDP communication, we find that the effect on communication from treatment is the same whether the main firm is the customer or supplier in the pair, a finding that is consistent with the treatment effect on expectations and actions being symmetric. We end the paper by investigating the implications of our findings in a New Keynesian pricing problem, where aggregate output (GDP) growth is exogenously given. Building on the pricing block of the production network model in Rubbo (2023), we incorporate a communication network that firms utilize when forming their expectations about output growth, the latter being imperfectly observed by firms. Motivated by our empirical 3 findings, we assume that the communication network is symmetric (equal communication upstream and downstream) and that firms are ambiguity-averse, as a tractable way for uncertainty to be relevant for decisions despite the fact that we log-linearize the model (Ilut and Schneider,2014).2Our setup allows us to show that, in equilibrium, firms’ pricing decisions are influenced by both the production and the communication networks. Consistent with our empirical evidence, the model implies a negative response of firms’ prices to a treatment of higher uncertainty about future output growth. We characterize the implications of communication using the model both theoretically and quantitatively. For the latter, we parameterize the model to closely match key components of firms in our survey data and simulate outcomes when a subset of firms is given information about higher uncertainty about future output growth. Our analysis yields three key insights. First, whether the treatment was provided to the supplier or the customer firm does not matter for its impact on all firms’ prices when firms communicate, highlighting that communication generates symmetry in upstream vs downstream transmission of a treatment. Second, communication reduces the dispersion of price response to a treatment across firms when compared to no communication. We empirically validate this result of the model by computing the connected firm’s price change associated with a 1 percentage point exogenous increase in the treated firm’s price in our model simulations and survey data. We show that when there is communication, the estimated price relationship between the treated and connected firm approaches unity both empirically and in the model, regardless of whether the treatment was provided to a customer or supplier firm. Third, communication results in a stronger and shorter-lived response of inflation to future output growth uncertainty, consistent with communication both propagating and homogenizing the initial price response of most firms, relative to no communication. Moreover, the response of the aggregate price level to future output growth uncertainty is, on average, higher when firms communicate with one another compared to when they 2Ambiguity-aversion refers to Knightian uncertainty whereby firms cannot assess the probability distribution of outcomes accurately. See Epstein and Wang (1994) for an early application of such uncertainty to asset pricing and Ilut and Schneider (2023) for a recent review. 4 age. Additionally, while all 1,074 pairs of firms were contacted for the follow-up, only 539 pairs of firms participated, because either one or both firms in the pairs did not answer the survey. Appendix Table A-3 shows that neither the treatment assignment nor the observable characteristics can predict participation in the follow-up survey. 3 Treatment Effects 3.1 Treatment Effects on Expectations We start by evaluating whether our treatments affected firms’ GDP expectations. To do so, we compare how treated and control firms changed their posterior GDP expectations relative to their prior GDP expectations. Specifically, we run the following regression, which is widely used in this type of setting (see, for example, Coibion et al.,2018b;Kumar et al.,2023)7: Posteriormean i=α+βPriormean i+ 2 X n=1 γnTn,i + 2 X n=1 θnPriormean i×Tn,i +εi,(1) where Priormean iis the belief of firm i’s manager about the mean of GDP growth in the baseline period before the treatment intervention. Posteriormean iis the belief after the treatment intervention. We use two measures of posterior beliefs. The first is an instantaneous measure, asked immediately after the treatment intervention in the baseline, and the second is a persistent measure, asked in the follow-up three months after the baseline. Tn,i is a dummy that takes a value of 1 if firm iis in a pair that received treatment n(n= 1 is mean, n= 2 is uncertainty) and 0 otherwise. We run the regression separately for the main firms in order to estimate the direct effect, and separately for the connected firms in order to estimate the spillover effects 7Some of these papers also employ Huber-robust regressions, which increase power by down-weighting observations with large residuals, typically those with substantial prior-posterior revisions. We report our results using this approach in Appendix C-3. The findings remain qualitatively unchanged and, if anything, become quantitatively stronger. 11 (corresponding to Figure 1). Note that the treatment status Tn,i is the same for both main and connected firms within the same pair; that is, a connected firm is treated if the main firm it is paired with is also treated. We also rerun the regression for the posterior and prior on uncertainty, rather than the mean. The coefficient βcaptures the correlation between prior and posterior for the control group. As the control received no information, we expect that βis close to one. β+θn captures the correlation between prior and posterior for treated group n. If treatment n is effective, we will see changes in expectations such that treated firms place some positive weight on the new information. Consequently, θnwill be negative, as the correlation between the prior and posterior would be lower than in the control group. Because the treatment is randomized, we can interpret θnas the causal effect of information on the prior-posterior correlation. γnis the the causal effect when prior expectations equal zero (the y-intercept), which we expect to be positive if the correlation (the slope) decreases. Visually, the relationship between the posterior and prior rotates clockwise due to treatment (see Figure 2). We present the results on the beliefs of mean GDP growth in Table 1. Columns (1) and (2) show the treatment effects in the baseline period for the main and connected firms, respectively. Columns (3) and (4) show the treatment effects in the follow-up period for the main and connected firms, respectively. Figure 2presents the corresponding distributions of posterior against prior beliefs in the four cases. As expected, the estimated correlation between the prior and posterior for the control group, β, is close to one across all four specifications in Table 1, and the distribution along the 45-degree line in Figure 2, indicating no systematic change in the control firms’ beliefs before or after treatment. The treatment effect on the main firm — the direct effect — in the baseline period (Column 1) from treatment one (provision of the mean official forecast of GDP growth) is θ1=−0.723, a reduction in correlation of approximately three-quarters relative to the control firms. Firms directly receiving the information, therefore, immediately update their priors. Treatment two (provision of the range of official GDP growth forecasts) also leads to a significant reduction in correlation, though of smaller magnitude. This is expected 12 Table 1: Treatment Effect on GDP Expectations in Baseline and Follow-up (1) (2) (3) (4) Priormean 0.972*** 0.964*** 0.945*** 0.938*** (0.023) (0.016) (0.020) (0.013) T11.799*** -0.063 1.787*** 1.772*** (0.068) (0.044) (0.070) (0.112) T21.567*** -0.040 1.773*** 1.433*** (0.068) (0.045) (0.095) (0.147) T1×Priormean -0.723*** 0.017 -0.603*** -0.586*** (0.032) (0.019) (0.032) (0.046) T2×Priormean -0.492*** 0.006 -0.503*** -0.502*** (0.032) (0.018) (0.046) (0.061) Constant 0.025 0.062 0.080 0.120** (0.048) (0.043) (0.047) (0.036) Period Posterior Baseline Baseline Follow-Up Follow-Up Type of firm Main Connected Main Connected Observations 999 1020 510 505 R-squared 0.739 0.955 0.760 0.743 Note: The table reports results of regression 1, where the outcome variable Posteriormean is the average GDP forecast of firm iafter the treatment. Priormean is the average GDP forecast before the treatment. T1is an indicator that is equal to one if firm ireceived the information treatment about the average GDP forecast and T2is an indicator that is equal to one if firm ireceived the information treatment about the GDP uncertainty. Columns (1) and (2) show results for the baseline survey, and columns (3) and (4) show results for the follow-up survey. Columns (1) and (3) show results for the firms that received the information treatment in the baseline period, and columns (2) and (4) show results for the firms that are connected to the treated firms. Robust standard errors are shown in parentheses. given that information about uncertainty in GDP growth is not directly informative about the mean growth. In Panel A of Figure 2, we see a corresponding clockwise rotation of the relationship between posterior and prior, reflecting the reduction in the correlation due to the treatment. The treatment effect on the connected firm — the spillover effect — in the baseline period (Column 2) from either treatment is insignificantly different from zero. Correspondingly, we see no rotation of the distribution in Panel B of Figure 2. As expected, this suggests no information has yet been diffused from the main to the connected firm in the 13 Figure 2: Correlation between Prior and Posterior for Main and Connected Firms in the Baseline and Follow-up Baseline A: Main Firm B: Connected Firm Follow-up C: Main Firm D: Connected Firm Note: This figure shows a scatter plot of the expectations about GDP asked before the treatment in the baseline period (prior, x-axis) with either the posterior in the baseline period or the posterior in the followup period (y-axis). Panels A and B plot the prior and the posterior in the baseline period. Panel A presents results for treated firms, while Panel B shows the same for connected firms. Panels C and D plot prior expectations in the baseline period against posterior expectations in the follow-up—Panel C for treated firms, Panel D for connected firms. Each dot represents a firm’s response; the lines are linear fits by group. Black indicates control firms, gray corresponds to those receiving Treatment 1 (average GDP forecast), and blue to those receiving Treatment 2 (uncertainty information). pair. This is because both firms within a pair were surveyed very close in time, while it conceivably takes time for information to be diffused between firms. Now, turning to the treatment effect in the follow-up period, the direct effect in the follow-up (Column 3) is very similar to the effect in the baseline (Column 1). This sug14 Table 2: Treatment Effect on Expected GDP Uncertainty in Baseline and Follow-up (1) (2) (3) (4) PriorUncertainty 0.960*** 0.993*** 0.978*** 0.974*** (0.019) (0.010) (0.019) (0.018) T11.395*** 0.025 1.310*** 2.044*** (0.198) (0.084) (0.302) (0.328) T21.145*** -0.015 1.142*** 1.139*** (0.163) (0.083) (0.264) (0.267) T1×PriorUncertainty -0.766*** -0.008 -0.717*** -0.761*** (0.033) (0.013) (0.042) (0.046) T2×PriorUncertainty -0.720*** -0.008 -0.689*** -0.610*** (0.031) (0.014) (0.042) (0.045) Constant 0.220* 0.067 0.187* 0.276* (0.095) (0.070) (0.090) (0.122) Posterior Period Baseline Baseline Follow-Up Follow-Up Firm Type Main Connected Main Connected Observations 1012 1022 514 513 R-squared 0.835 0.973 0.809 0.700 Note: The table reports results of regression 1, where the outcome variables Posterioruncertainty is the uncertainty in the GDP forecast of firm iafter the treatment, measured as the absolute value on the distance between the most and less likely scenario. Prioruncertainty is the uncertainty forecast before the treatment. T1 is an indicator that is equal to one if firm ireceived the information treatment about the average GDP forecast and T2is an indicator that is equal to one if firm ireceived the information treatment about the GDP uncertainty. Columns (1) and (2) show results for the baseline survey, and columns (3) and (4) show results for the follow-up survey. Columns (1) and (3) show results for the firms that received the information treatment in the baseline period, and columns (2) and (4) show results for the firms that are connected to the treated firms. Robust standard errors are shown in parentheses. gests that the treatment effect is highly persistent, with the beliefs of the main firm in the follow-up continuing to be highly influenced by the treatment three months earlier. More importantly, the spillover effect in the follow-up (Column 4) is now highly significant. That is, even though the connected firms did not directly receive the information in the baseline, their beliefs three months later had been updated as if they had received the information. Moreover, the magnitudes of spillover effects are remarkably similar to the direct effects (Column 4 vs Column 3). Panels C and D of Figure 2present the corresponding distributions, showcasing the similarity in their effect. 15 These findings on the spillover effects are the most interesting and novel part of this paper. This implies that the information about GDP expectations has been diffused from the main firm to the connected firm — i.e., along the supply chain network. In Section 4, we explore the mechanism of this diffusion, specifically whether the firms are engaging in direct communication about GDP expectations, or whether they are inferring them from observable actions. We present the analogous results for priors and posteriors on the uncertainty of GDP growth, rather than the mean, in Table 2. We find very similar results, both qualitatively and quantitatively. This shows that not only is information about the mean transmitted through the input-output network but also information about uncertainty. We examine the heterogeneity of the treatment effects with respect to firm characteristics (size, market share, age, and sector) in Table A-4 (a). We detect no systematic variation across these dimensions. This suggests that the information diffuses broadly, rather than being limited to a specific type of firm. 3.2 Treatment Effects on Actions In this section, we evaluate whether firms changed their decisions/actions due to the information treatment, suggesting that the information content is economically relevant and meaningful. We examine four measures of decisions: price, investment, employment, and wages. These are measured both as planned changes reported in the baseline survey (ex-ante plans for the next three months) and as actual actions recorded in the follow-up survey (ex-post decisions at the endline). First, we estimate the reduced-form effect of the treatment on the actions, revealing whether the information caused firms’ actions to be less correlated with their initial plans. Second, we use the treatment as an instrument for the firms’ GDP expectations to estimate the elasticity of a change in actions with respect to a change in GDP expectations. The reduced-form regression is the following: 16 Actioni=α+βPlani+ 2 X n=1 γnTn,i + 2 X n=1 θnPlani×Tn,i +εi,(2) where Actioniis the action the manager of firm ireported in the follow-up period. Plani is the firm’s plan reported in the baseline period. As in regression 1,Tn,i is a dummy that takes a value of one if firm ireceived the treatment nand zero otherwise. θnreflects the correlation of the action and the plan. If the treatment has an effect on the firm’s action, then the plan-action correlation will be reduced, corresponding to a negative θn. As before, the specification is run separately for main and connected firms to estimate the direct and spillover effects, respectively. We present the results in Table 3. We find significant treatment effects on prices, employment, and investment (Columns 1 to 6), though not on wages (Columns 7 to 8).8Most interestingly, this is the case not only for the direct effects (odd numbered columns) but also for the spillover effects (even numbered columns). Moreover, the magnitudes of the direct and spillover effects for an action are similar, especially for prices and investments. This suggests that the diffusion of information between firms is highly relevant and meaningful for firm operations. We examine heterogeneity of the treatment effects with respect to firm characteristics in Table A-4 (b). We detect no systematic variation across these dimensions. Next, we estimate the elasticities of actions with respect to expectations. This is useful to give a clearer sense of the magnitude of the changes in actions due to the treatment, as it accounts for the changes in expectations attributable to the information treatment. We extend the instrumental variable strategy for direct effects from Coibion et al. (2022,2023) and Kumar et al. (2023) to spillover effects. For the direct effects, the second stage is given by: Actioni=α+βPlani+γPosteriormean i+θPosterioruncertainty i+X′ iδ+εi,(3) The regression is run on the main firms i.Xiincludes priors for mean and uncertainty from the baseline period. The rest of the variables are defined as in specifications 1and 2. We instrument Posteriormean iand Posterioruncertainty iby the treatment interacted with 8No direct effect on wages is consistent with results in the literature in our setting (Kumar et al.,2023). 17 Table 3: Treatment Effect on Wage, Employment, and Investment Plans Price Investment Employment Wage (1) (2) (3) (4) (5) (6) (7) (8) Plan 1.006*** 1.012*** 0.975*** 0.979*** 1.014*** 1.017*** 0.995*** 0.998*** (0.009) (0.011) (0.018) (0.019) (0.020) (0.012) (0.015) (0.019) T11.583*** 1.841*** 3.448*** 3.128*** 2.837*** 2.291*** -0.024 0.011 (0.136) (0.136) (0.199) (0.205) (0.540) (0.498) (0.019) (0.041) T21.722*** 1.815*** 2.819*** 2.552*** 3.388*** 2.883*** -0.016 -0.028 (0.125) (0.125) (0.190) (0.167) (0.568) (0.472) (0.016) (0.028) T1×Plan -0.323*** -0.401*** -0.679*** -0.625*** -0.741*** -0.491*** 0.005 -0.040 (0.089) (0.080) (0.092) (0.096) (0.178) (0.145) (0.017) (0.033) T2×Plan -0.381*** -0.533*** -0.483*** -0.366*** -1.017*** -0.845*** -0.001 -0.005 (0.068) (0.081) (0.081) (0.069) (0.196) (0.181) (0.021) (0.023) Constant -0.013 -0.041 -0.002 -0.012 -0.050 0.009 0.012 0.030 (0.022) (0.026) (0.030) (0.029) (0.074) (0.047) (0.011) (0.028) Firm Type Main Connected Main Connected Main Connected Main Connected Observations 512 506 505 512 508 511 505 511 R-squared 0.715 0.629 0.577 0.586 0.324 0.438 0.980 0.981 Note. The table reports results of regression 2, where the outcome variables are actions the firm took in the three months leading up to the follow-up survey. Those actions are the change in prices (columns (1) and (2)), change in investment (columns (3) and (4)), change in employment (columns (5) and (6)), and change in wages (columns (7) and (8)). Plan is the plan that the firm had in the baseline survey for the next three months. T1is an indicator that is equal to one if firm ireceived the information treatment about the average GDP forecast, and T2is an indicator that is equal to one if firm ireceived the information treatment about GDP uncertainty. Columns (1), (3), (5), and (7) show results for the firms that received the information treatment in the baseline period, and columns (2), (4), (6), and (8) show results for the firms that are connected to the treated firms. Robust standard errors are shown in parentheses. the priors. As we control for the priors, the instrument uses the variation only from the change in expectations induced by the treatment. Therefore we can interpret the estimates β, γ as causal effects. To estimate the spillover effects, the specification focuses on connected firms i, while controlling for the corresponding action (and plan) of the main firm, which is instrumented by the treatment interacted with the main firm’s plan. The reason for the additional control is the exclusion restriction. The posterior instrument is valid if the only way the treatment affects the connected action is through the connected posteriors. However, it is also possible that the treatment affects the connected firm’s action through the main firm’s action, without ever having changed the connected posteriors (e.g., the connected firm simply changes its price in response to the main firm changing its price). This would violate the exclusion restriction. We control for the main firm’s action to militate against this possibility. 18 Table 4reports the results. A 1 percentage point increase in firms’ mean GDP growth expectations leads to a statistically insignificant 0.16 percentage point increase in the main firm’s prices and a significant 0.42 percentage point increase for connected firms. Employment rises significantly by 0.91 percentage points for the main firm and 0.64 percentage points for connected firms, respectively, relative to their initial plans.9We find no significant effect on investment or wages. Regarding expectations of uncertainty, a 1 percentage point increase in uncertainty leads to a 0.34 (0.33) percentage point decrease in the main (connected) firm’s prices, a 0.82 (0.52) percentage point decline in investment, and a 0.81 (0.78) percentage point drop in employment, all of which are significant. We find no significant effect on wages. Table 4: Causal Effect of Expectations on Actions Price Investment Employment Wage (1) (2) (3) (4) (5) (6) (7) (8) Posteriormean 0.163 0.419∗∗∗ 0.008 0.065 0.912∗∗ 0.644∗0.024 -0.019 (0.114) (0.125) (0.224) (0.170) (0.419) (0.386) (0.026) (0.015) Posterioruncertainty -0.335∗∗∗ -0.331∗∗∗ -0.824∗∗∗ -0.515∗∗∗ -0.810∗∗∗ -0.779∗∗∗ 0.005 0.007 (0.042) (0.071) (0.083) (0.103) (0.173) (0.217) (0.010) (0.011) Actionmain 0.236∗0.317∗∗∗ 0.091 0.348 (0.139) (0.083) (0.083) (0.323) Observations 485 453 478 452 479 454 479 452 Firm Type Main Connected Main Connected Main Connected Main Connected F(mean) 110.8 50.7 151.8 48.1 118.9 60.1 109.3 44.0 F(uncertainty) 365.3 187.8 777.3 158.7 402.0 191.0 386.8 191.9 F(action) 45.5 64.6 16.1 0.9 Note. The table reports results of regression 3, where the outcome variables are actions the firm took in the three months leading up to the follow-up survey. Those actions are the change in prices (columns (1) and (2)), change in investment (columns (3) and (4)), change in employment (columns (5) and (6)) and change in wages (columns (7) and (8)). P osteriormean is the GDP forecast of the firm in the follow-up period. Posterioruncertainty is the uncertainty about the GDP forecast of firm iin the follow-up period, measured as the absolute value of the distance between the most and least likely scenario. Actionmain is the action of the main firm in the follow-up period. Variables not shown but included in the specification: P lan is the plan that the firm had in the baseline survey for the next three months; Priormean is the GDP forecast of the firm in the baseline period before receiving the treatment, and Prioruncertainty is the uncertainty forecast before the treatment. We instrument the posterior variables with the priors interacted by the treatment dummy. For connected firms, we also instrument the corresponding action of the main firm with the plan interaction by the treatment dummy. Columns (1), (3), (5), and (7) show results for the firms that received the information treatment in the baseline period, and columns (2), (4), (6), and (8) show results for the firms that are connected to the treated firms. The first stage F-statistics are shown at the end of the table. Robust standard errors are shown in parentheses. 9When we pool main and connected firms, the average effects of mean expectations on prices and employment are significant across all firms; see Table A-6 in the Online Appendix. 19 The opposing effects of the posterior mean and uncertainty on firms’ actions align with economic intuition. When firms anticipate economic growth, they increase their prices and employment, as if they expect higher demand for their goods. Conversely, higher uncertainty reduces their prices, investment, and employment decisions, related to the contractionary effect of higher uncertainty (Baker et al.,2024). The estimated impact of uncertainty is particularly robust. Moreover, the magnitudes are very similar between main and connected firms. Summarizing, we find that changes in expectations (both first and second moments) significantly affect firms’ decisions; this result confirms the findings in Kumar et al. (2023). Most importantly, we present a novel finding: changes in expectation affect the connected firms’ actions, and with a magnitude similar to that of the main firms. These findings suggest that information from treated firms is reaching their connected firms, either through direct communication or by inferring expectations from observed changes in actions. We investigate these channels in Section 4. Additionally, in Section 5, we discuss the implications of these findings for the strength of communication. Regardless of the transmission channel, our findings have important implications for the contagion of expectations within the input-output network. From a policy perspective, central banks could leverage this mechanism to strategically disseminate information throughout the economy. At the same time, it also raises concerns about the potential for pessimistic expectations to propagate, amplifying downturns through network effects. 4 The Role of Communication In this section, we provide empirical evidence supporting the hypothesis that communication between a firm and its connected firm is an important driver of information diffusion. We especially rule out the alternative explanation that connected firms are solely updating their beliefs because they observe changes in the actions of the main firm. For instance, Table 4shows that an increase in GDP uncertainty causes the (main) firm that is directly receiving this information to reduce its investment (Column 3). A connected firm, observ20 5.1 Setup We consider the sector-level Phillips curve derived in Rubbo (2023) and assume each of the Nsectors is represented by a firm. The price vector ptis given by13 pt= ∆ κyt+βΩe Etpt+1+ Ωpt−1,(5) where ytis a measure of slack in the economy that we assume to be output growth in deviation from the steady state; e Etis a generic expectations operator, possibly different from the full-information rational expectations one; βdenotes the discount factor; Ωis an invertible matrix whose elements are convoluted expressions of the intensity of inputoutput linkages (IO ≡[ιij]matrix) among firms as well as their labor shares (α≡[αi] vector), price flexibility (Φ≡[ϕi]diagonal matrix), and consumption shares (ψ≡[ψi] vector); κis the vector of Phillips curve slopes; and ∆ = (I+βΩ)−1.14 Output growth is assumed to be exogenously given and is driven by an iid shock, ε∗ t+1, with mean zero and variance σ2 ε, and a deterministic sequence µ∗ t: yt+1 =µ∗ t+ε∗ t+1.(6) The long-run behavior of µ∗ tis assumed to converge to that of an iid normal stochastic process with mean 0 and standard deviation σµ∗, and that is independent of the process for ε∗ t. Similar to Ilut and Schneider (2014), we assume that firms cannot distinguish the deterministic sequence from the iid shocks even if they observe an infinitely large amount of data. As a result, equation (6) describes a large family of possible processes that can have rather different implications in the short run, for example, because they differ in the conditional mean µ∗ t. This is consequential because, by iterating equation (5) forward, a 13The vector of firm-level inflation rates is described by πt=pt−pt−1=βΩe Et[πt+1]+κyt−(I−Ω)pt−1. We note that our setting abstracts from productivity shocks, implying that all of our results go through even if the slack in the economy is measured by the output gap—which equals output in the absence of productivity shocks—as in Rubbo (2023). 14As proved by Rubbo (2023), Ωis invertible as long as no firm has fully flexible prices. We describe the structure of the matrices and vectors in equation (5) in Appendix B.1 in more detail. 27 firm’s optimal pricing decision depends on its expected future output growth, that is, its perceived µ∗ t. 5.2 Output Growth Expectations To solve the model we have to discipline firms’ expectations about future growth. In doing so, we consider three components that we describe in detail below. Uncertainty. We assume that firms face Knightian uncertainty and are averse to ambiguity arising from not being able to distinguish the deterministic component from the iid component of growth. Firms then base their actions on the most pessimistic possible outcome. To discipline the firms’ belief set for output growth, we follow a strategy similar to that in Ilut and Schneider (2014). Specifically, firm j’s perceived law of motion about output growth in deviation from the steady state is given by yt+1 =µjt +εj,t+1, µjt ∈[−ajt,−ajt + 2|ajt + ¯a|](7) where firm jperceives the deterministic component of growth to range between −ajt and −ajt + 2|ajt + ¯a|with ajt being a mean 0 iid shock around the steady-state ambiguity level ¯a > 0, and the realized ajt is assumed small enough so that ¯a+ajt >0.15 A wider range for µjt, that is, a larger |ajt + ¯a|or equivalently higher ajt, also implies a lower worst case scenario for output growth. Since firms base their actions on the most pessimistic possible outcome, their prior expectations about future output growth are given by e Eprior jt yt+1 = min µjt∈[−ajt,−ajt+2|ajt+¯a|]µjt =−ajt.(8) 15Ilut and Schneider (2014) lay out the equation that is analogous to our equation (7) before expressing variables in deviation from their steady state. The corresponding range around the deterministic component in that case would be −ajt −¯a, −ajt −¯a+ 2|ajt + ¯a|. Moreover, output growth and its deterministic component are perceived to converge to −¯a; hence subtracting by −¯ain the range above yields the range for µjt in equation (7). Therefore, ajt describes ambiguity around a forecast of output growth in deviation from the steady state that equals ¯a, or ambiguity around a forecast of no output growth. 28 Information treatment. As in the experiment, treated firm jreceives information about professional forecasters’ range around their output growth forecast, which firm jinterprets to equal 2|a∗ t+ ¯a|so that it is centered at ¯ajust like µjt.16 Upon receiving this information, the firm updates its expectations about future output growth to e Epost jt yt+1 =−ajt(1 −gj) + gjsjt,(9) where sjt =−a∗ tif firm jis treated and sjt = 0 otherwise; gj∈[0,1] denotes the gain from the information treatment.17 We hereafter interchangeably refer to sjt as a signal or treatment. Communication. Consistent with our empirical evidence, we assume firms communicate their expectations about future output growth with each other according to an exogenous communication matrix C, described in Definition 1, that firms take as given.18 DEFINITION 1. The communication network is described by matrix C= [cij], where cij ∈[0,1] quantifies the intensity with which firm jcommunicates its expectations about future output growth to firm i, so that PN j=1 cij = 1. No communication corresponds to C=I, and we define even communication as C=1N×N/N. Even communication is the case where all firms communicate equally with one-another, which is motivated by the empirical evidence of symmetric communication (Figure 4).19 16Our analysis goes through similarly in the case of a treatment about µ∗ t, corresponding to treatment 1 in our empirical analysis. 17The treated firm updates the lower bound of the deterministic component range to −(1 −gj)ajt −gja∗ t. 18This rules out firms strategically choosing to communicate parts of information with other firms (i.e., endogenous C). This is reasonable in our setting as we do not find evidence of any strategic behavior (see Section 4). 19Our empirical evidence highlights symmetry in communication between any supplier-customer pairs of firms, which we extend to apply to the rest of the network to which our pair is connected. It is plausible that the intensity of communication between the supplier or customer firms and the rest of the network is asymmetric. However, since we do not observe the intensities with which our supplier and customer firms communicate with the rest of their network, even communication is a useful and informative benchmark that also enables us to derive some analytical results. 29 The final expectations of any firm iabout output growth are given by e Eityt+1 = 1− N X j=i cij! | {z } =cii e Epost it yt+1 + N X j=i cij e Epost jt yt+1,(10) where PN j=icij = (1 −cii)is the total exposure to information from communication. The vector of all firms’ expectations about future growth can be written as e Etyt+1 =C[−(I−G)at+Gst](11) where yt=1yt,atis the vector of firm ambiguity, Gis a diagonal matrix whose diagonal equals firm gain from information treatment, and stis the vector of signals.20 5.3 Solution and Implications We now turn to the solution of the model and the implications of communication for firms’ prices, the aggregate price level, and inflation. Price vector. Proposition 1provides the equilibrium price vector and shows that an information treatment about higher uncertainty (lower sjt) leads to lower prices, as documented by our empirical results in Table 4. PROPOSITION 1. The equilibrium price vector is described by pt=βMC(Gst−(I−G)at) + Myyt+Mppt−1, where M=Mp×Myand all its elements are positive. 20We note that if there is perfect information about µ∗ t, and, as a result, there is no ambiguity about the deterministic component of growth, that is, ait = 0 for any firm i, then the model recovers the one in Rubbo (2023), which abstracts from imperfect information, ambiguity aversion, and communication networks. Firms being fully informed about µ∗ tand rational implies that firms’ communication about their expectations of output growth is irrelevant since all firms share the same expectations, e Eityt+1 =µ∗ tfor any i. 30 The impact of a treatment to firm jon the price of firm ican be decomposed into ∂pit ∂sjt =βMijcjjgj | {z } treated firm action channel +βX k=j Mikckjgj | {z } treated firm communication channel ≥0.(12) The first component describes the effect of treatments to the extent that the actions of the treated firm affect firm i, as captured by Mij. The second component describes the communication effect that results from the treated firm sharing information with its production network (including i) and those firms reacting to the new information. Absent communication (C=I), firm i’s price will only respond to the treatment sjt via the actions of the treated firm j(the first component). The communication channel (the second component) becomes more important for the effect on firm i’s price as communication increases.21 Corollary 1formalizes our symmetry result: under even communication (C=1N×N/N), the reaction of all firms’ expectations and prices is independent of where the treatment originates. Hence, even communication implies a symmetric upstream vs downstream propagation of shocks to output growth expectations. COROLLARY 1. Suppose all treated firms place the same weight on the treatment (gj=g,∀j). The firm where the treatment originates is irrelevant for the response of output growth expectations and prices under even communication, that is, ∂ e Eityt+1 ∂sjt =∂ e Eityt+1 ∂skt and ∂pit ∂sjt =∂pit ∂skt ,∀iand ∀j=k. In contrast to Corollary 1that characterizes the response of a given firm’s price when varying the treated firm, Corollary 2characterizes the dispersion in price responses across firms for a given treated firm. Specifically, Corollary 2proves that for a given information treatment sjt, the initial price response varies across firms when communication is absent. While, in the presence of even communication, there is price dispersion only to the extent that firms’ Phillips curve slopes are heterogeneous. COROLLARY 2. Suppose all treated firms place the same weight on the treatment (gj=g,∀j). Following a treatment to firm j, there will always be dispersion in the initial firm price responses 21We note that if all firms receive the same signal about future growth and update their expectations similarly (G=gI), communication has no effect on output growth expectations. 31 absent communication; under even communication, there will be dispersion in the initial firm price responses only to the extent that the Phillips curve slopes, κ, are heterogeneous. Aggregate price level and inflation. A one-time treatment about future output growth uncertainty causes a permanent shift in the price vector and in the aggregate price level, defined as Pt=ψ′pt, where ψis the vector of consumption shares. It is straightforward that the symmetry result in Corollary 1carries over similarly for the aggregate price. Firms adjust their prices until they converge to the new long-run aggregate price level, described by Proposition 2in the Appendix.22 Corollary 3formalizes the condition for which communication amplifies the response of the long-run aggregate price level to an information treatment received by firm j. COROLLARY 3. Relative to no communication, even communication amplifies the response of the long-run aggregate price to a treatment received by firm jif the following inequality is satisfied: λjκj(1 −ϕj) ϕj < N X i=j λiκi(1 −ϕi) ϕi(N−1) ,(13) where λ=ψ′(I−IO)−1is the vector of Domar weights that measure firm size. A more positive difference between the right-hand side and left-hand side in (13) implies a larger amplifying effect of communication on the long-run aggregate price compared to no communication. When multiplied by gj, the left-hand side of the inequality in Equation (13) coincides with the response of the long-run aggregate price to a treatment provided to firm j, in the absence of communication. An insight of Corollary 3is then that communication has stronger propagative effects—relative to no communication—on the long-run price level when treating a firm that, absent communication, triggers a weaker effect on the long-run aggregate price. In the special case when firms have similar price flexibility and Phillips curve slopes, communication has stronger propagative effects on the long-run aggregate price the smaller 22The response of the long-run aggregate price level to a one-time treatment about future output growth uncertainty, depends on the interaction of firms’ Domar weights, their price flexibility, their Phillips curve slopes, and the intensity of communication. 32 the treated firm’s Domar weight is relative to the rest of the firms in the network. If firms also have the same consumption shares (ψ=1/N), a smaller Domar weight corresponds to being more downstream, implying higher propagative effects of communication when the treatment originates from the customer firm (downstream) as opposed to the supplier firm (upstream) in any supplier-customer pair.23 Intuitively, a customer firm’s product price is less relevant for its supplier, than the supplier’s price is for the customer. Thus, absent communication, shock propagation is weaker when originating downstream. Aggregate inflation is equal to ¯πt=ψ′(pt−pt−1). Given that pt−1is pre-determined, the symmetry result of Corollary 1for ptcarries over with the treatment origin being irrelevant for aggregate inflation under even communication. Using Proposition 1to solve for aggregate inflation, ¯πt=ψ′βMC(Gst−(I−G)at) + Myyt+ (Mp−I)pt−1.(14) Noting that PN j=1(Mp−I)ij = 0 ∀i, then communication lowers the persistence of the aggregate inflation response to the extent that it homogenizes the initial price responses across firms. Intuitively, the treatment will affect future inflation to the extent that current prices have not reached the new long-term aggregate price level. Homogeneity in the initial price responses implies immediate adjustment of all prices to the new aggregate price level.24 5.4 Quantitative Analysis We now explore the role of communication quantitatively. To be close to the empirical setup, we consider a three-firm model, where one firm is the customer firm (firm 3), one the supplier firm (firm 2), and the other one captures the rest of the network (firm 1). The 23The upstreamness is measured by 1′((I−IO)−1−I); see Carvalho and Tahbaz-Salehi (2019). 24From Proposition 1and Pj(Mp)ij = 1 ∀i, it follows that if the initial price response is homogeneous, pt∝1, then pt+h=ptand Pt+h=Pt,∀h > 0. The dynamics in this case mirrors that of the representative firm model, with standard Phillips curve πt=βe Etπt+1 +κyt. A one-time treatment about future output growth uncertainty in period twill lead to a one-time change in inflation in period t, after which inflation reverts to its steady state. 33 customer firm purchases its inputs from firms 1 and 2, while the supplier purchases its inputs only from firm 1.25 We simulate the price vector response to a one-time unit information treatment for different values of the supplier’s and customer’s input shares in the case of no communication and even communication.26 We calibrate the model to match key characteristics of firms in our sample, such as price flexibility and labor cost share, while setting other parameters to standard values. We describe the calibration strategy and details of the simulation exercise in Appendix B.1 and focus next on our three results from the simulation exercise. Result 1: Communication generates symmetry in upstream vs downstream transmission of a treatment. Figure 5plots the distribution of the initial response of firm prices to an information treatment about higher growth uncertainty provided to the supplier (left panel) and to the customer (right panel). The red distributions in Figure 5show that when firms communicate, whether the treatment was provided to the supplier or the customer firm does not matter for its impact on prices, as stated in Corollary 1. By contrast, absent communication, the origin of the treatment matters for the price responses, as visualized by the vastly different blue distributions in the left and right panels. This result is consistent with our empirical evidence in Table 6of the symmetric spillover effects of treatments on connected firms. Result 2: Communication reduces the dispersion of price responses to a treatment. Figure 5further shows that communication heavily reduces the dispersion of price changes on impact following a treatment to the supplier or customer: as Corollary 2highlights, any remaining price dispersion when firms communicate is explained by their heterogeneous 25The assumed structure of the network implies the following input-output matrix and labor share vector: IO =  0 0 0 ι21 0 0 ι31 ι32 0 and α=1α2α3′, so that IO +α=1. 26In Online Appendix C-4, we consider another communication strategy with C= Ω, so that the intensity of communication equals the sensitivity of the firms’ price changes to the vector of future expected price changes. 34 Figure 5: Distribution of the Impact on Prices after Treatments of Higher Uncertainty -1.2 -1 -0.8 -0.6 -0.4 -0.2 0 Percent 0 1 2 3 4 5 6 7#10-3 Treatment to supplier -rm -1.2 -1 -0.8 -0.6 -0.4 -0.2 0 Percent 0 1 2 3 4 5 6 7#10-3 Treatment to customer -rm No communication Even communication Note: Distribution of initial price responses across all three firms when the treated firm is the supplier (left panel) and when the treated firm is the customer (right panel). In red: even communication; in blue: no communication. Phillips curve slopes.27 The low price dispersion under communication is consistent with our empirical results: most treated firms report communicating (Figure 3) and the average treatment effect on prices is almost identical for the main and connected firms (Table 3, Columns 1 and 2). A more direct empirical validation would be contrasting the treatment effects on prices for firms that do and do not communicate, expecting greater divergence in the latter. Although exogenous variation in communication would be needed for definitive evidence — which we do not have — we nonetheless show the results of this exercise in Table C-7 in the Appendix. In both the data and the simulations, we compute the connected firm’s price change associated with a 1 percentage point exogenous rise in the treated firm’s price. We find that when there is communication, the estimated price relationship between the treated and connected firm approaches unity both empirically and in the model, regardless of whether the treatment was provided to a customer or a supplier firm.28 Absent communication, the point estimate of the price relationship is always less 27Figure C-1 in the Online Appendix shows that the reduction in price dispersion holds true across firms within each three-firm network. 28This result can explain why other works, such as Carvalho et al. (2021), find a similar propagation of shocks for downstream and upstream firms. 35 then unity, but higher when the treatment is provided to the supplier compared to when the treatment is given to the customer—both in the survey data and in the model simulations. Figure 6: Evolution of Prices and Aggregate Inflation after Treatments of Higher Uncertainty 02468 Time -0.8 -0.6 -0.4 -0.2 0 Price level A: Prices, treatment to supplier 02468 Time -0.8 -0.6 -0.4 -0.2 0 Price level B: Prices, treatment to customer Firm 1, no comm Supplier, no comm Customer, no comm Firm 1, comm Supplier, comm Customer, comm 02468 Time -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 Percent C: In.ation, treatment to supplier 02468 Time -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 Percent D: In.ation, treatment to customer No communication Even communication Note: Panels A and B plot the evolution of price levels, averaged across simulations, when a treatment of higher uncertainty about future output growth is provided to the supplier and customer. Panels C and D plot the evolution of aggregate inflation, implied by the price dynamics in panels A and B. In red: even communication; in blue: no communication. Result 3: Communication leads to a stronger and shorter-lived response of inflation to future output growth uncertainty. Panels A and B in Figure 6plot the evolution of firm prices over time, averaged across simulations, when the supplier is treated (left panel) and when the customer is treated (right panel). Communication amplifies the average response of the long-run aggregate price level, with larger amplification compared to the no communication case when the treated firm is the customer compared to the supplier. This is consistent with Corollary 3, noting that the customer firm is the most downstream 36 Georgarakos, D., Gorodnichenko, Y., Coibion, O., and Kenny, G. (2024). The causal effects of inflation uncertainty on households’ beliefs and actions. Technical report, National Bureau of Economic Research. Ghassibe, M. (2021). Monetary policy and production networks: an empirical investigation. Journal of Monetary Economics, 119:21–39. Ilut, C. and Schneider, M. (2023). 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Keeping Up with the Jansens: Causal Peer Effects on Household Spending, Beliefs and Happiness. 44 Weber, M., Candia, B., Afrouzi, H., Ropele, T., Lluberas, R., Frache, S., Meyer, B., Kumar, S., Gorodnichenko, Y., Georgarakos, D., Coibion, O., Kenny, G., and Ponce, J. (2025). Tell me something i don’t already know: Learning in lowand high-inflation settings. Econometrica, 93(1):229–264. 45 Appendix A Additional Figures and Tables A.1 Figures Figure A-1: Communication about GDP: Upstream vs Downstream (Connected Firms) Note: This figure shows the treatment effect on the number of times the connected firm reported communicating with the main firm about GDP, during the three months prior to the follow-up. This is shown separately for each treatment, Tn, and separately whether the main firm is the supplier or customer in the pair. 95% confidence intervals are displayed. Figure A-2: Reasons for Sharing Information about GDP Note: The number of firms (main and connected) listing the labeled response as a reason for sharing information about GDP. 1 A.2 Tables Table A-1: Firm Counts and Percentages by Sector and Size Category 5 or less Workers 6–19 Workers 20–49 Workers 50+ Workers Totals Number % Number % Number % Number % Number % Panel A: Stats NZ Records Manufacturing 5286 48 3663 33 1239 11 771 7 10959 100 Wholesale Trade 4107 54 2328 31 705 9 396 5 7536 100 Retail Trade 7317 58 3945 31 735 6 618 5 12615 100 Totals 16710 54 9936 32 2679 9 1785 6 31110 100 Panel B: Firms Approached Manufacturing 2610 46 1934 34 729 13 347 6 5620 51 Wholesale Trade 2451 51 1622 34 433 9 307 6 4813 64 Retail Trade 3122 54 1996 35 295 5 364 6 5777 46 Totals 8183 50 5552 34 1457 9 1018 6 16210 52 Panel C: Main Wave Firms Sample Manufacturing 70 3 444 23 362 50 251 72 1127 20 Wholesale Trade 45 2 212 13 157 36 99 32 513 11 Retail Trade 95 3 195 10 175 59 43 12 508 9 Totals 210 3 851 15 694 48 393 39 2148 13 Panel D: Follow-up Firms Sample Manufacturing 31 44 230 52 198 55 130 52 589 52 Wholesale Trade 18 40 111 52 72 46 47 47 248 48 Retail Trade 33 35 109 56 73 42 26 60 241 47 Totals 82 39 450 53 343 49 203 52 1078 50 Note: This table summarizes the number of firms and their percentage shares by sector and firm size category across different survey stages. Panels A and B are population and approached samples, respectively, while Panels C and D represent the main and follow-up survey samples. Percentages in A and B are shares of the population and sum to 100 within a row (excluding the last column). Percentages in C and D are response rates: they are the share of observations relative to the same cell in the panel above (e.g. in our main wave sample, panel C, we have 70 manufacturing firms of 5 or less workers, which is 3% of the 2610 firms approached, panel B). 2 Table A-2: Treatment Prediction of Firms’ Characteristics (1) (2) (3) (4) (5) Employment (log) Industry N of Relationships Firm Age GDP Prior Treatment 1 -0.017 0.121 0.374 -2.891** 0.113 (0.053) (0.130) (0.450) (1.331) (0.097) Treatment 2 -0.077 -0.013 0.226 -6.752*** 0.031 (0.051) (0.128) (0.439) (1.279) (0.097) Constant 3.016*** 5.168*** 9.800*** 32.653*** 1.418*** (0.036) (0.093) (0.352) (0.928) (0.070) Observations 2,010 2,010 1,799 1,722 2,010 R-squared 0.001 0.001 0.000 0.016 0.001 Note. The table reports results of regression where the dependent variable is either Employment in logs (Column 1), whether the firm is in the manufacturing or trade industry (Column 2), number of firms’ customers and supplier (Column 3), firms’ age (Column 4), or the prior GDP expectation (Column 5). The independent variables take a value of one if the firm received treatment 1 or 2 and zero otherwise, respectively. Robust standard errors in parenthesis. 3 Table A-3: Predictability of Participation in the Follow-up Wave (1) (2) (3) (4) (5) (6) Treatment 1 0.036 0.036 0.039 0.038 0.023 0.034 (0.027) (0.027) (0.027) (0.027) (0.029) (0.032) Treatment 2 -0.023 -0.022 -0.021 -0.023 -0.023 -0.002 (0.027) (0.027) (0.027) (0.027) (0.029) (0.032) Employment (log) 0.019 0.016 0.014 0.004 0.004 (0.011) (0.012) (0.012) (0.013) (0.015) Industry: Trade -0.042* (0.022) Subsector: Equipment and Machinery 0.035 0.015 0.075 (N=203) (0.052) (0.056) (0.060) Subsector: Food and Beverage 0.087* 0.062 0.063 (N=268) (0.049) (0.053) (0.056) Subsector: Paper, wood, printing and furniture 0.092* 0.066 0.066 (N=262) (0.049) (0.053) (0.056) Subsector: Retail Trade 0.012 -0.005 0.001 (N=480) (0.045) (0.047) (0.051) Subsector: Textile and clothing 0.069 0.041 0.007 (N=155) (0.056) (0.059) (0.063) Subsector: Wholesale trade 0.025 -0.007 0.006 (N=485) (0.045) (0.048) (0.051) Number of Relationships 0.002 0.001 (0.002) (0.002) Firm age 0.000 (0.001) Constant 0.497*** 0.440*** 0.469*** 0.413*** 0.441*** 0.418*** (0.019) (0.040) (0.043) (0.055) (0.059) (0.063) Observations 2,024 2,024 2,024 2,024 1,790 1,534 R-squared 0.004 0.004 0.005 0.008 0.006 0.006 Note. The table reports results of regression where the dependent variable is a variable that takes a value of one if the firm participated in the follow-up, and zero otherwise. Number of Relationships is the number of supplier and customer firms that the firm has. Robust standard errors in parenthesis. The firm in the subsector “Other Store Retailing” is included in “Retail Trade” as there is only one firm belonging to that group. 4 Table A-4: Heterogeneous Treatment Effects: Firm Characteristics (a) Expectations Posteriormean P osterioruncertainty (1) (2) (3) (4) (5) (6) (7) (8) T1×Prior ×H0.070 0.020 0.003 -0.076 0.103∗∗ 0.007 0.060 -0.012 (0.047) (0.018) (0.066) (0.101) (0.052) (0.017) (0.066) (0.094) T2×Prior ×H0.009 0.019∗∗ -0.050 0.141 -0.040 -0.010 -0.062 -0.060 (0.056) (0.008) (0.094) (0.124) (0.054) (0.009) (0.063) (0.107) Heterogeneity, HEmployment Market Share Age Manufacturing Employment Market Share Age Manufacturing N505 275 419 505 513 280 427 513 (b) Actions Price Investment (1) (2) (3) (4) (5) (6) (7) (8) T1×Plan ×H-0.080 -0.039 -0.164 0.105 0.037 0.002 -0.041 0.163 (0.080) (0.037) (0.123) (0.158) (0.074) (0.020) (0.119) (0.173) T2×Plan ×H0.167∗∗ -0.013 -0.099 -0.321∗-0.054 0.041 -0.177∗0.270∗∗ (0.071) (0.020) (0.115) (0.169) (0.067) (0.031) (0.103) (0.132) Heterogeneity, HEmployment Market Share Age Manufacturing Employment Market Share Age Manufacturing N506 288 435 506 512 288 438 512 Employment Wages (1) (2) (3) (4) (5) (6) (7) (8) T1×Plan ×H0.197∗∗ 0.021 -0.009 -0.217 0.014 -0.008 -0.035 -0.107∗ (0.084) (0.103) (0.185) (0.296) (0.036) (0.007) (0.036) (0.060) T2×Plan ×H0.133 0.023 0.380 0.207 -0.045 -0.016 0.002 -0.015 (0.184) (0.068) (0.264) (0.400) (0.033) (0.012) (0.015) (0.048) Heterogeneity, HEmployment Market Share Age Manufacturing Employment Market Share Age Manufacturing N511 291 435 511 511 288 435 511 Note. Panels (a) and (b) extend the regressions of equations (1) and (2), respectively, to include an interaction of each term with variable H, for the sample of connected firms. Each column uses a different characteristic of the main firm for H, as labeled (log employment, market share, log firm age, and a dummy equal to one if in manufacturing). Only the triple interaction terms are displayed, which identifies the effect of Hon the correlation of the posterior with the prior, in the case of Panel (a), and the correlation of the action with the plan, in the case of Panel (b). Standard errors are displayed in parentheses. 5 Table A-5: Heterogeneous Spillover Effects on Actions: Network Characteristics Price Investment (1) (2) (3) (4) (5) (6) T1×Plan ×H-0.194 -0.014∗∗ -0.030 0.077 -0.006 -0.110 (0.158) (0.007) (0.158) (0.186) (0.008) (0.124) T2×Plan ×H-0.083 0.014∗0.090 0.189 0.004 -0.163 (0.163) (0.008) (0.121) (0.132) (0.009) (0.125) Heterogeneity, HUpstream Exp. Share N connections Upstream Exp. Share N connections N506 357 377 512 360 383 Employment Wages (1) (2) (3) (4) (5) (6) T1×Plan ×H-0.687∗∗∗ 0.024∗∗∗ 0.029 -0.019 -0.004 -0.031 (0.191) (0.007) (0.283) (0.064) (0.003) (0.031) T2×Plan ×H-0.485 0.009 0.217 0.080∗-0.001 -0.073 (0.321) (0.026) (0.277) (0.047) (0.003) (0.048) Heterogeneity, HUpstream Exp. Share N connections Upstream Exp. Share N connections N511 356 385 511 358 385 Note. The specifications extend the regression of equation (2) to include an interaction of each term with variable H, for the sample of connected firms. Each column uses a different characteristic of the main firm for H, as labeled (a dummy equal to one if the customer, share of sales to or expenditure on the connected firm, and number of customers or suppliers — if they are a supplier or customer, respectively, in the latter two). Only the triple interaction terms are displayed, which identifies the effect of Hon the correlation of the action with the plan. Standard errors are displayed in parentheses. 6 B.2.1 Proof of Proposition 1 The optimal price vector depends on the current output growth, vector of signals, vector of ambiguity, and the vector of past prices. Hence, we guess the following solution: pt=Msst+Myyt+Maat+Mppt−1, implying that expectations about the price vector in t+ 1 are e Etpt+1 =Mye Etyt+1 +Mppt=−MyC(I−G)at+MyCGst+Mppt. Plugging expectations into the optimal price equation and letting K=diag(κ), we have pt= ∆Kyt+ ∆Ωpt−1+β∆Ω [−MyC(I−G)at+MyCGst+Mppt] = (I−β∆ΩMp)−1∆Kyt+ ∆Ωpt−1+β∆Ω (−MyC(I−G)at+MyCGst). From here, it follows that Mp−β∆ΩM2 p= ∆Ω My= (I−β∆ΩMp)−1∆K Ma=−β(I−β∆ΩMp)−1∆ΩMyC(I−G) Ms=β(I−β∆ΩMp)−1∆ΩMyCG (17) It is straightforward to see from the first equation above that Ms=βMpMyCGand Ma= −βMpMyC(I−G). To ease notation, we set M=Mp×My. To solve for Mp, we rely on Theorem 3.5 in Uhlig (2001); to ensure that price dynamics are stable, we only consider the solution for Mpwhose eigenvalues are within the unit circle. To prove that all the elements of matrix Mare positive, we first prove the following lemma: LEMMA 1. All the elements of matrix Mpare positive and less than unity, and the sum of elements in each row of Mpequals 1. To prove the lemma above, we show that Mpand Ωshare the same eigenvectors. Recall 13 that Mpis the solution to the quadratic matrix equation: M2 p−(Ω−1/β +I)Mp+I/β =0N. Let Ξ =  Ξ11 Ξ12 Ξ21 Ξ22 = Ω−1/β +I−I/β I0N  Let λbe an eigenvalue of Ξ, then the eigenvector associated with it is the vector X= hX1X2i′, that is, (Ξ −λI)X= 0 ⇒(Ξ11 −λI)X1=X2/β, X1=λX2 Hence, the eigenvector associated with λis X=hλX2X2i′. Therefore, (Ξ11 −λI)X1−X2/β = 0 ⇐⇒ (Ω−1−(βλ −β+ 1/λ) | {z } e-value of Ω−1 I)X2= 0 Uhlig (2001) shows that the eigenvector of Mpis given by X2.Ω−1and Ωshare the same eigenvectors and, as a result, it follows that Mpand Ωalso share the same eigenvectors. The largest eigenvalue of Ωis 1; the eigenvector associated with it is e=1N. It follows that eis also an eigenvector of Mp, hence Mpe=e, implying that the sum of each row of Mequals 1 and that 1 is an eigenvalue of Mp. To guarantee a stable solution, it has to be that the remaining eigenvalues of Mpare within the unit circle. By the Gershgorin circle theorem, each eigenvalue λiof Mphas to be within the following range h1−PN j=1 mp ij −PN j=1 |mp ij|,1−PN j=1 mp ij +PN j=1 |mp ij|i. The bounds cannot exceed 1 or -1, implying that PN j=1 mp ij =PN j=1 |mp ij|, and that each element of Mpis positive. It is easy to see that MpMy=M2 pΩ−1K, where all the diagonal elements in Kare positive. Since Mpand Ω−1are stochastic matrices, it follows that M2 pΩ−1is also a stochastic matrix and that all the elements in Mare positive. B.2.2 Proof of Corollary 2 The response of the price vector is given by ∂pt ∂sjt =βgM2 pΩ−1diag(κ)C:j. Absent communication, the response is βgκj(M2 pΩ−1):,j; hence, price dispersion depends on the dispersion of the elements in the jth column of M2 pΩ−1. From the proof of Proposition 1, 14 Mp−β∆ΩM2 p= ∆Ω; pre-multiplying this expression by ∆−1, eigendecomposing Mpand Ω, and using the fact that Mpand Ωshare the same eigenvectors, we have that (I+βQΛΩQ−1)QΛpQ−1−βQΛΩΛ2 pQ−1=QΛΩQ−1⇒βΛΩΛ2 p−(I+βΛΩ)Λp−ΛΩ=0N,N , where Qis the matrix containing the eigenvectors; ΛΩand ΛΩare the diagonal matrices containing the eigenvalues of Mpand Ω, respectively. Pinning down the eigenvalues of Mpis equivalent to solving for the roots of Nquadratic polynomials. It is easy to see that 0 is an eigenvalue of Mponly if 0is also an eigenvalue of Ω, which cannot happen since Ωis invertible. As a result, 0is not an eigenvalue of M2 pΩ−1, thus the elements in any jth column of M2 pΩ−1are different from one another. Therefore, absent communication there is always dispersion in the initial response of prices to the information treatment. The response of the price vector under even communication is given by ∂pt ∂sjt =βg hPj(M2 pΩ−1)1jκj... Pj(M2 pΩ−1)Njκji′, where Pj(M2 pΩ−1)ij = 1,∀i. From above, we know that the elements in any column of M2 pΩ−1are distinct from one another. Hence, any dispersion in the initial response of the price vector has to be due to heterogeneous Phillips curve slopes. If all firms share the same Phillips curve slope κ, then the initial response of any price would be βgκ. B.2.3 Proof of Proposition 2 From Proposition 1in the paper, the vector of prices converges to lim h→∞ pt+h=βgjlim h→∞ Mh+1 pMyC:,j =βgjlim h→∞ Mh+2 pΩ−1diag(κ)C:,j,(18) where the second equality follows from the fact that MpMy=M2 pΩ−1diag(κ). As shown in the proof of Proposition 1,Mpand Ω−1share the same eigenvectors, and the absolute value of all the eigenvalues of Mp, other than the unit one, lie within the unit circle. Hence, 15 the eigendecomposition of Mh+2 pΩ−1as happroaches ∞is given by lim h→∞ Mh+2 pΩ−1=Q 10 0 0 Q−1=hQ11Q−1 1: Q12Q−1 1: ... Q1NQ−1 1: i′ The eigenvector of Mpassociated with the unit eigenvalue is Q1: =1, whereas Q−1 1: is the eigenvector of Ω′associated with its unit eigenvalue – since Mp,Ω, and Ω−1share the same eigenvectors. Rubbo (2023) proves in the Appendix that Q1: =λ(I−Φ)Φ−1, so that Ω′Q1: =Q1:. 16 Online Appendix July 10, 2025 C-1 Design Details C-1 Sample Our population in the survey is quite representative of the firms in New Zealand. Panel A in Table A-1 presents the total number and percentage of firms in manufacturing and trade (wholesale and retail). As per Statistics New Zealand, there are slightly over 31,000 firms in manufacturing, retail, and wholesale trade. More than half the firms in these industries are small firms employing fewer than six employees. The population of firms in this survey is drawn from these industries, and we use employment size distribution as the benchmark to control for sample representation. Our survey maintains fairly similar proportions of firms at each firm size distribution, that is, firms with fewer than 5 employees, 6-19 employees, 20-49 employees, and at least 50 employees. For example, 33 percent of manufacturing firms in New Zealand employ between 6-19 workers. In our survey, the proportion of manufacturers in this employment size group is around 34 percent. Comparing Panel A and Panel B shows the proportions of firms in each employment size distribution in our survey population. Overall, the survey population frame includes around 52 percent of firms from the general population of firms in these industries. It is not uncommon in surveys to attain varying response rates from firms across different industries. One of the objectives of the survey was to achieve higher response rates from firms that employ at least six employees. Firms that are too small in size are quite vulnerable and their business continuity is always questionable. Furthermore, during the process of developing the population data, it was evident that very small firms tend to change their input suppliers quite frequently; this is not ideal for our RCT exercise. In this survey, therefore, a lot of focus was given to firms that employ at least six employees. The response rates for different employment size groups are also reported in Panel C and D. The overall response rate is around 13 percent for the main wave and around 50 percent for the follow-up wave. With the assistance of survey recruitment specialists, the survey retained nearly half the firms to participate in the follow-up wave. The participants in the survey are managers or directors of the firm. One of the criteria 1 for participant recruitment was that the manager or director must play an integral role in the firm in setting product prices and wages, and also be an influential figure in investment and employment decisions. This criterion was applied to recruit participants for the population database compiled by New Zealand Market Research and Surveys Limited. Participant details and their firm’s supply chain relationships are regularly updated to keep the records active. The time gap in participation between the main wave and the follow-up wave was approximately three months. Participants from all RCT groups were surveyed throughout the survey period; that is, there was no case where a particular RCT group was prioritized in time. C-2 Power Calculations With the sample size of 150 (N1=75 treated and N2=75 control pairs), significance (α) equal to 5% and power (1−κ) equal to 80%, the minimum detectable effect (MDE) is 0.46SD. When we vary the sample size to 200, MDE = 0.398SD. Based on a pilot we collected information for 20 pairs of firms: 10 treated and 10 control. We are interested in network effects so we provide the power analysis for untargetted treated firms. The estimated effect size of treatment on the untargeted firm’s mean GDP expectations in the follow-up was 1.39, significant at the 5% level. We repeat the same estimation for the effects on economic decisions of the untargeted firms. The effect size for prices, investment, and employment are 3.39, 1.45, and 3.24, respectively. For wages, we detect zero effect in the pilot. We summarize this information in the table below: 2 Table B-1: Power Calculation Pilot Estimated Effect Size Minimum Detectable Effect N=150 N=200 GDP mean forecast 1.39 0.460 0.398 Prices 3.39 Employment 1.45 Investment 3.24 Wages - Notes: The variables all correspond to the follow-up wave for the linked firm. The effect sizes are in units of standard deviation. C-2 Survey C-1 Pre-Survey Information The survey company (New Zealand Market Research and Surveys Limited) provided some firm characteristics that they collected independently of, and months before, our survey. These include employment, inventory share from main supplier, number of customers, and number of suppliers. A few days before the baseline of our survey, the survey company verified supplier and customer identification. Specifically: Ask this question to customer/main supplier firm: Your firm is listed in the database at New Zealand Market Research and Surveys Limited. The database indicates that XXX [firm name] is your customer/main supplier of the main product line. Is this information correct? 1. Yes 2. No 3 C-2 Baseline Survey Section A. Firm Characteristics 1How many years old is the firm? Answer: years 2How many workers are employed in this firm? Answer: workers 3Out of the total revenue of the firm, what fraction is used for compensation of all employees and what fraction is used for the costs of materials and intermediate inputs (raw materials, energy inputs, etc. .. )? Share of revenues: Labor cost % , Cost of materials % 4For its main product line, what is the firm’s current market share? Answer: % 5How many weeks ago did your firm change the price of the main product? Answer: Weeks ago. 6Using the following frequencies, please identify how often this firm (formally) changes the price of its main product: (a) Daily (b) Weekly (c) Monthly (d) Quarterly 4 (e) Half annually (f) Annually (g) Less frequently than annually Section B. Manager Characteristics 7How many years of work experience do you have at this firm: Answer: years. 8What is your highest educational qualification? (a) Less than high school (b) High school diploma (c) Some college or Associate degree (d) College Diploma (e) Graduate Studies (Masters or PhD) Section C. Macroeconomic Expectations 9What do you think will be the annual growth rate of real GDP in New Zealand in twelve months? Answer: % per year. 10 Could you provide us with an approximate range of what you think annualized real GDP growth in New Zealand will be over the next 12 months? Between % per year (lowest forecast) and % per year (highest forecast). 5 C-3 Results with Huber Weights Table C-1: Treatment Effect on Expected GDP Uncertainty in Baseline and Follow-up with Huber Weights (1) (2) (3) (4) (5) (6) (7) (8) P riormean i0.972*** 0.977*** 0.964*** 0.964*** 0.945*** 0.957*** 0.938*** 0.934*** (0.008) (0.005) (0.016) (0.016) (0.020) (0.016) (0.013) (0.010) T11.799*** 1.825*** -0.063 -0.062 1.787*** 1.849*** 1.772*** 1.948*** (0.045) (0.030) (0.044) (0.044) (0.070) (0.050) (0.112) (0.063) T21.567*** 1.362*** -0.040 -0.039 1.773*** 1.821*** 1.433*** 1.681*** (0.074) (0.039) (0.045) (0.045) (0.095) (0.065) (0.147) (0.071) T1×P riormean i-0.723*** -0.749*** 0.017 0.017 -0.603*** -0.633*** -0.586*** -0.657*** (0.022) (0.015) (0.019) (0.019) (0.032) (0.024) (0.046) (0.027) T2×P riormean i-0.492*** -0.378*** 0.006 0.006 -0.503*** -0.508*** -0.502*** -0.604*** (0.039) (0.020) (0.018) (0.018) (0.046) (0.033) (0.061) (0.032) Constant 0.025 0.013 0.062 0.061 0.080* 0.038 0.120*** 0.101*** (0.024) (0.008) (0.043) (0.043) (0.047) (0.029) (0.036) (0.028) Regression OLS Huber OLS Huber OLS Huber OLS Huber Period Baseline Baseline Baseline Baseline Follow Up Follow Up Follow Up Follow Up Type Treated Treated Connected Connected Treated Treated Connected Connected Observations 999 956 1,020 1,020 510 507 505 494 R-squared 0.739 0.920 0.955 0.956 0.760 0.851 0.743 0.871 Note. The table reports results of regression 1, where the outcome variables Posteriormean iis the average GDP forecast of firm iafter the treatment. Priormean iis the average GDP forecast before the treatment. T1is an indicator that is equal to one if firm ireceived the information treatment about the average GDP forecast and T2is an indicator that is equal to one if firm ireceived the information treatment about GDP uncertainty. Columns (1), (2), (3) and (4) show results for the baseline survey, and columns (5), (6), (7) and (8) show results for the follow-up survey. Columns (1), (2), (5) and (6) show results for the firms that received the information treatment in the baseline period, and columns (3), (4), (7) and (8) show results for the firms that are connected to the treated firms. Columns (2), (4), (6) and (8) show results with Huber weights. Robust standard errors are shown in parentheses. 12 Table C-2: Treatment Effect on Expected GDP Uncertainty in Baseline and Follow-up with Huber Weights (1) (2) (3) (4) (5) (6) (7) (8) P rioruncertainty i0.960*** 0.997*** 0.993*** 0.993*** 0.978*** 0.989*** 0.974*** 0.994*** (0.019) (0.002) (0.010) (0.010) (0.019) (0.009) (0.018) (0.012) T11 1.395*** 1.157*** 0.025 0.025 1.310*** 0.958*** 2.044*** 1.953*** (0.198) (0.072) (0.084) (0.084) (0.302) (0.184) (0.328) (0.216) T21.145*** 1.414*** -0.015 -0.015 1.142*** 1.368*** 1.139*** 1.440*** (0.163) (0.065) (0.083) (0.083) (0.264) (0.132) (0.267) (0.154) T1×P rioruncertainty i-0.766*** -0.753*** -0.008 -0.008 -0.717*** -0.684*** -0.761*** -0.767*** (0.033) (0.012) (0.013) (0.013) (0.042) (0.025) (0.046) (0.031) T2×P rioruncertainty i-0.720*** -0.801*** -0.008 -0.008 -0.689*** -0.736*** -0.610*** -0.663*** (0.031) (0.012) (0.014) (0.014) (0.042) (0.020) (0.045) (0.025) Constant 0.220** 0.020 0.067 0.067 0.187** 0.117** 0.276** 0.100 (0.095) (0.017) (0.070) (0.070) (0.090) (0.050) (0.122) (0.063) Period Posterior Baseline Baseline Baseline Baseline Follow Up Follow Up Follow Up Follow Up Type of firm Treated Treated Connected Connected Treated Treated Connected Connected Observations 1,012 961 1,022 1,022 514 506 513 504 R-squared 0.835 0.965 0.973 0.973 0.809 0.910 0.700 0.856 Note. The table reports results of regression 1, where the outcome variablePosterioruncertainty iis the uncertainty on the GDP forecast of firm iafter the treatment, measured as the absolute value of the distance between the most and least likely scenario. Prioruncertainty iis the uncertainty forecast before the treatment. T1is an indicator that is equal to one if firm ireceived the information treatment about the average GDP forecast and T2is an indicator that is equal to one if firm ireceived the information treatment about GDP uncertainty. Columns (1), (2), (3) and (4) show results for the baseline survey, and columns (5), (6), (7) and (8) show results for the follow-up survey. Columns (1), (2), (5) and (6) show results for the firms that received the information treatment in the baseline period, and columns (3), (4), (7) and (8) show results for the firms that are connected to the treated firms. Columns (2), (4), (6) and (8) show results with Huber weights. Robust standard errors are shown in parentheses. 13 Table C-3: Causal Effect of GDP Forecast and Uncertainty on Actions with Huber Weights (1) (2) (3) (4) (5) (6) (7) (8) Price Price Inv Inv Emp Emp Wage Wage Posteriormean i0.292*** 0.232*** 0.138 0.158 0.868*** 0.848*** 0.003 -0.002 (0.082) (0.081) (0.141) (0.132) (0.295) (0.278) (0.013) (0.010) Posterioruncertainty i-0.369*** -0.388*** -0.805*** -0.808*** -0.834*** -0.882*** 0.005 0.004 (0.031) (0.031) (0.058) (0.053) (0.121) (0.114) (0.007) (0.006) Plans 0.741*** 0.754*** 0.534*** 0.549*** 0.519*** 0.574*** 0.990*** 0.991*** (0.027) (0.027) (0.038) (0.038) (0.066) (0.061) (0.007) (0.007) Priormean i-0.144** -0.104 -0.026 -0.042 -0.603*** -0.629*** -0.003 0.002 (0.067) (0.067) (0.107) (0.104) (0.229) (0.223) (0.012) (0.008) Prioruncertainty i0.268*** 0.291*** 0.594*** 0.612*** 0.685*** 0.710*** -0.004 -0.003 (0.029) (0.030) (0.053) (0.050) (0.120) (0.115) (0.004) (0.004) Constant 0.634*** 0.615*** 1.452*** 1.292*** 0.194 0.451 0.013 0.012 (0.130) (0.123) (0.227) (0.217) (0.471) (0.427) (0.020) (0.021) Type All All All All All All All All Regression OLS Huber OLS Huber OLS Huber OLS Huber F (mean) 143 379.7 169.2 369.4 140.8 362.8 138.3 363.6 F (uncert) 592.4 1406 740.8 1433 622.5 1483 599.4 1418 Observations 960 940 959 939 960 938 958 937 R-squared 0.639 0.665 0.480 0.507 0.272 0.323 0.981 0.982 Note. The table reports results of regression 3, where the outcome variables are actions that the firm took in the three months before the follow-up survey. Those actions are the change in prices (columns (1) and (2)), change in investment (columns (3) and (4)), change in employment (columns (5) and (6)) and change in wages (columns (7) and (8)). Columns (2), (4), (6) and (8) use Huber weights. P lan are the plans that the firm had in the baseline survey for the next three months. P osteriormean iis the GDP forecast of the firm in the follow-up period. Posterioruncertainty iis the uncertainty about the GDP forecast of firm iin the follow-up period, measured as the absolute value on the distance between the most and least likely scenario. P osteriormean iis the GDP forecast of the firm in the baseline period before receiving the treatment and Prioruncertainty iis the uncertainty forecast before the treatment. We instrument the posterior variables with the priors interacted by the treatment dummy and a treatment dummy. Robust standard errors are shown in parentheses. 14 Table C-4: Causal Effect of GDP Forecast and Uncertainty on Actions, for Treated Firms with Huber Weights (1) (2) (3) (4) (5) (6) (7) (8) Price Price Inv Inv Emp Emp Wage Wage Posteriormean i0.163 0.099 0.008 0.039 0.912** 0.732* 0.024 0.006 (0.114) (0.128) (0.224) (0.218) (0.419) (0.431) (0.026) (0.014) Posterioruncertainty i-0.335*** -0.357*** -0.824*** -0.822*** -0.810*** -0.906*** 0.005 -0.000 (0.042) (0.047) (0.083) (0.081) (0.173) (0.173) (0.010) (0.008) Plans 0.766*** 0.759*** 0.486*** 0.521*** 0.379*** 0.443*** 0.995*** 0.999*** (0.037) (0.038) (0.057) (0.055) (0.104) (0.100) (0.008) (0.007) Priormean i-0.061 -0.022 0.015 -0.025 -0.746** -0.642* -0.016 0.002 (0.093) (0.105) (0.157) (0.156) (0.325) (0.341) (0.022) (0.010) Prioruncertainty i0.258*** 0.282*** 0.571*** 0.586*** 0.631*** 0.725*** -0.009 -0.005 (0.039) (0.043) (0.073) (0.068) (0.161) (0.157) (0.007) (0.005) Constant 0.541*** 0.561*** 1.742*** 1.600*** 0.444 0.591 0.008 0.019 (0.168) (0.172) (0.355) (0.344) (0.766) (0.717) (0.031) (0.030) Type Treated Treated Treated Treated Treated Treated Treated Treated Regression OLS Huber OLS Huber OLS Huber OLS Huber F (mean) 110.8 233.2 151.8 228.8 118.9 235.6 109.3 233.7 F (uncert) 365.3 1132 777.3 1191 402 1229 386.8 1142 Observations 485 476 478 471 479 470 479 470 R-squared 0.688 0.689 0.448 0.480 0.174 0.229 0.978 0.983 Note. The table reports results of regression 3only for treated firms, where the outcome variables are actions that the firm took in the three months before the follow-up survey. Those actions are the change in prices (columns (1) and (2)), change in investment (columns (3) and (4)), change in employment (columns (5) and (6)) and change in wages (columns (7) and (8)). Columns (2), (4), (6) and (8) use Huber weights. Plan are the plans that the firm had in the baseline survey for the next three months. P osteriormean iis the GDP forecast of the firm in the follow-up period. Posterioruncertainty iis the uncertainty in the GDP forecast of firm iin the follow-up period, measured as the absolute value of the distance between the most and least likely scenario. P osteriormean i is the GDP forecast of the firm in the baseline period before receiving the treatment and Prioruncertainty iis the uncertainty forecast before the treatment. We instrument the posterior variables with the priors interacted by the treatment dummy and a treatment dummy. Robust standard errors are shown in parentheses. 15 Table C-5: Causal Effect of GDP Forecast and Uncertainty on Actions, for Connected Firms with Huber Weights (1) (2) (3) (4) (5) (6) (7) (8) Price Price Inv Inv Emp Emp Wage Wage Posteriormean i0.412*** 0.368*** 0.161 0.188 0.558 0.722** -0.015 -0.013 (0.116) (0.106) (0.176) (0.165) (0.365) (0.328) (0.012) (0.011) Posterioruncertainty i-0.425*** -0.443*** -0.842*** -0.844*** -0.902*** -0.912*** 0.007 0.008 (0.046) (0.041) (0.075) (0.071) (0.176) (0.165) (0.010) (0.010) Plans 0.712*** 0.742*** 0.583*** 0.585*** 0.644*** 0.693*** 0.986*** 0.984*** (0.041) (0.039) (0.048) (0.048) (0.083) (0.083) (0.012) (0.013) Priorimean -0.226** -0.191** -0.011 -0.019 -0.326 -0.476* 0.008 0.008 (0.094) (0.087) (0.140) (0.136) (0.294) (0.275) (0.010) (0.010) Prioruncertainty i0.302*** 0.321*** 0.663*** 0.679*** 0.787*** 0.768*** 0.001 0.000 (0.042) (0.041) (0.070) (0.071) (0.176) (0.175) (0.005) (0.005) Constant 0.717*** 0.691*** 1.257*** 1.083*** 0.148 0.354 0.009 0.006 (0.200) (0.187) (0.307) (0.295) (0.533) (0.490) (0.028) (0.029) Type Conn Conn Conn Conn Conn Conn Conn Conn Regression OLS Huber OLS Huber OLS Huber OLS Huber F (mean) 69.73 164.1 70.15 171.1 70.32 157.6 66.85 158.8 F (uncert) 247.7 487.3 233.1 492.7 260.5 517.4 249.2 495.4 Observations 475 459 481 463 481 463 479 462 R-squared 0.601 0.641 0.523 0.548 0.403 0.452 0.983 0.982 Note. The table reports results of regression 3only for connected firms, where the outcome variables are actions that the firm took in the three months before the follow-up survey. Those actions are the change in prices (columns (1) and (2)), change in investment (columns (3) and (4)), change in employment (columns (5) and (6)) and change in wages (columns (7) and (8)). Columns (2), (4), (6) and (8) use Huber weights. Plan are the plans that the firm had in the baseline survey for the next three months. P osteriormean iis the GDP forecast of the firm in the follow-up period. Posterioruncertainty iis the uncertainty in the GDP forecast of firm iin the follow-up period, measured as the absolute value of the distance between the most and least likely scenario. P osteriormean i is the GDP forecast of the firm in the baseline period before receiving the treatment and Prioruncertainty iis the uncertainty forecast before the treatment. We instrument the posterior variables with the priors interacted by the treatment dummy and a treatment dummy. Robust standard errors are shown in parentheses. 16 Table C-6: Causal Effects of GDP Forecast, Uncertainty and Others’ Actions on Connected Firms with Huber Weights (1) (2) (3) (4) (5) (6) (7) (8) Price Price Inv Inv Emp Emp Wage Wage Posteriormean i0.419*** 0.389*** 0.065 0.087 0.644* 0.826** -0.019 -0.016 (0.125) (0.110) (0.170) (0.164) (0.386) (0.354) (0.015) (0.016) Posterioruncertainty i-0.331*** -0.360*** -0.515*** -0.516*** -0.779*** -0.747*** 0.007 0.009 (0.071) (0.072) (0.103) (0.106) (0.217) (0.209) (0.011) (0.012) Action Otherj−i0.236* 0.199 0.317*** 0.337*** 0.091 0.111 0.348 0.583 (0.139) (0.144) (0.083) (0.088) (0.083) (0.082) (0.323) (0.521) Plani0.708*** 0.736*** 0.564*** 0.569*** 0.643*** 0.694*** 0.981*** 0.978*** (0.042) (0.040) (0.051) (0.050) (0.086) (0.086) (0.014) (0.016) Plan Action Otherj−i-0.103 -0.079 -0.192*** -0.195** -0.047 -0.048 -0.346 -0.581 (0.139) (0.145) (0.072) (0.080) (0.071) (0.074) (0.323) (0.519) Priormean i-0.230** -0.202** 0.023 0.018 -0.427 -0.594** 0.013 0.010 (0.099) (0.088) (0.138) (0.136) (0.314) (0.302) (0.012) (0.014) Prioruncertainty i0.230*** 0.257*** 0.492*** 0.490*** 0.673*** 0.617*** 0.002 0.001 (0.063) (0.067) (0.086) (0.095) (0.209) (0.211) (0.006) (0.007) Constant 0.486** 0.494*** 0.331 0.278 0.079 0.316 0.007 0.003 (0.194) (0.176) (0.314) (0.283) (0.554) (0.521) (0.028) (0.029) Regression OLS Huber OLS Huber OLS Huber OLS Huber F (mean) 50.68 114.8 48.08 119.7 60.13 116.1 43.98 110 F (uncert) 187.8 340.8 158.7 341.8 191 364.7 191.9 358.1 F (Action T) 45.47 41.95 64.57 61.14 16.08 17.74 0.851 0.629 Observations 453 438 452 435 454 437 452 436 R-squared 0.610 0.654 0.490 0.502 0.388 0.435 0.979 0.975 Note: The table reports results of regression 3, where the outcome variables are actions that the firm took in the three months before the follow-up survey. Those actions are the change in prices (columns (1) ans (2)), change in investment (columns (3) and (4)), change in employment (columns (5) and (6)) and change in wages (columns (7) and (8)). Planiare the plans that the firm had in the baseline survey for the next three months. Action Otherj−i are the actions of the directly treated firm that is connected to a firm in this sample. Plan Action Otherj−iare their plans. Posteriormean iis the GDP forecast of the firm in the follow-up period. Posterioruncertainty iis the uncertainty in the GDP forecast of firm iin the follow-up period, measured as the absolute value of the distance between the most and least likely scenario. P osteriormean iis the GDP forecast of the firm in the baseline period before receiving the treatment and Prioruncertainty iis the uncertainty forecast before the treatment. This regression is run for the connected firm. We instrument the posterior variables and Action Otherj−iwith the treatment dummy, priors interacted by the treatment dummy and the plan of the directly treated firm that is connected to a firm in this sample. Robust standard errors are shown in parentheses. C-4 Additional Results from the Model Within-network initial price response variation. Figure C-1 shows the histogram of the within-network variance of the initial price responses to a treatment of higher uncertainty. 17 Figure C-1: Distribution of Within-Network Price Variance after Treatment of Higher Uncertainty Treatment to supplier -rm 0 0.02 0.04 0.06 0.08 0.1 Variance of price responses 0 5 10 15 20 25 Treatment to customer -rm 0 0.01 0.02 0.03 0.04 Variance of price responses 0 5 10 15 20 25 No communication Even communication Note: Distribution of the variance of initial price responses across networks when the treated firm is the supplier (left panel) and when the treated firm is the customer (right panel). In red: even communication; in blue: no communication. Estimates of the relationship between the price of the treated and that of the connected firm. We estimate the change in the price of the connected firm that is associated with a 1 percentage point change in the price of the main (treated) firm in the model simulations and survey data. In the survey data, we instrument the price change of the main firm with interactions between the treatment dummy and the price plan that the firm had. In particular, we estimate β1and β2in the following regression Priceconnected j−i=β1(Pricetreated i|Talk GDPj−i) + β2(Pricetreated i|No Talk GDPj−i) + Xitδ′+εi, while instrumenting both regressors by firm i’s treatment indicator, the interaction between firm i’s treatment indicator and its planned price change, and the interaction between firm i’s planned price change and an indicator of whether the pair of firms communicated about GDP. Vector Xit embeds firm iand j’s planned price changes. Importantly, we separate the effect between the firms that communicated at least once about GDP and the firms that did not. While communication is also affected by the treat18 Table C-7: Price Pass-through from Treated to Connected with Different Levels of Communication (1) (2) (3) (4) Pricetreated|Talk GDP 0.816*** 0.810*** (0.158) (0.224) Pricetreated|No Talk GDP 0.261 0.631*** (0.179) (0.205) Pricetreated|Even Comm 1.020*** 0.980*** (0.004) (0.004) Pricetreated|No Comm 0.348*** 0.508*** (0.005) (0.009) Type Supplier Supplier Customer Customer Shock to Customer Customer Supplier Supplier Data Survey Model Survey Model F (Talk) 17.89 15.34 F (No Talk) 32.93 112 Observations 181 180 164 180 R-squared 0.513 0.820 0.441 0.662 Note: The table reports results of a regression that estimates the empirical price pass-through from the treated firm to the connected firm (columns (1) and (3)), and the equivalent regression in the model (columns (2) and (4)). We instrument both Pricetreated|Talk GDP and P ricetreated|No Talk GDP with the price change plans of the treated firm, interacted by the treatment, the treatment indicator and the interaction with whether they talked or not. We control for the treated and connected firms’ plans. Robust standard errors in all regressions. ment, potentially biasing these estimates, we see these results as suggestive evidence of the model mechanisms. Alternative communication matrix. Figure C-2 shows that in the case of C= Ω, the price responses are amplified relative to the no communication scenario, but not by as much as they are under even communication. Similar to the case of no communication, Ω communication implies that the price responses are bigger when the treatment originates from the supplier firm than when they come from the customer firm. 19 Figure C-2: Distribution of the Impact on Prices after Treatments of Higher Uncertainty -1.2 -1 -0.8 -0.6 -0.4 -0.2 0 Percent 0 1 2 3 4 5 6 7Treatment to supplier -rm -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 Percent 0 1 2 3 4 5 6 7Treatment to customer -rm No communication Even communication +communication Note: Distribution of price changes across all three firms when the treated firm is the supplier (left panel) and when the treated firm is the customer (right panel). In red: even communication; in blue: no communication; in black: Ωcommunication. 20