Essays on sticky information and on bank lending channel

Essays on sticky information and on bank lending channel

Essays on sticky information and on bank lending channel

ON BANK LENDING CHANNEL

A dissertation submitted in partial satisfaction

of the requirements for the degree of DOCTOR OF PHILOSOPHY

in INTERNATIONAL ECONOMICS

by

CESAR CARRERA June 2010

The Dissertation of Cesar Carrera

is approved:

Professor Carl Walsh, Chair

Professor Kenneth Kletzer

Professor Thomas Wu

Tyrus Miller Vice Provost and Dean of Graduate Studies

UMI Number: 3421263

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1.2.3 Where Does This Essay Stand in the Sticky Information Literature? 15

1.4.2 Methodological alternative to Khan and Zhu’s Strategy 20

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1.5.1 Sticky Information Phillips Curve for the U.S

1.5.2 Sticky Information Phillips Curve for Canada and the U.K

1.5.3 Sticky Information Phillips Curve for other OECD countries 1.6 Conclusions

Appendix I: Data Description References

2 ESTIMATING INFORMATION RIGIDITY 2.1 Introduction

2.2 Baseline Epidemiology Model and Information Rigidities 2.2.1 General Assumptions, Definitions, and Results

2.2.2 Firms and Inflation Process 2.2.3 Firms and Professional Forecasters Belief 2.2.4 Firms Expectations

2.3 Identification and Data Characteristics 2.3.1 Identification Strategy

2.3.2 Data Description 2.3.3 Granger Causality Test 2.4 Estimations and Empirics 2.4.1 Degree of Information Stickiness 2.4.2 Heterogeneous Expectations: Industry level 2.4.3 Heterogeneous Expectations: Firm level

2.5 Conclusions 72

3.2.2 Empirics on Bank Lending Channel and Identification Problem 95

3.5.2 Identification of the Bank Lending Channel: Panel Data of Banks 112

3.5.4 Relevance of the Bank Lending Channel: SVAR Estimations 118

Appendix I: Monetary Policy and External Credit Conditions 123

LIST OF FIGURES

2.3 Distribution of Financial Institutions Expectations on Inflation 85

2.6 Information Stickiness and Expectations: Industry Level 87 2.7 Information Stickiness and Disagreements: Industry Level 88

3.1 Share of the Sample of Banks on Total Loans Market 132

3.3 Annual Growth of Commercial and Consumption Loans 133

Vì

3.5 Annual Growth of Credit Quality Ratio 3.6 Credit Quality Ratio

3.7 Evolution of the Operative Target 3.8 Interbank Interest Rate

3.9 Monetary Policy and the Credit Quality Ratio 3.10 Monetary Policy Transmission to Economic Activity | 3.10 Monetary Policy, Banking, and Firm Variables

3.11 Monetary Policy and Banking Financing Ratio

LIST OF TABLES

1.1 Available Information for Forecasting Inflation and Output Gap 39

1.3 Sticky Information Phillips Curve for the U.S., High and Low Inflation 40 1.4 Sticky Information Phillips Curve for the U.S — Khan and Zhu 41

1.7 Sticky Information Phillips Curve for OECD Countries 43 1.8 Sticky Information Phillips Curve — Homogenous Sample 44

2.1 Annual Rate of Inflation in the Peruvian Economy 79

2.3 Inflation and Inflation and Expectations Statistics 80 2.4 Engle Granger Causality Test: Firms and Financial Institutions 80

2.6 Estimating and Testing for Information Rigidity: Industry Level 81 2.7 Estimating and Testing for Information Rigidity: Firm Level 81

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3.2 Effects of Monetary Policy over Loan Supply 130

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ABSTRACT

ESSAYS ON STICKY INFORMATION AND

ON BANK LENDING CHANNEL

CESAR CARRERA

One of the most important structural relationships for policy makers is the Phillips curve; as a result, there is an extensive literature focused on its properties, proposing alternative theoretical approaches and different strategies for its estimation The Mankiw and Reis (2002) proposal of sticky information about macroeconomic conditions has become an alternative to sticky price models regarding the treatment of information, the estimation of the Phillips curve, and a set up in general equilibrium models for evaluating monetary policy In Essay One, I estimate a sticky information Phillips curve for each OECD country following Khan and Zhu (2006) and document the period of time that firms need to update their information set I find evidence that

in countries with higher inflation, higher inflation volatility, or higher output gap volatility, the degree of information stickiness is lower This evidence suggests a degree of endogeneity of the slope of the Phillips curve which is consistent with state- contingent inflation processes

The slope of the sticky information Phillips curve is based on the degree of information rigidity on the part of the firms Carroll (2003) uses an epidemiology model of expectations and finds evidence for the U.S of a one year lag in the transmission of information from professional forecasters to households Using financial institutions and firms’ survey data from Peru and the model proposed by Carroll, in Essay Two, I estimate the degree of information rigidity This essay also considers heterogeneous responses and explores the cross-section dimension of these survey forecasts I find that the degree of information stickiness ranges between one and three quarters, a result that is robust to different specifications

In the past decade, the Peruvian economy has experienced important structural changes regarding monetary policy Those changes have affected the effectiveness of central bank’s mechanisms of transmissions The Essay Three objectives of are the identification of the bank lending channel as part of the transmission process to economic activity based on Bernanke, Gertler, and Gilchrist (1996) flight-to-quality argument and the evaluation of its effectiveness for transmission For identification, I use a panel of bank level data, and for effectiveness, I use structural VARs in which two scenarios are considered: (1) with an operating bank lending channel and (ii) without this channel I conclude that the bank lending channel has operated but this channel is not important as a mechanism of transmission to macroeconomic activity

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ACKNOWLEDGMENTS

I have the honor of working with Carl Walsh these essays I want to express my deepest gratitude to my advisor for his never ending help, continued patience, and strong support Carl has offered me valuable ideas, challenging critiques, and helpful suggestions based on his profound knowledge of monetary policy and rich research experience in Macroeconomics I am grateful to the Faculty members at UC Santa

Cruz, Kenneth Kletzer, Thomas Wu, Joshua Aizenman, Federico Ravenna, Aspen

Gore, Carlos Dobkin, and Mary Flannery for very helpful comments on early draft versions of these essays I am also thankful to my former advisor at Williams College, Peter Pedroni, for his constant guidance and support The comments and suggestions

of the presenters at the Economics Department Seminars at UCSC —specially to Peter

Klenow, Uwe Hassler, Yuriy Gorodnichenko, Carlos Carvalho, Andrea Ferrero,

George Alessandria, Guillaume Rocheteau, and John Fernald— were helpful in improving these essays and giving me useful research direction Finally, participants

at the Macro Workshop, the Econ PHD conference at UC Santa Cruz, and the Macro conference series at the Central Reserve Bank of Peru were important for broader discussions of the main results presented here

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ESSAY ONE

1 STICKY INFORMATION PHILLIPS CURVE:

EVIDENCE FOR OECD COUNTRIES

1.1 INTRODUCTION

The international policy environment is subject of continued research because policy makers require a better description of the underlying determinants of structural relationships than is currently available, including the link between inflation and the output gap This improved description will provide better tools for evaluating policy actions and their effects This is why recent work devotes time and effort to reconsidering the explanations contained in previous literature or to validating previous findings In this regard, most central banks rely on forecasts of future inflation using a Phillips curve to set their instruments which is the case of, for example, the FED, the Bank of England, and the Bank of Canada The central role of the Phillips curve framework has led to research focused on alternative approaches to validating its key parameters While estimations of the new Keynesian Phillips curve (NKPC thereafter) are centered on the frequency with which firms change prices, estimations of the sticky information Phillips curve (SIPC

thereafter) are focused on the level of inattentiveness of the firms, defined as the period needed for firms to update their information set

Regarding the NKPC (based on sticky prices), it has some problems which were identified in several studies Ball (1994) finds that the standard sticky price model implies that announced credible disinflations cause increases in production rather than recessions because inflation moves in anticipation of demand Fuhrer and Moore (1995) show that the sticky price model falls short of explaining inflation persistence in the U.S (inflation depends importantly on its own lags) Mankiw and Reis (2002) argue that the sticky price model cannot explain delayed and gradual effects on inflation due to monetary policy shocks

The current literature in NKPC argues that the theory is correct but that deterministically detrended GDP is an inappropriate measure of the output gap for the purpose of explaining inflation Recent sticky-price models imply that the actual driving variable in the NKPC is the real marginal cost As an alternative, Gali and Gertler (1999), Sbordone (2002), and others have suggested the use of the average unit labor costs as a proxy for nominal marginal cost This proxy for real marginal cost (and for the output gap) is the labor share of income Woodford (2001) argues that the labor share is a better measure of the output gap, at least for explaining variations in inflation.’

' The current NKPC literature also addresses issues of identification Rudd and Whelan (2005) conclude that the evidence in favor of labor income share as a good measure of the output gap or as an appropriate variable for incorporation in a monetary policy rule is weak The use of the labor share would imply that central banks should not follow traditional variants of the Taylor rule (short-term interest rates are set with reference to the levels of inflation and deterministically detrended output) The reformulated rule would call for the central bank to ignore measures of the output gap and instead raise interest rates in response to increases in labor’s share of income Because the labor share has spiked upward in every modern U.S recession, a policy rule based on this variable would have called for higher interest rates Mavroeidis (2005) shows that problems of weak instruments may arise depending on the properties of the “exogenous” variables and presents a relationship between identification and dynamic misspecification by examining the

2

About the dynamics of inflation, the literature on the NKPC has identified that inflation is related not only to a lead of inflation but also to a lag of inflation (hybrid sticky price model) Zhang et al (2008) find that forward-looking behavior plays a smaller role during the high and volatile inflation regime to 1981 than in the subsequent period of moderate inflation, providing empirical support for sticky price models over the last two decades.” The presence of the lag can be justified by the presence of rule-of- thumb as in Gali and Gertler (1999), by dynamic indexation as in Christiano, Eichenbaum, and Evans (2005), and by rigidities in information as in Kiley (2007) On the other hand, Calvo, Celasun, and Kumhof (2007) incorporate the argument of firm- specific inflation rate into the NKPC in order to obtain similar inflation dynamics as

Mankiw and Reis (2002).°

In contrast, a relatively new literature has focused on the sticky information argument proposed by Mankiw and Reis (2002) as a way to solve the earlier problems identified

(lack of) power of Hansen’s (1982) J test Dees et al (2009) focus on the instrument problem and the characterization of the steady states Using vector autoregressive model steady states, they estimate long- horizon expectations and construct valid instruments from global variables This measure of the steady state performs better than the Hodrick Prescott detrended measure, and the use of forei gn instruments

substantially increased the precision of the estimates of the output coefficient Neiss and Nelson (2005) provides estimates of the NKPC using theory-consistent estimates of the output gap which leads to a considerable improvement in the empirical performance of output-gap based Phillips curves They argue that marginal cost and the output gap are closely related, but that the latter needs to be measured in a manner consistent with dynamic general equilibrium models

* Zhang et al consider multiple structural changes in the NKPC for the U.S between 1960 and 2005, employing both inflation expectations survey data and a rational expectations approximation Rudd and Whelan (2007) argues that the use of rational expectations sticky-price models to capture inflation dynamics fail to provide a useful empirical description of the inflation process based on the ability of these models to fit the data; the importance of rational forward-looking expectations in price setting; and the appropriate measure of inflationary pressures

* Some other topics discussed on the current literature of the NKPC are discussed in Benati (2007), Graham and Snower (2008), and Smith (2008) Benati compares changes in the correlation between real activity and inflation at the business-cycle frequencies and document a positive correlation between the time-varying average gain of real activity over inflation at the business-cycle frequencies Graham and Snower use a dynamic general equilibrium model and show that the interaction of staggered nominal contracts with hyperbolic discounting leads to inflation having significant long-run effects on real variables Smith finds that Japan’s Phillips curve looks like Japan

with the NKPC by replacing the sticky price assumption Mankiw and Reis’ modeling strategy is based on the argument that information about macroeconomic conditions diffuses slowly through the population Thus, prices are always changing, but price decisions are not always based on current information Mankiw and Reis call this situation “sticky information.” They assume that each period a fraction of the population updates its information on the economy and computes optimal prices based on that information, while the rest of the population continues to set prices based on old plans and outdated information

In the context of the Phillips curve, the sticky information model implies that the price level depends on expectations of the current price level formed in the past, as some price setters are still setting prices based on past decisions and outdated information (because

of either costs of acquiring information or costs of reoptimization)

As previously discussed more recent work on sticky prices use unit labor cost as a measure of output gap In such context, firms reset prices on infrequent occasions so the relevant expectations term for firms is a weighted average of current expectations about future changes in unit labor cost In this setting, firms take into account periods when costs change but their prices do not In the sticky information model, firms and workers decide optimally to remain inattentive and the price level depends on past expectations of its current value, real marginal costs, and desired markups In this setting, unexpected shocks to any of the three price determinants will have an effect on inflation that is proportional to the share of price setters which are aware of the news

As Mankiw and Reis (2002) point out, the degree of information stickiness determines the inflation dynamics There are abundant empirical studies using sticky

4

information modeling for the U.S., and more limited work on the Euro area This essay provides consistent SIPC estimates across OECD countries, using the time series approach of Khan and Zhu (2006) I find evidence which rejects the flexible information hypothesis in favor of sticky information for all the countries in the sample, and I document the degree of information stickiness for each economy

In line with the discussion of Lucas (1980), Ball, Mankiw, and Romer (1998), and Kiley (2007) regarding the exogeneity of the degree of price stickiness, this essay supports a similar discussion in the context of the degree of information stickiness I find evidence that suggests a positive relationship between the degree of information stickiness and the level of inflation Thus my work contributes to the literature between state-contingent and time-dependent inflation processes in the context of the Phillips curve

The remaining of this essay can be described as follows: Section 2 is the review of recent literature on Sticky Information modeling both theory and empirics In Section 3 | present the baseline model of Mankiw and Reiss (2002) and in Section 4 I discuss the strategy that Khan and Zhu (2006) follow as well as an alternative strategy to their approach In Section 5 I present the results of my proposed strategy and discuss the properties of the degree of stickiness for the U.S and other OECD countries Section 6 concludes

1.2 LITERATURE REVIEW ON STICKY INFORMATION

The Mankiw and Reis (2002, MR thereafter) model pioneers the literature on sticky information and argues that a Phillips curve with this rigidity is an adequate representation of the structural relationship between inflation and the real side of the economy In particular, Reis has made most of the contributions by extending the original

MR (2002) model Thereafter, a new literature developed through extensions and critiques of MR (2002) both on theoretical and also on empirical grounds

1.2.1 Sticky Information Modeling The early formulation of the SIPC is MR (2002) which derives the Phillips curve based on the assumption that firms set price freely but the information for setting prices may or may not be updated Because information constraints could apply to all economic agents, the sticky information model potentially provides a unifying framework for explaining inertial behavior in different macroeconomic variables This approach is complemented by Reis (2006b) which provides the microfoundations for the aggregate time dependent process assumed by MR (2002) regarding the arrival of new information Reis bases his results on an inattentive producer model and costs of information planning.* MR (2007) estimate a general equilibrium model and solve for a Phillips curve, an IS curve, a wage curve, a standard production function and a Taylor rule and

* Reis discusses the three main assumptions of the SIPC: (1) producers are inattentive, only sporadically updating their information sets, (2) producers set plans for prices, and (3) the arrival of decision dates is a Poisson process In his paper, he assumes that there is a cost of acquiring, absorbing, and processing information, derives inattentiveness as the optimal response to such costs, and finds that in a world with many agents, the distribution of inattentiveness converges to that of an exponential distribution

6

confirm the results obtained in MR (2002).> MR argue that the combination of sticky information in consumption,” price setting, and wage setting’ is necessary to match stylized facts about the behavior of output, inflation, and real wages.® Mankiw, Reis, and Wolfers (2004) claim that a model which considers sticky information can account for observed cross-sectional differences in inflation forecasts (disagreements or dispersion in responses), a stylized fact that is not explainable by models that assume complete information for all agents.’

Two main critiques appear in the literature regarding how each firm receives information in MR (2002) and if each firm has symmetric information in the inattentive model proposed by Reis (2006b)

> MR (2002) basically test the SIPC against the NKPC with an equation for aggregate demand: m = p+ y; and incorporate in their research agenda a more realistic way of modelling, for example, adding an IS curve with an interest rate policy rule In their exercise, MR model the growth in the demand variable as Am, = p Am,.; + & and calibrate p=0.5 with U.S data for M1, M2 and nominal GDP MR also point out that Taylor (1999) observes that inflation persistence could be due to serial correlation of money Rather than persistence, MR argues that the most interesting features of SIPC is on the inflation dynamics

* Reis (2006a) studies the consumption decisions of agents who face costs of acquiring, absorbing, and processing information His model predicts that aggregate consumption adjusts slowly to shocks because news disperses slowly throughout the population Thus events have a gradual and delayed effect on aggregate consumption, i.e consumers rationally choose to only sporadically update their information and re-compute their optimal consumption plans In between updating, the consumer remains inattentive

” MR (2003) argues that inattentiveness is pervasive and set up a model where workers decide optimally to remain inattentive MR apply the sticky-information theory to the wage-setting process in the labor market and develop a SIPC which relates inflation to employment and productivity They invert the SIPC to write current employment in terms of assumed univariate processes for inflation and productivity Further, assuming that unemployment rate is a function of current employment they generate a predicted path of unemployment

® In General Equilibrium, there are three types of agents: consumers, workers and firms Consumers and workers share a household and strive to maximize the same utility function subject to the same budget constraint Within consumers, there are two members: a shopper, that decides the allocation of spending across the different varieties and is always attentive, and a planner that decides total expenditure and is often inattentive Firms have two departments: a purchasing department that is always attentive and chooses how much of each variety of labor to hire, and a sales department that is only sporadically attentive and sets the price of the firm’s output These agents meet in three sets of markets In the labor market, workers sell their labor to firms; in the goods market, firms sell their goods to consumers; and in the savings market, consumers trade bonds between themselves

” The authors study the survey data from the Michigan survey (to consumers), the Livingston survey (to academic, business, finance, market and labor economists) and the Survey of Professional Forecasters of inflation expectations Branch (2007) present maximum likelihood results that suggests a sticky information model with a time-varying distribution structure is consistent with the Michigan survey of inflation

expectations

Dupor and Tsuruga (2005) argue that the results of MR (2002) are sensitive to the

assumption about the timing of information updates They claim that the SIPC results

about the dynamics of inflation and output in response to monetary shocks hinges critically on the assumption that each firm has a random identical independent distributed probability of receiving information updates each period If each firm updates its information at infrequent but fixed intervals'’® the inflation and output responses are

different than the ones reported in MR (2002).'' Under a short fixed duration updating,

the inflation response suffers diminished persistence and an unrealistic hump shape and

the output response is not persistent and weakly hump-shaped.'? For fixed but longer duration, the inflation response remains unrealistic However the persistence and hump-

shaped response of output are maintained.'® Jinnai (2007) argues that the assumption made by Reis (2006b) that firms have symmetric information leads to a higher optimal inattentive time period By assuming that all the firms are attentive at time zero, Reis approximates around the point where all the firms are attentive But if all the firms are

NYN = (N + 1)/2 For comparisons, N can be determined under two criteria The first criterion matches the

expected duration of a newly set price for an individual firm (N = 4) and the second criterion matches the

cross-sectional age of a stale price (N = 7)

'? Inflation sees dramatically reduced persistence and the peak response after three quarters and declines immediately Inflation follows the path of the money growth rate from period four, because all firms are informed about the change in money growth at period three Output exhibits little persistence and peaks at period one Moreover, output has returned to the steady state by period three By this time, each firm is fully informed about the monetary disturbance

'5 Although a hump shape for output can be attained under the second criterion, the inflation response remains unrealistic Inflation gradually increases up to period six but decreases quickly in the next period because of inflation must catch up with the money growth rate in period seven Under an AR(1) money growth rate with p = 0.5 (another parameter value assumed in MR, 2002), the money growth rate at period seven is almost zero Therefore, inflation must decrease very quickly once all firms are informed about the shock,

initially attentive, they have no uncertainty about the future path of the aggregate price level In other words, every firm knows the future path because it is the same as its own price plan This explains why the aggregate price level is not included in the optimal inattentive length for the representative firm in the estimations of Reis.'* With Jinnai’s modification, the prediction of inattentiveness is between 2.1 to 6.3 quarters when costs

of planning are 4.6 % of profits while Reis estimates are in between 10 and 26 quarters for the same planning costs Jinnai’s result is consistent with the firm level cost estimated

by Zbaracki et al (2004).'°

The gradual diffusion of information across the population assumed by the sticky information modei has received some theoretical and empirical support as well Carroll (2003) claims to be the first attempt to provide microfundations to the sticky information model of MR (2002) based on a two-agent epidemiology expectation model of information transmission Carroll estimates the rate of diffusion of inflation forecasts from professional forecasters to the general population (households) and finds results in

line with those employed in MR (2002) Dépke et al (2008b) provide similar estimates for European countries using Carroll’s approach for the diffusion of information from

forecasters to households They find that the data support the epidemiology expectation model Carroll and Dépke et al find that the duration of information rigidity is

‘4 Jinnai points out that solving the individual firm’s problem under symmetric information among firms is undesirable because the objective of Reis (2006b) is giving a microfoundation to the sticky-information Phillips curve proposed on MR (2002) Asymmetric information due to staggering-information updating is the main component of MR (2002) Jinnai’s definition of expected difference between profits earned with

full information and profits earned while following a pre-chosen path (function G() in the paper) takes into

account the asymmetric information among firms

'° Zbaracki et al (2004) study the price adjustment practices and provide quantitative measurement of the managerial and customer costs of price adjustment using data from a large U.S industrial manufacturer and its customers They estimate that the total costs of price adjustment are 20% of profits, and managerial costs, which are a part of the total costs, are 4.6% of the profits

9

approximately one year Easaw and Ghoshray (2006) extend Carroll’s model and set up a

dynamic two-agent-based learning model where households learn from professional

forecasters based on both “anchoring” and “adjustment” information process.'® Using the

“Lucas-Phelps Island” scenario (difference between individual specific and aggregate shocks), Easaw and Ghoshray show that persistence of real effects arises as a result of observing the professional’s forecast imperfectly ”

Other research has relied on fully structural models to study the validity of the sticky

information approach with mixed results Laforte (2005) specifies a structural DSGE model, estimated by Bayesian methods, to compare the three pricing mechanisms:

Wolman, new Keynesian and sticky information pricing model.'® His results are do not support the sticky information model Arslan (2008) compares the dynamic responses of the sticky price and sticky information models to a cost-push shock in a DSGE framework He finds that the sticky information model produces more reasonable

dynamics through lagged, gradual and hump-shaped responses to a shock However, these responses depend on the persistence of the shock Andres et al (2005) estimate fully

'® In this model, a household (agent 1) forms subjective expectations by “anchoring” on a particular source

or initial approximation A household “anchor” to professional forecasters (agent 2) subjective expectations

as he feel that a professional forecaster has a superior information set which enables him to make more accurate forecasts The relevant information is not always be readily available and it is observed imperfectly (information gathering is a sticky process) A household may not readily observe the professional’s forecasts in which case he has to adjust his expectations over time The learning process in this model takes into account for “adjustment” (or “absorption”)

'’ In this model professional forecaster’s expectations are formed independently Any changes in his forecasts depend on expected productive shock to economic growth based on new information Household’s subjective expectations depend on his relative income expectations formed in the current and past periods and expected productive shock to economic growth (professional’s forecasts is part of household’s information set) Nevertheless, those expectations are partially adjusted Hence, any monetary disturbances are accounted for both agents However, the household is only able to account for it partially and any real effects of monetary disturbances will persist The persistence of real effects will depend on how frequently the householder observes the professional’s forecasts (degree of information rigidity as in Caroll’s epidemiology model)

'® The pricing models are based on Wolman (1999), Gali and Gertler (1999), and MR (2002)

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structural models with either sticky price or sticky information price setting and find that the SIPC yields the largest likelihood statistic.'? Klenow and Willis (2007) simulate general equilibrium models” to derive responses of price changes to past inflation movements They find support in the micro level data for the proposition that price changes only slowly incorporate past aggregate information on nominal demand As the information becomes stickier among firms, the change in prices responds to older inflation innovations Just as sticky information theories predict, price changes in the U.S CPI micro data reflect information older than predicted by a flexible information model.” Wang and Wen (2007) also solve for a general equilibrium model but for a two-countries set up They present evidence that the average cross-country correlation of inflation is significantly and systematically stronger than that of output, while the cross-country correlation of money growth is essentially zero Wang and Wen test whether standard monetary models driven by monetary shocks are consistent with the previous facts They find that neither the new Keynesian sticky price model (following Christiano et al., 2005) nor the sticky information model (following MR, 2002) can fully explain the data

Some of the previous mentioned literature focuses only on the firm level sticky information and following only on MR (2002) MR (2007) argue that information

'? They assume a very low truncation of the SIPC (J = 3 quarters) making this result difficult to compare with other papers which take into account higher level of information rigidity

*° Klenow and Willis (2007) propose a reconciliation between micro flexibility and macro rigidity and set

up a model in which firms have price adjustment costs (price stickiness) and information costs (information stickiness) In their model, firms solve a dynamic optimization problem to maximize profits and assume bounded rationality (firms form inflation expectations based on a limited set of information) They call sticky information theory to different aspects of the work of Sims (1998), Woodford (2003) and MR (2002) and point that these theories take into account that macro information is stickier than micro prices

71 MR (2010) point out that Klenow and Willis (2007) also find that the prevalence of predictable “sales” are precisely the price plans on Reis (2006) and these plans seem to only slowly incorporate available information Sales-related price changes respond to macro information at least as much as regular price changes do This result of Klenow and Willis suggests that sales prices should not be filtered out of data used for analysis of macroeconomic responsiveness

II

stickiness is pervasive and it applies to firms, workers, and consumers In words of MR,

“some recent research has estimated empirical dynamic stochastic general equilibrium models with sticky information on the part of firms, assuming fully informed workers and consumers Our results suggest that these models were misspecified; this misspecification can potentially explain reported poor fits of the models.” This comment raises the question of, for example, how incorporating inattentive consumers would change the results reported on Duport and Tsuraga (2005), Laforte (2005), or Wang and Wen (2007)

1.2.2 A “Race Horse”: NKPC versus SIPC The MR (2003) paper presents a SIPC which relates inflation to employment and productivity In their set-up, current employment is assumed to be a process derived from inflation and productivity Assuming unemployment rate as a function of current employment, they generate a predicted path of unemployment The 4 which maximizes the correlation between predicted and actual unemployment equals 0.25.77 Using Michigan Survey data and the Survey of Professional Forecasters, Carroll (2003) estimates a X equals to 0.27 The value of these parameters suggests that the duration of information rigidity for the U.S economy is one year

Following the MR (2003) estimation of the SIPC, more work has been focused on the empirical estimations of this relationship For a review of the time-series approach, I

*? MR (2002) calibrate a model with U.S quarterly data from 1960 to 1999, use three different measures of inflation (CPI, core CP! and GDP deflator) and compare three Phillips curves from standard models (Sticky Information, Backward Looking, and Sticky Prices) They conclude that the sticky information model fits the main features of the data better, as well as gives a better pattern of inflation dynamics, using a A equals

to 0.25

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survey Khan and Zhu (2006), Dépke et al (2008a), Coibion (2010), and Kiley (2007) For a Bayesian approach, I survey Korenok (2008)

Khan and Zhu (2006), Dépke et al (2008a) and Coibion (2010) directly estimate the structural parameters of the sticky information model applied to price setting suggested in

MR (2002) For different levels of truncation, Khan and Zhu (KZ thereafter) find that the duration of information stickiness for the U.S ranges from three to seven quarters and on average the degree of information stickiness is 0.24 which is in line with the findings of

MR (2003) and implies that firms update their information approximately once a year.”*

Dépke et al find that information on inflation in France, Germany, and the United Kingdom are updated about once a year, while in Italy, about once each six months.” Coibion finds that there is no sticky information in price setting In order for the SIPC

model to be consistent with the data, Coibion suggests that firms must update their

information approximately once every four years on average.”°

Some empirical work expanding on the arguments of MR (2002) test the validity of

the SIPC by comparing its predictive power against the NKPC, the hybrid NKPC, and

against time series reduced forms Korenok (2008) statistically compares the validity of the two models By assuming that marginal! costs follow an exogenous autoregressive

process, he solves for the inflation process implied by both the sticky price and sticky

*° Khan and Zhu (2006) use U.S quarterly data from 1969 to 2000 and estimate a SIPC for the period 1980

— 2000 based in univariate and bivariate VAR forecasts (for inflation and for the output gap), estimate the sticky information parameter by nonlinear OLS, and bootstrapped confidence intervals for such parameter

** Dépke et al (2008) estimate the SIPC model following on MR (2002) using survey expectations of professional forecasters from France, Germany, the United Kingdom and France The use of survey data limits their estimations to four and six period truncation period

*° Coibion (2010) uses U.S quarterly data from 1971 to 2004, compares survey expectation data and VAR- based expectations, estimates a SIPC via nonlinear IV OLS In addition to the measure of the output gap,

my main concern on this paper is the estimation of forecasts of output gap departing from survey data Similar to Dépke et al (2008a), this paper is restricted to a low level of truncation, a point discussed in the next section

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information models After constructing an encompassing model, Korenok evaluates the weighting parameter by Bayesian methods and finds that point estimates favor the sticky

1.7° Kiley (2007) combines each of the sticky price and sticky information price mode

Phillips curves’’ with VAR representations of the rest of the model to solve for model- consistent rational expectations within a full information maximum _ likelihood framework He finds that a hybrid NKPC outperforms the SIPC.”®

Some comments on the previous papers: Korenok (2008) cannot formally reject the SIPC and Kiley (2007) finds that the SIPC and one-lag hybrid NKPC have similar performance for the sub-sample 1982-2002 Even though, from the mid 1960s to the mid 2000s, the SIPC estimates are statistically dominated by some hybrid representation of the NKPC (in which case, the backward looking component of the hybrid NKPC suggests

a role for imperfect information, as suggested in Kiley), and when different sub-samples are considered the estimates differ According to Kiley (2007), a comparison of his 1982-

2002 results with his full sample 1965-2002 results may provide a clue as to an important source of imperfect information over the last 40 years One potential explanation is that monetary policy has been more stable over more recent period and that has lowered the importance of learning (or updating) new information about the inflation goal of monetary policy authorities

*° Korenok (2008) uses U.S quarterly data from 1960 to 2002 to explain the relationship between aggregate price and labor share (unit labor cost/price ratio), applies Bayesian full information likelihood approach, encompasses in a general model both sticky price and sticky information model

*” Of a special note, Kiley (2007) has the greatest variety of Phillips curve specifications as well as time series reduced forms

*® Kiley (2007) uses U.S quarterly price level for the nonfarm business sector for 1965-2002 Kiley measures nominal marginal cost by unit labor costs, estimates sticky-price and sticky-information models of price setting via maximum-likelihood techniques Another conclusion from this paper is that hybrid sticky price models fit the data as well as simple reduced forms if long lags are included

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1.2.3 Where Does This Essay Stand in the Sticky Information Literature?

As emphasized by Lucas (1976), a model’s ability to fit past data, especially when it relies upon ad hoc assumptions about individual or firm behavior, is not sufficient grounds for using it to analyze future changes in policy The recent work on imperfect information, which includes sticky information, has been focused on _ providing microfundations leading to suggested reduced forms.””

This essay in particular strengthens a recent growing body of work that has followed

up on the arguments of MR (2002) for replacing sticky price models with their sticky information alternative 1 provide direct estimations of the degree of information rigidity (slope of the SIPC) using VAR-based expectations from OECD countries, following on

KZ (2006) strategy The results suggest different degrees of information rigidity across countries and across different time periods I argue that the estimated levels of information rigidity appear to be driven primarily by state-contingent conditions of low and high inflation scenarios, In other words, in environments of low inflation, agents tend

to be more inattentive to macroeconomic conditions, result which is suggested in previous literature

1.3 BASELINE STICKY INFORMATION PHILLIPS CURVE

Every firm sets its price every period, but firms gather information and re-compute optimal prices slowly over time

?2 See MR (2010) for a recent survey on this literature

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In each period, a fraction 1 of firms obtain new information about the state of the economy and compute a new path of optimal prices, and (1- 4) firms continue to set prices based on old plans and outdated information

Each firm has the same probability of being one of the firms updating their information sets, regardless of how long it has been since its last update The expected time between price updates is therefore 1/2

A firm’s optimal price that maximizes expected profits at any given point in time is

P, =p,+ay,, where p, is the overall price level and y, is the output gap (or aggregate demand related variable).*° Notice that the desired price depends on the overall price level and output gap, so a firm’s desired relative price rises in booms and falls in recessions Also notice that a small o means that each firm gives more weight to the changes in prices set by other firms than to the level of aggregate demand

A firm that last updated its plans / periods ago sets its price as the expected value of the optimal price / periods ago: x/ =E_ j LÊ

The aggregate price level is the average of the prices of all firms in the economy, assuming that the arrival of decision dates is a Poisson process given by:

to expand the level of truncation to twelve periods According to my review, there is no major difference between KZ and other studies which use different strategies

In what follows, I replicate the methodology of KZ and describe the difference between their estimates and my estimations

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1.4.1 Khan and Zhu’s Estimation Strategy

The most important point in the KZ strategy is the truncation of Equation (1) The empirical counterpart of the SIPC suggested by KZ is:

For a given A, this approximation error gets theoretically smaller with an increase in the forecasting horizon KZ examine the sensitivity of their estimates to the choice of the truncation point Based on their methodology and the sample period, the longest forecasting horizon suggested is 20 quarters (7 = 19)

To estimate equation (2), KZ need a total of (7 +1) past expectations (or forecasts)

of current variables m and Ay, for each t Each of these forecasts is based on past information from periods t — 1, t —2, , t— 1 —j”™, respectively

KZ consider two methods for the output gap: the Hodrick—Prescott filter output gap and the quadratic detrended output gap They also consider three measures of inflation: consumer price index, core inflation, and the GDP deflator

To obtain the forecasts required for this database, KZ consider two methods for generating out-of-sample forecasts:

- Univariate autoregressive models for inflation and the output gap The lags are selected on the basis of the forecasting performance

- VAR-based methodology for inflation and output gap KZ estimate bivariate VARs using six financial and non-financial forecasting variables and then take a

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simple average of the forecasts from each bivariate VAR Each VAR is defined

3! For inflation forecasts, KZ use the short-term interest rate (federal funds rate, level), dividend yield (S&P

500 stock dividend yield, logarithm), term spread (difference between the 10-year government bond rate and the short-term interest rate, level), unemployment rate (level), capacity utilization (level), and output gap (logarithm) For output gap forecasts, the variables are short-term interest rate (level), dividend yield (logarithm), term spread (level), stock market price index (S&P stock price index, growth), capacity utilization (level) and inflation (level)

32 KZ (2006) use a equal to 0.10, Reis (2006b) uses a equal to 0.11, while Coibion (2010) uses a equal to 0.20 for the U.S Dépke et al (2008a) estimates of the SIPC include both values of a, 010 and 0.20 for robustness As discussed for Reis, the parameter a has two important implications First, a small @ would lead to both long periods of inattentiveness and a small 4 (in the context of the “inattentive producer”) Moreover, a smaller a generates larger real effects of nominal shocks, if ) be fixed Reis points out that the smaller is a, the stronger are strategic complementarities in pricing, implying that firms that are adjusting prices wish to set their individual prices close to those set by non-adjusting firms Through these two roles,

a small a leads to limited adjustment of prices and thus large real effects of nominal shocks Reis cite the work of Woodford (2003) who discusses the calibration of a at length Taking into account both micro and aggregate evidence Woodford concludes that a value between 0.10 and 0.15 is adequate Reiss also cite Chari, Kehoe, and McGrattan (2000, a = 0.17); Rotemberg and Woodford (1997, a = 0.13); and Ball and Romer (1990, a = 0.13) as reasonable values for o in the literature

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1.4.2 Methodological Alternative to Khan and Zhu’s Strategy The purpose of this section is to describe and present a consistent methodology for estimating a Phillips curve for every OECD country in the context of sticky information, following KZ (2006) strategy

Similar to KZ I test the null hypothesis Ho: 4 = 1 (no information stickiness), against the alternative, H,: 4 < 1 (some information stickiness)

KZ do not discuss the problems of Phillips curve single-equation estimation methods This type of estimations is subject to the endogeneity problem between output gap and inflation (single-equation bias) A second problem is the time period selected for their estimation KZ study covers a period of relatively lower inflation than the 70s and data of the 70s is only used to estimate the past expectations In this essay I incorporate both critiques: the sample period for the SIPC for the U.S goes from 1971 to 2007 and I use the lag of output gap as an instrument for output gap.*°

1.4.2.1 Building the data base

I collect quarterly data for all countries in the sample and use an eight years data period for iteratively forecasting inflation and output gap in order to generate expectations

of inflation and output The estimation of the SIPC for each country is based on aj” equivalent to five years.”

As Coibion (2010) points out, the estimation of X by non-linear least squares should

be biased given the endogeneity problem between inflation and output gap in equation

*? Another common critique in the literature for this paper is the lack of comparison of the SIPC predictive power with other estimation approaches like a NKPC or reduced forms I discuss this point in detail in the next section

** See Appendix for a detailed discussion of the database used in this essay

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(2) Coibion proposes IV non linear least squares as well as valid instruments I use the lag of the output gap as an instrument for the gap, in order to correct for the endogeneity problem between inflation and output gap

Rather than forecasting power in the time series approach for estimating the expectations of inflation and output, I use the log likelihood function of the time series specification I use Schwarz Information criterion for the optimal length of the ARIMA model This method contrasts with KZ (2006) who choose the optimal number of lags based on the smallest root-of-mean-squared forecasting errors in the ARIMA A similar argument applies to the VAR estimations.”°

Following KZ, { also eliminate the largest and the smallest forecast when taking the average in order to reduce the sensitivity to large outliers*° and use the forecast of output gap growth as the output gap forecast I use Newey-West heteroskedasticity and autocorrelation consistent (HAC) standard errors for the non-linear estimations of the

°° For more details, see Stock and Watson (2001)

°7 KZ take into account the “generated regressors” problem, generate 1000 bootstrapped samples for relevant variables, and obtain an estimate A, from the i“ bootstrap and its associated standard error, o,; where i = I, 2, B, and B = 1000 However, actual inflation and past expectations are not related in the estimation procedure, thus there is no need to consider the “generated regressors” problem

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1.4.2.2 Some important remarks Similar to KZ strategy, in this essay I am interested in the degree of information stickiness Thus my results are first focused on whether the data can reject the null of flexible information (A=1)

As pointed out before, I take into account the main critiques of KZ’s strategy Moreover, I expand the range of countries as well as consider the main factors that characterize the degree of information stickiness across countries In this regard, my results are mainly focused on the relationship between the degree of information stickiness and measures of uncertainty defined as high inflation, high variance of inflation, and high variance of the output gap

1.5 RESULTS

In this section, I present the main results of the paper First, 1 describe the estimation results for the U.S Most of the recent literature has been focused on the main results of the SIPC for the U.S given the long-period availability of data I find that my methodology is able to replicate the main results of KZ for a similar sample period for the degree of information stickiness Moreover, I compare two scenarios (low and high inflation) and document a change in the slope of the SIPC for the U.S., as suggested in Kiley (2007)

I also consider the cases of Canada and the U.K., countries which have a similar range

of data than that of the U.S I compare two scenarios and report the change in the slope of the SIPC following Kiley (2007) argument

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Then, I estimate the degree of information stickiness for other OECD countries Given the data availability and the required data to implement the SIPC estimation, I focus only

on 12 countries Finally, I homogenize the sample period for all the countries and document the relationship between the level and volatility of inflation and output gap

1.5.1 Sticky Information Phillips Curve for the U.S

For the case of the U.S., | use quarterly data from 1958 to 2007 and, as mentioned before, 32 quarters for forecasting inflation and output gap The /”"™” of the SIPC is equivalent to five years Within this framework, I am able to estimate the key parameter

of the SIPC: the degree of information stickiness The range of the SIPC goes from 1971

to 2007

Table 1.2 presents the regression results for equation (2) These results indicate that the degree of information stickiness in the U.S ranges between 0.35 (when the quadratic detrended output gap is considered) and 0.38 (when the Hodrick Prescott output gap is used) This implies that firms update information every 3 quarters on average for the sample period 1971 — 2007

In Figure 1.1, it is possible to contrast periods of high inflation (from the 70s to early 80s) with periods of low inflation (from early 80s to 2007) which suggests a change in the regime (state) of the inflation patterns as pointed out in Kiley (2007)

I split the sample in two: from 1971 to 1982 (period of high inflation, with an average

of 7.6 percent) and from 1983 to 2007 (period of low inflation, with an average of 3.1 percent) Not only the average level of inflation decreases but also the variance of the inflation rates decreases and goes from 0.09 in the first part to 0.01 in the second part

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Table 1.3 presents the regressions for these two sample periods For the period 1971 ~

1982, the degree of information stickiness (parameter 4) is 0.50, which suggest that price setters update information more frequently (two quarters in average) when inflation is higher In contrast, the degree of information stickiness is around 0.16 which implies an average duration of information stickiness of six quarters when a low inflation period is considered These results are robust to different measures of output gap

Under the modifications suggested in this essay for forming past expectations of current values, I obtain estimates of 4 that range between 0.35 and 0.38 for the period

1971 — 2007, which implies an average duration of information stickiness of three quarters This result contrasts with the four quarters that KZ estimate As another test of robustness of my strategy I estimate the SIPC for 1980 — 2000 which is the same sample period employed for KZ My A equals to 0.25 which is similar to the 0.24 obtained for

KZ (see Table 1.4) The changes proposed in this essay make the estimations of the degree of information stickiness more efficient and allows for taking into account periods

of high inflation

Moreover, I find that the degree of information stickiness is lower when a period of high inflation is considered This suggests that firms update information more frequently when they are facing a high level of inflation In contrast, the degree of information stickiness is higher when a period of low inflation is considered This hypothesis is tested for countries with similar sample periods as well as for a cross country analysis in the following sub-sections

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1.5.2 Sticky Information Phillips Curve for Canada and the U.K

Similar to the case of the U.S., the data for Canada and the U.K samples from 1958 to

2007 Eight years are used for forecasting inflation and output gap and aj” equal to 20

is considered I am able to estimate an SIPC that ranges from 1971 to 2007 In both cases, the average duration of information stickiness increases by one quarter between a period

of high inflation to a period of low inflation (see Table 1.5 and 1.6)

In the case of Canada, the degree of information stickiness is 0.26 for the period 1971

— 2007 The average rate of inflation is 4.6 percent, which takes into account a period of high inflation and a period of low inflation In between 1971 and 1982, the average inflation is 8.3 percent which contrasts with the average inflation in the period 1983 —

2007 which is only 2.8 percent In the first period, the degree of information stickiness is 0.27 (3.7 quarters) while in the second period is 0.22 (4.5 quarters) considering the quadratic detrended output gap

Both the level of inflation and the volatility of the inflation rates decrease between the first and second period The variance of inflation goes from 0.07 to 0.02 in between these two periods Similar to the case of the U.S., the level of information stickiness increases and moves from 0.27 (3.7 quarters) to 0.22 (4.5 quarters) when the quadratic detrended output gap is considered, and moves from 0.35 (2.9 quarters) to 0.27 (3.7 quarters) when the Hodrick Prescott output gap is considered (see Table 1.5)

For the U.K., 4 is 3.4 during the period 1971 — 2007 which takes into account an average inflation is 6.5 percent During 1971 — 1982, the period of higher inflation, the U.K economy has an inflation of 12.3 percent and my estimation of the lambda

*8 Similar results hold for the Hodrick Prescott output gap

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parameter is 0.33 (consistent with 3.4 quarters of information stickiness) During 1982 —

2007, the period of low inflation, the average inflation is 3.7 percent and the lambda parameter for that period is 0.23 (implying 4.3 quarters of inattentiveness)

Similar to the cases of the U.S and Canada, the volatility of inflation gets lower as well For the period of high inflation, the variance is 0.21; while for the period of low inflation, the variance is only 0.04 The average duration of information stickiness is also greater, going from three to four quarters Similar to the previous cases, this suggests that price setters up date information more frequently when inflation is higher (see Table 1.6)

In what follows, I also try cross country analysis for robustness of this result

1.5.3 Sticky Information Phillips Curve for other OECD Countries

I follow the same strategy used for the U.S., Canada, and the U.K for the remaining countries of the sample I consistently estimate the degree of information stickiness for different countries for different sample periods as reported in Table 1.7 In all the cases, |

am able to reject the null hypothesis of flexible information

The degree of information stickiness consistent with the sample data for each country ranges from 0.10 (Germany)” to 0.35 (the U.S.) when the quadratic detrended output gap

is considered When the Hodrick Prescott output gap is considered, X goes from 0.15 (Germany) to 0.38 (the U.S.) In terms of quarters of inattentiveness, it ranges from 2.8 quarters to 9.5 quarters when the quadratic detrended output gap is considered; and from 2.7 quarters to 6.6 quarters when the Hodrick Prescott output gap is considered

*° The unification process of Germany in the 90s makes it difficult to consistently have information at the aggregate level for CPI | use the data available from IFS in this case

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