Pricing decisions in an experimental dynamic stochastic general equilibrium economy

Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C. Pricing decisions in an experimental dynamic stochastic general equilibrium economy Charles N. Noussair, Damjan Pfajfar, and Janos Zsiros 2014-93 NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. References in publications to the Finance and Economics Discussion Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers.

Pricing decisions in an experimental dynamic stochastic general equilibrium economy (cid:3) Charles N. Noussair Damjan Pfajfar Janos Zsiros y z x University of Tilburg Federal Reserve Board Cornell University October 24, 2014 Abstract. We construct experimental economies, populated with human subjects, with a structure based on a nonlinear version of the New Keynesian Dynamic Stochastic General Equilibrium (DSGE) model. We analyze the behavior of (cid:133)rms(cid:146)pricing decisions in four di⁄erent experimental economies. We consider how well the experimental data conform to a number of accepted empirical stylized facts. Pricing patterns mostly conform to these patterns. Most price changes are positive, and in(cid:135)ation is strongly correlated with average magnitude, but not the frequency, of price changes. Prices are a⁄ected negatively by the productivity shock and positively by the output gap. Lagged real interest rate has a negativee⁄ectonprices,unlesshumansubjectschoosetheinterestrate,or(cid:133)rmssellperfect substitutes in the output market. There is inertia in price setting, (cid:133)rms integrate wage increases into their prices, and there is evidence of adaptive behavior in price-setting in our laboratory economy. The hazard function for price changes, however, is upward-sloping, in contrast to most empirical studies. JEL: C91; C92; E31; E32 Keywords: Experimental Economics, DSGE Economy, Pricing Behavior, Menu Costs. (cid:3)WewouldliketothankJohnDu⁄y,JohnRoberts,ShyamSunder,OlegKorenok,Ste⁄anBall,RicardoNunes, MichielDePooter,WolfgangLuhan,andparticipantsattheFederalReserveBoard,theUniversityofInnsbruck, the1stand2ndLeeXInternationalConf. onTheoreticalandExperimentalMacroeconomics(Barcelona),the2011 ComputationalEconomicsandFinanceConf. (SanFrancisco),the2011MidwestMacroMeetings(Nashville),the 2011 SEA Meetings (Washington), the DSGE and Beyond Conf. at the National Bank of Poland (Warsaw), the 2010 North American ESA Meetings (Tucson), the WISE International Workshop on Experimental Economics and Finance (Xiamen), the 5th Nordic Conf. on Behavioral and Experimental Economics (Helsinki), and the 2010 International ESA Meetings (Copenhagen) for their comments. We are grateful to Bla(cid:181)z Z(cid:181)akelj for his help with programming. The views expressed in this paper are those of the authors and do not necessarily re(cid:135)ect those of the Federal Reserve Board. yCentER, Department of Economics, Tilburg University, P.O. Box 90153, NL-5000 LE Tilburg, Netherlands. E-mail: C.N.Noussair@uvt.nl. Web: https://sites.google.com/site/charlesnoussair/. z20th and Constitution Ave. NW, Washington, D.C. 20551, USA. E-mail: Damjan.Pfajfar@frb.gov. Web: https://sites.google.com/site/dpfajfar/. xDepartment of Economics, Cornell University, 404 Uris Hall, Ithaca, N.Y. 14853, USA. E-mail: zsiros@gmail.com. 1

2 1. Introduction Any accurate model of the macro-economy must be able to generate the stylized facts that characterize empirical data. One important feature of the macroeconomy is the existence of consistent patterns in how (cid:133)rms set and update their prices over time. Motivated by the importance of micro-level pricing behavior for generating business cycles, a number of studies havedocumentedclearempiricalpatternsinpricesettingdecisions(forasurveyseeKlenowand Malin,2010). Inthispaper,weconsiderwhichenvironmentsbestreproduceanumberofstylized factsaboutpricing. Weexploretheimplicationsofdi⁄erentassumptionsonthestructureofthe economy for the pricing decisions of individual (cid:133)rms. The environments we study all have the Dynamic Stochastic General Equilibrium (DSGE) structure, which is currently the workhorse paradigm for macroeconomic policy making. Weemployanexperimentalapproach. Theuseofanexperimentallowsustospecifyandvary the structure of the economy as desired, while permitting complete freedom for the individuals placed in the role of (cid:133)rms to make their pricing, production, and factor purchase decisions. The key di⁄erence between employing experimentation with human subjects, as we do here, and conducting simulations, is that we leave agents(cid:146)decision making uncontrolled. For the questions of interest here, we do not wish to impose any structure exogenously on the strategies agents use. The experimental design consists of four di⁄erent environments. Each environment di⁄ers from one of the others in terms of exactly one feature. This structure allows the e⁄ect of that one feature on pricing behavior to be isolated. Our experimental economy is based on a New Keynesian DSGE model. In the DSGE framework, inertia in output prices can generate persistence of demand and supply shocks. In turn, macroeconomic events, such as shocks to demand, productivity, or monetary policy, a⁄ect pricing behavior of individual (cid:133)rms. There are four treatments, that vary in terms of frictions, which may potentially create price inertia, that are present in the economy. Pairwise comparisons of our treatments isolate the e⁄ect of the presence of monopolistic, rather than perfect, competition, as well as the existence of menu costs, in the output market. Another comparisonbetweentwotreatmentsisolatesthee⁄ectofdiscretionaryinterestratesettingversus strict adherence to a Taylor-type policy rule. Note that this treatment introduces another layer of uncertainty in the economy that could potentially change pricing behavior. Additionally, the shocks in the economy could be propagated in a di⁄erent manner in the case of human central banker. Inouranalysis, wecomparepricingpatternsinourdatatothosedescribedinNakamuraand Steinsson(2008),BilsandKlenow(2004),andKlenowandMalin(2010),andtestthehypotheses that the stylized facts they document appear in our data.1 We then compare the behavior of the four environments. Speci(cid:133)cally, we measure the average frequency and magnitude of price changes, and how these correlate with overall in(cid:135)ation. We evaluate whether positive changes are more frequent than negative changes, and by what percentage. We check how the frequency and size of price changes covary with in(cid:135)ation. We consider whether the hazard rate of price 1These studies use product-level data from the US.

3 changes is decreasing or increasing over time. The hazard rate of price changes indicates the probability of a price change, as a function of the length of time that the same price has been in e⁄ect. In addition, we conduct some exploratory analysis on the data. We estimate the markup that producers charge. We analyze the e⁄ect of macro variables such as productivity, output gap, and interest rate on prices set by (cid:133)rms in our economy. We also evaluate how micro level variablesin(cid:135)uenceprices,inparticularhowpastprices,currentwagecosts,andpastpro(cid:133)tability a⁄ect the prices set by (cid:133)rms in di⁄erent treatments. We also check whether the behavior of human central bankers is in line with the Taylor principle, i.e., the response of the nominal interest rate to in(cid:135)ation must be greater than 1 in the long-run. The principal (cid:133)ndings, which are presented in section four, are the following. Pricing patterns mostly conform to empirical stylized facts. Which treatment conforms most closely to (cid:133)eld data depends on the speci(cid:133)c variables considered. Most price changes are positive, with the percentage of positive changes remarkably close to that observed in (cid:133)eld data. In(cid:135)ation is strongly correlated with the average magnitude, but not the frequency, of price changes. The hazard function for price changes, however, is upward-sloping. This means that the likelihood that a (cid:133)rm changes its price in a period is greater the longer it has kept its price constant. This stands in contrast to most empirical studies, but is consistent with the DSGE model with menu costs (see e.g., Alvarez, Lippi, and Paciello, 2011). Our data analysis yields a number of other basic relationships between macroeconomic variables, as well as between these variables and institutions that would be di¢ cult to isolate in non-experimental economies. Menu costs reduce the variability of in(cid:135)ation. Prices are a⁄ected negatively by productivity shocks and positively by the output gap under most regression speci(cid:133)cations. The lagged real interest rate has a negative e⁄ect on prices, unless the output market is very competitive. There is inertia in price setting, (cid:133)rms integrate wage increases into their prices, and there is evidence of adaptive behavior in price setting. Results regarding "central bankers" suggest that they set the nominal interest rates where they respond more than one-to-one with respect to changes in the in(cid:135)ation.2 2. Experimental Design In this section, we describe the DSGE model that is the basis for the experimental design. Additional details about the implementation are described in the online appendices. The analysis of the macroeconomic data in the economy is reported in a companion paper (Noussair, Pfajfar, and Zsiros, 2013). Subjects were all undergraduate students at Tilburg University. Four sessions were conducted under each treatment for a total of sixteen sessions. Six subjects participated in each session (three consumers and three producers), with the exception of sessions of the Human Central Banker treatment. In this treatment, there were 9 participants, three consumers, three producers, and three central bankers. No subject participated in more than one session. Only 2Engle-Warnick and Turdaliev (2010) also study the monetary policy decisions of inexperienced human subjects. They(cid:133)ndthatthesensitivitytoin(cid:135)ationis,onaverage,closetoorabove1intheirinterestratedecisions.

4 one treatment was in e⁄ect in any session. The sessions consisted of 50 70 periods,3 and took (cid:0) onaverageroughlyfourhours. Participantearningsaveraged49:50Euro(roughly66USD).The experiment was computerized and used the Z-Tree platform developed by Fischbacher (2007). 2.1. The DSGE model. The dynamic stochastic general equilibrium (DSGE) model is the workhorse of modern macroeconomic research and policy.4 In the model, there are three types of agent: households, (cid:133)rms, and a central bank, who interact over an in(cid:133)nite horizon. Households choose labor supply, consumption, and savings to maximize the discounted present value of the utility of consumption and leisure. Firms choose the quantity of labor to employ, and output to produce, to maximize pro(cid:133)ts. The central bank sets the nominal interest rate to maximize a speci(cid:133)c function of in(cid:135)ation and output. Speci(cid:133)cally, in each period, the representative consumer works, consumes, and decides on a saving level at each time t, in order to maximize the expected discounted value of her utility of consumption and leisure u(C ;(1 L )) over an in(cid:133)nite horizon. The consumer solves: t t (cid:0) maxE 1 (cid:12)i C t 1 +(cid:0)i (cid:27) L1 t+ + i (cid:17) ; (1) t 1 (cid:27) (cid:0) 1+(cid:17) ( ) i=0 (cid:0) X subject to the following budget constraint P C +B = W L +(1+i )B +P (cid:5) ; (2) t t t t t t 1 t 1 t t (cid:0) (cid:0) where # 1 # 1 # 1 C = c (cid:0)# dj (cid:0) ; # > 1: (3) t jt (cid:18)Z0 (cid:19) # is the elasticity of substitution in consumption in the Dixit-Stiglitz aggregator, P is the t corresponding price index, C is consumption, L is labor supplied, i is nominal interest rate, t t t B denotes savings, W is the market wage, (cid:12) is the intertemporal discount factor, (cid:17) is the t t inverse of the Frisch elasticity of labor supply, (cid:27) is the intertemporal elasticity of substitution in demand, and (cid:5) is the total pro(cid:133)t of (cid:133)rms at t. t Firms have a stochastic production technology, given by: f (L ) = A L ; (4) jt jt t jt where A is a technology shock, which is common to all (cid:133)rms. It has the functional form t A = A+(cid:23)A +& ; (5) t t 1 t (cid:0) 3While this experiment involves very lengthy sessions compared to most experimental studies, we felt that these long sessions were appropriate for two main reasons. The (cid:133)rst is that the complexity of the experiment required subjects to spend more time on training and practice than in the typical experiment. The second is that, because we were interested in the dynamics of price setting behavior, and prices might not be changed for long spells, we felt that a long time series was necessary to accurately observe the patterns of price changes. 4For a detailed discussion of the model, see the books by Walsh (2003) and Woodford (2003).

5 where & is independent white noise & N(0;(cid:14)). The (cid:133)rms(cid:146)objective is to minimize their t t (cid:24) expenditure for a certain level of production: W t min L ; (6) jt P t subject to c = Z L ; jt t jt where c is the (cid:133)rm(cid:146)s level of production of the good that it produces.5 jt There is perfect competition in the labor market, and monopolistic competition (Dixit and Stiglitz, 1977) on the output market. The market power for producers in the output market follows from the elasticity of substitution in consumption in the Dixit-Stiglitz aggregator, represented by # in equation (3). The nominal interest rate in the economy (see, for example, Woodford, 2003) is set to minimize the loss function minL = ((cid:25) (cid:25) )2+(cid:21)(x x )2; (7) t (cid:3) t (cid:3) (cid:0) (cid:0) where (cid:25) is actual in(cid:135)ation, (cid:25) is the in(cid:135)ation target, x x is the output gap, and (cid:21) is a t (cid:3) t (cid:3) (cid:0) parameter that indicates the relative weight of in(cid:135)ation and output in policy determination. 2.2. Departures from the DGSE model. The actual model implemented in the laboratory was a modi(cid:133)cation of the DSGE model described above. The changes we made were guided by concerns about what was feasible given the resources we had available. The standard DSGE model has no explicit timing within each period. However the implementation in the laboratory requires that some decisions be taken before others. We cannot expect the consumers to submit the full schedules of their demand of (cid:133)nal products and supply of labor contingent on all possible realizations of other relevant variables. Therefore, we had to make a number of decisions regarding the timing of activities within a period. Here we were guided by evidence about production processes in the (cid:133)eld (real world). We assumed that the technology shock was observed before the labor market began to operate, with the e⁄ect that it reduced the uncertainty regarding the number of units produced. After the labor market closed,6 production took place transforming labor into output. Then producers posted prices on the output market, and consumers had an opportunity to make purchases at the posted prices. Discounting was implemented by reducing the induced value of consumption of each of the output goods, as well as the utility cost of labor supply, by 1 (cid:12) = 1% in each period. (cid:0) 5Thisoptimizationproblemcouldbereformulatedintermsofpro(cid:133)tmaximization,wheretheobjectiveofthe (cid:133)rm is to maximize pro(cid:133)t in each period. 6Thelabormarketwasimplementedwithacontinuousdoubleauctiontradingmechanism(Smith,1962;Plott and Gray, 1990), where consumers and producers could exchange labor. A continuous double auction market is knowntogeneratecompetitiveoutcomes,evenwithasmallnumberofagentsoneachsideofthemarket(Smith, 1982).

6 Creating a monopolistically competitive environment in the (cid:133)nal good market necessitated a substantive departure from the model. Direct implementation of Dixit-Stiglitz preferences, as inequation(3), isnotfeasibleinthelaboratory. Thisisbecauseitrequiresanin(cid:133)nitenumberof goods, whichinturnrequiresanin(cid:133)nitenumberofproducers. Thisisnotpossibletoimplement unless we resort to having arti(cid:133)cial agents as producers. We pursue an alternative way to create imperfect substitutability between goods, where we impose a di⁄erent utility valuation of goods across consumers. Using taste shocks with di⁄erent drifts for each good-consumer match we are able to create an environment, where from the point of view of each consumer, each good has a di⁄erent value,7 and partial substitutability between goods is maintained. While producers have equal market power, its overall degree is ex-ante uncertain in this environment. Therefore, we use the data from the experiment to compare the implied elasticities of substitution with the estimates that are used in the literature to investigate the actual degree of market power. In the experiment, each consumer was endowed with an induced valuation (Smith, 1982) for the following objective function: u (c ;c ;c ;(1 L )) = (cid:12)t 3 H c i 1 j(cid:0)t (cid:18) (cid:11) L1 it +(cid:15) ; (8) it i1t i2t i3t it ijt (cid:0) 8 1 (cid:18) (cid:0) 1+(cid:15)9 ! <X j=1 (cid:0) = where c is the consumption of the ith consum:er of good j, and L is the ;labor i supplies, at ijt it time t. H denotes the preference (taste) shock, which is speci(cid:133)c to each consumer and good ij in each period, and follows the process: H = (cid:22) +(cid:28)H +" : (9) ijt ij ijt 1 jt (cid:0) The white noise processes " , " , and " are independent, and " N(0;(cid:16)). The preference 1t 2t 3t jt (cid:24) shocks follow an AR(1) process. 2.3. Treatments. Table 1 gives a summary of the di⁄erences between the four treatments. Treatment Monopolistic competition Human central banker Menu cost for price change Baseline Yes No No Menu Cost Yes No Yes Human CB Yes Yes No Low Friction No No No Table 1: Summary of treatments The Baseline treatment was based on the model above, but with a number of di⁄erences, 7Forexample,forthe(cid:133)rstunitofgood1consumer1willgeta"highlevel"ofutility,whileconsumer2willget a"medium level"ofutility and consumer3willgeta"low level"ofutility. Forthe(cid:133)rstunitofgood 2consumer 2 will get the "high level" of utility, while consumer 3 will get the "medium level" of utility and consumer 1 will get the "low level" of utility, etc.

7 which are detailed in Appendix B.8 The three other treatments each di⁄ered from the Baseline treatment in one aspect. The Menu Cost treatment was identical to Baseline, except that each (cid:133)rm incurred a small cost if it posted a price in the output market that was di⁄erent from the price it posted in the immediately preceding period. The Low Friction treatment di⁄ered from the Baseline treatment in that the output of all (cid:133)rms were perfect substitutes for each other. This means that from the viewpoint of consumers, all three goods are perfect substitutes at all times, regardless of prior consumption in the current period. Thus, in e⁄ect, the parameter # in equation (3) is set to or in terms of our 1 experimental implementation H was replaced with H in equation (8). ijt t Lastly, the Human Central Banker treatment was di⁄erent from the Baseline treatment in that human participants chose the interest rate in each period.9 They received incentivized payments based on how close actual in(cid:135)ation from one period to the next was to the target rate of 3 percent. Table 2 contains a summary of parameter values used in the experiment. The parameters of the model are taken from empirical estimates when possible, with each period t corresponding to one three-month quarter in the (cid:133)eld. Exactly the same parameters were in e⁄ect in all treatments, except for the preference shock process in the Low Friction treatment. (cid:12) (cid:18) (cid:15) (cid:11) (cid:28) (cid:23) A (cid:14) (cid:16) (cid:25) (cid:22) (cid:3) 95 62 37:8 0:99 0:5 2 15 0:8 0:8 0:7 0.2 1 0:03 38:2 93 64 0 1 33 59:6 97 @ A Table 2: Parameters 3. Hypotheses We advance four sets of hypotheses. The (cid:133)rst asserts that treatment di⁄erences exist. The second relates to the patterns of price setting. The third concerns the relationships between prices and macroeconomic variables. The fourth hypothesis relates to the behavior of human central bankers. We evaluate the hypotheses in section four. The (cid:133)rst set of hypotheses relates to di⁄erences between treatments that are consequences of basic microeconomic relationships. In the Low Friction treatment the (cid:133)nal products are perfect substitutes. Therefore, we expect that the market power of individual (cid:133)rms would be lower compared to a treatment with monopolistic competition, and thus the average markup would be lower. In the baseline theoretical New Keynesian DSGE model, there are no e⁄ects of menu costs on average markup, although the presence of nominal frictions produces time 8Appendices B, C, and D are available in online Supplementary Material at https://sites.google.com/site/dpfajfar/publications. 9At the beginning of each period, each of the three central bankers submits a proposed interest rate for the period. The median proposal became the interest rate in e⁄ect for the period. This procedure e⁄ectively implements the median voter(cid:146)s ideal point.

8 varying markups. There is also no reason to suppose a priori that human central bankers would have a consistent e⁄ect on markups. However, it might be expected that in the Menu Cost treatment, price changes would be less frequent compared to other treatments, because the (cid:133)rm pays a cost to change its price. Among the other treatments, there is no reason to suppose that the frequency of price changes would di⁄er. Hypothesis 1: Treatment di⁄erences (and non-di⁄erences) (a) Hypothesis 1a: Average markups are lower under the Low Friction treatment than under the other three treatments. (b) Hypothesis 1b: Average markups are equal in the Baseline, Human Central Banker and Menu Cost treatments. (c) Hypothesis 1c: In the Menu Cost treatment, price changes are less frequent than in the other treatments. (d) Hypothesis 1d: The frequency of price changes is equal in the Baseline, Human Central Banker and Low Friction treatments. The second set of hypotheses originates in empirical stylized facts from the (cid:133)eld. Klenow and Malin (2010) and Nakamura and Steinsson (2008) report that positive price changes are more frequent than negative changes in disaggregated data for the US. Klenow and Kryvtsov (2008) (cid:133)nd that in their sample, also using US data, that in(cid:135)ation is only weakly correlated with the fraction of prices that change. The average size of changes, however, has a correlation with in(cid:135)ation of nearly 1. The time pro(cid:133)le of the hazard rate of price changes has been debated in the literature. An upward sloping hazard rate would bring DSGE models more in line with the stylized facts about the behavior of in(cid:135)ation and output gap, see Sheedy (2010) and Alvarez et al. (2011). However, the empirical literature has mostly found that the hazard rate is not upward-sloping (see, e.g., Klenow and Kryvtsov, 2008 and Nakamura and Steinsson, 2008). Hypothesis 2 is that the empirical patterns described above would appear in our data. Hypothesis 2: In the output markets, price changes between periods t and t+1 exhibit the following patterns: (a) Hypothesis 2a: Positive price changes are more frequent than negative changes. (b) Hypothesis 2b: The average absolute magnitude of price changes covaries strongly with in(cid:135)ation, but the frequency of price changes does not. (c) Hypothesis 2c: The hazard rate of price changes is decreasing, that is, price changes are less likely, the longer the same price has been in e⁄ect. The next hypothesis relates prices to macroeconomic variables in the economy. These are productivity, output gap, and wages. In a perfectly competitive product market, marginal revenueisequaltomarginalcost,thereforeifproductivityincreases,thenpriceshavetodecrease

9 when wages are (cid:133)xed. In a monopolistically competitive output market, similar logic drives prices to decrease as a consequence of increased productivity. However, the decrease is the smallest in the case of perfect competition on the market.10 Gali and Gertler (1999) and Gali, Gertler, and Lopez-Salido (2005) estimate the hybrid New Keynesian Phillips curve. Both papers (cid:133)nd a positive and signi(cid:133)cant relationship between in(cid:135)ation and marginal cost. Gali and Gertler (1999) show that under certain conditions there is a log-linear relationship between the two variables. This implies a positive and signi(cid:133)cant relationship between the output gap and in(cid:135)ation in the US economy. Furthermore, the output gap is serially correlated. Therefore, we expect a positive sign of the lagged output gap on prices in our estimation, and a smaller e⁄ect under the Baseline than under the Low Friction treatment.11 The empirical work discussed above serves as the basis for hypothesis 3. Hypothesis 3: Price setting and macroeconomic variables (a) Hypothesis 3a: Prices that individual (cid:133)rms charge are negatively correlated with productivity shocks. (b) Hypothesis 3b: Prices that individual (cid:133)rms charge are positively correlated with the lagged output gap. (c) Hypothesis 3c: Prices that individual (cid:133)rms charge are positively correlated with wages. The fourth hypothesis concerns the behavior of the human central bankers. It is that their behavior follows the Taylor principle. The Taylor principle states that the response of the nominal interest rate to in(cid:135)ation must be greater than 1 in the long-run in order to guarantee determinacy (Woodford, 2003). The rationale for this hypothesis is both theoretical and empirical. Application of the principle is optimal in the New Keynesian framework, and central bank policies tend to satisfy the principle. Furthermore, the available evidence suggests that the principle is fairly transparent to typical experimental subjects in the role of central bankers in simple economies. Hypothesis 4: Taylor Principle: Under the Human Central Banker treatment, interest rate policy follows the Taylor principle. 10Someempiricalstudies(cid:133)ndnegativeestimatesfortherelationshipbetweenproductivityandin(cid:135)ation. However, Cameron, Hum, and Simpson (1996) show that this negative relationship is due to a statistical bias from attempting to cointegrate stationary and non-stationary variables. They (cid:133)nd no evidence for a connection between in(cid:135)ation and productivity, but do (cid:133)nd a strong relationship between productivity growth and in(cid:135)ation, which is internally inconsistent, thus they claim it is implausible. There is also ambiguity about the direction of the causality between in(cid:135)ation and productivity. Ram (1984) (cid:133)nds that productivity changes have no Granger casualimpacton in(cid:135)ation,butthatin(cid:135)ationdoeshavean impacton productivity. Inlinewith economictheory, we expect a negative relationship between productivity and prices, because we can perfectly control for wage changes. 11Based on the discussion in the previous paragraph, the expected sign of the e⁄ect of changes in the macroeconomic variables on the probability of price change can be inferred. If a variable a⁄ects the magnitude of a price, then by de(cid:133)nition it has to increase the probability of changing the price. However, these e⁄ects on the probability of price changes are smaller in case of menu costs, since (cid:133)rms have to pay an additional cost, and thus they are less likely to change prices.

10 4. Results 4.1. Markups and hypothesis 1a and 1b. Hypotheses 1a and 1b are mostly supported in the data. The costs of price changes, substitutability of the goods, and the manner in which policy is determined all a⁄ect average price markup levels. Low Friction generates the lowest markup among the four environments, and discretionary central banking does not have a systematic e⁄ect on markups compared to the use of a (cid:133)xed Taylor rule. However, the presence of Menu Costs lowers average markups sharply. Result 1 summarizes how our results accord with Hypothesis 1a and 1b. Result 1a: Average markups are lower under the Low Friction treatment than under the other three treatments. Result 1b: Low Friction generates the lowest markup among the four environments. Average markups are similar in the Baseline and Human Central Banker treatments. The markup that (cid:133)rms charge for their product is a measure of market power in a DSGE economy. Toinvestigatethedegreeofmarketpowerinourexperimentaleconomies, weestimate theinversedemandfunction. Thisallowsustoevaluatethelevelofmonopolisticcompetitionwe havecreatedwithourexperimentaldesignacrosstreatmentsandcompareittolevelscommonly assumed in the DSGE literature. We estimate the following inverse demand function: 1 lnp lnP = (lnC lnc )+" ; (10) jt t t jt t (cid:0) # (cid:0) P istheaveragepriceandC istotalconsumption. Weestimate 1 usingapaneldatapopulation t t # average estimator with cluster-robust standard errors. # is then the markup, according to # 1 (cid:0) the theoretical DSGE model. We can compare these elasticities with # = 10, corresponding to a markup of roughly 11%, which is a typical estimate in the DSGE literature (Fernandez- Villaverde, 2009). Table 3 shows the estimated, as well as the actual average, markups observed in the experiment. The average markup is measured as the actual pro(cid:133)t per unit produced, divided by its price. Baseline Human CB Menu Cost Low Friction Elasticity of substitution in demand, # 4.27 4.58 16.40 31.73 Markup implied by # 30.6% 27.8% 6.5% 3.2% Observed average markup 37.5% 37.5% 22.1% 11.1% Table 3: Estimated elasticities of substitution in demand and markups for each treatment. Thegreatestvalueoftheelasticityofsubstitutionindemand(#),andthusthelowestmarkup (3:2%),isfoundintheLowFrictiontreatment. TheMenuCosttreatmenthasamarkuproughly twice as great as the Low Friction treatment. Both the Baseline and Human Central Banker treatmentshavemuchlowervaluesof#thantheMenuCostandLowFrictiontreatments. Their

11 markups are 30:6 % and 27:8%, respectively. The actual markup displays similar treatment di⁄erences as the estimates, though they are typically greater in magnitude. This shows that the presence of menu costs or perfect substitutability between products decreases the market power of (cid:133)rms, although the e⁄ect of menu costs is smaller.12 This exercise enables us to assess the level of market power created in our experiment. Our implementation of perfect substitution between products is indeed close to perfect competition, though the small number of sellers still gives them a bit of market power. The monopolistic competition environment results in a fair degree of market power. 4.2. Price Changes and Hypotheses 1c, 1d and 2. Frequency of price changes. We next evaluate the remaining two statements in Hypothesis 1 (c and d) by focusing on the overall frequency of price changes.13 Table 4 contains a summary of the incidence and direction of price changes in our economy as a percentage of the total number of opportunities to change prices. The percentages of increases and decreases, conditional on a price change occurring, are indicated in parentheses. In our experiment, (cid:133)rms change their prices in 74:5% of periods on average. As a comparison, for (cid:133)eld data, Klenow and Kryvtsov (2008) calculate that the average monthly frequency of price changes is 36:2%, or equivalently 73:8% per quarter, (under the assumption of a constant hazard rate) for posted prices between 1988 and 2005.14 While it may be questionable to directly compare these frequencies with our experimental data due to potential di⁄erences in the de(cid:133)nition of a period, the percentages are close to those in our data if each of our periods is compared to one 3-month quarter. Indeed, theparametersoftheeconomywerecalibratedonthebasisofonethree-month quarter being equivalent to one period. Price changes Positive price changes Negative price changes Treatment (as a % of all cases) (as a % of all cases) (as a % of all cases) All 74.5 47.5 (64%) 27.0 (36%) Baseline 85.9 52.1 (61%) 33.8 (39%) Human CB 84.8 52.6 (62%) 32.1 (38%) Menu cost 40.9 31.1 (76%) 9.8 (24%) Low friction 86.3 53.9 (63%) 32.4 (37%) Table 4: Summary of positive and negative price changes 12When studying the dynamics of the actual markup we (cid:133)nd that it tends to exhibit a slight increase over time. 13Inalloftheanalysesinthispaper,onlythe(cid:133)rst50periodsofeachsessionareused. Wehavealsoconductedall ofouranalysesseparatelyforthe(cid:133)rst20periods,andforperiods30-50ofoursessions,inordertocompareearly and late periods. Some modest di⁄erences appear between these two subsets of data. Similar small di⁄erences appear between each subset and the pooled data from the entire session. The average magnitude of absolute price changes tends to increase over time. Regressions analysis shows that price inertia is more pronounced in early periods. See the Appendix B in the online Supplementary Material for details. 14Their estimation is based on monthly data from all products in the three largest metropolitan areas in the US, from monthly data for food and fuel products in all areas, and bimonthly data for all other prices. Their estimated weighted median frequency of monthly price changes is 27:3%.

12 There is virtually no di⁄erence between the Baseline, Human Central Banker and Low Friction treatments (the price changes in about 85% of possible instances). Standard nonparametric tests (Wilcoxon/Mann-Whitneym, Kruskal-Wallis and van der Waerden), using sessions as observations, show no signi(cid:133)cant di⁄erences in the frequency of price changes between these treatments. However, there are signi(cid:133)cant di⁄erences between the Menu Cost and each of the other treatments at about 3% signi(cid:133)cance level. In the Menu Cost treatment, (cid:133)rms change their prices 40:9% of the time, which is roughly half of the average percentage of instances that (cid:133)rms change their prices in the other treatments. Thus, the introduction of menu costs has a signi(cid:133)cant e⁄ect on the price setting behavior of (cid:133)rms. Results 1c and 1d are part of the evaluation of hypothesis 1 that concerns treatment di⁄erences.15 Result 1c: In the Menu Cost treatment, price changes are less frequent than in the other treatments. Result 1d: The frequency of price changes is equal in the Baseline, Human Central Banker and Low Friction treatments. Vermeulen, Dias, Dossche, Gautier, Hernando, Sabbatini, and Stahl (2007) (cid:133)nd that the degree of competition a⁄ects the frequency of price changes. The greater the degree of competition, the greater the frequency of price changes, especially decreases. Here, we also (cid:133)nd the greatest frequency of changes in the Low Friction treatment, the most competitive condition, although it is not statistically di⁄erent from the Baseline treatment. Our (cid:133)ndings with regard to the Hypothesis 2a are summarized as Result 2a. Result 2a: Positive price changes are more frequent than negative changes. Nakamura and Steinsson (2008) report that 64:8% of price changes are increases.16 This percentage corresponds closely to our experiment, as can be seen in table 4, in the values given in parentheses. In our data, 64% of price changes are price increases, and 36% are decreases. The behavior in the Menu Cost treatment is once again signi(cid:133)cantly di⁄erent from the other treatments at the 5 percent level. Under Menu Cost, 76% of price changes are increases, while only 24% are decreases. The percentages in the other three treatments are not signi(cid:133)cantly di⁄erent from each other. One potential reason we observe more positive price changes is that in our experiment (as in the case of the U.S.) there was on average a positive rate of in(cid:135)ation. Size of price changes. Table 5 gives a summary of the average, and average absolute, price changes in the experiment. The average absolute price change, indicated in the second columnofdata,is16:2%overalltreatments. Theaveragepricechange,showninthe(cid:133)rstcolumn 15Thefrequencyofthepricechangesissimilarinearlyandlateperiodsofthesessions. Howeverpositiveprice changes are more frequent in the beginning of the sessions than at the end. 70% of the price changes are price increases in the (cid:133)rst 20 periods (for the (cid:133)rst 20 periods), while only 58% are increases in the last 20 periods. Negative price changes occur more often late in the sessions. 16They use product-level price data, as employed to construct the CPI and PPI in the US.

13 of data, is 2:3%. These numbers suggest that price decreases are an important component of the price setting behavior of (cid:133)rms. The size of average and average absolute price changes is comparable to the empirical results of Klenow and Kryvtsov (2008), who report a 14% average absolute price change, and a 0:8% average price change. ComparisonbetweentreatmentsrevealsthattheMenuCostandLowFrictiontreatmentsare di⁄erent from the other two treatments in their price-setting behavior. Average price changes range between 0:5 1:5% in the Baseline, Human Central Banker, and Low Friction treatments. (cid:0) For the Menu Cost treatment, the average price change is approximately 4:5%. The average absolutepricechangeis22:3%and15:8%intheBaselineandHumanCentralBankertreatments. In contrast, it is 8:8% and 11:0% in the Menu Cost and Low Friction treatments. Therefore, both the competitiveness of the market, and the introduction of a menu cost, a⁄ect the pricing behavior of (cid:133)rms. The introduction of a menu cost decreases, while monopolistic competition increases, average absolute price changes. However, the variability of in(cid:135)ation was lower in the Menu Cost treatment compared to other treatments (Noussair et al., 2013).17 Average price Average abs. price Average pos. price Average neg. price Treatment changes in ECU (%) changes in ECU (%) changes in ECU (%) changes in ECU (%) All 1.112 (2.28%) 7.890 (16.23%) 7.364 (15.15%) -8.813 (-18.13%) Baseline 0.239 (0.54%) 9.921 (22.27%) 8.404 (18.87%) -12.260 (-27.53%) Human CB 3.270 (4.52%) 11.421 (15.80%) 12.302 (17.02%) -9.978 (-13.80%) Menu Cost 0.407 (1.25%) 2.865 (8.81%) 2.530 (7.69%) -3.901 (-12.00%) Low friction 0.694 (1.49%) 5.113 (10.97%) 4.737 (10.16%) -5.738 (-12.31%) Table 5: Average and average absolute price changes Table 5 also presents the average positive and negative price changes of the experiment both in terms of experimental currency (ECU) and in percentage terms. The average positive price change is 15:2%, while the average negative price change is 18:1% in the experiment. In all treatments, except for Human Central Banker, the average magnitude of positive price changes is smaller than that of negative price changes. Thus, the experiment con(cid:133)rms the stylized fact that price decreases are greater than increases. However, the di⁄erence in the size of positive and negative price changes is not statistically signi(cid:133)cant in any treatment. Similarly, Nakamura and Steinsson (2008) also report that price decreases tend to be larger than increases. The median absolute size of price changes is 8:5%, the median size of price increases is 7:3%, and the median of price decreases is 10:5%.18 Price changes and in(cid:135)ation. KlenowandKryvtsov(2008)decomposemonthlyin(cid:135)ation 17In Appendix, Table A4, we replicate Table 5 by showing median price changes, rather than mean values. 18Klenow and Malin (2010) discuss higher moments of the price change distribution. They report that the kurtosisofthedistributionofpricechangesis10.0forpostedprices,and17.4forregularprices. Inourexperiment, the distribution of all price changes has a kurtosis of 22.3. The kurtosis is 11.3 in the Baseline treatment, 17.4 in Human Central Banker, 119.4 in Menu Cost, and 33.1 in Low Friction. This heterogeneity con(cid:133)rms the di⁄erences in price setting behavior between treatments. The (cid:133)gures from the Baseline and Human Central Banker treatments are close to empirical (cid:133)ndings. In the Menu Cost treatment there are more extreme price changes.

14 into the fraction of prices that change and the average size of those price changes. In their sample, they (cid:133)nd that the correlation between the fraction of prices that change and the overall in(cid:135)ation rate is 0:25, which means that the fraction is not highly correlated with in(cid:135)ation. The average size of changes, however, has a correlation with in(cid:135)ation of 0:99, and thus comoves almost perfectly with in(cid:135)ation. In our data we (cid:133)nd similar patterns. The fraction of prices changing is relatively stable and not highly correlated with in(cid:135)ation (0:10) in the pooled data from all treatments. However, the average magnitude of price changes has a higher correlation (0:53) with in(cid:135)ation. The Baseline and Human Central Banker treatments exhibit similar correlation between magnitude and in(cid:135)ation ( 0:5), while the Menu Cost and Low Friction (cid:25) treatments have much greater correlations of roughly 0:84 and 0:79, respectively. Generally, the Menu Cost treatment (cid:133)gures are the closest to the (cid:133)eld data. There we can state the following result that corresponds to Hypothesis 2b: Result 2b: The average absolute magnitude of price changes covaries strongly with in(cid:135)ation, but the frequency of price changes does not. Time Pro(cid:133)le of Hazard Rate of Price Changes. Thehazardfunctionofpricechanges indicatestheprobabilityofapricechangeasafunctionofthelengthoftimethatthesameprice has been in e⁄ect. Intuitively, one might anticipate an upward sloping function (see Sheedy, 2010 and Alvarez et al., 2011), i.e. the longer a price has remained unchanged, the greater the probability it is changed in a given period, particularly if there is a positive underlying rate of in(cid:135)ation. However, di⁄erent theoretical models and empirical results suggest the possibility of a (cid:135)at or downward sloping hazard function. Klenow and Malin (2010) summarize the theoretical predictions for the hazard functions of di⁄erent price-setting models. They show that the Calvo model assumes a (cid:135)at hazard function, while the Taylor model predicts a zero hazard except at a single point in time, when the hazard is one. Furthermore, they point out that menu cost modelscangenerateavarietyofshapes. Whenpermanentshocksarerelativelymoreimportant, the hazard function tends to be upward-sloping, while transitory shocks tend to (cid:135)atten or in some circumstances even yield a downward-sloping hazard function. Intheempiricalliterature,thegeneralresultisthathazardfunctionsarenotupward-sloping. Klenow and Kryvtsov (2008) (cid:133)nd the frequency of price changes conditional on reaching a given age is downward sloping or constant if all goods are considered, depending on the exact speci(cid:133)cation. Nakamura and Steinsson (2008) estimate separate hazard functions for di⁄erent classes of goods, and they (cid:133)nd that hazard functions are downward sloping in the (cid:133)rst few months and constant after that. Ikeda and Nishioka (2007), using Japanese CPI data (cid:133)nd, contrary to previous empirical research, upward sloping hazard functions. They use a (cid:133)nitemixture model and assume a Weibull distribution for price changes. They estimate increasing hazard functions for some products, and constant functions for others.19 19Ikeda and Nishioka (2007) estimate the hazard function for goods and for services separately. They assume aWeibulldistribution,aswedohere,buttheyestimateamodelwithheterogeneoustypes. Alvarezetal.(2011) derive a non-monotonic hazard function from their model. The shape of the function depends on the relative sizes of the observation costs and the menu costs in their model. Our model does not include observation costs.

15 Table 6 shows the di⁄erences between treatments in the duration of price spells, the number of periods that a (cid:133)rm(cid:146)s price remains unchanged. The average durations are 1:16, 1:18 and 1:16 in the Baseline, Human Central Banker and Low Friction treatments. The Menu Cost treatment has an average of 2:42, signi(cid:133)cantly di⁄erent at 3% from any of the other treatments using a battery of non-parametric tests. Treatment Obs Mean Std. Dev. Min Max All 2104 1.34 1.12 1 21 Baseline 612 1.16 0.45 1 4 Human CB 561 1.18 0.57 1 6 Menu cost 287 2.42 2.47 1 21 Low friction 641 1.16 0.56 1 8 Table 6: Descriptive statistics of price spells (number of periods price remains unchanged) Theslopeofthehazardfunctioncanbeevaluatedforourdata. Weassumeahazardfunction of the following form: (cid:21) (t x ) = (cid:23) (cid:21) (t)weibull(x (cid:12)); (11) i j i 0 i;j j whereiindexesproducers, j indexesobservations, (cid:23) isaproducer-speci(cid:133)crandomvariablethat i re(cid:135)ects unobserved heterogeneity in the level of the hazard, (cid:21) (t) is a nonparametric baseline 0 hazard function, x is a vector of covariates, and (cid:12) is a vector of parameters. We assume ij that (cid:23) Gamma(1;(cid:27)2). As in Ikeda and Nishioka (2007), we assume a Weibull distribution i (cid:23) (cid:24) in the hazard function, given by weibull(x (cid:12)) = x (cid:12) h th 1, where h is a parameter to i;j i;j (cid:0) (cid:1) (cid:1) be estimated. Under this distributional assumption, we can test explicitly whether the hazard function is upward sloping so that h > 1, downward sloping with h < 1, or constant with h = 1. The independent variables in the regressions are the wage of the (cid:133)rm, amount of labor hired, lagged value of the (cid:133)rm(cid:146)s price, lagged value of its pro(cid:133)t, lagged value of its unsold products, technology shock, lagged value of the real interest rate and lagged value of the output gap. Individual di⁄erences are captured by producer-speci(cid:133)c dummies ((cid:23) ). The hazard rate i is estimated for the pooled data, for each treatment and also for each subject separately. The estimation results can be found in Table A1 in the Appendix. There are signi(cid:133)cant explanatory variables in the regressions. Wage, amount of labor hired, lagged value of unsold products, lagged pro(cid:133)ts, and a dummy for positive pro(cid:133)t in the previous period, are signi(cid:133)cant in the regression for the pooled data from all treatments. The hazard functions in each treatment are upward sloping. When menu costs are present, average price spells are longer.20 As shown in Table A1, the estimated values of h are about 2:5 in all treatments except under Menu Cost, where h = 1:55. All of these estimates are signi(cid:133)cantly greater than 1 at the 1% signi(cid:133)cance level, indicating a signi(cid:133)cantly increasing hazard rate. These results are in line with Ikeda and Nishioka (2007), though they di⁄er from the (cid:133)ndings generally reported in the literature.21 20Price spells can be found in Figure C1 in the Appendix C that can be found in the online Supplementary Material. 21We have also investigated di⁄erences between early and late periods of the sessions. The overall estimate of

16 Thus, we can reject Hypothesis 2c in favor of the following result: Result 2c: The hazard rate of price changes is increasing. 4.3. Price setting, macroeconomic variables, and hypothesis 3. The statements in Hypothesis 3 receive mixed support in the data. Productivity shocks result in lower prices in thecurrentperiodunderallofourspeci(cid:133)cations, andthusthereisstrongsupportforhypothesis 3a. The support for a positive relation between lagged output and gap is considerably weaker, and there is no signi(cid:133)cant relationship between current wages and prices once other variables are taken into account. Result 3a: Prices are negatively correlated with productivity shocks. Result 3b: There is weak support for a positive correlation between prices that individual (cid:133)rms charge and the lagged output gap. Result 3c: There is no signi(cid:133)cant correlation between prices that individual (cid:133)rms charge and wages (when controlling for other variables). Table 7 displays regression results for the pooled data from all treatments. Separate regression results for each treatment are reported in the online Appendix C. To evaluate our hypothesis concerning the e⁄ects of macroeconomic variables on prices we speci(cid:133)ed the (cid:133)rm(cid:146)s price in period t as the dependent variable, and included productivity, the lagged output gap, and lagged real interest rate as independent variables. Moreover, we added (cid:133)rm-level variables such as the (cid:133)rm(cid:146)s price in the last period, the average wage it paid for a unit of labor, and its past pro(cid:133)tability to consider price inertia and the e⁄ect of wages on price setting.22 The estimation employs the linear dynamic panel-data GMM estimation developed by Arellano and Bover (1995) and Blundell and Bond (1998). The standard errors are clustered by session and obtained by bootstrap estimations with 1000 replications. Theproductivityshockistheonlymacroeconomicvariablethatissigni(cid:133)cantandnegativein all speci(cid:133)cations in Table 7, which is in line with hypothesis 3a. The coe¢ cient on productivity shocks is also negative and signi(cid:133)cant in all treatments when they are considered separately, except for the Human Central Banker treatment. The lagged output gap (x ) is positive and t 1 (cid:0) signi(cid:133)cant in some models, but insigni(cid:133)cant in models 3 5 in Table 7. In fact, the estimated (cid:0) coe¢ cient on the lagged output gap is positive and signi(cid:133)cant only in the Menu Cost treatment. However, this variable becomes insigni(cid:133)cant when the interaction between lagged pro(cid:133)ts and a dummy of past positive pro(cid:133)t is added. The sign of the variable is in line with our expectations, h is larger in the (cid:133)rst twenty periods of the sessions than in the last 20 periods. The same pattern is observed in the Baseline and Human Central Banker treatments. In the Menu Cost and Low Friction treatments, h becomes larger late in the sessions. Another interesting observation is that the coe¢ cient of (cid:5)+ is positive jt 1 and signi(cid:133)cantin the mostofthe speci(cid:133)cationsin the late periods. Thissuggeststhat,late in thes(cid:0)essions,(cid:133)rms who had an increase in their pro(cid:133)t in the past period are more likely to change their price, while early in the sessions, this pattern is not signi(cid:133)cant. 22Several variables are used to capture the past pro(cid:133)tability of (cid:133)rms. See the note to Table 7 for a complete explanation.

17 p (1) (2) (3) (4) (5) (6) (7) jt p 0.8827*** 0.8877*** 0.8516*** 0.8516*** 0.8523*** 0.8866*** 0.8884*** jt 1 (cid:0) (0.0729) (0.0669) (0.0837) (0.0836) (0.0836) (0.0677) (0.0685) w 0.0218 0.0237 0.0235 0.0231 0.0234 0.0236 0.0234 it (0.0284) (0.0275) (0.0279) (0.0281) (0.0282) (0.0266) (0.0274) A -6.8030*** -6.3637*** -7.2280*** -7.2502*** -7.0987*** -6.8342*** -7.4121*** t (2.0284) (1.8955) (2.2149) (2.2121) (2.1190) (2.2121) (2.3506) x 0.0942* 0.0881** -0.0037 -0.0032 -0.0096 0.1233* 0.1313** t 1 (cid:0) (0.0505) (0.0440) (0.0718) (0.0711) (0.0701) (0.0667) (0.0609) iR -0.2261 -0.2204 -0.2333 -0.2331 -0.2326 -0.2232 -0.2729 t 1 (cid:0) (0.1909) (0.1852) (0.1945) (0.1945) (0.1940) (0.1938) (0.1889) (cid:5)R 0.0166 (cid:151) (cid:151) -0.0023 (cid:151) (cid:151) (cid:151) jt 1 (cid:0) (0.0356) (cid:151) (cid:151) (0.0072) (cid:151) (cid:151) (cid:151) D (cid:151) 6.1555 (cid:151) (cid:151) 1.5355 (cid:151) (cid:151) 1 (cid:151) (4.6598) (cid:151) (cid:151) (2.5631) (cid:151) (cid:151) D (cid:151) (cid:151) 0.1142 0.1166 0.1122 (cid:151) (cid:151) 2 (cid:151) (cid:151) (0.0780) (0.0810) (0.0780) (cid:151) (cid:151) D (cid:151) (cid:151) (cid:151) (cid:151) (cid:151) 1.3058 (cid:151) 3 (cid:151) (cid:151) (cid:151) (cid:151) (cid:151) (1.0942) (cid:151) D (cid:151) (cid:151) (cid:151) (cid:151) (cid:151) 1.1653 (cid:151) 4 (cid:151) (cid:151) (cid:151) (cid:151) (cid:151) (1.3572) (cid:151) D (cid:151) (cid:151) (cid:151) (cid:151) (cid:151) (cid:151) 0.2876 5 (cid:151) (cid:151) (cid:151) (cid:151) (cid:151) (cid:151) (1.5388) D (cid:151) (cid:151) (cid:151) (cid:151) (cid:151) (cid:151) -0.854 6 (cid:151) (cid:151) (cid:151) (cid:151) (cid:151) (cid:151) (0.7020) D (cid:151) (cid:151) (cid:151) (cid:151) (cid:151) (cid:151) 4.4837 7 (cid:151) (cid:151) (cid:151) (cid:151) (cid:151) (cid:151) (2.8642) D (cid:151) (cid:151) (cid:151) (cid:151) (cid:151) (cid:151) 3.4833 8 (cid:151) (cid:151) (cid:151) (cid:151) (cid:151) (cid:151) (5.5482) Cons: 29.4603*** 22.7210*** 24.9356*** 25.0267*** 23.1319*** 29.6074*** 31.7737*** (8.8499) (5.6356) (7.5684) (7.5568) (6.2969) (9.7488) (9.8564) N 2806 2806 2806 2806 2806 2758 2758 (cid:31)2 421 418 404 411 442 509 1104 Table 7: Regressions on prices (All treatments (cid:150)pooled data). Notes: The linear dynamic paneldata GMM estimation developed by Arellano and Bover (1995) and Blundell and Bond (1998) is used for the estimation. Standard errors in parentheses. The standard errors are clustered by sessions and obtained by bootstrapestimationswith1000replications. D 1 dummymeasureswhetherthe(cid:133)rmmadepro(cid:133)tintheprevious period, and the e⁄ect of the amount of pro(cid:133)t when positive pro(cid:133)t was made in the previous period (D 2 dummy D wh 4 ic = his 1 th if e p in t te 2 ra < ctio p n t D 3 1 a (cid:1) n (cid:5) d R j (cid:5) t (cid:0) t 1 ) 1 . > D 3 0 t , a a k n es d o 0 n o a th v e a r lu w e is o e f . 1 D ,i 5 fp is t (cid:0) a 2 d > um p m t (cid:0) y 3 v a a n ri d ab (cid:5) le t (cid:0) w 1 h > ich 0 e , q a u n a d ls 0 t o o th 1 e , r w w h is e e n . (cid:0) (cid:0) (cid:0) priceincreaseint 2isfollowedbyapro(cid:133)tincreaseint 1. D 6 isadummyvariablewhichequalsto1,when (cid:0) (cid:0) priceincreaseint 2isfollowedbyapro(cid:133)tdecreaseint 1. D 7 isadummyvariablewhichequalsto1,when (cid:0) (cid:0) pricedecreaseint 2isfollowedbyapro(cid:133)tincreaseint 1. D 8 isadummyvariablewhichequalsto1,when (cid:0) (cid:0) pricedecreasein t 2isfollowed by a pro(cid:133)tdecreasein t 1. */**/*** denotessigni(cid:133)canceat10/5/1 percent (cid:0) (cid:0) level.

18 and the coe¢ cient on the lagged output gap is greater in magnitude, but not signi(cid:133)cant, in the Low Friction treatment. Overall, there is some weak support for hypothesis 3b. There is signi(cid:133)cant inertia in prices. A one ECU increase in price in the previous period resultsinanincreaseinpriceofabout0:85ECUinthecurrentperiod. However,itscoe¢ cientof 0:421intheLowFrictiontreatmentishalfofthevalueinothertreatments. Perfectcompetition in the output markets as in the Low Friction treatment appears to create more pressure on prices to adjust than in a monopolistically competitive market, leading (cid:133)rms to set prices more independently of past prices. Lagged real interest rates are negative and signi(cid:133)cant in the Baseline and Menu Cost treatments, and positive and signi(cid:133)cant in the Human Central Banker and Low Friction treatments. Wage enters positively and signi(cid:133)cantly in the Baseline, Human Central Banker and Low Friction treatments. Recall that wages represent the only cost of production in our economy. Firms do pass wage increases through to prices. The e⁄ect is largest (with a coe¢ cient approximately 0:20) in the Low Friction treatment. Hence, each ECU average wage increase leads to a 0:20 ECU increase in prices. Signi(cid:133)cant coe¢ cients on past pro(cid:133)t variables show evidence of adaptive behavior in price setting based on pro(cid:133)t feedback in the Baseline, Menu Cost and Low Friction treatments. Past pro(cid:133)t and the interaction between past pro(cid:133)t and a positive past pro(cid:133)t dummy are both signi(cid:133)cant and positive in the Baseline treatment. In the Menu Cost treatment, the D dummy 5 is signi(cid:133)cant and positive, which means that a (cid:133)rm adapts its behavior after a successful price increase in the recent past. Firms charge a 0:714 ECU higher price in period t if a past price increase in t 2 resulted in increased pro(cid:133)t. Similar behavior is observed in the Low Friction (cid:0) treatment with a slightly smaller parameter value (0:54). This adaptive behavior is reversed in the Human Central Banker treatment, where (cid:133)rms signi(cid:133)cantly decrease their price after a successful price increase in the past or a greater previous period pro(cid:133)ts. Thus, hypothesis 3a is strongly supported, while 3b and 3c receive mixed support in the data.23 Probability of price changes. Table A3 in the Appendix contains the regression results with the probability of price change as the dependent variable. The online Appendix C reports the results for each treatment separately. It is possible to argue that prices should change in response to both a positive and negative productivity shocks. Thus, we include an additional independent variable, AR , which measures the absolute magnitude of the productivity in time t t compared to the steady state level of productivity. The lagged output gap and lagged real (cid:12) (cid:12) (cid:12) (cid:12) interest rate do not increase the probability of price changes except in the Baseline treatment, even though theoretical considerations and regression results on the magnitude of price changes suggest that price would increase. A productivity shock has a negative e⁄ect on prices. The parameter for productivity is negative and signi(cid:133)cant in the pooled data as well as for the Human Central Banker and Menu 23We have also investigated potential asymmetries in the determinants of price setting between the beginning andtheendofthesessions. Priceinertiaisstrongerinthe(cid:133)rst20periods,whiletheproductivityshockexertsa stronger impact around the end of the experiment compared to the beginning of the experiment. These results are available upon request from the authors.

19 Cost treatments alone. This result reveals that an increase in productivity decreases the probability of price changes and appears to occur because (cid:133)rms are averse to decreasing prices when they associate decreases in prices with decreases in pro(cid:133)t. On the contrary, when productivity decreases, producers tend to increase prices, leading to a signi(cid:133)cant increase in the probability of a price change. However, the parameter on the absolute magnitude of the productivity shock is positive and signi(cid:133)cant in the pooled data. Thus a shock of greater magnitude increases the likelihood of changing the price. However, this variable is only signi(cid:133)cant in the pooled data and when (cid:133)rms have to pay a menu cost when they change prices. The negative and signi(cid:133)cant parameter of the D dummy suggest that positive past pro(cid:133)t makes (cid:133)rms less likely to change 1 their pricing behavior in the pooled data, and in the Baseline treatment. In other treatments, this behavior is not observed. In the Low Friction treatment, none of the variables is signi(cid:133)cant except for the lagged dummy of price change. The parameter value for the lagged price change dummy suggests that a (cid:133)rm is more likely to change its price if the price was changed in the previous period. The presence of perfect substitution in the product market can explain why all of the dependent variables are insigni(cid:133)cant. 4.4. Behavior of human central bankers, and hypothesis 4. Hypothesis 4 proposed that human central bankers(cid:146)interest rate decisions satisfy the Taylor principle. We evaluate the hypothesis with the following regression: i = (cid:12) i +(1 (cid:12) )((cid:12) (cid:25) +(cid:12) y )+" (12) t 1 t 1 1 2 t 1 3 t 1 t (cid:0) (cid:0) (cid:0) (cid:0) As in Table 7, the estimation employs the linear dynamic panel-data GMM estimator. We estimate two di⁄erent speci(cid:133)cations, one for individual decisions over interest rates (ind) and onefortheactualinterestrate(group)intheeconomy(recallthattheinterestrateimplemented is the median choice of the subjects in the role of central bankers). The estimates of (12) are reported in Table 8. group ind i 0.9295*** 0.9026*** t 1 (cid:0) (0.0139) (0.1331) (cid:25) 0.1517*** 0.1431** t 1 (cid:0) (0.0115) (0.0606) y -0.0170** -0.0207* t 1 (cid:0) (0.0072) (0.0120) N 225 625 (cid:31)2 5415.1 51.5 Table 8: Taylor-rule regressions. Notes: Two di⁄erent speci(cid:133)cations, one for individual decisions over interest rates (ind) and one for the actual interest rate (group) in the economy (the interest rate implemented isthemedianchoiceofthesubjectsintheroleofcentralbankers). Coe¢ cientsarebasedonBlundell-Bondsystem GMM estimator. Standard errors in parentheses are calculated using bootstrap procedures (1000 replications) that take into account the potential presence of clusters in sessions. */**/*** denotes signi(cid:133)cance at 10/5/1 percent level.

20 The test of hypothesis 2 is whether (cid:12) satis(cid:133)es the Taylor principle. The Taylor principle 2 is that the response of the nominal interest rate to in(cid:135)ation must be greater than 1 in order to guarantee determinacy (Woodford, 2003). In our economy, determinacy is guaranteed if (cid:12) +(1 (cid:12) )(cid:12) > 0:24 This condition is clearly satis(cid:133)ed in our case. (cid:12) in our case is 1:47, 1 1 2 2 (cid:0) which is very close to 1.5, the coe¢ cient originally proposed by Taylor, and (cid:12) is 0:90.25;26 This 1 indicates that Hypothesis 4 is supported. Result 4: Under the Human Central Banker treatment, interest rate policy follows the Taylor principle. Engle-Warnick and Turdaliev (2010) also study the monetary policy decisions of inexperienced human subjects. Their economy is a log-linearized variant of the standard DSGE model. They assume that the objective of the monetary policy is to minimize a loss function E (cid:14)t 1((cid:25) (cid:25))2. They (cid:133)nd that Taylor-type rules explain much of the variation of t 1t=1 (cid:0) t (cid:0) the interest rate decisions of subjects who successfully stabilize the economy. These subjects(cid:146) P (approximately 82% of all participants) behavior is consistent with interest rate smoothing, and the sensitivity to in(cid:135)ation is, on average, close to or above 1 in their interest rate decisions. 5. Conclusion In this study, we construct a laboratory DSGE economy populated with human decision makers. The experiment allows us to create an economy with a structure similar to a standard New Keynesian DSGE economy, without making any assumptions about the behavior of agents. Di⁄erent treatments allow us to study how the presence of menu costs and monopolistic competition a⁄ect (cid:133)rms(cid:146)price-setting behavior. Which of the treatment speci(cid:133)cations conforms most closely to empirical stylized facts depends on the particular variables used in the comparison. Our results show that the stylized facts of pricing behavior documented in the (cid:133)eld can be reproduced in a class of experimental economies, andare robusttoanumberofchangesin theeconomicenvironment. Thesepatterns may be general characteristics of production economies populated with human agents. Weconsideredwhetheranumberofstylizedempiricalfactsaboutpricingareobservedinour economies. We (cid:133)nd that price changes are frequent, occurring in 74:5% of possible instances, compared to 73:8% quarterly in US data. A majority of roughly 64% of price changes are increases, compared to 64:8% in the US data. In percentage terms, price changes are also similar to empirical estimates, and the ratio of magnitudes between the average positive and negative price change is similar. We (cid:133)nd that the fraction of prices that change from one period to the next is not highly correlated with in(cid:135)ation, but the average magnitude of changes does exhibit a strong correlation with in(cid:135)ation. However, in contrast to most empirical studies, but 24The full set of conditions is given in Bullard and Mitra (2007). 25We also tested for a nonlinearity in policy. In particular, we considered whether there was an asymmetry in the sensitivity of interest rates to in(cid:135)ation, depending on whether in(cid:135)ation was above or below the target level of 3 percent. We found that there was no asymmetry of that form. 26Welfare is somewhat lower in the Human Central Bankers treatment. It is on average about 7% lower compared to the Baseline treatment.

21 in a manner consistent with the theoretical models of Sheedy (2010) and Alvarez et al. (2011), the hazard function of price changes is upward sloping. Menu costs, although calibrated in line with the estimations of Nakamura and Steinsson (2008), prove to be too high, and reduce the frequency of price changes considerably below the estimates from the (cid:133)eld. Asexpected,we(cid:133)ndthatpricemarkupsarelower,thoughstillpositive,whentheproductsin the economy are perfect substitutes compared to other treatments that implement monopolistic competition. Among the latter treatments, we observe that markups are signi(cid:133)cantly lower and the elasticity of substitution in demand is greater when menu costs are introduced. The treatment with human central bankers does not signi(cid:133)cantly di⁄er in terms of markups from the baseline speci(cid:133)cation with automated Taylor-type policy rules. Prices are a⁄ected negatively by increased productivity, and positively by the output gap, unlessmonetarypolicyissetbyhumansubjects. Laggedrealinterestrateshaveanegativee⁄ect on prices, except when human subjects choose the interest rate, or there is perfect competition intheoutputmarket. Price-settingbehaviordependssigni(cid:133)cantlyonpastprices,withthee⁄ect weakest when the output market is characterized by perfect competition. Wage cost increases a⁄ect prices signi(cid:133)cantly and positively, except when menu costs are present, and the e⁄ect is the strongest when there is perfect competition in the output market. Therefore, production costs are found to be a more important determinant of prices in treatments where we observe lower markups. We (cid:133)nd evidence of adaptive behavior in price-setting; (cid:133)rms charge higher prices after a positive pro(cid:133)t in the previous period, or after a successful price increase in the past, when menu costs are present. When human subjects set the interest rates, the behavior of price setting changes signi(cid:133)cantly, althoughthebasicstylizedfactsregardingthefrequencyofupdating, proportionofprice decreases, and average markups, remain the same. The behavior of human subjects in the role of central bankers is in line with the Taylor principle. Two stylized facts that we have not been able to reproduce in our data are a downwardsloping hazard rate for price changes, and an absence of an e⁄ect of menu costs on the average markup. The upward-sloping hazard rate is intuitive in our environment, in which the central bank tried to adhere to a positive in(cid:135)ation target. With nominal wage costs that tend to increase over time, and competitors that can also change the prices they are charging, a (cid:133)rm(cid:146)s output price may depart considerably from its optimal level when not changed for some time. Therelativelysmallmarkupundermenucostsmayre(cid:135)ectthereluctancetoupdatepricesinthe face of increasing wage costs. Firms may adjust their prices too late as their markup shrinks. When they do adjust prices, they may be unwilling to do so by a su¢ cient amount to be able to maintain a high markup for a su¢ cient number of future periods, as they fear charging too high a price relative to competitors. References Alvarez, F. E., Lippi, F., Paciello, L., 2011. Optimal price setting with observation and menu costs. The Quarterly Journal of Economics 126 (4), 1909(cid:150)1960.

22 Arellano, M., Bover, O., Jul. 1995. Another look at the instrumental variable estimation of error-components models. Journal of Econometrics 68 (1), 29(cid:150)51. Bils, M., Klenow, P. J., 2004. Some evidence on the importance of sticky prices. The Journal of Political Economy 112 (5), 947(cid:150)985. Blundell, R., Bond, S., Aug. 1998. Initial conditions and moment restrictions in dynamic panel data models. Journal of Econometrics 87 (1), 115(cid:150)143. Bullard, J., Mitra, K., 08 2007. Determinacy, learnability, and monetary policy inertia. Journal of Money, Credit and Banking 39 (5), 1177(cid:150)1212. Cameron, N., Hum, D., Simpson, W., 1996. Stylized facts and stylized illusions: in(cid:135)ation and productivity revisited. Canadian Journal of Economics 29 (1), 152(cid:150)162. Dixit,A.K.,Stiglitz,J.E.,Jun.1977.Monopolisticcompetitionandoptimumproductdiversity. The American Economic Review 67 (3), 297(cid:150)308. Engle-Warnick, J., Turdaliev, N., Jun. 2010. An experimental test of taylor-type rules with inexperienced central bankers. Experimental Economics 13 (2), 146(cid:150)166. Fernandez-Villaverde, J., Jan. 2009. The econometrics of DSGE models. National Bureau of Economic Research Working Paper Series No. 14677. Fischbacher, U., Jun. 2007. z-Tree: zurich toolbox for ready-made economic experiments. Experimental Economics 10 (2), 171(cid:150)178. Gali, J., Gertler, M., Oct. 1999. In(cid:135)ation dynamics: A structural econometric analysis. Journal of Monetary Economics 44 (2), 195(cid:150)222. Gali, J., Gertler, M., Lopez-Salido, J. D., 2005. Robustness of the estimates of the hybrid new keynesian phillips curve. Journal of Monetary Economics 52 (6), 1107(cid:150)1118. Ikeda, D., Nishioka, S., 2007. Price Setting Behavior and Hazard Functions: Evidence from Japanese CPI Micro Data. Tech. rep., Bank of Japan Working Paper 07-E-10. Klenow, P.J., Kryvtsov, O., 2008.State-DependentorTime-Dependentpricing: Doesitmatter for recent U.S. in(cid:135)ation? Quarterly Journal of Economics 123 (3), 863(cid:150)904. Klenow, P. J., Malin, B. A., March 2010. Microeconomic evidence on price-setting. Working Paper 15826, National Bureau of Economic Research. Nakamura, E., Steinsson, J., Nov. 2008. Five facts about prices: A reevaluation of menu cost models. Quarterly Journal of Economics 123 (4), 1415(cid:150)1464. Noussair, C. N., Pfajfar, D., Zsiros, J., 2013. Frictions in an experimental dynamic stochastic general equilibrium economy. Mimeo, Tilburg University.

23 Plott, C. R., Gray, P., Mar. 1990. The multiple unit double auction. Journal of Economic Behavior & Organization 13 (2), 245(cid:150)258. Ram, R., 1984. Causal ordering across in(cid:135)ation and productivity growth in the post-war united states. The Review of Economics and Statistics 66 (3), 472(cid:150)477. Sheedy, K. D., November 2010. Intrinsic in(cid:135)ation persistence. Journal of Monetary Economics 57 (8), 1049(cid:150)1061. Smith, V. L., 1962. An experimental study of competitive market behavior. The Journal of Political Economy 70 (2), 111(cid:150)137. Smith, V. L., Dec. 1982. Microeconomic systems as an experimental science. The American Economic Review 72 (5), 923(cid:150)955. Vermeulen, P., Dias, D., Dossche, M., Gautier, E., Hernando, I., Sabbatini, R., Stahl, H., Feb. 2007. Price setting in the euro area: Some stylised facts from individual producer price data. SSRN eLibrary. Walsh, C. E., 2003. Monetary theory and policy. the MIT Press. Woodford,M.,2003.InterestandPrices: FoundationsofaTheoryofMonetaryPolicy.Princeton University Press.

24 Appendix A. Additional Tables Hazard ratio Pooled Baseline Human CB Menu cost Low friction p 1.0000 1.0014*** 0.9992* 1.0234** 0.9982 jt 1 (cid:0) (0.0004) (0.0005) (0.0005) (0.0109) (0.0043) w 1.0007* 0.9981** 1.0013 0.9796*** 1.0023 it (0.0004) (0.0009) (0.0009) (0.0062) (0.0015) A 1.0262* 0.9684 0.9632 1.1983*** 1.0226 t (0.0154) (0.0289) (0.0290) (0.0521) (0.0249) y 0.9311 1.3261** 0.8368 0.5055*** 0.9904 jt (0.0616) (0.1497) (0.1113) (0.1074) (0.1355) x 1.0000 1.0040 1.0002 0.9994 1.0020 t 1 (cid:0) (0.0015) (0.0025) (0.0029) (0.0050) (0.0035) iR 0.9986 0.9990 0.9921** 1.0024 0.9991 t 1 (cid:0) (0.0016) (0.0023) (0.0032) (0.0087) (0.0033) y c 0.9777** 0.9516** 0.9875 0.9374** 0.9745 jt jt (cid:0) (0.0112) (0.0188) (0.0238) (0.0300) (0.0343) (cid:5) 1.0008** 0.9996 1.0011** 0.9994 0.9994 jt 1 (cid:0) (0.0004) (0.0007) (0.0005) (0.0018) (0.0019) (cid:5)+ 0.6807*** 0.6219*** 0.7798 0.6565** 0.7041 jt 1 (cid:0) (0.0639) (0.1028) (0.1491) (0.1379) (0.1521) h 2.3518*** 2.6535*** 2.5452*** 1.5581*** 2.7462*** (0.0361) (0.0706) (0.0720) (0.0648) (0.0717) N 2029 599 543 272 615 (cid:31)2 29 23 17 43 22 Table A1: Parametric hazard rate regressions Notes: Standard errors in parentheses. */**/*** denotes signi(cid:133)cance at 10/5/1 percent level. in(cid:135)ation All Baseline Human CB Menu Cost Low friction fraction 0.1043 0.0463 0.1751 0.2672 0.1434 size 0.5348 0.5522 0.4768 0.8489 0.7987 Table A2: Correlation of size and fraction with in(cid:135)ation

25 )8( )7( )6( )5( )4( )3( )2( )1( fo .borP egnahc ecirp 0 0 0 5000.0 5000.0 4000.0 0 3000.0 w ti )1000.0( )1000.0( )1000.0( )2100.0( )2100.0( )2100.0( )1000.0( )1100.0( 9300.0- 400.0- 1500.0- 9200.0 8200.0 9400.0 5400.0- 8110.0 L tj )6500.0( )6600.0( )9600.0( )7340.0( )8440.0( )2240.0( )2600.0( )5430.0( (cid:151) **2650.0- *6050.0- ***8014.0- ***4584.0- ***9814.0- **1940.0- ***4124.0- A t (cid:151) )4520.0( )3620.0( )5731.0( )6831.0( )3241.0( )7220.0( )3811.0( **0160.0 (cid:151) (cid:151) (cid:151) (cid:151) (cid:151) (cid:151) (cid:151) RA t )7820.0( (cid:151) (cid:151) (cid:151) (cid:151) (cid:151) (cid:151) (cid:151) (cid:12) (cid:12) *7920.0 9820.0 1030.0 (cid:151) (cid:151) (cid:151) 4130.0 (cid:151) p (cid:12) p(cid:12) 1 t 1 tj )0610.0( )8020.0( )5020.0( (cid:151) (cid:151) (cid:151) )6020.0( (cid:151) (cid:0) (cid:0) (cid:0) 1000.0 6000.0 2000.0 3100.0 5300.0 9100.0 (cid:151) (cid:151) x 1 t (cid:0) )5000.0( )7000.0( )8000.0( )4300.0( )5300.0( )6300.0( (cid:151) (cid:151) 5000.0- 4000.0- 3000.0- 2700.0- *7700.0- 1700.0- (cid:151) (cid:151) Ri 1 t )5000.0( )7000.0( )7000.0( )8400.0( )6400.0( )8400.0( (cid:151) (cid:151) (cid:0) (cid:151) (cid:151) (cid:151) (cid:151) **9050.0 (cid:151) (cid:151) (cid:151) c y 1 tj 1 tj (cid:0) (cid:0) (cid:0) (cid:151) (cid:151) (cid:151) (cid:151) )5020.0( (cid:151) (cid:151) (cid:151) (cid:151) (cid:151) 0 5000.0 *9000.0 (cid:151) (cid:151) (cid:151) R(cid:5) 1 tj (cid:151) (cid:151) )1000.0( )5000.0( )5000.0( (cid:151) (cid:151) (cid:151) (cid:0) **0650.0- **0460.0- (cid:151) (cid:151) (cid:151) (cid:151) (cid:151) (cid:151) D 1 )5420.0( )7520.0( (cid:151) (cid:151) (cid:151) (cid:151) (cid:151) (cid:151) ***0177.0 ***9699.0 ***3719.0 (cid:151) (cid:151) (cid:151) ***7509.0 (cid:151) :snoC )4140.0( )6590.0( )4790.0( (cid:151) (cid:151) (cid:151) )6360.0( (cid:151) 8572 8572 8572 7572 7572 7572 8572 7572 N 61 32 21 41 42 41 31 41 2(cid:31) ytilibaborp eht gnizylana rof desu si ledom tigol lenap tce⁄e dex(cid:133) ehT :setoN .stnemtaert llA - egnahc ecirp fo ytilibaborp eht no noissergeR :3A elbaT serusaem ymmud D .snoitacilper 0001 htiw snoitamitse partstoob yb deniatbo dna snoisses yb deretsulc era sesehtnerap ni srorre dradnats ehT .segnahc ecirp fo 1 .level tnecrep 1/5/01 ta ecnac(cid:133)ingis setoned ***/**/* .doirep suoiverp eht ni t(cid:133)orp edam mr(cid:133) eht rehtehw

26 Median price Median abs. price Median pos. price Median neg. price Treatment changes in ECU (%) changes in ECU (%) changes in ECU (%) changes in ECU (%) All 0.000 0.00% 2.000 6.98% 2.000 6.67% -2.000 -7.59% Baseline 0.200 1.16% 2.000 7.92% 2.000 7.14% -3.000 -9.62% Human CB 0.200 1.01% 1.300 8.00% 1.900 7.14% -1.000 -8.33% Menu cost 0.000 0.00% 2.000 6.25% 2.000 6.06% -3.000 -7.14% Low friction 0.100 0.68% 1.900 5.88% 2.000 6.13% -1.600 -5.56% Table A4: Median price changes