Information stickiness in general equilibrium and endogenous cycles

Gomes, Orlando Working Paper Information stickiness in general equilibrium and endogenous cycles Economics Discussion Papers, No. 2012-46 Provided in Cooperation with: Kiel Institute for the World Economy – Leibniz Center for Research on Global Economic Challenges Suggested Citation: Gomes, Orlando (2012) : Information stickiness in general equilibrium and endogenous cycles, Economics Discussion Papers, No. 2012-46, Kiel Institute for the World Economy (IfW), Kiel This Version is available at: https://hdl.handle.net/10419/62348 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. http://creativecommons.org/licenses/by-nc/2.0/de/deed.en Information Stickiness in General Equilibrium and Endogenous Cycles Orlando Gomes Lisbon Higher Institute of Accounting and Administration, and Business Research Unit, University of Lisbon Abstract Traditionally, observed fluctuations in aggregate economic time series have been mainly modelled as being the result of exogenous disturbances. A better understanding of macroeconomic phenomena, however, surely requires looking directly at the relations between variables that may trigger endogenous nonlinearities. Several attempts to justify endogenous business cycles have appeared in the literature in the last few years, involving many types of different settings. This paper intends to contribute to such literature by investigating how we can modify the well-known information stickiness macro model, through the introduction of a couple of reasonable new assumptions, in order to trigger the emergence of endogenous fluctuations. JEL E32, E10, C61, C62 Keywords Endogenous cycles; information stickiness; macroeconomic fluctuations; general equilibrium; periodicity and chaos Correspondence Orlando Gomes, Lisbon Higher Institute of Accounting and Administration, (ISCAL/IPL), Av. Miguel Bombarda 20, 1069-035 Lisbon, Portugal; e-mail: [email protected] The author would like to thank organizers and participants of the 2011 ASSET conference (held in Évora, Portugal) and of the cycle of seminars on Economics held in ISCTE (especially the organizer Alexandra Ferreira-Lopes), where this paper was presented. The usual disclaimer applies. © Author(s) 2012. Licensed under a Creative Commons License - Attribution-NonCommercial 2.0 Germany Discussion Paper N o. 2012-46 | September 12, 2012 | http://www.economics-ejournal.org/economics/discussionpapers/2012-46 Information Stickiness in General Equilibrium and Endogenous Cycles ’Chaos represents a radical change of perspective on business cycles. Business cycles receive an endogenous explanation and are traced back to the strong nonlinear deterministic structure that can pervade the economic system. This is di¤erent from the (currently dominant) exogenous approach to economic ‡uctuations, based on the assumption that economic equilibria are determinate and intrinsically stable, so that in the absence of continuing exogenous shocks the economy tends towards a steady state, but because of stochastic shocks a stationary pattern of ‡uctuations is observed.’ Barnett, Medio and Serletis (1997), pages 36-37. 1 Introduction The benchmark macroeconomic paradigm is one in which the relations between relevant variables are essentially linear. Linear dynamic models allow to obtain one of two long-term outcomes: instability (divergence away from a …xed-point) or stability (convergence towards a …xed-point). This becomes a simplistic view of the economic system, since all sources of ‡uctuations in the long-run will be exogenous. A way to circumvent this excessively simpli- …ed view of the world is to look with further detail into the type of relations that explain the interaction among economic agents. This increased detail might allow to encounter nonlinearities that open the dynamic analysis to a wide range of possible long-term outcomes. Cycles of any periodicity or complete a-periodicity may be found, allowing for an intuitive endogenous explanation for business ‡uctuations. Periodic, a-periodic and even chaotic outcomes are forms of bounded instability that are compatible with the observed evolution of macro time series. In macroeconomics, there have been many attempts to provide explanations for business cycles based on the notion of endogenous ‡uctuations [see Gomes (2006) for a survey]. In recent years, this …eld of study has remained active, with relevant contributions being published. Table 1 presents some meaningful studies published since 2007. 1 Information Stickiness in General Equilibrium and Endogenous Cycles Author (year) Type of model Source of ‡uctuations Fanti and M anfredi Neoclassical labor Consumption and leisure are (2007) market model modeled as weak substitutes Jaim ovich Dynamic general Interaction b etween …rm s’ entry-and-exit (2007) equilibrium m odel decisions and changes in competition Yoshida and Asada Keynes-Goodwin Lags in the im plementation (2007) model of the of stabilization policies growth cycle Chen, Li and Lin Overlapping generations model M yopic and adaptive expectations (2008) with capital accumulation Fujio Two-sector optim al growth model The shap e of the production function (2008) with a Leontief technology Hallegatte, G hil, Non-equilibrium dynam ic Investm ent-pro…t instability Dumas and Hourcade model that introduces (2008) investm ent dynam ics into a Solow growth m odel Yokoo and Ishida Economy with a continuum Im perfect inform ation (2008) of …rms that engage in innovation activities Dieci and A model that integrates the stock Heterogeneous agents: technical Westerho¤ markets of two countries via the traders and fundam entalists (2009) foreign exchange m arket Kikuchi and Two-country growth Interaction between unequal Stachurski (2009) model countries through credit m arkets Stockmam (2009) Two-sector growth model Sector-speci…c externalities Gomes (2010) Sticky-inform ation partial equilibrium Form ation of expectations under a macroeconomic m odel learning rule Lines and M acro m odel com posed by Okun’s Heterogeneous exp ectations Westerho¤ (2010) law, expectations-augm ented Phillips (trend-following and curve and an aggregate dem and relation rational exp ectations) Sushko, Gardini Hicksian trade-cycle Capital stock as a capacity lim it and Puu (2010) model (ceiling) for production Table 1 –Recent literature on endogenous ‡uctuations. As we observe in the table, there are many ways to justify the emergence of endogenous business cycles in relatively di¤erent contexts. If we 2 Information Stickiness in General Equilibrium and Endogenous Cycles want to systematize this information, we might say that most of the mentioned studies are inspired in two or three successful approaches to the issue of endogenous volatility; we highlight the following: (i) the heterogeneous agents framework …rst developed by Brock and Hommes (1997, 1998), where fundamentalist agents work as a stabilizing force and technical traders as the force triggering temporary departures from stability; (ii) optimal growth models with non-conventional production functions and externalities in production, in the tradition of Nishimura and Yano (1995) and Christiano and Harrison (1999); and (iii) environments where bounded rationality in the formation of expectations have an important role, as in the case of Bullard (1994) and Schonhofer (1999). In this paper, endogenous cycles are explored in a popular macroeconomic framework –the sticky-information general equilibrium (SIGE) model, developed by Mankiw and Reis (2006, 2007) and Reis (2009). The original goal of this model was to explain the gradual response or the inertia of aggregate variables to exogenous shocks. It allows for a steady-state analysis, where policy shocks may temporarily deviate the economy from its …xedpoint long-run locus. This setup involves a dynamic result of stability, i.e., of convergence of any initial state towards a steady-state point, for the relevant macro variables. In the absence of exogenous disturbances, once the steady-state is accomplished, it will never be abandoned again. How can endogenous cycles eventually emerge within this setup? The answer is given in this paper through the relaxation of two benchmark assumptions of the model. In the original framework, (i) perfect foresight or rational expectations hold independently of the distance in time between the moment in which expectations are formed and the moment they respect to; (ii) the pace of information updating is considered constant. Alternatively, we will consider that: (i) perfect foresight is not universal; (ii) information updating is counter-cyclical. The two new assumptions are reasonable and introduce a larger degree of realism into the analysis: on one hand, economic agents will have di¢ culties in predicting future values with accuracy, when the future is distant in time. On the other hand, the degree of attentiveness to news about the state of the economy changes in time; in particular, it makes sense to recognize that periods of lower economic growth are necessarily periods of stronger exposure to news and, therefore, these will be periods of a more frequent in3 Information Stickiness in General Equilibrium and Endogenous Cycles formation updating. Our conclusion will be that the introduction of further realistic details into the macro model allows to explain, at least partially, the observed volatility in the time series of aggregate variables. We will emphasize that the two new assumptions are, individually, necessary but not su¢ cient conditions for a long-term nonlinear outcome; only when we consider both simultaneously, we will be able to identify the presence of endogenous ‡uctuations. The baseline version of the model that we will take is the one in Gomes (2012), which is similar to the Mankiw-Reis framework, with only a few changes that help in treating the model from an analytical point of view. Nevertheless, these changes are innocuous in terms of the results one will obtain. The changes will appear later with the characterization of the model and they are essentially two: 1) the degree of information stickiness will be the same across the di¤erent types of economic agents (namely, price-setting …rms, households who formulate consumption plans and wage-setting workers); 2) the monetary policy rule will ignore real stabilization, and it will focus solely on price stability (this allows to better highlight the condition under which monetary policy is active or aggressive). Besides these remarks, we should stress that any kind of stochastic disturbance (e.g., technological innovations) will be overlooked, in order to emphasize the possible presence of endogenous ‡uctuations. The remainder of the paper is organized as follows. Section 2 presents the model, through the characterization of pro…t maximization by …rms, utility maximization by households and wage optimization by labor suppliers. In section 3, the two new assumptions, concerning the formation of expectations and the updating of information, are introduced. Section 4 con…rms the stability result under perfect foresight. In sections 5 and 6 the model with the new assumptions is analyzed, respectively, under local and global perspectives. The study of global dynamics allows to detect endogenous ‡uctuations for reasonable values of parameters. Finally, section 7 concludes. 4 Information Stickiness in General Equilibrium and Endogenous Cycles 2 The Information-Stickiness General Equilibrium Model Consider a general equilibrium setting in which …rms and households behave optimally. Firms act with the goal of maximizing pro…ts, while households have a two-fold concern: to optimize consumption plans and to select an e¢ cient level of labor supply. In this environment, a source of rigidity exists, namely there is stickiness in the dissemination of information. We start by addressing the problem faced by …rms. There is an unspeci…ed number of …rms, in the unit interval, indexed by j. For each …rm j, a production function is assumed, with labor as the unique input (capital is ignored and the technology level is implicitly normalized to 1). The production function takes the form Yt;j =N t;j, with Yt;j the output or income generated by …rm jat time tand Nt;j the amount of labor employed in production by the same …rm at the same time period. Parameter 2(0;1) represents the output-labor elasticity and indicates that the production is subject to decreasing marginal returns. Each …rm produces a unique variety of the single assumed good, and does it by resorting to a unique variety of labor hired from households. The aggregate labor supply and the aggregate level of output may be presented under the form of Dixit-Stiglitz indexes: Nt=Z1 0 N  1 t;j dj(1)= Yt=Z1 0 Y  1 t;j dj(1)= with  > 0the elasticity of substitution between di¤erent varieties of labor and  > 0the elasticity of substitution between di¤erent varieties of goods. The aggregate production function takes the form Yt=N t. The model will be analyzed under a log-linear presentation of variables, and thus we de…ne nt:= ln Ntand yt:= ln Yt. With these variables, yt= nt.1 By solving the pro…t maximization problem of …rms, we arrive to the 1We will skip most of the derivation of the model and just present the main intuition and the main results. Details on the development of the optimization problems of the several agents can be found in the already cited references on the Mankiw-Reis framework. 5 Information Stickiness in General Equilibrium and Endogenous Cycles following desired price: p t=pt+mct, with ptthe logarithm of the price level and mcta variable that represents real marginal costs, which are given by mct= +(1 )(wtpt) + 1 +(1 )yt(1) Variable wtis the logarithm of the nominal wage rate. According to (1), marginal costs increase whenever positive changes are observed in the real wage rate and in the level of output. The desired price, p t, is the price that all …rms would like to set at time t(since …rms are identical, except for the variety of labor they hire and the variety of the good they produce). The desired price rises above the aggregate price level whenever the measure of marginal costs mctis positive; the opposite occurs for mct<0. Larger marginal costs lead to a desire for setting higher prices. Now, we introduce into the analysis the assumption of sticky information. Firms will want to set price p tbut they are sluggish in the way they update information (…rms face costs when acquiring, absorbing and processing information). This signi…es that the information that is necessary to choose the mentioned price has been collected, by di¤erent …rms, at di¤erent time periods in the past. The infrequent information updating implies that a …rm that last updated its information set jperiods ago will generate the following expectation, pt;j =Etj(p t). Note that the index jrepresents simultaneously di¤erent varieties of goods and the number of periods a …rm remains inattentive; the implicit assumption is that a …rm producing variety jis a …rm that has formed expectations about prices jperiods in the past. We de…ne 2(0;1) as the share of …rms that, at each time moment, recompute the optimal price by updating the corresponding information set. Looking from another angle, will also represent the probability of a …rm updating its information set at the current time period. The consideration of this share allows presenting the aggregate price level under the form of a weighted average of past expectations about the current price level, pt= 1 X j=0 (1 )jpt;j (2) 6 Information Stickiness in General Equilibrium and Endogenous Cycles Let t:= ptpt1be the in‡ation rate and consider, as well, mctas being the change on the real marginal costs from t1to t. By applying …rst-di¤erences to expression (2), we can present a central equation of the information stickiness analysis: the sticky-information Phillips curve. t= 1mct+ 1 X j=0 (1 )jEt1j(t+ mct)(3) The Phillips curve in (3) involves a contemporaneous positive relation between marginal costs and in‡ation; in‡ation is also dependent on past expectations about the current state of the economy. Consider now the behavior of households relating utility maximization. As …rms, households are also indexed by jin the unit interval (each variety jof the assumed good is produced by a variety jof labor and consumed by a variety jof household). Consumer jpossesses preferences given by the following utility function: U(Ct;j;Lt;j) = C11= t;j 1 11=  {L1+1= t;j 1+1= The utility function has two arguments: consumption, Ct;j, and an index respecting to labor supply, Lt;j. Obviously, @U @Ct;j >0and @U @Lt;j <0, i.e., utility increases with a larger level of consumption and additional hours of leisure. Parameters  > 0and > 0represent the intertemporal elasticity of substitution for consumption and the elasticity of labor supply, respectively. The value of  > 0translates the relative weight attributed to leisure in the utility function. Taking a discount factor 2(0;1), the optimization problem faced by each household is Max 1 X t=0 tU(Ct;j;Lt;j) The above problem is subject to a conventional budget constraint, where the households’ wealth increases with labor income and …nancial returns and decreases with consumption. By solving the optimal control problem, we encounter an Euler equation of the type: ct;j =Etj(Rt)(4) 7 Information Stickiness in General Equilibrium and Endogenous Cycles Figure 1 displays function (11) for 0= 0:25 and = 0:1: Note that in the vicinity of 0,(gt)is a decreasing and slightly convex function; this nonlinearity is a necessary ingredient for the result on ‡uctuations we will be able to obtain. -5 -4 -3 -2 -1 0 1 2 3 4 5 0.2 0.4 0.6 0.8 1.0 x y Fig. 1 - Information updating function In this section, we have introduced two assumptions that allow the SIGE model to approach the observed reality: economic agents are certainly unable to predict with full accuracy no matter how far apart are the relevant time moments, and information updating tends to be countercyclical. With these new assumptions the system will be able to provide a rich set of possible long-term outcomes. 4 Perfect Foresight and Stability Taking into account the new assumptions and de…ning the rate of change of the real wage by R t:= tt, the dynamic SIGE system can be further rearranged and presented under the form of a pair of di¤erence equations: gt+1 =f11[(gt)]gt+f12[(gt)]R t R t+1 =f21[(gt)]gt+f22[(gt)]R t (12) where: f11[(gt)] = (1 ) + 1 (1)26; f12[(gt)] = (1)(1) (1+3)6; f21[(gt)] = 1 (1)266+1 ; f22[(gt)] = 1 1+3h1 + 31 66+1 i and 14 Information Stickiness in General Equilibrium and Endogenous Cycles 1:= a  1(1) 2(1); 2:=  (1)(1)  +(1); 3:=  1(1)h +(1) + i; 4:=  1(1)h1 +(1)1 (+ )i; 5:=  1(1) +  a; 6:= 415 1+3 1 , with =(gt): To analyze system (12) under perfect foresight, we just need to recall that this corresponds to the case where condition = 1 applies. In this case, dynamics are reduced to (gt+1 = [1 (gt)] gt R t+1 = [1 (gt)] R t (13) The dynamic behavior of system (13) is straightforward to characterize. The result is synthesized in proposition 1. Proposition 1 Under perfect foresight, there is stability in the SIGE model. This result holds for constant information updating and for counter-cyclical information updating. Proof. The linearization of system (13) in the vicinity of the steadystate point g;R= (0;0) allows to write it under matricial form: "gt+1 R t+1 #="100 0 1 0#"gt R t#: Recall that 0is the steady-state level of (gt)when information updating is taken as counter-cyclical. The system is precisely the same for a constant =0. Because 02(0;1), both eigenvalues of the Jacobian matrix are inside the unit circle and, therefore, stability holds, i.e., we observe convergence towards g;R= (0;0) independently of parameter values and initial state The result in proposition 1 indicates that the way we approach information updating or the degree of information stickiness is not relevant for the model’s dynamics as long as we maintain that agents formulate expectations under perfect foresight. In perfect foresight settings, parameter 0just indicates the velocity of convergence towards the steady-state when taking an initial point g0; R 0 in the vicinity of that state, but it cannot change the stable nature of the 15 Information Stickiness in General Equilibrium and Endogenous Cycles system. The linearized system has the following solution, gt= (1 0)tg0 t= (1 0)t0 The velocity of convergence is given precisely by parameter 0, which indicates that the more sluggish information updating is, the slower will be the process of convergence. However, since 0is positive, the model remains stable. Under perfect foresight, any remark about the degree of information stickiness may be used to evaluate how fast the steady-state is reached, but the stability result cannot be questioned. 5 Partial Perfect Foresight: Local Analysis In this section, we address the stability properties of system (12) for  < 1, i.e., in the absence of full perfect foresight. A …rst result relates to the case of a constant attentiveness share . Proposition 2 Independently of the degree in which perfect foresight prevails in the formation of past expectations about current events, as long as the updating of information remains constant in time, nonlinearities will not exist. Proof. Just observe that for a constant value of the parameter , system (12) is linear. Thus, only two outcomes are conceivable: stability or instability (convergence or divergence relatively to the steady-state). The …nding of a stable or of an unstable outcome will depend on the values of the parameters of the model The analysis of local and global dynamics under constraint  < 1cannot be feasibly undertaken for the model on its generic form. We need to proceed with a numeric example and we adopt the same values of parameters as in Mankiw and Reis (2006): = 4,= 2=3,= 1,= 10,= 20. Besides these, we take as well the following: = 0:75,a= 0:01. Relatively to these two last values, changing them would have no signi…cant impact on the qualitative results as long as they remain bounded below 1. The policy parameter will be our bifurcation parameter in the analysis. For now, we consider that information is updated every four periods, if the corresponding 16 Information Stickiness in General Equilibrium and Endogenous Cycles parameter is constant or, in the case of counter-cyclical information updating, if the economy’s growth rate is zero; hence, =0= 0:25. With the described data, the following result is obtained. Proposition 3 For the considered array of parameter values, the SIGE model with partial perfect foresight is stable for  > 1:1808: Proof. The linearized SIGE model with the assumed parameter values is: "gt+1 R t+1 #="0:2547=(1) + 0:5625 0:2167 0:2149=(1) 0:6709 #"gt R t# Local dynamics are identical for constant information updating and counter-cyclical inattentiveness as long as =0, as it is the case. Stability conditions are: (i)1Det = 0:622 6 + 0:2174=(1) >0; (ii)1Tr +Det = 0:143 6 + 0:0373=(1) >0; (iii)1 + Tr +Det = 2:6107 0:4721=(1) >0. with Tr and Det representing, respectively, the trace and the determinant of the Jacobian matrix of the above system. The …rst two conditions are satis…ed for any  > 1; the third stability condition requires  > 1:1808 The result in proposition 3 is graphically depicted in …gure 2. This …gure represents the relation between the trace and the determinant; the three lines that form the inverted triangle are the bifurcation lines and the area inside the triangle represents the region of stability. The bold line translates the dynamics of the system; while inside the stability area, this line implies a value of larger than 1:1808. When equals this value, the bifurcation line 1 + Tr +Det = 0 is crossed (a ‡ip bifurcation occurs), and the stability region is abandoned for values of below the referred threshold value. 17 Information Stickiness in General Equilibrium and Endogenous Cycles φ = 1.1808 Det Tr Fig. 2 –Trace-determinant diagram in the partial perfect foresight case The obtained result is relevant and intuitive: it indicates that a departure from perfect foresight will require a more active policy by the monetary authorities, in order for stability to hold. Agents with a less than perfect capacity in forecasting future values will turn harder monetary policy implementation, because it will need to be more aggressive than in the benchmark case. Now, let us consider other possible values for or 0. Table 2 shows how the stability condition changes when changes. Stability Condition 0:1 > 1:9787 0:2 > 1:2720 0:3 > 1:1293 0:4 > 1:0750 0:5 > 1:0475 Stability Condition 0:6 > 1:0311 0:7 > 1:0200 0:8 > 1:0118 0:9 > 1:0053 1 > 1 Table 2 –Stability condition for various degrees of agents’attentiveness. The interpretation of table 2 is straightforward, and we synthesize it in the following proposition, Proposition 4 For the chosen array of parameter values, in the case of partial perfect foresight, in order for stability to hold, the stronger the level of inattentiveness the more aggressive monetary policy is required to be. Proof. Table 2 furnishes the data that is necessary to con…rm this result Figure 3 illustrates the result in proposition 4. 18 Information Stickiness in General Equilibrium and Endogenous Cycles 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0.05 0.25 0.45 0.65 0.85 λ φ S U Fig. 3 –Stability in the space of parameters The above result is robust to changes in parameter values. Any other numerical experimentation, using admissible parameter values, will lead to a same kind of outcome. This is also an intuitive result: given some rule for the formation of expectations, the more inattentive agents are, the more the monetary authority needs to intervene (with a more aggressive policy), in order for stability to hold. 6 Partial Perfect Foresight: Global Analysis Until now, the results of the constant attentiveness case and of the countercyclical attentiveness scenario have coincided: under perfect foresight, a result of stability holds in any of the cases. With partial perfect foresight, a same bifurcation condition separates, for both cases, regions of stability from regions of instability. This region of instability, however, will have different meanings under the two di¤erent assumptions about inattentiveness: constant information updating implies that the model is linear, local and global dynamics will coincide and there will be no exogenous ‡uctuations. On the opposite, counter-cyclical information updating triggers the formation of endogenous cycles in the region one has identi…ed of being of local instability. Recover the values 0= 0:25 and = 0:1and remember that, in this case, stability holds for  > 1:1808. Figure 4 illustrates the long-term behavior of the model for the output variable gt, and considering an interval of possible values of . The displayed bifurcation diagram allows to con- …rm where the region of stability is placed and to observe how the system 19 Information Stickiness in General Equilibrium and Endogenous Cycles behaves for values of between 1and 1:1808. There is a period doubling bifurcation process that culminates in a small region of chaotic cycles, after which cycles of low periodicity return. In this way, we con…rm the possibility of endogenous cycles of various periodicities and complete a-periodicity in the model of counter-cyclical attentiveness and partial perfect foresight: endogenous volatility is associated with a not su¢ ciently aggressive monetary policy. We can infer, from the analysis, that periods of larger volatility in the time paths of the main macroeconomic variables can be at least partially explained by a policy that is not active or aggressive enough given economic conditions relating agents’inattentiveness and agents’ability to accurately predict the future. Fig. 4 –Bifurcation diagram Figure 5 shows the type of strange attractor that emerges when a point of the system located at the chaotic zone is considered. The diagram shows all the possible points representing pairs of values (gt; R t)that are obtainable in the long-run for a policy parameter value = 1:1. Fig. 5 –Attractor 20 Information Stickiness in General Equilibrium and Endogenous Cycles 7 Conclusion The analysis has shown how a benchmark macroeconomic general equilibrium model with information stickiness can be adapted, by including two reasonable assumptions that allow to approach real life conditions, in order to display endogenous ‡uctuations on a setting that is, otherwise, inherently stable. The two assumptions, departures from perfect foresight and counter-cyclical information updating are, individually, necessary but not su¢ cient conditions for the generation of endogenous cycles. One needs to consider both in order to achieve the mentioned outcome. With the provided interpretation of macro relations, we have proven that the perspective put forward in the paper’s initial sentence by Barnett, Medio and Serletis (1997) can be adapted to a macro environment involving information stickiness. The study o¤ers some intuitive results: it says that endogenous volatility arises through the combination of, on one hand, two anomalies relatively to what can be interpreted as an e¢ cient behavior of economic agents – inattentiveness and non pervasive perfect foresight –with, on the other hand, an eventual di¢ culty of the central bank in understanding how aggressive its behavior must be, given the departures from ‘perfect behavior’by the private agents. 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