Achieving two policy targets with one policy instrument: Heterogeneous expectations, countercyclical fiscal policy, and macroeconomic stabilization at the effective lower bound

Lima, Gilberto Tadeu; Setterfield, Mark; da Silveira, Jaylson Jair Working Paper Achieving two policy targets with one policy instrument: Heterogeneous expectations, countercyclical fiscal policy, and macroeconomic stabilization at the effective lower bound FMM Working Paper, No. 86 Provided in Cooperation with: Macroeconomic Policy Institute (IMK) at the Hans Boeckler Foundation Suggested Citation: Lima, Gilberto Tadeu; Setterfield, Mark; da Silveira, Jaylson Jair (2023) : Achieving two policy targets with one policy instrument: Heterogeneous expectations, countercyclical fiscal policy, and macroeconomic stabilization at the effective lower bound, FMM Working Paper, No. 86, Hans-Böckler-Stiftung, Macroeconomic Policy Institute (IMK), Forum for Macroeconomics and Macroeconomic Policies (FMM), Düsseldorf This Version is available at: https://hdl.handle.net/10419/274240 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. 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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. https://creativecommons.org/licenses/by/4.0/legalcode FMM WORKING PAPER No. 86 • January 2023 • Hans-Böckler-Stiftung ACHIEVING TWO POLICY TARGETS WITH ONE POLICY INSTRUMENT: HETEROGENEOUS EXPECTATIONS, COUNTERCYCLICAL FISCAL POLICY, AND MACROECONOMIC STABILIZATION AT THE EFFECTIVE LOWER BOUND Gilberto Tadeu Lima 1 , Mark Setterfield 2 , Jaylson Jair da Silveira 3 ABSTRACT We explore the short-term macrodynamics of stabilization policy at the effective lower bound (ELB) of the nominal interest rate, in an environment characterized by heterogenous and endogenously time-varying private-sector output and inflation expectations driven by evolutionary dynamics. We show that at the ELB, fiscal policy conducted in accordance with a well-specified policy rule is particularly effective for purposes of macroeconomic stabilization. This is because fiscal interventions have both a direct effect on output and inflation (via aggregate demand formation) and an indirect effect on these same target variables, via the management of heterogenous and evolving expectations. As a result of the two channels through which it operates, and seemingly despite the logic of the Tinbergen (targets-instruments) principle, fiscal policy is thus revealed as a single policy instrument capable of achieving two policy goals. ————————— 1 Department of Economics, University of São Paulo, Brazil, [email protected] 2 Department of Economics, New School for Social Research, USA; FMM fellow. [email protected] 3 Department of Economics and International Relations, Federal University of Santa Catarina, Brazil, [email protected] Achieving two policy targets with one policy instrument: heterogeneous expectations, countercyclical fiscal policy, and macroeconomic stabilization at the effective lower bound Gilberto Tadeu Lima Department of Economics, University of São Paulo, Brazil [email protected] Mark Setterfield Department of Economics, New School for Social Research, USA [email protected] Jaylson Jair da Silveira Department of Economics and International Relations Federal University of Santa Catarina, Brazil [email protected] January 2023 Abstract: We explore the short-term macrodynamics of stabilization policy at the effective lower bound (ELB) of the nominal interest rate, in an environment characterized by heterogenous and endogenously time-varying private-sector output and inflation expectations driven by evolutionary dynamics. We show that at the ELB, fiscal policy conducted in accordance with a well-specified policy rule is particularly effective for purposes of macroeconomic stabilization. This is because fiscal interventions have both a direct effect on output and inflation (via aggregate demand formation) and an indirect effect on these same target variables, via the management of heterogenous and evolving expectations. As a result of the two channels through which it operates, and seemingly despite the logic of the Tinbergen (targets-instruments) principle, fiscal policy is thus revealed as a single policy instrument capable of achieving two policy goals. Keywords: Stabilization policy, effective lower bound, fiscal policy, heterogeneous inflation and output expectations, satisficing evolutionary dynamics. J.E.L. Classification Codes: E12, E52, E62, E63, E71. 2 1. Introduction During the past two decades, confronting the zero lower bound (ZLB) for the nominal interest rate has been one of the most important challenges for monetary policy in the U.S. and various other developed economies. A key issue at stake concerns the extent to which, and how, the ZLB represents a genuine constraint on attainable targets for inflation (and possibly real output) as stable equilibrium outcomes. As theoretically articulated and empirically confirmed, the ZLB represents an important constraint on what conventional monetary stabilization policy can achieve, forcing monetary policy to rely on unconventional monetary policy tools. In principle, further monetary policy accommodation at the ZLB can be achieved by means of policy tools such as forward guidance (which provides market participants with information about the intentions of monetary policy makers for the future path of the nominal interest rate) and quantitative easing (which involves large-scale purchases of public and in some cases private assets). It is often argued that these unconventional monetary policy tools were effective, to varying degrees and in different ways, in the wake of the 2008 financial crisis.1 The obstacles and challenges to stabilization policy posed by the ZLB have been extensively explored in the mainstream theoretical and empirical literature on monetary policy making.2 Indeed, similar challenges are understood to arise if the economy operates sufficiently near to the ZLB – hence the notion of an effective lower bound (ELB) to the nominal interest rate, to which we consistently refer hereafter. However, the connection between policy-making at the ELB and endogenously time-varying heterogeneity of inflation and output expectations – for which there is indeed considerable empirical and experimental evidence – has been absent from this literature. Neither has this connection been explored 1 See, for example, Gambacorta, Hofmann and Peersman (2014), who provide evidence from eight advanced economies, Kuttner (2018) for evidence from the United States, and Dell’Ariccia, Rabanal and Sandri (2018) for evidence from the Euro Area, Japan and the United Kingdom. 2 For recent examples, see the “Symposium on Monetary Policy at the Effective Lower Bound” featured in the Fall 2018 issue of the Brooking Papers on Economic Activity, and the “Session on Monetary Policy Frameworks and the Zero Lower Bound” featured in the 2019 issue of the American Economic Association Papers & Proceedings. 3 in the heterodox macroeconomic literature: although heterogeneous inflation and output expectations formation are considered in Lima, Setterfield and Silveira (2014, 2020), there is no exploration of the potential role of fiscal policy at the ELB. This neglect on the part of the heterodox macroeconomic literature is surprising given the weight attached by Keynes himself to the importance of expectations as a key driver of economic behavior, and Keynes’s consideration of what can be done to stabilize the economy when it falls into a ‘liquidity trap’ – that is, when the nominal interest rate is reduced to a level below which it cannot fall further in response to monetary policy.3 The effective management of inflation and output expectations is evidently key to successful stabilization policy at all times, not just in the relatively unusual (from a longer-term perspective) circumstances imposed by reaching the ELB. However, when the latter is reached, and thus conventional monetary policy based on the further lowering of the nominal interest rate becomes infeasible, an issue that arises is whether fiscal policy can substitute for conventional monetary policy as a device for macroeconomic management, especially (but not only) when unconventional monetary policy tools such as forward guidance or quantitative easing are unavailable. Consider, for example, an explicit fiscal policy rule, according to which aggregate-demand-creating (and thus expansionary) fiscal policy is adopted more (less) intensively when output (inflation) is below (above) its official target. We show that with heterogenous and endogenously time-varying inflation and output expectations, fiscal policy contributes to the achievement of both inflation and output targets by operating directly as a policy instrument and indirectly, as an instrument for managing output and inflation expectations. While management of 3 As Keynes stated in chapter 15 of the General Theory on the psychological and business incentives to liquidity: “There is the possibility…that, after the rate of interest has fallen to a certain level, liquidity-preference may become virtually absolute in the sense that almost everyone prefers cash to holding a debt which yields so low a rate of interest. In this event the monetary authority would have lost effective control over the rate of interest. But whilst this limiting case might become practically important in future, I know of no example of it hitherto.” (1936, p.207). In fact, in modern parlance, the situation envisioned by Keynes seems closer to a (strictly positive) effective lower bound rather than a zero lower bound. In any case, the future in which Keynes supposed that such a limiting situation might become practically important has arrived. 4 expectations is a central feature of monetary policy making discussion, at the ELB fiscal policy may be the only conventional instrument capable of such management. Moreover, fiscal policy is rendered surprisingly effective in this management role as long as there is endogenously time-varying disagreement among private decision makers, whose expectation formation is influenced by public-sector policy targets acting as ‘anchors’. Specifically, our analytical results demonstrate that at the ELB, fiscal policy can be used to ensure that the dynamics of heterogeneous inflation and output expectations are not only benign, but actively contribute to the achievement of two explicit policy targets (inflation and output). Prima facie this analytical result is surprising, in that it would appear to violate the Tinbergen (1952) principle according to which there needs to be as many linearly-independent policy instruments as there are linearlyindependent policy goals to be achieved. In our model, however, the evolutionarily satisficing dynamic driving heterogeneous private-sector inflation and output expectations formation acts as a ‘surrogate’ policy instrument in its key role as an adjusting variable, so that the Tinbergen principle is in this sense satisfied. The remainder of the paper is organized as follows. Section 1 outlines the baseline macrodynamics on which our analysis is based, while in Section 2 we describe a complementary micro-structure based on noisy satisficing evolutionary dynamics in the spirit of the evolutionary contributions of Simon (1955, 1956) on bounded rationality. Section 3 analyses the interaction between our microand macro-dynamics with a particular focus on the capacity of fiscal policy to stabilize the economy, despite its being a single instrument operating on two policy targets (output and inflation). Section 4 discusses the significance and policy implications of our results and finally, section 5 concludes. 5 2. Macrodynamics: a benchmark model We begin with the following benchmark dynamic macroeconomic model: (1) 0 ee yy r g y δ λγ =− ++ , (2) e p py βϕ α =++ , (3) ( )( ) TT g yy pp µψ =−−− −  , (4) ee r ip= − , (5) (1 )( ) eT p kpp=−− −  , (6) (1 )( ) eT y ky y=−− −  , where y is the level of real output, 0 y represents non-interest sensitive components of aggregate spending, e r is the real interest rate, g is a fiscal policy variable contributing to aggregate spending,4 e y denotes the expected real output, T y denotes the policy authorities’ target level of real output and T p their target rate of inflation, both exogenously given, p and e p are the actual and expected rates of inflation, respectively, and i is the fixed level of the nominal interest rate, capturing the idea that the economy is at or close enough to the zero lower bound – in other words, that it is at the effective lower bound (ELB). As usual, a dot over a variable denotes its rate of change (i.e., /x dx dt=  ). Finally, β denotes an exogenous component in inflation dynamics and the other Greek letters represent strictly positive parameters. Equation (1) is simply an aggregate demand schedule also featuring a positive impact of expected output, which captures the idea that current spending and hence output varies positively with expected 4 Following Setterfield (2007), the fiscal policy variable g can be thought of as representing, for example, the size of the public-sector borrowing requirement (PSBR) in real terms. 6 future output (and hence income). Equation (2) is an expectations-augmented Phillips curve, in which it is reasonable to assume that 1 ϕ < , which is consistent with the notion that workers lack the bargaining power to fully index expected inflation into nominal wage growth. Equation (3) describes the conduct of fiscal policy in terms of a “pseudo Taylor rule” (Setterfield, 2007), with the public-sector borrowing requirement (PSBR) behaving in a countercyclical manner by falling (rising) whenever either output or inflation is above (below) its official target. Equation (4) is a Fisher-like relationship, relating the expected real interest rate to the nominal rate of interest and the expected rate of inflation.5 Observe that the ELB means that there is a lower bound on the (expected) real interest rate of e ip− . In addition to the expected rate of inflation, the precise value of this lower bound will, of course, depend on the precise value of the ELB, which may be slightly greater than zero, equal to zero or (following recent experience in Sweden, Denmark, Japan, Switzerland, and the euro area) even slightly lower than zero (see, e.g., Agarwal and Kimball, 2019, on negative nominal interest rates). What is most relevant for stabilization policy in the first instance, however, is not so much the precise value of the ELB, denoted by i in equation (4), but rather that the nominal interest rate cannot be lowered further, so that /0di dt = .6 Therefore, we abstract from the possibility of a negative interest rate to focus more sharply on the implications for stabilization policy of a nominal interest rate the value of which cannot be further reduced even if it is still but only slightly greater than zero. The reader will notice the upward (as well as downward) rigidity of the nominal interest rate that is implied by this assumed fixity of the nominal rate. Upward rigidity of the nominal rate can be plausibly justified by the assumption that the central bank operates on a non-Neo-Fisherian view 5 Mainstream economists typically believe that, in the long run, the real interest rate is independent of nominal factors, which means that a long-run increase in the nominal interest rate translates into a one-for-one increase in inflation. Since we do not (and do not need to) endorse this strict interpretation of the Fisher relationship, we simply refer to (4) as a “Fisher-like” relationship. 6 In fact the precise value of the ELB on the nominal interest rate might matter in the event that it could become strictly negative. We abstract from such a possibility to avoid overloading the model with further structure, since a strictly negative nominal interest rate raises additional conceptual and analytical issues. 7 (NNFV) of the economy. The so-called Neo-Fisherian view (NFV – see, e.g., Williamson, 2016, and Garín, Laster and Sims, 2018) holds that the monetary authority should raise (rather than lower) interest rates in order to stimulate the economy. The hypothesis behind the NFV is that an increase in the nominal interest rate can raise inflation expectations (via the cost channel of monetary policy, for example – see Lima and Setterfield, 2014) and so reduce the real rate of interest in the Fisher equation. The NNFV rejects the NFV and instead holds to the more orthodox view that a nominal rate cut is required to stimulate the economy. A central bank operating on a NNFV of the economy will not raise the nominal interest rate at the ELB precisely because of the macroeconomic circumstances (a depressed economy) that have brought it to the ELB in the first place. In short, the ELB renders the nominal rate rigid downwards, while the combination of macroeconomic circumstances and a NNFV of the economy render it effectively (if not literally) rigid upwards. The nominal interest rate at the ELB can therefore be regarded as fixed. The recent (and not entirely successful) experience of some countries with lowering the nominal interest rate from slightly above to slightly below zero is suggestive that a non-zero ELB is likely to be endogenous, statedependent, and time-varying rather than exogeneously fixed. We abstract from this possibility, however, in order to sharpen focus on the implications for stabilization policy of a given ELB. Nevertheless, and as elaborated below, even with a fixed ELB on the nominal interest rate the effective lower bound on the (expected and actual) real interest rate, which is considerably more relevant for the macrodynamics of the economy, is endogenously time-varying. Equations (5) and (6) are motivated by the considerable empirical evidence from survey data and laboratory experiments suggesting that both inflation and output expectations are persistently heterogeneous and formed (predominantly) through boundedly rational mechanisms (see, e.g., Hommes, 2013 and Coibion, Gorodnichenko and Kumar, 2018). They posit that, rather than interacting with homogeneous decision makers who base expectations on a single salient and time-invariant ‘true model’, 14 The level of the “policy (in)effectiveness indicator” that is acceptable to an agent depends, inter alia, on idiosyncratic features which are exogenously determined. We therefore assume that acceptable indicators are randomly and independently determined across agents and over time. More precisely, we assume that the acceptable level of policy (in)effectiveness, 22 ( )( ) jT jT pp yy− +− , is a random variable with cumulative distribution function : [0,1]F + →⊂ which is continuously differentiable. Therefore, the probability of randomly choosing a given agent j who considers the current observed policy (in)effectiveness indicator 22 ( )( ) TT pp yy− +− as unacceptable is given by: (11) ( ) ( ) 2 2 2 22 Pr( )( )( )( ) ( )( ) jTjT TT TT ppyy ppyyFppyy−+−<−+−= −+− . Note that, in particular, if the economy achieves both targets (,) TT py , we have (0) 0 F= , so that the measure of agents who consider that the current policy making is not acceptably effective is null. Meanwhile, the probability that a randomly drawn agent j will consider that the currently observed policy (in)effectiveness indicator is acceptable is simply: (12) ( ) () 2 2 2 22 Pr( )( )( )( )1 ( )( ) jTjT TT TT ppyy ppyy Fppyy−+−≥−+−=− −+− . The measure of credulous agents who become incredulous is then given by: (13) ( ) 22 (1 ) ( ) ( ) TT kF p p y y − − +− . Analogously, the measure of incredulous agents who becomes credulous is represented by: (14) ( ) 22 1 ( )( ) TT k Fpp yy  − − +−  . Hence subtracting equation (14) from equation (13) yields the following satisficing evolutionary dynamics: 15 (15) ( ) ( ) 22 22 (1)( )( ) 1 ( )( ) TT TT k kFpp yy k Fpp yy  =− − +− − − − +−   . Next, we consider the reasonable possibility that the satisficing evolutionary dynamics in equation (15) operate in the presence of a noise term, analogous to mutation in natural environments. In a biological setting, mutation is interpreted literally as comprising random changes in genetic codes. In economic settings, as interpreted in Samuelson (1997, Ch. 7), mutation describes a situation in which a decision maker refrains from comparing payoffs and switches strategy at random. Hence the present specification features mutation as exogenous noise in the satisficing evolutionary protocol, leading a certain proportion of agents to choose an inflation and output foresight strategy at random. This disturbance component is meant to capture the effect of (for instance) exogenous institutional factors, such as changes of administration in the fiscal and monetary authorities, or changes in the policy-making framework other than an abandonment of the inflation and output targeting regime (or the expectation thereof by private agents). Alternatively, and following Kandori, Mailath and Rob (1993), random choice behavior can be associated with: an agent exiting the economy with some (fixed) probability, who is then replaced with a new agent who knows nothing about (or is still not sufficiently experienced in) the relevant decisionmaking process; and/or agents who, for idiosyncratic reasons (from whose determination we abstract), “experiment” once in a while, with exogenously fixed probability. Drawing on the specification suggested in Gale, Binmore and Samuelson (1995), mutation can be straightforwardly incorporated into the satisficing evolutionary dynamics in equation (15) as follows. Let (0,1) ε ∈⊂ be the measure of mutant agents that choose an inflation and output foresight strategy in a given revision period independently of the respective payoffs. Therefore, there are (1 ) k ε − credulous agents and k ε incredulous agents behaving as mutants. 16 Although mutant agents choose an inflation and output foresight strategy in a given revision period independently of the respective payoffs, an incredulity bias can reasonably arise as the ELB is approached from a strictly positive level of the nominal interest rate. In other words, for a given value of the policy (in)effectiveness indicator, credulous (incredulous) mutants may become less credulous (more incredulous) as the ELB is approached, changing their foresight strategy with higher (lower) probability, as they may arguably come to think that the achievement of a given inflation and/or output target becomes more difficult as the ELB is approached. A possible way to capture this enhanced skepticism about the central bank’s capacity to achieve its targets, which should manifest (given the payoff differential and the mutation rate) in an increased proportion of incredulous agents as the economy approaches the ELB zone from above, is to make the likelihood that a mutant switches strategy endogenous to the value of the nominal interest rate. More precisely, and recalling that we abstract from the possibility of a negative nominal interest rate, if we assume that the fraction of credulous mutants who switch strategy is given by 1 (1 )i+ , the number of credulous mutants who become incredulous is given by (1 ) (1 )ki ε −+ , so that as i goes to zero eventually all credulous mutants become incredulous. Analogously, when the fraction of incredulous mutants who switch strategy is given by (1 )ii+ , which is decreasing with respect to i , the measure of incredulous mutants who become credulous is given by (1 )ki i ε + , so that as i goes to zero none of the incredulous mutants becomes credulous. For a given nominal interest rate i , the net flow of mutant agents becoming incredulous agents at the ELB in a given revision period is then the following: (16) 11 (1 ) 1 11 i kk k i ii ε εε     −− =−     + ++     . Following Gale, Binmore and Samuelson (1995), this noise can be simply added to the evolutionary mechanism (17) to yield the following noisy satisficing evolutionary dynamics: 17 (17) ( ) ( ) { } 22 22 (1 ) (1 ) ( ) ( ) 1 1 ( )( 1 ) TT TT k kFpp yy k Fpp yy k i ε ε  =− − − +− − − − +− +  −  +    . 4. The coevolution between macroand micro-dynamics The state transition of the economy is determined by the system composed of equations (8), (10), and (17), the state space of which is represented by { } 3 ( , , ) :0 1ypk k + Θ= ∈ ≤ ≤ . Considering the subsystem composed of equations (8) and (10), we have 0y=  and 0p=  for a given k if, and only if, the following condition is satisfied: (18) 0 0 T T ab yy ac pp α −−  −    =     −−−     . Since (1 ) 0ak λµ γ ≡ + −> for all [0,1]k∈⊂ and (1 ) 0cb k αϕ − = −> for all [0,1)k∈⊂ , it follows that ( )0 ab ac b ac α α −− =−> −− for all [0,1)k∈⊂ . Therefore, the homogeneous linear system in (18) has a unique solution for any [0,1)k∈⊂ , given by 0 TT yy pp−=−= , which is equivalent to T yy= and T pp= . Given that (0) 0F= when T pp= and T yy= , setting 0k=  in the noisy satisficing evolutionary dynamics in equation (17) yields: (19) 1 (1 0 1 )k i k εε  −  +  − −+ = , the solution to which is given by: 18 (20) * 1k i k ε ≡ + = . Note that (0,1) ε ∈⊂ and i+ ∈ ensures that * (0,1)k∈⊂ , which is a polymorphic equilibrium characterized by the coexistence of credulous and incredulous agents. Although the strategies deployed to form inflation and output expectations are different across types of agents, they nonetheless yield the same prediction of such variables in the equilibrium configuration, which is characterized by the achievement of the policy targets for inflation and output. Essentially, while credulous agents are always credulous, incredulous agents practice the ‘incredulity of Saint Thomas’: unless they see that the policy targets have been achieved, they do not believe in the prospect of their achievement.11 Thus, the (unique) equilibrium configuration of the dynamic system represented by equations (8), (10), and (17) is given by ( ) * ,, TT ypk . In this equilibrium, it follows from equation (20) that the proportion (0,1)k∈⊂ of incredulous agents whose expectations are not anchored to the official inflation and output targets varies positively (negatively) with the mutation rate (effective lower bound of the nominal interest rate). Intuitively, the higher the effective lower bound, the lower the proportion of incredulous agents in the equilibrium with achievement of the official inflation and output targets, given the incredulity bias in the satisficing evolutionary dynamics of foresight strategy switching that arises as the ELB is approached. Meanwhile, in the absence of mutation ( ε0= ), the (likewise unique) equilibrium solution is given by ( ) , ,0 TT yp , with the achievement of the official inflation and output targets being accompanied by a configuration in which all agents have adopted the credulous strategy to form inflation and output expectations. Moreover, it follows from equation (3) that the fiscal policy variable represented 11 The reference here is to the passage in the Bible involving the Apostle Thomas, who declined to believe that the resurrected Jesus had appeared to a group other apostles unless he, himself, could see and feel the injuries suffered by Jesus on the cross: “Unless I see the nail marks in his hands and put my finger where the nails were, and put my hand into his side, I will not believe it” (John 20: 19-29). In secular terms, incredulous agents respond to policy targets on a strict “seeing is believing” basis. 19 by the PSBR becomes stationary in the unique equilibrium configuration of the economy, which in conjunction with the stationarity of output at its official target value implies that the PSBR to output ratio is also stationary. Let us now conduct the corresponding stability analysis. The Jacobian matrix evaluated around the equilibrium is given by: (21) ( ) * 0 ,, 0 001 TT ab Jy p ak c α −− =−− −      . We recall that * (1 0)a k λµ γ ≡+−> , *)(1 0b k δ λψ ≡−+ > , and * ( )(1 0)c k ϕ αδ αλψ ≡+ − + > . Let ξ be an eigenvalue of the Jacobian matrix in expression (21). We can set the following characteristic equation of the linearization around the equilibrium: (22) 0 0 0 01 . ab JI a c ξ ξα ξ ξ −− − − = − −− −− This characteristic equation can be re-written as follows: (22-a) 2 ( ) ( ) (1 ) 0a c ac b ξ ξαξ  ++ + − +=  , whose solutions are the eigenvalues of the Jacobian matrix in expression (22), which are given by: (23) 2 1 ()()4( ) 2 ac ac ac b α ξ −++ + − − = , 2 2 ()()4( ) 2 ac ac ac b α ξ −+− + − − = , and 3 10 ξ =−< . 20 As 0ac+> and * (1 ) 0cb k αϕ −=−> for all *[0,1)k∈⊂ , then 1 Re( ) 0 ξ < and 2 Re( ) 0 ξ < such that the unique equilibrium given by ,1 , TT i yp ε +    is locally asymptotically stable. 5. Discussion At first sight, policy-making in the model faces an insoluble ‘Tinbergen problem’, in that policy makers can manipulate only a single instrument (fiscal policy) in the pursuit of two targets (for inflation and output). However, the model features the Tinbergen problem being ultimately solved, as there are two adjusting variables (viz. the expansionary-fiscal policy variable, g , and the private sector’s degree of credulity in the effectiveness of policy-making, as measured by 1k− ), the coupled dynamics of which result in the achievement of the two targets as a stable equilibrium configuration. It follows that stabilization policy prosecuted adequately conducting fiscal policy as the single policy instrument can actually work in stabilizing the economy in accordance with the policy-makers’ chosen policy targets. In fact, full credulity in the effectiveness of policy-making can be interpreted as another implicit policy target, the achievement of which is a by-product of achieving the official targets for inflation and output (at least when 0 ε = ). Interestingly, private agents actively contribute to effective fiscal policy by adopting heterogeneous strategies to form inflation and output expectations, and by possibly switching such strategies based on a boundedly rational, evolutionarily satisficing protocol. Therefore, endogenously time-varying heterogeneity in the strategies adopted by the private sector to construct inflation and output expectations in accordance with satisficing evolutionary dynamics may actually (albeit unintentionally) facilitate instead of impede successful target-based stabilization policy. Also, our analytical results show that inflationand ouput-targeting may actually succeed in anchoring inflation and output expectations 21 even if heterogeneity in the strategies adopted by private agents to form inflation and output expectations emerges as an equilibrium outcome of satisficing evolutionary dynamics. The intuition underlying this result is that despite there is heterogeneity in the strategies to form inflation and output expectations, the two available strategies yield the same prediction of such variables in the equilibrium configuration, which is characterized by the achievement of the policy targets for inflation and output. While incredulous agents form expectations in accordance with current inflation and output, credulous agents’ expectations are firmly anchored to the official inflation and output targets. Fiscal policy contributes to the achievement of two policy targets at the ELB also by substituting for monetary policy as a way of affecting the expected real interest rate through expected inflation. In fact, fiscal policy, by having both a direct (via the fiscal policy rule) and an indirect effect (via inflation and output expectations), is able to engender changes in the expected real interest rate at the ELB. However, our stability conditions reveal that fiscal policy achieves two targets with one instrument if 0 ϕ > – in other words, as long as there is a link between inflation and inflation expectations in equation (2). Hence observe that 0 ϕ = , by breaking the link just noted, implies that 0cb α −= in equation (23), and the stability result reported above is lost. Intuitively, 0 ϕ = erodes the two-way interaction between the evolution of macroeconomic outcomes and the evolution of expectations in our model sufficiently to eliminate the indirect channel of adjustment through which (in part) a stabilization policy with two targets but just one (fiscal) instrument effectively works. Note also that we posit 01 ϕ << , giving our economy a Post-Keynesian structure. A more mainstream interpretation of the Phillips curve in equation (2) would posit 1 ϕ = , consistent with full indexation of expected inflation into nominal wage growth (real wage bargaining). In this case, the equilibrium solution of equation (2) would yield /y βα = − , and if we assume that /T n yy βα −== (where n y is the “natural” level of output determined on the supply-side of the economy), our analysis would be consistent with that arising from a mainstream New Consensus 22 model. The point to be clearly made here is that 1 ϕ = does not affect the stability result derived earlier. In other words, our key policy result – that it is possible to achieve two targets with one (fiscal) policy instrument when operating at the ELB in the presence of heterogeneous, evolutionarily time-varying expectations – holds regardless of the precise (Post-Keynesian versus mainstream) specification of our underlying model. As suggested in Section 2, the functional dependence of the expected real interest rate on inflation expectations means that unlike the (fixed) ELB, the lower bound on the expected real rate of interest is, itself, evolutionarily time-varying. In effect, it follows from equation (5) that the rate of change of this lower bound depends on both the deviation of inflation from its official target and the frequency distribution of strategies used to form inflation and output expectations in the private sector. Yet, although the lower bound on the expected real interest rate is evolutionarily time-varying, in principle, policymakers can still directly affect the expected real interest rate at the ELB. To see this, note that it follows from equation (4) that ee rp= −  , with which, using equation (5), can be used to express the rate of change of the expected real interest rate as follows: (24) (1 )( ) eT r kpp=−−  , so that: (25) / (1 ) 0 eT rp k∂ ∂ =−− <  . Recalling that [0,1]k∈⊂ denotes the proportion of incredulous agents (who form expectations in accordance with current inflation and output), it follows intuitively that the success of the policy authorities in engineering a temporary fall in the expected real interest rate by raising the inflation target is increasing in the proportion of credulous agents ( 1k− ). Starting from a position of equilibrium, where 23 0 e r=  in equation (24), a rise in the inflation target T p will result in 0 e r<  for any * (0,1)k∈⊂ , which holds for all (0,1) ε ∈⊂ and i+ ∈ . In other words, the policy authorities can reduce the expected real interest rate at the ELB (and hence boost aggregate demand) simply by increasing their inflation target. However, this rise in the inflation target (which will be accompanied by an equivalent rise in the current rate of inflation once equilibrium is regained) may have negative side effects during the course of the system’s transitional dynamics. In particular, it may, in and of itself, undermine agents’ confidence in the inflation target as a potentially reliable conventional anchor for expectations.12 Even a one-time and modest rise in the inflation target might undermine confidence in the inflation target as a reliable predictor of inflation, for reasons other than those already accounted for by the noisy satisficing evolutionary dynamics in equation (17).13 Finally, note that although both the ELB itself and the equilibrium proportion of credulous agents in the private sector are invariant with respect to the inflation target, they nevertheless affect the out-ofequilibrium dynamics associated with changes in pT. Based on equations (20) and (24), we have that for all (0,1) ε ∈⊂ and i+ ∈ : (26) * * (1 ) 1 0 1 e T kk rk pi ε = ∂=−− = −< ∂+  . In other words, the magnitude of e r  immediately following a rise in the inflation target is decreasing in the mutation rate ε and increasing in the ELB on the nominal interest rate i . Therefore, a lower ELB – in and of itself a good thing if monetary policy-makers are trying to reduce the real interest rate in 12 It may also create the potentially-destabilizing expectation of further increases in the inflation target, leading private agents defer changes in behavior in favour of adopting a ‘wait and see’ approach. 13 Note also that a permanently higher inflation target causes only a temporary boost in output (the equilibrium value of which remains equal to its official target value) at the cost of a permanently higher rate of inflation.