Behavioural Macroeconomic Policy: New perspectives on time inconsistency
aa r X i v : . [ ec on . T H ] J u l Behavioural Macroeconomic Policy: Newperspectives on time inconsistency
Michelle BaddeleyJuly 19, 2019
Abstract
This paper brings together divergent approaches to time inconsistencyfrom macroeconomic policy and behavioural economics. Developing Barroand Gordon’s models of rules, discretion and reputation, behaviouraldiscount functions from behavioural microeconomics are embedded intoBarro and Gordon’s game-theoretic analysis of temptation versus enforce-ment to construct an encompassing model, nesting combinations of timeconsistent and time inconsistent preferences. The analysis presented inthis paper shows that, with hyperbolic/quasi-hyperbolic discounting, theenforceable range of inflation targets is narrowed. This suggests limits tothe effectiveness of monetary targets, under certain conditions. The pa-per concludes with a discussion of monetary policy implications, exploredspecifically in the light of current macroeconomic policy debates.
JEL codes:
D03 E03 E52 E61
Keywords: time-inconsistency behavioural macroeconomics macroeconomicpolicy
Contrasting analyses of time inconsistency are presented in macroeconomic pol-icy and behavioural economics - the first from a rational expectations perspec-tive [12, 6, 7], and the second building on insights from behavioural economicsabout bounded rationality and its implications in terms of present bias andhyperbolic/quasi-hyperbolic discounting [13, 11, 8, 9, 18]. Given the divergentassumptions about rational choice across these two approaches, it is not so sur-prising that there have been few attempts to reconcile these different analysesof time inconsistency.This paper fills the gap by exploring the distinction between inter-personaltime inconsistency (rational expectations models) and intra-personal time incon-sistency (behavioural economic models). This raises questions about the roleof institutional reform (e.g. inflation targetting and other monetary targets,central bank independence) versus behaviour change (”nudging”) in ameliorat-ing the negative impacts from these different forms of time inconsistency. In1eveloping this analysis, sections I and II outline the key features of the ratio-nal expectations and behavioural economics models. Then, in Section III, thedivergent approaches are reconciled via an encompassing model of strategic in-teractions between macroeconomic policy-makers and agents, building on Barroand Gordon’s monetary policy model [7]. Section IV outlines macroeconomicpolicy implications and conclusions.
Mainstream macroeconomic theory assumes rational expectations and inter-temporal utility maximisation, building on microfoundations consistent withsubjective expected utility theory [23, 21]. Preferences - including time andrisk preferences - are assumed to be independent, complete, stationary andconsistent. Specifically for the rate of time preference, time-separable utilityrequires that preferences are consistent through time so that inter-temporaltrade-offs are independent of when they occur. For example, with a stable rateof time preference, a choice between consumption in a year versus a year and aday would be equivalent to a choice between consumption in a decade versus adecade and a day. When the additional assumption of efficient financial marketsis added, agents will balance their rate of time preference with the real interestrate. These assumptions are embedded in the ”policy ineffectiveness” critiquesof Lucas, Sargent, Wallace and others, which focussed on the limitations ofdiscretionary demand management and its reliance on counter-cyclical monetaryand fiscal policy levers [14, 15, 19, 20].Building on these insights, Kydland and Prescott proposed time inconsis-tency as an explanation for the stagflationary episodes of the 1970s [12]. Effec-tively operating as if in a strategic game with policy-makers, forward-lookingrational agents will predict inflationary consequences from current expansionarypolicies, pre-empting inflationary erosion of their future real wages by increasingtheir nominal wage demands today. The consequences will be macroeconomicbecause, if all rational agents raise their nominal wage demands at the sametime, then inflation will become a self-fulfilling prophecy as prices are pushedup by increasing wage costs. A sub-optimal Nash equilibrium will emerge inwhich rational agents’ dominant strategy of increased nominal wage demands isneutralised by inflation, and everyone suffers from the inflationary bias whichemerges as a consequence.Kydland and Prescott developed their concept of time inconsistency to cap-ture the consequences of discretionary policy-making when rational privateagents have opportunities to plan for the consequences of policies. Policies aretime inconsistent when a policy devised to be optimal in one period will changethe world (in this case by changing rational agents’ expectations). Consequently,a policy designed to be optimal in the first period is no longer optimal in thenext period, and the cause of its sub-optimality is itself i.e. its own impacts on2rivate agents’ expectations. In the case of discretionary demand management,private agents will shift their inflation expectations when discretionary policiesare announced, rationally foreseeing the inflationary consequences of pushingan economy beyond full employment. So the policy designed to be optimal ex-ante, assuming static expectations, will not be optimal ex-post because rationalagents expectations shift in response to the policy.What are the rational expectations alternatives to discretionary policy-making?Rational expectations theorists argued that, if the rules of the policy-makinggame are clear and transparent, then there will be no incentive for rationalagents strategically to raise their wage demands. Sub-optimal outcomes emergefrom strategic interactions between rational agents and macroeconomic policy-makers because policy-makers lack credibility in terms of their commitments toa full-employment target. If rational agents can be made to believe that policy-makers will stick to their full-employment targets, then the problem disappears.Important theoretical contributions to the analysis of credibility in macroe-conomic policy-making include the models of Barro and Gordon, which addreputation-building by macroeconomic policy-makers into the rational expecta-tions story [6, 7]. Barro and Gordon argue that concomitant high inflation andhigh unemployment were the consequence of non-credible commitments by mon-etary policy-makers, reflecting the fact that policymakers are tempted to pushthe economy beyond full employment in order to boost employment and produc-tion in the short term. When rational private agents know that policy-makershave these incentives to ”cheat” by inflating the economy beyond full employ-ment equilibrium, then those policies can be undermined. A non-cooperativeequilibrium will emerge, in much the same way as described by Kydland andPrescott and, under these circumstances, the twin macroeconomic policy goalsof controlling inflation and reducing unemployment to its natural rate cannotbe attained. Nonetheless, policy-makers can be distracted from the tempta-tion to cheat on their policy commitments in short-term if they are concernedby their reputations for policy-making credibility in the long-term. Far-sightedpolicy-makers will take into account rational private agents’ perceptions of theircredibility. If policy-makers are aware that their policy levers will be bluntedin the future if their reputations are damaged today, then they will have incen-tives to change their strategies. There is an inter-temporal trade-off and so thepolicy-maker’s rate of time preference becomes salient and the strategic policygame described by Kydland and Prescott shifts to a dynamic context and theNash reversion strategy (”grim trigger” strategy) will be determined by discountrates. Specifically, forward-looking decision-makers, with a lower rate of timepreference, will value their reputations more highly than decision-makers witha higher rate of time preference. It follows that forward-looking policy-makerswill be less likely to cheat on their commitments, even though - if they wereplaying just a one-shot game - they would otherwise revert to a non-cooperativestrategy [10, 3, 2].In addressing these insights, received wisdom in macroeconomic policy-makingcircles shifted towards advocacy of inflation targetting and central bank inde-pendence as solutions. These insights had applications to other policy questions3oo, including industrial organisation and regulatory policy. For monetary pol-icy, institutional reforms were widely adopted across the OECD, including inthe UK and Australia - with New Zealand as a pioneer. Inevitably, however,debates around best practice have moved on, especially quickly in the case ofmonetary policy given the low inflation/low interest rate environment affectingmost OECD economies in the aftermath of the 2007/8 financial crises. With thebehavioural economics revolution, new insights can be added to these debates,as explored in the next section.
The rational expectations account has significant limitations - extensively ex-plored in enduring debates between what are sometimes simplistically cate-gorised as ”Keynesians” and ”Monetarists”. These old debates reached an im-passe in the 1970s, and contributed to significant ennui about macroeconomictheorising in policy-making circles, partly because there was little agreementabout the behavioural assumptions. Alongside the seismic change in policyenvironment, economic theory generally has been shifting away from a focus onrational choice towards behavioural assumptions incorporating behavioural andpsychological constraints.Broadly, behavioural economics allows that decisions are boundedly rational- not necessarily irrational, but limited by a range of cognitive constraints inter-acting with the informational constraints, including adverse selection and moralhazard, as applied extensively across other fields of economics too, e.g. by Ak-erlof and Shiller. Macroeconomics has been slow to embed these insights, partlybecause behavioural economics is largely confined to experimental data aboutindividual decisions and choices. The simplifying assumptions of rational, inde-pendent, self-interested and homogenous agents that enable aggregation in con-ventional macroeconomic models are precluded in behavioural macroeconomicmodels, though empirical techniques such as agent-based modelling provide al-ternatives [4, 5]. Nonetheless, behavioural economics’ reach is now extendingas new macroeconomic insights are uncovered using the lens of behavioural eco-nomics.Temporal discounting is a promising area for behavioural macroeconomistsgenerally, and specifically for macroeconomic policy where discounting assump-tions can be adapted to build a deeper understanding of the nature and con-sequences of the strategic games between policy-makers and private agents, asexplored in the preceding section.There are, however, some fundamental differences in definitions of time in-consistency that need to be addressed explicitly in order to build a coherent These debates spawned a complex range of intermediate models - including New Keynesianand neo-Keynesian models, which combine traditionally Keynesian assumptions about stickyprices and imperfect markets, with the traditionally monetarist behavioural assumptions ofoptimisation and rational expectations. In the aftermath of the 2007/8 financial crises, forsome macroeconomic policy-makers, the exclusion of the financial side from these modelsfurther eroded the credibility of mainstream macroeconomic theorising. inter-personal time inconsistency - consis-tent with the rational expectations account outlined above, and intra-personaltime inconsistency . Intra-personal time inconsistency is sometimes described bybehavioural economists as the outcome of intra-personal struggles between dif-ferent selves [9], building on Strotz’s early insight that inter-temporal decision-making was characterised by intertemporal tussles between different incarna-tions of the individual through time, manifested when the preferences of thepresent self and future selves collide [22]. These tussles manifest in present biasand preference reversals. For example, when a person is planning for a longdistant future, they may believe themselves capable of resisting temptation, butwhen temptation becomes more immediate and tangible, then their preferenceschange and they are not able to resist temptation after all. Their preference forresisting temptation reverses.The behavioural concept of intra-personal time inconsistency connects withthe more general literature on behavioural bias in behavioural economics. To summarise the different impacts of inter-personal time inconsistency ver-sus intra-personal time inconsistency: in rational expectations models of inter-personal time inconsistency, rational agents’ stable time preferences are char-acterised by an exponential discount function. Given dynamic strategic gamesbetween policy-makers and rational agents in the rational expectations modelsexplored above, this creates what can be understood as a form of institutional present bias. Its behavioural corollary, emerging when assumptions of perfectlyrational decision-making and rational expectations are relaxed, is behaviouralpresent bias , and this is a product of intra-personal time inconsistency. The dif-ferent impacts of behavioural present bias on inter-temporal decision-making arecaptured by embedding hyperbolic or quasi-hyperbolic discount functions intointer-temporal trade-offs instead of the standard exponential discount functions[13, 11]. An empirical advantage for models incorporating behavioural discount func-tions is the wide-ranging experimental evidence from psychological and be-havioural economic studies confirming the endemicity of present bias in decision-making by humans and other animals, demonstrating that individuals’ rate oftime preference is not stable as assumed in standard economic discounted utilitymodels [9, 8, 18]. Behavioural time inconsistency is manifested as shifts in an in-dividuals rate of time preference depending on the time horizons over which theyare constructing their choices. This interpersonal time inconsistency problemcreates a problem of present bias, i.e. a disproportionate focus on short-term Though, it should be acknowledged that there is considerable divergence across be-havioural economists about the meaning and significance of behavioural bias. There is more conscilience in the definitions than commonly acknowledged because be-havioural present bias is not precluded in seminal ”orthodox” neo-classical accounts of inter-temporal decision-making. Early on, Samuelson acknowledged that exponential discountingwas potentially an excessively restrictive assumption [needs ref]. max ∞ X t =1 u τ ( c τ ) D ( τ ) dτ (1)where u is utility and c is consumption and D ( · ) is the discount function: D ( t ) = δ t = ( 11 + r ) t ≈ e − rt (2)where δ is the discount factor and r is the discount rate.In behavioural dynamic models, the discount factor declines at a greater ratein the short run than in the long run and is inversely related to the length of delayin rewards. So the value of future rewards is disproportionately low relative tothe value of current rewards. Mathematically behavioural/intra-personal time-inconsistency can be captured using hyperbolic and quasi-hyperbolic discountfunctions, where the discount rate varies according to when the payoffs arereceived [13, 11]. The discount factor becomes: D ( t ) = βδ t = β (cid:2)
11 + r ] t (3)where δ represents the time-consistent rate of time preference, and β is thepresent bias parameter, capturing time-inconsistent preferences for immediategratification. If β = 1, then preferences are time-consistent; but if β is lessthan 1 then the agent will over-weight short-term rewards relative to long-termrewards, and the inter-temporal Euler consumption relation will break down.There will be heterogeneity in preferences and choices. Intra-personal timeinconsistency may be moderated if agents embed pre-commitment mechanismsinto their decision-making. Angeletos et al. observe that some hyperbolic dis-counters value commitment, and thus hold illiquid assets as for them the cost ofdoing so is offset by the value of commitment [1]. O’Donoghue and Rabin pos-tulate that different individuals will respond in different ways to the potentialfor pre-commitment, depending on their type, identifying four types of individ-uals [16, 17]. These types of agents are categorised according to two factors:first, the extent to which they are aware of their time-inconsistency; and second,what they do to overcome their predispositions towards present bias and prefer-ence reversals. Adapting these definitions to the macroeconomic policy-makingecosystem, policy makers differ in their reactions to time-inconsistency, and canbe categorised as follows:1. Na¨ıve : These types are forward-looking but completely unaware of theirtime inconsistency and likelihood of preference reversal. They na¨ıvely as-sume that their future selves will behave tomorrow as they do today; thattheir preferences formed in time t + n will be identical to those anticipatedin time t. Na¨ıfs do not take into account their own time inconsistency whenplanning future actions; they choose their plans as viewed from today’s6erspective. If ˆ β is the individual’s own estimate of their quasi-hyperbolicpresent bias parameter, capturing their beliefs about their own potentialfor self-control, and β is their actual present bias parameter, then - forna¨ıve individuals ˆ β = 1 > β . In a macroeconomic policy context, na¨ıvepolicy-makers would believe that they were making good policy choicesfor the long-term, and would be unaware when their policy choices aretime inconsistent. This would increase the chances of sub-optimal Nashequilibrium outcomes, as predicted by the rational expectations modelsdescribed above2. Resolute : These individuals are aware of, and anticipate ex-ante, theirown intra-personal time inconsistency and so bind themselves to pre-commitment strategies. For example, they could bind themselves withcommitment mechanisms such as long-term contracts and illiquid invest-ments. If their pre-commitment strategies are effective in removing presentbias, then ˆ β = β = 1. The ”tie me to the mast” example of Ulysses isoften used to illustrate this idea. The corollary for macroeconomic policy-makers is the policy-maker who binds themselves to a policy target, e.g.an inflation target, with costly sanctions for deviating from this target.Whilst these sanctions have been implemented, in theory, as part of cen-tral bank reform across the OECD from the 1990s onwards, sanctions oncentral bankers have been difficult to implement in practice.3. Sophisticated : These individuals backward induct to anticipate ex-antetheir own dynamic time-inconsistency. Sophisticates are aware that theirpreferences change in the future and so decide not to participate, toavoid the negative consequences of inconsistency. The common analogy isUlysses deciding to take a take a different route to avoid the irresistibleand deadly call of the Sirens (Hey and Panaccione, 2011). For these types,ˆ β = β in theory, but without practical implications given their decisionto avoid the inter-temporal conflict. In a macroeconomic policy context,this would be a policy-maker who anticipates the dilemma identified byLucas and others, and therefore abstains from intervening to control themacroeconomy.4. Myopic : Myopic types decide on the basis of static preferences. Theyare essentially uber-na¨ıfs in that they not only fail to recognise the pitfallof time inconsistency but also fail to recognise the dynamic nature of theproblems they face. So they are not forward-looking at all: their presentbias parameter approaches zero, leading to a situation equivalent to aninfinite rate of time preference, and so their discount factor on futurerewards approaches zero. A ”one-shot game” discretionary policy-makeris myopic in this sense. This could be interpreted as a link between short-termist policy and Keynes’s famousquote about ”in the long run we are all dead” as a justification for macroeconomic policy-making myopia. But Keynes continues: ”Economists set themselves too easy, too uselessa task, if in tempestuous seasons they can only tell us, that when the storm is long past, β ∈ ( β, In a macroeconomic policy framework, inflationary bias created by institutionalpresent bias will be magnified in the context of behavioural present bias, butseparating inter-personal and intra-personal time inconsistency to identify in-stitutional present bias versus behavioural present bias is a complex task. Thissection explores some of the implications of these complexities specifically inthe context of the macroeconomic policy debates, building on the Barro andGordon model introduced above.
To recap: Kydland and Prescott describe a strategic game between rational pri-vate agents and policy-makers, explaining inflation bias as the outcome of thesub-optimal Nash equilibrium that emerges in the context of non-cooperativestrategic decision-making [12]. Building on Kydland and Prescott, Barro andGordon develop the idea that sub-optimal Nash equibria emerge in the macroe-conomy as the outcome of non-co-operative strategies between agents and policy-makers, but with additional complexity emerging from policy-makers’ concernsabout their credibility and reputation [6, 7]. Barro and Gordon specify thepolicy-maker’s objective function as: z t = ( a/ π t ) − b t ( π t − π et ) (4)where a, b t > π t is inflation at time t, and π et are inflationary expectations attime t. To link with a non-accelerating rate of inflation target (NAIRU) target,this will be achieved when π t = π et . When the economy deviates away fromthe NAIRU, there will be a cost in terms of inflation bias, given by:( a/ π t ) ) (5)But there will also be benefits from inflationary policies, e.g. from increasesin employment and/or government revenue. These will be given by: the ocean is flat again” ( A Tract on Monetary Reform (1923), p. 80). Keynes’s wordsin their entirety could be more subtly interpreted as foreshadowing the policy-maker’s timeinconsistency problem: if we focus on the long-distant future then we will fail to recognise,and resolve, the temptations that policy-makers face in the short-term. Barro and Gordon do not refer directly to NAIRU and monetarism more generally fo-cusses on a natural rate equilibrium (implying labour market clearing), but their analysisis also logically consistent with a NAIRU equilibrium concept (which allows for involuntaryunemployment). t ( π t − π et ) (6)Taking into account these benefits and costs and expressing in expectedpresent value terms, the policy-maker will be minimising the following loss func-tion: Z t = E [ z t + (1 / (1 + r t )) · z t+1 + (1 / (1 + r t )(1 + r t+1 )) · z t+2 + ... ] (7)where r t denotes the discount rate between period t and t+1, and the discountfactor is given by: q t = 1(1 + r t ) (8)In Barro and Gordon’s model, when policy-makers transgress by cheating ontheir policy commitments to a NAIRU target, then they will be punished. Thispunishment is delivered via enforcement from private agents, who adjust theirexpectations to the detriment of the policy-maker, making it harder for policy-makers to achieve their NAIRU targets in the future. With exponential dis-counting, the expected present value of this enforcement cost is given by: Enf orcement = E [ q t ( z t+1 − z *t+1 )] = ˜ q · (1 / b ) a (9)The policy-maker balances this cost against their temptation, i.e. the bene-fits they will accrue in the short-term if they cheat on their commitments. T emptation = (1 / b ) /a (10)So the policy-maker will cheat on their commitments where the benefitscaptured in the temptation relation (10) are greater than the costs captured inthe enforcement relation (9). Note that the discount factor in Barro and Gordon’s model is given by equation(8). But the trade-offs facing the policy-maker will change if behavioural insightsabout intra-personal time inconsistency are embedded into this game, specifi-cally if the exponential discounting assumption is replaced with a behaviouraldiscount function, e.g. Laibson’s quasi-hyperbolic discounting function [13, 11].Specifically, q can be replaced with the behavioural quasi-hyperbolic discountfactor: D ( t ) = βδ t = β [ 11 + r ] t (11)where 0 < β < Enf orcement = βδ · (1 / b ) a (12)Note that the present bias parameter is less than 1 i.e. 0 < β <
1, soit follows that βδ < q . Therefore, with the present bias associated with quasi-hyperbolic discounting, the present value of the enforcement costs from cheatingare less, and therefore - ceteris paribus - the likelihood that the policy-makerwill cheat is increasing in the degree of present bias, i.e. as β approaches zero.In this way, behavioural present bias magnifies the degree of inflationary biasseen in Barro and Gordon’s baseline model. Note also that when β = 1, thenBarro and Gordon’s rational expectations result holds because, in that case, βδ = q . The model introduced in this paper takes basic insights about time inconsistencyfrom the behavioural and rational expectations literature to capture dynamicstrategic interactions between policymakers and private (rational) agents in themacroeconomy. Relaxing the assumption of rationality to embed present biashas implications in terms of the discounting of future consequences from currentpolicy choices, leading to interactions between intra-temporal time-inconsistencyand inter-temporal/institutional time-inconsistency. Thus this paper provides abehavioural economics alternative to the rational expectations account of strate-gic interactions between private agents and policy-makers, demonstrating howbehavioural biases, specifically present bias in the context of time inconsistency,change policy-makers’ trade-offs. Whilst applied here to macroeconomic policy-making, it also has implications for policy-making more generally, for exampleindustrial regulation and public-sector infrastructure investment policy.What does it add to the policy debates? In the rational expectations liter-ature, time inconsistency is essentially an inter-personal/institutional problememerging from self-interested strategic interactions between rational optimisingagents and policy-makers. Rational agents anticipate that policy-makers willhave incentives to reverse initial policy announcements, reducing welfare rela-tive to a position in which a policy-maker credibly commits to a stable policy.Aware of the possibility of policy reversal, individual agents will anticipate thesepolicy reversals, and thus these policies will be ineffective. Overall, interactionsbetween private agents and unreliable policy-makers deliver outcomes that aresocially sub-optimal but, from an individuals perspective - whether a privateagent or a policy-maker, their decisions cannot be improved, which is why in-stitutional reforms are important. In the context of macroeconomic policy, in-dependent central banks are an example of an institutional reform designed toresolve self-interested conflicts between rational agents and policy-makers. Dele-gation to independent policy-makers, removed from political pressures, can helpto reduce problems created by time-inconsistency, assuming that the delegatedauthorities are not prone to rent-seeking in other ways.10his paper shows, however, that institutional present bias and time incon-sistency are only part of the problem. Problems are likely to be magnified inthe context of behavioural present bias, when intra-personal time inconsistencymagnifies inter-personal time inconsistency. In terms of solutions, well-designedinstitutions can play a role in mitigating time-inconsistency problems, if comple-mented by behavioural macroeconomic policy solutions. For example if effectivepre-commitment mechanisms for policy-makers, e.g. long-term contracts, canbe enforced, then this will ensure that policy-makers’ decisions are more far-signted. There also connections with other areas of behavioural economics thatdevelop new theoretical insights about trust and reciprocity. If trust can be builtbetween private agents and policy-makers then that will operate to decrease theprobability that either party will default on their announced commitments.In terms of future directions for this research, to assess the real world impactsof this analysis quantitative analysis is needed to infer something about the de-gree of present bias affecting policy-makers’ decisions - more likely via calibratedsimulations given the difficulties around identifying policy-makers’ behaviouralparameters from published statistics. In addition - theoretically, further anal-ysis is being conducted to explore how the balance between temptation andenforcement will vary across the 4 types of agents identified by O’Donoghueand Rabin, with these insights applied to the policy-making eco-system.
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