Fiscal policy impact when exposed to sovereign risk at zero interest rates : assuming bounded rationality in an agent based model

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Master’s Thesis

Fiscal policy impact when exposed to

sovereign risk at zero interest rates

Assuming bounded rationality in an agent based model

Paul van der Boor

Student number: 10655468

Date of final version: January 11, 2016 Master’s programme: Econometrics

Specialisation: Mathematical Economics Supervisor: dr. I.L. Salle

Second reader: Prof. C.H. Hommes

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Abstract

In an agent based model where agents use heuristics to form expectations on output and inflation I examine the effects of sovereign risk when interest rates are at their zero lower bound. I find that that the ZLB episode can be a sufficiently large pessimistic shock to expectations to send the economy into an unstable deflationary spiral. Alleviating levels of sovereign risk create instability for a wider range of initial conditions. Furthermore I find that exogenous and endogenous fiscal policy have different effects in anchoring expectations. This implies that exogenous austerity measures are self defeating, while any choice between endogenous counter or fiscal policies depends on the length of the zero lower bound episode and the level of sovereign risk.

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Introduction

In this thesis we will consider the effects of a sovereign risk channel through which sovereign default risk raises funding costs in the private sector. Under normal circumstances the standard policy in response to alleviating levels of sovereign risk is to accommodate monetary policy in such a way that it lowers borrowing costs, counteracting a decrease in economic output and the threat of deflation. However when policy rates are already close to zero and cannot be lowered further, it is not possible to intervene this way. This is not merely a theoretical situation as recent developments at the time of writing this thesis have shown. In response to the 2008 financial crises all major central banks lowered their policy interest rates to try dampen the negative economic consequences of the crisis. In figure (1.1) it can be seen that The Bank of England, the Bank of Japan, the European Central Bank, and the Federal Reserve all brought their policy rates to their respective effective zero lower bounds (”ZLB”) in late 2008 or early 2009. The Euro crisis that followed led to higher credit risk premia for European economies that had high public debt levels and were running budget deficits. Meanwhile their central banks were constrained in off setting these effects. A situation like this can similarly arise when a currency peg is in effect or in other situations where political or institutional considerations prevent central bank action.

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CHAPTER 1. INTRODUCTION 2

Figure 1.1: Short term interest rates major economies.

Sources: Williams (2014), Board of Governors of the Federal Reserve System (2013); Organi-sation for Economic Co-operation and Development (OECD; 2013).

The discussion following the crisis on what policy actions should be taken in a scenario of high credit risk premia while the central bank is constrained was significantly influenced by Blanchards and Leighs IMF working paper ’Growth Forecast Errors and Fiscal Multipliers’. Their results supported research indicating that fiscal multipliers are large when the output gap is strongly negative. It therefore suggested that the IMF had under estimated the neg-ative consequence of austerity measures and that fiscal multipliers were lower than assumed in their models. Research conducted later by the Dutch Central Planning Bureau, M¨ohlman et al. (2015), opposed this view by concluding that using their approach on a larger sample did not provide evidence that during the recent crises fiscal multipliers were indeed higher than expected. Many other academics also took part in this discussion showing that it is a contagious academic topic. As such a discussion that will strongly influence public policy and has a large impact on society seemed one highly suited to study in this Master thesis.

In this thesis I would like to contribute to this discussion by studying, under the previously described conditions, how sovereign credit risk premia affects macroeconomic dynamics and stabilisation policy. However I will do so when we no longer assume rational expectation form-ing as is standard in macro economics. As argued by Woodford (2003), expectations are crucial elements of any dynamic Keynsian model and will be the deciding factor in the equilibrium rela-tion between inflarela-tion and real activity. It is for that reason that we need to treat this important

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CHAPTER 1. INTRODUCTION 3 driver of the sovereign risk model with care. Rationality assumes that all agents behave the same and more so that these agents are fully informed. These assumptions seem unreasonable when observing economic activity. For one when observing forecasts of economic variables, for instance of inflation, there is lots of heterogeneity among the expectations. This already pro-vides some proves that not all agents can be similarly rational. That is not surprising since the assumptions that each agent is fully informed is quite strong and furthermore it is unrealistic for each person to use all that information into their decision making, something only a computer could do. It is therefore more realistic to consider individuals to have cognitive limitations, which are not fully capable of understanding the complexity of the world. I will therefore model the economy such that it contains different types of agents that use heuristics to form expecta-tions following de Grauwe (2012) in my approach. Heuristics are simple decision making rules, in this thesis’ agent based model we will consider trend following and fundamental decision rules. To model the situation of sovereign risk while the ZLB binds, I will extend the tractable model proposed by Corsetti et al. (2013) by introducing heuristic using agents. The tractable model describes an economy that starts with interest rates at the ZLB which can exogenously return to a normal situation. We are particularly interested in the stability of such a model and will examine stability conditions for different levels of sovereign risk and length of the ZLB episode. Furthermore we will investigate the impact of fiscal policy for exogenous and endogenous spend-ing rules durspend-ing the ZLB episode.

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Chapter 2

Literature Review

Woo et al. (2015) identify six factors through which high public debt impacts long-run economic growth: (1) higher long-term interest rates and sovereign risk spillovers to corporate borrowing costs, (2) higher future distortionary taxation (3) lower future public infrastructure spending (4) higher inflation (5) greater uncertainty about prospects and policies and (6) by constraining counter cyclical fiscal policies.

As mentioned earlier we will study this first factor identified by Woo et al. (2015); the spillover of sovereign risk to corporate borrowing costs. Prior to 2008 the literature was focused on emerging economies when estimating the impact of sovereign risk transfers since problems with sovereign credit worthiness are most pressing there. The financial crisis generated an interest in measuring the sovereign risk impact also in developed economies. Let us review two papers in which this has been investigated: Acharya et al. (2014) examine financial services firms while Bedendo et al. (2015) examine non-financial firms both in the Eurozone countries. The Eurozone is interesting since its single currency rules out the application of currency controls; another common sovereign risk transfer channel.

Acharya et al. (2014) find evidence for a significant transfer of credit risk from the govern-ment to the banking sector, and in the opposite direction during a bailout. The banking sector is exposed to government debt explicitly through bond holdings and government guarantees and implicitly by a safety net. Any bailout raises the riskiness of sovereign debt which in turn has a negative effect on the financial service firms assets and might increase the need for government intervention. This two way relation creates a bank-sovereign feedback loop. Bedendo (2015) shows that not only financial firms are exposed to sovereign credit risk. The author estimates that a 10% increase of sovereign spreads lead to a 0.5%-0.8% increase of non-financial companys spreads. The effect is highest for firms that enjoy government guarantees, place most of their output on the domestic market, or rely heavily on bank financing.

As expected the transfer of sovereign risk has a significant effect on the financing costs in

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CHAPTER 2. LITERATURE REVIEW 5 emerging and developed economies. Therefore policy makers will need to compensate allevi-ating levels of sovereign risk by reducing policy rates. However when these rates cannot be lowered, it is of interest to examine what actions should be taken then. Such a scenario arises when rates are at their zero lower bound or when monetary policy is constrained due to a cur-rency peg or due to other political or institutional considerations. How should policy makers then deal with a situation of implied low inflation, output and employment?

Woodford (2012) discusses monetary policy actions but considers only those that have gen-erated academic interest and a fair amount of policy experimentation. As such the author discusses two measures: forward guidance and balance-sheet policies. Forward guidance can be defined as explicit statements on the outlook of future policy on top of the policy actions that will immediately be undertaken by the central bank. Balance-sheet policies refer to actions taken by a central bank that vary either the size or the composition of its balance sheet for reasons other than influencing the interest rate. While both policies can be applied in situa-tions outside the ZLB episode, this is not very common and application of these policies where mainly limited to the recent financial crises. As Woodford notices: ”Central Banks are much more willing to experiment and were forced to provide additional policy accommodation after the financial crisis”. Woodford concludes that the most effective policies are those that combine a fiscal stimulus with a commitment to a nominal GDP level. It is therefore of interest to understand what fiscal stimulus are most effective.

Many conflicting academic views exist on the effectiveness of fiscal stimulus. We will discuss some of the views brought up in the literature on the fiscal multiplier, namely: Baum et al. (2012), Eggertsson et al. (2010), Christiano (2011), Mertens et al. (2014) and Corsetti et al. (2013).

Firstly we review the effect of fiscal multipliers when monetary policy is not constrained. Baum et al. (2012) show that fiscal multipliers differ across countries and on the position of the econ-omy in the business cycle. They find that government spending is larger in downturns than during economic expansions on average. These findings are in line with the popular belief that in times of economic slack and constrained monetary policy by the ZLB, fiscal multipliers are higher than one. This belief can for instance be found in the IMFs World Economic Outlook in October 2012, which lists a number of authors that support this view: Auerbach et al. (2012); Batini et al. (2012) and Woodford (2011).

Eggertsson et al. (2010) also support this popular view and have considered a variety of pos-sible fiscal stimulus measures in order to determine their effectiveness. They considered: tax cuts on labour or capital income, increased government spending and a combination of reducing government spending and cutting taxes at the same time. Using a new Keysian DSGE model

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CHAPTER 2. LITERATURE REVIEW 6 the authors conclude that insufficient demand is the main economic problem when policy rates are at the ZLB. As such the authors conclude that those policies that stimulate spending most effectively should be applied, while policies that expand supply might be counterproductive. It is therefore suggested that a targeted and temporary government spending is the most effective policy measure. More so, like Woodford (2012) suggested this measure works best in combina-tion with forward guidance.

The model presented in Eggertsson (2010) shows that the effect of tax cuts and government spending is fundamentally different at the ZLB compared to normal circumstances. It is there-fore of interest how government spending affects the economy at the ZLB. Christiano (2011) argues that the government-spending multiplier can be much larger than one when the nominal interest rate does not respond to an increase in government spending, something that occurs at the ZLB. In response to shocks that make the ZLB binding, government spending should therefore be substantially raised.

Opposing the popular view that government spending multipliers are higher when policy rates are at the ZLB are Mertens et al. (2014). In their paper the authors argue that the underlying weaknesses in the economy is the most important factor to be considered when evaluating policy effects. In particular they differentiate between liquidity trap equilibra that are fundamental and those that are expectation driven. Using this distinction the authors then show that when a liquidity trap is caused by a long-lasting state of low consumer confidence, a government spending stimulus has deflationary effects and becomes relatively ineffective at the ZLB. Fur-thermore they show that cuts in marginal labour tax rates are inflationary and generate much larger expansionary effects than when interest rates are positive.

When policy interest rates are at the ZLB this denies policy makers to use their standard approach to dealing with alleviating credit spreads and its subsequent negative effect on the economy. Under such conditions it is of particular interest what the effect is of fiscal stimulus when public finances are more fragile. Corsetti et al. (2013) find that negative demand causes a deeper recession when the ZLB episode is longer and the sovereign risk channel is stronger. Furthermore the fiscal multiplier is reduced when debt to GDP levels are higher. While the effect is fairly modest as long as sovereign risk is contained, it becomes strong when public fi-nances are very fragile and monetary policy is constrained for an extended period. For extreme cases the multiplier even changes its sign.

So far we have considered literature in which rationality is assumed, in particular rational ex-pectations. Under this assumption agents are fully informed, with the result that agents always choose model consistent expectations to forecast future variables. However various psychologi-cal research has shown that this is not very realistic and individuals are cognitively limited, see

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CHAPTER 2. LITERATURE REVIEW 7 e.g. Kahneman (2002).

In the literature two main approaches are taken when modelling departures from rationality, which are statistical learning and heuristic based decision making. Statistical learning assumes that agents are learning like econometricians; they estimate a regression equation and in this way learn more about the underlying model over time. The paper by Arifovi et al. (2012) show such a deviation from rationality has major implications on fiscal policy effect. In par-ticular, the authors assume constant gain learning, which implies that agents update estimates using least squares while discounting historic estimates. Earlier Eggertson and Woodford (2003, 2004) showed that by forward guidance the length of the ZLB can be reduced. However, when Arifovi et al. (2012) re-examine this by introducing agents with constant gain learning, this acommodative monetary policy has to be combined with significant fiscal stimulus in order to stabilize expectations and economic activity at the ZLB.

A problem with assuming statically learning as pointed out by De Grauwe (2010) is that agents still are assumed to have advanced cognitive abilities and only base their data on a quantita-tive basis. De Grauwe therefore lets agents form expectations based on simple decision rules, heuristics. Psychological research has shown that agents can only understand a small part of the economic system, contrary to what is assumed under rationality. To be able to make de-cisions and act in such an uncertain environment agents will therefore rely on these heuristics, something we will also introduce in this thesis. This does not imply necessarily that agents are irrational and agents will start to make any sort of expectation. Rather it can be seen as a richer definition of rationality, one closer to the true behaviour of economic agents and something that will increase our understanding of macroeconomic dynamics. In de Grauwe (2012) the author shows that by introducing agents with cognitively limited abilities who use heuristics, the observed nonnormality of economic output can be explained.

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Chapter 3

The Model

In order to analyse sovereign risk and its effect on fiscal policy and monetary stability we first introduce the tractable model proposed by Corsetti et al. (2013). To avoid imposing the unrealistic rationality assumption on individual economic agents, we then follow de Grauwe (2010) by letting agents form expectations using heuristics, which is explained in the second part of this chapter.

3.1 Macro economic model

In this paragraph we will discuss the tractable model proposed in Corsetti et al. (2013), which consists of four equations: a Philips curve, a dynamic IS-relationship, a Taylor rule and a definition for the interest rate spread above the risk free rate. The tractable model is a log-linearization around the equilibrium conditions from the full model. By applying this tractable model rather than the full model we gain computational ease and make it easier to follow the model’s dynamics, but this comes at the cost of using two simplifying assumptions. These are: (1) the probability of sovereign default depends on the expected primary deficit, rather than on the level of debt and (2) the expected duration of the ZLB episode is exogenously given. Throughout this thesis some of the Corsetti et al. (2013) notation will be applied, hence we denote for the output gap: ˜yt = yt− y, the difference in government spending to steady state:

˜

gt= gt− g and the log difference to steady state inflation: ˆΠt = log(Π_Πt). Variables without a

time subscript refer to steady-state values.

We are now ready to introduce the model, firstly we have the Philips curve which relates inflation to expected inflation, output and government spending:

ˆ

Πt= βEt ˆΠt+1+ κyy˜t− κgg˜t (3.1)

where κy = κ(v + ¯σ−1) and κg = κ¯σ−1, with κ = (1−α)(1−αβ)_α . The value and meaning of these

and all other parameters is given in appendix 7.1.

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CHAPTER 3. THE MODEL 9 Secondly a dynamic IS-relationship links output to real government spending and the effec-tive real interest rate, where the effeceffec-tive interest rate is dependent on the spread above the risk free rate ((πb+ σΩ)ˆωt) and shocks to the time discount factor(Γt) which are non-zero at

the ZLB:

˜

yt− ˜gt= Et˜yt+1− Et˜gt+1− ¯σ[ˆitd+ (πb+ σΩ)ˆωt− Et ˆΠt+1+ Γt] (3.2)

where ˆωt:= log(1 + ωt)/(1 + ω), ˆidt := log((1 + idt)/(1 + id)), and Γt:= Etlog(et+ 1) − log(et)

Thirdly a Taylor rule describes monetary policy in the model, when the policy interest rates are not at the ZLB:

ˆid

t = φπΠˆt− φωωˆt (3.3)

When applying the calibration used by Corsetti et al. (2013), it is assumed that under this Taylor rule the central bank fully neutralises the effects of the sovereign risk premium on the aggregate economic activity. This implies that if the ZLB binds, that the central bank is no longer able to neutralise the sovereign risk premium effects.

The model starts at the ZLB and it is then assumed that nominal interest rates remain at zero with probability µ and return to the Taylor rule (3.3) with probability 1 − µ, where µ ∈ (0, 1). The transition probabilities given in matrix P for this Markov chain are given by:

P = " p1,1 p1,2 p2,1 p2,2 # = " µ 1 − µ 0 1 #

This implies that if moving out of the ZLB is considered a ’success’, it takes on average _1−µ1 periods to move out of the ZLB. As such _1−µ1 gives the expected length at the ZLB. At the time of a binding ZLB a temporary increase in the effective discount factor is assumed, triggered by 0 < et= eL < 1, which implies that Γt= µlog(eL) − log(eL) during the ZLB episode and zero

otherwise.

A consequence of assuming that the probability of sovereign default depends on the primary deficit is that the interest rate spread depends on the expected deficit. The degree to which a weak fiscal position adversely affects the private-sector spread is captured by the parameter ξ ≥ 0. This parameter can also be viewed as the slope of the private sector interest rate spread with respect to the fiscal deficit for different average lengths (in quarters) of the ZLB episode and for different debt to GDP ratios. The value of ξ will therefore be higher for a longer ex-pected duration of the ZLB period and for higher values of initial debt of the sovereign. ξ is thus dependent on the parameter µ and the slope of the private-sector interest rate spreads (ξ’) and can be calculated as following:

ξ = ξ’1 + µ(1 − µ) µ(1 − µ)

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CHAPTER 3. THE MODEL 10 The following table gives empirical values of ξ’ for various levels of initial debt and converts these into values of ξ for some given µ.

Table 3.1: Quantifying Parameter ξ

ξ by length of ZLB episode (qtrs) Debt/GDP (%) ξ’ 6 7 8 9 10 90 0.0016 0.014 0.015 0.017 0.018 0.020 110 0.0030 0.025 0.028 0.031 0.034 0.037 130 0.0051 0.042 0.047 0.052 0.057 0.062 140 0.0065 0.054 0.060 0.066 0.073 0.079 150 0.0083 0.068 0.076 0.084 0.092 0.100

Finally the fourth equation of the model describes the spread that enters the IS-relationship over and above the risk-free deposit, ˆωt, and is given by:

ˆ

ωt:= (πb+ sΩ)ˆωt= ξEt(˜gt+1− φT ,yy˜t+1) (3.4)

where parameter φT ,y ∈ (0, 1) measures the sensitivity of tax revenue with respect to economic

activity.

3.2 Bounded rationality

To avoid imposing the rationality assumption on the behaviour of economic agents we follow the approach taken in De Grauwe (2010). The author envisions an economic system inhabited by agents that are cognitively limited and therefore can only understand and observe a small part of the whole. In order to coop with the enormous complexity of the economic system these agents form expectations on the basis of heuristics - simple decision making rules. In the model by Corsetti et al. (2013) which was outlined in the previous section, three economic variables will have to be forecasted by agents: output, government spending and inflation. In this thesis we will consider two types of forecasting rules: an extrapolative forecasting rule and a fundamentalist forecasting rule. Furthermore we impose that agents learn adaptively, i.e. they learn by ”trial and error”. This means that the agents continuously evaluate the performance (”fitness”) of their chosen forecasting rule and will switch when another rule preforms better.

3.2.1 Output heuristics

We start by outlining the decision making rules that economic agents use to forecast the output gap. Firstly we have an extrapolative forecasting rule; the simplest example of a trend following rule. The agents that apply this rule are not aware of any changes in the macro-economic environment and only base their decisions on historic information. We will refer to agents that

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CHAPTER 3. THE MODEL 11 apply this heuristic as naive agents.

Ee_tyt+1= yt−1⇔ Eety˜t+1= ˜yt−1

Secondly economic agents can apply a fundamentalist forecasting rule. These agents base their decisions on the fundamentals of the economy and therefore are aware of changes in the macro-economic environment. As such when interest rates are at the ZLB, the fundamental value of output, yL is different to its fundamental value in normal times, y. The value of yl can be

found in appendix 7.2.1. under exogenous government spending and 7.2.2 under endogenous government spending. This implies that during normal times the estimation of the output gap, ˜

yt is zero, formally we have:

Ef_tyt+1= y ⇔ Efty˜t+1= 0

Fundamental agents are uncertain how long the ZLB episode will last. They know that with probability µ the stays another period at the ZLB, the fundamental output forecast therefore is:

Ef_t[˜yt+1|ˆitd= 0] = µ(yL) + (1 − µ)(0) = µyL

In the heterogeneous economic system, where both types of agents are active, the final forecast is the weighted average of the two types. Therefore the market forecast for economic output, in deviation of the steady state, ˜yt is given during normal times and at the ZLB respectively by:

Ety˜t+1= αe,tEety˜t+1+ αf,tEfty˜t+1= αe,ty˜t−1

Ef_t[˜yt+1|ˆidt = 0] = αe,tEety˜t+1+ αf,tEfty˜t+1= αe,ty˜t−1+ µαf,tyL

where αe,t and αf,t are the probabilities that the agent uses a extrapolative or a fundamentalist

forecasting rule respectively, which implies they add up to one: αe,t+ αf,t= 1.

Agents are rational in the sense that they continuously evaluate the utility obtained from the heuristic’s performance and will switch their type if the other rule has proven to be more prof-itable. It is assumed that past performance is calculated as a mean absolute forecasting error:

Ue,t= − ∞ X k=1 ωk q [yt−k− Eet−k−1y˜t−k]2 Uf,t= − ∞ X k=1 q ωk[yt−k− Ef_t−k−1y˜t−k]2

where Ue,t and Uf,t are the forecast performances of the extrapolators and fundamentalist rules

respectively. ωk are weights that decline exponentially over time and are included such that we

can incorporate the characteristic that people put more importance on recent events than on those further into the past. This tendency to be forgetful is measured by the parameter ρ in ωk

that scale the importance of the observed forecast errors: ωk= ρ(1 − ρ)k

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CHAPTER 3. THE MODEL 12 where ρ ∈ (0, 1), with ρ is zero implying no memory and ρ is one implying infinite memory. Applying this definition for the declining weights, enables the rewriting of the definition for the forecast performances into:

Ue,t(˜yt) = ρUe,t−1− (1 − ρ)

q

[˜yt−1− Eet−2y˜t−1]2

Uf,t(˜yt) = ρUf,t−1− (1 − ρ)

q

[˜yt−1− Ef_t−2y˜t−1]2

Now we have all the building blocks for a rational but cognitively limited agent to form ex-pectations according to the heuristic that preformed best. However research in psychology has shown that humans are not such rational choice makers to only consider performance. When agents have to choose between alternatives, they not only consider each alternative’s rational merits but are also influenced by their state of mind. We model this state of mind as a random component, which is parameterised by e,t and f,t for leading to a extrapolative or

fundamen-talist type respectively. Now the probability of the agent applying the exptrapolative rule in spite of a fundamental rule, αe,t, is given by:

αe,t= P (Ue,t+ e,t > Uf,t+ e,t)

Now we apply discrete choice theory, which commonly follows a logit distribution, to give us the final probability that an agent will use either rule. The share of naive agents now is:

αe,t=

exp(γUe,t)

exp(γUf,t+ exp(γUe,t)

= 1 − αf,t

where γ measures the intensity of choice. This parameter measures the variance of the random components e,tand f,t. When γ becomes increasingly closer to zero this variance becomes very

high. In that case the utility is fully deterministic and agents choice of heuristic is completely random with equal probability of becoming an extrapolator or fundamentalist. Conversely if the intensity of choice goes to ∞ then the variance of the random component becomes zero.

3.2.2 Inflation heuristics

Similarly to output agents forecast inflation based on fundamentalist and extrapolator type of heuristics, we repeat some of the steps in order to introduce the notation. We assume in this thesis that the choice to rely on a certain type of heuristic is independent for output and inflation. In economies where the Central Bank is targeting inflation rates one can give a slightly dif-ferent intuition behind the heuristics. In such an environment the agent can either deem the inflation target by the central bank as credible or not. If the agents decides it is credible, the agent will apply a fundamentalist forecasting rule and if not an extrapolative rule, the last is formally given by:

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CHAPTER 3. THE MODEL 13

Ee_tΠt+1= Πt−1⇔ EetΠˆt+1= ˆΠt−1

The fundamental value of inflation during normal times is given by: Ee_tΠt+1= Πt−1⇔ EftΠˆt+1= 0

The fundamental value of inflation during the ZLB episode is given by: Ef_tΠˆt+1= µΠL

The market forecast is a weighted average of these two forecasts during normal times: EtΠˆt+1= λe,tΠˆt−1

The market forecast is a weighted average of these two forecasts during the ZLB episode: EtΠˆt+1= λe,tΠˆt−1+ (1 − λe,t)µΠL

where λe,t and λf,t are the probabilities that the agent uses a extrapolative or a fundamentalist

forecasting rule. Therefor: λe,t+ λf,t= 1.

Fitness of the two types of heuristics is measured according to: Ue,t( ˆΠt) = ρUe,t−1− (1 − ρ)

q

[ ˆΠt−1− Eet−2πˆt−1]2

Uf,t( ˆΠt) = ρUf,t−1− (1 − ρ)

q

[ ˆΠt−1− Eft−2Πˆt−1]2

Which results in the following probability of applying a extrapolative forecasting rule for infla-tion, βe,t:

λe, t = exp(γUe,t) exp(γUf,t+ exp(γUe,t)

= 1 − βf,t

3.2.3 Government spending

Finally we also need to consider the expectations of government spending as required for the dynamic IS-relationship (3.4). In this thesis we will consider three possible situations of govern-ment spending at the ZLB, which are: governgovern-ment spending remains at its steady state value, government spending is exogenously changed and government spending is endogenously related to output. These scenarios have an effect on the determinacy conditions of the rational model as has been shown in Corsetti et al. (2013). As such it will also have an effect on our model, since fundamental agents can only form expectations under conditions that lead to determinacy.

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CHAPTER 3. THE MODEL 14 Exogenous

We denote the government’s choice of spending at the ZLB in deviations from its steady state value: gL. We let the agent’s heuristic type of government spending be related to its output type.

The assumption is that when an agent has a fundamental view on output, the same agent will also have an fundamental view on government spending. Visa versa for an extrapolating agent. This will give the following expectations for fundamental and extrapolating agents respectively:

Ee_tgt+1= gt−1

Ef_tgt+1= µgL

Propisition 1 of Corsetti et al. (2013) establishes parameter restrictions that yield a (locally) determinate equilibrium when government spending is exogenous. In each subsequent period, let the interest rate remain at zero with probability µ ∈ (0, 1). Otherwise, let monetary policy be able to permanently return to Taylor rule. Let a := µ + µξφT ,yσ and b := µ + µ¯¯ σξ. Then

there is locally unique bounded equilibrium if and only if:

1) a < 1 βµ and

2) (1 − βµ)(1 − a) > µ¯σκy

Endogenous

In a second set-up we let a change to government spending at the ZLB be directly related to output when the ZLB binds, via parameter ϕ:

˜ gt= ϕ˜yt

When ϕ is negative government policy is counter-cyclical, when it is positive it is pro-cyclical. We assume that the nature of this fiscal policy rule and the value of $ is known to all agents, however agents will still differ in their forecasts of output and thus in their expectation of government spending. Government spending for fundamentalist and extrapolating output types at the ZLB will therefore respectively be:

Ef_t˜gt+1= ϕµyL

Ee_t˜gt+1 = ϕ˜yt−1

Resulting in the total expected government spending at the ZLB: Etgt+1= ϕ[αe,tyt−1+ µαf,tyL]

Propisition 2 of Corsetti et al. (2013) sets boundaries for the parameters in order to have (locally) determinate equilibria when government spending is set endogenously on the basis of output. Again, let the interest rate remain at zero with probability µ ∈ (0, 1) in each period.

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CHAPTER 3. THE MODEL 15 Otherwise, let monetary policy be able to permanently return to Taylor rule. Let government spending ˜gt = ϕ˜yt when the economy is at the ZLB, and ˜gt = 0 otherwise. Furthermore let

ϕ < 1, a∗ := µ + µξφ∗_{T ,y}σ¯∗, κ∗_y = κy− ϕκg, ψt,y∗ := ψt,yϕ and ¯σ∗ = ¯σ/(1ϕ).Then there is locally

unique bounded equilibrium if and only if:

When a∗> 0: 1) a∗ < 1 βµ and 2) (1 − βµ)(1 − a∗) > µ¯σ∗κ∗_y When a∗< 0: 1) (1 + βµ)(1 + a∗) > −µ¯σ∗κy and 2) (1 − βµ)(1 − a∗) > µ¯σ∗κ∗_y

3.3 Solving the model

The solution of the model is found by first substituting the Philips curve (3.1) and IS-relationship (3.2) and rewriting those in matrix notation. We later substitute in equations (3.3) and (3.4), where (3.3) is dependent on being bounded at the ZLB or not. For some of the time series we also will add some exogenous shocks to inflation and output: t, ηt ∼ N (0, 0.5). The solution

in matrix notation is then as follows: " 1 −κ_y 0 1 # " ˆ_Π_t ˜ yt # = " β 0 ¯ σ 1 # " EtΠˆt+1 Ety˜t+1 # + " −κ_g 1 # ˜ gt+ " 0 −1 # Etg˜t+1+ " 0 −¯σ # ˆ ¯ ωt+ îdt + Γt + " t ηt # ⇔ AZt= BZt+1+ D˜gt+ FEt˜gt+1+ C ˆ ¯ ωt+ îdt + Γt + G Zt= A−1[BZt+1+ D˜gt+ FEt˜gt+1+ C ˆ ¯ ωt+ îdt + Γt + G] (3.5)

3.3.1 Endogenous government spending at the ZLB

If government spending directly depends on output we slightly need to alter the above expression to get an explicit solution for output and inflation. We let government spending at the ZLB, gL depend linearly on output through the parameter ϕ, i.e. ˜gt = ϕ˜yt. After the ZLB episode

government spending will return to its steady state value, independent of output. The value of the parameter ϕ is assumed to be known to all agents. We leave out the exogenous shocks since

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CHAPTER 3. THE MODEL 16 we will not introduce those when examining the effects of an endogenous government spending rule when the ZLB binds. We then obtain:

" 1 κgϕt− κy 0 1 − ϕt # " ˆ_Π_t ˜ yt # = " β 0 ¯ σ 1 − ϕt # " EtΠˆt+1 Ety˜t+1 # + " 0 −¯σ # ˆ ¯ ωt+ ˆidt + Γt

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Chapter 4

Results

In our analysis we will either let government spending stay at its steady state level or change spending exogenously or endogenously during the ZLB episode. We do so for three types of the economic model: with only rational agents, with only trend extrapolating agents and finally when both type of agents exist and each agent can switch its type. The first two homogeneous forms of the model will help us understand the dynamics of the 2-type system. The standard calibration of the model, based on the parameters of Corsetti et al. (2013) and De Grauwe (2010) can be found in the appendix. For all of our results we have assumed that the duration of the ZLB episode is exactly as long as expected. 1

4.1 Time series without government intervention

We will firstly consider some time series when the government doesn’t react when it finds interest rates bound by the ZLB. Using these time series we can examine how the different types of expectation forming by agents will influence output and inflation. Furthermore it helps us understand the influence of various parameters.

Fundamental agents

When we only allow for fundamental type of expectation forming we are back at the standard assumption in macro-economics; that agents are fully rational. These fundamental agents are fully aware of the expectations of all other agents and thus set their own expectations as model consistent. However even the fundamental agents are not aware when the ZLB episode will end since this is exogenously determined and therefore the agents’ expectations are dependent on the probabilistic parameter µ. Larger values of µ will increase the likelihood that interest rates are zero next period.

When the economic system only contains fundamental agents, output and inflation will drop to

1

Alternatively we could have taken the averages of numerous simulations, but these should converge to the actual vales anyway.

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CHAPTER 4. RESULTS 18 during the ZLB episode but will immediately return to their steady state values when monetary policy is no longer constrained. This is the same for all parameter calibrations. In figure (4.2) output and inflation are plotted over time, when the interest rate is expected to be 6 and 14 periods (1.5 and 3.5 years respectively) at its ZLB. We can deduce that output will drop by about 4.66% as a percentage of steady state and inflation will drop by 1.28% when the ZLB is expected to last 6 periods. When the ZLB episode is expected to last longer these values are significantly lower. This shows that with the agents’ increased expected duration of the ZLB the recession deepens. This is the result of the imposed Markov structure on the ZLB episode length and the discount rate, which take the actual duration of the ZLB as exogenously given therefore making the uncertainty that the ZLB will last another period higher for higher values of µ.

Figure 4.1: Time series with rational agents, µ = 5/6

Figure 4.2: Time series with rational agents, µ = 13/14

The level of sovereign risk also has an significant impact on the economic output and the level of output, through parameter ξ’ and therefore on ξ. When we increase the debt to GDP level to 130%, output decreases by 0.5% and 0.2% inflation on top of the previously mentioned

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CHAPTER 4. RESULTS 19 reductions when µ = 5/6 as can be seen in figure (4.3) below.

Figure 4.3: Time series with rational agents and sovereign risk, µ = 5/6

The parameter with the biggest effect on the model outcomes is eLwhich determines the value

of the shock to the discount factor, i.e. Γt= µlog(eL) − log(eL). Similar to Corsetti et al. (2013)

we have chosen eL = 0.8965, which as mentioned earlier leads to drop of output by 4.66% and

inflation by 1.28% annualized when the ZLB is expected to last 6 periods. If we would lower eLto 0.87, which in turn increases the shock to the discount rate, this would lead to an output

gap of -8.1% while inflation drops by 5.7% during the ZLB episode. Extrapolative agents

Now we consider what happens if all economic agents extrapolate the last observed economic variable. We find, for all choices of parameters, that inflation and output dynamics are ex-ploding. That is over time both variables are exceedingly further away from their equilibrium values. It depends on the initial conditions and the length of the ZLB whether the divergence will be upwards or downwards. Although expectations are only formed on the basis of past observations, a change in parameter µ changes the value of the discount factor Γ. With longer ZLB, Γt becomes smaller, turning the first output and inflation realisations from negative when

µ = 5/6 to positive when µ = 13/14. Sovereign risk levels have hardly any effect, since it doesn’t drive expectations in case of naive agents unlike in the fundamental agent case. Overall we can conclude that naive type of agents have a destabilizing effect on the economy.

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CHAPTER 4. RESULTS 20 Figure 4.4: Time series with naive agents, µ = 5/6

Figure 4.5: Time series with naive agents, µ = 13/14

Two type system

We now consider an economic system in which both types of forecasters exist and individual agents change their forecasting method based on past performance. We start again at the equi-librium levels for output and inflation, but after the first period interest rates drop to its ZLB level. We have plotted figures (4.6) and (4.7) in which time series are shown of output, inflation and the share of extrapolators in the system for both variables for an expected length of the ZLB of 6 and 14 quarters. Lets start with figure (4.6), in which output drops by 2.6% in the first period up to 5.4% in the last period of the ZLB episode. In the first couple of periods the share of naive agents is dropping, since these naive agents were unaware that interest rates would drop to zero unlike the fundamentalist who were expecting a drop in output causing the forecasting errors of naive agents to be relatively higher than of fundamental agents. However in subsequent periods these extrapolators increase in numbers due to two reasons: (1) the

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fun-CHAPTER 4. RESULTS 21 damentalist are each period wrong as they are uncertain whether the economy stays at ZLB or not, which increases their forecasting errors (2) the forecasting errors of naive agents decreases with being longer in the ZLB since the difference over time of output and inflation decreases. However these mechanics still ensure that sufficient fundamentalist are left over at the end of the ZLB to drive back the economy to its steady state.

When the economy is longer at the ZLB in a system with both type of agents, output and inflation will not return to steady state values when the ZLB episode ends. We consider figure (4.7), where the same graphs have been plotted for an economy that is expected to be 14 periods in the ZLB. The large fraction of extrapolating type of agents drive the economy away from its steady state. Two mechanisms make this happen: (1) the recession is deeper from the start, so when the economy returns to SS the fundamentalist are penalised more in the subsequent period after the ZLB (2) the naive agents benefit from staying longer at the ZLB, since the difference between each period becomes smaller. At the end of the ZLB, not enough fundamentalist are left to pull the economy back to the steady state values during normal times.

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CHAPTER 4. RESULTS 22

Figure 4.7: Two type of agents, µ=13/14

In the following figure we have introduced exogenous shocks to output and inflation, other than that the same parametrisation as in figure (4.7) has been used. It is interesting to see that adding exogenous shocks ensure that the system does not diverge away as happened without shocks. The shocks have increased the forecasting errors of naive agents relatively more than the errors of fundamentalists which ensures that just enough fundamentalists remain in the system at the end of the ZLB episode to pull the economy back to steady state values. In some sense the inclusion of exogenous shocks leads to more stability, a topic that we will discuss next.

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CHAPTER 4. RESULTS 23

Figure 4.8: Two type of agents with shocks, µ=13/14

4.2 Initial conditions and stability

Until now, we have considered standard values of the various parameters, and have varied µ and sovereign risk levels. We have observed that for some configurations the dynamics explode and inflation and output will not return to steady state values when interest rates are no longer bound at the ZLB. This begs the question for what configurations of the different variables and parameters, inflation and output will return to their steady state values. We will still assume government does business as usual and does not its spending when interest rates are bound at zero.

In the following series of graphs we will change the economy’s initial debt to GDP level from 90% to 150% and thus influence the sovereign risk levels. For each of these we will then exam-ine the stability of the economic system when it enters the ZLB episode from different initial states of the economy. To do so we will vary the initial output and inflation levels prior to the ZLB episode between -10 and 10 percent in deviations of steady state. The initial state of the economy will drive the expectations of naive agents and will therefore have an important

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CHAPTER 4. RESULTS 24 influence on stability. In the figures below, the x-axis gives the starting values of inflation and y-axis values gives the starting values of output. We have defined stability as following: the economic is stable when in 40 periods (10 years) after the ZLB the economy has returned to steady state and unstable when it has not. In the following figures the yellow colour implies that the economy is stable and black when it is not.

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CHAPTER 4. RESULTS 25 µ = 7/8

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CHAPTER 4. RESULTS 26 From these figures we can observe a number of things on the stability of an economy that is confronted with a ZLB interest rate episode. First of all we can observe that the occurrence of the ZLB episode can be a sufficiently large pessimistic shock to expectations to send the economy into an unstable deflationary spiral as evidenced by the occurrence of black in the various figures. Secondly we can deduce that higher values of the initial conditions lead to stability, this is the result of expectations being anchored higher making the landing at the ZLB more soft compared to when these expectations were already anchored at low values before the ZLB episode to begin with. Thirdly the economy becomes unstable for a wider set of initial conditions when it is exposed to alleviating levels of sovereign risk. Which is the result of sovereign risk negatively impacting the spreads, which in turn negatively influences fundamental expectations of output and inflation at the ZLB, making the deflationary spiral more imminent.

4.2.1 Robustness

Now we will change some of the parameters and see what impact they will have on the system’s stability. First we change the memory parameter ρ from the standard ρ = 0.5 to ρ = 0.1. When the memory parameter is set to 0.5, this implies that just as much importance is given to the last observations as the new one. When ρ is decreased to 0.1, all agents put more emphasis on the newest observation with a 90% weight to the currently observed forecasting error and only 10% to the last errors. The results on the stability of the system for various initial conditions is graphically shown in figure (4.9). We can conclude based on the figure that when agents put less emphasis on the past this leads to more instability. This is the result of quicker switching, since the fitness of the two types of forecasting will diverge faster, leading to more naive agents into the system that destabilize the economic system.

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CHAPTER 4. RESULTS 27 Now we change the intensity of choice γ from 1 to 0.5, the results are given in figure (4.10). The intensity of choice tells us to what extent the choice between type is deterministic for each agent is. This implies that when γ = 0: the choice is completely random and the share of each type will equal. On the other hand when γ = ∞ the choice is completely deterministic, this is the ’neo-classical’ limit and each agent will choose the best strategy. As such when we decrease the intensity of choice the model becomes more stable. This is because the share of naive agents doesn’t rise as high during the ZLB episode compared to when γ is 1, which implies that more initial conditions lead to stability.

Figure 4.10: Caption

4.3 Government spending

Now that we have analyzed the situation that arises during and after the ZLB episode and the influence of various parameters, we can turn our attention to policy measures. It is important to answer the question how policy makers should counter the deficit and support the economy while monetary policy is constrained. We will subsequently consider exogenous and endogenous government spending rules at the ZLB and their effect on output, the primary budget deficit and the spreads.

When an economic system only contains fundamental agents the same output values will be realised throughout the length of the ZLB episode. This is not the case when extrapolating type of agents are introduced into the model. This poses a minor issue when graphically representing the impact of changes in policy during the ZLB, since the impact of a change in government spending is different for each period during the ZLB episode. Therefore when showing the im-pact of changes in government spending on output, the primary deficit and interest rate spreads

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CHAPTER 4. RESULTS 28 we will consider averages over the length of the ZLB episode.

In our analysis we so far have assumed that the expected length of the ZLB is equal to the actual length of the ZLB. We will continue to do so in the next sections, something that is by itself unrealistic in a case by case basis but does give a true picture of the average effect of policy measures.

4.3.1 Exogenous government spending

We are now considering a situation in which the level of government spending is changed exoge-nously when the ZLB is binding. We denote the government’s choice of spending at the ZLB in deviations from its steady state value: gL. In order to examine the impact of the various

choices of government spending we consider the following scenario: we reduce gL by 1 percent

of steady-state GDP for the length of the ZLB episode. By analysing such a situation we can evaluate whether austerity measures are helpful or not. For each situation we analyse the effects on economic output, the deficit and spreads. Figures (4.11), (4.12) and (4.13) show these when the economic system contains rational, naive and mixed types of economic agents respectively. For each of the figures the y-axis give the effect of the spending cut on the variable either in percentages of steady state GPD or in in annualized base points. The x-axis gives the respon-siveness of interest rate spreads to expected deficit. The z-axis gives the actual length of the ZLB (1/(1-µ)), which is the same as the expected length for the fundamental agents.

As mentioned we need to apply proposition 1 of Corsetti et al (2013). Accordingly the range of parameters that ensure determinacy shrinks in the presence of sovereign risk. The deficit (in deviation from the steady state) is given by gL− φT,yyL. Wher φT ,y captures the semi-elasticity

of tax to output. Government spending will thus be self financing if 1 − φT ,yϑg < 0.

Analytically it has been shown in Corsetti et al. (2013) that the government spending multiplier under the rationality assumption is positive when:

(1 − µ) − µ¯σκg

1 − βµ > µξ ¯σ (4.1) From this result we can deduce that the impact of government spending depends critically on the parameters µ and ξ.

Fundamental agents

We first analyse the effects of a spending cut when only fundamental agents are in the economic system, the results of which can be reviewed in figure (4.11). The following analysis is similar to Corsetti et al. (2013) but will provide a benchmark to help us understand the implications of avoiding the rationality assumption.

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CHAPTER 4. RESULTS 29 We start by analysing what happens to output, the primary deficit and interest rates spreads when we consider an economy when ξ is low, specifically between 0 and 0.04. A spending cut causes a decline in output when the economy is at the ZLB for all values of the expected length of the ZLB episode (1/(1-µ)). With an increase in µ and therefore an increase in the expected length of the ZLB, the spending cut will reduce output even more. The additional deflation caused by the spending cut cannot be counteracted by a reduction in the policy rate as would normally happen under the Taylor rule, causing an increase in the real interest rate during the entire ZLB episode. This in turn weakens private demand which is determined by expected and future real interest rates. This effect is increased when ξ is increasing, since the sovereign risk premia will increase interest rates and reduce demand further.

In the panel right to the output graph, the effects of a spending cut on the primary deficit is shown. The spending cut reduces the deficit when the expected ZLB episode is relatively short and ξ is still low. In these cases the spending cut is successful in the sense that it does help balance the government budget and lower interest rate spreads (lower panel). However with longer expected ZLB episodes the benefit of this spending cut is outweighed by the reduction in a government’s income. As we have seen that the government multiplier increases with µ, making the difference between output with additional government spending and without bigger as long as the expected length rises. As such the government’s source of income from taxes reduced with a reduction of output invoked the fiscal consolidation. At some point, the indirect effect of decreased tax revenue starts to dominate and the austerity measure has a counteracting influence: the deficit rises in response to a spending cut. The lower panel gives the effects on interest rate spreads, when there is no sovereign risk (i.e. ξ is 0) there obvious is no change in the spreads. For higher ξ the spreads react to the deficit.

Now we consider the effects of a government spending cut when the sovereign risk channel is very active, i.e. ξ > 0.04. Firstly we notice that when the expected ZLB episode is low, with an increase in in the transfer of sovereign risk because initial debt levels are higher (i.e. an increase in ξ), the effect of the spending cut becomes smaller. This is due to the fact that the fiscal multiplier is decreasing with higher values of ξ. Still for a short expected ZLB episode a cut in spending still reduces output. That said, spending cuts do succeed in lowering the deficit and therefore in reducing the interest rate spread (lower panel) in these cases. However when the ZLB is binding for a longer period, the impact of the sovereign risk channel becomes much larger. As can be deduced form the left panel, for high values of ξ and long expected ZLB episodes the sign of the output multiplier may actually turn negative: a spending cut becomes a stimulus for the economy. This can be explained by the response of the deficit which in turn reduces the interest rate spreads. If fiscal strain is sever at the outset, the lower deficit leads to a considerable decline in the risk premium, which reduces the interest rate spreads. By reducing these spreads private demand will pick up, an impact particularly felt when the ZLB is binding

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CHAPTER 4. RESULTS 30 for a longer time. A situation in which output is increased by reducing government spending is empirically relevant, for instance when the ZLB lasts 10 quarters and ξ is 0.061 which converts to an initial debt to GDP level of about 130 percent.

Overall the effect of a spending cut on output and the deficit depends on subtle and non monotonic ways on the initial fiscal position and the expected length of the ZLB.

Figure 4.11: Fundamental agents

Naive agents

The analysis of the effects of an exogenous spending cut is straighter forward when an economy consists only of naive agents. As can be deduced from the left panel of figure (4.12), output is significantly reduced, while the deficit (right panel) and interest rate spreads (lower panel) increases for all combinations of ξ and µ. That the spending cut does not reduce the deficit but rather increases it is due to significant drops in output. This drop causes a deterioration of tax income that is larger than any gains made by decreasing spending. The drop in output and conversely the increase in the deficit mainly increase when µ increases and only slightly with an increase in ξ. This effect on output caused by increasing µ is not driven by expectations but rather by the actual length of the ZLB. Unlike fundamental agents, naive agents do not form any expectations so this is not an influence. However the length of the ZLB does have an effect

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CHAPTER 4. RESULTS 31 since inflation and output are moving away from their steady state values over time with naive agents only. In other words: if we would fix length of the ZLB episode for all µ, there wouldn’t have been any effect when we increase the probability µ of staying another period at the ZLB. As can be seen from the lower panel the spending cut has a counteracting effect on interest rates spread, which rise in response to the spending cut when ξ is nonzero. That the spreads only rise when ξ is larger than zero makes sense; fundamentally spreads will only rise when an economy is exposed to sovereign risks. We can conclude that it is not beneficiary to decrease spending in an economic system only containing naive agents.

Figure 4.12: Naive agents

Two type system

Finally we consider the effects of an exogenous government spending cut when an economy contains both types of agents and each agent can change its type. It is apparent that austerity measures in almost all cases make the situation worse. An increase in sovereign risk will make the fiscal austerity measure a more viable option, since credit risk premia will rise and therefore

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CHAPTER 4. RESULTS 32 make pro-cyclical policy more expensive. On the other hand an increase in the expected and actual length of the ZLB leads, especially with low levels of sovereign risk, makes the spending cut more detrimental to the economy. Something that is caused by the increase of the govern-ment multiplier with the length of the ZLB.

However, similar to the rational scenario some combinations of high levels of sovereign risk and a longer ZLB episode make the austerity measures expansionary and highly successful. For these boundary combinations ξ and µ, the austerity measures have a positive effect by increas-ing output while decreasincreas-ing the deficit. I call these combinations boundary since we cannot ensure determinacy for larger combinations of the two parameters and therefore cannot plot values beyond these. However whereas in the rational case Corsetti et al. (2013) found that the spending cut becomes expansionary for empirically relevant values in this case it here does not. We only find this expansionary effect when ξ is larger than 0.9 when the ZLB is expected to last under 10 periods. This value of ξ implies that the debt to GDP level has to be close to 150%, which is so high we can discard it for all economies.2 Hence the spending cut might only be effective when considering very long ZLB episodes (longer than 2.5 years) and extremely high debt to GDP levels. As such we can conclude that when assuming bounded rationality with only two types of agents, fiscal austerity has negative effects on the deficit and on economic output.

2_{Only Japan is known to have such a high debt/GDP, but this debt/GDP is financed domestically with savings}

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CHAPTER 4. RESULTS 33 Figure 4.13: Two types of agents

Robustness

Changing the memory parameters ρ or the the shock to discount factor eL, which effectively

determines the severity of the recession at the ZLB, doesn’t change the policy recommendation. Also the intensity of choice γ doesn’t have a profound effect on output and the deficit. Only for high values of γ something can change, in figure (4.14) we have increased the intensity of choice to 5. As a result, for very high values of ξ, a government spending cut has an expansionary effect and reduces the deficit. However these values are so high that it is not empirically relevant.

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CHAPTER 4. RESULTS 34 Figure 4.14: Two typs of agents

4.3.2 Endogenous government spending

When an automatic government spending rule is implemented at an economy that is exposed to sovereign risk while at the ZLB, it is of interest what rule type is best able to deal with deflation while ensuring that the deficit is not increased. Similar in setup to our previous exogenous analysis we will examine a change from counter to pro-cyclical policy in order to evaluate whether such a change is in the best interest of the sovereign’s public finances and general economy.3 Specifically we will compare government spending during the ZLB episode of ˜

gt= −0.1˜yt to ˜gt= 0.1˜yt. Subsequently we will do so for economies that contain fundamental,

naive and both types of agents. Fundamental agents

When comparing counter to pro-cyclical fiscal policy this is very similar to comparing a fiscal stimulus with a fiscal spending cut. This is apparent when we examine figure (4.15), which shows the impact of a rule change from counter to pro-cyclical for output, the deficit and interest rate spreads. In fact this figure gives exactly the same trends as we have seen previously with the exogenous spending cut when we only have fundamental agents, as in figure (4.11). Therefore there is no need to analyse this in detail. Again, counter-cyclical policy is only effective in reducing the deficit when the expected length of the ZLB episode is long and sovereign risk is relatively low.

3

In order to avoid that fundamentalist expect the economy to expand during the ZLB episode we have slightly changed the shock to the economy down from eLis 0.8965 to 0.88.

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CHAPTER 4. RESULTS 35 Figure 4.15: Fundamental agents

4.3.3 Two type system

We will now introduce naive agents to the economy and allow agents to switch between types. We have omitted a discussion of a system that contains only naive agents, as by itself the dy-namics are not very interesting. Choosing between pro- or counter-cyclical policy does not have a significant effect on output or for that matter on the deficit. Since output will hardly drop and therefore government spending won’t change significantly when only trend following agents are involved.

Unlike our analysis of the exogenous government spending cut in a system that contains both type of agents we can deduce from figure (4.16) that the introduction of bounded rationality via the agent based model doesn’t have a tremendous impact on the policy recommendation. In general our findings are similar to the fundamental agents results, except when sovereign risk is low. When the two type of agents are involved, for shorter lengths of the ZLB episode a reduction of the deficit is realised by a fiscal stimulus. Therefore the set of ZLB lengths for which counter cyclical policy is effective at both increasing output spending and reducing the deficit has increased compared to the fundamental agents only case.

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CHAPTER 4. RESULTS 36 Overall, when we have an endogenous spending rule counter fiscal policy is preferred when sovereign risk is low and the ZLB episode is long. On the other hand when sovereign risk is high (debt to GDP over 130 %) and the ZLB episode is long, pro-cyclical policy is warranted as this will result in an expansion of the economy. For lower lengths of the ZLB and or lower levels of the ZLB it depends on the policy maker’s objective to either increase output or reduce the deficit.

Figure 4.16: Mixed agents

e

Robustness

The shock to the discount factor at the times of the ZLB, eL, has an effect on the policy

recommendation when sovereign is low and the ZLB episode relatively short, albeit a small one. Specifically when the shock is increased and output and inflation are decreasing, the set of values for which the length of the ZLB episode ensures that counter-cyclical policy reduces the deficit is decreased. A similar effect is noticeable when the intensity of choice γ is increased.

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CHAPTER 4. RESULTS 37 Comparing endogenous and exogenous policies

Let us examine more closely why the nature of the fiscal policy stimulus, either endogenous or exogenous, leads to different policy recommendations when we deviate from the rationality assumption. In order to do so we have plotted government spending, output and the primary deficit over 6 periods at the ZLB (µ = 5/6) for an economy exposed to low sovereign risk (ξ = 0.02) on the next page. This choice of parameter was arbitrary, for another configuration of parameters the same holds true. We have done so for four instances, firstly when govern-ments don’t intervene and government spending stays at its steady state throughout the ZLB. Secondly when spending is exogenously increased by 1 percent of steady state output. Thirdly and fourthly we have plotted the results of counter cyclical endogenous policy rules that com-pensates 10% (ϕ = −0.1) and 100% (ϕ = -1) of the drop in output by increasing spending. In the plots we have included a first period that gives the situation prior to the ZLB, to show that we assume that all variables are at their steady state values before entering the ZLB episode.

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CHAPTER 4. RESULTS 38 Government spending, output and deficit Naive agents

No government gL= 0 or ϕ = 0 Exogenous spending increase by 1% (gL= 0.01) Endogenous Counter-cyclical (ϕ = −0.1) Endogenous Counter-cyclical (ϕ = −1)

We start by analysing the first series when government spending is kept at steady state levels during the ZLB episode. This will form a benchmark from which we can examine the effects of the nature of the fiscal stimuli. As can be observed, output (blue line) will continuously drop during the ZLB episode and with it the primary deficit (orange line) will rise due to decreased

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CHAPTER 4. RESULTS 39 tax income. This output decrease is mainly caused by a continuous drop in market expectations on output and inflation, which is driven by the increased share of naive agents (left panel) and the negative updating of their expectations. Overall this causes a deflationary spiral with falling prices and output and an increasing primary deficit.

The previous dynamics can be altered when the government increases spending at the ZLB. We now consider the second two graphs where we have increased government spending by 1 percent of steady state output (gL= 0.01). It can be concluded that the spending increase

suc-cessfully halts the deflationary spiral and ensures that output starts to rise again even during the ZLB episode. The number of extrapolating agents also increases, since in particular the forecasting error of the fundamental agents is increasing. This rise in output and the avoidance of the deflationary spiral is a consequence of the naive expectations which were still anchored at pre-ZLB episodes and therefore ensure that the realised output is not too negative. Further-more the naive agents expect additional government spending since they implicitly assume that the economy will be at the ZLB next period, which is an advantage as long as interest rates stay at the ZLB. Now market expectations are high enough to ensure that output and inflation are pulled back to their equilibrium levels. For this configuration of parameters, despite not having particular high government spending multipliers as shown by Corsetti et al. (2013) the additional government spending is enough to avoid the deflationary spiral.

Now we consider the two cases of endogenous spending. We have plotted the same graphs for a case of mild counter-cyclical policy (ϕ = −0.1) and strong counter-cyclical policy (ϕ = −1). From the graphs it is apparent that a fiscal endogenous stimulus is unsuccessful in countering the deflationary spiral during the ZLB episode. As a consequence the deficit rises since govern-ment spending has to be increased and increased to keep overall output from falling too low. With a known endogenous rule, fundamental agents are relatively better at predicting output than in the case of exogenous government spending. For one this is caused by the government spending which is now dependent on output. In such a scenario it is better to form a fundamen-tal view for the first periods at the ZLB than simply extrapolating the past. The dominance of fundamental expectations leads the naive agents to form increasingly negative expectations on output, finally launching the economy into a deflationary spiral.

The difference between the exogenous and endogenous type of government spending is espe-cially apparent when considering gL= 0.01 and ϕ = −1. In the first output realisation during

the ZLB episode, output drops by 1.9% when the government has committed to an endogenous stimulus while it drops by -2.0% in case of an exogenous spending increase. Even when the ac-tual output realisations are close, the share of naive agents is quite different for both scenarios. When the endogenous rule is in effect the number of naive agents drops while it increases with an exogenous stimulus on the other hand. The difference lies in the expectation of the

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fun-CHAPTER 4. RESULTS 40 damental agents. When the government is committed to an endogenous stimulus these agents expect the landing to be softer, i.e. that output shouldn’t drop too much even during a ZLB episode. Meanwhile a minor exogenous spending increase only slightly increases output. It is this difference in the anchoring of expectations that explains why impact is not the same for an exogenous and an endogenous stimulus. While the endogenous fiscal policy rule might be very effective in avoiding a very deep recession its success is self defeating: it ensures that too many agents will become fundamental in their approach to the ZLB episode at the beginning of the ZLB episode. An exogenous government spending increase on the other hand, while it is not as successful in increasing the expectations of fundamental agents, it does ensure that more agents become naive in their expectations early in the ZLB episode on. Furthermore with the spending increase these naive agents have higher expectations than in the case without government spending and are with the additional government spending ushered back to steady state values.

Fiscal policy impact when exposed to sovereign risk at zero interest rates : assuming bounded rationality in an agent based model

Master’s Thesis