Download Heterogeneous Agents, Financial Constraints and Government Debt

Financial Constraints and Government Debt Financing Strategies1
Ayobami E. Ilori2
Department of Economics
University of Sheffield
United Kingdom
February, 2016
Abstract
This paper analyses the implications of government debt financing strategies for heterogeneous
households. Two significant contributions are made: first, household heterogeneity is modelled
along agents’ preference structure; second, the degree of valuation of public resources is allowed to
vary across households. Taking into consideration the degree of financial constraints among households, with rich specification of the fiscal sector, the model is fitted to the UK data using Bayesian
estimation approach. Evidence from the results shows that: (1) household agents differ considerably in preference structure and valuation of public resources, and this influences agent-specific
policy responses to fiscal adjustments; (2) Irrespective of the choice of fiscal strategy, financially
constrained households are made worse off by the government consolidation plan, consuming less
while working more compared to unconstrained households; (3) The government’s debt consolidation plan can be frustrated by stringent fiscal policy which further constrains households’ finances
and increases the proportion of financially constrained households. Given the policy implications of
this analysis, the fiscal authority must exercise great caution in implementing consolidation policies
while addressing public debt crisis, possibly through selective implementation.
Key words: Fiscal policy; Debt consolidation; Heterogeneous agents; Rule-of-thumb consumers; Financial constraints
JEL classification: E62, H31, H63
1
This paper is part of my dissertation for the award of PhD in Economics at the University of Sheffield, United
Kingdom.
2
E-mail: [email protected]. I acknowledge the contributions, suggestions and mentorship of my erudite supervisors; Professor Christoph Thoenissen and Dr Juan Paez-Farrell. I am also indebted to the Department of Economics,
University of Sheffield, for their financial support (GTA scholarship) in funding this PhD programme
1
“The budget deficit is forecast to fall to 3.7% this year, which is less than half the 10% we inherited
in 2010. But all that progress is at risk if we do not finish the job. While we move from deficit to
surplus, this Charter commits us to keeping debt falling as a share of GDP each and every year.
Only when... we have GDP growth of less than 1% a year... will that surplus no longer be required.
[We] are continuing to devote a greater share of state support to the most vulnerable. [Those] with
broadest shoulders [the richest] are bearing the greatest burden. For we are all in this together.”
- George Osborne, Summer Budget Speech 2015
1
Introduction
The current public debt crisis swaying across Europe and many other developed countries, as well
as the various fiscal consolidation strategies proposed to address it, have generated significant debate
among policy makers and in academic circles. Following the recent global financial crisis, public
debt in many industrially advanced economies surge to record level. Between 2007 and 2009, public
debt rose by about 75% for some epicentre countries (such as the United States, United Kingdom,
Spain, Ireland and Iceland) with systemic financial risks much prone to crisis, and by about 20% for
countries with lesser influence of the crisis (Reinhart and Rogoff, 2010). This has been attributed to
the government-initiated fiscal stimulus during the crisis period, especially the costs associated with
direct bailout of privately-owned financial institutions and other industries, and the decline in public
revenue generation. As public debt grew beyond its sustainable level, this dampened growth while
interest rate responded nonlinearly with market interest rate rising as higher premium was demanded
to mitigate against the risk of default. The poor economic outlook further tricks the government into
imposing stringent consolidation policy, which further worsen the economic situation. This is what
Reinhart and Rogoff referred to as “debt intolerance.”
As part of the plan to deleverage the rising public debt, some governments (especially in the United
Kingdom, Greece, Ireland, Portugal, Spain and Italy) adopted various consolidation measures ranging
from tax hikes to to reduction in running-costs of government, strong caps on social benefit payouts,
public employees pay-freeze, minimum wage reduction, limited tax credits, outright privatisation of
government-owned ventures among others.3 These consolidation measures have generated a strong
debate among policy makers, especially with regards to the nature of fiscal consolidation implemented,
the choice of fiscal instruments employed, the anticipated cut in public debt over a specific time-period,
and the target-end of each consolidation measure. Some pro-consolidation policy makers have argued
that such fiscal measures are justified and should affect all spectrum of households alike. Their
argument is based on the premise that, as the government adjusts its fiscal instruments relative to the
public debt level, all household agents respond accordingly by adjusting their preferences to sufficiently
accommodate such a drastic change. This notion is quite synonymous with the Ricardian Equivalence
3
For instance, in the United Kingdom, the government is cutting down benefit payout and politicians pay, freezing
wages of public employees, abolishing housing benefit for young people (18-20) as well as limiting tax credit to the lowest
income group. In Greece, the situation is similar with the addition of an increase in VAT on consumption goods and
a cut in the minimum wage. In Ireland, the situation seems to be more complex with each successive fiscal year, since
2008, coming with some major fiscal consolidation announcements, including pay cut for young people (20-24), reduction
in national minimum wage, increase in personal tax and a significant cut in social security payment.
1
Figure 1. General government public sector debt as a percentage of GDP. Source: World Bank Database
hypothesis in the economic literature. The seminal paper by Reinhart and Rogoff (2010) is a very
good example of one of these pro-consolidation studies. Also, George Osborne, the UK Chancellor,
while addressing the government’s debt-consolidation plans, asserted that “we are all in this together”
- that is, all households are equally affected by the government’s stringent fiscal policy.4 Similarly,
international policy institutions, such as the ECB,5 have continually encouraged countries with high
level of public debt to impose strict fiscal measures across board.
However, recent evidence seems to diminish the validity of the pro-consolidation assertions. First,
despite the various consolidation policies in several countries, evidence from the World Bank data
shows that public debt remains high and even keeps rising for some countries (see Figure 1). Also, the
pace of recovery in most of these economies has been sluggish with some countries, such as Greece, even
falling into new recession with severe budget crisis. Secondly, while recommending fiscal adjustments
to governments, the pro-consolidation policy makers often neglect the heterogeneous nature of the
constituent households in the economy. Whereas, a large body of the literature has analysed the
case of some household agents that are financially constrained with near-zero net-worth follow rule of
thumb behaviours in making decisional choices (Campbell and Mankiw, 1989, 1990 & 1991; Aiyagari,
1994; Mankiw, 2000; Kaplan and Violante, 2014; Kaplan et al., 2014). Also, the existence of these rule
of thumb behaviours has been widely documented to significantly alter the response of heterogeneous
agents economy to structural shocks (Gali et al., 2004 & 2007; Coenen and Straub, 2005; Bilbiie, 2008;
Forni et al., 2009; Di Bartolomeo et al., 2011; Kollmann, 2012; Coenen et al., 2013; Rossi, 2014). Aside
that, differences in households’ preferences and how they value public goods could strongly influence
their responses to policy shocks, hence should be taken into consideration.6 Thirdly, some studies,
4
See for instance the 2009 and 2014 Conservative Conference Speeches as well as the 2015 budget speech
For instance, the ECB’s Six-pack and Fiscal Compact agreements defines a mandatory precise debt reduction path
for its country-members debt-GDP ratio exceeding the Maastricht threshold of 60%.
6
It is a common knowledge the poor people tend to value core public goods, such as education and health, relatively
5
2
such as Eggertsson and Krugman (2012), have suggested that the aftermath effect of financial crisis
(which preceded the current debt crisis) on household finances could cause more household agents
to become financially constrained, thereby resulting to more households depending on government
resources (social benefits) and living from “hand to mouth.” This in turn leads to loss of tax revenues
for the government while benefit pay-outs remain high, thereby necessitating more public borrowing
and further worsening off the debt crisis.
In the light of the above, this paper aims to contribute to this debate by analysing the implications
of fiscal consolidation strategies in the United Kingdom, taking into consideration: (i) the recent
surge in public debt level which is currently above its trend level, (ii) the existence of rule of thumb
behaviours among some households, and (iii) differences in households’ preference structure and the
degree to which they value public goods. Specifically, this paper seeks to offer answers to the following
policy questions:
• Given specific fiscal strategies, how do different groups of households respond to government
consolidation policy aimed at reducing public debt?
• How does the proportion of financially constrained households affect the government’s debt
consolidation plan?
• What are the effects of alternative fiscal financing strategies on government debt-reduction plan
and the overall performance of the economy?
Given the aims of the research, the paper builds on existing studies (Leeper, 2010a & 2010b;
Coenen et al., 2013; Rossi, 2014) by developing a heterogeneous agents DSGE model comprising a
continuum of Ricardian and rule-of-thumb households with robust fiscal sector. In order to analyse
the distinctive response of heterogeneous agents economy to fiscal shock, the paper modelled households heterogeneity along differences in agents’ preference structure (relative risk aversion and Frisch
elasticity) and valuation of public resources (consumption CES elasticity), rather than just differences
in wealth endowment as it is case in most existing literature. This new approach is motivated by the
fact that agent-specific responses differ considerably from representative agent responses (Aiyagari,
1994), and this distinction is not just driven by differences in wealth endowment, but also by the
intrinsic nature of different groups of households. The theoretical model is then estimated using the
Bayesian estimation approach and the results were simulated to obtain the responses of the economy
to alternative debt financing strategies, with emphasis on government consumption spending shocks,
transfers shocks and labour tax shocks, which characterised the choice of fiscal strategies adopted in
the UK recently.
Evidence from the results shows that household agents differ considerably in preference structure
and valuation of public resources, and this influences agent-specific policy responses to fiscal adjustments. Precisely, rule-of-thumb consumers are more risk-averse, less likely to adjust hours in response
to after-tax compensation, and strongly value public resources compared to Ricardian households.
This result proffer a novel insight into the limited asset market participation of rule-of-thumb consumers – they are not just financially constrained as portrayed by existing literature, but also less
willing to take financial risks. Also, irrespective of the fiscal strategy adopted by the government,
financially constrained households are made worse off by consolidation plan, consuming less while
more compared to the rich since they can not afford private provisions of such essential goods.
3
working more compared to unconstrained households. Furthermore, a stringent fiscal policy which
further constrains households’ finances can frustrate government’s debt consolidation plan in the long
run. This is because such stringent policy tends to increase the proportion of financially constrained
household, causing more households to depend on public resources, thereby weakening the effectiveness
of the fiscal instruments in achieving the targeted consolidation.
The rest of this paper is arranged as follows: A brief review of related literature is presented in
section 2, the theoretical model for the analysis is presented in section 3, with model calibration and
estimation presented in section 4, while the results are presented in section 5, and section 6 concludes.
2
Literature Review
The analysis of public debt gained a central focus in macroeconomy literature about five decades ago
through the seminal works of two award-winning economists. The first is the Diamond-Samuelson (Diamond, 1965) model of overlapping-generations which posits that, although agents smooth consumption
over time, government debt policy decreases capital accumulation, causing output and consumption
to fall, thereby making some generations better off compared to others despite no intergenerational
bequest. The second is the Barro-Ramsey (Barro, 1974) model of infinitely-lived (intergenerational)
agents which posits that forward-looking agents, which have unlimited access to the financial market,
view current government debt as higher future tax; hence, they redistribute tax burden among generations by leaving bequest for future generations while smoothing consumption over time.7 This is
often referred to as the “Ricardian Equivalence” hypothesis. In other words, the Ricardian equivalence
hypothesis states that the choice of government finance strategy (taxes and debt) is not relevant for
understanding the equilibrium effects of changes in government spending.
Some recent studies have empirically confirmed some of the propositions of the standard theoretical
models with regards to the macroeconomic effects of public debt. Woo and Kumar (2015), Cecchetti et
al. (2011) and Reinhart and Rogoff (2010) found that higher public debt-GDP ratio in excess of about
90% could have significant deleterious effect on output. Reinhart and Rogoff (2011) further observed
that (external) sovereign debt crises are often preceded by such high level of public debt. Baldacci et
al. (2015) also found that public debt reduction driven by fiscal consolidation could slow down growth
when the economy is credit-constrained, but output may rise when fiscal adjustment processes are
smooth with a combination of spending and tax measures. Similarly, Cafiso and Cellini (2014) found
that, for European economies, fiscal consolidation does not stem the growth of debt in medium run,
even though it may curb it in short-run. They attributed the difference in timing to the adverse effect
of consolidation policy on output. More so, in an analysis for Greece, Papageorgiou (2012) found that
consolidation policies worsen economic activities in the short run, but could be significantly beneficial
in the medium and long run at the end of the consolidation policy. The channels through which
public debt affect output, as Woo and Kumar (2015) observed, include via higher long-term interest
rates, higher future taxes and/or lower future public investment spending, higher inflation, higher
uncertainty about future government plans, and binding constraint on the scope of fiscal policies. In
contrast to the above findings, Ludvigson’s (1996) analysis suggested that higher public borrowing
may increase output and consumption if most of government debt is held within the country. This
result is supported by Afonso and Jalles (2013) which found that fiscal consolidation and high public
7
See Mankiw (2000) for a review of these two canonical models.
4
debt-GDP ratio could be beneficial to growth.
Although these canonical models formed the bedrocks of subsequent models and analysis of public
debt and fiscal financing, they have also been criticised on several grounds. For instance, the Ricardian
equivalence hypothesis is based on an implicit assumption that public debt is offset in the future by
a higher lump-sum taxes. However, when distortionary taxes are considered, the hypothesis breaks
down (Ludvigson, 1996; Rossi, 2014). Also, Aiyagari (1994) observed that, while the representative
agent models, such as these canonical models, try to portray the completeness of the market system,
agent-specific decisional choices of consumption, leisure and labour, wealth and other asset portfolio
holdings tend to differ markedly from the perfect market postulations. Mankiw (2000) also argued
that these models ignore the excessive sensitivity of consumption to income changes, as observed in
both micro and macro data, which might be as a result of rule of thumb behaviours among some
household agents who have limited access to the financial market (See Bilbiie, 2008) and, hence,
cannot smooth consumption over time as proposed by Hall (1978). More so, these models fail to
consider steady-state income and wealth inequality among households; whereas, evidence has shown
that some households have near-zero wealth or assets, both financial and non-financial (Mankiw, 2000;
Kaplan et al., 2014). This group of households simply consume their current income and often make
decisional choices based on adaptive expectation rather than rational expectation as often suggested
in the literature. Earliest among these studies that have found evidence in favour these rule-of-thumb
behaviours include Campbell and Mankiw (1989, 1999, 1991) and Krusell and Smith (1996, 1997,
1998).
Based on these observations, some contemporary studies have considered heterogeneity among
constituent households in macroeconomic modelling in order to show the degree to which agentspecific dynamics and uncertainties influence aggregate variables and policy responses. For instance,
Coenen and Straub (2005) and Gali et al. (2007) showed that the existence of rule-of-thumb consumers
partially cushions the negative wealth effect of higher taxes on aggregate demand, thereby causing
private consumption to increase in response to positive government spending shock, as well as making it
more sensitive to agents’ disposable income. In furtherance of Gali et al. (2007) analysis, Natvik (2012)
observed that when steady-state wealth inequality is fully considered, wage rigidity and labour market
power are two essential features that could guarantee a stable solution that rule-of-thumb behaviours
might cause private consumption to rise in response to public spending. Mayer et al. (2013) further
extended Gali’s rule-of-thumb model by interacting an interest rate policy rule with the government
fiscal rule. They found non-monotonic responses of macroeconomic variables to spending shocks at
higher level of public debt, which they attributed to the interaction between inflation dynamics and
public debt at higher steady-state level.
Also, Forni et al. (2009) modelled a fraction of the households who exhibit rule-of-thumb behaviour
in a DSGE model estimated for the euro area to study the effect of fiscal policy during the pre-crisis
era, and they found that fiscal policy has mild Keynesian effect on the area. In a similar study, Coenen
et al. (2013) quantified the impact of the European Economic Recovery Plan (EERP) on the euro
area GDP in the post financial crisis period by extending the ECB’s New Area-Wide Model (NAWM)
to include rule-of-thumb consumers so that government transfers may have real effect on the economy.
More so, Rossi (2014) found that, whether public debt is zero or positive at steady state, the share of
rule-of-thumb consumers significantly alters the interactions and feedback consequences of fiscal and
monetary policy. Furthermore, in a recent study, Drautzburg and Uhlig (2015) extended the Smets
5
and Wouters (2007) New-Keynesian model to include rule-of-thumb consumers while attempting to
quantify the fiscal multiplier in response to the American Recovery and Reinvestment Act (ARRA).
They found that the fraction of transfers given to the rule-of-thumb households significantly affect the
fiscal multiplier.
On the monetary policy side, Amato and Laubach (2003) and Gali et al. (2004) observed that
rule-of-thumb behaviours alters monetary policy designs especially when the proportion of consumers
who exhibit such behaviour is considerably large. In an international business cycle, Kollmann (2012)
found that the consumption-real exchange rate puzzle can be explained by a model which explicitly
considers rule-of-thumb behaviour among some households, and that this behaviour causes the real
exchange rate and net export to be more volatile. Also, Erceg and Linde (2013) considered rule-ofthumb behaviour among some households in order to study the effect of fiscal consolidation, driven by
spending cuts and tax hikes, in a monetary union. They found that tax-financed consolidation policy,
though more costly in the long run, has lesser adverse effects on output compared to expenditure-based
consolidation policy in the short run.
Despite the contributions of the existing literature on fiscal financing of government debt, none
of them has analysed the role of heterogeneity in households’ preference structure (differences in
the preference parameters across income-groups such as the rate of risk aversion, Frisch elasticity
and consumption CES elasticity) and how this affects agents’ responses to policy shocks. Although
some studies have modelled heterogeneity among households along agents’ degree of impatience (as in
Iacoviello, 2005 & 2015) or wealth endowment (as in Gali-type models), heterogeneity in households’
preferences has not been considered in any macroeconomic model, especially in dynamic stochastic
general equilibrium (DSGE) models, at least to the best of the author’s knowledge.
However, in order to understanding agent-specific responses to policy shocks and why they differ
from aggregate responses, heterogeneity in households’ preference structure needs to be considered.
This is because, each preference parameter plays a significant role in the dynamic response of macroeconomic variables. For instance, the Frisch labour supply elasticity, which measures the response of
labour effort to small changes in after-tax compensation, drives the amount of labour hours supplied
by households, which in turn affects the level of output and consumption. But there is a caveat: the
Frisch elasticity is based on the assumption that wealth effect is constant across households. Thus, in
a model where some households have positive wealth/assets, while some have near-zero wealth (such
as in Gali-type models), imposing a unified Frisch elasticity for both types of households seems to
be a significant restriction. Also, the rate at which current consumption is willingly substituted for
future consumption depends on the household’s consumption rate of risk aversion (CRRA) which is
determined by the degree to which the household consider the certainty equivalence of return on asset
to be compensating enough. Thus, in a model where some households are more patient to substitute current consumption for future income (as in Iacoviello-type model) or where only a fraction of
households participate in assets market (as in Bilbiie or Gali-type model), imposing a unified relative
risk aversion parameter across all households is quite contestable. Also, very few studies (such as
Coenen and Straub, 2005) have analysed differences in preference choices (consumption and labour)
of Ricardian and non-Ricardian households, while a few studies (such as Natvik, 2012) have considered
steady state inequality in consumption among households.
Therefore, this paper builds on studies by Leeper (2010a, 2010b), Coenen et al. (2013) and Rossi
(2014) by developing a heterogeneous agents DSGE model comprising a continuum of Ricardian and
6
rule-of-thumb agents, characterised with different preference structures, and productive fiscal sector.
3
Model
This analysis is carried out within a standard real business cycle (RBC) model with heterogeneous
agents.8 The model is motivated by Rossi (2014), Coenen et al. (2013) and Leeper et al. (2010a &
2010b), and adapted to accommodate some real frictions (such as habit formation in consumption,
investment adjustment costs, existence of rule-of-thumb consumers) commonly employed in DSGE
models. There are three distinct agents in this closed-economy model: households (Ricardian and
Non-Ricardian), firms and the government. Households determine the optimal choices of private
consumption and labour supply, firms determine the optimal choices of labour and private capital to
employ in order to produce a given level of output, while the government augments private sector
activities with spending on public consumption and public investment goods as well as social transfers
which are all financed with distortionary taxes and bond issuance.
3.1
Households
There is a continuum of households, indexed with i ∈ [0, 1], which comprises two groups: (i) The
Ricardian (forward-looking, financially unconstrained) households, indexed by r ∈ (λ, 1], have access to
the financial market and accumulate physical and financial assets. As a result, this class of households
can smooth consumption across time - intertemporal optimisation - in response to structural shocks.
(ii) The non-Ricardian (rule-of-thumb, hand-to-mouth, myopic, financially constrained) households,
indexed with h ∈ [0, λ), do not own any physical or financial assets due to liquidity constraints and
financial market imperfections. As a result of their limited asset market participation (Bilbiie, 2008;
Kollmann, 2012), this group of households does not smooth consumption intertemporally; rather it
simply consumes its current labour income each period - intratemporal optimisation.
Each group of households has separable preferences comprising the utility derived from effective
consumption, C̃ti , and disutility from labour effort, Nti .9 In this economy, although public goods
remain non-rivalry and non-excludable, households however differ in their valuation of government
resources.10 Hence, in a similar fashion to Bouakez and Rebei (2007), Pappa (2009), Coenen et al.
(2013), Ercolani and Azevedo (2014) and Pappa et al. (2015), the effective consumption of household-i
is specified as a non-separable constant elasticity of substitution (CES) aggregator of the household’s
own-private consumption and government consumption:
C̃ti
= (1 − %)
1
ϕi
Cti
ϕi −1
ϕi
+%
1
ϕi
Ctg
ϕi −1
ϕi
ϕi
ϕi −1
(1)
where Cti and Ctg are the household-specific private consumption and government consumption respectively, % ∈ (0, 1) is the share of government consumption in the effective consumption aggregator,
8
The choice of pure RBC model is justified by the fact that some fiscal choices are independent of monetary policy.
Unlike the Gali et al. (2004 & 2007) model with non-separable preferences, this paper adopts separability in each
group of households preferences in order to track unique responses of consumption and labour effort to structural shocks
while fully taking into account any wealth effect.
10
Household agents differ in their valuation of public goods such as public healthcare and education. Since the rich
households can easily afford private provision of these services, they place smaller value on public goods, while the poor
households value the public goods much higher.
9
7
and ϕi ∈ (0, ∞) is the household-specific CES substitution elasticity between Cti and Ctg . As ϕi → 0,
private and public consumption tend to become perfect complements, while they tend towards perfect substitutes as ϕi → ∞; and a Cobb-Douglas case is obtained as ϕi → 1. In this model, the
CES substitution elasticity is defined in terms of household-specific rather than an economy-wide parameter in order to make the model less restrictive as well as to capture the degree of valuation of
public goods by household-i; households with smaller value of the CES substitution elasticity (more
complementarity in consumption) tend to value public goods relatively more compared to others, and
this will affect the overall utility derived from the effective consumption. Unlike some studies, such as
Papageorgiou (2012) and Natvik (2009), with separable government consumption, this paper adopts
non-separability between public and private consumption, which is a more general specification, to
ensure that government consumption directly affects private consumption decisions, thereby lead to
co-movement of both.11
More so, in this economy, it is assumed that households’ preference structure differ across income
groups. At any given period of time, households plan to maximise the following utility function:
Et
(∞
X
t=0
"
β t ψtu
1+ η1
i )1−θi
(C̃ti − χi κC̃t−1
Ni
−ψ t
1 − θi
1+
i
1
ηi
#)
(2)
where β ∈ (0, 1) is the subjective discount factor, θi and ηi are the group-specific consumption rate of
risk aversion (CRRA - the inverse of intertemporal substitution elasticity) and Frisch labour supply
elasticity respectively. These parameters are defined in terms of group-specific rather than economicwide parameters in order to analyse how differences in households’ preferences affect their responses
to fiscal shocks, which is one of the thrusts of this discussion. κ ∈ (0, 1) is the external habit formation
parameter, while χi is a binary variable such that when i = r (Ricardian households), χr = 1, and when
i = h (HtM households), then χh = 0 (Di Bartolomeo et al., 2011). The implication of this is that,
unlike the Ricardian households, HtM households do not habitually smooth consumption in response
to shock since they consume their current income each period; hence the restrictive assumption of
steady state equality of consumption between the two groups of households is relatively ruled out
since the Ricardian marginal utility of consumption is now discounted by the smoothing factor (1 − κ)
at steady state (See equations 23 and 24 in Appendix 1).12 ψ is a positive parameter relating to the
marginal disutility of labour while ψtu is the preference shock which follows an AR(1) process, such that
u +u , where u ∼ N IID(0, σ ) is a pure random error to consumer’s preference. Although
ψ̂tu = ρu ψ̂t−1
u
t
t
households’ utility negatively depends on hours, Nti , the HtM households utility positively depends
on own-group current effective consumption, C̃th , while the Ricardian households utility depends on
r , effective consumption.
the positive difference between own-group current, C̃tr , and the lagged, C̃t−1
11
For instance, government consumption spending on primary healthcare and basic education directly impacts on
private consumption decisions.
12
This is a clear departure from most studies involving non-Ricardian households, such as Rossi (2014), Coenen et al.
(2013), Gali et al. (2004 & 2007) etc.
8
3.1.1
Ricardian Households
Following the specification in Rossi (2014), Ricardian households maximise utility subject to the
following budget constraint:
(1 + τtc )Ctr +
It
Bt+1 −1
Kt
Bt
+
R = (1 − τtw )Wt Ntr + [rtk − τtk (rtk − δp )]
+
1−λ 1−λ t
1−λ 1−λ
(3)
and a capital accumulation equation with investment adjustment-costs in the fashion of Christiano et
al. (2005):
"
Kt+1 = (1 − δp )Kt + It ψtI
φ
1−
2
It
It−1
2 #
−1
(4)
At the beginning of each period, the Ricardian household receives labour income, Wt Ntr (where
Wt is the real wage) and rental income on its capital holding, Kt , rented to the firm at a real cost
rtk ; which are then used to finance purchases of private consumption and private capital goods (Ctr
and It ). It also holds a one-period riskless government bond, Bt+1 , purchased at time t, with a gross
real return Rt . The capital adjustment costs, φ(.), determine the degree to which costly investment
spending affects changes in capital stock, where φ is the adjustment cost parameter and δp is the
depreciation rate of private capital and ψtI is the investment-specific technology (IST) shock which
I + I , where I ∼ N IID(0, σ ) is a pure random error
follows an AR(1) process, such that ψ̂tI = ρI ψ̂t−1
I
t
t
to private investment. The fiscal authority imposes distortionary taxes on the private consumption,
τtc , capital, τtk , and labour income, τtw , in order to finance its expenditure.
3.1.2
Hand-to-mouth Households
Unlike the Ricardian households, the hand-to-mouth (HtM) households maximise their single-period
utility function subject to the following budget constraint:
(1 + τtc )Cth = (1 − τtw )Wt Nth +
Zt
λ
(5)
As earlier stated, HtM households do not hold any physical or financial assets. Rather, in each
period they simply consume their labour income, Wt Nth , which is further augmented with lump-sum
government transfers, Zt , as a form of social insurance.13 Cth is the amount of private consumption
good that HtM household purchases each period.
3.2
Firms
Firms operate in a competitive market with the aim of maximizing profits:
Πt = Yt − Wt Nt − rtk Kt
(6)
At the beginning of each period, firms employ labour, Nt , from both types of household agents,
paying a universal wage, Wt , since it does not discriminate between types of labour; and rent capital
Kt , from the Ricardian household at a rental cost, rtk . In a similar fashion to Cantore et al. (2012), a
13
It is assumed that only the hand-to-mouth household receives government transfers.
9
CES technology is applied to the input combinations to produce output:14
ν
ν−1
ν−1 ν−1
1
1
ν
ν
Yt = At α ν K̃t
+ (1 − α) ν Nt
(7)
where α ∈ (0, 1) is the share of capital, ν ∈ (0, ∞) is the elasticity of substitution between labour
and capital input, while At is the technology shock which follows an AR(1) process such that Ât =
ρa Ât−1 +at , for at ∼ N IID(0, σa ) is a pure random error to technology. In a similar fashion to Coenen
et al. (2013), K̃t , which is the economy’s aggregate physical capital, is defined as a CES aggregator
of private capital services, Kt , and public capital goods, Ktg :
h
i ω
ω−1 ω−1
ω−1
1
1
K̃t = (1 − γ) ω Kt ω + γ ω Ktg ω
(8)
where γ ∈ (0, 1) is the share of public capital stock in the aggregate capital and ω ∈ (0, ∞) is the
elasticity of substitution between private and public capital goods.15
3.3
Government
In each period, the government decides on a set of fiscal instruments that satisfy its budget constraint
as follows:
Ctg + Itg + Zt + Bt = τtc Ct + τtw Wt Nt + τtk (rtk − δp )Kt +
Bt+1
Rt
(9)
Rearranging this, the evolution of government debt can be written as:
n
h
io
Bt+1 = Rt Bt + [Ctg + Itg + Zt ] − τtc Ct + τtw Wt Nt + τtk (rtk − δ p )Kt
(10)
which simply states that the level of public debt at the end of period t is a discounted sum of the
stock of debt up to time t and the current primary deficit. Itg is government investment spending at
period t which evolves according to the government capital accumulation process:
g
= (1 − δg )Ktg + Itg
Kt+1
(11)
where δg is the depreciation rate of public capital.
To ensure stability, a set of fiscal rules is specified to track the time-path of government debt for
effective financing, deleveraging and moderation towards steady state. With regards to the design of
the fiscal rule, the model follows the UK experience of fiscal consolidation in recent times where the
government is more interested in cutting public consumption spending and transfers to households,
as well as adjusting labour income tax. Based on this fact, and in line with Leeper et al. (2010a &
14
This paper adopts a CES production function since it is less restrictive and allows for a more flexible substitutability
between labour and capital inputs.
15
The model assumes that there is an interaction between private and public capital goods. This is quite plausible
as government investment spending can enhance (or crowd-out in some cases) private investment. Although there is no
consensus in the literature with regards to the degree of substitutability between public and private capital, however,
most studies suggest weak complementarity or low substitutability between both (see Coenen et al., 2013; Ercolani and
Azevedo, 2014).
10
2010b), the following set of fiscal rules in linearised form is specified for the economy:
Ĉtg = −ϑcg ŝbt − ςcg Ŷt + ξˆtcg
(12)
Iˆtg = ξˆtig
(13)
Ẑt = −ϑz ŝbt − ςz Ŷt + ξˆtz
(14)
τ̂tc = ξˆtτ c + ζck ξˆtτ k + ζcn ξˆtτ w
(15)
τ̂tk = ξˆtτ k + ζck ξˆtτ c + ζkn ξˆtτ w
(16)
τ̂tw = ϑτ w ŝbt + ςτ w Ŷt + ξˆtτ w + ζcn ξˆtτ c + ζkn ξˆtτ k
(17)
where hatted variables are percentage deviations from steady state. sbt is the (stochastic) ratio of
government debt to GDP such that:
Bt = sbt Yt
(18)
x
and ξtx are the fiscal policy shocks which follow AR(1) processes; ξˆtx = ρx ξˆt−1
+ xt , where xt ∼
N IID(0, σx ) capture the unexpected changes to fiscal policy, for x ∈ (cg , ig , z, τ c , τ k , τ w ). ϑx and
ςx are the fiscal adjustment parameters to government debt-ratio and output respectively. More so,
shocks to distortionary taxes are allowed to have unpredicted cross-effects among themselves, where
ζck , ζcn and ζkn are the parameters of the unpredicted cross-effects.
Substituting equations (12), (14) and (17) into the linearised evolution of government debt in
equation (10), the stability condition for the model suggests that:
|ϑx | > (1 − β)
B/Y
X/Y
(19)
where X/Y is the ratio of government consumption, government transfer and labour tax revenue to
GDP respectively. Here, it is assumed that the government debt is non-zero at steady state, and only
public consumption, transfers and income tax are allowed to adjust to output in order to capture
automatic stabiliser (apriori, government consumption and transfers are countercyclical while labour
tax is pro-cyclical).
3.4
Aggregations
The consolidated economy-wide resource constraint is the aggregations of both public and private
consumption and investment spending:
Yt = Ct + Ctg + It + Itg
(20)
where Ct is total private domestic consumption in the economy, which is the weighted-sum of the
Ricardian and HtM agents’ consumption:
Ct = (1 − λ)Ctr + λCth
(21)
Unlike Gali et al. (2004, 2007), Rossi (2014) and several other related studies, this paper does not
assume equality between consumption of different groups of households at steady-state (see Appendix 1
11
for computed steady states).16 Rather, following Natvik (2012), the steady-state values of consumption
for each group of agents are endogenously derived from the model. Similarly, the total labour effort,
which clears the labour market, is the weighted-sum of the Ricardian and HtM agents’ labour effort:
Nt = (1 − λ)Ntr + λNth
(22)
with the assumption that steady state hour is the same across households.17
4
Estimation
To solve this model, the first order solutions and constraints of the model are log-linearised, using
Uhlig’s (1997) method, to generates a system of equations which contains variables that are percentage
deviations from the steady-state. The linearised model is then estimated using the Bayesian estimation
techniques as described in An and Schorfheide (2007).
4.1
Calibration and Prior Distributions
Table 1 presents the values assigned to calibrated parameters and steady state ratios. The values
have been kept constant due to the fact that the model observables have been detrended and cannot
uniquely estimate many free parameters and steady state values during the estimation procedure. The
subjective discount factor, β, is set to 0.9926, suggesting an annualised real interest rate of 3%. In
conformity to the RBC literature, α is set equal to 0.33, implying that capital income share is about
one-third. Also, δp and δg are set equal to 0.025 and 0.020 respectively, suggesting that private capital
stock depreciates at an annual rate of 10%, while public capital depreciates at a lower rate of 8% per
annum, which are consistent with the values used in Leeper et al (2010b).
With respect to the productivity of public spending in the economy, on the demand side, the
share of government consumption in the effective consumption CES, %, is set to 0.23 (this is a rough
approximation of the share of government consumption to total final consumption for the UK), which
is consistent with the estimate of about one-quarter used in Coenen et al. (2013) for the euro area.
On the supply side, the share of government capital in the aggregate capital CES, γ, is set to 0.125,
suggesting that government contributes about 12.5% of the aggregate capital in the economy, which
is close to the value of 10% used in Coenen et al. (2013).
Concerning the fiscal sector, the steady-state distortionary tax rates τ c , τ w and τ k are set to 20%,
23% and 32% respectively, which are close to the estimates used in Coenen et al. (2013) for the euro
area. The consumption tax rate is obtained from the definition of consumption tax revenue in the
model, which involves dividing the the consumption tax revenue by total private consumption. Labour
tax rate is set to the average income tax on UK median wage (which currently stands at about £26,000
per annum). The capital tax rate is set to the average capital gains tax over the sample period. From
the data series, the ratios of public consumption and public investment to GDP are obtained to be
16
Gali et al. (2007) and several other papers assume that, at steady-state, C h = C r = C. The problem with this
equality assumption is that individual private consumption of different classes of agents are forced to be equal irrespective
of their income and wealth differentials at steady-state. This kind of equality constraint may, however, be valid only in
models with no private capital accumulation and no wage differentials.
17
In standard RBC models, steady state hour is taken as 1/3 which is equivalent to 8 hours per day. But Natvik (2012)
analysed a case where each class of households belongs to different labour unions, thereby supplying different units of
labour hour at steady state.
12
Table 1: Calibrated parameters and steady state ratios
Parameter/share
β
α
δp
δg
%
γ
τc
τw
τk
C g /Y
I g /Y
K g /K
B/Y
Description
Subjective discount factor
Share of capital in production CES
Private capital depreciation rate
Public capital depreciation rate
Public consumption share in CES aggregate
Public capital share in CES aggregate
Consumption tax
Labour income tax
Capital income tax
Public consumption to GDP ratio
Public investment to GDP ratio
Ratio of public to private capital
Debt to GDP ratio
Value
0.9926
0.33
0.025
0.020
0.23
0.125
0.20
0.23
0.32
0.19
0.03
0.28
0.48
about 19% and 3% respectively. Given the depreciation rates as earlier discussed, the ratio of public
to private investment is then constructed to be about 28%, which is consistent with other estimates
found in the literature (see for instance Leeper et al., 2010b). The debt-to-GDP ratio is then obtain
to be about 48% which is consistent with the Stability and Growth Pact as outlined in the Maastricht
Treaty. Based on these values, the ratio of government transfers to GDP is then calibrated to around
12%, which is consistent with the actual value of UK spending on social benefits.
Table 2 presents the prior distributions for all other parameters of the model estimated using the
Bayesian procedure. The prior means were set in conformity to the existing literature on euro area
(see for instance Smets and Wouters, 2003; Coenen and Straub, 2005; Christoffel et al., 2008; and
Coenen et al., 2013), while the standard errors were set to ensure that meaningful results were obtained
within an empirically and theoretically acceptable domain of the parameter value. For the structural
parameters, Gamma distribution was assumed for both groups of households relative risk aversion, θi ,
and Frisch labour elasticity, ηi , with respective means of 1.75 and 0.50, and standard deviation of 0.35
and 0.10, implying that both households preferences begin from points higher than the logarithmic
case. The habit formation parameter, κ, is assumed to follow Beta distribution with a mean of 0.50
and standard deviation of 0.10. To set the prior for the share of rule-of-thumb consumers, λ, (for the
model with estimated λ), this paper relies on the findings of Campbell and Mankiw (1989, 1990, 1991),
Chyi and Huang (1997), Gali et al. (2007), Kaplan and Violante (2014), and Kaplan et al. (2014),
by assuming Beta distribution with mean equals 0.50 and standard error of 0.0625, which allows the
proportion of HtM agents in the economy to range between zero and half. It was also assumed that
the group-specific effective consumption CES elasticity, ϕi , and the aggregate capital CES elasticity,
ω, both follow Gamma distribution with means of 0.30 and 0.80, and standard deviations of 0.10
and 0.25 respectively, implying that private and public consumption are closely complementary, while
private and public capital are weakly complementary as the literature suggests (see Bouakez and
Rebei, 2007; Coenen et al., 2013; Ercolani & Azevedo, 2014). Also, the production CES elasticity,
ν, follows Gamma distribution with a mean of 0.99 and standard error of 0.0275, suggesting a near
Cobb-Douglas case. The adjustment costs parameter is also distributed along the Gamma distribution
with a mean of 5.00 and a standard error of 0.50.
With regards to the fiscal rule parameters, to ensure stability in the model which satisfy the
13
Table 2: Prior and posterior distributions for the estimated parameters: Comparison of λ values
Prior distribution
Parameter
Structural
Risk aversion
Frisch elasticity
Cons. CES elasticity
Habit formation
Share of HtM
Prod. CES elasticity
Cap. CES elasticity
Adjustment costs
Fiscal Rule
Gov cons. adj. to B
Transfer adj. to B
Labor tax adj. to B
Gov cons. adj. to Y
Transfer adj. to Y
Labor tax adj. to Y
Cap/lab co-term
Cons/cap co-term
Cons/lab co-term
AR(1) Coefficients
Preference
Investment
Technology
Govt consumption
Govt investment
Govt transfer
Consumption tax
Capital tax
labour tax
Std. of Shocks
Preference
Investment
Technology
Govt consumption
Govt investment
Govt transfer
Consumption tax
Capital tax
labour tax
Measurement error
Log data density
Posterior distribution - Mean
[5% and 95%]
Density
Mean
Std.
Benchmark λ = 0
Estimated λ ∈ (0, 0.5)
Fixed λ = 0.50
θr
θh
ηr
ηh
ϕr
ϕh
κ
λ
ν
ω
φ
Gamma
Gamma
Gamma
Gamma
Gamma
Gamma
Beta
Beta
Gamma
Gamma
Gamma
1.75
1.75
0.50
0.50
0.30
0.30
0.50
0.50
0.99
0.80
5.00
0.35
0.35
0.10
0.10
0.10
0.10
0.10
0.0625
0.0275
0.25
0.50
1.61
–
0.52
–
0.45
–
0.50
–
0.96
0.84
4.71
1.49
1.88
0.62
0.50
0.46
0.32
0.55
0.34
0.96
0.84
4.70
1.47
2.07
0.71
0.52
0.39
0.33
0.52
–
0.96
0.83
4.70
ϑcg
ϑz
ϑτ w
ςcg
ςz
ςτ w
ζkn
ζck
ζcn
Beta
Beta
Beta
Gamma
Gamma
Gamma
Normal
Normal
Normal
0.20
0.20
0.20
0.10
0.25
0.50
0.00
0.00
0.00
0.10
0.10
0.10
0.075
0.15
0.25
0.10
0.10
0.10
0.07 [0.013, 0.13]
0.09 [0.019, 0.17]
0.10 [0.015, 0.20]
0.09 [0.001, 0.22]
0.13 [0.012, 0.27]
0.60 [0.17, 1.05]
0.085 [0.003, 0.17]
0.047 [-0.018, 0.11]
-0.005 [-0.092, 0.082]
0.059 [0.01, 0.11]
0.068 [0.012, 0.13]
0.091 [0.012, 0.18]
0.11 [0.002, 0.25]
0.14 [0.015, 0.29]
0.67 [0.20, 1.16]
0.087 [0.004, 0.17]
0.046 [-0.019, 0.11]
-0.006 [-0.093, 0.082]
0.052 [0.007, 0.10]
0.063 [0.008, 0.12]
0.082 [0.013, 0.16]
0.12 [0.004, 0.28]
0.13 [0.015, 0.28]
0.72 [0.24, 1.24]
0.088 [0.005, 0.17]
0.045 [-0.02, 0.11]
-0.006 [-0.96, 0.082]
ρu
ρi
ρa
ρcg
ρig
ρz
ρτ c
ρτ k
ρτ w
Beta
Beta
Beta
Beta
Beta
Beta
Beta
Beta
Beta
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.20
0.20
0.20
0.20
0.20
0.20
0.20
0.20
0.20
0.38
0.26
0.93
0.76
0.52
0.70
0.64
0.54
0.44
0.44
0.26
0.94
0.77
0.51
0.71
0.65
0.55
0.44
0.45
0.26
0.94
0.77
0.52
0.72
0.66
0.55
0.45
σu
σi
σa
σcg
σig
σz
στ c
στ k
στ w
σM E
Inv.
Inv.
Inv.
Inv.
Inv.
Inv.
Inv.
Inv.
Inv.
Inv.
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
0.10
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
0.038 [0.029, 0.048]
0.059 [0.024, 0.10]
0.014 [0.012, 0.016]
0.014 [0.012, 0.016]
0.10 [0.06, 0.14]
0.016 [0.013, 0.018]
0.021 [0.018, 0.024]
0.058 [0.049, 0.066]
0.034 [0.029, 0.039]
0.02 [0.017, 0.024]
1924.30
Gamma
Gamma
Gamma
Gamma
Gamma
Gamma
Gamma
Gamma
Gamma
Gamma
[1.14, 2.11]
[0.35, 0.69]
[0.27, 0.65]
[0.37, 0.63]
[0.91, 1.02]
[0.33, 1.37]
[3.80, 5.64]
[0.23, 0.53]
[0.041, 0.50]
[0.86, 0.98]
[0.61, 0.90]
[0.22, 0.79]
[0.54, 0.85]
[0.45, 0.82]
[0.36, 0.72]
[0.25, 0.63]
[0.98, 2.01]
[1.21, 2.58]
[0.45, 0.82]
[0.32, 0.71]
[0.22, 0.78]
[0,15, 0.52]
[0.39, 0.71]
[0.25, 0.43]
[0.91, 1.01]
[0.32, 1.36]
[3.80, 5.66]
[0.30, 0.57]
[0.037, 0.50]
[0.87, 0.99]
[0.62, 0.91]
[0.21, 0.80]
[0.56, 0.87]
[0.46, 0.83]
[0.37, 0.73]
[0.25, 0.63]
0.045 [0.035,
0.063 [0.025,
0.014 [0.012,
0.014 [0.012,
0.098 [0.053,
0.016 [0.013,
0.021 [0.018,
0.058 [0.049,
0.034 [0.029,
0.021 [0.017,
1927.59
0.057]
0.11]
0.016]
0.016]
0.14]
0.018]
0.024]
0.066]
0.039]
0.025]
[0.92, 2.11]
[1.36, 2.85]
[0.51, 0.92]
[0.32, 0.72]
[0.061, 0.66]
[0.16, 0.52]
[0.35, 0.68]
[0.91, 1.01]
[0.33, 1.35]
[3.80, 5.65]
[0.28, 0.59]
[0.036, 0.50]
[0.88, 0.99]
[0.63, 0.91]
[0.20, 0.80]
[0.57, 0.87]
[0.47, 0.84]
[0.37, 0.73]
[0.26, 0.64]
0.049 [0.037,
0.066 [0.026,
0.013 [0.012,
0.014 [0.012,
0.095 [0.049,
0.016 [0.013,
0.021 [0.018,
0.058 [0.049,
0.034 [0.029,
0.021 [0.016,
1922.16
0.061]
0.12]
0.015]
0.016]
0.14]
0.018]
0.024]
0.066]
0.039]
0.025]
Note: This table presents the prior distributions and compares the posterior distributions of estimated parameters in the preferred
model (with estimated shared of rule of HtM consumers) to the benchmark model with no HtM consumers, and the model with
fixed 50% proportion of HtM consumers. The values in the square bracket are the 5% and 95% confidence interval of the posterior
mean. Under the structural parameter panel, subscripts r and h represent the group-specific parameters for the Ricardian and
HtM households respectively. Measurement error is introduced into the model to correct for errors in the observables.
Blanchard-Khan conditions, priors for fiscal instruments adjustment to debt, ϑx , follow Beta distribution with mean of 0.20 and standard error of 0.10, which allows them to only take on values between
zero and one to avoid explosive debt path. On the other hand, the priors for fiscal instruments adjustment to output are allowed to follow Gamma distribution, with mean of ςcg , ςz and ςτ w set to 0.10, 0.25
and 0.50 respectively, and standard error of 0.075, 0.15 and 0.25 respectively, suggesting that public
consumption response to output is relatively smaller compared to that of transfers and labour tax,
which are consistent with the domains of estimated values in the literature (see for instance Blanchard
and Perroti, 2002; and Leeper et al., 2010a, for the US; and Coenen et al., 2013, for Europe). With
respect to the parameters of the interactions between shocks to distortionary taxes, ζj , there is no
specifically known priors for these co-terms for the UK or EU. Thus, they were assumed to follow
14
Figure 2. The observables 1987Q1-2010Q2. This figure shows the detrended time series used in the estimation of this model. The
vertical axis measures percentage deviations from the (stochastic) steady-state, represented by the zero-line, while the horizontal
axis is the nth quarter.
Normal distribution with zero mean and small standard deviation of 0.10.
More so, the AR(1) coefficients of exogenous shock processes, ρi , were assumed to follow a Beta
distribution with prior means set to 0.50 and standard deviation set to 0.20, which sufficiently allows
the parameter values to reflect their level of persistence. Finally, an Inverse Gamma distribution was
assumed for the standard deviation of the shocks, σi with the mean and standard deviation set to 0.10
and 2.00 respectively.
4.2
Data and Estimation Procedure
Given the focus of this paper, the model is estimated using the United Kingdom (UK) data spanning
the period 1987Q1 to 2010Q2 (a total of 94 periods), which coincides with the period just before
the implementation of fiscal consolidation policy. The study period is further extended to cover
the consolidation period, 1987Q1-2015:Q3 (a total of 115 periods), so as to check the stability and
robustness of the estimated parameters. Nine observables are used for the estimation, including:
private consumption, hours worked, total investment, government debt, government consumption,
government transfers, consumption tax revenue, capital tax revenue and labour tax revenue. Since
this is an RBC model, all variables need to be in real terms. However, as Pfeifer (2013) noted, the
economic resource constraint, as in equation (19), does not always add up when the components of
national income are expressed in real terms deflated with respective prices. To resolve this issue, the
real variables are computed by deflating the nominal variables with GDP deflator at 2012 prices. The
real variables are then divided by the active population (age 16 to 59/64) to obtain the per capita
variables. The data series were detrended using one-sided HP-filter, and the filtered series were further
15
demeaned.18
Figure 2 shows the stochastically detrended time series of observables. From the figure, it can be
observed that during the financial crisis period 2008Q3 - 2010Q2 (75-94th quarter), all macroeconomic
variables fell below their trend levels, with total investment and government revenues (especially capital
tax revenue) witnessing much larger falls compared to other variables, while the government-initiated
bailout plans aimed at stemming the effects of the crisis led to a rise in government debt above its
trend level, which confirms the earlier argument in this paper. On average, government debt tends to
be highly volatile with large changes over time.
The model is initially estimated in three different versions, inclusive of all fiscal instruments: the
benchmark standard RBC model with no rule-of-thumb consumers (λ = 0), the preferred model
with the proportion of rule-of-thumb consumers estimated (λ ∈ (0, 0.5)), and the model with a fixed
proportion of rule-of-thumb consumers arbitrarily set to 50% (λ = 0.5) as it is the case in most existing
analytical studies. Thereafter, the preferred model is re-estimated to include only specific choice of
fiscal instruments permitted to respond to debt: government consumption only, government transfer
only and labour tax only.
To estimate the model, the observables (the de-trended variables) are mapped directly to the model
variables with a measurement error introduced on the hours. Then, the data likelihood and priors are
combined to maximise the log posterior function using Chris Sims’s optimization routine, followed by
the initiation of the Metropolis-Hasting (MH) algorithm which samples from the posterior distribution
using 1,000,000 draws over two chains, with the first 200,000 draws used as burning period. The MH
jump-scale (step-size) is sufficiently tuned up, for each estimated model, such that it resulted to an
average acceptance rate of 28.24% which is comfortably within the expected band (See Adjemian et
al., 2014). Finally, the Brooks and Gelman’s (1998) convergence diagnostic is performed to ensure
that the MCMC chains converge to unique posterior value.
5
Estimation Results
In this section, the results of the Bayesian estimation are discussed and the impulse responses for
the various forms of the model are analysed comparatively. Sensitivity analysis was also conducted
to check the identification and sensitivity of the estimated parameters (especially the preference and
fiscal adjustment parameters) to alternative model specification.
In accordance with the analysis of An and Schofheide (2007), Canova and Sala (2009), Iskrev
(2010), Ratto and Iskrev (2011) and Pfeifer (2014), the identification strength of the parameters to
be estimated is checked relative to the priors assigned to them in the preceding section, and given the
information contents of the observables (see Appendix 2 for the graphical result of the identification
test). The result shows that all the estimated parameters (in the preferred model) are distinctively
identified, with no serial correlation. This suggests that each estimated parameter plays a distinctively
significant role in the dynamics of the model.
18
The latter process of demeaning is necessary because detrended data from one-sided HP-filter does not sum to zero.
In fact, in most cases, estimation results from the non-demean filtered series always show evidence of unit-roots and
serial correlation.
16
5.1
Posterior Distributions
Table 2 presents the Bayesian estimation results for models with no HtM consumers (the benchmark
model), with estimated proportion of HtM consumers (the preferred model), and with fixed proportion
of HtM consumers. The result shows the posterior mean for each parameter along with the 5% and 95%
confidence interval for the posterior mean. For the non-policy parameters, all estimated values tend to
the relatively stable across the three variant of the model, except for preference and consumption CES
parameters. The mean estimate of the proportion of HtM consumers for the UK economy is about onethird which perfectly coincides with the estimate of 34% in Forni et al. (2009). Regarding Ricardian
households habitual consumption smoothing, current effective consumption is explained by about 5055% of past pair-group (external) effective consumption. The production CES substitution elasticity
between capital and labour is estimated to be 0.96 at mean, which is consistent with the findings of
Cantore et al. (2012) that labour effort (hours) responds positively to technological improvements but
with a less than unitary elasticity of substitution between capital and labour. The mean estimate of the
aggregate capital substitution elasticity is about 0.84, suggesting that public and private capital are
weakly complimentary with strong probability that they could be substitutes, which is also consistent
with the mean estimate of 0.98 by Coenen et al. (2013). For the AR(1) coefficients, only technology
shock, government consumption shock and transfer shock show significant level of persistence with
mean estimates above 0.70.
With regards to the preference parameters, the mean estimate of the CRRA parameter is greater
than unity in all the model variants, which is consistent with estimates found in the literature (see
Smets and Wouters, 2007; Leeper et al., 2010a & 2010b) and implies that household agents are “risk
averters”.19 However, the HtM CRRA is significantly larger than that of the Ricardian households,
which suggests that rule-of-thumb consumers are relatively more risk averse compared to the Ricardian
consumers. This finding therefore contribute a new knowledge to existing literature on another factor
influencing the limited asset market participations of non-Ricardian households – not only are they
financially constrained, but they are also less willing to risk or forego current consumption for future
returns in the financial market. Also, compared to the CRRA in the model with no rule-of-thumb
consumers, HtM CRRA is larger in models with rule-of-thumb consumers while Ricardian CRRA is
lower. Similarly, there are significant differences between Ricardian and non-Ricardian Frisch labour
elasticity. In the model with no rule-of-thumb consumers, the Frisch elasticity is about 0.52, which is
consistent with the estimates found in literature (see Chetty et al., 2011; Reichling and Whalen, 2012;
Peterman, 2014). However, as λ increases, the Ricardian labour elasticity increases systematically
while HtM labour elasticity remains relatively the same. This suggests that, for a given temporary
change in current or future disposable income, Ricardian agents are more likely to vary their hours of
work as the proportion of HtM consumers increases.20 More so, in the benchmark model with λ = 0,
the effective consumption CES elasticity of substitution is about 0.45 with a range between 0.27 to
0.65, suggesting that public and private consumption are complementary. This range comfortably
accommodates Coenen et al. (2013) estimate of 0.37 for the euro area, and Bouakez & Rebei (2007)
estimate of 0.33 for the United States. However, in the variant of the model with rule-of-thumb
consumers, the CES elasticity for HtM households is relatively smaller compared to that of Ricardian
19
The intertemporal substitution elasticity, 1/θi , is less than one
This actually makes economic sense in reality since rich households are more likely to adjust their hours of work as
the proportion of poor people who are willing to work increases
20
17
households, which suggests that HtM households relatively value public goods much more compared
to the Ricardian households.21
Concerning the parameter estimates of the fiscal policy rule, all the chosen fiscal instruments
considerably play significant roles in financing public debt. The policy parameter estimates are all
positive since sign restrictions have been imposed in the fiscal rule ab initio. Contrary to the findings
of Leeper et al. (2010a), labour taxes have the highest response magnitude while government consumption has the least response magnitude. Also, as λ increases, the parameter estimates of fiscal
adjustment to debt gradually diminish in value, implying that fiscal instruments targeted at reducing public debt become weaker as the proportion of HtM agents increases. The implication of this
is that government’s debt-consolidation policy may be frustrated as such policy takes excessive toll
on household finances, leading to more households being financially constrained, thereby causing low
productivity (due to low investment spending), loss tax revenue (especially capital tax), and high
dependence on government resources (e.g. increase in unemployment allowance). More so, labour tax
has a very strong pro-cyclical response to output, compared to the weak counter-cyclical response of
government consumption, suggesting that changes in government spending have weak effect on output
performance. Furthermore, evidence is found in support of simultaneous cross-effects of exogenous
shocks to capital and labour taxes with a range of (0, 0.17), and to some extent between exogenous
shocks to consumption and capital taxes, while no such evidence is found between exogenous shocks
to consumption and labour taxes.
Finally, the Bayesian estimation procedure seem to favour the preferred model, with estimated
share of rule-of-thumb consumers, compared to other specifications since it has the highest log data
density. As Koop (2003) suggests, a model with the highest log marginal density tends to be better,
and should be chosen over other variants of the model but with low log marginal density, provided
they are generated from the same data process. Therefore, the rest of the analysis in this paper is
based on this preferred model.
5.2
Analytical Impulse Responses
Figures 3-5 show the estimated impulse responses to a temporary one standard deviation change
in fiscal policy shocks targeted at financing government debt. The plots also demonstrate how the
existence and proportion of HtM consumers alter the dynamics of the economy in response to fiscal
shocks. The smooth, dashed and dotted-dashed lines respectively represent models with no HtM
consumers, with estimated proportion of HtM consumers (which is about one-third from the estimation
result presented earlier), and with the proportion of HtM consumers fixed ab initio at 50%. In
each plot, the first row contains responses of aggregate macroeconomic variables, the second row
contains responses of agent-specific preference variables, while the third row contains responses of
other variables of interest (factor prices, public debt and fiscal instruments). The standard deviation
of each shock is set to the estimated mean value of the shock scaled by 100, such that the values on
the vertical axis can be directly interpreted as percentage deviation from the steady state over the
different quarters express on the horizontal axis.
In line with the standard RBC theory, Figure 3 shows that a decrease in public consumption
spending, targeted at reducing government debt, contemporaneously raises private consumption due
21
This is particularly true since poor households can not afford private provision of essential commodities or services,
such as education and health, and would rather relying on government provision of such goods.
18
Figure 3. Impulse responses to a negative one standard deviation shock to government consumption in the model with all fiscal
instruments. The smooth line is the model with λ = 0, the dashed line the model with estimated λ ∈ (0, 1) and the dotted-dashed
line is the model with fixed λ = 0.50, where λ is the share of HtM consumers.
Figure 4. Impulse responses to a negative one standard deviation shock to government transfer in the model with all fiscal
instruments. The smooth line is the model with λ = 0, the dashed line the model with estimated λ ∈ (0, 1) and the dotted-dashed
line is the model with fixed λ = 0.50, where λ is the share of HtM consumers.
19
Figure 5. Impulse responses to a positive one standard deviation shock to labour tax in the model with all fiscal instruments.
The smooth line is the model with λ = 0, the dashed line the model with estimated λ ∈ (0, 1) and the dotted-dashed line is the
model with fixed λ = 0.50, where λ is the share of HtM consumers.
to substitution effect which causes households to consume more private goods in compensation for
loss of public goods. Since leisure rises, total labour effort falls on impact while wages rises. As a
consequence, output falls contemporaneously. To stimulate the economy back to equilibrium, interest
rate has to fall, causing crowding-in of private investment, which in turn improves the marginal
productivity of labour. Thus, labour effort rises after second quarter, causing output to rise as well.
This result confirms the findings of Ercolani and Azevedo (2014) which observed that government
spending shock has a counter-cyclical effect on private consumption, but negates the results of Bouakez
and Rebei (2007) and Gali et al. (2007) which observed a procyclical response of private consumption
to government spending shock.
With regards to household-specific dynamics, although total private consumption rises in response
to spending cuts on public consumption, agents’ effective consumption fall. This is because public
consumption plays a significant, non-separable role in the households’ aggregate consumption bundles
(productive government spending). However, HtM effective consumption fall by about four times
relative to that of the Ricardian households. There are two factors responsible for this: (1) The
intertemporal substitution effect augmented with own-group external habit effect in consumption ensures that the Ricardian households effective consumption is partially insured (moderately smoothed)
against shocks, hence the hump-shape in their effective consumption. (2) As the results in Table 2
suggest, compared to Ricardian households, there is a stronger complementarity effect of public goods
in HtM aggregate consumption CES bundle which allows shocks to government consumption spending to have greater effect on HtM aggregate consumption bundle. On the other hand, in response to
government spending shock, while the HtM labour effort falls and remains below its potential level for
20
at least 5 years (20 quarters), the Ricardian labour effort, which initially fell by about twice that of
HtM households, rapidly adjusts back to steady state after just 6 quarters. These differences in labour
supply dynamics across households is possibly driven by different Frisch elasticities across groups of
households, as well as the fact that HtM households cannot intertemporally optimise and would only
offer to work up to the amount that is just sufficient enough to finance their consumption.
Figure 4 depicts the response of the economy to a debt-financing consolidation strategy with cuts in
government transfers. As expected, a one percent standard deviation decrease in lump-sum transfers
leads to a fall in total private consumption. Since the transfer cuts implies decrease in HtM households
income receipts, they substitute leisure for labour, thereby causing total labour hours to rise, while real
wage falls. As a consequence, productivity rises with increase in private investment and output. Since
the rule-of-thumb consumers are the only recipient of government transfer in the model, HtM effective
consumption falls significantly in response to negative transfer shock; on the other hand, the Ricardian
effective consumption rises in response to transfer shocks. This is because, to Ricardian households,
public transfer to the HtM households is equivalent to a lump-sum tax. Thus, the Ricardian labour
effort falls as leisure rises.
In Figure 5, a one standard deviation increase in labour tax shock discourages labour efforts on average due to the negative wealth effect of distortionary taxes, thereby causing output to fall while real
wage rises as demand for labour outweighs supply. As households income falls, private consumption,
as well as agents effective consumption, decline contemporaneously. The positive interaction between
capital and labour tax shocks further interact with the low labour supply to dampen marginal productivity of capital, thereby causing private investment to fall. This result conflicts with a recent study
by Leeper et al. (2010a) which observed that private investment rises in response to labour tax shock
in a model with no productive government spending. More so, as disposable income (which is the
primary source of livelihood for HtM households) falls, HtM effective consumption falls by about three
times as much as that of the Ricardian households in response to labour tax shocks. As a result, HtM
households have to increase their labour effort to compensate for the loss in after-tax compensation.
On the other hand, the increase in labour tax is strong enough to significantly discourage Ricardian
labour effort, which outweighs the rise in HtM labour effort, thus, the average labour effort declines.
Turning the focus to the effect of rule-of-thumb behaviours in the model, evidence from the simulated results presented in Figures 3-5 suggests that the share of HtM consumers in the economy
significantly influence the dynamic response of key macroeconomic variables both at aggregate and
individual households levels. For instance, with the share of HtM consumers estimated at about 34%
in the preferred model, irrespective of the shock hitting the economy, the larger the proportion of
HtM consumers in the economy, the longer the period it takes for government debt to return to steady
state equilibrium. This result further confirms the earlier findings of this paper that debt-consolidation
projections may become ineffective or frustrated over time as fiscal instruments becomes weaker due
to increase in private sector dependence on public resources caused by a rise in the share of financially
constrained households. Also, depending on the shocks hitting the economy, the proportion of rule-ofthumb consumers significantly affects the dynamics of macroeconomic variables. In Figure 4, the larger
the share of HtM consumers, the more amplified is the response of output, total labour, real wage and
Ricardian effective consumption to government transfer shock. This is due to the non-distortionary
nature of government transfer which ensures proportionates amplification of these macro-variables as
the share of HtM consumers (who depends on transfers) increases. Also in Figures 3 and 5, as the
21
share of financially constrained households rises, private investment becomes less volatile and more
persistent. Furthermore, the contemporaneous response of interest rate is negatively influenced by
the proportion of rule-of-thumb consumers, though the amplification fizzle out in the medium run.
This result is consistent with the findings of Amato and Laubach (2003) and Gali et al. (2004) which
concluded that rule-of-thumb behaviours alter monetary policy response.
In summary, the above discussion shows that household agents responds quite differently to government debt-financing fiscal strategies. Irrespective of the choice of fiscal strategy adopted, the
Ricardian labour effort falls in response to government consolidation policy and their consumption
level is higher compared the HtM households. One way to interpret this behaviour is this: government’s fiscal financing of public debt position, which is solely held by the Ricardian agents, translates
into higher interest-income on financial assets (government bond) for the Ricardian households, which
in turn raises their level of consumption, causing leisure to rise while labour falls. On the other hand,
in response to fiscal shocks, HtM agents intensify labour effort in order to meet up with their current
consumption. Overall, compared to the Ricardian households, government’s debt-financing strategies
tend to make HtM households worse off, since they relatively consume less and work more.
5.3
Alternative Fiscal Consolidation Strategies
Table 3 presents and compares the estimated parameters of the preferred model (with estimated
share of rule-of-thumb consumers) to the model where alternative fiscal strategies singly adjust to
public debt. The four models are qualitatively similar across the common parameters. Even the
fiscal adjustment parameters in the alternative models with individual policy instrument are quite
close to that of the preferred model with all fiscal instruments inclusive, save for marginal mark-ups.
The simulated results based on these estimated parameters are presented in Figures 6 and 7. While
Figure 6 contains responses of aggregate macroeconomic variables, Figure 7 contains responses of
agent-specific variables. In each plot, the first row shows responses to cuts in public consumption
spending, the second row shows responses to transfer cuts, while the third shows responses to labour
tax increase.
From these plots, it can be observed that the choice of fiscal consolidation strategy significantly
influences the dynamics of macroeconomic variables. For instance, irrespective of the fiscal shock
hitting the economy, private investment, Ricardian effective consumption and HtM labour hour respond with different amplification magnitudes for different consolidation strategies: while investment
response tends to be more (less) amplified when labour tax only (all instruments) adjusts to debt,
Ricardian effective consumption and HtM labour effort are more (less) amplified when government
consumption (transfers) only adjusts to debt. Also, while responding to spending (public consumption
and transfers) shocks, the amplification magnitude in output and total labour effort tends to be minimised when transfers only adjusts to debt, while the amplification of private consumption response
is minimised when public consumption only responds to debt. Whereas, output, private consumption
and total labour hours seem to be indifferent to choice of consolidation strategy when responding to
labour tax shock, while HtM effective consumption and Ricardian labour do not necessarily adjust
differently to specific consolidation strategies irrespective of the fiscal shock.
The policy implication of this result is that government should selectively adopt fiscal strategies
that maximise responses of specific sectors of the economy or minimise losses of a particular incomegroup of households. This can be achieved by specifically targeting fiscal instruments which the sector
22
Table 3: Posterior mean: Alternative debt-financing strategies
Posterior Mean
Parameter
Structural
Risk aversion
Frisch elasticity
Cons. CES elasticity
Habit formation
Share of HtM
Prod. CES elasticity
Cap. CES elasticity
Adjustment costs
Fiscal Rule
Gov cons. adj. to B
Transfer adj. to B
Labor tax adj. to B
Gov cons. adj. to Y
Transfer adj. to Y
Labor tax adj. to Y
Cap/lab co-term
Cons/cap co-term
Cons/lab co-term
AR(1) Coefficients
Preference
Investment
Technology
Govt consumption
Govt investment
Govt transfer
Consumption tax
Capital tax
labour tax
Std. of Shocks
Preference
Investment
Technology
Govt consumption
Govt investment
Govt transfer
Consumption tax
Capital tax
labour tax
Measurement error
All instruments
Govt cons. only
Transfers only
Labour tax only
θr
θh
ηr
ηh
ϕr
ϕh
κ
λ
ν
ω
φ
1.49
1.88
0.62
0.50
0.46
0.32
0.55
0.34
0.96
0.84
4.70
1.48
1.90
0.60
0.50
0.46
0.32
0.55
0.34
0.96
0.84
4.72
1.48
1.91
0.61
0.50
0.43
0.32
0.55
0.34
0.96
0.84
4.70
1.59
1.92
0.62
0.51
0.37
0.32
0.56
0.35
0.96
0.84
4.71
ϑcg
ϑz
ϑτ w
ςcg
ςz
ςτ w
ζkn
ζck
ζcn
0.059
0.068
0.091
0.11
0.14
0.67
0.087
0.046
-0.006
0.063
–
–
0.11
0.13
0.62
0.084
0.045
-0.002
–
0.075
–
0.10
0.14
0.62
0.084
0.045
-0.003
–
–
0.096
0.11
0.13
0.66
0.087
0.046
-0.007
ρu
ρi
ρa
ρcg
ρig
ρz
ρτ c
ρτ k
ρτ w
0.44
0.26
0.94
0.77
0.51
0.71
0.65
0.55
0.44
0.45
0.26
0.94
0.77
0.49
0.71
0.65
0.54
0.41
0.44
0.26
0.93
0.79
0.52
0.72
0.65
0.55
0.41
0.41
0.26
0.93
0.79
0.53
0.71
0.65
0.55
0.45
σu
σi
σa
σcg
σig
σz
στ c
στ k
στ w
σM E
0.045
0.063
0.014
0.014
0.098
0.016
0.021
0.058
0.034
0.021
0.046
0.063
0.014
0.014
0.096
0.016
0.021
0.058
0.033
0.021
0.046
0.063
0.014
0.014
0.098
0.016
0.021
0.058
0.033
0.021
0.045
0.065
0.014
0.014
0.097
0.016
0.021
0.058
0.034
0.02
Note: This table compares estimated parameters in the preferred model (with estimated share of HtM consumers) to models where
specific alternative fiscal instruments adjust to public debt.
or the income-group is quite indifferent to. With this, the government can successfully finance its
spending without causing significant ripples in the business cycle.
5.4
Fiscal Consolidation and the Time-Path of Government Debt
In this section, the time horizon of debt innovations as financed by government’s choice of consolidation
strategies is discussed. First, it is worth noting from earlier findings of this paper that the government
debt policy is strongly influenced by the proportion of rule-of-thumb consumers in the economy.
Hence, for the purpose of this analysis, only models with estimated share of rule-of-thumb consumers
are considered. Figure 8 shows the time-path of government debt in the preferred model with all fiscal
instruments inclusive (the left panel) compared to cases where specific alternative fiscal instruments
individually adjust to government debt (the right panel). The dashed, dotted-dashed and smooth lines
represent public consumption, transfers and labour tax adjustments to government debt respectively.
The plots simply show the proportion of a one-unit innovation in government debt in quarter t,
23
Figure 6. Impulse responses to fiscal policy shocks (aggregate variables) in the preferred model with all fiscal instruments
compared to models with alternative fiscal instruments as adjustment variables. The dotted, dashed, smooth and dotted-dashed
lines respectively represent models with all fiscal instruments, public consumption only, transfers only and labour taxes only.
Figure 7. Impulse responses to fiscal policy shocks (agent-specific variables) in the preferred model with all fiscal instruments
compared to models with alternative fiscal instruments as adjustment variables. The dotted, dashed, smooth and dotted-dashed
lines respectively represent models with all fiscal instruments, public consumption only, transfers only and labour taxes only.
24
Figure 8. Time-path of public debt in the preferred model and models with alternative fiscal strategies. The left shows the case
where all fiscal instruments adjusts to public debt, while the right panel shows the case where specific alternative fiscal strategies
singly adjusts to public debt.
explained by each of the three fiscal shocks in consideration, fully financed by period t + M , where M
represents the chosen quarters on the horizontal axis.
From these figures, it can be observed that it takes a considerably long period of time for government debt innovations to be fully financed and restored to its steady state equilibrium when all
chosen fiscal instruments simultaneously adjust to debt, and even much longer period when only a
specific instrument adjust to debt. From the left panel, it takes about 80 quarters (20 years) for labour
tax shock to fully restore the present-value balance of government debt, while it takes about 90-100
quarters (23-25 years) for transfers and government consumption to fully finance same one-unit of
debt innovation in the preferred model with all fiscal instruments. This result might not be surprising
as earlier simulated results have shown that labour tax shock affects both the supply (low labour
supply and investment crowd-out) and the demand sides (households consumption and income) of the
economy, thereby causing more leakages in order to finance government debt within a short period of
time. Whereas, for both government consumption and transfers shocks, only the demand sides were
affected significantly, while firms investment demand and output rises; thus, it takes a little longer
period to fully financed debt innovation. In a recent study of government debt-financing strategies for
the United States, Leeper et al. (2010a) found that consumption taxes, capital taxes and transfers
could fully finance debt innovations within 20 to 25 years, while it takes nearly double of that period
(about 40 years or more) for government spending and labour tax adjustments to achieve same feat.
More so, as Carlin and Soskice (2006) have shown, the path of any public debt is determined by
three main factors: productivity level measured by output growth, real interest rate, and the primary
deficit. Hence, given a constant growth of output, a consolidation policy that significantly drives any
component of discounted primary deficit (see equation 10) will sufficiently restore government debt
back to its equilibrium path within the shortest possible time. And this is the case for labour tax
since it directly affects households income (Wt Nt ) and consumption via employment, and indirectly
affects investment via spillover effects on capital tax shock (ζtkn ) - see equation (17).
On the other hand, the right panel shows that none of the alternative fiscal adjustments could fully
finance the present-value balance of government debt independently after 25 years despite initialising
from the same spot as in the previous case with all instruments adjusting simultaneously. But labour
tax adjustments still seem to be much faster compare to transfers and public consumption. However,
25
compared to the preferred model, these models with individual fiscal adjustments seem to adopts
a stronger “cold-turkey approach” within the first 2-3 years and a perpetual gradualist approach
afterwards while financing debt innovations, thereby making them less tenable for policy making
purpose for a government constrained with medium run targets.
In summary, this analysis suggests that the speed at which debt innovation is being offset by government’s fiscal strategies significantly depends on the alternative choice of fiscal instruments employed
and the extent to which such instrument affects households’ preference decisions and productivity,
which in turn have significant implication for the economy. This is consistent with the findings of
Baldacci et al.(2015) which concluded that government should preserve public investment spending in
order to sustain medium-term growth since it enhances productivity on the supply-side of the economy. It is also consistent with the results of Papageorgiou (2012) which asserted that, for effective
consolidation policy, government should increase public investment spending and consumption tax,
but reduce public consumption spending and labour tax.
5.5
Sensitivity Analysis
Table 4 shows the degree of sensitivity of estimated parameters to different specifications of the model
and time. From the results presented in the table, it can be observed that all common parameters
across the various specification are qualitatively similar. Also, their log data densities are practically similar, suggesting that any of the three alternative model specification is acceptable. However,
one feature distinctively stood out in the preferred model: while the model with unified households
preference parameters simply assume that all consumers behave as if they were Ricardians (all preference parameters here perfectly coincides with that of the Ricardian households) even when some
are obviously non-Ricardian, the preferred model, on the other hand distinctively estimated the HtM
preferences, which are significantly different from that of Ricardian households. This distinctive features across groups of households could assist the policy makers to understand the heterogeneous
nature of the constituent households and make well-informed decisional choices targeted at a specific
groups of households rather than a universal policy of “one cap fits all ”. With regards to the model
with Cobb-Douglas production technology, which restricted the degree of substitution between labour
and capital on one hand, and between public and private capital on another hand, the results seem
to slight alter households preferences. Finally, when the estimation period is extended to cover the
consolidation era, the result still remains qualitatively similar, save for some slight adjustments in
the preference parameters, suggesting that the estimated parameters of the preferred model are truly
stable across time - that is, the estimated parameters are time-invariant. The log data density of the
extended model may not be directly compared to others since it was generated from a different, much
longer data series.
6
Summary and Conclusion
Motivated by the recent trend of consolidation policies which are targeted at reducing public debt especially across Europe, this paper analyses the dynamic effects of government debt financing strategies
on the economy, especially as it concerns the degree to which households are financially constrained.
Specifically, the paper aims to analyse the policy responses of different groups of households to fiscal
shocks, how the proportion of financially constrained households influence these responses and the
26
Table 4: Posterior mean: Estimates sensitivity to alternative model specific and time
Posterior Mean
Parameter
Preferred
Structural
Risk aversion
Frisch elasticity
Cons. CES elasticity
Habit formation
Share of HtM
Prod. CES elasticity
Cap. CES elasticity
Adjustment costs
Fiscal Rule
Gov cons. adj. to B
Transfer adj. to B
Labor tax adj. to B
Gov cons. adj. to Y
Transfer adj. to Y
Labor tax adj. to Y
Cap/lab co-term
Cons/cap co-term
Cons/lab co-term
AR(1) Coefficients
Preference
Investment
Technology
Govt consumption
Govt investment
Govt transfer
Consumption tax
Capital tax
labour tax
Std. of Shocks
Preference
Investment
Technology
Govt consumption
Govt investment
Govt transfer
Consumption tax
Capital tax
labour tax
Measurement error
Log data density
Modela
Unified preferencesb
C-D Prod. Func.c
Preferred Model Extendedd
1.55
1.94
0.68
0.51
0.37
0.34
0.58
0.33
0.95
0.85
4.62
θr
θh
ηr
ηh
ϕr
ϕh
κ
λ
ν
ω
φ
1.49
1.88
0.62
0.50
0.46
0.32
0.55
0.34
0.96
0.84
4.70
1.49
0.56
0.33
0.96
0.84
4.70
1.69
1.96
0.67
0.51
0.28
0.31
0.56
0.34
–
–
4.65
ϑcg
ϑz
ϑτ w
ςcg
ςz
ςτ w
ζkn
ζck
ζcn
0.059
0.068
0.091
0.11
0.14
0.67
0.087
0.046
-0.006
0.058
0.068
0.091
0.11
0.14
0.69
0.088
0.046
-0.006
0.053
0.067
0.095
0.13
0.14
0.64
0.086
0.044
-0.004
0.051
0.059
0.099
0.12
0.12
0.61
0.068
0.05
-0.01
ρu
ρi
ρa
ρcg
ρig
ρz
ρτ c
ρτ k
ρτ w
0.44
0.26
0.94
0.77
0.51
0.71
0.65
0.55
0.44
0.44
0.26
0.94
0.77
0.51
0.72
0.65
0.55
0.44
0.41
0.24
0.95
0.77
0.49
0.71
0.65
0.54
0.44
0.39
0.23
0.94
0.78
0.56
0.72
0.61
0.51
0.46
σu
σi
σa
σcg
σig
σz
στ c
στ k
στ w
σM E
0.045
0.063
0.014
0.014
0.098
0.016
0.021
0.058
0.034
0.021
1927.59
0.046
0.064
0.014
0.014
0.098
0.016
0.021
0.058
0.034
0.021
1927.62
0.044
0.070
0.014
0.014
0.095
0.016
0.021
0.057
0.034
0.019
1929.00
0.043
0.060
0.013
0.014
0.095
0.015
0.021
0.062
0.031
0.019
2412.64
0.62
0.47
Note: This table compares estimated parameters in (a) the preferred model over the pre-consolidation period 1987:Q1-2010:Q2
to (b) the model with unified households preferences, (c) the model with Cobb-Douglas production function, and (d) the preferred
model with estimation date extended to 1987:Q2-2015:Q3.
overall effect of alternative fiscal strategies on the economy. To achieve these objectives, the paper
builds on existing studies, such as Gali et al. (2007), Coenen et al. (2013) and Rossi (2014), by developing a heterogeneous agents DSGE model comprising a continuum of Ricardian and rule-of-thumb
households with robust productive fiscal sector. This paper develops a new approach to analysing
household heterogeneity within the DSGE framework by modelling different groups of households
along different preference structure and valuation of public resources, rather than just differences in
wealth endowment as it is case in most existing literature. This new approach is motivated by the
fact that agent-specific responses differ considerably from representative agent responses, and this
distinction is not just driven by differences in wealth endowment, but also by the intrinsic nature of
different groups of households.
The theoretical model was estimated using the Bayesian estimation approach and the results were
simulated to obtain the responses of the economy to specific debt financing strategies, with emphasis
27
on government consumption spending shock, transfers shock and labour tax shock, which characterised the choice of fiscal strategies adopted in the UK recently. The results show that households
differ considerably in preference structure, and their responses to fiscal adjustments vary significantly,
depending on the choice of fiscal strategy.
First, evidence from the estimated results shows that financially constrained (hand-to-mouth)
households are more risk-averse and less likely to adjust their supply of labour in response to small
changes in after-tax compensation compared to the financially unconstrained (Ricardian) households.
The implication of this result for government’s fiscal policy is that: (1) the limited participations
of the HtM households in the asset market is also driven by their nature as being more risk-averse
(that is, the certainty equivalence of returns on wealth is quite low and not compensating enough to
forgone current consumption), and not just because they are financially constrained (poorly endowed)
as earlier portrayed in the literature. Hence, the extent to which government can finance spending
with new bond issuance is further limited. (2) Changes in government taxes strong influence Ricardian households’ decision to work and this effect is propagated into the system through the agents’
intertemporal labour supply. Due to this heterogeneity in preference structure and its implications on
households’ choices, each group of households responds distinctively to government fiscal policy. On
average, compared to the Ricardian households, the non-Ricardian households are made worse off by
government consolidation policy irrespective of the adopted strategy employed, since they consume
less and work more.
Secondly, the proportion of financially constrained households significantly influences the dynamics
of the economy and has strong implications for the achievement of government’s debt-consolidation
plan. From the result, it was observed that fiscal instruments targeted at reducing public debt become
weaker as the proportion of financially constrained households increases, thereby frustrating government’s debt-consolidation plan as more households depend on government resources. Thus, stringent
fiscal measures may not necessarily be the best means to sustainable debt-reduction path. Also,
Ricardian households tend to adjust their labour supply rapidly as the proportion of rule-of-thumb
consumers changes, thereby impacting on private investment and output.
Thirdly, the economy tends to respond differently depending on the choice of fiscal strategy. The
results tend to favour the model where all fiscal instruments simultaneously adjust to government debt
compared to models with individual fiscal adjustment strategies. Responses of aggregate variables
(consumption, investment and output) also vary depending on the choice of adjustment process.
Also, the choice of fiscal strategy significantly affects the rate of adjustment of government debt
to long run equilibrium. On average, for the UK economy, public debt returns faster to steady
state equilibrium with labour tax adjustments compared to adjustments in government consumption
spending or transfer.
In conclusion, this paper shows that the response of different groups of households to government’s
consolidation policy vary considerably, depending on the preference structure and the degree to which
the household is financially constrained, which in turn have important implications for the overall
debt-reduction plan of the government. Therefore, to effectively achieve a growth-consistent debt consolidation plan, government must be cautious in implementing stringent fiscal strategies by selectively
targeting fiscal policy at distinct income-groups that are less responsive to the policy, rather than a
universal policy across the board.
28
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32
Appendix
Appendix -1: Solutions to the Model
First Order Conditions
Ricardian Households:
The first order conditions with respect to the Ricardian consumption, hours, government bond holding,
investment and capital are:
r
ψtu C̃tr − κC̃t−1
−θr
"
C̃ r
(1 − %) tr
Ct
#
1
ϕr
= µrt (1 + τtc )
1
ψtu Ntr ηr = µrt (1 − τtw ) Wt
"
qt ψtI
φ
1−
2
It
It−1
(23)
(24)
βEt µrt+1 Rt = µt
(25)
#
2
µrt+1 It+1
1
It
It
It+1 2
=
+ φβEt qt+1 r
−1
− φqt
−1
−1
It−1
It−1
µt
It
It
1−λ
(26)
i
µrt+1
1 h k
k
k
βEt r
r
− τt+1 (rt+1 − δp ) + (1 − δp )qt+1 = qt
(27)
µt
1 − λ t+1
Hand-to-mouth Households:
The first order conditions with respect to the HtM consumption and hours are:
ψtu C̃th
−θh
"
Ĉ h
(1 − %) th
Ct
#
1
ϕh
= µht (1 + τtc )
(28)
1
ψtu Nth ηh = µht (1 − τtw ) Wt
(29)
where µrt and µht are the Lagrangian multipliers for the Ricardian and HtM households respectively
Firms:
The first order conditions for firms optimal choice of labour and capital inputs are:
ν−1
ν
W t = At
ν−1
rtk = At ν
1
Yt ν
(1 − α)
Nt
#1
1 "
Yt ν
K̃t ω
(1 − γ)
α
Kt
K̃t
33
(30)
(31)
Steady State Solutions
R=
1
β
1−β
+ δp
β(1 − τ k )
ω
g ω−1
ω−1
1 K
1
= γω(
) ω + (1 − γ) ω
K
"
#ν
K̃ ω
α
= k ν (1 − γ)
K
(r )
ν

! ν−1  ν−1
1 1
ν
ν
ν
α
1
K̃

−
=
1−α
1−α
Y
rk =
K̃
K
K̃
Y
N
Y
1
N ν
= (1 − α)/
Y
N
1
= k 1−W
Y
r
K
= δp
Y
I
Cg
Ig
=1− −
−
Y
Y
Y
C
N
K
B
= (1 + τ c ) − (1 − τ w )W − τ k (rk − δp ) − (1 − β)
Y
Y
Y
h
iY
W
K
Y
I
Y
C
Y
Z
Y
h
(1 − τ w )W NY + YZ /λ
Ch
=
Y
1 + τc
r
C
1 C
λ Ch
=
−
Y
1−λY
1−λ Y
r
"
ϕr −1
g ϕr −1 # ϕϕr −1
r
ϕr
ϕr
1
1
C̃ r
C
C
= (1 − %) ϕr
+ % ϕr
Y
Y
Y
 ϕh

h ϕϕh −1
g ϕh −1 ϕh −1
h
1
1
ϕh
h
C
C
C̃

= (1 − %) ϕh
+ % ϕh
Y
Y
Y
34
Linearised Solutions of the Model
Ricardian consumption FOC:
−
θr ˆ r
τc
1 ˆr
r
C̃t − Ĉtr = µ̂rt +
τ̂ c − ψ̂tu
C̃t − κC̃ˆt−1
+
1−κ
ϕr
1 + τc t
Ricardian Hours FOC:
1 r
τw
τ̂ w − ψ̂tu
N̂t = µ̂rt + Ŵt −
ηr
1 − τw t
Ricardian Euler:
µ̂rt = Et µ̂rt+1 + R̂t
Ricardian Consumption CES:
C̃ r
Y
! ϕr −1
ϕr
1
C̃ˆtr = (1 − %) ϕr
Cr
Y
ϕr −1
ϕr
Ĉtr
+%
1
ϕr
Cg
Y
ϕr −1
ϕr
Ĉtg
Investment Equation:
q̂t + ψ̂tI = φ(1 + β)Iˆt − φIˆt−1 − φβEt Iˆt+1
Tobin’s Q:
k
k
q̂t = β(1 − δp )Et q̂t+1 + βrk (1 − τ k )Et r̂t+1
− βτ k (rk − δp )Et τ̂t+1
+ Et µ̂rt+1 − µ̂rt
Private Capital Accumulation:
K̂t+1 = (1 − δp )K̂t + δp Iˆt + ψ̂tI
HtM Consumption FOC:
1 ˆh
τc
−θh C̃ˆth +
C̃t − Ĉth = µ̂ht +
τ̂ c − ψ̂tu
ϕh
1 + τc t
HtM Hours FOC:
1 h
τw
N̂t = µ̂ht + Ŵt −
τ̂ w − ψ̂tu
ηh
1 − τw t
HtM Budget Constraint:
(1 + τ c )
Ch h
Ch c
WNh
WNh w 1 Z
Ĉt + τ c
τ̂t = (1 − τ w )
(Ŵt + N̂th ) − τ w
τ̂t +
Ẑt
Y
Y
Y
Y
λY
HtM Consumption CES:
C̃ h
Y
! ϕh −1
ϕh
1
C̃ˆth = (1 − %) ϕh
Ch
Y
ϕϕh −1
h
Ĉth + %
1
ϕh
Cg
Y
ϕh −1
CES Production Function:
1
Ŷt = Ât + α ν (
1 N ν−1
K̃ ν−1 ˆ
) ν K̃t + (1 − α) ν ( ) ν N̂t
Y
Y
35
ϕh
Ĉtg
Aggregate Capital CES:
K̃
K
! ω−1
ω
ˆ = γ ω1
K̃
t
Kg
K
ω−1
ω
1
K̂tg + (1 − γ) ω K̂t
Real Wage:
Ŵt =
ν−1
ν
Ât +
1
Ŷt − N̂t
ν
Rental Cost of Capital:
r̂tk
=
ν−1
ν
Ât +
1
ˆ + 1 K̃
ˆ − K̂
Ŷt − K̃
t
t
t
ν
ω
Public Capital Accumulation:
g
K̂t+1
= (1 − δg )K̂tg + δg Iˆtg
Government Budget Flow:
B
C g g I g ˆg Z
c C τ̂ c + Ĉ +τ w W N τ̂ w + Ŵ + N̂ +τ k (r k −δ ) K τ̂ k + K̂ +
Ĉ
I
Ẑ
+
B̂
=
τ
+
+
p
t
t
t
t
t
t
t
t
t
t
t
Y
Y
Y
Y
Y
Y
Y
β YB B̂t+1 − R̂t
Debt Ratio:
B̂t = ŝbt + Ŷt
Consumption Aggregation:
C
Cr
Ch
Ĉt = (1 − λ) Ĉtr + λ Ĉth
Y
Y
Y
Labour Hour Aggregation:
N̂t = (1 − λ)N̂tr + λN̂th
Economy Resource Constraint:
Ŷt =
C
I
C g g I g ˆg
Ĉt + Iˆt +
Ĉ + It
Y
Y
Y t
Y
36
rk
rk −δ
k +
r̂
t
p
Appendix -2 Parameter identification test for the preferred model with estimated share of HtM
consumers
37
Appendix -3 Priors vs Posterior Distributions
38
Appendix -4 Shocks Decomposition
(a) Output
(b) Consumption
(c) Investment
(d) Hours
(e) Real Wage
(f) Govt Debt
39