Banque de France Working Paper #643 September 2017

Time-varying fiscal spending multipliers in the UK

Christian Glocker1, Giulia Sestieri2 & Pascal Towbin3

September 2017, WP #643

ABSTRACT

We study fiscal spending multipliers of the UK economy using a time-varying parameter factor augmented vector autoregressive (TVP-FAVAR) model. We show that government spending multipliers vary over time and that most of the variation is cyclical: multipliers are typically above one in recessions and below one in expansions. Regarding the drivers of the cyclical variations, our results are consistent with theories emphasizing the role of financial frictions and economic slack. We find no evidence that multipliers are larger at the zero lower bound. Structural factors seem to play a lesser role and multipliers do not exhibit a clear trend. We conclude that policy recommendations based on average multipliers that do not take into account the position of the economy in the cycle are potentially misleading and that the impact of government spending shocks is rather limited in the UK in non-recessionary periods.4

Keywords: Government spending shocks, Fiscal transmission mechanism, Time-varying parameter models, Business cycle

JEL classification: C32, E62, H30, H50

1 Austrian Institute of Economic Research, christian.glocker@wifo.ac.at 2 Banque de France, giulia.sestieri@banque-france.fr 3 Swiss National Bank, pascal.towbin@snb.ch 4 The authors would like to thank Laurent Ferrara, Christian Kleiber, Matthieu Lemoine and seminar participants at the Banque de France for helpful comments and discussions. We are very grateful to Valérie Ghiringhelli for outstanding research assistance. The views, opinions, findings, and conclusions or recommendations expressed in this paper are strictly those of the author(s). They do not necessarily reflect the views of the Banque de France, the Eurosystem or the Schweizerische Nationalbank (SNB). The institutions take no responsibility for any errors or omissions in, or for the correctness of, the information contained in this paper.

Working Papers reflect the opinions of the authors and do not necessarily express the views of the Banque de France. This document is available on publications.banque-france.fr/en

Banque de France Working Paper #643 ii

NON-TECHNICAL SUMMARY

In this paper, we study whether the effect of fiscal stimuli on economic activity – the so-called government spending multiplier – varies over time, taking the example of the UK. The UK is an interesting example since in its recent economic history there have been several moments characterized by intense debates about how changes in government spending may affect the economy. In 2008, the UK was one of the major advanced countries, together with the U.S., who implemented a strong counter-cyclical fiscal expansion as a response to the financial crisis. The reversal of the fiscal stimulus, begun in 2010, has given rise to a harsh debate on austerity. Currently, there is again a debate on whether a renewed fiscal stimulus is appropriate to contain the potential negative effects of the Brexit implementation on economic growth. The debate mentioned above clearly illustrates that it is important to understand if and why government spending multipliers vary over time. Economic theory offers a number of reasons why fiscal spending multipliers may be time-varying, with different policy implications. On the one hand, there are cyclical theories that predict that government multipliers should be larger in recessions, when there is a lot of spare capacity in the economy and people are credit constrained. On the other hand, structural theories, linking for example the multipliers to the degree of trade openness or the degree of fiscal space, predict that the multipliers should vary only slowly over time following structural changes in the economy. In this paper, we employ an econometric framework (a time-varying parameter factor augmented vector autoregressive model, TVP-FAVAR) that is flexible enough to distinguish cyclical variations from structural drivers and rich enough to discriminate between different explanations for time variation.

UK fiscal spending multiplier for output (2-year cumulative multiplier)

Source: authors’ computations.

Banque de France Working Paper #643 iii

Our results show that UK government spending multipliers vary over time and that most of the variation is cyclical. They are typically above one in recessions and below one in expansion periods. By contrast, they do not exhibit a visible structural trend. When we dig deeper to understand which factors drive the cyclical variation, our results indicate that both spare capacity and credit constraints play a significant role. Typically, the larger impact on output in recessions is accompanied by strong effects on private sector credit generation, suggesting that fiscal expansions help relieving credit constraints in this particular state of the world. Our findings do not support the zero lower bound hypothesis for the UK, as spending multipliers in the Great recession are not found to be higher than in other recessions where the policy interest rate was not constrained at zero. Given the evidence from our model, we conclude that policy recommendations based on average fiscal multipliers may be misleading, as several factors should be taken into account to gauge the effects of fiscal stimuli to the economy. In particular, we find that in non-recessionary periods the impact of fiscal spending shocks is limited, while it is much larger in recession, suggesting a cautionary tale for fiscal policy to stimulate output in the UK in expansions or to consolidate in recessions.

Multiplicateurs de dépenses publiques au Royaume-Uni et leur évolution dans le temps

RÉSUMÉ Nous étudions les multiplicateurs de dépenses publiques au Royaume-Uni en utilisant un modèle autorégressive à facteurs FAVAR à coefficients variables dans le temps. Nous montrons que les multiplicateurs de dépenses publiques varient dans le temps et que la plupart de cette variation est cyclique : les multiplicateurs sont typiquement supérieurs à un dans les périodes de récession est inférieures à un dans les périodes d’expansion. En ce qui concerne les moteurs des variations cycliques, nos résultats sont en accord avec les théories économiques qui mettent l’accent sur le rôle des frictions financières et des capacités excédentaires dans l’économie. Nous ne trouvons pas d’éléments de preuve à l’appui de l’hypothèse que les multiplicateurs soient plus élevés quand les taux d’intérêts sont proches de la borne du zéro. Certains facteurs structurels semblent joueur un moindre rôle dans l’évolution des multiplicateurs budgétaires dans le temps, ces derniers ne présentant pas de tendance claire. A la lumière de ces résultats, nous concluons que les recommandations de politique économique basées sur des valeurs moyennes des multiplicateurs, ne prenant pas en compte la position de l’économie dans le cycle, sont potentiellement trompeuses. Par ailleurs, l’effet sur les variables macroéconomiques de chocs de dépenses publiques semblerait plutôt limité au Royaume-Uni dans des périodes non récessives.

Mots-clés : chocs de dépenses publiques, mécanisme de transmission budgétaire, modèles à paramètres qui varient dans le temps, cycle économique.

Les Documents de travail reflètent les idées personnelles de leurs auteurs

et n'expriment pas nécessairement la position de la Banque de France. Ce document est disponible sur publications.banque-france.fr

1. Introduction

In this paper we investigate if and why government spending multipliers vary across

time, taking the example of the United Kingdom over the past fifty years. This paper

contributes to the empirical literature on fiscal policy by using an econometric framework

flexible enough to distinguish cyclical variations from structural changes in fiscal spending

multipliers and rich enough to discriminate between different transmission mechanisms

proposed by the economic theory.

In the recent economic history of the UK there have been several moments characterized

by intense debates about how changes in government spending may affect the economy.

In 2008, the UK was one of the major advanced countries, together with the U.S., who

implemented a strong counter-cyclical fiscal expansion as a response to the financial crisis.

The reversal of the fiscal stimulus, begun in 2010, has given rise to a harsh debate on

austerity. Advocates of austerity were of the view that the measures were necessary to

ensure the confidence of financial markets about the sustainability of public debt (Rogoff,

2013) and could possibly crowd-in private consumption and investment (Trichet, 2010).

Opponents criticised that the program would put at risk the timid recovery and feared

large negative effects, arguing that fiscal multipliers were particular large at that moment

because of the presence of idle economic resources and of monetary policy being con-

strained by the zero lower bound (Krugman, 2015). Currently, there is again a debate on

whether a renewed fiscal stimulus is appropriate to contain the possible negative effects

of the Brexit implementation on economic growth.

Understanding whether the effects of fiscal policy actions may vary according to the

position of the economy in the business cycle is indeed important as the debate mentioned

above clearly illustrates. Economic theory offers a number of reasons why fiscal spending

multipliers may vary over time, which result, accordingly, in different policy implications

and prescriptions. They can be broadly divided into two groups: cyclical theories and

structural theories.

Prominent examples of cyclical theories put forward three explanations for time vari-

ation: economic slack, financial frictions and the zero lower bound on interest rates.

According to the economic slack hypothesis, government spending multipliers should be

larger in recessions because government spending can mobilize idle resources without gen-

erating inflationary pressures (Michaillat, 2014). The financial friction theory emphasizes

access to credit rather than idle resources. Financial frictions increase in recessions and

impede the access of the private sector to credit. Government spending alleviates these

frictions through its stabilizing effect on output (Canzoneri et al., 2016a; Galı et al., 2007).

1

2

The zero lower bound hypothesis posits that at the zero lower bound central banks will

not tighten monetary policy to contain inflationary pressures generated by positive fiscal

shocks, as they would otherwise. This could create larger multipliers (Coenen et al., 2012;

Christiano et al., 2011; Woodford, 2011).

On the structural side, explanations for time-variation in fiscal multipliers include trade

openness and the amount of fiscal space, among others. The trade integration theory

predicts a downward trend in the size of fiscal multipliers, as higher trade integration

should increase the share of the government spending impulse that leaks abroad through

higher imports. According to the fiscal space theory, government spending multipliers

should be larger when governments have more time to stabilize debt after an expansion,

i.e., when public debt or the interest rates payments on debt are low (Nickel and Tudyka,

2014; Perotti, 1999).

To shed light on the time-variation of UK government spending multipliers and their

drivers, we estimate a time-varying parameters factor augmented vector autoregressive

model (TVP-FAVAR) and identify government spending shocks. Our results show that

UK government spending multipliers vary over time and that most of the variation is

cyclical. They are typically above one in recessions and below one in expansion periods.

By contrast, they do not exhibit a visible structural trend. Regarding the different de-

mand components of GDP, the increase of the multiplier in recession is mainly driven by

the behaviour of investment, which contributes positively in recession, while it responds

negatively or negligibly in normal times. The positive effect on consumption is also sub-

stantially larger in recessions. The amplifying effects of consumption and investment are

dampened to some extent by a stronger response of imports.

Regarding the drivers of the cyclical variations, the results of the model are consistent

with theories emphasizing the role of financial frictions and economic slack. Typically,

the larger impact on output in recessions is accompanied by stronger effects on private

sector credit generation, suggesting that fiscal expansions help relieving credit constraints

in this particular state of the world. Regarding economic slack, we do find that prices

are somewhat less sensitive to spending stimuli in recessions, although the evidence for

this channel is weaker. Finally, our findings reject the zero lower bound hypothesis, as

we do not find UK spending multipliers in the Great recession being higher than in other

recessions where the policy interest rate was not constrained at zero.

As an additional exercise, we then regress the time series of the estimated UK ouput

multiplier on a number of potential cyclical and structural determinants. The results

from this regression confirm that cyclical factors account for most of the variation, in

particular the output gap and the real policy rate, which is suppose to capture the degree

3

of monetary policy accommodation. We also find a role for structural factors, in particular

the government interest payments to GDP (a proxy for fiscal space) and the import ratio.

These structural effects remain, however, of second order importance in explaining the

variation of the multiplier over time when compared to the effect of more cyclical drivers.

With regard to the existing literature, our technique to estimate time-varying param-

eters (Primiceri, 2005; Koop and Korobilis, 2010; Del Negro and Primiceri, 2015) allows

for both short term - cyclical - variations and long term - structural - changes. This is

different from studies that model the multiplier as a function of output to investigate cycli-

cal variations only (Auerbach and Gorodnichenko, 2012a,b; Riera-Crichton et al., 2015)

and from papers using rolling regression techniques to investigate structural changes only

(Cimadomo and Benassy-Quere, 2012). To our knowledge, there are only few papers that

employ time-varying parameter models to study fiscal policy question. These studies,

however, are generally limited to the use of small scale time-varying VAR models (Berg,

2015; Cleaud et al., 2013; Rafiq, 2014).

The use of a large scale factor model in this paper has two main advantages. First, it

allows us to track the responses of a large number variables to a government spending

shock, including the main components of GDP, as well as price and credit variables. This

allows us to better assess which channel is most relevant to understand time-variation

in UK government spending multipliers. Second, and more technically, factor models

increase the amount of information considered, thereby addressing the limited information

problem from which many small scale VARs suffer (Bernanke et al., 2005; Forni and

Gambetti, 2014). A special variant of the limited information problem is fiscal foresight

(Fragetta and Gasteiger, 2014), i.e. economic agents might have anticipated the increase

in government spending. To address the problem of limited information, factor models

have been applied to fiscal policy questions by Forni and Gambetti (2010) and Fragetta

and Gasteiger (2014). These studies do not allow, however, for time-variation.

Most of the research on time-variation in government spending multipliers has focused

on the U.S. (Auerbach and Gorodnichenko, 2012a; Bachmann and Sims, 2012; Ramey

and Zubairy, 2014).1 Whether there is actually time-variation remains, however, still

controversial (see for instance Ramey and Zubairy (2014)). Our study is one of the few

that analyses the UK. The UK economy is interesting for several reasons. As pointed out

above, it is one of the major countries where the debate about fiscal stimulus and austerity

was particularly intense in recent years. Second, the UK economy exhibited significant

cyclical variations and structural changes over the period considered. It suffered from

1See Berg (2015) and Cleaud et al. (2013) for evidence on Germany and France.

4

severe recessions in the 70s and during the last financial crisis, liberalized its financial

sector in the beginning of the 80s with the so-called ’Big Bang’ reforms, and its public

debt displayed large swings. This makes it an interesting case to test different theories.

Among the studies that have analysed the time-variation of UK government spending

multipliers, Cimadomo and Benassy-Quere (2012) have employed rolling regressions in a

VAR with global factors. They find positive fiscal multipliers in the 70s and 2000s but

insignificant multipliers in the 80s and 90s. According to their analysis this is mainly due

to several important structural changes occurred in the economy over these two decades.

Differently from them, our results do not suggest that UK fiscal multipliers incurred

significant structural changes over this period, the high value of the output multiplier in

the 70s and 2000s being largely explained by the three recession episodes occurred in these

two decades. Rafiq (2014) uses a small scale Bayesian time-varying VAR model to study

UK fiscal multipliers, finding support for the fact that government multipliers are larger

in recessions than in expansion periods. Our findings are broadly consistent with this

result, but our TVP-FAVAR model is flexible enough to allows us to study both cyclical

variations and structural changes in fiscal multipliers and to perform a refined analysis of

the mechanisms behind their variation.

The rest of the paper is organized as follows: section 2 presents the model and the

data, detailing the estimation of the factors, the identification scheme and the multipliers’

definition used in the paper. Section 3 presents and discusses the main empirical results

of the model while section 4 focuses on the possible transmission channels and tries to

assess their respective importance in the case of the UK economy. Section 5 presents

some robustness exercises and section 6 concludes. Technical details on the estimation

technique and more information on the database are left to the Appendix.

2. The model

The time-varying parameters factor augmented vector autoregressive (TVP-FAVAR)

model used here closely follows Koop and Korobilis (2010) and Korobilis (2013) and the

description here is kept relatively short.

In general, FAVAR models are a hybrid between dynamic factor models (DFM) and

the standard structural vector autoregressive (SVAR) model: a joint VAR is specified for

some factors ft [k × 1] that are extracted from a large panel of time series Xt [nx × 1]

and some observable policy variables yt [ny × 1]. Factor models allow to work with high

dimensional data, as the approach extracts the common dynamics from a wide set of time

series Xt. The FAVAR Model consists of a state and an observation equation.

5

The FAVAR state equation describes the joint dynamics of the factors ft and the ob-

servable policy variables yt. This system of equations is capturing the main dynamics of

the economy and modelled as a VAR:

(I − Φt(L))

ft

yt

= ut(1)

ut ∼ N(0,Ωut )(2)

where ut is the time t reduced form shock. The error term ut has mean zero and

a variance-covariance matrix Ωut . Φt(L) is a matrix polynomial of order p. Both the

regression coefficients as well as the covariance are allowed to vary over time.

The observation equation specifies the relationship between the individual time series

Xt and the the vector of the variables of the state equation. Specifically, Xt depends on

the state vector [ft, yt] and an idiosyncratic component et:

Xt =[

Λf Λy

] ft

yt

+ et(3)

et ∼ N(0,Ωe)(4)

Ωet = diag

((ωe1)2, ..., (ωenx)

2)

(5)

where Λf [nx × k] denotes the matrix of factor loadings of the factors ft and λy [nx × ny]

the matrix of the parameters of the observable variables yt. The error term et has mean

zero and a variance-covariance matrix Ωe, which is assumed to be diagonal.

Note that the time variation in the model is restricted to the FAVAR state equation, i.e

to the relationship between the common factors driving the economy. Since the observa-

tion equation of the FAVAR model does not feature any time-varying parameters, a two

step estimation method as in Korobilis (2013) can be employed to estimate the factors

and their loadings.

The modelling of time variation in the state equation follows the specifications employed

for time-varying structural VARs (Primiceri, 2005; Del Negro and Primiceri, 2015). In

particular, we allow for time variation in the regression coefficients Φt and in the covariance

matrix Ωut . The covariance matrix is thereby decomposed into on diagonal and off-diagonal

elements.

(6) Ωut = A−1

t Σt

(A−1t Σt

)′

6

where Σt = diag(σ1,t, . . . , σk+ny ,t) and At is a lower triangular matrix with ones on the

main diagonal:

(7) At =

1 0 . . . 0

a(2,1),t 1. . .

......

. . . . . . 0

a(k+ny ,1),t . . . a(k+ny ,k+ny−1),t 1

We stack the dynamic system given in equation (1) into the matrices Φt = (φ

′1,t, . . . , φ

′p,t),

where φ′i,t ∀i ∈ 1, . . . , p represents the vector of coefficients of the i’s equation in (1),

at = (a′

(i,1),t, . . . , a′

(i,i−1),t) ∀i ∈ 1, . . . , k+ny, σt = (log(σ1,t), . . . , log(σk+ny ,t)), and follow

Primiceri (2005); Del Negro and Primiceri (2015) by assuming that the drifting parameters

(Φt, at and σt) follow independent random walks:

(8)xt = xt−1 + εxt

εxt ∼ N(0, Qx)

∀ x ∈

Φ, a, σ

where εxt ∀ x ∈ Φ, a, σ represent innovation vectors for the associated parameter

vectors. We closely follow Primiceri (2005); Del Negro and Primiceri (2015) and impose

that the matrix Qa is block-diagonal, where each block’s parameters refer to separate

equations. Each block consists of the coefficients a(i,j),t which are in the same row as in

At.

2.1. The data. The time series used to estimate the TVP-FAVAR model were down-

loaded from Datastream and cover the period from 1960 to 2015, at quarterly frequency.

The data set includes a total of about eighty UK time series, ranging from standard

macroeconomic series (output and its components, employment series, production inde-

ces, inflation measures, etc.), financial series (effective exchange rates, interest rates on

loans and deposits, stock prices, etc.) and series of governmental expenditure and taxes.

Table 2 in the Appendix B provides details of each series along with classification codes.

To achieve stationarity, some of the series were transformed. More details concerning

these transformations can be found in the Appendix B.

2.2. Estimation of the model. Following Korobilis (2013) the FAVAR model is esti-

mated using a two-step procedure. In the first step, the common components of ξt =[f ′t y′t

]′, are determined and the static observation equation is estimated.2 In a second

2In the paper we only consider constant factor loadings. See also Korobilis (2009), the working paper

version of Korobilis (2013), who finds that the strongest evidence for the parameters to vary over time

applies to the dynamic equation (1), while the parameters in the observation equation (3) show only a

modest amount of variation over time.

7

step, the dynamic state equation is estimated, treating the factors as observed variables.3

We model time-varying relationships between the common components using the tech-

niques developed for time-varying VARs. While it possible to estimate dynamic factor

models with one step estimators, using likelihood-based or Bayesian techniques, such

estimations become quickly computationally demanding if the cross-section is large or

parameters are time-varying4.

To estimate the FAVAR model we choose two factors according to the Bai and Ng (2002)

information criterion BIC3 (notation as in Bai and Ng (2002)) to the sample covariance

matrix of Xt. The factors are estimated using the first k = 2 principal components of Xt.

The variable considered in the vector of the policy variables yt is government consumption

expenditure. Hence yt is a scalar and the state equation of the model is three-dimensional.

We choose a lag length of one in the state equation, to have a parsimonious lag structure

for the time-varying model5.

In the observation equation (3) there are nx independent equations, so we can sample

the parameter matrices Λf and Λy equation-by-equation. We use uninformative priors.

In the state equation (1) all time-varying parameters are sampled sequentially using

the Gibbs sampler. As explained in Korobilis (2013) and Koop and Korobilis (2010), con-

ditional on the principal components estimates and the estimated parameters in equation

(3) each time-varying parameter can be sampled from a conditionally Normal density

using standard state space filter and smoothing techniques (see for instance Carter and

Kohn (1994), Durbin and Koopman (2001)). Gibbs sampling is carried out in four steps,

drawing in turn time varying coefficients (ΦT ), simultaneous relations (AT ), volatilities

(ΣT ) and hyperparameters (QΦ, Qa, Qσ), conditional on the observed data and the rest of

the parameters. Following Cogley and Sargent (2002, 2005), Primiceri (2005); Del Negro

and Primiceri (2015) and Canova et al. (2007) we reject unstable draws - thus enforcing

a stationarity constraint on the VAR.

Following the literature we set informative priors for the regression coefficients Φ0 and

the covariance matrix Ω0 in the initial period, as well as for the hyperparameters Qx that

determine the variance of the drift of the parameters. The priors are set on the basis of

a training sample from 1960:Q1 to 1965:Q4. Details are in the Appendix A.

3Bai and Ng (2006) show in a frequentist setting that factors estimated via principal components can

be treated as observed, if the panel is sufficiently large in both dimensions.4Bates et al. (2013) show that the principal components estimator remains consistent in models with

parameter variation if the variation is not too large5Time-varying model quickly run into problems with overparametrization. This is why most of the

literature chooses few lags (see for instance Korobilis (2013) and Amir-Ahmadi et al. (2015) and the

references therein).

8

We burn the first 2 million draws of the MCMC iterations and then take every 40th

draw. We introduced multiple checks to ensure that the MCMC algorithm has converged.

First, we run the algorithm for multiple initial random seed numbers and starting values.

Second, we calculate the autocorrelation of the draws and inefficiency factors as in Geweke

(1992). We conclude that our results are not subject to convergence problems. Details

about the convergence statistics are reported in Appendix A.4.

2.3. Identification of the government spending shocks. Our identification of the

government spending shock applies the scheme of Blanchard and Perotti (2002) using

methods developed for dynamic factor and FAVAR models (Stock and Watson, 2005,

2015).

The observation and state equation of the FAVAR system can be unified into the fol-

lowing joint expression:

X1t = Λ1 [Φ(L)ξt + ut] + e1

t

= Λ1Φ(L)ξt + Λ1ut + e1t(9)

where X1t are the first k+ny variables of the time series panel (in our case k+ny = 3).

The extended error term ut := Λ1ut has the following statistical properties: ut ∼ N(0, Ωut )

with Ωut := Λ1Ωu

t (Λ1)′. We proceed by taking the Cholesky decomposition of the variance-

covariance matrix of the extended error term ut:

(10) Ωut = Ht ·H ′t

which implies that the structural error term εt is given by:

(11) εt := H−1t · ut = H−1

t · Λ1ut

where the structural errors are orthonormal E [εtε′t] = I. In our identification scheme

government spending is the last (i.e., k + nyth) variable of the vector X1t . Since Ht is

a lower-triangular matrix by construction, the ordering of the variables in X1t entails

that government spending does not respond within a quarter to macroeconomic shocks

(Blanchard and Perotti, 2002). In our case X1t consists of the following variables: pri-

vate household consumption expenditures, total investment, and government consumption

expenditure, all in real terms; and we impose that government spending does not contem-

poraneously respond to variation in consumption and investment. We also experimented

with various alternative set of variables for identification. We found the results where not

sensitive to these assumptions and that the quantitative differences were minor.

9

2.4. Definition of government spending multipliers. We consider the responses of

economic variables to an increase of government spending that amount to one percent

of GDP. As the share of government spending with respect to GDP varies over time we

need to rescale the impulse responses of output (and the other variables) to a government

spending shock by the government spending share. The size of the output response

may then be interpreted as spending multiplier, that is GDP increases by x percent if

government spending increase by one percent of GDP. Our main specification considers

the impact over two years.

More technically, let xk(Ξt) denote the output response, that is, the impulse response

function at horizon k of the TVP-FAVAR estimates as of period t, gk(Ξt) the corresponding

government spending response, and µt the government expenditures share of output; in

each case Ξt comprises all coefficients and variance-covariance matrix estimates of the

TVP-FAVAR model as of time t. The measure for the fiscal multiplier considered is the

so-called cumulative multiplier and takes the following form:

(12) CMP|t =P∑j=1

xj(Ξt)

µt ·∑Pd

j=1 gj(Ξt)

where Pd is set to one. There is one degree of choice here though, namely the length of

the horizon P over the impulse response functions. As discussed in section 5 our results

are robust to alternative definitions.

3. Time Variation in UK Government Spending Multipliers

This section shows evidence that the effects of government spending shocks on output

and its main aggregate components vary over time. We look at government spending

multipliers at two-year horizons over the sample from 1966:Q1 to 2015:Q4. For the same

set of key variables we also show the impulse response functions averaged over the full

sample as well as for specific dates of interest. A deeper analysis of the drivers of time-

variation is left to the following section.

3.1. Time-varying fiscal spending multipliers. Figure 1 shows cumulative govern-

ment spending multipliers over two years (see equation (12), P = 8) for output and its

main aggregate components (private consumption, total investment, imports and exports,

all in real terms). The cumulative multipliers for the GDP deflator and for a measure

of credit to the private sector (including both nominal credit to households and to non-

financial corporates, divided by the GDP deflator) are also displayed. These two responses

will be useful for our discussion on the transmission mechanisms in Section 4.

10

In each graph, the solid line refers to the median of the posterior distribution of the

impulse response functions and the gray shaded area represents the 68 percent error bands.

The gray bars in turn indicate recession episodes where recessions are defined as at least

two consecutive quarters of negative GDP growth.

Figure 1 highlights some important insights:

(1) The government spending multiplier for output shows a significant degree of vari-

ation over time and most of that variation is cyclical. In general, during and around

recession episodes, the multipliers tend to increase in size. An exception is the recession

of the early 90s, where no increase in the value of multipliers is observed. Section 4 will

deal with this episode in more detail.

(2) A model specification based on the assumption of constant coefficients would im-

ply a mis-specification. The average value of the multiplier over the sample is clearly

below one (0.43), suggesting substantial crowding out effects. However, it is important

to differentiate between recessions, where the average multiplier is above one (1.15), and

non-recession periods, where the average multiplier is below one (0.33).

(3) The cyclical variation of the output multiplier is driven by private consumption and

investment, whereas the behaviour of imports moderate the variation. In order to investi-

gate which component of output drives the variation, we look at consumption, investment,

exports and imports separately. The time profile of the multipliers of consumption and

investment display a qualitatively similar pattern and are larger in recessions. In line with

its general business cycle properties, the amplitudes of the swings of the multiplier for

investment are larger. It is on average close to zero in expansionary periods, suggesting

the existence of crowding-out effects. In recession, however, it is clearly above one. The

multiplier for consumption is positive over the entire sample, consistent with what found

by Galı et al. (2007). The multiplier for imports is positive and statistically significant

over the entire sample, consistent with the idea that part of a fiscal stimulus leaks abroad,

as higher output increases the demand for imports. The reaction of imports is stronger in

recessions, in line with the stronger response of output and hence higher import demand.

This moderates the expansionary effect of fiscal policy on output. The exports multiplier,

by contrast, is stable and close to zero over the entire sample. This result is consistent

with the idea that, in a small open economy, exports depend mainly on exogenous foreign

demand.

(4) There is no visual evidence of structural changes in the size of multipliers over time.

Across the various decades, the multipliers for output, consumption and investment are

on average below unity, with spikes around recession years. The two-year cumulative

government spending multiplier for output has an average value of 0.98 in the 1970s, 0.21

11

in the 1980s, 0.27 in the 1990s, and 0.45 in the rest of the sample. The decrease in the

magnitude of the multiplier from the 1970s to the 1980s has been documented also by other

studies, see in particular Cimadomo and Benassy-Quere (2012). In this paper, however,

they study the variation of the output multiplier over time using rolling regressions. This

leads them to explain the fall in its size in the 1980s as the result of a structural change

of the economy that materialized with the appearance of non-Keynesian effects on output

in the context of the fiscal consolidation carried out under the government of Margaret

Tatcher. What our results highlight instead is that the higher value of the GDP multipliers

in the 1970s is primarily due to the two severe recessions that occurred in this decade, in

other words by short term effects that raised the average value of the multiplier for the

whole decade. We do not find evidence of significant structural changes in the size of the

multiplier over time.

3.2. Impulse response functions. Figure 2 shows the impulse response functions (IRFs)

to a government expenditure shock for the same set of variables shown in section 3.1 over

the first 8 years (32 quarters). The previous subsection focused on multipliers over a two-

year horizon, whereas Figure 2 allows us to investigate whether the effects vary across

different horizons, i.e. whether persistence is affected. The IRFs reported here were used

to construct the fiscal multipliers discussed in the previous section. The black line in each

graph is the median of the posterior distribution and the dotted lines the 68 percent error

band of the posterior distribution. The size of the shock is normalized to one percent of

GDP.

The charts in the first row show the average impulse response functions over the whole

period from 1966:Q1 to 2015:Q4. On average, an increase in government spending is asso-

ciated with an increase in output, consumption and investment of similar magnitude. The

reaction of these variables occurs rather quickly and tends to be persistent. Consumption

and investment display a qualitatively similar pattern, with consumption reacting weaker

and investment reacting stronger than output. In line with the more volatile nature of

investment, its IRF is less persistent than the response of consumption. A part of the

fiscal stimulus spills to foreign countries as the response of imports is positive and highly

persistent.6 Overall, the results for the full sample are consistent with the constant coef-

ficient VAR literature (cf., for instance, Galı et al. (2007), Blanchard and Perotti (2002)

and Mountford and Uhlig (2009)).

6The exports response, which we do not report here to save space, is small in magnitude and not

significantly different from zero over the entire horizon as well as at specific dates of interest.

12

Rows 2 to 6 of Figure 2 show the impulse response functions for some selected years,

corresponding to different phases of the UK business cycle. In light of the results in the

previous section, we chose three years out of the four severe recessions experienced by

the UK economy over the sample: 19747, 1990 and 2008. We also look at two expansion

years: 1998 and 2015. It can bee seen that the response of government spending itself

follows a similar pattern in expansion and recession. This suggests that the variation

in the response of GDP and ist other components is not driven by a variation in the

persistence of the government shock.

Consistently with what we have seen in Figure 1, the effects on output are particularly

strong in recessionary years 1974 and 2008, whereas they are much weaker in expansionary

years 1998 and 2015. In addition, it can now be seen that the effects of government

spending shocks are not only stronger in recessions, but also more persistent. In the

two selected expansionary years, output returns to its pre-shock path relatively quickly,

while in the two recessionary periods, output stays above its pre-shock path for the entire

horizon considered. As regards the subcomponents of output, the observed pattern is

again driven by consumption and investment. In 1974 and 2008 the effect on investment

is large and persistent, whereas in 1998 and 2015 the response is insignificant on impact

and turns negative over the medium term. This is consistent with the idea that there

are strong crowding out effects for investment in normal times. The initial response of

consumption is positive both in recessions and expansions, but in expansions the reaction

is more short-lived and turns statistically insignificant after about two years. As shown

in Figure 1, the response of output in 1990 is different from the other recessions and

resembles the response of the expansionary years. This suggests that the government

multiplier does not increase automatically in every recession. The next section analyses

the drivers of time-variation and treats in more detail the case of the 1990 recession.

4. The transmission mechanism

Starting from the evidence from the previous section that most of the variation of the

UK government spending multipliers is of cyclical nature, this section looks at different

transmission channels that may generate this type of variation and tries to assess their

respective importance in the case of the UK economy. In section 4.1 we review some

possible theories that generate fiscal multipliers that vary over the business cycle. We

also briefly recall some structural determinants that may influence the size of the fiscal

multipliers over time. In section 4.2 we first discuss how the results shown in section

3 may support the different transmission channels. We then investigate empirically the

7Results for the 1979 recession episode are qualitatively and quantitatively similar to those of 1974.

13

relevant factors for the time variation in spending multipliers by regressing the estimated

series of fiscal spending multiplier for output described in section 3.1 on a set of plausible

theory-based determinants. We conclude by providing a decomposition of the fitted values

from the regression into the contribution of each regressor.

4.1. Theoretical views on the determinants of spending multipliers. Economic

theory offers a number of reasons why the government spending multiplier of output

may vary over time in a cyclical manner. Three transmission mechanisms are worth

being examined in the case of the UK economy: the presence of economic slack, the

existence of financial frictions, and monetary policy being constrained at the zero lower

bound. According to the economic slack hypothesis, fiscal multipliers should be larger

in recessions, because of the existence of idle resources in the economy that government

spending can mobilize without generating inflationary pressures. In a boom, by contrast,

the economy is at full capacity and resources are scarce. The role of slack in influencing the

optimal level of fiscal stimulus has been recently investigated in a labor market model by

Michaillat (2014). These state-dependent effects may be also augmented by second round

effects. The expansion in good times may bring the economy closer to or even above the

full employment equilibrium putting upward pressure on prices. In economies following

inflation targeting, nominal rates would then increase in order to dampen inflation and

increase real rates. On the contrary, the stimulus in recession brings about much smaller

inflationary effects as the economy is operating at low capacity, reducing the need for

monetary authority to react. The monetary policy stance, which can be measured by

the gap between the real policy rate and an ’equilibrium’ or ’natural’ rate of interest, is

hence an additional factor that may dampen or amplify cyclical movements in government

spending multipliers.

According to the financial frictions hypothesis, financial frictions increase in recessions

and restrict the financial market access to the private sector. Government spending alle-

viates these frictions through its stabilizing effect on output. This mechanism is modelled

for instance in Canzoneri et al. (2016b). Fissel and Jappelli (1990) pointed out that the

share of households which face limited asset market participation strongly co-moves with

the financial cycle. As a consequence the share of households with limited asset mar-

ket participation is high in recessions. This puts upward pressure on the economy-wide

marginal propensity to consume resulting in higher fiscal spending multipliers. A related

mechanism is described in Galı et al. (2007), where a higher share of liquidity constrained

agents increases fiscal multipliers. Relatedly, as regards episodes of elevated financial

market stress, it is argued that fiscal policy could help lessen financial market frictions,

14

thereby lifting fiscal multipliers (see, e.g. Corsetti et al. (2013) and Rafiq (2014), among

others). A caveat to this hypothesis is that, if financial market stress coincides with fiscal

stress, i.e., situations in which investors are concerned about the sustainability of public

debt, increased spending may well be less effective since risk premia are likely to rise.

Recent papers have also studied the effect of fiscal policy when monetary policy is at

the zero lower bound. Away from the zero lower bound, the central bank will tighten

monetary policy in response to a government spending impulse to contain inflationary

pressure. This is not the case at the zero lower bound. Accordingly, interest rates will

not respond to a government spending shock, generating larger multipliers. The role of

the zero lower bound has been theoretically investigated by, for instance, the works of

Eggertsson (2011), Christiano et al. (2011), Woodford (2011) and Coenen et al. (2012).

Apart from theories linking fiscal multipliers to the business cycle, a series of structural

determinants may also influence the size and evolution of multipliers. Standard open-

economy versions of the IS-LM undergraduate model argue that the size of the spending

multiplier depends, inter alia, on two structural factors: (1) the propensity to save and

(2) the degree of trade openness. In particular, comparative statics suggests that the

multiplier is large when the saving rate is low and the degree of trade openness is low.

Under these conditions, leaks are predicted to be small and multipliers large.8

The degree of fiscal space is another factors that may influence the size of fiscal multipli-

ers. In particular, the level of public debt and the interest expense on this debt may have

an impact on fiscal multipliers. Some studies find that the overall cumulative effect of a

spending shock on real GDP is positive and significant at moderate debt-to-GDP ratios

but null or negative as the ratio increases (see for instance Nickel and Tudyka (2014)).

When public debt is high, Ricardian agents would expect that the fiscal consolidation

that follows a fiscal stimulus is imminent. Accordingly, they will spend less and save

more than in the case in which public debt is low.

8The exchange rate regime or the degree of financial liberalization are two additional factors that

may influence fiscal multipliers. Standard open-economy theory, such as the Mundell-Fleming model,

predicts that government spending multiplier should be larger under a fixed exchange rate regime. Under

flexible exchange rate the additional demand leads to an appreciation of the currency, a loss in external

competitiveness and a deterioration of the trade balance, resulting in a lower overall effect on output. In

this paper we do not explore this channel empirically since the UK economy has experienced a flexible

exchange rate regime under most of the sample considered. According to the financial liberalization

hypothesis, government multipliers exhibit a downward trend (Kirchner et al., 2010), as increased liber-

alization strengthens the Ricardian consumption smoothing motive in response to government spending

shocks, which would in turn dampen the response of output. We do not test this channel in the paper.

15

4.2. Which factors drive the variation of UK fiscal multipliers? Results in Fig-

ures 1 and 2 give a first insight about which transmission channels may be important

in explaining the cyclical variation of UK fiscal multipliers. The findings seem mainly

consistent with the financial frictions theory. The multiplier for credit displays a strong

business cycle dependency. The large effects of government spending shocks on economic

activity during recessions are accompanied by large effects on

to the private sector, suggesting that a fiscal expansion in downturns relieves credit

constraints to the private sector.

We also find more limited evidence for theories that emphasize the role of economic

slack. The multipliers for prices and output tend to move in opposite directions during

recessions. While the effect of a positive government expenditure shock is on average infla-

tionary over the sample, the GDP deflator multiplier is somewhat lower during recessions

(see Figure 1), suggesting that fiscal expansions do bring about smaller effects in periods

where the economy is operating at low capacity. However, the results in Figures 1 and

2 also show that the statistical evidence for the cyclical variation in price multipliers is

rather weak. Confidence bands about the responses of the GDP deflator typically increase

in recession (the impulse responses are not significant) and compared to this uncertainty,

the magnitude of the cyclical variation appears rather small.

Finally, the results do not support the notion that the fiscal multipliers are larger at

the zero lower bound. The output spending multiplier in the Great recession of 2008 is

smaller than in the recessions of the 70s, where interest rates were further away from zero.

In what follows we will test empirically the relevance of different transmission channels

for the UK economy in a more rigorous way. The discussion in the previous section on

the possible importance of various cyclical and structural determinants to explain the size

and the variation of fiscal spending multipliers gives rise to testable hypotheses. First, to

test the hypothesis that spending multipliers may be higher the higher the share of credit

constraint agents in the economy, we construct a measure of ’credit impulse’, equal to the

year-on-year change in the stock of credit to the private sector relative to nominal GDP.

Second, to test the economic slack hypothesis that spending multipliers may be lower if

output is close or above its potential level, it would be optimal to include a measure of the

capacity utilization rate. In the absence of such a variable dating back to 1970, we use a

measure of the output gap instead, taken from the OECD. We also include the real policy

interest rate as a proxy for the monetary stance, constructed as the difference between

the Bank of England policy rate and the contemporaneous CPI inflation rate. This allows

us to capture the ’real’ monetary policy accommodation, with high real interest rates

expected to be associated with lower multipliers. To gauge the effect of financial market

16

stress on the value of fiscal multipliers, we use a financial market stress indicator taken

from Corbet and Twomey (2014).

To test whether some structural determinants may influence the size of fiscal multipliers,

we also consider the following variables: i) the households saving ratio, with higher ratios

expected to be associated with lower multipliers; ii) the import ratio (constructed as the

ratio of imports to GDP, in nominal terms), with a higher ratio also expected to lead

to a smaller multiplier due to a bigger share of the domestic stimulus leaking abroad;

and iii) interest rate payments on public debt over GDP9 as a proxy for fiscal space,

with higher payments expected to be associated with lower private spending because of

higher expected future taxes. A more detailed description of these variables is provided

in Appendix B.

Figure 3 shows the explanatory variables used in the regression and discussed above.

We also control for a constant term, a time trend and use lagged values of the regressors

to address the problem of reverse causation from the output multiplier to the business

cycle. We finally add a dummy variable in order to control for monetary policy being at

the zero lower bound (a dummy equal to 1 starting from 2009:Q1 when the UK policy

rate reached the floor of 0.5%).

In what follows we test the different transmission mechanisms by means of a linear

Bayesian regression analysis carried out over the sample going from 1970:Q1 to 2015:Q4.

We take as dependent variable the 2-year cumulative government spending output multi-

plier described in Section 3.1.

The regression equation takes the following form:

(13) yt = αyt−1 + β′xt−1 + εt

where yt is the two-year cumulative output multiplier and xt−1 is the vector of regressors.

We specify diffuse prior densities for both the mean and the standard deviation of

the regression coefficients. The regression equation is estimated using a Gibbs sampling

algorithm with 5,100 draws dropping the first 100 draws (see Geweke (1993) for details).

The estimation is carried out for each draw of the Ξt matrices from the Bayesian TVP-

FAVAR model, that is, each draw of the spending multiplier is used once in the regression

analysis. This procedure allows us to account for two sources of uncertainty, one stemming

from estimation uncertainty of the coefficients in the regression, the other from the fact

that the left-hand side variable in the Bayesian linear-regression model is estimated and

hence prone to measurement errors due to the estimation uncertainty resulting from the

TVP-FAVAR model.

9The annual series is taken from the UK Institute for Fiscal Studies

17

The results of the regression exercise are provided in Table 1 and correspond to the long-

run impact of the regressors on the UK cumulative output multiplier. In other words,

the estimates of β depicted in the table are based on the long-run specification of the

estimation equation: β = β/(1 − α). The point estimates of the regression coefficients

are the median of the corresponding posterior distribution. The statistical significance of

the regression coefficients is shown by two different error bands: the 68% error band as

well as the 95% error band. The Durbin-Watson statistic as well as the adjusted R2 are

median values too.

The results in Table 1 confirm that cyclical variables can account for the time-variation.

In particular, we find evidence for a role of credit constraints, economic slack and the

stance of monetary policy. These coefficients have the expected sign and are statistically

significant at the 95% level. A positive output gap has a negative effect on the value of the

UK fiscal multiplier, confirming that the amount of slack in the economy do matter for the

effectiveness of a fiscal stimulus to the real economy. In a similar vein, the credit-impulse

measure is negatively associated with the size of the spending multiplier, confirming the

evidence from Figure 1 and 2 on the importance of credit constraints. If we associate a

low credit impulse with a high share of non-Ricardian agents in the economy, this implies

that the degree of limited asset market participation matters for the effectiveness of fiscal

policy. Finally, a low real policy rate increases the output multiplier, suggesting that

multipliers are larger when monetary policy is loose. The financial stress indicator does

not enter significantly, hence providing no support to the hypothesis that financial market

stress is connected to the size and the dynamics of UK fiscal spending multipliers. The

dummy for the zero lower bound episode does not show up significantly either, in line

with previous visual evidence that output multipliers did not increase at the zero lower

bound.

Regarding the influence of structural variables, we find evidence that the measures of

fiscal space and trade openness affect the size of the multiplier. Both the import ratio

and ratio of government interest payments to GDP enter negatively and are statistically

significant, as suggested by the theory. The savings ratio enters with the sign predicted

by Keynesian textbook theory, but it is only weakly statistically significant (at 68 %

level). Overall, these results indicate that structural factors also play a role. This was not

evident by just looking at the time profile of the output multiplier in Figure 1. However,

as we will show below, cyclical factors remain more important than structural factors to

explain multiplier’s time-variation.

To conclude our empirical analysis, we provide a decomposition of the fitted values from

regression (13) into the contribution of each regressor. Figure 4 shows the contribution of

18

Table 1. Estimated parameters from the Bayesian linear regression

Saving ratio −23.72[−61.23 −5.75][−115.45 0.23]

Import ratio −31.98[−118.36 −8.04][−167.84 −2.52]

Output gap −36.98[−186.78 −4.02][−279.02 −0.49]

Real policy rate −9.16[−31.82 −3.02][−49.44 −1.57]

Credit impulse −5.72[−28.01 −2.43][−36.53 −0.72]

Interest payments −13.54[−20.13 −8.25][−103.17 −3.41]

Financial stress 0.24[−0.90 0.41][−1.72 0.98]

ZLB −4.02[−15.02 1.81][−21.57 2.94]

Trend 0.02[−0.12 0.19][−0.35 0.28]

Constant term 10.47[2.73 39.24][0.93 54.98]

Standard Error 0.01[0.00 0.08][0.00 0.47]

Observations 184

Durbin-Watson 1.95

Adjusted R2 0.93

Notes: The dependent variables is the posterior distribution of the various fiscal spending multipliers for output

defined in Section 3.1 and shown in Figure 1. All regressions are estimated using a Gibbs sampling algorithm with

5,100 draws and 100 omitted draws, which leaves us with with 5,000 total draws for the regressions coefficients.

The Bayesian estimation carried out here takes the uncertainty of the dependent variable into account: For each

draw of the multipliers we estimate one Bayesian linear regression model - each with 5,000 draws saved. This

exercise is carried out for all the 9,000 draws of the posterior distribution of the multipliers which leaves us with

45,000 total draws for the parameter estimates present in this table - the point estimates refer to the median

of the posterior distribution of the corresponding parameters. The statistical significance of the regression

coefficients is shown by two different error bands: the 68 % error band as well as the 95% error band. The

Durbin-Watson statistic as well as the adjusted R2 are median values too.

each regressor in explaining the variation of the output multiplier over time. Consider the

subplot of regressor i, the graph shows the time series of the cumulative output multiplier

generated by our TVP-FAVAR model (equal to the solid line in Figure 1), next to the

gap (black bars) between the predicted values (1) once using all values of regressor i for

computing the predicted value relative to a measure for the predicted value (2) when

regressor i is kept fixed at its mean value. Note that since the series are correlated,

19

the plots should not be interpreted as a counter-factual simulation, but to provide some

intuition about the contribution of a variable in a particular period.

Several results are worth mentioning:

(1) The output gap variable is explaining an important part of the cyclical variation of

the multiplier, with spikes at each recession episode, including the 1990 one.

(2) The real policy rate seems to be one of the key factor behind the small value of the

fiscal spending multipliers in the 1980s and 1990s, including the 1990-91 recession episode.

The fall in the size of the multiplier for output at the beginning of the 1980s and its small

value throughout this decade and the following one correspond well to the strong increase

observed in the real rate over the same period, and are consistent with the negative and

persistent contribution of this variable to the fitted value of our regression. In fact, the

negative contribution of the real policy rate outweighs the positive contribution from the

output gap during the recession episode of the early 90, explaining why this recession is

indeed different from the others in our sample.

(3) The contribution of the credit variable is small, suggesting a smaller role than

expected of this variable in explaining the UK output multiplier evolution. The contri-

bution of credit is however positive during the Great recession of 2008-09, comforting the

idea that the fiscal stimulus helped alleviating the credit crunch experienced by the UK

economy at that time.

(4) Interest payments on government debt contributed positively to the fitted values of

the UK output multiplier during the past 15 years. This is true also from 2008 onwards,

even though government debt has skyrocketed during the same period passing from about

40% of GDP in 2007 to about 90% of GDP in 2015. This was made possible by an economic

environment characterized by very low interest rates as a result of the very accommodative

monetary policy stance carried out by the UK central bank and suggests that the UK had

still a positive fiscal space in 2015.

(5) The contributions of the saving ratio and in particular of the import ratio are

small, confirming the idea that, although these structural parameters of the economy

are significant and have the expected sign in the regression, they are of second order

importance to explain the size and the variation of the UK output multiplier over time.

To summarize, the results from our regression show that that cyclical factors account

for most of the variation, in particular the output gap and the real policy rate. Among

the structural factors, government interest payments to GDP (a proxy for fiscal space)

are the most important factor, whereas the import ratio plays a smaller role.

20

5. Robustness

We check the robustness of our results across various dimensions. First, as there is

nothing like the fiscal multiplier we investigate the extent to which different measures

for fiscal spending multipliers change the picture of the multipliers outlined in Figure 1.

Furthermore, we also check the robustness of our results with respect to the stationarity

restriction of the VAR parameters in the FAVAR model, the extent to which different

horizons for the multiplier matter for the regression results presented in section 4.2, the

sensitivity of the results with respect to the calibration of certain prior hyper-parameters

and, finally, we make a comparaison of our results using a time-varying parameter ap-

proach with the results from a simpler rolling regression approach.

5.1. Different measures for the multipliers. It is important to note at this stage

that the fiscal multipliers are not unique. In this sense there is no such thing as a fiscal

multiplier per se. Against this background, we consider several different measures for

fiscal spending multipliers, which the literature has so far focused upon. Each of these

measures has their advantages and disadvantages but considering various measures for

the fiscal spending multiplier allows us to judge the robustness of our preferred measure

described in equation (12).

In addition to the cumulative multiplier, we consider the following measures:

Maximum Multiplier. This corresponds to the maximum output response over a P

period horizon divided by the impact response of government spending (see for instance

Bachmann and Sims (2012), among others):

(14) MMP|t =max (xP(Ξt))

µt · g0(Ξt)

Present Value Multiplier. The present value multiplier is similar to the cumulative

multiplier but extended with a discount factor rt which is the real interest rate (ex post),

equal to the the Bank of England policy rate minus the CPI inflation rate. This implies

that the multiplier at time t is expressed in terms of period P = 0 units (see, e.g.,

Mountford and Uhlig (2009), among others).

(15) PVMP|t =P∑j=1

(1 + rt)−jxj(Ξt)

µt ·∑P

j=1(1 + rt)−jgj(Ξt)

Impact Multiplier. Our final measure relates the initial output response to the impact

size of the government spending shock (see, for instance, Blanchard and Perotti (2002);

Bachmann and Sims (2012) among others):

(16) IMP|t =x0(Ξt)

µt · g0(Ξt)

21

These four different definitions of fiscal spending multipliers are distinct measures for

the effectiveness of fiscal policy. Note that they are different to each other as long as

P > 0. For P = 0, that is, in the period when the shock originates, they are identical.

Figure 5 shows the path of the different output multipliers as defined previously. The

results highlight that different definitions of fiscal multipliers basically give the same

picture. All of the three additional measure have a high correlation with the cumulative

multiplier described in section 2.4.

5.2. Calibration of the priors. This subsection investigates the role of priors for our

results. As detailed in Appendix A, priors need to be specified about the regression

coefficients at the beginning of the estimation period (initial states) as well as the degree

to which these coefficients can change over time. Our baseline priors are as follows:

Φ0 ∼ N(

Φ0,OLS, 4 · V ar(

Φ0,OLS

))(17)

A0 ∼ N(A0,OLS, 4 · V ar

(A0,OLS

))(18)

σ0 ∼ N(σ0,OLS, Iny+k

)(19)

QΦ ∼ IW(k2QΦ· 40 · V ar

(Φ0,OLS

), 40)

(20)

Qa ∼ IW(k2Qa· 2 · V ar (A0,OLS) , 2

)(21)

Qσ ∼ IW(k2Qσ· 4 · Iny+k, 4

)(22)

The parameters with subscript OLS correspond to the point estimates of a training

sample from 1960:Q1 to 1965:Q4. Furthermore, we set kQΦ= 0.01, kQa = 0.01, kQσ =

0.01. Choosing a value of 0.01 for the hyperparameters corresponds to a standard error

of the innovations in the random walk processes that describe the evolution of the time-

varying parameters in equation (3) equal to 1% of the standard error of the OLS estimates

(see for instance Stock and Watson (1996) and Cleaud et al. (2013)).

While the choice of the priors for the initial states is completely innocuous, the selection

of the hyperparameters kQΦ, kQa and kQσ is more important. It is worth noting that

they do not parameterize time variation, but just prior beliefs about the amount of time

variation. In large samples, as usual, the posterior mean converges to the maximum

likelihood estimator. But with limited data, posterior inference is affected by the choice

of the hyperparameters. Our values for kQΦand kQσ correspond to those in the literature

(Stock and Watson, 1996; Cogley and Sargent, 2002; Primiceri, 2005). kQa is set smaller

than standard (the standard value in the literature is 0.1). As detailed below, we found

that the results become volatile and unstable with the standard calibration and therefore

22

chose a parameter that implies less variation in the off-diagonal matrices of the covariance

matrix.

In the left panels of Figure 6 we contrast our results for the cumulative output multiplier,

as depicted in Figure 1, with estimates based on different values for all hyperparameters

(kQΦ, kQa and kQσ). The figure shows the baseline result jointly with the confidence

intervals. Additionally, we plot in green the median value of the fiscal output multiplier for

alternative calibrations of the hyperparameters (four times smaller and four times larger).

We observe that once choosing higher or smaller values, though still in a reasonable range,

our results remain basically unchanged. In particular, the difference in the estimates of

the fiscal multiplier are not statistically significant, as shown in the bottom part of the

panels (note that, for all models, the same random draws are used). The main difference

is that in the case of a higher value for the hyperparameters, the confidence intervals

expand noticeably (see Stock and Watson (1996); Cleaud et al. (2013), among others, for

similar findings).

The right panels in Figure 6 show the sensitivity of the results with respect to kQa

only. Changing this hyperparameter within a reasonable range leaves our results fairly

unchanged. However, if we were to increase this parameter up to a value close to 0.1, as it is

standard in the literature, then the results of the median multiplier would become volatile

and confidence bands increase considerably. The difference to our baseline specification

remains, however, statistically insignificant.

5.3. Imposing a stationarity restriction. The MCMC algorithm for the VAR coef-

ficients of the FAVAR model includes a restriction as specified in equation (39) outlined

in section A.3 of the Appendix. This extension discards draws that do not satisfy the

stationarity conditions. Though this condition is commonly used in time-varying param-

eter models, it might at times be difficult to defend from an economic point of view. In

particular, there may have been instabilities in the effects of fiscal policy during some

specific periods of time. In this context, Cogley and Sargent (2002) were the first to

propose the imposition of a prior restriction on the VAR coefficients saying that draws

from the Gibbs sampler which do not satisfy the stationarity conditions are discarded.

The downside of imposing a stationarity restriction is that this may in turn deplete the

amount of variation in the data in response to a potentially large amount of unstable

draws. Against this background, we check the sensitivity of our results to the stationarity

restrictions. We do so by re-estimating the TVP-FAVAR model without the stationarity

restriction and compare the new results with those outlined in Figures 1 and 2.

23

The comparison indicates that there are no significant differences to the previous results.

This applies to all variables captured in Figure 1. As a whole, imposing the stationarity

restriction on the VAR parameters of the FAVAR model induces only negligibly small

changes to the results documented in section 310.

5.4. Horizon of the the multipliers. Finally, we also performed various extensions to

the Bayesian linear regression model presented in section 4.2. The first element of choice

therein is the length of the horizon P of the cumulative multiplier. We extended the

horizon P from eight in several steps up to 32 which corresponds to eight years. None of

the regressors’ sign changed. Moreover, also the evidence concerning the level of statistical

significance outlined in Table 1 remained unchanged11.

5.5. Estimate of the multiplier based on a rolling-regression approach. In this

section we compare our estimation approach to the simpler alternative of using rolling

regressions. We estimate the model as depicted in equations (1)-(5) with a rolling window

of 80 quarters. We leave the size of the window fixed and move it iteratively forward with

each new observation. Having estimated the model we calculate the output multiplier as

depicted in equation (12). As in our baseline approach the factor loadings are kept fixed.

Figure 7 shows the corresponding path of the multiplier jointly with a 68-confidence-

band. Overall, the results indicate that a rolling regression approach might lead to mis-

leading inference about the evolution of the spending multiplier. While the approach

confirms that the fiscal multiplier has increased after 2008 recession, the increase is de-

layed and occurs when the recession has ended. Before the global financial crisis, the

estimation suggests a slight structural downward trend, contrary to our finding using a

time-varying parameter approach. The confidence band is on average rather wide and

would at times even consider a negative value for the output multiplier as reasonable.

Compared to our time-varying parameter method, we cannot make any statements about

the multiplier in recession during the Seventies, as they are part of the initial window.

Finally, we found that that exact profile of the multiplier to be sensitive to the size of the

window. Naturally, a shorter window size produced more volatile and imprecise estimates

of the multiplier.

6. Conclusion

So, do UK fiscal spending multipliers vary over time? Based on the results from our

TVP-FAVAR model estimated over the past 50 years, it looks like they do. To summarize,

10The results are available upon request.

11The results are available upon request.

24

we find that government spending multipliers are typically above one in recessions and

below one in expansion periods, so that most of their variation is of cyclical nature. This

applies to output, as well as to other demand aggregates, such as private consumption,

investment and imports. In contrast, price multipliers tend to decrease in recessions,

although statistical evidence for such variation is weak. Regarding the drivers of the

cyclical variation, our results are consistent with theories emphasizing the role of financial

frictions and economic slack. We find no evidence instead for recent theories arguing that

multipliers should be larger at the zero lower bound. The role of monetary policy, however,

is relevant. In particular, the degree of monetary accommodation, measured by the level

of the real policy rate, is an additional factor driving the size of the UK output multiplier,

in particular in the 80s and 90s. Finally, we find that UK multipliers do not exhibit a

clear trend and that structural factors play a lesser role than cyclical ones in explaining

their variations.

Although our econometric framework is flexible enough to distinguish cyclical variations

from structural changes in fiscal spending multipliers and rich enough to discriminate

between different transmission mechanisms, other relevant questions related to the broad

topic of the effects of fiscal policy to the economy remain beyond the scope of this paper.

In particular, we do not explore the composition of fiscal adjustments in assessing their

effects on output since we only consider shocks to government consumption expenditure.

Some papers have emphasized that the composition between spending and tax shocks

does matter for the size of fiscal multipliers (cf., for instance, Alesina et al. (2016)), as

well as the role of more disaggregate fiscal instruments, such as public investment, wages,

transfers or different types of taxes (cf., for instance, Alesina et al. (2015)). Another factor

we ignore in this paper is the response of taxes to government spending shocks, so that

the overall fiscal policy effect may be different. Finally, since we estimate a one-country

model, we discard international feedback effects other than those captured by the response

of UK imports, as well as possible cross-country fiscal spillover effects. We can assume

however that, being the UK a small open-economy, such effects should be limited.

Given the evidence from our model, we conclude that policy recommendations based

on average fiscal multipliers may be misleading as several factors should be taken into

account to gauge the effects of fiscal stimuli to the economy. In particular, we find that in

non-recessionary periods the impact of fiscal spending shocks is limited, while it is much

larger in recession, suggesting a cautionary tale for fiscal policy to stimulate output in the

UK in expansions or to consolidate in recessions.

25

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Appendix A. Markov Chain Monte Carlo (MCMC) estimation

In this appendix we explain the Bayesian estimation and the simulation of the observa-

tion and state equation of the TVP-FAVAR model, i.e., equation (3) and (1), and provide

diagnostic checks for the convergence of the Markov Chain Monte Carlo algorithm. We

refer to Primiceri (2005); Baumeister et al. (2008); Del Negro and Primiceri (2015) and

Baumeister and Peersman (2013) for a more detailed outline.

A.1. Simulating the observation equation. There are nx independent equations in

equation (3), so we can sample the parameter matrices Λf and Λy equation-by-equation.

Subsequently, we have nx univariate regression models and a standard conjugate prior that

can be used for the parameters is the Normal-Gamma (Koop et al., 2007). In particular,

we use a non-informative prior of the form:

Λf ∼ N(0, ζ · I)(23)

(ωei )−2 ∼ Γ(α, β)(24)

where Ωe = diag((ωe1)2, ..., (ωenx)

2). We specify uninformative values for the parameters

α, β and ζ.

A.2. Prior distributions for the TVP-FAVAR state equation. As regards the prior

distributions, we closely follow Primiceri (2005); Del Negro and Primiceri (2015) and

Korobilis (2013). The choice of the prior distributions is established on the basis of

conjugate priors, which are introduced in order to keep the computations of the high

dimensional posterior distributions tractable. We use the first 6 years (from 1960:Q1 to

1965:Q4) to calibrate the various prior distributions. The mean and the variance of Φ0

are chosen to be the OLS point estimates (Φ0,OLS) and four times its variance in a time

invariant VAR model, estimated on the small initial training sample. In the same way, a

corresponding prior density for A0 can be obtained. For Σ0 , the mean of the distribution

is chosen to be the logarithm of the OLS point estimates of the standard errors of the same

time-invariant VAR model, while the variance-covariance matrix is arbitrarily assumed

to be the identity matrix. Finally, degrees of freedom and scale matrices are needed for

the inverse-Wishart prior distributions of the hyperparameters. The degrees of freedom

are set to four for Qσ and two for Qa. The reason why the degrees of freedom are

chosen differently is that for the inverse-Wishart distribution to be proper the degrees

of freedom must exceed the dimension respectively of Qσ and Qa. For QΦ the degrees

of freedom are set to forty (Primiceri, 2005; Del Negro and Primiceri, 2015). Following

the literature Cogley (2005); Cogley and Sargent (2005) and Cogley and Sargent (2002),

among others, the scale matrices, QΦ, Qσ and Qa are chosen to be constant fractions of

31

the variances of the corresponding OLS estimates on the initial subsample (multiplied by

the degrees of freedom, because, in the inverse-Wishart distribution, the scale matrix has

the interpretation of a sum of squared residuals). Summarizing, the priors take the form:

Φ0 ∼ N(

Φ0,OLS, 4 · V ar(

Φ0,OLS

))(25)

A0 ∼ N(A0,OLS, 4 · V ar

(A0,OLS

))(26)

σ0 ∼ N(σ0,OLS, Iny+k

)(27)

QΦ ∼ IW(k2QΦ· 40 · V ar

(Φ0,OLS

), 40)

(28)

Qa ∼ IW(k2Qa· 2 · V ar (A0,OLS) , 2

)(29)

Qσ ∼ IW(k2Qσ· 4 · Iny+k, 4

)(30)

The results are obtained using the following values: kQΦ= 0.01, kQa = 0.01, kQσ = 0.01.

A.3. Simulating the posterior distribution of the TVP-FAVAR state equation.

We simulate the posterior distribution of the hyperparameters and the states conditional

on the data via the following MCMC algorithm, combining elements of Primiceri (2005);

Del Negro and Primiceri (2015) and Cogley and Sargent (2002, 2005). In what follows,

ξt denotes the entire history of the vector ξ up to time t, i.e., ξt = [ξ′1, ...ξ′t]′ ∀ t = 1, ..., T ,

where T is the sample length; and the same for Φt = (Φ1, ..., Φt), At = (A1, ..., At) and

Σt = (Σ1, ...,Σt).

To simulate the joint posterior distribution of (ΦT , AT ,ΣT , QΦ, Qσ and Qa), we use a

Gibbs sampling algorithm. The Gibbs sampler is a MCMC method and is carried out

by sequentially drawing time varying coefficients (ΦT ), contemporaneous relations (AT ),

stochastic volatilities (ΣT ) and hyperparamters (Qσ and Qa), given the data.

For convenience we define νt = [ε′t, (εΦt )′, (εat )

′, (εσt )′]′ and assume that:

(31) νt ∼ N (0, V ) , V =

I 0 0 0

0 QΦ 0 0

0 0 Qa 0

0 0 0 Qσ

where the error vector εt is such that ut = A−1

t Σtεt. As discussed in Primiceri (2005);

Del Negro and Primiceri (2015), there are two justifications for assuming a block-diagonal

structure for V . First, parsimony, as the model is already quite heavily parameterized.

Second, allowing for a completely generic correlation structure among different sources of

uncertainty would preclude any structural interpretation of the innovations.

The steps for the Gibbs sampling are:

32

A.3.1. Step 1: Drawing coefficient states ΦT . Conditional on AT ,ΣT and V , the state-

equation (1) is linear, and has Gaussian innovations with a known covariance matrix. As

shown in Fruhwirth-Schnatter (1994) and Carter and Kohn (1994), the density p(ΦT |

ξT , AT ,ΣT , V ) can be decomposed according to:

(32) p(ΦT | ξT , AT ,ΣT , V ) = p(ΦT | ξT , AT ,ΣT , V )T−1∏t=1

p(Φt | Φt+1, ξT , AT ,ΣT , V )

Conditional on AT ,ΣT and V , the standard Kalman-filter recursions pin down the first

element on the right hand side of equation (32), Φt | ξt, At,Σt, V ∼ N(Φt|t+1, Pt|t+1), with

Pt|t+1 being the precision matrix of Φt|t+1 produced by the Kalman filter. The remaining

elements in the factorization can then be computed via the backward recursion algorithm

found, e.g., in Kim and Nelson (1999) or Cogley and Sargent (2005). Given the conditional

normality of Φt, we have:

Φt|t+1 = Φt|t + Pt|tP−1t+1|t

(Φt+1 − Φt

)(33)

Pt|t+1 = Pt|t − Pt|tP−1t+1|tPt|t(34)

which provides, for each t from T − 1 to 1, the remaining elements in equation (1),

p(Φt | Φt+1, ξT , AT ,ΣT , V ) = N(Φt|t+1, Pt|t+1). Specifically, the backward recursion starts

with a draw from N(ΦT , PT ), call it ΦT . Conditional on ΦT , (33)-(34) give us ΦT+1|T and

PT+1|T , thus allowing us to draw ΦT−1 from N(ΦT+1|T , PT+1|T ), and so on until t = 1.

A.3.2. Step 2: Drawing covariance states AT . Conditional on ΦT , ΣT and V we draw,

following Primiceri (2005); Del Negro and Primiceri (2015), the elements of At (or at

in particular) as follows: The FAVAR state equation (1) can be rewritten as Atξt =

At(ξt − Ξ′tΦt) = Σtεt, with V ar(εt) = I, implying

ξ1,t = ε1,t(35)

ξ2,t = −a21,tξ1,t + ε2,t(36)

ξ3,t = −a31,tξ1,t − a32,tξ2,t + ε3,t(37)

ξ4,t = −a41,tξ1,t − a42,tξ2,t − a43,tξ3,t + ε4,t(38)

Based on the observation equations (35)-(38), and the transition equation for at in

equation (8), the elements of At can then be drawn by applying the same algorithm we

described in the previous paragraph separately to (36), (37) and (38).

33

A.3.3. Step 3: Drawing volatility states ΣT . Conditional on ΦT and AT , the orthogo-

nalised innovations εt = At(ξt − Ξ′tΦt), with V ar(εt) = I, are observable. Following Cog-

ley and Sargent (2002), we then sample the hi,t’s by applying the univariate algorithm of

Jacquier et al. (1994) element by element.

A.3.4. Step 4: Drawing hyperparameters QΦ, Qa, Qσ. The hyperparameters of the model

are the diagonal blocks of the matrix V : QΦ, Qa and Qσ. Conditional on ΦT ,ΣT , AT and

ξT , each square block has an inverse-Wishart posterior distribution, independent of the

other blocks. Moreover, conditional on ΦT ,ΣT , AT and ξT , it is easy to draw from these

inverse-Wishart posteriors because the innovations are observable.

Finally, following, e.g., Primiceri (2005); Cogley and Sargent (2002, 2005); Del Negro

and Primiceri (2015) and Canova et al. (2007) the state equation’s time-varying parame-

ters, collected in the vector Φt, are postulated to evolve according to:

(39) p(Φt | Φt−1, QΦ) = I(Φt)f(Φt | Φt−1, QΦ)

with I(Φt) being an indicator function rejecting unstable draws - thus enforcing a

stationarity constraint on the VAR - and with f(Φt | Φt−1, QΦ) given by the corresponding

expression for QΦ in equation (8).

A.4. Computational details. This section is to assess convergence related issues of the

Markov chain Monte Carlo algorithm within the application involving UK data. Since the

Gibbs sampler is a dependence chain algorithm, posterior draws are correlated. However,

the higher the correlation, the lower is the quality of the draws. In what follows we discuss

the extent to which our results are not subject to convergence problems.

First of all, different starting points of the chain (randomly selected) produce the same

results. These results are also not sensitive to the initial number of discarded draws or the

total number of passes of the Gibbs sampler. In order to judge how well the chain mixes,

common practice is to look at the autocorrelation function of the draws. Low autocorrela-

tions suggest that the draws are almost independent, which increases the efficiency of the

algorithm. With some exceptions the autocorrelations remain below 0.1 and in most cases

below 0.0412. In close relation to this, Figure 8 presents the draws’ inefficiency factors

(IFs) for the posterior estimates of the parameters. The IFs are defined as the inverse

of the relative numerical efficiency measure of Geweke (1992): RNE = 12πS(0)

∫ π−π S(ω)dω

where S(ω) is the spectral density functions of the sequence of draws from the Gibbs sam-

pler for the quantity of interest at the frequency ω. We estimate the spectral densities

by smoothing the periodograms in the frequency domain by means of a Bartlett spectral

12The corresponding figures are not shown here, but available upon request.

34

window. Following Berkowitz and Diebold (1998), we select the bandwidth parameter

automatically via the procedure introduced by Beltrao and Bloomfield (1987).

In particular, Figure 8 shows the draws’ IFs for the model’s time-varying coefficients

of the VAR (the Φt’s), the volatilities (the Σt’s), and the non-zero elements of the matrix

At. As the figure clearly shows, the autocorrelation of the draws is uniformly very low,

being in the vast majority of the cases fairly small - values of the IFs below or around

twenty are generally regarded as satisfactory.

To conclude, considering the very high dimensionality of the problem, the convergence

diagnostics seem satisfactory.

Appendix B. The data used in the TVP-FAVAR model

Data used for the FAVAR model: All series were download from the statistical

Database of DataStream and cover the period Q1:1960 until Q4:2015 on a quarterly

frequency.

All variables are transformed to be approximately stationary. In particular, if zi,t is

the original untransformed series, the transformation codes are: 1 - no transformation

(xi,t = zi,t), 2 - first difference (xi,t = ∆zi,t), 3 - second difference (xi,t = ∆2zi,t), 4 -

logarithm (xi,t = log(zi,t)), 5 - first difference of logarithm (xi,t = ∆ log(zi,t)). ∆ denotes

the difference operator. The transformations of the variables are indicated in column TC

in Table 2.

The variables shown in Figure 3 are - with the expection of the saving ratio - not part

of the FAVAR model. The further variables in Figure 3 are defined as follows: the import

ratio is constructed as nominal imports relative to nominal GDP; the measure of the

output-gap is taken from the OECD statistics database; the real policy rate is constructed

as the difference between the Bank of England policy rate minus the contemporaneous

CPI inflation rate; the credit impulse variable is constructed as the year-on-year change in

the stock of credit to the private sector relative to nominal GDP; the variable capturing

interest rate payments on public debt over GDP is taken from the UK Institute for

Fiscal Studies; and finally, the financial market stress indicator is taken from Corbet and

Twomey (2014). Their measure of financial market stress uses twenty-three headline UK

financial data series and is constructed by applying a logistic regression framework in

order to provide a parsimonious representation of financial market stress in the UK.

Table 2. Data used in paper

35

Name Code Source TC

1 BoP: current account balance as per cent of

GDP, Current Prices, SA, GBP [BoP: current

account balance as per cent of GDP] [ BOP:

CURRENT ACCOUNT BALANCE (% OF

GDP) ]

UKAA6H..Q Office for Na-

tional Statistics

SA 1

2 Balance of Payments: Trade in Goods &

Services: Total exports, Constant Prices,

SA, GBP [ BOP: EXPORTS - TRADE IN

GOODS & SERVICES ]

UKIKBK.. Office for Na-

tional Statistics

Constant

prices, SA

5

3 BoP: trade in goods and services balance as

per cent of GDP, Current Prices, SA, GBP [

BOP: GOODS & SERVICES BALANCE (%

OF GDP) ]

UKD28L..Q Office for Na-

tional Statistics

SA 1

4 Balance of Payments: Trade in Goods & Ser-

vices: TOTAL IMPORTS OF GOODS &

SERVICES, SA, GBP, 2005 CHND PRC [

BOP: IMPORTS - TRADE IN GOODS &

SERVICES ]

UKIKBL..D Office for Na-

tional Statistics

Constant

prices, SA

5

5 Changes in inventories including alignment

adjustment, Constantt Prices, SA, GBP [

CHANGES IN INVENTORIES ]

UKCAFU..D Office for Na-

tional Statistics

Constant

prices, SA

1

6 Income Approach, Gross Domestic Product

Components, Compensation of Employees,

Total, Current Prices, SA, British Pound

Sterling [ UK COMPENSATION OF EM-

PLOYESS ]

UKDTWM..B Office for Na-

tional Statistics

Current prices,

SA

5

7 Construction Output, All Work, Constant

Prices, SA, Index, 2012 = 100 [ CONSTRUC-

TION OUTPUT - TOTAL WORK ]

UKCVCONAG Office for Na-

tional Statistics

Volume index,

SA

5

8 Main Gross Domestic Product Aggregates

(ESA2010), Gross Domestic Product and

Main Components, Final Consumption Ex-

penditure and Gross Capital Formation, Cal-

endar Adjusted, SA, Index, 2010 = 100 [ DO-

MESTIC DEMAND (VOL.) ]

UKESFKKZE EUROSTAT Constant

Prices, SA

5

9 Implicit Price Deflator (IPD), Gross domestic

expenditure, SA, Index, 2006=100 [Total do-

mestic expenditure deflator: SA] [ DOMES-

TIC EXPENDITURE DEFLATOR - TO-

TAL ]

UKYBFV..E Office for Na-

tional Statistics

Price index, SA 5

Continued on next page

36

Name Code Source TC

10 Household final consumption expenditure:

National concept, Constant Prices, SA, GBP

[ FINAL CONSUMPTION EXPENDITURE:

HOUSEHOLD - NATIONAL CONCEPT ]

UKABJR..D Office for Na-

tional Statistics

Constant

prices, SA

5

11 Production Approach, Gross Domestic Prod-

uct, Total, Constant Prices, SA, GBP, 2006

chnd prices [ GDP AT CONSTANT PRICES

(CVM) ]

UKGDP...D Office for Na-

tional Statistics

Constant

prices, SA

5

12 GROSS FIXED CAPITAL FORMATION

(CVM), SA, GBP, 2005 CHND PRC [ GFCF

(CVM) ]

UKGFCF..D Office for Na-

tional Statistics

Constant

prices, SA

5

13 Expenditure Approach, Gross Final Expen-

diture, Total, Constant Prices, SA, GBP,

2006 chnd prices [ GROSS FINAL EXPEN-

DITURE ]

UKABMG..D Office for Na-

tional Statistics

Constant

prices, SA

5

14 Income Approach, National Income, Gross

Disposable, at market prices, Constant

Prices, SA, Index, 2006=100 [ GROSS NA-

TIONAL DISPOSABLE INCOME INDEX ]

UKYBFP..G Office for Na-

tional Statistics

Volume index,

SA

5

15 Income Approach, National Income, Gross,

at market prices, Current Prices, SA, GBP

[ GROSS NATIONAL INCOME ]

UKGNP...B Office for Na-

tional Statistics

Current prices,

SA

5

16 Income Approach, Allocation of Primary

Income Account, Resources, Private Non-

Financial Corporations, Gross operating sur-

plus, Current Prices, SA, GBP [ GROSS OP-

ERATING SURPLUS: PRIVATE ]

UKCAER..B Office for Na-

tional Statistics

Current prices,

SA

5

17 Income Approach, Allocation of Primary In-

come Account, Public Corporations, Gross

operating surplus, Current Prices, SA, GBP [

GROSS OPERATING SURPLUS: PUBLIC ]

UKCAEQ..B Office for Na-

tional Statistics

Current prices,

SA

5

18 Production Approach, Value Added, Gross,

Service Industries Total, Constant Prices, SA,

Index, 2012 = 100 [ SERVICE INDUSTRIES

- TOTAL VOLA ]

UKL2NC..G Office for Na-

tional Statistics

Volume index,

SA

5

19 HN:Households saving ratio, SA, GBP [ HN:

HOUSEHOLDS SAVING RATIO ]

UKNRJS..E Office for Na-

tional Statistics

SA 1

20 HN: Real households disposable income, Con-

stant Prices, SA, GBP [ HN: REAL HOUSE-

HOLDS DISPOSABLE INCOME ]

UKNRJR..D Office for Na-

tional Statistics

Constant

prices, SA

5

Continued on next page

37

Name Code Source TC

21 HN: Resources: Disposable income gross:

B.6g, Current Prices, SA, GBP [ HN:

RESOURCES: DISPOSABLE INCOME

GROSS ]

UKRPHQ..B Office for Na-

tional Statistics

Current prices,

SA

5

22 HN: Resources: Wages and salaries: D.11,

Current Prices, SA, GB [ HN: RESOURCES:

WAGES & SALARIES ]

UKROYJ..B Office for Na-

tional Statistics

Current prices,

SA

5

23 Production Approach, Value Added, Gross,

Production Total, Constant Prices, SA, In-

dex, 2012 = 100 [ INDUSTRIAL PRODUC-

TION - ALL PRODUCTION INDUSTRIES

VOLA ]

UKK222Q.G Office for Na-

tional Statistics

Volume index,

SA

5

24 Main Gross Domestic Product Aggregates

(ESA2010), Gross Domestic Product and

Main Components, Taxes Less Subsidies On

Products, Constant Prices, Calendar Ad-

justed, SA, Euro, 2010 Chained Prices [

TAXES LESS SUBSIDIES ON PRODS.,

2010 EUR(ESA2010) (WDA) CONA ]

UKES1O0QD EUROSTAT Constant

prices, SA

5

25 Implicit Price Deflator (IPD) OF EXPORTS

OF GOODS AND SERVICES, SA, Index,

2005=100 [ Implicit Price Deflator (IPD) OF

EXPORTS OF GOODS AND SERVICES ]

UKIPDEXPE Datastream

International

Ltd.

Price index, SA 5

26 Implicit Price Deflator (IPD) OF FINAL

SALES, SA, Index, 2005=100 [ Implicit Price

Deflator (IPD) OF FINAL SALES ]

UKIPDEXPEFS Datastream

International

Ltd.

Price index, SA 5

27 Implicit Price Deflator (IPD) OF GDP MAR-

KET PRICES, SA, Index, 2005=100 [ Im-

plicit Price Deflator (IPD) OF GDP MAR-

KET PRICES ]

UKIPDGDP Office for Na-

tional Statistics

Price index, SA 5

28 Implicit Price Deflator (IPD) OF GENERAL

GOVERNMENT FINAL CONSUMPTION,

SA, Index, 2005=100 [ Implicit Price Defla-

tor (IPD) OF GENERAL GOVERNMENT

FINAL CONSUMPTION ]

UKIPDPUBE Datastream

International

Ltd.

Price index, SA 5

29 Implicit Price Deflator (IPD) OF GROSS

DOM. FIXED CAPITAL FORMATION, SA,

Index, 2005=100 [ Implicit Price Deflator

(IPD) OF GROSS DOM. FIXED CAPITAL

FORMATION ]

UKIPDINVE Datastream

International

Ltd.

Price index, SA 5

Continued on next page

38

Name Code Source TC

30 Implicit Price Deflator (IPD) OF HOUSE-

HOLD CONSUMPTION, SA, Index,

2005=100 [ Implicit Price Deflator (IPD) OF

HOUSEHOLD CONSUMPTION ]

UKIPDHSHE Office for Na-

tional Statistics

Price index, SA 5

31 Implicit Price Deflator (IPD) OF IMPORTS

OF GOODS AND SERVICES, SA, Index,

2005=100 [ Implicit Price Deflator (IPD) OF

IMPORTS OF GOODS AND SERVICES ]

UKIPDIMPE Datastream

International

Ltd.

Price index, SA 5

32 Income Approach, Allocation of Primary In-

come Account, Non-Financial Corporations,

Gross operating surplus, Current Prices, SA,

GBP [ NONFINL. CORPS.: GROSS OPER-

ATING SURPLUS ]

UKROZQ..B Office for Na-

tional Statistics

Current prices,

SA

5

33 Output per Filled Job : Whole Economy

SA: UK, SA, Index, N/A [ OUTPUT PER

FILLED JOB - WHOLE ECONOMY ]

UKLNNN.. Office for Na-

tional Statistics

Price index, SA 5

34 Auxiliary Indicators (ESA2010), Population

and Employment, Total Population Na-

tional Concept, Calendar Adjusted, SA [

TOTAL POPULATION NATIONAL CON-

CEPT (ESA2010) (WDA) VOLA ]

UKES9YULO EUROSTAT Volume, SA 5

35 Labour Productivity, Output per worker,

whole economy, SA, Index, 2006=100 [ PRO-

DUCTIVITY - OUTPUT PER WORKER:

WHOLE ECONOMY ]

UKA4YM..E Office for Na-

tional Statistics

Volume index,

SA

5

36 Whole Economy index of LFS Employment:

2006=100, SA, Index, N/A [ UK WHOLE

ECONOMY - EMPLOYMENT ]

UKTXEL..E Office for Na-

tional Statistics

Volume index,

SA

5

37 UNIT LABOUR COST INDEX - WHOLE

ECONOMY, SA, Index, 2003=100 [ UNIT

LABOUR COST INDEX - WHOLE ECON-

OMY ]

UKLCOST.E Office for Na-

tional Statistics

Price index, SA 5

38 Monetary authorities, Monetary liabilities,

NOTES&COIN IN CIRC.W/PUBLIC, GBP

[ CENTRAL BANK: CURRENCY IN CIR-

CULATION ]

UKQ14A..A IMF Interna-

tional Financial

Statistics

Current prices,

not SA

5

39 Depository corporations survey/monetary

survey, Domestic credit, CLAIMS ON

PRIVATE SECTOR, GBP [ DOMESTIC

CREDIT: CLAIMS ON PRIVATE SECTOR

]

UKQ32D..A IMF Interna-

tional Financial

Statistics

Current prices,

not SA

5

Continued on next page

39

Name Code Source TC

40 Exchange rate, fund position or interna-

tional liquidity, FOREIGN EXCHANGE in

UK Pound [ FOREIGN EXCHANGE RE-

SERVES ]

UKQ.1D.DA IMF Interna-

tional Financial

Statistics

Current prices,

not SA

5

41 Interest rates prices, production or labour,

Earnings, AV EARN PROD IND SA,

BASEYEARTEXT 2005 [ WEEKLY WAGES

]

UKQ65..CE IMF Interna-

tional Financial

Statistics

Price index, SA 5

42 UK DOMESTIC CREDIT: CLAIMS ON OF-

FICIAL ENTITIES CURN [ ]

UKQ32BX.A IMF Interna-

tional Financial

Statistics

no SA 5

43 AVERAGE BRENT OIL PRICE, USD [ OIL

PRICE ]

UKOILBREN Department of

Energy, U.K.

Price index,

not SA

5

44 Policy Rates, Bank Rate (Shorter History),

End of Period, GBP [ Monetary Policy Rate

(EP) ]

UKPRATE. Bank of Eng-

land

Interest Rate 1

45 CBI SURVEY - OPTIMISM BALANCE

(MONTHLY INTERPOLATED) [ CBI SUR-

VEY - OPTIMISM BALANCE (MONTHLY

INTERPOLATED) ]

UKCBICONR Office for Na-

tional Statistics

Not SA 1

46 Composite Leading indicators, Trend [ COM-

POSITE LEADING INDICATOR (TREND

RESTORED) ]

UKCYLEAD Main Economic

Indicators,

Copyright

OECD

Trends 5

47 RETAIL SALES (MONTHLY ESTIMATE,

DS CALCULATED), Constant Prices,

SA, GBP, 2000 prices [ RETAIL SALES

(MONTHLY ESTIMATE DS CALCU-

LATED) ]

UKRETTOTD Datastream

International

Ltd.

Constant

prices, SA

5

48 RPI- INFLATION RATE [ RPI- INFLA-

TION RATE ]

UKRPANNL Office for Na-

tional Statistics

1

49 RPI:Percentage change over 12 months - all

items excluding housing, GBP [ RPI: ALL

ITEMS EXCLUDING HOUSING (%YOY) ]

UKCZBI.. Office for Na-

tional Statistics

1

50 RPI:Percentage change over 12 months -

Clothing and footwear, GBP [ RPI: CLOTH-

ING & FOOTWEAR (%YOY) ]

UKCZDO.. Office for Na-

tional Statistics

1

51 RPI:Percentage change over 12 months - Food

excluding seasonal, GBP [ RPI: FOOD EX-

CLUDING SEASONAL (%YOY) ]

UKCZBQ.. Office for Na-

tional Statistics

1

Continued on next page

40

Name Code Source TC

52 RPI:Percentage change over 12 months -

Housing, GBP [ RPI: HOUSING (%YOY) ]

UKCZCP.. Office for Na-

tional Statistics

1

53 RPI:Percentage change over 12 months - Sea-

sonal food, GBP [ RPI: SEASONAL FOOD

(%YOY) ]

UKCZBP.. Office for Na-

tional Statistics

1

54 BIS, Real Narrow Effective Exchange Rate

Index, Average, GBP [ EFFECTIVE EX-

CHANGE RATE NARROW INDEX - REAL

CPI ]

UKBISRXNR Bank for Inter-

national Settle-

ments

Not SA 1

55 FTSE, All-Share, Index, Price Return, End

of Period, GBP [ FT ALL SHARE INDEX

(EP) ]

UKSHRPRCF Reuters Price index,

not SA

5

56 GROSS REDEMPTION YIELD ON 10

YEAR GILT EDGED STOCKS (AVER-

AGE) [ bond yield 10 YEAR (AVERAGE)

]

UKMEDYLD Bank of Eng-

land

Interest Rate 1

57 London Interbank Rate - 3 Month (EP) [ LI-

BOR ]

UKINTERB Bank of Eng-

land

Interest Rate 1

58 Output Prices, All manufactured products,

Index, 2005=100 [ PPI - OUTPUT OF MAN-

UFACTURED PRODUCTS ]

UKPROPRCF Office for Na-

tional Statistics

Price index,

not SA

5

59 Unemployment, Rate, SA [ ] UKUNEMRAT Office for Na-

tional Statistics

SA 1

60 Consumer Surveys, GfK, Consumer Confi-

dence Index, Total [ ]

UKCONSENT Office for Na-

tional Statistics

1

61 Domestic Trade, Retail Trade, All Retailing,

Constant Prices, SA, Index [ ]

UKRETTRAD Office for Na-

tional Statistics

constant prices,

SA

5

62 Consumer Price Index, Total, Index [ CPI ] UKCPITI Office for Na-

tional Statistics

Price Index 5

63 Consumer Price Index, Core CPI, Total [ ] UKCPICOR Office for Na-

tional Statistics

Price Index 5

64 GDP AT MARKET PRICES, SA, GBP [

GDP AT MARKET PRICES ]

UKGDP...B Office for Na-

tional Statistics

Current prices,

SA

65 GENERAL GOVERNMENT: FINAL CON-

SUMPTION EXPENDITURE(CVM), SA,

GBP, 2005 CHND PRC [ GENERAL GOV-

ERNMENT: FINAL CONSUMPTION EX-

PENDITURE ]

UKCNGOV.D Office for Na-

tional Statistics

Constant

prices, SA

5

66* TOTAL CREDIT TO THE NON-

FINANCIAL SECTORS - PRIVATE

NON-FINANCIAL SECTOR - ALL SEC-

TORS - MARKET VALUE - ADJUSTED

FOR BREAKS [ Stock of Credit to non-

financial Corporates ]

UKNFCDBT. Database of the

BIS

Continued on next page

41

Name Code Source TC

67* OUTPUT GAP [ ] UKYGAP.. Databse of

the OECD

[OECD.STAT]

68* PUBLIC SECTOR NET DEBT INTEREST

PAYMENTS AS A SHARE OF NATIONAL

INCOME [ ]

UKYINTEXP.. from THE

INSTITUTE

FOR FISCAL

STUDIES

69* UK - FINANCIAL MARKET STRESS IN-

DICATOR [ ]

UKFMSI FROM Corbet

and Twomey

(2014)

* Data used in the Bayesian linear regression of section 4.2 only.

42

Figure 1. Fiscal spending multipliers for various demand aggregates

The figure shows 2-year cumulative government spending multipliers for output, private

consumption, investment, imports, exports, the GDP deflator and a measure of credit

to the private sector. The horizon P considered for the cumulative multipliers is eight

quarters. In each case, the solid lines refer to the median of the posterior distribution of

the impulse response functions and the gray shaded area represents the 68 percent error

band of the posterior distribution. The dotted line indicates the unity-line. The gray

bars indicate recession episodes where recessions are defined of at least two consecutive

quarters of negative GDP growth.

Output

1970 1980 1990 2000 2010

0

2

4

6Consumption

1970 1980 1990 2000 2010

0

1

2

3

4

Investment

1970 1980 1990 2000 2010

0

2

4

6

8

Imports

1970 1980 1990 2000 2010

0

5

10

Exports

1970 1980 1990 2000 2010

-10

-5

0

5

GDP Deflator

1970 1980 1990 2000 2010-10

-5

0

5

real Credit

1970 1980 1990 2000 2010

0

2

4

43

Figure 2. Impulse response functions

The Figure reports the impulse response functions to a surprise innovation in governement

spending. The shock is identified - as explained in section 2.3 - by means of an orthogonal

structure of the variance-covariance matrix Ωut of equation (1). The impulse response

functions are shown for a horizon of up to 32 quarters (8 years). The first row shows

the responses for the full sample going from 1966 to 2015, the remaining rows show the

responses for selected years corresponding to different phases of the UK business cycle.

0 20

-0.5

0

0.5

1

1966

-201

5

Output

0 20

-0.5

0

0.5

1

Consumption

0 20

-0.5

0

0.5

1

Investment

0 201

1.5

2

2.5

3Imports

0 20-5

0

5

10GDP Deflator

0 20-0.5

0

0.5

1

1.5real Credit

0 20

0.6

0.8

1

1.2Gov. Cons

0 20

2

4

6

8

1974

0 20

2

4

6

8

0 20

2

4

6

8

0 202

4

6

8

10

0 20-5

0

5

10

15

0 200

2

4

6

0 20

0.6

0.8

1

1.2

0 20

-1

-0.5

0

0.5

1990

0 20

-1

-0.5

0

0.5

0 20

-1

-0.5

0

0.5

0 200.5

1

1.5

2

2.5

0 20-5

0

5

10

0 20-1

-0.5

0

0.5

1

0 20

0.6

0.8

1

1.2

0 20-1

-0.5

0

0.5

1998

0 20-1

-0.5

0

0.5

0 20-1

-0.5

0

0.5

0 200.5

1

1.5

2

2.5

0 20-2

0

2

4

6

0 20-1

-0.5

0

0.5

1

0 20

0.6

0.8

1

1.2

0 200

1

2

3

4

5

2008

0 200

1

2

3

4

5

0 200

1

2

3

4

5

0 200

2

4

6

8

0 20-5

0

5

10

0 20-1

0

1

2

3

0 20

0.6

0.8

1

1.2

0 20

Quarters

-1

-0.5

0

0.5

2015

0 20

Quarters

-1

-0.5

0

0.5

0 20

Quarters

-1

-0.5

0

0.5

0 20

Quarters

0.5

1

1.5

2

0 20

Quarters

-5

0

5

10

0 20

Quarters

-1

-0.5

0

0.5

1

0 20

Quarters

0.6

0.8

1

1.2

44

Figure 3. Exogenous variables

The figure shows the variables used in the Bayesian linear regression analysis. The measure

of the real interest rate is the difference between the policy rate (Bank of England base

rate) and the CPI inflation rate. The credit impulse is the year-on-year change in the

stock of credit relative to (nominal) GDP; this specification makes sure that stock and

flow variables are not confused. The import share has been detrended. The output

gap measure is taken from the OECD whereas the series of interest rate payments on

government debt is taken from the UK Institute for Fiscal Studies.

savings ratio

1970 1980 1990 2000 2010

0.05

0.1

0.15

imports/GDP

1970 1980 1990 2000 2010

0.2

0.25

0.3

0.35

output gap

1970 1980 1990 2000 2010

-0.02

0

0.02

0.04

0.06real rate

1970 1980 1990 2000 2010

-0.15

-0.1

-0.05

0

0.05

credit impulse/GDP

1970 1980 1990 2000 2010

-0.1

-0.05

0

0.05

0.1

interest payments/GDP

1970 1980 1990 2000 2010

0.02

0.03

0.04

financial stress

1970 1980 1990 2000 20100.2

0.4

0.6

0.8

1

1.2

1.4

45

Figure 4. Bayesian linear regression - decomposition

The Figure shows the contribution of each regressor in explaining the variation of the

cumulative multiplier for output. Consider the subplot of regressor i, the plot shows the

time series of the prediction for the impact multiplier (solid line) next to the gap (black

bars) between the predicted values (1) once using all values of regressor i for computing

the predicted value relative to a measure for the predicted value (2) when regressor i is

kept fixed at its mean value.

1970 1980 1990 2000 2010

0

1

2

savings ratio

1970 1980 1990 2000 2010

0

1

2

imports/GDP

1970 1980 1990 2000 2010

0

1

2

output gap

1970 1980 1990 2000 2010

0

1

2

real rate

1970 1980 1990 2000 2010

0

1

2

credit impulse/GDP

1970 1980 1990 2000 2010

0

1

2

interest payments/GDP

1970 1980 1990 2000 2010

0

1

2

financial stress

46

Figure 5. Fiscal spending multipliers for output

The figure shows the government expenditures multipliers for output for different multi-

pliers’ measures as defined in section 5.1. The horizon P considered for the cumulative,

maximum and present value multipliers is eight quarters. In each case, the solid lines

refer to the median of the posterior distribution of the impulse response functions and

the gray shaded area represents the 68 percent error band of the posterior distribution.

Impact Multiplier

1970 1980 1990 2000 2010

0

2

4

6

Cumulative Multiplier

1970 1980 1990 2000 2010

0

2

4

6

Maximum Multiplier

1970 1980 1990 2000 2010

0

2

4

6

Present Value Multiplier

1970 1980 1990 2000 2010

0

2

4

6

47

Figure 6. Prior hyperparameters

The figure shows the government expenditures output multiplier for different values of the

hyperparameters kQΦ, kQa and kQσ . The baseline result uses: kQΦ

= kQa = kQσ = 0.01.

The confidence intervals shown are the ones from the baseline calibration. Each subplot

also shows the difference between the baseline multiplier and the extended one jointly

with the 68% confidence interval.

1970 1980 1990 2000 2010

0

2

4

6

Out

put M

ultip

lier

-0.5

-0.25

0

0.25

0.5

Diffe

renc

e

original [ kQ ,a,

= 0.01 ]

kQ ,a,

= 0.04

1970 1980 1990 2000 2010

0

2

4

6

Out

put M

ultip

lier

-0.5

-0.25

0

0.25

0.5

Diffe

renc

e

original [ kQ ,a,

= 0.01 ]

kQ ,a,

= 0.0025

1970 1980 1990 2000 2010

0

2

4

6

Out

put M

ultip

lier

-0.5

-0.25

0

0.25

0.5

Diffe

renc

e

original [ kQa

= 0.01 ]

kQa

= 0.04

1970 1980 1990 2000 2010

0

2

4

6

Out

put M

ultip

lier

-0.5

-0.25

0

0.25

0.5

Diffe

renc

e

original [ kQa

= 0.01 ]

kQa

= 0.0025

1970 1980 1990 2000 2010

0

2

4

6

Out

put M

ultip

lier

-0.5

-0.25

0

0.25

0.5

Diffe

renc

e

original [ kQa

= 0.01 ]

kQa

= 0.1

48

Figure 7. Output multiplier based on a rolling-regression approach

The figure shows the government expenditures multiplier for output based on a rolling-

estimation approach (with a rolling windows of 80 quarters). The confidence intervals

shown are 68%-confidence bands.

Cumulative Multiplier

1985 1990 1995 2000 2005 2010 2015-1

-0.5

0

0.5

1

1.5

2

2.5

49

Figure 8. Convergence statistics

The figure shows the inefficiency factors for the draws from the ergodic distribution for the

model’s time-varying parameters in order to check for convergence of the Markov Chain.

500 1000 1500 2000 2500 3000 35000

2

4

6Elements of Φ(t)

200 400 600 800 1000 12000

0.5

1

1.5

2

2.5Elements of A(t)

100 200 300 400 500 600 700 8000

2

4

6Elements of Σ(t)