Disaggregate income and wealth effects in the largest euro area countries.
Date: 2020-06-12
Institutions: European Central Bank
Subjects: consumption, econometrics, economic forecasting, euro area, wealth

Gabe de Bondt, Arne Gieseck,  
Pablo Herrero, Zivile Zekaite 

Working Paper Series 

Disaggregate income and  
wealth effects in the  
largest euro area countries 

No 2343 / December 2019 

Disclaimer: This paper should not be reported as representing the views of the European Central Bank 
(ECB). The views expressed are those of the authors and do not necessarily reflect those of the ECB. 

 
 
 
Abstract 

This study extends a thick modelling tool for aggregated euro area real private consumption of de Bondt 

et al. (2019) to the four largest euro area countries. The suite of error correction models performs well in 

and out of sample. The ranges and averages of estimated elasticities are, however, sensitive to the exact 

model  specification.  We  also  show  that  decomposing  disposable  income  into  labour,  property  and 

transfer  income  is  essential  for  understanding  and  forecasting  consumption.  Finally,  substantial  cross-

country heterogeneity in marginal propensities to consume out of income and wealth components calls for 

caution when interpreting aggregate euro area developments.  

Keywords: private consumption, income, wealth, thick modelling 

JEL codes: C53, D12, E21, E27 

ECB Working Paper Series No 2343 / December 20191 
 
Non-technical summary 

This paper presents a thick modelling application of private consumption for the euro area as well as the 

four  largest  euro  area  countries.  Thick  modelling  considers  a  multiplicity  of  model  specifications  rather 

than a single “best” one. This is in particular advantageous when facing model uncertainties, which is the 

case because euro area data typically start only in 1999, resulting in a comparatively short sample and 

the measurement of income and wealth is surrounded with ambiguity. Using this method, a large number 

of model  specifications  are  tested and  the  best ones  are then combined  by  giving  equal  weights  to  the 

selected  equations.  In  our  case,  we  keep  those  specifications  that  explain  and  forecast  private 

consumption well using standard determinants from the consumption literature.  

Private  consumption  is  largely  determined  by  expected  lifetime  income,  which  is  typically  proxied  by 

disposable income and wealth. Nevertheless, the empirical literature provides ample evidence that other 

determinants, such as interest rates, uncertainty and consumer debt, might also play important roles. In 

addition,  many  studies  have  looked  into  the  differential  effects  of  wealth  components,  i.e.  financial  and 

non-financial wealth, on household consumption. However, income components can also be expected to 

have  different  effects  on  consumption  and  the  marginal  propensities  to  consume  out  of  labour,  transfer 

and  property  income  are  not  necessarily  the  same.  This  disaggregation  of  income  has  remained 

comparatively unnoticed in the empirical literature.  

We  use  quarterly  sector  accounts  data  to  decompose  disposable  income  into  labour,  transfer  and 

property  income  as  well  as  to  split  total  wealth  into  financial  and  non-financial  (mainly  housing)  wealth 

when modelling private consumption. In addition to income and wealth components, we consider a wide 

set  of  other  potential  determinants  in  the  short  run:  interest  rates  and  spreads,  measures  of  consumer 

indebtedness, government debt measures capturing Ricardian equivalence effects, several measures of 

uncertainty  and  demographics.  We  generate  multiple  (6½  thousand)  single-equation  error  correction 

models for private consumption growth estimated by General Method of Moments (GMM) over the period 

1999Q1  to  2018Q2.  We  then  select  a  set  of  best  performing  equations  by  applying  pre-determined  in-

sample and out-of-sample criteria, focusing on a final set of 50 equations that meet all criteria and have 

shown the best out-of-sample performance. Finally, we perform several robustness checks to account for 

various  approaches  of  model  specification  and  for  various  possibilities  to  define  income  and  wealth 

variables. 

ECB Working Paper Series No 2343 / December 20192  
 
 
 
 
Three main findings emerge. Firstly, our estimates show that it is not only essential to distinguish between 

components  of  wealth,  but  also  between  components  of  income  when  analysing  private  consumption. 

The estimated long-run elasticity of labour income is in all cases substantially larger than that of property 

income  and  transfer  income.  In  terms  of  marginal  propensities  to  consume  (MPC),  the  differences 

between  income  components  are  less  pronounced.  Nevertheless,  the  MPC  out  of  property  income  is 

comparatively small in France, Italy and Spain. With respect to wealth, the average long-run elasticity of 

financial  wealth  is  often  found  to  be  larger  than  of  non-financial  wealth.  This  finding  is  in  line  with  the 

literature. The average marginal propensity to consume out of financial wealth is found to be up to 3 cents 

per  euro  (in  Spain)  while  it  is  up  to  0.2  cents  for  non-financial  wealth  (in  Germany  and  Spain).  The 

estimated short-run elasticities are also found to differ across income and wealth components.  

Secondly, our thick model-based estimation results in wide ranges of elasticities of private consumption 

with  respect  to  income  and  wealth  components.  In  particular,  we  find  that  the  elasticities  of  property 

income in France and Italy and the elasticity of transfer income in Spain can be significantly different from 

zero on both sides. The same finding holds for the estimated long-run elasticities of non-financial wealth 

in  the  euro  area,  Germany  and  France,  and  for  financial  wealth  in  Germany.  A  number  of  robustness 

checks also reveal that the sign of the estimated coefficients may depend on the model specification and 

the respective definition of wealth components. 

Thirdly, our results show that aggregate euro area income and wealth effects mask striking cross-country 

differences. Property income is found to be essential for German consumption, whereas consumption in 

France,  Italy  and  Spain  is  best  explained  by  focusing  on  non-property  income.  Long-run  MPCs  out  of 

financial wealth are on average estimated to be 1 to 3 cents on a euro in France and Spain, but less than 

1 cent in Italy and close to zero in Germany. Long-run MPCs out of non-financial wealth are estimated to 

be on average close to zero in Germany, France and in Italy, whereas they are found to be significantly 

positive (on average 0.2 cents) in Spain.  

ECB Working Paper Series No 2343 / December 20193  
 
 
 
 
 
 
 
 
1. 

Introduction 

Economic theory links consumption expenditure of an individual to his/her lifetime resources that consist 

of  human  wealth,  i.e.  current  and  expected  future  income,  and  total  net  asset  wealth.  According  to  the 

life-cycle  hypothesis,  households  adjust  their  total  resources  to  ensure  relatively  stable  and  smooth 

consumption  expenditure  over  the  lifetime  (Ando  and  Modigliani,  1963).  Since  the  publication  of  that 

paper, the literature has augmented the basic consumption model in several ways. First, the adjustment 

of  consumption  to  changes  in  income  and  wealth  might  be  slow  leading  to  an  error  correction 

representation. Second, different components of net worth might have different marginal propensities to 

consume  (MPCs)  leading  to  a  decomposition  of  total  net  worth  into  financial  and  non-financial  assets. 

Third, other determinants such as interest rates, household leverage, public indebtedness, uncertainty, or 

unemployment can also affect consumption. Our paper deviates from the existing work on consumption in 

two ways.  

The  first  substantive  contribution  is  an  extension  of  a  thick  model  application  of  euro  area  private 

consumption  as  reported  in  de  Bondt  et  al.  (2019)  to  the  four  largest  euro  area  countries.  This 

methodology is in the spirit of the early thick modelling pioneers Granger and Jeon (2004) and Aiolfi and 

Favero (2005) and considers a multiplicity of model specifications rather than a single “best” one to take 

into  account  model  uncertainty.  In  particular  we  account  for  uncertainty  about  which  short-term 

determinants  other  than  income  and  wealth  have  an  effect  on  private  consumption.  In  more  detail,  our 

first  step  generates  a  large  set  of  candidate  error  correction  models  by  exploiting  a  vast  number  of 

potential  explanatory  variables  for  consumption  including  disposable  income  and  wealth,  the  standard 

consumption determinants. The next section briefly reviews the empirical literature on income and wealth 

effects.  Using  both  in-sample  and  out-of-sample  model  selection  criteria,  we  identify  a  large  number  of 

well-specified  equations  for  real  private  consumption,  utilising  an  encompassing  set  of  explanatory 

variables.  We  show  the  potential  value  added  of  the  presented  thick  modelling  tool  in  enhancing 

monitoring and forecasting private consumption in the four largest euro area countries. We also account 

for uncertainty about model specification  and  definition of  income and  wealth  components by  running  a 

large number of robustness checks.  

The  second  contribution  is  that  we  decompose  disposable  income  into  labour,  transfer  and  property 

income  by  exploiting  non-financial  sectoral  account  data.  While  the  idea  that  MPCs  might  differ  across 

income  types  goes  back  to  Taylor  (1971),  relatively  few  studies  actually  considered  disaggregating 

income.  Several  studies  for  the  United  States  compare  the  elasticities  of  transfer  versus  non-transfer 

income  in  estimated  consumption  functions  (Davis  and  Palumbo,  2001;  Benjamin  et  al.,  2004; 

Aladangady  and  Feiveson,  2018)  or  split  transfer  income  further  into  retirement  transfers  and  non-

ECB Working Paper Series No 2343 / December 20194  
 
 
retirement  transfers  and  also  look  at  capital  income  (Hawkins  and  Wallace,  2006).  With  respect  to 

property  income  as  a  separate  consumption  determinant,  several  central  banks,  including  the  Federal 

Reserve,  allow  for  property  income  to  enter  the  consumption  function  in  their  models  used  for 

macroeconomic  simulations  and  forecasting  (Brayton  and  Tinsley,  1996;  Fagan  and  Morgan,  2005). 

Nevertheless,  disaggregate  income  effects  have  not  been  well  addressed  in  the  empirical  literature, 

especially  with  respect  to  euro  area  countries.  The  sectoral  account  data  enable  us  to  use  wealth  data 

from a single and consistent database, instead of creating proxies for wealth levels using equity or house 

prices indices. In particular, the financial accounts data enable us to split total wealth in various ways into 

financial  and  non-financial  wealth,  and  we  can  use  these  accounts to  calculate  measures  of  household 

leverage and debt ratios as explanatory factors for private consumption. 

Three conclusions emerge from the thick modelling of private consumption in the four largest euro area 

countries.  First,  it  is  essential  to  distinguish  between  components  of  both  wealth  and  income,  because 

estimated long-run elasticities do differ across income and wealth components. Secondly, the ranges of 

estimated  elasticities  with  respect  to  income  and  wealth  components  are  wide.  Most  striking  is  that 

property income elasticities in France and Italy and transfer income elasticity in Spain can be significantly 

different  from  zero  on  both  sides  in  the  long  run.  The  same  finding  holds  for  the  estimated  long-run 

elasticities of non-financial wealth in Germany and France, and for financial wealth in Germany. A number 

of  robustness  checks  also  reveal  that  the  sign  of  the  estimated  coefficients  may  depend  on  the  model 

specification and the respective definition of wealth components. Finally, aggregate euro area income and 

wealth  effects  mask  striking  cross-country  differences.  Property  income  is  found  to  be  essential  for 

German consumption, whereas consumption in France and Spain is best explained by focusing on non-

property income. Long-run MPCs out of financial wealth are on average estimated to be 1 to 3 cents on a 

euro in France and Spain, less than 1 cent in Italy and close to zero in Germany. Long-run MPCs out of 

non-financial  wealth are estimated to be on  average close to zero  in Germany, France  and  in Italy and 

significantly positive (on average 0.2 cents) in Spain.  

This paper is structured as follows. Section 2 provides a literature review, focusing on income and wealth 

effects for the euro area and the four largest euro area countries. Section 3 describes the thick modelling 

of real private consumption. It introduces the basic consumption specification, followed by a description of 

the  applied  thick  modelling  selection  process.  Section  4  describes  the  data.  Section  5  discusses  the 

empirical results, focusing on the estimated income and wealth effects, the model validation in terms of 

out-of-sample performance, and the robustness of the empirical results. Section 6 concludes. 

ECB Working Paper Series No 2343 / December 20195  
 
 
 
2. 

Literature 

This section briefly reviews existing empirical evidence on income and wealth effects on consumption in 

the  four  largest  euro  area  countries  and  the  euro  area  as  a  whole.  Table  1  provides  an  overview  of 

empirical evidence on income and wealth effects in the long run based on macroeconomic studies. They 

all examine disaggregate effects with respect to wealth only.  

Several  observations  emerge  from  the  overview  of  the  empirical  evidence  of  the  long-run  income  and 

wealth  effects  in  the  euro  area  and  the  largest  countries.  First,  the  empirical  estimates  for  income 

elasticities exhibit a wide range, from 0.4 to 0.9 in the case of the euro area, being somewhat narrower 

and higher for Germany (0.8 to 1.0), somewhat lower for Spain and rather wide for France and Italy. The 
estimates for the MPC out of income are around 60 to 80 cents.1  

Second, the evidence supports a significant financial wealth effect on consumption in the long run in the 

euro area and the major countries. The range of empirical estimates for financial wealth effects is wide, 

including cases of negative effects. This may reflect different samples, difficulties in the measurement of 

financial  wealth  (often  approximated  by  equity  price  indices)  and  a  lack  of  a  common  estimation 

framework. The long-run financial wealth elasticities mostly amount between -0.03 and 0.30, whereas the 

MPC  range  is  again  very  wide  (-3  to  +15  cents).  For  Germany  and  Italy,  financial  wealth  effects  have 

been estimated to be negative in some cases. Third, the housing wealth effect tends to be weaker in the 

euro  area  and  across  countries  and  is  sometimes  statistically  insignificant.  The  estimated  long-run 

housing wealth elasticities vary between -0.07 and 0.18 and the MPCs between -7 and 8 cents. Spain is 

the only country for which only positive housing wealth effects have been estimated.  

Finally,  disaggregate  wealth  effects  differ  substantially  across  the  largest  euro  area  countries  and 

sometimes the results are inconclusive for the same country across studies. The evidence of significant 

financial wealth effects is mixed for Germany while it is typically found that housing wealth does not have 

an  impact  on  German  consumption  expenditure.  Financial  wealth  is  usually  found  to  be  an  important 

long-run determinant of French consumption and some evidence is also supportive of a likely smaller but 

significant  housing  wealth  effect.  With  respect  to  Italy,  the  long-run  financial  wealth  effect  is  typically 

significant and positive but the evidence of housing wealth effect is rather mixed. It seems that both types 

of wealth are important for consumption expenditure in Spain.  

1 Note that some studies report MPCs in terms of the US dollar. 

ECB Working Paper Series No 2343 / December 20196  
 
 
 
 
 
                                                      
Table 1 Empirical estimates of long-run income and wealth elasticities and MPCs 

Paper

Sample

Methodology

Country

Long‐run [MPC] and (elasticity)
FW

HW

Income

Be rta ut (2002)

De pe nds  on a  
country

Fi rs t‐di ff. 
e qua ti ons , ECM

Byrne a nd Da vi s  
(2003)

 1972‐1998

ECM

Ca tte  e t a l  (2004)

De pe nds  on a  
country

ECM

Pa che co  a nd 
Ba ra ta  (2005)

De pe nds  on a  
country

ECM

Al ‐Eyd e t a l . (2006)

1974 ‐ 2002

Si ngl e ‐country 
a nd pa ne l  ECM

Ba s s a ne tti  a nd 
Zol l i no (2008)

 1980‐2006

VECM

Sl a ca l e k (2009)

1980‐2008 (EA)

Skude l ny (2009)

1981(95) ‐2006 

Sous a  (2009)

1980‐2007

Country‐ a nd 
group‐l e ve l 
re gre s s i ons : 
Ca rrol l  e t a l . 
(2011) a pproa ch 

Long‐run 
e qua ti ons ; ECM

ECM, Ca rrol l  e t 
a l . (2011) 
a pproa ch

Cha uvi n a nd 
Da me tte  (2010)

1987‐2006

VECM, l ong‐run 
e qua ti ons

Ke rdra i n (2011)

De pe nds  on a  
country

ECM

De  Boni s  a nd 
Si l ve s tri ni  (2012)

1997 ‐ 2008

Ba rre l l  e t a l . 
(2015)

1972‐2012

Pa ne l  ECM, 
country‐l e ve l  
ARDL 

Long‐run 
e qua ti ons , 
Ca rrol l  e t a l . 
(2011) a pproa ch

Pa ne l  l ong‐run 
a nd fi rs t‐di ff. 
e qua ti ons

Rodi l ‐Ma rza ba l  
a nd Me ne ze s ‐
Fe rre i ra ‐Juni or 
(2016)

Rodri gue z‐
Pa l e nzue l a  a nd 
De e s  (2016)

2000‐2010

2000‐2013

Pa ne l  ECM

Wi nkl e r (2016)

1995‐2013

 VECM

Gue rri e ri  a nd 
Me ndi ci no  (2018)

 1999‐2017

Country‐ a nd 
group‐l e ve l 
re gre s s i ons : 
Ca rrol l  e t a l . 
(2011) a pproa ch 

FR

DE

FR

IT

DE

FR

IT

ES

DE

FR

IT

DE

FR

IT

ES

EA

IT

DE

FR

IT

ES

EA

EA

EA

FR

EA

DE

FR

IT

ES

IT

EA

EA

DE

IT

DE

FR

IT

ES

BIG 5

(0.80)

(0.10)  [2.7]

 (0.85‐0.97)

(0.09)  [2‐2.3]

(0.81‐1.07)

(0.16)  [2.9‐3]

(0.90‐1.14)

(0.10)  [1.3‐2]

(0.91)

(0.86)

(0.42)

(0.42)

(0.83)

(0.07)

(0.44)

(0.03)  [2]

(0.03)  [2]

(‐0.03)

(0.08)

(0.03)

(0.93‐0.97)

(0.03‐0.07)

(0.89‐1.00)

(0.01‐0.11)

(‐0.84‐0.85)

(0.15‐1.84)

(0.35‐0.95)

(0.05‐0.65)

(0.58‐0.87)

(0.02‐0.12)

‐

‐

‐

‐

‐

‐

‐

‐

‐

‐

‐

‐

‐

‐

(0.04)  [1]

(0.09)  [1]

(0.07)  [2]

(0.15)  [2]

(0.76‐1.1)   
[60‐70]

‐

‐

‐

‐

‐

‐

(0.09‐0.19)    

[4‐6]

[14.2]

 [2.9]

 [10.3]

[5.3]

[1‐3.8]

[0.6‐3.6]

(0.05‐0.08)  
[1.5‐2]

[2.9]

[2.3]

[‐1.1]

[6.2]

[‐1.3‐2]

[0.7‐2.5]

(0.65‐0.91)  
[55.5‐77.7]

(0.12‐0.15) 
[1.4‐1.9]

(‐0.07‐0.05)    
[‐0.47‐0.3]

(0.53‐0.92)

(0.08‐0.12)  
[4.4‐11.9]

(0.05‐0.08)  
[0.8‐4.3]

‐

‐

‐

‐

‐

[5‐7]

[0‐2]

[‐0.4]

[3.4]

[‐0.7]

[2.8]

[‐0.8]

[‐1.6]

[0.3]

 [0.2]

(0.36‐0.4)

(0.23)         

(0.09)         

[2.4‐2.8]

[‐0.3‐0.7]

 (0.55‐0.90)

(0.29)

(0.04)

(0.43‐0.58)

(0.01‐0.03)

(0.05‐0.09)

 (0.77)  [61.2]

(0.87)  [69.6]

‐

‐

(0.18)  [3.6]

(0.10)  [1.9]

‐

‐

‐

‐

‐

[‐2.9 to ‐2.8]

[‐7.3 to ‐4]

[4.1‐4.2]

[5.8‐6.1]

[9.6‐14.6]

[4.1]

[3‐3.1]

[6.3‐7.3]

[4.1‐7.7]

[3.3]

ECB Working Paper Series No 2343 / December 20197  
 
The differences in the estimated elasticities and MPCs out of wealth components may reflect a number of 

aspects. In particular, non-financial (mainly housing), equity and non-equity financial wealth differ in terms 

of  liquidity,  risk  and  collateral  characteristics  (see  Altissimo  et  al.  (2005)  and  references  therein).  The 

MPC  out  of  liquid  assets  (mostly  financial  assets)  is  likely  to  be  greater  than  that  out  of  illiquid  (mostly 

housing) wealth. The MPC out of assets associated with strong bequest motive (housing wealth) is likely 

to  be  smaller.  Assets  with  less  volatile  prices,  such  as  non-equity  wealth  should  have  higher  MPCs  as 

price  changes  are  likely  to  be  perceived  to  be  more  permanent.  Furthermore,  the  MPC  out  of  wealth 

could also depend on the distribution of an asset across households. Some assets, such as equities, are 

concentrated  at  the  top  of  the  income  distribution  and  wealthy  households  tend  to  have  lower  MPCs 

(Sierminska and Takhtamanova, 2012). Evidence of a decreasing MPC out of wealth across the wealth 

distribution  in  France  is  reported  by  Arrondel  et  al.  (2015).  Overall,  non-equity  financial  assets  should 

have  the  largest  MPCs  while  the  relative  size  of  equity  and  housing  wealth  MPCs  is  somewhat 

ambiguous.  The  cross-country  divergences  in  the  estimated  MPCs  could  be  explained  by  different 

regulatory and institutional frameworks, demographic characteristics, or the degree of credit constraints of 

households (Cooper and Dynan, 2016). 

Concerning the large range of estimated housing wealth effects, there are two forces acting in opposite 

directions  as  households  both  own  housing  assets  and  consume  housing  services  derived  from  these 

assets  (Catte  et  al.,  2004;  Cheng  and  Fung,  2008;  Buiter,  2010;  Aron  et  al.,  2012).  On  the  one  hand, 

higher house prices could force potential first-time buyers to save more in order to buy a property in the 

future. On  the other  hand,  higher  house prices increase the  wealth of those  who  already  own  a  house. 

Housing assets can be used as collateral to obtain a loan or, alternatively, owners could sell a house and 

earn capital gains. Consequently, the size and sign of the overall MPC out of housing wealth depends on 

which effect dominates. This is subject to many factors, such as country’s homeownership rate, the size 

of the rental and mortgage market, and the possibility to benefit from equity withdrawal (see also Cooper 

and Dynan, 2016).   

3.  Methodology 

3.1  Basic specification 

Our  basic  specification 

follows  a  conventional  approach  by  exploiting  co-integration  between 

consumption, income and wealth. The  most widespread  estimation approach in the literature is either a 

single equation error correction model (ECM) or a vector ECM assuming long-run co-integration between 

consumption, income and wealth (Byrne and Davis, 2003; Catte et al., 2004; Al-Eyd, 2005; Hamburg et 

al., 2008; Kerdrain, 2011; Rodriguez-Palenzuela and Dees, 2016; Winkler, 2016). See also the pioneering 

ECB Working Paper Series No 2343 / December 20198  
 
 
work  by  Ludvigson  and  Steindel  (1999),  Lettau  and  Ludvigson  (2001)  and  Fernandez-Corugedo  et  al. 

(2003)  that  impose  co-integration  between  consumption,  income  and  wealth.  Nevertheless,  several 

studies  (Slacalek,  2009;  Sousa,  2009;  Chauvin  and  Damette,  2010;  Barrell  et  al.,  2015;  Guerrieri  and 

Mendicino,  2018)  employ  an  alternative  method,  either  exclusively  or  in  addition  to  the  standard  ECM, 

developed  by  Carroll  et  al.  (2011)  based  on  consumption  growth  sluggishness.  However,  when 

comparing the estimates based on this approach it is important to note that the long-run (“eventual”) MPC 

refers  to  the  period  after  a  few  years.  Others  simply  estimate  level  and/or  first-difference  equations  of 

consumption expenditure (Rodil-Marzabal and Menezes-Ferreira-Junior, 2016). 

The  applied  error  correction  model  specification  has  the  advantage  that  it  distinguishes  between  short- 

and long-run elasticities. Our estimates indeed show that the estimated short- and long-run income and 

wealth elasticities do differ in almost all cases. At the same time, the significance of the estimated error-

correction coefficients, again consistently found for all countries, indicate that consumption, income and 

wealth are co-integrated as defined by Engle and Granger (1987).  

Income and wealth variables are assumed to affect consumption in both the short and the long run. We 
use  euro  area  sector  accounts  data  to  split  real  disposable  income  into  labour  income  (ly),  transfer 

income (ty), and property income (py). In addition, real wealth (nominal household total wealth deflated by 

the  private  consumption  deflator)  is  split  into  non-financial  wealth  (nfw)  and  financial  wealth  (fw),  i.e. 

financial assets less financial liabilities).  

All  other  determinants  of  private  consumption  considered  are  assumed  to  affect  private  consumption  in 

the short run only and have been checked on stationarity and are therefore typically included by taking a 

change (∆xi). Appendix A provides an overview of the other determinants, the transformation considered 

and the unit root tests. Most variables are expressed in natural logarithms with the exception of interest 

rates, unemployment rate, leverage / debt ratios and survey measures. To ensure long-run homogeneity, 

the long-run parameters for income and wealth components are restricted to sum up to 1. This approach 

has  also  been applied  by  others (Barrell and Davis, 2007; Estrada  et al., 2014). The basic equation for 

consumption growth is an error correction model presented in Equation (1):  

∆(cid:4666)(cid:1855)(cid:3047)(cid:4667) (cid:3404) (cid:2009) (cid:3397) (cid:2010)(cid:2868)∆(cid:4666)(cid:1864)(cid:1877)(cid:3047)(cid:4667) (cid:3397) (cid:2010)(cid:2869)∆(cid:4666)(cid:1872)(cid:1877)(cid:3047)(cid:4667)	(cid:3397)	(cid:2010)(cid:2870)∆(cid:4666)(cid:1868)(cid:1877)(cid:3047)(cid:4667) (cid:3397) (cid:2010)(cid:2871)∆(cid:4666)(cid:1858)(cid:1875)(cid:3047)(cid:2879)(cid:2869)(cid:4667) (cid:3397) (cid:2010)(cid:2872)∆(cid:4666)(cid:1866)(cid:1858)(cid:1875)(cid:3047)(cid:2879)(cid:2869)(cid:4667) (cid:3398) (cid:2011)(cid:3435)(cid:4666)(cid:1855)(cid:3047)(cid:2879)(cid:2869)(cid:4667) (cid:3398) (cid:4666)1 (cid:3398) (cid:2016)(cid:2869) (cid:3398) (cid:2016)(cid:2870) (cid:3398) (cid:2016)(cid:2871) (cid:3398)
(cid:2016)(cid:2872)	(cid:4667)(cid:4666)(cid:1864)(cid:1877)(cid:3047)(cid:2879)(cid:2869)(cid:4667) (cid:3398) (cid:2016)(cid:2869)(cid:4666)(cid:1872)(cid:1877)(cid:3047)(cid:2879)(cid:2869)(cid:4667) (cid:3398) (cid:2016)(cid:2870)(cid:4666)(cid:1868)(cid:1877)(cid:3047)(cid:2879)(cid:2869)(cid:4667) (cid:3398) (cid:2016)(cid:2871)(cid:4666)(cid:1858)(cid:1875)(cid:3047)(cid:2879)(cid:2870)(cid:4667) (cid:3398) (cid:2016)(cid:2872)(cid:4666)(cid:1866)(cid:1858)(cid:1875)(cid:3047)(cid:2879)(cid:2870)(cid:4667)(cid:3439) (cid:3397) (cid:2012)(cid:3036) (cid:4674)∆(cid:1876)(cid:3036)(cid:3295)(cid:3127)(cid:3285)(cid:4675) (cid:3397) (cid:1873)(cid:3047)																																																(cid:4666)1(cid:4667)   

ECB Working Paper Series No 2343 / December 20199  
 
 
 
 
 
where ∆ denotes quarter-on-quarter changes, (cid:2011) is the error correction term (ECM) on the lagged log level 

of consumption, (cid:2010)(cid:3036)  and  (cid:2016)(cid:3036)  represent short-run and long-run income and  wealth  elasticities,  respectively. 
Across different models, the number of additional short-run determinants other than income and wealth (i) 

can  range  between  1  and  3  and  they  might  be  included  with  lags  (j)  varying  between  0  and  2.  With 

respect  to  the  ECM,  a  highly  statistically  significant  (cid:2011)  parameter  would  be  consistent  with  the 

cointegrating relation in the long-run vector. Typically, the absolute value of the t-statistic for (cid:2011) is expected 

to be greater than 3 (Kremers et al., 1992; Banerjee et al., 1993; Al-Eyd et al., 2006; Barrell and Davis, 

2007). Note that wealth variables are lagged by one period in the short and long run as they reflect stocks 

as  of  the  end  of  the  period.  Hence,  current  consumption  is  assumed  to  be  dependent  on  the  stock  of 

financial and non-financial wealth as recorded in the previous quarter.  

The  empirical  literature  offers  various  methods  to  estimate  consumption  functions.  Using  a  log-linear 

specification  as  pursued  here,  we  estimate  elasticities  directly  and  then  calculate  the  respective  MPCs 

based  on  average  consumption-to-wealth/income  ratios.  Some  issues  may  arise  however  due  to  time-

variation in these ratios (Labhard et al., 2005; Chauvin and Damette, 2010). Alternatively, the MPCs can 

be estimated directly using a ratio specification. While many studies estimate the MPCs directly (Slacalek, 

2009; de Bonis and Silvestrini, 2012; Guerrieri and Mendicino, 2018), the elasticity-based approach is at 

least  equally  popular  (Bertaut,  2002;  Catte  et  al,  2004;  Pacheco  and  Barata,  2005;  Al-Eyd  et  al.,  2006; 

Bassanetti and Zollino, 2008; Sousa, 2009; Rodil-Marzabal and Menezes-Ferreira-Junior, 2016). Several 

studies provide and compare the results based on both approaches (Chauvin and Damette, 2010; Barrel 

et al., 2015; Winkler, 2016). As the third option, logged income and consumption variables are used by 

some  in  combination  with  unlogged  wealth  variables  expressed  as  ratios  to  income  (Byrne  and  Davis, 

2003; Kerdrain, 2011; Aron et al., 2012). 

Short-run determinants other than income and wealth components are grouped in five categories: (i) real 

interest rates and interest rate spreads, including several measures of the external finance premium; (ii) 

measures of consumer indebtedness; (iii) measures of government indebtedness capturing the Ricardian 

equivalence effects; (iv) uncertainty measures; (v) other variables. Table A1 in the Appendix provides a 

detailed  list  of  variables  in  each  category.  Each  estimated  equation  always  includes  one  of  the  interest 

rate-based measures and, additionally, up to two other determinants each taken from a different category 

in various combinations.  

These additional short-term determinants capture the effects of interest rates (de Bondt, 1999; Geiger et 

al.,  2014;  Premik  and  Stanislawska,  2017),  fiscal  stance  and  policy  to  capture  Ricardian  equivalence 

(Rohn,  2010;  Estrada  et  al,  2014),  consumer  confidence,  and  demographic  characteristics  (Hufner  and 

ECB Working Paper Series No 2343 / December 201910  
 
 
 
Koske, 2010). Many other empirical studies consider these and other variables, such as unemployment 

rate,  consumer  price  inflation  (Bachmann  et  al.,  2015;  Arioli  et  al.,  2017)  or  uncertainty  more  general 

(Dees and Brinca, 2013; Bahmani-Oskooee et al., 2015; Gieseck and Largent, 2016, Lahiri et al., 2016; 

Rodil-Marzabal  and  Menezes-Ferreira-Junior,  2016;  Premik  and  Stanislawska,  2017).  A  positive  and/or 

negative impact of household debt on consumption is also analysed (Pacheco and Barata, 2005; Carroll 

et  al.,  2011;  Dynan,  2012;  Estrada  et  al.,  2014;  Albuquerque  and  Krustev,  2015;  Arrondel  et  al.,  2015; 

Kim  and  Setterfield,  2016;  Guerreri  and  Mendicino,  2018).  Furthermore,  it  is  also  common  to  include 

income  and  wealth  effects  not  only  in  the  long  run  but  also  in  the  short-run  (Catte  et  al.,  2004;  Sousa, 

2009, Časni, 2016).  

3.2  Selection of equations  

The  starting  point  of  our  empirical  methodology  is  the  application  of  Generalised  Method  of  Moments 

(GMM)  estimation  of  a  vast  number  of  ECMs  as  in  Equation  (1)  using  data  over  the  sample  period 

1999Q1 to 2018Q2. The GMM is chosen as an estimation method here in order to account for potential 

endogeneity  among  variables  and  possible  measurement  errors  in  particular  in  the  income  and  wealth 

components.  For  every  equation,  5  lags  of  the  dependent  and  independent  variables  are  used  as 

instruments. After accounting for data transformation and lags the actual estimation sample begins in late 

2001, albeit it varies slightly across specifications. The sample period is short, but due to data constraints 

it is not possible to extend the sample backwards. Notwithstanding this important caveat, our sample has 

the advantage that it does not contain synthetic euro area data, given that it starts with Stage Three of the 

Economic and Monetary Union.  

In  addition,  thick  modelling  considers  the  uncertainty  stemming  from  model  specification  and  is  thus 

particularly useful for empirical applications using a short sample where model uncertainty is expected to 

play a role, because it does not rely on a single “best” model specification. Averaging over 50 models is in 

our  view  sufficiently  thick  in  practice.  Bayesian  model  averaging  using  the  Occam’s  window  reduce  in 

many  practical  cases  the  number  of  models  to  fewer  than  25  (Clyde,  1999).  While  the  latter  provides 

better  predictive  performance  than  selecting  the  single  “best”  model,  averaging  over  a  larger  set  of 

models often leads to better predictive performance. We therefore set the number of model equations at 

two times 25.  

After  generating  around  6,500  consumption  equations  per  country,  we  follow  a  four-step  selection 

process to filter the best ECM specifications, with first three in-sample selection criteria, followed by one 

out-of-sample criterion:  

ECB Working Paper Series No 2343 / December 201911  
 
 
 
1)  the  error  correction  coefficient  (γ)  should  be  statistically  significant  at  the  1%  level  to  ensure  that 

consumption is co-integrated with income and wealth;  

2) the F-statistic should be at the 5% level to ensure that short-term coefficients (δ) are jointly significant;  

3) the P-value of the Ljung-Box Q-statistics should be above 0.05 for the lags 1-4 as well as 12, i.e. there 

should be no residual autocorrelation as a sign of model misspecification; 

4) the out-of-sample root mean squared error (RMSE) should be at least as low as those from a AR(1) 

benchmark model and the focus is then on the 50 equations with the lowest RMSE.  

Following the three in-sample selection criteria of the selection process, between 2089 (France) and 4876 

(Spain)  equations remain,  i.e.  between  32% and  75%  of  the original  equations. For the  fourth  selection 

criterion, equations are estimated recursively with end-dates ranging from 2012Q4 to 2016Q2 to generate 

conditional forecasts for quarterly consumption growth for horizons between 1 and 8 quarters ahead, i.e. 

over  the  pseudo  out-of-sample  period  spanning  2013Q1  to  2018Q2.  RMSE  are  calculated  over  all 

horizons. For instance, if the forecast horizon is 4 quarters, the RMSE is calculated based on forecasts 1, 

2, 3 and 4  quarters ahead. The ECM  equations are sorted according to an average RMSE based on 8 

horizons  (from  the  lowest  to  the  highest).  In  addition,  the  relative  average  RMSEs  against  a  AR(1) 

benchmark model are computed and only specifications with a RMSE lower than the benchmark model 

are selected. The benchmark is an AR(1) model, which is known to be hard to beat and often used. The 

autoregressive benchmark in many cases outperforms in forecasting consumption growth for the current 

quarter  for  the  euro  area  and  the  three  largest  euro  area  countries  (Dreger  and  Kholodilin,  2013). 

Eventually, we select the top 50 equations out of the between 788 (Spain) and 2618 (Italy) pre-selected 

models that perform better than the AR(1) benchmark model in terms of RMSE.  

4.  Data  

The source for all quarterly time series for the period 1999Q1 to 2018Q2 is the European Central Bank’s 

Statistical Data Warehouse (SDW). Income, wealth and debt variables are taken from the integrated euro 

area  accounts data  for the household  sector,  while  real  private  consumption,  government consumption, 

public debt and deficit series are taken from Eurostat National Accounts. Rather than using financial and 

housing price indices (Ludwig and Sløk, 2004; Rodriguez-Palenzuela and Dees, 2016) we use quarterly 

sector  accounts  data  on  households  financial  balance  sheets.  With  respect  to  survey-based  measures, 

we  use  two  surveys:  the  ECB’s  Survey  of  Professional  Forecasters  and  the  European  Commission 

Consumer  Survey.  All  series  are  seasonally  adjusted  either  at  the  source  or  by  applying  Census  X-13 

method, the latter mainly refers to series from financial accounts such as wealth and loans for households 

ECB Working Paper Series No 2343 / December 201912  
 
 
that  are  not  available  as  seasonally  adjusted.  Also,  nominal  series  are  deflated  using  the  private 

consumption deflator. 

Total  disposable  income  is  decomposed  into  labour,  transfer  and  property  income.  Labour  income  is 

calculated as the sum of total compensation of employees and gross mixed income (i.e. income of self-

employed)  less  net  social  security  contributions  and  labour  income  share  of  direct  taxes.  The  share  of 

taxes  paid  on  labour  income  is  approximated  by  the  share  of  labour  income  (compensation  and  mixed 

income)  in  the  pre-tax  income  of  households  before  taking  into  account  social  security  contributions. 

Property  income,  from  which  direct  taxes  are  also  deducted  on  a  pro  rata  basis,  is  the  sum  of  gross 

operating surplus excluding mixed income, net interest income and net other  property income. Transfer 

income is then the remaining component, i.e. total disposable income less labour and property income. It 

is calculated as the sum of social benefits and net other current transfers minus imputed transfer taxes. 

Appendix B provides further details on how the income and wealth splits are calculated.  

Concerning our choice of variables, we choose to model total consumption expenditure as a function of 

total  disposable  income.  Empirical  studies  differ  substantially  in  how  key  variables  in  the  consumption 

function  are  defined.  In  line  with  theory,  some  define  consumption  expenditure  as  that  of  non-durable 

goods  (Hamburg  et  al.,  2008;  Chauvin  and  Damette,  2010).  Nevertheless,  the  vast  majority  of  studies 

uses  total  consumption  expenditure.  It  is  also  argued  that  total  consumption  is  the  important  variable 

when  analysing  wealth  effects  (Mehra,  2001;  Ludwig  and  Sløk,  2004;  Sousa,  2009;  Guerrieri  and 

Mendicino,  2018).  Similarly,  non-property  income  is  theoretically  a  preferred  measure  of  income 

(Benjamin et al., 2004; Catte et al, 2004; Labhard et al, 2005; Slacalek, 2009; Kerdrain, 2011; Aron et al., 

2012).  However,  many  others  still  utilise  total  disposable  income  (Byrne  and  Davis,  2003;  Ludwig  and 

Sløk, 2004; Časni, 2016; Rodriguez-Palenzuela and Dees, 2016; Winkler, 2016; Guerrieri and Mendicino, 

2018). Finally, the measures of wealth components also vary. Instead of the stock of wealth, equity and 

house price indices may be used (Ludwig and Sløk, 2004; Rodriguez-Palenzuela and Dees, 2016). Total 

net worth may be split into its components by either keeping one of them in gross terms or expressing all 

in net terms (Sousa, 2009). In line with most of the existing literature our specification looks at gross non-

financial  wealth  and  financial  net  worth.  The  robustness  section  considers  alternative  definitions  and 

disaggregation of wealth found in the literature.  

Table  2  presents descriptive statistics for the income  and  wealth components. Labour income accounts 

for about half of total disposable in the euro area, Germany, France and Italy. In Spain the labour income 

share  in  total  disposable  income  has  been  comparatively  high  at  64%.  Transfer  income  has  been 

consistently the second most important income component for the euro area, France and Spain, while for 

ECB Working Paper Series No 2343 / December 201913  
 
 
 
Germany  and  Italy  transfer  and  property  income  has  been  of  similar  importance.  Property  and  transfer 

income  are  more  volatile  than  labour  income  and  the  differences  across  countries  are  substantial.  The 

large share of property income in total disposable income justifies its inclusion in the regression and the 

difference in volatilities justifies allowing for different elasticities.  

The  major  component  of  total  wealth  has  always  been  non-financial  wealth.  Its  share  has  been  on 

average about two-third in all cases with the exception of Spain where its share has been between 70% 

and  90%  since  1999  (see  Table  2).  Non-financial  wealth  consists  almost  entirely  (89%  and  100%)  of 

housing  wealth  in  all  five  cases.  Around  one  third  (Spain  lower  with  on  average  18%)  of  total  wealth 

consists  of  financial  wealth,  of  which,  in  turn,  about  half  relate  to  pension  wealth  in  the  euro  area, 

Germany and France and about one quarter in Italy and Spain. The wealth to income ratio has been most 

of  the  time  on  a  rising  path.  This  ratio  has  been  on  average  about  700%  in  the  euro  area,  France  and 

Italy, lower in Germany  (525%)  and  higher  in Spain  (862%). Turning to the  household leverage  ratio, it 

has  varied  a  lot  across  countries.  The  loans  to  income  ratio  has  been  comparatively  low  in  Italy  (53%) 

and high in Spain (108%) and has predominantly declined in Germany (10% of all observation has seen a 

negative annual change) and rising in France (94% of all observations). 

Table 2 Income and wealth components  
(1999Q1 to 2018Q2; in % total disposable income, respectively, wealth) 

Euro area

France

Italy

Spain

Labour income
Transfer income
Property income
Non-financial wealth
    Housing wealth
Financial wealth

Mean
53
27
21
68
64
32
14
674
76
90
63

Std
1.26
1.77
2.23
1.06
1.13
1.94
1.00

Germany
Mean 
51
26
23
68
61
32
17
525
80
94
10

Std
1.30
2.16
3.79
0.96
1.04
2.60
0.75

Mean 
51
32
17
68
65
32
15
693
76
74
94

Std
1.30
1.10
1.88
1.02
1.07
1.72
0.99

Mean 
47
24
28
62
57
38
8
756
60
53
70

Std
1.21
1.07
1.57
0.98
1.04
2.09
1.12

Mean 
64
22
14
82
82
18
5
862
67
108
49

Std
0.91
1.46
4.20
1.16
1.17
1.88
0.74

Pension wealth
Wealth to income ratio
     % increasing
Loans to income ratio
     % increasing
Notes: Non-financial wealth, housing wealth financial wealth and pension wealth in % of total net-worth. 
%  increasing  is  number  of  observations  with  a  positive  4-quarter  change  in  the  ratio.  Financial  wealth 
refers to net financial wealth, pension wealth to net pension wealth. Wealth to income ratio is the ratio of 
total wealth (net worth) to total disposable income. Std refers to standard deviation in the change relative 
to the standard deviation in the change of total disposable income, respectively, wealth. 

ECB Working Paper Series No 2343 / December 201914  
 
 
 
 
5.  Empirical results 

5.1  Estimates 

Two  main  conclusions  emerge  from  Table  3  that  summarises  the  estimation  results.  It  reports  the 

average estimated income and wealth elasticities in the long and short run based on the selected top 50 

equations,  the  long-run  MPCs  out  of  income  and  wealth  as  well  as  the  range  and  average  of  the 

estimated error-correction coefficient (speed of adjustment towards the co-integration relationship).  

The first conclusion is that the thick model estimates confirm that a split of income as well as wealth is 

indeed  required.  The  long-run  labour  income  elasticities  are  always  greater  than  those  of  transfer  and 

property  income.  In  addition,  their  average  estimates  are  outside  the  range  of  those  of  transfer  and 

property  income  for  the  euro  area  aggregate  and  Spain  and  outside  the  range  of  property  income  for 

Germany and Italy. The estimated transfer income elasticities are typically larger than those of property 

income.  Based  on  the  ranges  of  the  estimates,  the  difference  between  transfer  and  proper  income  is 

more apparent in France and Italy. Similarly, a wealth split has value added for the euro area, France and 

Spain. Here, the long-run elasticities with respect to financial wealth are outside (for France mostly) the 

range  of  those  with  respect  to  non-financial  wealth.  Consequently,  it  is  important  to  split  disposable 

income and wealth. 

Secondly, euro area estimates mask striking cross-country differences. For the income split, most marked 

country  difference  relates  to  the  role  of  property  income.  It  plays  on  average  a  limited  role  for 

consumption in France, Italy and Spain, whereas property income is estimated to be essential for German 

consumption developments. The MPC out of transfer income is estimated to be on average close to 100 

cents  in  Germany,  France  and  Italy,  more  than  twice  as  large  as  in  Spain.  The  thick  model  estimates 

show on average small wealth effects, albeit in most cases significantly different from zero. The MPC out 

of non-financial wealth for Spain is estimated to be on average about 0.2 cents on the euro, whereas for 

Germany, France, Italy and the euro area the MPCs are not significantly different from zero. The long-run 

as  well  as  short-run  MPCs  out  of  financial  wealth  are  estimated  to  be  larger  than  those  with  respect  to 

non-financial wealth in all cases except in the long-run for Germany where both MPCs are estimated to 

be on average close to zero. Another cross-country difference is that the estimated speed of adjustment 

towards equilibrium is quicker in Germany and Italy (around 0.3) compared to France and Spain, where 

the average estimated adjustment coefficient is about 0.2. It is difficult to provide a definitive explanation 

for  this  difference,  but  it  could  relate  to  the  more  prominent  role  of  property  income  in  Germany  and  of 

transfer income in Italy.  

ECB Working Paper Series No 2343 / December 201915  
 
 
 
Table 3 Estimation results  

Average 

Short run
Elasticity  MPC
Average 
euro area
0.30 ***
0.08 ***
0.09 ***
0.00

50

27

41

-0.26

0.06

0.30

Germany
0.29 ***

0.14 ***

0.14 ***

-0.10

0.06

France
-0.01

0.15 **

0.00

0.14 **

0.07 ***

Italy

0.02
0.04
0.11 ***
-0.03
0.01

49

46

54

-0.64

0.76

-2

42

1

0.67

0.74

4.3
14
37
-0.17
0.10

Labour income

Transfer income

Property income

Non-financial wealth

Financial wealth
Speed of adjustment

Labour income

Transfer income

Property income

Non-financial wealth

Financial wealth

Speed of adjustment

Labour income

Transfer income

Property income

Non-financial wealth

Financial wealth

Speed of adjustment

Labour income
Transfer income
Property income
Non-financial wealth
Financial wealth
Speed of adjustment

Long run
Elasticity 

MPC 

Range

Average 

Range

Average

0.35 - 0.51

0.47 ***

58 - 85

0.21 - 0.31

0.26 ***

0.17 - 0.31

0.20 ***

69 - 100

73 - 131

-0.02 - 0.03

0.05 - 0.07
0.37 - 0.65

0.01
0.06 ***
0.49 ***

-0.08 - 0.15

0.53 - 0.73

0.30 - 0.71

0.47 ***

0.13 - 0.38

0.24 ***

0.20 - 0.29

0.24 ***

-0.20 - 0.20

0.04

-0.07 - 0.09
0.15 - 0.54

0.00
0.29 ***

50 - 120

45 - 126

73 - 105

-1.19 - 1.26

-0.90 - 1.23

0.16 - 0.75

0.51

-0.01 - 0.61

0.35 **

-0.17 - 0.20

-0.05 - 0.08

0.01

0.00

28 - 127

-4 - 164

-87- 99

-0.22 - 0.38

0.07 - 0.17

0.11 *

0.70 - 1.72

0.12 - 0.27

0.20 ***

79

83

85

0.04

0.66

79

80

87

0.23

0.06

86

95

7

0.03

1.13

0.31 - 0.79
0.28 - 0.44
-0.10- 0.21
-0.04 - 0.00
-0.02 - 0.14
0.20 - 0.36

0.49 ***
0.35 ***
0.09
-0.01
0.08 **
0.28 ***

57 - 145 
103 - 161
-0.30 - 68
-0.20 - 0.03
-0.17 - 1.14

91
127
25
-0.06
0.61

Spain
0.05
0.00
0.00
0.09
0.05 ***

6
21
2
0.28
0.80

Labour income
Transfer income
Property income
Non-financial wealth
Financial wealth
Speed of adjustment
Notes:  Ranges  and  averages  based  on  selected  top  50  equations  using  GMM  estimation.  Marginal 
propensity to consume (MPC) is reported in euro cents (100*elasticity*C/X, where C is the average level 
of real consumption level and X is the average level of relevant income/wealth over 1999Q1 to 2018Q2. 
 *, **, *** denote significantly differently from zero in at least 90%, 95%, respectively, 99% out of the 50 
selected equations. 

0.48 - 0.65
-0.15 - 0.19
-0.01 - 0.12
0.06 - 0.11
0.14 - 0.33
0.14 - 0.25

68 - 92
-61 - 78
-12 - 82
0.18 - 0.38
2.20 - 5.19

0.55 **
0.12
0.05
0.07 **
0.20 **
0.20 ***

78
49
31
0.23
3.12

ECB Working Paper Series No 2343 / December 201916Overall,  our  results  are  in  line  with  the  consumption  literature  for  the  euro  area  as  a  whole  and  for 

individual countries. The finding that the long-run MPCs out of financial wealth are greater than that out of 

non-financial  wealth is also  reported in  Guerrieri  and Mendicino  (2018) for France  and  Spain. Similarly, 
they  do not  find evidence  of  a  wealth  effect for Germany.2  Hamburg  et al. (2008) show that permanent 

shocks  to  income  rather  than  to  wealth  have  played  the  predominant  role  for  German  private 

consumption.  For the  euro area, Sousa (2009) finds  that the long-run MPC to  consume  out of financial 

wealth is between 1.4 and 1.9 cents per euro, while the MPC to consume out of gross housing wealth is 

much  smaller  (at  most  0.3  cents  per  euro).  In  both  cases  the  pre-Great  Recession  estimates  are  a  bit 

higher  than  the  thick  model-based  averages.  Slacalek  (2009)  also  shows  that  financial  wealth  is 

associated with higher MPCs as compared to non-financial wealth in the euro area as well as for France 

and Italy. With respect to France, Arrondel et al. (2015) find that the MPC out of financial wealth tends to 

be higher compared with the effect of housing wealth except in the top of the wealth distribution. Navarro 

et al. (2015) report for Spain that the main long-run wealth effect is coming from financial wealth followed 

by residential wealth.  

An explanation for the low and, in the case of Italy, on average negative non-financial wealth elasticity is 

that housing has the dual functions as both an investment asset yielding a flow of capital income and a 

commodity  yielding  a  flow  of  housing  services.  Consequently,  a  rise  in  housing  price  has  a  positive 

impact on wealth caused by an increase in capital income and a negative effect due to an increase in the 

cost of housing services (Cheng and Fung, 2008). Interestingly, Cheng and Fung also link the dual impact 

of  housing  wealth  to  the  leverage  ratio,  with  a  low  (like  in  Italy)  and  or  declining  leverage  ratio,  like  in 

Germany,  resulting  in  a  dominant  or  large  role  for  the  negative  impact.  Moreover,  the  on  average 

negative estimated  long-run MPCs out of non-financial  wealth for Italy is in line  with  empirical evidence 

reported by Slacalek (2009).  

5.2  Out-of-sample validation 

A closer look at the out-of-sample performance of the 50 selected equations from the thick modelling tool 

shows a clear improvement compared to the forecasting properties of the AR(1) benchmark model. Table 

4 reports the out-of-sample performance of the top 50 thick model equations and the AR(1) benchmark 

model. The models are recursively estimated with end-dates between 2012Q4 and 2016Q2 and are then 

used to produce conditional forecasts for 1 up to 8 quarters ahead  over the period 2013Q1 to 2018Q2. 

2 See page 14 at the bottom:  “(i) both financial and  housing wealth effects are remarkable for Spain, with financial wealth effects 
larger than housing; (ii) Italy displays sizable financial wealth effects and not significant housing wealth effects; (iii) for France the 
two wealth effects are quite similar, although the MPC out of financial assets tends to be higher compared with the effect of housing 
assets; (iv) Germany reports not significant effects of changes in either types of wealth.”  

ECB Working Paper Series No 2343 / December 201917  
 
 
                                                      
The ratio between the thick model based root mean squared errors (RMSE) and the AR(1) model based 

RMSE is in all cases below 1. The forecast gain is the strongest in Italy and the euro area, with a RMSE 

ratio of about 0.4 to 0.5, thus gaining 60% to 50% even at the longer ahead forecast horizons. The RMSE 

ratio is about 0.6 to 0.8 for Germany and Spain and around 0.9 for France. With the exception of France, 

there are 2 to 4 out of the 8 forecast horizons where the out-of-sample forecast accuracy from the thick 

model significantly differ from AR(1) model based forecasts according to the Diebold-Mariano test at the 

10% significance level. For the euro area, there is a consistent significant forecast gain for 2 to 5 quarters 

ahead.  This  promising  finding  suggests  valued  added  in  the  use  of  this  thick  modelling  approach  in 

forecasting private consumption growth, given the AR(1) model is in practice hard to beat.  

Table 4 Relative average RMSE ratio of top 50 thick model against AR(1) benchmark model 
h

France

Spain

Italy

Euro area
0.72
0.56 **
0.52 *
0.42 **
0.42 *
0.49
0.54
0.59

1
2
3
4
5
6
7
8

Germany
0.85
0.74
0.60
0.54 *
0.52
0.60 **
0.68
0.64

0.79
0.89
0.96
0.94
0.81
0.89
0.93
0.88

0.45
0.36 ***
0.38 ***
0.40 **
0.43 **
0.52
0.62
0.68

0.87
0.91
0.90
0.89 **
0.77
0.73
0.78 *
0.74

Notes: RMSE ratio is RMSE averaged of thick model selected top 50 equations in terms of RMSE from 
AR(1) for the out-of-sample period 2013Q1 to 2018Q2. h = forecast horizon h quarters ahead. 
***, **, * denote Diebold-Mariano test at 10%, 5%, respectively, 1% significance level.  

Chart 1 plots mean forecasts for quarterly growth rates in consumption together  with  actual  real private 

consumption growth for the period 2016Q3 to 2018Q2 based on equations estimated up to 2016Q2 and 
all  explanatory  variables  available  up  to  2018Q2.  The  shaded  areas  denote  the  range  between  the  5th 
and  95th  percentiles  of  the  forecast  range  (darker  shade)  as  well  as  the  top  and  bottom  5%  percent 

(lighter shade). Overall, the thick model-based mean forecast broadly tracks the actual data in the short-

term (forecast horizon, h, is 1 to 4), while being more inaccurate over the longer horizon (h=5 to h=8). 

With  a  couple  of  exceptions,  the  actual  growth  rate  series  are  within  the  forecast  range  between  the 

lowest and highest forecast values and it also tends to fall within the middle 90% of the forecast range. 

Some  of  these  differences  can  in  part  be  explained  by  (one-off)  factors  not  captured  by  the  model 

determinants like the impact of terror attacks (France 2016Q3), reluctance to buy new cars due to diesel 

emission issues (Germany) and weather conditions. In addition, the forecast errors can be revised away 

with  the  release  of  new  data  vintages  as  the  real-time  errors  in  private  consumption  growth  can  be 

ECB Working Paper Series No 2343 / December 201918  
 
 
 
 
sizeable.  The  absolute  average  real-time  revision  in  quarterly  real  private  consumption  growth  between 

2003 and 2013 has been 0.2 percentage points in the euro area, 0.3 in France and Italy, 0.4 in Spain and 

0.5 in Germany. The thick-model based ranges are about 0.2 percentage points for the euro area, about 

0.4 percentage points for Germany and Italy and much larger for France.  

Chart 1 Pseudo out-of-sample consumption growth forecasts: thick model 

Euro area 

Germany 

France 

ECB Working Paper Series No 2343 / December 201919Chart 1 Pseudo out-of-sample consumption growth forecasts: thick model (continued) 

Italy 

Spain 

Notes:  this  chart  plots  quarter-on-quarter  growth  rates  of  actual  real  private  consumption  (solid  line) 
together  with  the mean forecast (dashed  line)  based on the  top 50  selected  equations  over  the sample 
period  2016Q3  to  2018Q2.  The  darker  shaded  area  denotes  the  range  between  the  5th  and  95th 
percentiles of the overall forecast range while the lighter shaded areas denote the top and bottom 5% of 
forecast range. 

5.3  Robustness 

Given the various options shown in the literature to estimate consumption functions, we have run a set of 

robustness  checks.  First,  we  estimate  the  equations  based  on  non-property  income  to  address  the 

possibility  of  double-counting  of  wealth  effects.  Non-property  income  is  typically  preferred  from  the 

theoretical  point  of  view  (Catte  et  al.,  2004;  Kerdrain,  2011).  Second,  we  change  the  decomposition  of 

wealth by calculating net financial wealth excluding housing related debt, which is in turn deducted from 

non-financial assets to compute net non-financial assets. Sousa (2009) shows that this choice may affect 

the magnitude of the estimates. Third, we estimate the equations with the debt to income ratio as a third 

wealth variable in the long-run equation. Fourth, we exclude pension wealth from net financial wealth. As 

discussed  in  the  methodology  section,  several  alternatives  to  the  log-level  estimation  exist.  Hence,  the 

ECB Working Paper Series No 2343 / December 201920fifth  and  six  robustness  checks  estimate  the  models  using  income  ratios  and  per  capita  ratios, 

respectively. Finally, we compare the estimated wealth and income elasticities from the top 50 equations 

with  those  from  all  accepted  models  using  only  the  in-sample  criteria.  This  way,  we  check  whether  we 

experience loss of information or forecast accuracy if only top 50 models are considered.  

The  seven  robustness  checks  all  show  that  the  two  main  findings  remain:  (i)  a  split  of  total  disposable 

income  and  total  wealth  is  essential;  and  (ii)  cross-country  heterogeneity  in  income  and  wealth  effects 

exists. The thick model-based estimates for the long-run income and wealth MPCs are generally robust, 

but they also illustrate that the treatment of debt is crucial for the estimated non-financial wealth effects. 

Similarly, the out-of-sample performance can differ on whether property income is included (in particular 

key for Germany and the euro area) or excluded. In more detail, the outcomes of the robustness checks 

are as follows. 

Firstly,  the  exclusion  of  property  income  results  in  similar  estimates  as  in  the  basic  specifications  that 

include  it  for  France,  Italy  and  Spain.  The  exclusion  of  property  income  results  for  Germany  in  only  12 

selected  equations (mainly  due  to residual  autocorrelation)  with  often implausible  long-run  MPCs out of 

transfer income. Consequently, the estimated long-run MPCs for the euro area, all outside the estimated 

range from the top 50 selected basic specifications,  have to  be treated  with caution. The  out-of-sample 

performance  deteriorates  a  lot  for  the  euro  area  (1.04  versus  0.64  for  the  basic  specification)  and 

improves a bit for France, Italy and Spain. All three countries have close to zero long-run property income 

elasticities  for  the  basic  specifications.  For  this  reason,  Banque  de  France  (2018)  decided  to  exclude 

property income in their consumption model. 

Secondly, the  exclusion of debt from  household  liabilities results  in similar long-run MPCs as  estimated 

from  the  selected  basic  specifications.  They  are  all  within  the  estimated  range  for  the  basic  equations, 

with  the  exception  of  the  long-run  MPC  out  of  non-financial  wealth  in  Spain.  Instead  of  on  average  0.2 

cents per euro it becomes -0.2 cents. This finding is as expected, because due to the different treatment 

of  debt  the  wealth  measure  used  differs  and  household  debt  in  Spain  is  known  to  have  shown  large 

swings since 1999. The negative effect from the cost of housing on average dominates if household debt 

(capturing the positive housing wealth channel from collateral and capital income) is taken into account.     

The third robustness check includes the debt to income ratio into the analysis. The non-financial wealth 

effect turns negative in the long run in two cases, Germany and Italy (these findings are in line with some 

studies  discussed  in  Section  2.2.).  It  may  be  due  to  the  fact  that  the  negative  impact  of  non-financial 

ECB Working Paper Series No 2343 / December 201921  
 
 
 
 
wealth (higher housing services costs) dominates the positive impact (from higher capital income out of 

housing). For Germany and France the average debt to income ratio is estimated to be negative. For Italy 

and  Spain  in  all  50  cases  positive  debt  to  income  ratio  coefficients  have  been  estimated.  Household 

leverage has thus over the sample period been positively associated with consumption in Italy and Spain 

and  negatively  in  Germany  and  France.  With  respect  to  income  and  wealth  effects,  the  estimates  are 

broadly  similar  for  the  euro  area,  Italy  and  Spain,  while  for  Germany  and  France  they  differ  somewhat 

more. 

Fourthly, the  exclusion  of  pension  wealth from financial  wealth  has not  changed the  estimated long-run 

wealth  and  income  effects  much.  The  three  cases  where  the  average  estimated  MPC  lies  outside  the 

estimated  range  from  the  basic  specifications  is  financial  wealth  and  transfer  income  for  the  euro  area 

and  transfer  income  for  Spain.  This  notwithstanding,  the  long-run  MPCs  out  of  transfer  income  are 

consistently larger than those in the basic specification. A likely explanation is that transfer income in part 

includes  pension  related  transfer  income.  Similarly,  the  average  estimated  MPCs  out  of  non-financial 

wealth are consistently larger than those in the basic specifications. The MPCs remain, however, small. 

They are at most 0.6 cents per euro.  

The fifth robustness check is to estimate income ratio specifications, i.e. the change in the ratio between 

private consumption and total disposable income as dependent variable and the respective income and 

wealth  components  also  expressed  in  terms  of  total  disposable  income.  This  specification  has  the 

advantage  that  the  propensities  to  consume  are  directly  estimated.  In  order  to  avoid  non-singularity  we 

removed in the short run  the change in the  property income ratio. Unit elasticity with  respect to income 

and wealth is no longer imposed. The thick model estimates for the long-run MPCs out of income mostly 

remain within the range as estimated with the basic specification, but those out of wealth typically become 

larger. The latter applies in particular to France and Spain and to both wealth components. For France, 

Italy  and  Spain  the  estimated  speed  of  adjustment  is  quicker  than  the  range  estimated  from  the  basic 

specification. The out-of-sample performance of the income ratio specification is, however, poor for Italy 

and Spain with no improvement compared to the benchmark AR(1).  

The sixth robustness check is the basic specification where all the variables are expressed in per capita 

terms.  Overall,  as  shown  in  Table  5  the  estimated  income  and  wealth  effects  are  again  broadly 

unchanged, especially so for France, Italy and Spain. The final and seventh robustness check shows the 

income  and  wealth  effects  from  the  top  50  selected  equations  hardly  deviate  from  the  selected  much 

larger  pool  of  equations  (between  2089  (France)  and  4876  (Spain)  equations)  that  fulfil  the  in-sample 

criteria. 

ECB Working Paper Series No 2343 / December 201922  
 
 
 
Table 5 Robustness in thick model long-run estimates and out-of-sample performance  

Notes:  Long-run  MPC  averaged  over  the  top  50  equations.  RMSE  average  across  i)  forecast  horizon  (up  to  eight  quarters);  ii) 
recursive  sample  ending  in  2012Q4  to  2016Q2;  and  iii)  the  50  selected  equations.  RMSE  from  the  AR(1)  benchmark  model  are 
0.0020  (EA);  0.0037  (GE);  0.0038  (FR);  0.0032  (IT);  0.0039  (SP).  NA  =  not  available,  only  12  equations  selected  for  Germany 
mainly due to residual autocorrelation. Underlined is outside the range of the basic specification or more than 10 pp. change in out-
of-sample forecast performance. *, **, *** denote significantly differently from zero in at least 90%, 95%, respectively, 99% out of the 
50 selected equations. Check 1: Property income excluded; Check 2: Debt excluded from liabilities; Check 3: Debt to income ratio 
included  as  long-run  determinant;  Check  4:  Pension  wealth  excluded  from  financial  wealth;  Check  5:  Income  ratio  specification; 
Check 6: Per capita specification; Check 7: In-sample selected equations only. 

ECB Working Paper Series No 2343 / December 201923  
 
6.  Conclusions 

This  study  applies  a  thick  model  methodology  to  real  private  consumption  in  the  four  largest  euro  area 

economies and compares the outcomes with those for the euro area. Our thick model considers multiple 

error correction model specifications rather than only a single “best” one. Thick modelling is particular of 

use in the context of model uncertainty where it is hard to decide which model to use, which is here the 

case due to our short sample. All specifications incorporate the two most important macro determinants of 

private  consumption,  i.e.  disposable  income  and  wealth,  in  the  short  and  long  run.  In  addition,  they 

include  an  interest  rate  measure  as  well  as  up  to  two  other  variables  from  a  rich  set  of  explanatory 

variables in the short run: consumer leverage, government indebtedness, various uncertainty measures, 

and demographics. In addition, we split total wealth into financial and non-financial wealth and disposable 

income  into  labour,  property  and  transfer  income.  Overall,  our  results  stress  the  importance  to 

decompose not only household wealth but also disposable income for analysing private consumption as 

well  as  the  usefulness  of  thick  modelling  for  forecasting  private  consumption  in  the  largest  euro  area 

countries. They also show cross-country heterogeneity in disaggregated income and wealth effects. This 

finding stresses the need for caution when interpreting income and wealth effects estimated directly from 

euro area data.   

Against the background of recent attempts to link micro and macro data on household income and wealth 

(see,  among  others,  Fesseau  et  al.,  2013;  Honkkila  and  Kavonius  2013;  Arrondel  et  al.  2015),  most 

promising  for  future  work  is  to  consider  also  distributive  information  on  income  and  wealth  for  private 

consumption at the aggregated macro level. More generally, an important avenue for future consumption 

research is to further improve the micro-macro link.  

ECB Working Paper Series No 2343 / December 201924  
 
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ECB Working Paper Series No 2343 / December 201928  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Transformation

Integration order*

I(1)
I(1)
I(1)
I(1)
I(1)
I(1)

Real
Real
Real
Real
Real
Real

I(0)
I(0)
I(1)
I(1)
I(1)
I(1)
I(1)
I(1)
I(1)
I(1)

Log
Real, log, 1‐period lagged
Real, log, 1‐period lagged 
Real, log
Real, log
Real, log

I(1)
Log, 1‐period lagged
1‐ and 2‐period lagged 
I(1)
4‐quarter moving sum, 1‐ and 2‐period lagged  I(1)
4‐quarter moving sum, 1‐ and 2‐period lagged  I(1)
I(1)
1‐ and 2‐period lagged 

Appendix A 
Table A1 Additional short-run consumption determinants add unit root / integration order tests 
Description
Long‐run variables
Private consumption, chain linked volume
Financial net worth
Gross non‐financial assets
Real labour income net of taxes
Real property income net of taxes
Real transfer income net of taxes
Interest Rates
10‐year government bond yield
Interest rate on loans to households for consumption
Interest rate on households deposits
Interest rate on loans to households for house purchases 
3‐month Euribor
10‐year government bond yield  (‐) 3‐month Euribor
Interest rates on loans for house purchases  (‐) deposit rate
Interest rateson loans for house purchases (‐) 3‐month Euribor
Interest rates on consumption loans (‐) deposit rate
Interest rate on consumption loans (‐) 3‐month Euribor
Consumer indebtedness
Loans to Households (amounts outstanding)
Loans to households (/) 4‐quarter moving sum of nominal GDP
Interest income paid (/) nominal GDP
Interest Income paid (‐) received (/) nominal GDP 
Outstanding loans to households / total disposable income
Government indebtedness
Government deficit
 Government deficit
Government deficit (/) nominal GDP
Government debt (/) 4‐quarter moving sum of nominal GDP 
Government final consumption
Government debt outstanding
Uncertainty
Consumer Inflation Expectations, EC survey
Consumer confidence, EC survey
Consumers' financial expectations, EC survey
General economic situation, EC survey
Economic sentiment, EC survey
Expected Major Purchases, EC survey
Consumer savings expectations, EC survey
Unemployment expectations, EC survey
1‐Year ahead inflation expectations (SPF)
2‐Year ahead inflation expectations (SPF)
Aggregate uncertainty (mean) 
Aggregate uncertainty (first principal component) 
Economic policy uncertainty 
Forecast uncertainty 
Forecast disagreement 
Conditional volatility measure of uncertainty 
Financial market uncertainty
Macroeconomic uncertainty
Survey‐based uncertainty
Total unemployment
HICP excluding food and energy 
HICP
CPI deflated effective exchange rate against 38 trading partners
CPI deflated effective exchange rate against 18 trading partners
Real effective exchange rate against 38 trading partners 
Real effective exchange rate against 18 trading partners 
1‐Month forward price of Brent oil 
Others
Old age dependency ratio (older than 65 / working age 15 to 64)
Log
Population
*short-run variables enter the equation in differences according to their integration order. 

I(0)
I(1)
I(1)
I(1)
I(0)
I(1)
I(1)
I(1)
I(1)
I(1)
I(0)
I(0)
I(0)
I(0)
I(0)
I(0)
I(0)
I(0)
I(1)
I(1)
I(0)
Yearly change
I(0)
Yearly change
I(1)
Log 
Log
I(1)
8‐period backward moving standard deviation I(0)
8‐period backward moving standard deviation I(0)
I(0)
Log

Yearly change
Four‐quarter moving sum

Shifted three quarters
Shifted seven  quarters

I(1)
I(0)
I(1)
I(1)
I(1)
I(1)

Log
Log

I(1)
I(1)

Log 

ECB Working Paper Series No 2343 / December 201929  
 
Appendix B 
Income and wealth split definitions 

Total disposable income (Y) is decomposed into labour, transfer and property income.  

Labour income (LY) is defined as the sum of total compensation received (D1R) and gross mixed income 

(B3G,  i.e.  remuneration  of  work  done  by  self-employed  and  their  families)  and  deduct  social  security 

contributions  (D61)  and  imputed  labour  taxes  (i.e.  current  taxes  paid  (D5P)  weighted  with  the  labour 

share  in  taxable  income).  In  other  words,  we  define  net  labour  income  as  total  labour  income  (out  of 

dependent and independent activity) after social security contributions and taxes.  

Transfer income (TY) is defined as the sum of social benefits (D62) and net other current transfers (D7) 

minus imputed transfer taxes, i.e. net transfer income after taxes.  

Property  income  (PY)  is  defined  as  the  sum  of  gross  operating  surplus  (B2G,  mostly:  imputed  rents  of 

home-owner occupiers in providing services to themselves) and net property income (D4, i.e. net interest 

earnings plus net other property income such as dividends paid by companies) minus imputed property 

taxes, in other words: net capital income after taxes. 

LY = D1R + B3G – D61 – D5P * (D1R+B3G) / (D1R+B3G+B2G+D4+D62) 

TY = D62 + D7 - D5P * (D62) / (D1R+B3G+B2G+D4+D62) 

PY = B2G +D4 – D5P * (B2G+D4) / (D1R+B3G+B2G+D4+D62)   

Wealth is split for the basic specification into: 

Non-financial wealth = gross non-financial wealth;  

Net financial wealth = total financial assets – total financial liabilities. 

For robustness check no. 2 the wealth split is as follows: 

Net non-financial wealth= non-financial wealth minus loans to households; 

Net financial wealth = total financial assets – total financial liabilities (excluding loans to households). 

ECB Working Paper Series No 2343 / December 201930  
 
 
 
 
 
 
 
Acknowledgements 

All views expressed in this paper are those of the authors and do not necessarily reflect the position of the ECB or the Central Bank of 
Ireland. We thank a number of colleagues at the ECB as well as participants of the February 2018 1st Vienna Workshop on Economic 
Forecasting, the May 2018 22nd International Conference on Macroeconomic Analysis and International Finance, the June 2018 38th 
International Symposium on Forecasting 2018, the July 2018 and July 2019 International Conference on Economic Modelling and the 
Eurosystem Working Group of Forecasting Work Programme Meetings held in January 2018, September 2018 and June 2019 for 
constructive comments. We also thank Michele Lenza, an anonymous referee and the editorial board of the WP series for valuable 
comments. 

Gabe de Bondt 
European Central Bank, Frankfurt am Main, Germany; email: gabe.de_bondt@ecb.europa.eu 

Arne Gieseck 
European Central Bank, Frankfurt am Main, Germany; email: arne.gieseck@ecb.europa.eu 

Pablo Herrero 
European University Institute, Florence, Italy; email: pablo.herrero@eui.eu 

Zivile Zekaite 
Central Bank of Ireland, Dublin, Ireland; email: zivile.zekaite@centralbank.ie 

© European Central Bank, 2019 

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