UK Macro Model



I have set out on this page details of a simple data-driven model that I use to help me think about current macro-economic issues in the UK.  A full list of equations and variables is provided at the end of this post.

The model incorporates many of my views about how best to understand the workings of the UK economy.  That is not to say I think this is the only way of looking at it, nor that I think that no insight can be gained from very different models.  However, in terms of seeing how the main pieces work together in the context of real numbers, this is what I turn to.

I build models because I learn a lot from the process.  All models should help develop an understanding of how things work together, but getting your hands dirty building empirical models has the additional advantage of making you think much more about what the actual data means.

I use the model to look at how different policies and events might impact on the economy.  I try to be realistic in what the model can tell me.  There are too many unknowns to be able to expect to do reliable forecasting.  All I can hope is that the model will tell me that policy A is more likely to achieve outcome X than policy B.  I also appreciate that relationships can change over time, including in response to policy driven changes.

This is very much work-in-progress.  I am continuing to build bits into it and hopefully improve it.  At this stage, I can only run historical counterfactuals, but I intend shortly to set it up to look at future projections.  It is my intention to keep this page updated with any major changes I make.

Estimated parameters are based on quarterly data from 1997 Q1 to 2013 Q1.



Overview 

The model uses a standard post-Keynesian framework.  Output is demand led, with fiscal policy acting either directly, through government expenditure, or indirectly through its impact on private disposable income.  Monetary policy operates through its impact on asset prices, interest rates and the exchange rate.  Prices are largely determined on a cost mark-up basis.  The general structure is illustrated in the schematic below.







Accounting Structure 

The model is constructed around the UK flow of funds and balance sheet accounts for the different sectors.  The private sector is disaggregated into households (including NPISH), funds and firms.

The division between funds and firms is different to the sectoral breakdown in the national accounts.  In the model, funds is used as a sort of conduit for all financial assets and liabilities.  Firms represents purely UK production.  Therefore all household asset are represented as liabilities of the funds sector.  The value of UK productive capital (referred to below as net investment in UK production) is calculated as the balancing item from the national accounts, but does actually mirror very closely the FTSE.  This division into funds and firms is just a practical step, reflecting the difficulty in extracting accurate cross investment information from the data, but I believe little is lost by taking this approach. 

Government includes public corporations.  RoW is rest of world.  Variable names are the same as used in the equations.




Financial Balance Sheet






H'holds
Funds
Firms
Gov't
RoW






Household deposits
MH
-MH



Household equity
EH
-EH



Pension rights
AP
-AP



Household borrowing
-LH
LH



Public sector debt

LG

-LG

Public sector assets

-AG

AG

Overseas assets

FA


-FA
Overseas liabilities

-FL


FL
Net investment in UK production

E
-E











The flow of funds account also includes a separate production account.  A +ve indicates net cash inflow and a -ve net cash outflow.  All rows and columns sum to zero.  Disposable income and the surplus / deficit of government and rest of world are summations, not additional flows.


Flow of Funds








H'holds
Funds
Firms
Gov't
RoW
Prod a/c









Primary Income Account







Production taxes



TAXS

-TAXS

Wages
WB




-WB

Imputed rent of owner occupiers
IROO




-IROO

Gross operating surplus
MIQC

OSC
OSG

-OS

Earnings

EARN
-EARN




Household equity income
YEH
-YEH





Household deposit income
YDH
-YDH





Household debt expense
-XLH
XLH





less FISIM

-FISIM



FISIM

Property income from abroad

FII


-FII


Property income paid abroad

-FOI


FOI


Return on public sector FA

-YAG

YAG



Interest on government debt

XLG

-XLG











Secondary Income Account







Employer pension contributions

PCF



-PCF

Employers' NI



TAXE

-TAXE

Social benefits
BEN
-BENF

-BENG



Grants


GRANT
-GRANT



Income taxes
-TAXY


TAXY



Corporation taxes


-TAXC
TAXC



Employees' NI
-TAXN


TAXN



Pension contributions
-PCH
PCH





Net transfer income from RoW



-OFTR
OFTR


Disposable Income
YD














Use of Income and Acquisition of Non-Financial Assets




Consumer spending
-CX




CX

less FISIM
FISIM




-FISIM

Business investment


-BI


BI

Construction of dwellings
-HB




HB

Government spending



-G

G

Change in inventories


-SB


SB

Exports




-X
X

Imports




M
-M

Sale of intangibles


-INTG
INTG



Surplus / Deficit



PSBR
CAB










Financial Account







New loans
dLH
-dLH





Investment in securities
-dEH
dEH





Investment in pensions
-dPH
dPH





Other saving
-dMH
dMH





Investment in UK business

-dE
dE




Public sector financial assets

dAG

-dAG



Government debt

-dLG

dLG



Foreign assets

-dFA


dFA


Foreign liabilities

dFL


-dFL











0
0
0
0
0
0














(Household interest income and expense and consumer spending are adjusted for FISIM to align with the treatment in the national accounts.)



Exogenous Variables 

Currently, the model uses the following exogenous variables:
  • All tax rates and public sector spending (except interest on government debt, which is endogenous)
  • World trade volume, overseas prices and overseas interest rates.
  • Net lending to households
  • The bank rate, the exchange rate, the earnings yield on UK capital, the long gilt yield and the rental yield on housing.
In reality, net lending to housing is probably partly dependent on other variables within the model.  However, I believe that other factors have been much more important over the data period, particularly related to developments in the banking sector.  These are well beyond the scope of this model and I am doubtful that they can be effectively modelled anyway.

My intention at some point is to include some equations for the exchange rate and asset yields (other than the bank rate).  I would not expect these equations to be much good for historical  simulations or forecasting as these variables depend so much on expectations and are extremely difficult to capture effectively.  The purpose would simply be to try to reflect factors which might push them in one or other direction, so as to be able to better compare different policy approaches.


House Prices 

I believe the relationship between household borrowing, house prices and consumer spending play a crucial role in the UK economy.  This is reflected in the model. 

House prices factor into consumer spending via the wealth term.  The parameter is small, but over the long term it has a significant effect on the path of spending. 

The determination of house prices within the model starts with a concept of a target investment in housing.  This measure is based on population (proxied by the workforce) as well as available finance.  This latter amount is based on the amount of household debt and some proportion of gross household non-pension assets.  This is very similar to the portfolio allocation function I have used in some of the simple theoretical models described in posts on this blog (see, for example my mini minsky model).

Unlike with financial investments however, it is assumed that the housing market takes time to adjust towards target levels.  House prices are therefore determined at the margin based on new mortgage lending (net of expenditure on new construction of dwellings) and some fraction of the gap between target and actual housing investment.

This formulation seems to provide a good determination of house prices over the observation period.  Although, there has undoubtedly been elements of bubble, which are not possible to estimate, I believe that much of this is picked up in the (exogenous) pattern of lending.

The house price mechanism plays a crucial role in enabling the model to pick up the downturn.  The sudden drop in net lending to households leads to a fall in private sector spending via its effect on house prices.  Lending does not figure directly in any of the expenditure functions.


 Equation Listing 

The equation listing below is pretty much a print out from excel.  I might get round to setting it out in a more user friendly format at some point.

Equations in bold are identities.  Equations not in bold are relationships estimated from the data.  The expression for the target dwellings has been substituted into the equation for house prices to aid the solving algorithm.





Expenditure (volume measure)


CXr
=0.231*(YD/pc)+0.00655*(VR/pc)-146*T_1+0.671*(CXr.1-FISIM.1/pc.1)+FISIM/pc
Bir
=0.121*Yr-0.642*GIr-144*T_1
HBr
=Hr.1*(0.00756*(ph/phb)-0.00929*T_1)
Xrz
=EXP(1.956-0.0975*LN(px/pw)-0.00347*T_1+0.47*LN(Xrz.1))
Xr
=WTVr*Xrz+DUM_M
Mrz
=EXP(-0.334-0.144*LN(pm/pc)+0.000666*T_1+0.743*LN(Mrz.1))
Mr
=(CXr+Bir+Xr)*Mrz+DUM_M
SLr
=CXr+Bir+HBr+GIr+Gr+Xr-Mr
Yr
=Yr.1+0.742*((SLr+SBrt)-Yr.1)


Change in Inventories


INVrt
=(0.622+0.000773*T_1)*SLr
SBrt
=0.415*(INVrt-INVr.1)
SBr
=Yr-SLr


Employment


PRn
=PRn.1*0.9995813*(Yr/Yr.1)^0.72
Nt
=Yr/PRn
N
=N.1*(Nt/N.1)^0.335
U
=WF-N
Uz
=U/WF


Wages and Price Deflators


w
=w.1*EXP(0.0972-0.179*Uz-0.0459*LN(w.1/pc.1))
lc
=w*(1+tauE+PCF/WB)
pw
=pf/eer
pk
=lc*EXP(-1.525+0.12*LN(pm/lc)-0.00331*T_1)
phb
=phb.1*EXP(-1.219+0.597*LN(lc/phb.1)+0.00125*T_1)
px
=px.1*EXP(-0.209+0.631*LN(pm/px.1)+0.1254*LN(lc/px.1)-0.000626*T_1)
pm
=pm.1*EXP(-0.107+0.0635*LN(lc/pm.1)+0.118*LN(pw/pm.1)-0.000423*T_1)
pg
=pg.1*EXP(-0.549+0.293*LN(lc/pg.1)-0.00112*T_2)
pc
=pc.1*EXP(-0.197+0.15*LN(1+tauS)+0.0483*LN(pm/pc.1)+0.104*LN(lc/pc.1)-0.00011*T_1-0.00136*T_2)


Asset Prices


Hrt
=0.614*WF-67000*rlh+0.172*(EH+MH)/ph+LH/ph
ph
=-(0.06609*LH+0.01136*(EH+MH)+(LH-LH.4)/4-HB)/(0.04056*WF-4426*rlh-0.06609*Hr.1)
pe
=(E+EARN-dE)/E.1*pe.1
peh
=peh.1*(pe/pe.1*EXP(0.00627)-reh/4)
pfa
=EXP(0.0208-0.455*LN(eer)+0.00326*T_1+0.583*LN(pfa.1))
pfl
=EXP(0.0288-0.368*LN(eer)+0.00232*T_1+0.65*LN(pfl.1))
plg
=EXP(-0.208-0.0775*LN(rg)+0.597*LN(plg.1))


Asset Yields


rdh
=0.00243+0.412*rp+0.0056*IF(HPM/LH>0.1,1,0)+0.346*rdh.1
reh
=0.00902+0.0874*re+0.566*reh.1
rlh
=0.00862+0.556*rdh+0.595*rlh.1
rag
=0.0139+0.771*rp
rlg
=0.213*rg+0.113*rp+0.727*rlg.1
rfa
=0.0149+0.421*rp+0.137*rf
rfl
=0.0141+0.266*rp+0.261*rf


Expenditure (current prices)


CX
=CXr*pc
FISIM
=(MH.1*(rp-rdh)+LH*(rlh-rp))/4
BI
=Bir*pk
HB
=HBr*phb
G
=Gr*pg+GIr*pk
X
=Xr*px
M
=Mr*pm
SB
=SBr*pk
Y
=CX+BI+HB+SB+G+X-M


Primary Income Account


WB
=w*N
IROO
=rooh*Hr.1*ph.1/4
OS
=Y-TAXS-WB-TAXE-PCF-IROO
MIQC
=EXP(0.272+0.123*LN(OS)+0.835*LN(MIQC.1))
OSG
=EXP(-0.421+0.184*LN(OS)+0.806*LN(OSG.1))
OSC
=OS-MIQC-OSG
EARN
=OSC-TAXC
YDH
=rdh*MH.1/4
YEH
=reh*EH.1/4
XLH
=rlh*LH.1/4
YAG
=rag*AG.1/4
XLG
=rlg*LG.1/4
FII
=FA.1*rfa/4
FOI
=FL.1*rfl/4


Secondary Income Account


BENF
=BENF.1+0.106*(0.0648/4*AP.1-BENF.1)
BEN
=BENF+BENG
PCF
=(0.0277+0.000336*T_1)*WB-0.000577*AP.1+0.57*PCF.1
PCH
=0.0487*WB-0.12*PCF+0.377*PCH.1
TAXC
=tauC*OSC
TAXE
=tauE*WB
TAXS
=CX*tauS/(1+tauS)
TAXN
=tauN*WB
TAXY
=tauY*(WB+MIQC+YDH+YEH+BEN)


Income and Surplus Measures


YD
=WB+IROO+MIQC+YDH+YEH-XLH+BEN-TAXY-TAXN-PCH
PSBR
=G+BENG+GRANT+OFTR+XLG-(OSG+TAXY+TAXE+TAXN+TAXC+TAXS+YAG+INTG)
CAB
=X-M+FII-FOI-OFTR


Financial Account


dEH
=EH.1*(0.00514-0.00733*LN(pe)-0.02*E.1/(E.1+MH.1))
dPH
=(0.0699-0.00265*T_1)*WB
dMH
=YD-(CX-FISIM)-HB+dLH-dEH-dPH
dLG
=PSBR+dAG
dE
=BI+SB+INTG-GRANT
dFA
=(0.396-0.00521*T_1)*Y
dFL
=dFA-CAB
INVr
=INVr.1+SBr


Balance Sheet


Hr
=Hr.1+HBr*0.00266
AP
=(LG*plg-AG)+(FA-FL)+(LH-MH)+E-EH
E
=EARN/re*4
EH
=EH.1*peh/peh.1+dEH
MH
=MH.1+dMH
LH
=LH.1+dLH
VR
=Hr.1*ph+EH.1*peh/peh.1+MH.1-LH.1
AG
=AG.1+dAG
HPM
=HPM.1+dHPM
LG
=LG.1+dLG
FA
=FA.1*pfa/pfa.1+dFA
FL
=FL.1*pfl/pfl.1+dFL









Variables

Definitions of variables are listed below.

I tend to use the following nomenclature.  Uppercase denotes a quantity, whether a stock or a flow, real and nominal.  Prices and returns are then in lower case.  A prefix "d" indicates change in a variable.  Suffixes "r", "z", "t" and "n" indicate real (volume) measure, ratio, target and trend respectively.

A suffix ".1" denotes that a variable is lagged by one quarter and ".4" a lag of four quarters.

AG
Public sector financial assets
AP
Household equity in pension funds
BEN
Total benefits
BENF
Private social benefits
BENG
Public social benefits
BI
Business investment (cp)
Bir
Business investment (cvm)
CAB
Current account balance
CX
Consumer spending (cp)
CXr
Household consumption expenditure (cvm)
dAG
Public net acquisition of financial assets
dE
Net investment in UK production
dEH
Household net equity investment
dFA
Net acquistion of foreign assets
dFL
Net acquisition of foreign liabilities
dHPM
Change in base money
dLG
Public sector debt issuance
dLH
New household loans
dMH
Household acquisition of monetary assets
dPH
Household pension acquisition
DUM_M
MTIC dummy
E
Value of UK productive capacity
EARN
Corporate earnings
eer
Effective exchange rate
EH
Household equity
FA
Total foreign assets
FII
Investment income from RoW
FISIM
FISIM
FL
Total foreign liabilities
FOI
Investment income paid to RoW
G
Public sector spending (cp)
GIr
Public sector fixed capital formation (cvm)
Gr
Public sector consumption expenditure (cvm)
GRANT
Government grants
HB
Construction of dwellings (cp)
HBr
Construction of dwellings (cvm)
HPM
Base money
Hr
Stock of dwellings
Hrt
Target stock of dwellings
INTG
Public sector sale of intangible assets
INVr
Inventories (cvm)
INVrt
Target inventories (cvm)
IROO
Imputed rent of owner-occupiers
lc
Labour cost
LG
Public sector debt
LH
Household financial liabilities
M
Imports (cp)
MH
Household monetary assets
MIQC
Mixed income and withdrawal from quasi corporations
Mr
Imports (cvm)
Mrz
Import ratio
N
Employment
Nt
Target employment
OFTR
Net transfer income to rest of world
OS
National gross operating surplus
OSC
Corporate operating surplus
OSG
Public sector share of operating surplus
pc
Consumer price deflator
PCF
Employers' pension contributions
PCH
Household pension contributions
pe
Total return index on UK equity
peh
Price of household equity investment
pf
World price index
pfa
Price of foreign assets
pfl
Price of foreign liabilities
pg
Government consumption price deflator
ph
House prices
phb
Price deflator for dwelling construction
pk
Price deflator for business and public sector investment
plg
Price of government debt
pm
Import price deflator
PRn
Normal labour productivity
PSBR
Public sector net borrowing
pw
Sterling equivalent of world prices
px
Export price deflator
rag
Return on public sector assets
rdh
Rate of return on household deposits
re
Earnings yield on UK capital
reh
Dividend yield on household equity
rf
Foreign interest rate
rfa
Return on foreign assets
rfl
Return on foreign liabilities
rg
Long gilt yield
rlg
Return on government debt
rlh
Cost of funds on household debt
rooh
Imputed return on owner-occupied housing
rp
Bank rate
SB
Change in inventories (cp)
SBr
Change in inventories (cvm)
SBrt
Target change in inventories (cvm)
SLr
Sales (cvm)
T 1
Basic time series
T 2
Wage time series
tauC
Corporation tax rate
tauE
Employer's national insurance rate
tauN
Employees' national insurancerate
tauS
Effective rate of production taxes
tauY
Income tax rate
TAXC
Corporation tax
TAXE
Employers' national insurance
TAXN
Employees national insurance
TAXS
Production taxes
TAXY
Income taxes
U
Unemployment
Uz
Unemployment rate
VR
Revalued household net wealth
w
Wage rate
WB
Wages
WF
Workforce
WTVr
World trade volume
X
Exports (cp)
XLG
Government debt service cost
XLH
Household debt expense
Xr
Exports (cvm)
Xrz
Export ratio
Y
GDP (cp)
YAG
Return on government financial assets
YD
Household disposable income
YDH
Household deposit income
YEH
Household equity income
Yr
GDP (cvm)


8 comments:

  1. Hi Nick.
    Great to see your newish blog and am fascinated to see you were a student of Prof Godley in the 80s.
    I remember him writing or saying that in the early days he had no real knowledge of modelling and it is something he got to grips with later on, perhaps when you were with him.
    Can you tell me if you use a specific modelling software or programming language to code your models ?

    Thanks
    Andy

    ReplyDelete
    Replies
    1. Hi Andy

      I think WG learned most of his modelling skills fairly early on, but when I started helping him he was not used to actually sitting down with a computer and putting in the code. So he was just working out how to do all that for himself using an early version of MODELER. And, in those days, you had to enter all the data by hand so having students willing to lend a hand must have been quite useful. But he was already well versed in the architecture of models from his time at the Treasury and with the CEPG. And he was very generous with his time with those like myself that shared his interest in that sort of thing.

      I actually just use Excel with VBA programmes for all my modelling. It may not be the best, but I'm familiar with it and it's versatile enough for me to be able to play around with very different formats.

      Regards
      Nick

      Delete
  2. I find it incredible that there is so little interest in this part of your website. The longer I am working on stock-flow consistent models, the more I am convinced that this is the only proper way to model our economic system as a whole. How is it possible that so few economists are interested in SFC modelling?

    Anton

    ReplyDelete
    Replies
    1. People do view this and have contacted me directly, even if there are few comments here. I'm aware though that what I've done here is a bit brief and not terribly easy to follow. I should do a proper write-up, but at the moment, I'm just thinking through some things I want to do to re-structure some aspects of it. It's taking me a bit of time to work through the theory, which is why I haven't updated the model for a bit.

      I wouldn't personally say its the only proper way to model our economic system, but I definitely find it the most useful and provides the most insight. As to why it is not more widely used, I think that's just because the mainstream does not see it as properly micro-founded.

      Delete
  3. You state "because the mainstream does not see it as properly microfounded". But is that really true? If you build an SFC model which is as dis-aggregated as the available economic data make possible, using stock-flow norms (of possibly functions) derived from these economic data, that seems proper microfoundation to me.

    Or to state it in another way, can you build better microfoundations than by using the avalable economic data as much as possible?

    Anton

    ReplyDelete
    Replies
    1. Microfounded, for the mainstream, means starting with a theory of rational inter-temporal utility maximising households and building up from there. These models are not necessarily stock-flow inconsistent, although finding a solution may involve short cuts which break that consistency. It's a really big topic, much more than I can go into here, but it has prompted some of my blog posts. It comes down to the fact that SFC models are seen by the mainstream to fail the Lucas Critique (http://en.wikipedia.org/wiki/Lucas_critique).

      Delete
  4. Regarding Lucas' critique, I read: "Given that the structure of an econometric model consists of optimal decision rules of economic agents, and that optimal decision rules vary systematically with changes in the structure of series relevant to the decision maker, it follows that any change in policy will systematically alter the structure of econometric models."

    Isn't it true this problem is "automatically" tackled in SFC-models that include the central bank and the government, because changes in flows (and thus in stocks) which arre caused by their policies automatically lead to a response by the other sectors in these models, even if their behavior (stock-flow norms) do not change?

    ReplyDelete
    Replies
    1. You could perhaps make the argument that an SFC model is a bit less susceptible, but on the whole I think the Lucas Critique is a problem for this type of approach. However, I think you just ahve to live with it and view the results in that light. All models have their limitations and to my mind this is still probably the most useful way of modelling.

      Delete