Modelling the Services Sector

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28 Οκτ 2013 (πριν από 3 χρόνια και 7 μήνες)

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Modelling the Services Sector

Stephen Millard

Bank of England, Durham University Business School
and Centre for Macroeconomics

Phil King

Bank of England

16 October
2013

Motivation

1.
Recent poor UK productivity performance most obvious in
service sector. Is this a permanent feature or will service
-
sector
productivity recover as demand picks up?

2.
Firms in standard macroeconomic models look like
manufacturers. Would better modelling of the service sector
improve our understanding of inflation dynamics in the economy
as a whole?

Motivation: Contributions of
sectoral

productivity to
aggregate productivity relative to trend

Motivation


Standard firms combine labour and capital to produce output sold
in spot markets


For the service sector:


Output is hard to define/measure


Intangible inputs are extremely important (maybe for manufacturing
too)


How are wages determined given impossibility of measuring
productivity?


Markets are rarely (if ever) ‘spot markets’


So how are prices determined?

Roadmap


Motivation


Related literature


What we learnt from our firm visits


Model


Response of
sectoral

productivity to demand shocks


An experiment: Model response to a ‘financial crisis’ shock


Conclusions

Related literature


Product market frictions


Drozd

and Nasal (2012): Need to build and maintain a customer
base can explain some international pricing ‘puzzles’


Gourio

and
Roudanko

(2011): Customer base acts as a form of
intangible capital


Bai

et al
(2012): Search frictions mean that ‘demand’ shocks affect
productivity


Nakamura and
Steinsson

(2011): Importance of brand loyalty


Hall (2012):
Procyclical

marketing spend implies
procyclical

profit
margins

Related literature


Intangible capital


McGrattan

and Prescott (2010): Addition of intangible capital to an
otherwise standard RBC model can help explain US 90s boom


Corrado
,
Hulton

and
Sichel

(2009): Add intangible capital to a
standard ‘sources of growth’ framework and find that capital
deepening takes over from TFP as the main source of US post
-
war
growth


Goodridge
, Haskel and Wallis (2012): Similar exercise for the UK


intangible investment much more important than tangible investment

Related literature


Increasing returns to scale


Romer

(1990): Once you’ve created the blueprint, replication is
costless. Price cannot equal marginal cost in this environment.


Two
-
part tariffs


Oi

(1971): How do you price a ‘
mickey

mouse monopoly’ like
Disneyland?


Schmalensee

(1982): All you ever wanted to know about two
-
part
tariffs


Laffont

and
Tirole

(2000): Pricing telecommunications services


What we learnt from our firm visits


We visited around 30 firms


Size varied from ‘one man and his laptop’ consultants all the way
up to a major international financial corporation



Even spread across private sector services (SIC Groups G, H, I,
J, K, M, N and R)


Most visits carried out as part of the general ‘intelligence
gathering’ job of our Agents …


The rest consisted of face
-
to
-
face interviews with smaller firms

What we learnt from our firm visits


Output and price
-
setting


Three types of service
-
sector firm


Output produced using labour and capital at increasing marginal cost
and sold in spot markets (
ie
, ‘standard’ firms)


Bespoke services where the value of the service depends on the match
between providers and buyers



Scaleable
’ services (
ie
, high fixed cost and low


if not zero


marginal
cost)


Inputs and investment


Intangible inputs were important: especially ‘the brand’!


Lots of emphasis on the importance of customer base and
marketing spend to maintain this


So, important to model choice between using labour on production
of services vs. marketing



Bespoke services


Complex bundles of services, unique to each customer.


No two bundles are ever exactly the same


Firms are multi
-
product firms


Firms don’t face a demand curve


Instead, bilateral negotiation between firm and customer over
specification and value of the service


So we model the matches between individual customers and
firms, and their bargaining over price


We observed demand
-
side frictions


Costly/time
-
consuming for a firm to build up its customer base via
marketing


Customers are ‘sticky’ (
ie
, have brand loyalty, which is why the
‘brand’ is such an important intangible input)


We think this follows from the bespoke nature of many services.







We observed that these frictions affect firms’ price
-
setting and
output. Evidence from price
-
setting surveys supports this

Bespoke services give rise to demand
-
side frictions

Bespoke nature
of services

Markets
characterised by
search
-
matching

Demand
-
side
frictions

Increasing returns to scale


Some services firms have high fixed costs and low (negligible)
marginal costs


Examples include telecoms, publishing, software, finance,
insurance, musicians ...


Although CRS may not be a bad assumption for service sector
as a whole

Source:
Inklaar

(2007)

The model


Closed economy


Sticky wages and prices


We split the private sector into
scaleable

services, bespoke
services (which we equate with business services), other
consumer services, and goods (
ie
, agriculture, production and
construction)


Households own the capital stock and face costs of adjusting
capital


Households can also decide how intensively their capital is used

The model: Households


Households have Cobb
-
Douglas preferences over
scaleable

services, other consumer services and non
-
services


They minimise the cost of purchasing these



Minimise



Subject to



Implying

The model: Households


Maximise utility subject to a budget constraint, the demand for
their differentiated labour and sticky wages (
Calvo

parameter
x
w
)



Maximise




Subject to

The model: Households


First
-
order conditions imply:



Is Curve



Marginal benefit of more intensive utilisation equals marginal cost
of so doing



Marginal product of capital equals marginal cost



The model: Households


Household’s that cannot change their wages index them to
lagged inflation





This leads to the ‘Wage Phillips Curve’

The model: Goods


Goods producers maximise profits subject to their production
function, the demand for their goods and ‘menu costs’ a la
Rotemberg

(
ie
, absolutely standard problem)


First
-
order conditions imply


Demand for labour



Demand for capital



Production function



New Keynesian Phillips Curve

The model: Bespoke service sector

Household demand

Retailer
r

Combines labour and service inputs to
produce output

Business Service Provider
j

Produces bespoke services using
labour only


The model: Search and matching


In order to trade, business service providers and retailers have to
match


Once matched, they trade one unit per period


Matches dissolve with exogenous probability
δ
q


Retailers search randomly over producers. There is a real cost
to search
χ


They match with certainty


the question is with whom

The model: Search and matching


To attract customers, business service providers need to put
resources into marketing, sales, and advertising


We model this as investment in marketing capital,
m


Business service providers increase the likelihood of matching
with customers by increasing their relative marketing capital


Building up
m

requires labour. And it depreciates:




New customers in period
t

=


Output is:




Number of searching retailers
s

will depend on search costs and
the marginal product of the business services they purchase

The model: Price of bespoke (business) services


Once a business service provider and a retailer are matched, the
price of the service is determined by bilateral bargaining.


Total surplus from a match:





How to split the surplus?


A Nash bargaining solution:


Assume relative bargaining strength of producer is
θ
, and of
customer 1


θ


Solve:


Solution:






Marginal revenue product
of the service

Service provider’s
marginal cost

S = net value of match for retailer

+ net value of match for service provider

=
J
(
p
) +
λ
(
p
)

The model: Price of retail services


Retailers operate in monopolistically competitive markets and
face menu costs a la
Rotemberg


They maximise the present discounted value of their profits,
where profit in period
t

is given by:





Optimisation leads to the New Keynesian Phillips curve:


Monopoly producer in a contestable market


Production function:


Fixed costs:


Overhead labour


Sunk costs: producing engineering designs, writing software,
producing films, recording CDs, writing general economic reports,
writing generic insurance contracts...


With increasing returns to scale, we have the viability constraint:


Price ≥ Average cost


Fully linear pricing may not allow firm to cover fixed costs, given
demand


Two
-
part tariff


A way to increase profits relative to fully linear prices → fixed costs
can be recouped





The model:
Scaleable

services


We allow our firm to charge two
-
part tariffs
a

+
p
(
q
)


In a flexible price world, firm sets price equal to marginal cost, as
shown by
Oi

(1971)





But we have costs of adjusting prices


So firm’s problem is to maximise present discounted profit flow:





The model:
Scaleable

services


The first
-
order conditions in this sector imply:



Aggregate production


New Keynesian Phillips curve






a

is set as high as possible


Contestability implies zero profit








The model:
Scaleable

services


The central bank operates a Taylor rule:




All markets clear:





The model: Monetary policy and market clearing

Calibration


We set the consumption shares as follows:


Goods (Agriculture, production and construction) 59%


Scalable services (Information and communication, Finance and
insurance, Arts, entertainment and recreation) 18%


Other consumer services (Retail, Repair of motor vehicles, Rail
transport, Air transport, Accommodation and food, Real estate, Vets)
29%


Business services (Wholesale, Transportation and storage ex. rail
and air transport, Professional, scientific and technical ex. vets,
Admin and support)


This implied values for

1
,

2

and

3

of , 0.5513, 03016 and
0.1471, respectively

Calibration


We set the employment shares as follows:


Goods

(Agriculture, production and construction)
28%


Scalable services
(Information and communication, Finance and
insurance, Arts, entertainment and recreation)


Fixed labour 3%


Variable labour 11%


Other consumer services
(Retail, Repair of motor vehicles, Rail
transport, Air transport, Accommodation and food, Real estate, Vets)
27%


Business services
(Wholesale, Transportation and storage ex. rail
and air transport, Professional, scientific and technical ex. vets,
Admin and support)


Billable hours 25%


Non
-
billable hours 6%

Calibration


Log utility,
ie
,

c
=1


Frisch labour supply elasticity of 2, implying

h
=0.5


Discount factor,

, of 0.99


Steady
-
state wage mark
-
up of 1.5, implying

w
=0.5


Average duration of wages of 1 year, implying
x
w
=0.75


Degree of wage indexation,

w
, of 0.3


Taylor rule




Demand shock

Calibration


Goods sector


Depreciation rate of 10% pa, implying

=0.025


Elasticity of capital adjustment costs,

k
, set to 0.5


Scale of capital adjustment costs,

k
, set to 201


Elasticity of capital utilisation costs,

z
, set to 0.56


Elasticity of output with respect to capital input,

1
, set to 0.395


Steady
-
state price mark
-
up of 1.1, implying

=10/11


Average duration of prices of 1 year, implying
x
1
=116.5501


Degree of price indexation,

1
, set to 0.3


Response of productivity to demand shocks:

Goods



Consumption risk premium
shock



Monetary policy shock


Response of productivity to a negative demand shock is positive
on impact in the goods sector


This follows from the production function






Since capital utilisation adjusts by less than labour input


Once capital adjusts down, productivity falls


Addition of labour hoarding can alter this result


As can the presence of a fixed costs as we’ll see later



Effects of a demand shock: Goods sector

Calibration


Bespoke services sector


Steady
-
state price mark
-
up of 1.1, implying

=10/11


Average duration of prices of 1 year, implying
x
2
=116.5501


Degree of price indexation,

2
, set to 0.3


Depreciation rate for marketing capital,

m
, set to 0.6


Depreciation rate for matches,

q
, set to 0.1


Elasticity of output with respect to business services input,

2
, set
to 0.241


Bargaining power of business services producers,

, set to 0.5


Response of productivity to demand shocks:

Retail/Business services



Consumption risk premium
shock



Monetary policy shock


Response of productivity to a negative demand shock is negative
in the business services sector


Labour used for marketing is valuable and so is held on to, though it
is not measured as being productive


Retail productivity is higher than base after a year in the case of
a consumption risk premium shock


We’re still investigating what exactly is going on here



Effects of a demand shock: Business services and
retail sectors

Calibration


Scalable services sector


Average duration of prices of 1 year, implying
x
3
=11.655


Degree of price indexation,

3
, set to 0.3


Steady
-
state fixed charge,
a
, is equal to 0.0386 given
consumption and employment shares

Response of productivity to demand shocks:

Scaleable

services



Consumption risk premium
shock



Monetary policy shock


Response of productivity to a negative demand shock is negative
in the
scaleable

services sector


This follows given the increasing returns to scale in this sector …


… as you’d expect given the above




Effects of a demand shock: 3

Using the model to analyse the financial crisis


Model the financial crisis as a negative demand (consumer risk
premium) shock


Calibrate the shock based on rise in consumer credit spread


Likely to understate the true size of the shock o/a


Shock assumed to have no effect on investment in the model


No net trade shock (unlike in the real world)


No fiscal consolidation (ditto)


Peak effect is to push down on GDP by 2% (vs. 7% fall in GDP in
the data)

Response of productivity to the financial crisis

60
70
80
90
100
110
120
130
1997
Q1
1998
Q1
1999
Q1
2000
Q1
2001
Q1
2002
Q1
2003
Q1
2004
Q1
2005
Q1
2006
Q1
2007
Q1
2008
Q1
2009
Q1
2010
Q1
2011
Q1
2012
Q1
Scalable services
Business services
Consumer services
Other private sector
2007=100

Sectoral

productivity relative to pre
-
crisis
tred

Response of productivity to the financial crisis

Simulated response of
sectoral

productivity to the negative
demand shock

-5
-4
-3
-2
-1
0
1
2007
2009
2011
2013
2015
2017
Percentage deviation from trend

Business services

Scalable

services

Other private sector

Other consumer services

Response of productivity to the financial crisis


Our model suggests that the demand shock resulting from the
financial crisis led to a peak fall in business services productivity
of 4.3% relative to trend, as firms allocated relatively more labour
to building and maintaining their customer base, as opposed to
direct production


The shock also generates a fall in ‘scalable’ services productivity,
through the increasing returns channel, though it is small: 0.4%
relative to trend


Of course, the shock we model does not shed any light on the
additional fall in productivity from 2010 onwards, and is also likely
to understate the true size of the demand shock experienced by
the UK economy in the wake of the financial crisis




More careful calibration and/or estimation


More on the response of productivity to a demand shock


How different is the response of aggregate productivity to the shock
compared with the same impulse response in, say, the
Smets

and
Wouters

model?


Simulate responses of inflation (in the aggregate and in each
sector) to a monetary policy shock


Does the model provide new insights into inflation dynamics at a
sectoral

and aggregate level?


Again, how different is the response of aggregate inflation to a
monetary policy shock relative to the
Smets

and
Wouters

model?


Ideas and comments welcome




Next steps