Modelling the Services Sector

Stephen MillardBank of England, Durham University Business School and Centre for Macroeconomics

Phil KingBank 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

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The model: Households

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

• Maximise

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

• Marginal product of capital equals marginal cost

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The model: Households

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

• This leads to the ‘Wage Phillips Curve’

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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

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The model: Bespoke service sector

Household demand

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Business Service Provider j

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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 δq

• 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

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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:

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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:

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• 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

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• 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

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• 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

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• The central bank operates a Taylor rule:

• All markets clear:

The model: Monetary policy and market clearing

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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 y1, y2 and y3 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, sc=1

• Frisch labour supply elasticity of 2, implying sh=0.5

• Discount factor, b, of 0.99• Steady-state wage mark-up of 1.5, implying lw=0.5

• Average duration of wages of 1 year, implying xw=0.75

• Degree of wage indexation, gw, of 0.3

• Taylor rule

• Demand shock

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Calibration – Goods sector

• Depreciation rate of 10% pa, implying d=0.025• Elasticity of capital adjustment costs, ek, set to 0.5

• Scale of capital adjustment costs, ck, set to 201

• Elasticity of capital utilisation costs, fz, set to 0.56

• Elasticity of output with respect to capital input, a1, set to 0.395

• Steady-state price mark-up of 1.1, implying r=10/11• Average duration of prices of 1 year, implying x1=116.5501

• Degree of price indexation, g1, set to 0.3

Response of productivity to demand shocks:Goods

• Consumption risk premium shock

• Monetary policy shock

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• 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

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Calibration – Bespoke services sector

• Steady-state price mark-up of 1.1, implying r=10/11• Average duration of prices of 1 year, implying x2=116.5501

• Degree of price indexation, g2, set to 0.3

• Depreciation rate for marketing capital, dm, set to 0.6

• Depreciation rate for matches, dq, set to 0.1

• Elasticity of output with respect to business services input, a2, set to 0.241

• Bargaining power of business services producers, q, set to 0.5

Response of productivity to demand shocks:Retail/Business services

• Consumption risk premium shock

• Monetary policy shock

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• 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 x3=11.655

• Degree of price indexation, g3, 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

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• 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

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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

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Business services

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Other private sector

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Sectoral productivity relative to pre-crisis tred

Response of productivity to the financial crisis

Simulated response of sectoral productivity to the negative demand shock

2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017-5

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Percentage deviation from trend

Business services

Scalable services

Other private sectorOther 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