Is Equipment Price Deflation aStatistical Artifact?

Bart Hobijn

FRBNY

What is an Artifact?

• Artifact:An inaccurate observation, effect, or result, especially one from the technology used in scientific investigation or from experimental error.“The apparent pattern in the data was an artifact of the collection method”

American Heritage Dictionary of the English Language

Example: PC microprocessor prices

Price per MHz increasing in speed of processor !

Hypothesis

Measured equipment price deflation overstated because statistical methods do

not take into account imperfect competition in equipment markets

Outline• Step 2 (real world): Positive correlation between markup

and quality biases measures of equipment price deflation.– Notation

– Measures of equipment price deflation

– Example: PC microprocessors

• Step 1 (my world): Imperfect competition causes markups to be positively correlated with the quality of the machine.– Model market for machines

– Equilibrium outcome

• How do real world methods do in my world? – numerical example

• Conclusion and big picture

Stylized example

Chip 500MHz

1GHz

2GHz

Averageprice per

MHzPrice 500 2000 -

Year 1Market share ½ ½

1.66

Price - 1000 4000Year 2

Market share ½ ½1.66

Suppose quality of MPU is proportional to clock speed

Notation• time t

• vintage indicator v

• efficiency units embodied in v Av

• price of vintage v at time t Pt,v

• vintage age =t-v

• number of v machines sold at time t Xt,v

One vintage introduced in each period

Technological progress: Av>Av-1

Vintage price schedules

• Modus operandi

– Relative prices reflect relative qualities

– Implicit: No markups and production costs constant per quality unit.

level price aggregate , tvtvt PAPP

'',, // vvvtvt AAPP

Vintage price schedules

• Modus operandi

• I will argue

– market power is higher for newer vintages t,v> t,v-

1

– market power decreases as vintage ages t,v> t+1,v

– note: t,v=1 gives back conventional schedule

level price aggregate , tvtvt PAPP

powermarket of measure ,,, vtvtvtvt APP

Matched model method• Set of vintages in market today and

yesterday, M.

• Measured equipment price inflation, t

Apply measure to vintage price schedule with markups

Mvvt

vt

vtvtt P

Pweightsdependent -index 1 ,

,1

,,

Matched model method• Vintage price schedule:

• Measured equipment price inflation, t

Measured deflation captures price decrease as well as market power erosion

11

1

11,1

,,

,1

,,

t

t

v t

t

vt

vtvt

v vt

vtvtt

P

P

P

P

P

P

M

M

vtvtvtvtvtvtvt APP ,1,1,,,, and

Stylized example revisited (1)

Chip 500MHz

1GHz

2GHz

Averageprice per

MHz

Matchedmodelindex

Price 500 2000 -Year 1

Market share ½ ½1.66 100

Price - 1000 4000Year 2 Market share ½ ½ 1.66 50

Hedonic price method• Vintage price schedule

• Quantify part of price determined by quality using regression

Apply measure to vintage price schedule with markups

vvvtvtvt AQAuAPP assume exp ,,

vtvtvt uQPAP ,, lnlnlnln

Hedonic price method• Vintage price schedule

• Estimate regression

– Omitted variable bias:lnQv is correlated with the omitted markup variable.

– Too big a part of price changes attributed to quality differences!

– Too little attributed to price increases!

vvvtvtvtvt AQAuAPP assume exp ,,,

vtvtvt uQP ,, lnln

Stylized example revisited (2)Chip 500

MHz1

GHz2

GHzAverageprice per

MHz

Hedonicpriceindex

Price 500 2000 8000Year 1

Market share ½ ½1.66 100

Price 250 1000 4000Year 2

Market share ½ ½1.66 50

Conclusion• Imperfect competition leads to markups

being positively correlated with quality

• positive correlation between markups and quality bias measures of equipment price deflation

• equipment price deflation overestimated

• Important aggregate implications