1

Sector-Specific Technical Change

Susanto BasuBoston College and NBER

Jonas Fisher Federal Reserve Bank of Chicago

John FernaldFederal Reserve Bank of San

Francisco

Miles Kimball University of Michigan and NBER

Very preliminary

2

Where does growth originate?

• Technical change differs across industries

• Recent work has highlighted that the final-use sector in which technical change occurs matters• Greenwood, Hercowitz, Krusell

• Use relative price data

• We reconsider the evidence• Extending GHK to situations where relative prices

might not measure technology correctly

• Top down versus bottom up

3

Outline

• Motivation: Consumption-technology neutrality

• How to think about terms of trade?

• Disaggregating: Manipulating the input-output matrix

• Comparing bottom-up versus top-down estimates

4

Consumption Technology Neutrality

• Suppose utility is logarithmic

• Suppose there is some multiplicative technology A for producing non-durable consumption goods

• The stochastic process for consumption-technology A affects only the production of nondurable consumption goods

• It does not affect affect labor hours N, investment I, or an index of the resources devoted to producing consumption goods X.

5

Consider social-planners problem for two-sector growth model, with CRS, identical production technologies

0, , ,

0

1

max [ln( ) ( )]

. . ( , )

( , )

,

(1 )

tt t

N C X It

C N

I I

C I C I

t t t

E C v N

s t C AZ F K N

I Z F K N

K K K N N N

K I K

6

This is Special Case of Following, Simple Social Planner’s Problem

0, , ,

0

1

max [ln( ) ( )]

. .

( , , )

(1 )

tt t

N C X It

t t t

t t t

E C v N

s t C A X

X I G F K N Z

K I K

0, ,

0

1

max [ln( ) ln( ) ( )]

. . ( , , )

(1 )

tt t t

N X It

t t t t t t

t t t

E A X v N

s t X I G F K N Z

K I K

Equivalent problem:

7

Comments

• Because ln(A) is an additively-separable term, any stochastic process for A has no effect on the optimal decision rules for N, X and I.

• There is a weaker, but still important result for the more general King-Plosser-Rebelo case: - anticipated movements in A act like changes in the utility

discount rate- unanticipated movements in A have no effect on the optimal

decision rules for N, X and I.

8

King-Plosser-Rebelo Utility with EIS < 1 (γ>1)

1

0, , ,

0

1

( )max

1

. .

( , , )

(1 )

t t t

C I N Xt

t t t

t t t

C NE

s t C A X

X I G F K N Z

K I K

1 11

0 0, , , 00

1

( )max

1

. . ( , , )

(1 )

t t tt

C I N Xt

t t t t t t

t t t

X NAA E A

s t X I G F K N Z

K I K

Equivalent problem:

9

An Example: Mean-Reverting Consumption Technology

• If A follows an AR(1) process, then At /A0 < 1 after an increase in A above the steady-state level at time zero.

• This makes (At /A0)1-γ > 1, which has the same effect as if

the discount factor β were larger. • Higher β (greater patience) would lead to an increase in

investment I, an increase in labor hours N, and a reduction in the resources devoted to consumption X.

• Thus, At /A0 < 1 leads to an increase in investment I, an increase in labor hours N, and a reduction in the resources devoted to consumption X.

• However, C=AX may increase even though X decreases.

10

Empirical Implications: Standard RBC Parameters

• With the standard parametrizations of the utility function consumption technology shocks will have very different effects from investment technology shocks.• consumption technology shocks have no effect on labor

hours or investment.• investment technology shocks have the same effect on

labor hours and investment as pervasive technology shocks.

• therefore, like pervasive technology shocks in standard RBC models, investment technology shocks should have a large effect on labor hours and investment.

11

Empirical Implications: Low EIS and Permanent Tech Shocks

• With permanent technology shocks and King-Plosser-Rebelo utility and relatively low elasticity of intertemporal substitution (≈ 0.3), investment technology shocks also have very little immediate effects on labor hours, though they do raise investment in a way that consumption technology shocks do not.

12

A More General Question

• Example of consumption technology neutrality raises possibility that shocks to different final sectors have different effects on aggregate labor hours and investment.

• Therefore, we would like to construct technology shocks for goods of different levels of durability to see empirically if these have different effects.

13

Motivation: A novel test of price stickiness

• In the log case, a change in consumption technology should have no effect on investment and hours

• For plausible deviations from log utility of consumption and permanent technology shocks (EIS<1and AR(1) technology as analyzed above), improvements in consumption technology should raise investment

• But with sticky prices, Basu-Kimball (2001) show that improved consumption technology should lower investment and hours in the short run

• Reason is that with price stickiness, relative price of consumption cannot jump down on impact

• However, consumption technology should have RBC-style effect once effective price stickiness ends

14

Terms of Trade as Technology

• In a closed economy, relative prices are always driven by domestic factors, including domestic technology

• But this is not true with an open economy—the relative price faced by a small open economy can change due to changes in foreign technology or demand

• We classify such price changes as “technology shocks” because they enable home consumers to have more consumption with unchanged labor input

• View trade as a special (linear) technology, with terms of trade changes as technology shocks

• However, this type of technology is special—for one thing, it has very different trend growth

15

Terms of Trade as Technology, cont’d

• Thus, need to allow ToT to follow a different stochastic process than more conventional technical change

• Ultimately a definitional question:Should ‘technology’ represent a change in the possibility frontier for consumption and leisure, or be restricted to a change in the production functions for domestic C and I?

• We use the first, broader, definition. Labeling does not matter, so long as one takes into account both ToT changes and domestic PF shifts

16

Issues in using industry/commodity data to measure sectoral technical change

• Final use is by commodity, productivity data are by industry • I-O make table maps commodity production to industries

• Can translate industry technology into final-use technology, using

dzCommodity = M-1dzIndustry,

where dzIndustry is vector of industry technologies

• Industry/commodity TFP is in terms of domestic production, whereas final-use reflects total commodity supply• Domestic commodity production plus commodity imports

• I-O use table tells us both production and imports

• Requires rescaling domestic-commodity technology

17

Rearranging the standard input-output table

Rearrangement in terms of "supply":

t t t

Supply Supply Domestictt t t t tB Y C J G NX Y Y M

��������������

where is ( 1) ( 1), all other variables are ( 1) 1tB n n n

The (n+1)'th sector is "trade". We include "exports" as

an intermediate input into producing "trade goods" (imports plus NX).

The NX column is zeros except for row ( 1)n

Standard input-output table for commodities:

t t

Supply Domestict tt t tt

n

A Y C J G X M Y ��������������

18

Defining final-use technology

1

Rearranging yields:

[ ]t

Supplytt t t tY I B C J G NX

��������������

Ci

t

For industry , define final-use "column shares", e.g.,

b / ,where

sum(C ).

it t

t

i

C C

C

1 Commodity

1 Commodity

1 Commodity

1 Commodity

We define final-use technology as:

[ ]

[ ]

[ ]

[ ]

CC t

JJ t

GG t

TradeTrade t

dz b I B dz

dz b I B dz

dz b I B dz

dz b I B dz

19

Notes

• Trade technology is the terms of trade

• Suppose there are no intermediate-inputs and one of each final-use commodity (e.g., a single consumption good)• Final-use technology is technology in that commodity

• Otherwise, takes account of intermediate-input flows