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Sector-Specific Technical Change
Susanto Basu
John Fernald
Boston College and NBER
Federal Reserve Bank of San
Francisco
Jonas Fisher
Miles Kimball
Federal Reserve Bank of Chicago
University of Michigan and NBER
Very preliminary
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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
2
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
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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.
4
Consider social-planners problem for two-sector growth
model, with CRS, identical production technologies

max E0   t [ln(Ct )  v( N t )]
N ,C , X , I
s.t.
t 0
C  AZ  F ( K C , N N )
I  Z  F (KI , NI )
K  KC  K I ,
N  NC  N I
K t 1  I t  (1   ) K t
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This is Special Case of Following, Simple Social
Planner’s Problem

max E0   [ln(Ct )  v( N t )]
t
N ,C , X , I
s.t.
t 0
Ct  At X t
X  I  G  F (K , N , Z )
K t 1  I t  (1   ) K t
Equivalent problem:

max E0   [ln( At )  ln( X t )  v( N t )]
t
N , X ,I
s.t.
t 0
X t  I t  Gt  F ( K t , N t , Z t )
K t 1  I t  (1   ) K t
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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.
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King-Plosser-Rebelo Utility with EIS < 1
(γ>1)
1
C
( Nt )
t
t
max E0  
C ,I ,N , X
1 
t 0
s.t. Ct  At X t

X  I  G  F (K , N , Z )
K t 1  I t  (1   ) K t
Equivalent problem:
A01
s.t.
1
1
 t  At

X
( Nt )

t
max E0    


A
C ,I ,N , X
0 

1 
t 0 

X t  I t  Gt  F ( K t , N t , Z t )

K t 1  I t  (1   ) K t
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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.
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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.
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Empirical Implications: Low EIS and Permanent
Tech Shocks
• With permanent technology shocks and King-PlosserRebelo 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.
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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.
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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
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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
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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
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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
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Rearranging the standard input-output table
Standard input-output table for n commodities:
Supply
At Y t
Domestic
 C t  J t  Gt  X t  M t  Y t
Rearrangement in terms of "supply":
BtYt Supply  Ct  J t  Gt  NX t  Yt Supply  Yt Domestic  M t
where Bt is (n  1)  (n  1), all other variables are (n  1)  1
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 ( n  1)
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Defining final-use technology
Rearranging yields:

Yt Supply  [ I  Bt ]1 Ct  J t  Gt  NX t

For industry i, define final-use "column shares", e.g.,
bCi  Cit / Ct , where
Ct  sum(C t ).
We define final-use technology as:
dz C  bC [ I  Bt ]1 dz Commodity
dz J  bJ [ I  Bt ]1 dz Commodity
dz G  bG [ I  Bt ]1 dz Commodity
dz Trade  bTrade [ I  Bt ]1 dz Commodity
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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
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