1. Sector-Specific Technical Change
Susanto Basu
Boston College and NBER
Jonas Fisher
Federal Reserve Bank of Chicago
John Fernald
Federal Reserve Bank of San Francisco
Miles Kimball
University of Michigan and NBER

2. Objective: Measure technology by final-use sector (esp
Objective: Measure technology by final-use sector (esp. consumption versus equipment investment)
Idea: Estimate technology residuals from industry data, then aggregate through the input-output tables
Contribution: Do not identify final-use technology from relative price data
Makes our method more general than existing literature
We can test (and reject) the assumptions needed for relative price approach to work
Robust to differing factor shares, time-varying markups, sticky prices, variable factor utilization, increasing returns, changing tax rates, …

3. Using input-output tables to map disaggregated technology shocks into final-use technology
Direct technology estimates from industry production functions
vector dz of (gross-output) technology shocks, [dz1 , dz2 , …]’
Implicit production function for delivering output to final consumption or investment. Intuition:
Matrix B is (nominal) intermediate input shares
bij is share of commodity j in producing commodity i
Technology for deliveries to final demand
Weight by final-use shares, e.g.:

4. Given TFP for final-use commodities, ZC, ZJ, etc. easy4

5. What is “net exports technology”
In data, have to confront that economy is open
Some commodity supply is imported
Purpose of exports is to import (allowing use of those commodities)
“Technology”: Terms of trade
Final-use net-exports technology captures ability to obtain imports from exports
Terms of trade improvements
Technology improvements in goods we export

6. Two issues arise in input-output data to measure relevant intermediate-input matrix B
Final use is by commodity, productivity data (dzi) are by industry
I-O make table maps commodity production to industries
Final-use is from total commodity supply, not domestic production
I-O use table tells us both production and imports
where dzIndustry is vector of industry technologies
Rescale domestic-commodity technology 6 6 6

7. What does an input-output use table look like?
Nominal commodity-by-commodity use table
Columns give inputs into domestic production
Rows give “uses” of the commodity 7 7

8. We define a “trade goods” commodity, which uses commodity exports as an input to produce imports
Nominal commodity-by-commodity use table
Exports represent intermediate inputs into trade-goods production.
Imports are used as intermediate inputs to produce commodity supply 8 8

9. We define a “trade goods” commodity, which uses commodity exports as an input to produce imports
Nominal commodity-by-commodity use table
Exports represent intermediate inputs into trade-goods production.
Imports are used as intermediate inputs to produce supplies of other commodities 9 9

10. We define a “trade goods” commodity, which uses commodity exports as an input to produce imports
Nominal commodity-by-commodity use table
Exports represent intermediate inputs into trade-goods production.
Imports are used as intermediate inputs to produce commodity supply 10 10

11. Net exports are one use of trade goods, representing a claim on future imports
Nominal commodity-by-commodity use table
NX are a form of final expenditure, much like investment. 11 11

12. Tables now add up, in terms of commodity supply!
Nominal commodity-by-commodity use table 12 12

13. Start with KLEM productivity data from Jorgenson et al.
Key collaborators include Fraumeni, Ho, Stiroh, Gollop, and others
Annual input-output tables underlying these productivity data
35 industries/commodities
Includes final use, which allows us to distinguish
ND-S Consumption (don’t have owner-occ housing)
Consumer Durables
Government purchases of G&S (not govt administration)
Equipment investment
Structures investment
Exports and Imports 13

14. We modify original data to incorporate alternative deflators for durable goods
Key work of Gordon (1983), updated by Cummins-Violante (2002)
New deflators redefine output for each industry
Aggregate using I-O tables to get new measures of C, I, etc.
Of course, also new prices for each category of expenditure

15. Need vector of industry technology innovations
Production function
Could use industry Solow residuals:
Concerns:
Non-constant returns
unobserved variations in labor effort Ei and capital’s workweek Si
Thus use BFK (2006, AER) “purified” Solow residuals instead

16. Feeding industry BFK shocks through I-O tables: Equip and con. dur
Feeding industry BFK shocks through I-O tables: Equip and con. dur. technology rise fastest
Cumulated log change in final-use BFK technology 16

17. Consumption and investment technology (exogenous component—zero out ToT, natural resources)

18. Relative sectoral technology diverges from typical macro proxy of relative prices
Correlation of growth in relative TFP, relative BFK technology, and relative output prices
Relative TFP
Relative BFK Technology
Relative Final-goods prices
(dzEquipment – dzConsumption) 1
Relative BFK Technology (dzBFK, Equipment – dzBFK, Consumption)
0.28
Relative final-goods prices
(dpConsumption – dpEquipment)
0.76
0.23
That the sum of the first two lines should equal the third lines ought to be an identity. I think that I’m not properly incorporating trade goods (non-competing imports into final consumption/investment; and the terms of trade isn’t being included in either
Gap reflects:
Share-weighted input price growth (lower in equipment)
Foreign commodity supply price growth (price of imported equipment falling relative to price of imported consumption)
Sales tax wedge (sales/excise taxes, primarily on consumption goods, drives time-varying wedge between producer/purchaser price)
Relative price changes have correlation (in annual data) of only 0.23 with relative BFK technology 18

19. Relative prices respond to relative technology with long lags
d Relative Technology (Lag)
Cumulative 1 2 3
effect
d Relative Price
0.28
0.15
0.17
0.23
0.83
(cons to equip)
(0.13)
(0.20)
(0.14)
(0.19)
(0.31)
Relative Price (LHS var): growth in price of consumption (ND and services) relative to price of equipment
Rel. Technology (RHS var) : Growth in equipment technology relative to consumption (ND and services) 19

20. Conclusions
Theory suggests that “final use” sector where technology change occurs matters for its effects
E.g., consumption-technology neutrality, 2-sector sticky-price model
Measure sectoral technical change using a new method that doesn’t require relative prices
Gives similar long-run results, but very different short-run implications
Effects of sector-specific technology shocks look like business cycles
Equipment technology improvements reduce output, hours, investment, and consumption
Consumption technology improvement raise output, hours, investment, and consumption 20

21. 21

22. Equipment investment technology and consumption technology have very different macroeconomic effects
Note: This is a linked spreadsheet to shortsummary-from-exp-regs.xlsx, which was, in turn, produced by C:\Documents and Settings\l1jgf01.RB\My Documents\Papers\BFFK\data\final2004\NIPAregs\exp-regs-feb09-1e.tsp. If we keep this set of regressions, we should perhaps have it produced in the “main” spreadsheets. But at this point, the regressions themselves remain experimental. I tried doing JECD and “other” which was share-weighted CNDS, G, JS, and NX. But having the NX shock explicitly makes a notable difference to the magnitudes of the responses to both JECD and “other”. Without NX, those shocks still have same signs and are still significant, but the magnitudes are smaller. I need to see whether I can reject that CNDS, G, and JS have the same coefficient. It’s not an obvious way to aggregate, except that we can only have three of the shocks or standard errors explode
Each row is a separate regression of log change in variable shown on current and lagged tech shocks
Equip tech. includes con dur and govt equip. Cons. (Nondur) tech includes structures and nonequip. govt.
Intrumental variables estimation. Instruments zero out terms of trade and industry shocks not estimated via BFK. Annual data 22 22 22

23. Technology shocks explain a lot of the variation in equipment…
Corr = 0.59 23

24. …as well as hours
Corr = 0.64 24

25. 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. 25

26. 26

27. Comments With log preferences, ln(A) is additively-separable:
Any stochastic process for A has no effect on optimal decision rules for N, X and I.
More general King-Plosser-Rebelo preferences:
If A follows a geometric random walk it has no effect on optimal decision rules for N, X and I. 27

28. What is “technology”? Is ‘technology’ the economy’s PPF?
The change in production functions for domestic C and I?
We use the first, broader, definition. 28

29. 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
Our definition is correct for typical two-sector macro model
Otherwise, takes account of intermediate-input flows
If all sectors face same input prices and have identical factor shares (including intermediates), then relative final-goods prices reflect relative technologies
Again, our definition is correct for typical special cases used in macro (e.g., Greenwood, Hercowitz, Krusell) 29

30. Two issues arise in using industry/commodity data to measure final-use sector technical change
Final use is by commodity, productivity data are by industry
I-O make table maps commodity production to industries
We assume:
MAKE*dzCommodity = dzIndustry,
Final-use is from total commodity supply, not domestic production
I-O use table tells us both production and imports
where dzIndustry is vector of industry technologies
Rescale domestic-commodity technology 30

31. We aggregate commodity technology shocks to final uses with constant-share aggregation31

32. Motivation: In benchmark RBC model, consumption-technology shocks are neutral
Suppose utility is logarithmic U = ln(C) – v(L)
Let A be multiplicative technology for producing non-durable consumption
Consumption-technology neutrality proposition:
In two-sector RBC model, stochastic process for A does not affect labor hours L, investment J, or the quantity of resources devoted to producing consumption goods (X)
A affects only production of nondurable consumption goods 32

33. Social-planner’s problem for two-sector growth model, with CRS, identical production technologies33

34. This is special case of following problem, where At is additively separable, and thus doesn’t affect decision rules 34

35. This is special case of following problem, where At is additively separable, and thus doesn’t affect decision rules
Equivalent problem:
Empirically, do shocks to different final sectors have different economic effects? 35

36. Relative sector-specific TFP reflects relative output prices and relative primary input prices
“Primal” (standard) TFP for commodity i equals dual:
In vector/matrix form:
Intermediate input prices are sNdn ≈ Bdp, so: 36

37. Seek a more robust way to measure relative technology
What we do instead
Seek a more robust way to measure relative technology
Use industry data to estimate underlying shocks
Production-function regressions a la BFK (2006)
Then aggregate using I-O tables to final-use technology changes for C, I, etc.
Present findings, implications for business-cycle models

38. Outline Introduction: Declining relative price of equipment
Motivation: Consumption-technology neutrality
Conceptual issues in empirical measurement
Mapping simple dynamic model to complicated world
Terms of trade as a form of technology
Manipulating input-output (I-O) tables
Data and empirical results: Bottom-up v. top-down
Interpretation 38

39. Motivation: In benchmark RBC model, consumption-specific technology shocks have no dynamic effects
Suppose period utility is logarithmic U = ln(C) + v(1-L)
Let A be multiplicative technology that affects only production of non-durable consumption 39

40. Note: This model is benchmark Greenwood-Hercowitz-Krusell model, with a different normalization of the two shocks
We normalized on:
Investment-specific technical change literature normalizes differently: 40

41. What is trade goods “technology”? The terms of trade
We export in order to import
Commodity exports are (intermediate) inputs into producing trade goods
‘Output’ is imports plus net exports
nominal value = export value PXX
Real output = Goods we can import = PXX/PM 41

42. Sectoral TFP diverges from typical macro proxy of relative prices
Relative TFP, output prices, input prices, and wedges (percent change, annual rate)
Full Sample
(1)
(2)
(3)
Accel.
((3) – (2))
Relative TFP
(dzEquipment – dzConsumption)
2.42
1.60
3.24
1.65
(2) Relative price
(dpConsumption – dpEquipment)
2.54
1.57
3.52
1.95
(3) Relative primary input prices
(equip. rel. to NDS cons.)
0.19
0.09
0.29
0.20
(4) Relative import prices
-0.43
-0.27
-0.59
-0.32
(5) Relative sales tax wedge
0.11
0.21
0.02
-0.19
That the sum of the first two lines should equal the third lines ought to be an identity. I think that I’m not properly incorporating trade goods (non-competing imports into final consumption/investment; and the terms of trade isn’t being included in either 42 42

43. Does typical orthogonality assumption between “neutral” (consumption) and “investment-specific” technology hold?
Correlations of final-use TFP
(1) Corr(dzJ, dzC)
0.83
0.90
0.75
(2) Corr(dzJE, dzC)
0.74
0.82
0.67
(3) Corr(dzJE - dzC, dzC)
0.18
0.27
-0.02
(4) Corr(dzJE- dzC, dzJ)
0.61
0.58
0.54
Note that the average subsample correlation is higher than the sample correlations. That’s because the series means change, which affects the standard deviations of the series.
Subscripts: J is overall investment, JE is equipment and software, C is nondurables and services consumption. 43 43

44. Equipment investment technology and consumption technology are quite positively correlated…
Correlations of BFK “purified” final-use technology
(1) Corr(dzJ, dzC)
0.70
0.73
0.75
(2) Corr(dzJE, dzC)
0.45
0.43
0.60
(3) Corr(dzJE - dzC, dzC)
-0.06
-0.09
-0.01
(4) Corr(dzJE- dzC, dzJ)
0.59
0.53
0.57
Note that the average subsample correlation is higher than the sample correlations. That’s because the series means change, which affects the standard deviations of the series.
Subscripts: J is overall investment, JE is equipment and software, C is nondurables and services consumption. 44 44

45. Equipment technology improves reduce output and hours—consumption technology improvements raise output
Dep. Variables are growth rates of variables shown. Regressors are BFK final-sector technology shocks. Instruments are corresponding measures, with shocks to terms of trade, ag, mining, and govt. zeroed out. Std errors robust to heteroskedasticity and autocorrelation. 45 45

46. Table 6 46 46

47. Begin by using industry TFP
Assume (for a start) that industry Solow (TFP) residual is the right measure of industry technical change
Jorgenson data give us input-output (make) table B and the final-use vectors b

48. E&S and con. durables TFP rises faster than for nondurables and services, government, or structures48
Cumulated log change in final-use TFP