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Effects of Terms of Trade Gains and
Tariff Changes on the Measurement
of U.S. Productivity Growth
Rob Feenstra, UC Davis
Marshall Reinsdorf, BEA
Matt Slaughter, Dartmouth
2008 World Congress on National Accounts and
Economic Performance Measures for Nations
Rosslyn, Virginia
May 13, 2008
Motivation for Paper
▪ US productivity speedup of 1 percent per year
starting in 1995, with ITC as key driver.
▪ Trading gains can look like productivity gains.
▪ Growth of imports may have price driver.
▪ Multilateral elimination of tariffs on ITC goods
over 1997-1999 under the WTO Information
Technology Agreement.
▪ Improvement in non-petroleum terms of trade
coincided with the productivity speedup.
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2
Globalization of ITC Industry
Table 1: International Trade in ICT Industries ($million)
Industry
1992
1996
2000
Exports
Imports
Trade Balance
Exports
Imports
Trade Balance
8,277
5,042
3,235
16,730
26,659
-9,929
10,422
6,927
3,495
27,550
54,590
-27,040
10,263
14,284
-4,022
34,686
75,514
-40,828
Semiconductors
(End-use 21320)
Exports
Imports
Trade Balance
11,527
15,477
-3,950
24,135
36,713
-12,579
45,118
48,341
-3,223
Telecommunications
Equipment (End-use 214)
Exports
Imports
Trade Balance
Exports
Imports
Trade Balance
10,520
10,773
-253
47,054
57,952
-10,898
19,137
14,505
4,633
81,244
112,735
-31,491
28,987
38,203
-9,216
119,054
176,343
-57,289
Exports
Imports
Trade Balance
10.7
12.0
24.1
13.3
15.4
26.6
15.4
16.0
17.2
Computers (End-use 21300)
Computer accessories
(End-use 21301)
Total (End-use 213+214)
Share in Overall Trade (percent)
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US Nonpetroleum Terms of Trade, MFP and Detrended MFP
(1995=100)
120
115
110
105
100
Nonpetroleum terms of trade
95
MFP of Private Business
Deviation of MFP from its post-1987 average
90
1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
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Trade in GDP
▪ In current dollars, GDP = D + X – M,
where D = C+I+G, “gross domestic purchases” or
“domestic absorption.”
▪ Diewert and Morrison’s (1986) GDP function treats
M as intermediate inputs and D and X as outputs.
▪ Can also think of GDP as consolidated Value Added
for the whole economy in which the domestic
intermediate inputs cancel out (but note that M is
measured at tariff-free prices in calculating GDP.)
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5
Terms of Trade Effects can Resemble
Productivity Effects
Terms of Trade defined as PX/PM, where
PGDP  sDPD + sXPx – sMPM.
▪ Real income depends on production (GDP)
and on gains from trade, which grow when
terms of trade improve.
▪ Improved terms of trade raise nominal GDP
and the real D attainable for a given current
account balance, ceteris paribus.
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6
Change in Terms of Trade from PP to PP Reduces Real Consumption from D to D
but Shift in Production from A to A has no Effect on Real GDP
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7
Theory of Productivity Measurement
with International Trade
The revenue function for the economy gives its gross value added at basic prices:
M
Rt(Pt, t, vt) 
max 

y t 0


 i 1
pit q it
N

i 1
p txi x it
N
C

i 1 j1
t
p mij
(1  ijt )mijt

| y  S ( v )

t
t
t
where:
 Domestic final goods i = 1,…,M have quantities q it > 0 and prices p it > 0
t
 Exports i = 1,…,N have quantities x it > 0 and international prices p xi
> 0.
 Imported intermediate inputs i = 1,…,N, in j = 1,…,C varieties indexed by country
t
t
(1   ijt ) .
 Import quantities m ijt > 0, international prices p mij
> 0, domestic prices p mij
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Tariff Revenue in GDP
GDP function differs from Rtby the amount of tariff revenue.
N C
t
G (P ,  , v ) = R (P ,  , v )   p mij
 ijt m ijt ,
t
t
t
t
t
t
t
t
i 1 j1
Proposition 1
Holding fixed Pt and vt, the value of GDP is maximized at t = 0.
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Figure 4: Tariff on an Imported Final Consumption Good
y2 (import)
P'1
P1
C
U1
A
A
0
G*
R
G
y1 (export)
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10
Theoretical Measures of Productivity
We define “true” productivity, as in Diewert and Morrison (1986):
A
t 1
R t ( P t 1 ,  t 1 , v t 1 )
 t 1 t 1 t 1 t 1 ,
R (P ,  , v )
or
R t (P t ,  t , v t )
A  t 1 t t t .
R (P ,  , v )
t
These concepts of productivity change are not measurable because both the
numerator of At-1 and the denominator of At are unobservable. Yet their geometric mean
can be measured, once we assume a specific form for the revenue function.
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Measure of True Productivity
A
t 1
A

t 1/ 2
 Rt 
~
=  t 1  / [PT( ~P t 1 , P t ,yt-1,yt) QT(vt-1, vt, wt-1, wt)] ,
R 
~
where PT( P t 1 , ~P t ,yt-1,yt) is a Törnqvist price index over final goods, exports and imports,
and QT(vt-1, vt, wt-1, wt)is a Törnqvist quantity index over primary factors.
The Törnqvist price index is defined as:
~
ln PT( ~P t 1 , P t ,yt-1,yt)
t 1 t 1
t
t

xi
p xi
x it   p xi
1  p it 1q it 1 p it q it   p it  N  1  p xi








   

ln


ln
t 1
t   t 1    
t 1
t   t 1 
R   p i  i 1  2  R
R   p xi 
i 1  2  R
M
t 1
t 1
t 1
t
t
t
C
t
Cj1 p mij (1   ij ) m ij   ~

p
 1   j1 p mij (1   ij ) m ij
mi
 ln
.
  

t 1
t
t 1 

~


R
R
i 1  2 
  p mi 
N
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Adjustment for Net Entry of Varieties
from New Supplying Countries
Our price indexes incorporate the effect of new (and also disappearing) countries that sell
good i using Feenstra (1994), which shows that the ratio of CES price aggregates is:
t
t
~

p mi
t 1,t   mi 
 t 1  = PmiG  t 1 
~
  mi 
 p mi 
1 /( i 1)
,
where the terms tmi < 1 equal one minus the share of period t expenditure of “new”
suppling countries. As new supplying countries sell more, tmi falls.
1
We construct (tmh / tmh
) for each HS product h, raising to the power 1/(h – 1);
then take the geometric mean across products h  H i within an End-use industry i:
tmi
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

hH i
tmh

t
t 1 w mhi /(  h 1)
.
/  mh
Conventional TFP – True Productivity

ln TFP – ln A
t
t 1
A

t 1/ 2
 Gt 
 G t 1 
= ln  t   ln  t 1 
R 
R 
t 1 t 1
t t  t 
t 1 t 1
t t
 1  p xi
xi
p xi
xi
p xi
xi
p xi
xi
1  p xi

t 1, t 
 ln
   
 ln PxiL


+   

t 1
t   t 1 
t 
 G t 1
2
2




R
R
p
G

i 1 

  xi 



N
t 1
t 1
t 1
t
t
t
C
t 
Cj1 p mij (1   ij ) m ij   ~
p
 1   j1 p mij (1   ij ) m ij
mi
 ln

  

t

1
t
t

1


~


R
R
p
i  1  2 


mi

N
t 1 t 1
t
t
C
Cj1 p mij m ij 
 1   j1 p mij m ij
 ln P t 1,t .
  

miL


G t 1
Gt
i 1  2 

N
Gap between conventional and true TFP comprises:
 Difference between exact (Törnqvist) and Laspeyres formula for exports
 Difference between exact and Laspeyres formula for imports
 Correction for tariffs in the “true” import prices and weights
 Correction for net growth in import variety in the “true” import prices
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Estimation of Influence of Unmeasured
Gains from Trade on GDP/Productivity
▪ BEA aggregates Laspeyres indexes from BLS
to find deflators for exports/imports in GDP.
▪ We calculate alternative versions of the
indexes used by BEA to construct deflators.
▪ To aggregate our indexes, we use weights
from the NIPAs and Fisher index formula.
▪ Removing nonmarket sectors of GDP leaves
Value Added of Private Business, the output
part of aggregate productivity calculation.
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15
Three Kinds of Corrections Tested
▪
▪
▪
Törnqvist rather than Laspeyres formula
for deflators of trade components of GDP.
Tariff-inclusive weights and index for M.
Adjust PM for net entry of new countries
supplying imports using CES formula.
True detailed index = (linked index)(   )
t
t-1 1/(1)
t = 1 – share of new supplying countries in period t
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16
Nonpetroleum terms of trade before
If the improvement
in the terms of trade
understated, then
productivity
overstated.
taking
account
ofisBEA’s
use
of isFisher
Sources of mismeasurement: see Figure 2.
Figure 2: Alternative Terms of Trade Indexes
120
115
110
105
100
Tornqvist
w/ Tariff
w/ Variety
7
1
19
99
0
7
19
99
0
1
19
98
0
7
19
98
0
1
19
97
0
7
19
97
0
1
19
96
0
7
19
96
0
1
19
95
0
7
19
95
0
1
19
94
0
7
19
94
0
1
19
19
93
0
7
Laspeyres
93
0
1
19
92
0
7
19
92
0
1
19
91
0
7
19
91
0
1
19
BLS
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90
0
7
90
0
19
89
0
19
19
89
0
1
95
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96
19 01
96
19 03
96
19 05
96
19 07
96
19 09
96
19 11
97
19 01
97
19 03
97
19 05
97
19 07
97
19 09
97
19 11
98
19 01
98
19 03
98
19 05
98
19 07
98
19 09
98
19 11
99
19 01
99
19 03
99
19 05
99
19 07
99
19 09
99
11
19
Example of Detailed Indexes:
Semiconductor Imports
Figure 9: Import Prices, Semiconductors (21320)
100
90
80
70
60
50
40
BLS
Laspeyres
Tornqvist
w/ Tariff
w/ Variety
19
96
19 01
96
19 03
96
19 05
96
19 07
96
19 09
96
19 11
97
19 01
97
19 03
97
19 05
97
19 07
97
19 09
97
19 11
98
19 01
98
19 03
98
19 05
98
19 07
98
19 09
98
19 11
99
19 01
99
19 03
99
19 05
99
19 07
99
19 09
99
11
Example of Detailed Indexes:
Semiconductor Exports
Figure 10: Export Prices, Semiconductors (21320)
100
90
80
70
60
50
40
BLS
www.bea.gov
Laspeyres
Tornqvist
96
19 01
96
19 03
96
19 05
96
19 07
96
19 09
96
19 11
97
19 01
97
19 03
97
19 05
97
19 07
97
19 09
97
19 11
98
19 01
98
19 03
98
19 05
98
19 07
98
19 09
98
19 11
99
19 01
99
19 03
99
19 05
99
19 07
99
19 09
99
11
19
Telecom Equipment Imports
Figure 11: Import Prices, Telecommunications (21400)
100
95
90
85
80
75
BLS
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Laspeyres
Tornqvist
w/ Tariff
w/ Variety
19
96
19 01
96
19 03
96
19 05
96
19 07
96
19 09
96
19 11
97
19 01
97
19 03
97
19 05
97
19 07
97
19 09
97
19 11
98
19 01
98
19 03
98
19 05
98
19 07
98
19 09
98
19 11
99
19 01
99
19 03
99
19 05
99
19 07
99
19 09
99
11
Telecom Equipment Exports
Figure 12: Export Prices, Telecommunications (21400)
105
100
95
90
85
80
BLS
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Laspeyres
Tornqvist
Effects on Price Indexes
(Averages for 1996-1999)
Revision to
Corrections
Törnqvist formula
Exports Index
Imports Index
Revision to
Terms of Trade
0.6 %/year
0.2 %/year
Add: Tariffinclusive prices
0.7 %/year
0.3 %/year
Add: New import
suppliers
1.5 %/year
1.1 %/year
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0.4 %/year
Revision to
Table 6: Effect of Lower-level Index Formula on Aggregate Fisher
Price Indexes for Exports and Imports
1997
1998
1999
Ave
96-99
104.1 104.1 102.5
103.5 103.4 101.5
99.4
97.7
98.2
96.1
101.1
99.7
1994 1995
1996
I. Export Indexes
Formula for lower-level aggregates
Laspeyres
Törnqvist
100
100
Growth rate difference of Törnqvist from Laspeyres
Contribution of ICT goods to above difference
-0.58
-0.10
-0.16
-0.18
-0.33
-0.23
-0.66
-0.41
-0.43
-0.27
-0.40
-0.27
103.2 101.6
102.8 100.9
102.6 100.5
102.6 99.8
99.0
97.6
97.3
95.7
95.1
93.2
92.8
90.3
93.5
91.0
90.4
87.5
97.3
95.7
95.3
93.3
-0.35
-0.55
-0.60
-0.01
-0.62
-0.60
-1.54
-0.78
-0.65
-0.82
-1.77
-0.59
-0.72
-0.87
-1.41
-0.56
-0.59
-0.69
-1.47
-0.57
II. Import Indexes
Formula for lower-level aggregates
Laspeyres
Törnqvist
Törnqvist, tariffs included in prices
Törnqvist, adjusted for tariffs and varieties
Growth rate difference from Laspeyres
Törnqvist
Törnqvist, tariffs included in prices
Törnqvist, adjusted for tariffs and varieties
Contribution of ICT goods to above difference
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100
100
100
100
-0.37
-0.48
-1.14
-0.33
23
Effects on Measures of GDP and
Productivity
▪ Reduction in real GDP growth is about 0.1
percent per year after 1995 (allowing for lack
of effect of capital goods & tariffs.)
▪ Growth rate of price index for private
business value added increased by 0.2%/year.
▪ Growth of productivity reduced by almost 0.2
%/year, a fifth of the productivity speedup.
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Price and Volume Indexes for GDP and
Value Added of Private Business
1994
1995
1996
1997
1998
1999
Price index for GDP
Official (rebased to 1994=100)
After adjustment for Törnqvist formula, tariffs & variety
Growth rate difference
100 102.0 104.0 105.7 106.9 108.4
100 102.1 104.1 106.0 107.3 108.9
0.01 0.10 0.13 0.13 0.12
Price Index for Private Business Value Added
Official Laspeyres
Törnqvist formula without tariffs
Törnqvist formula with tariffs in prices and weights
Törnqvist formula, with tariffs and variety adjustment
100
100
100
100
Difference from Laspeyres in annual growth rate
Törnqvist
Törnqvist, tariffs included in prices
Törnqvist formula, with tariffs and variety adjustment
Implied difference in growth rate of real output
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101.8
101.7
101.8
101.8
103.4
103.4
103.4
103.5
104.9
104.9
105.0
105.3
105.5
105.6
105.7
106.1
106.5
106.7
106.8
107.3
-0.01 0.03 0.05 0.02 0.06
0.01 0.07 0.06 0.06 0.09
0.02 0.16 0.19 0.19 0.16
0.01 -0.13 -0.20 -0.18 -0.15
25
End
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