Effects of Terms of Trade Gains and Tariff Changes on the Measurement of U.S. Productivity Growth

Rob Feenstra, UC DavisMarshall Reinsdorf, BEA Matt Slaughter, Dartmouth

2008 World Congress on National Accounts and Economic Performance Measures for Nations

Rosslyn, Virginia

May 13, 2008

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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.

2

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Globalization of ITC IndustryTable 1: International Trade in ICT Industries ($million)

Industry 1992 1996 2000

Computers (End-use 21300) Exports 8,277 10,422 10,263 Imports 5,042 6,927 14,284 Trade Balance 3,235 3,495 -4,022

Computer accessories Exports 16,730 27,550 34,686 (End-use 21301) Imports 26,659 54,590 75,514 Trade Balance -9,929 -27,040 -40,828

Semiconductors Exports 11,527 24,135 45,118 (End-use 21320) Imports 15,477 36,713 48,341 Trade Balance -3,950 -12,579 -3,223

Telecommunications Exports 10,520 19,137 28,987 Equipment (End-use 214) Imports 10,773 14,505 38,203 Trade Balance -253 4,633 -9,216 Total (End-use 213+214) Exports 47,054 81,244 119,054 Imports 57,952 112,735 176,343

Trade Balance -10,898 -31,491 -57,289

Share in Overall Trade (percent) Exports 10.7 13.3 15.4 Imports 12.0 15.4 16.0 Trade Balance 24.1 26.6 17.2

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US Nonpetroleum Terms of Trade, MFP and Detrended MFP (1995=100)

90

95

100

105

110

115

120

1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007

Nonpetroleum terms of trade

MFP of Private Business

Deviation of MFP from its post-1987 average

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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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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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Change in Terms of Trade from PP to PP 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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Theory of Productivity Measurement

with International TradeThe revenue function for the economy gives its gross value added at basic prices:

Rt(Pt, t, vt)

)v(Sy|m)1(pxpqp ttt

N

1i

C

1j

tij

tij

tmij

M

1i

N

1i

ti

txi

ti

ti0y

maxt

where:

Domestic final goods i = 1,…,M have quantities tiq > 0 and prices t

ip > 0

Exports i = 1,…,N have quantities tix > 0 and international prices t

xip > 0.

Imported intermediate inputs i = 1,…,N, in j = 1,…,C varieties indexed by country

Import quantities tijm > 0, international prices t

mijp > 0, domestic prices )1(p tij

tmij .

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Tariff Revenue in GDP

GDP function differs from Rtby the amount of tariff revenue.

Gt(Pt, t, vt) = Rt(Pt, t, vt)

N

1i

C

1j

tij

tij

tmij mp ,

Proposition 1

Holding fixed Pt and vt, the value of GDP is maximized at t = 0.

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A

P'1

P1

G* R G

U1

y2 (import)

0

C

Figure 4: Tariff on an Imported Final Consumption Good

y1 (export)

A

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Theoretical Measures of Productivity

We define “true” productivity, as in Diewert and Morrison (1986):

)v,,P(R

)v,,P(RA

1t1t1t1t

1t1t1tt1t

, or )v,,P(R

)v,,P(RA

ttt1t

ttttt

.

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 2/1t1t AA =

1t

t

R

R / [PT( 1tP

~ , tP~ ,yt-1,yt) QT(vt-1, vt, wt-1, wt)] ,

where PT( 1tP~ , tP~ ,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( 1tP~ , tP~ ,yt-1,yt)

M

1i1t

i

ti

t

ti

ti

1t

1ti

1ti

p

pln

R

qp

R

qp

2

1

N

1i1t

xi

txi

t

ti

txi

1t

1ti

1txi

p

pln

R

xp

R

xp

2

1

N

1i1t

mi

tmi

t

tij

tij

tmij

1t

1tij

1tij

1tmij

p~p~

lnR

m)1(p

R

m)1(p

2

1 C1j

C1j

.

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Adjustment for Net Entry of Varieties from New Supplying

CountriesOur 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:

1t

mi

tmi

p~p~

= )1/(1

1tmi

tmit,1t

miG

i

P

,

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.

We construct )/( 1tmh

tmh

for each HS product h, raising to the power 1/(h – 1);

then take the geometric mean across products iHh within an End-use industry i:

)1/(w

Hh

1tmh

tmh

tmi

htmhi

i

/

.

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Conventional TFP – True Productivity

ln TFPt – 2/1t1t AA ln =

t

t

R

Gln

1t

1t

R

Gln

+

N

1i

t,1txiLt

ti

txi

1t

1ti

1txi

1txi

txi

t

ti

txi

1t

1ti

1txi Pln

G

xp

G

xp

2

1

p

pln

R

xp

R

xp

2

1

N

1i1t

mi

tmi

t

tij

tij

tmij

1t

1tij

1tij

1tmij

p~p~

lnR

m)1(p

R

m)1(p

2

1 C1j

C1j

t,1tmiLt

tij

tmij

1t

1tij

1tmij

N

1i

PlnG

mp

G

mp

2

1 C1j

C1j

.

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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Three Kinds of Corrections Tested

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True detailed index = (linked index)(tt-1)1/( 1)

t = 1 – share of new supplying countries in period t

▪ 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.

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If the improvement in the terms of trade is understated, then productivity is overstated.

Sources of mismeasurement: see Figure 2.

Figure 2: Alternative Terms of Trade Indexes

95

100

105

110

115

120

1989

01

1989

07

1990

01

1990

07

1991

01

1991

07

1992

01

1992

07

1993

01

1993

07

1994

01

1994

07

1995

01

1995

07

1996

01

1996

07

1997

01

1997

07

1998

01

1998

07

1999

01

1999

07

BLS Laspeyres Tornqvist w/ Tariff w/ Variety

Nonpetroleum terms of trade before taking account of BEA’s use

of Fisher

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Figure 9: Import Prices, Semiconductors (21320)

40

50

60

70

80

90

100

BLS Laspeyres Tornqvist w/ Tariff w/ Variety

Example of Detailed Indexes: Semiconductor Imports

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Figure 10: Export Prices, Semiconductors (21320)

40

50

60

70

80

90

100

BLS Laspeyres Tornqvist

Example of Detailed Indexes: Semiconductor Exports

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Telecom Equipment Imports

Figure 11: Import Prices, Telecommunications (21400)

75

80

85

90

95

100

BLS Laspeyres Tornqvist w/ Tariff w/ Variety

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Telecom Equipment Exports

Figure 12: Export Prices, Telecommunications (21400)

80

85

90

95

100

105

BLS Laspeyres Tornqvist

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Effects on Price Indexes (Averages for 1996-1999)

Corrections Revision to

Exports Index Revision to

Imports Index Revision to Terms of Trade

Törnqvist formula 0.4 %/year 0.6 %/year 0.2 %/year

Add: Tariff-inclusive prices 0.7 %/year 0.3 %/year

Add: New import suppliers 1.5 %/year 1.1 %/year

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Table 6: Effect of Lower-level Index Formula on Aggregate Fisher Price Indexes for Exports and Imports

1994 1995 1996 1997 1998 1999 Ave

96-99

I. Export Indexes Formula for lower-level aggregates Laspeyres 100 104.1 104.1 102.5 99.4 98.2 101.1 Törnqvist 100 103.5 103.4 101.5 97.7 96.1 99.7 Growth rate difference of Törnqvist from Laspeyres -0.58 -0.16 -0.33 -0.66 -0.43 -0.40

Contribution of ICT goods to above difference -0.10 -0.18 -0.23 -0.41 -0.27 -0.27 II. Import Indexes Formula for lower-level aggregates Laspeyres 100 103.2 101.6 99.0 95.1 93.5 97.3 Törnqvist 100 102.8 100.9 97.6 93.2 91.0 95.7 Törnqvist, tariffs included in prices 100 102.6 100.5 97.3 92.8 90.4 95.3 Törnqvist, adjusted for tariffs and varieties 100 102.6 99.8 95.7 90.3 87.5 93.3 Growth rate difference from Laspeyres Törnqvist -0.35 -0.37 -0.62 -0.65 -0.72 -0.59 Törnqvist, tariffs included in prices -0.55 -0.48 -0.60 -0.82 -0.87 -0.69 Törnqvist, adjusted for tariffs and varieties -0.60 -1.14 -1.54 -1.77 -1.41 -1.47 Contribution of ICT goods to above difference -0.01 -0.33 -0.78 -0.59 -0.56 -0.57

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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) 100 102.0 104.0 105.7 106.9 108.4 After adjustment for Törnqvist formula, tariffs & variety 100 102.1 104.1 106.0 107.3 108.9 Growth rate difference 0.01 0.10 0.13 0.13 0.12 Price Index for Private Business Value Added Official Laspeyres 100 101.8 103.4 104.9 105.5 106.5 Törnqvist formula without tariffs 100 101.7 103.4 104.9 105.6 106.7 Törnqvist formula with tariffs in prices and weights 100 101.8 103.4 105.0 105.7 106.8 Törnqvist formula, with tariffs and variety adjustment 100 101.8 103.5 105.3 106.1 107.3 Difference from Laspeyres in annual growth rate Törnqvist -0.01 0.03 0.05 0.02 0.06 Törnqvist, tariffs included in prices 0.01 0.07 0.06 0.06 0.09 Törnqvist formula, with tariffs and variety adjustment 0.02 0.16 0.19 0.19 0.16 Implied difference in growth rate of real output 0.01 -0.13 -0.20 -0.18 -0.15

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End