Measuring the Effects of Terms of Trade in National Accounts

Marshall ReinsdorfPresentation for PWT Workshop University of PennsylvaniaMay 11, 2008

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Real Income depends on Production and Gains from Trade▪ Current-dollar GDP = D + X – M,

where D = C+I+G, gross domestic purchases.

▪ Price index for GDP is: PGDP sDPD + sXPx – sMPM

▪ Though PX and PM have no direct effect on real GDP, they affect D compatible with current account balance.

▪ “Command-basis GNP” or “real gross national income” tracks command over goods and services that is made possible by domestic production and foreign trade.

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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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Common Deflator for X and M required for Command-Basis

GDP▪ If trade is always balanced, so that

income = expenditures, D/PD is correct measure of real gross domestic income.

▪ Real GDP = D/PD + X/PX – M/PM.

▪ Same deflator P* for X and M ensures that CB GDP = D/PD if X = M since CB GDP becomes equal to D/PD + (X – M)/P*.

▪ P* is deflator for net exports.

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Disagreement on Choice of Deflator for the Current Account

Balance ▪ NIPAs deflate exports by imports index PM to

calculate CB GDP. So does Kehoe (2006).

▪ Denison (1981) said other definitions for P* are possible, and the SNA lists at least three.

▪ Diewert deflates by consumption price index.

▪ Kohli uses gross domestic purchases index.

▪ Others use average of X and M indexes.

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Silver and Mahdavy’s (1989) Principle for Selecting a

Deflator“The effect on real income of a

change in terms of trade ultimately depends on what the surplus is spent on, or the nature of the response to the deficit, be it … cutting expenditure, … exporting more, or curtailing consumption of imported goods.”

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Valuing the Trade Deficit under a Homotheticity-like Assumption

Instead of reducing M to eliminate trade deficit reduce every item in D in proportion to some For items also in X, this directly increases X. For items also in M, this directly reduces M. For items just in D, this frees up productive capacity to make more of the X and M items. Under assumptions implying that ratios of marginal costs equal price ratios, value of growth in X – M equals value of decline in D.

Solution of= GDP/D eliminates the trade deficit.

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Dilemma avoided if we let P* = PD

Laspeyres-perspective index of CB GDP is:

D1/PD + (X1 – M1)/P* —————————— . D0 + X0 – M0

Paasche-perspective quantity index is:

D1 + X1 – M1

—————————– PDD0 + P*(X0 – M0 )

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Lasp & Paasche Agree if P* = PD

In general, for Laspeyres and Paasche to agree we must let P* = PD.

Otherwise, we’ll have to calculate

Laspeyres and Paasche versions of CB GDP

using Paasche and Laspeyres deflators,

then find Fisher.

Simplicity is advantage in national

accounts.

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“Fisher” real gross domestic income

▪ In COLI theory, Fisher is average of upper and lower bounds (though concept being bounded is not same in absence of homotheticity.)

▪ In CB GDP theory, assuming that all adjustment is via X gives one bound, and that all adjustment is via M gives another.

▪ Laspeyres vs Paasche gives further sets bounds.▪ Fisher [min(b1,b2 ,b3 ,b4 )max(b1,b2 ,b3,b4)]0.5

.

▪ In case of incomplete pass-through, PD may understate effect of rise in PM so Fisher approach may be more reliable than PD approach.

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Why PD is a better choice for the net exports deflator than PM

1. From a theoretical point of view, reasonable assumptions justify use of PD.

2. To find influence of PX and PM just omit them from basket. This gives PD.

3. Use of PD results in a simple decomposition

and in CB GNP = (Real D)(GNP/Nominal D).

4. PM results in understatement of effects of import prices, given trade deficit.

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Given Negative Net Exports, Measure of CB GDP is High if PM Rises and X Deflated by

PM▪ With PM as deflator for net exports, CB GDP

tracks the real level of D that would result from cutting M enough to eliminate the trade deficit.

▪ Due to rising deflator for the trade deficit, this understates the welfare loss from a rise in PM.

▪ Terms of trade is defined as PX/PM.

▪ With PM, Törnqvist quantity index for CB GDP is:

(quantity index for GDP) × (Terms of Trade)(2-period average share of X in GDP)

.

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Figure 1: Difference in Growth Rate of Command-Basis GNP from Real GNP

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Imports Index as Trade Deflator

Domestic Purchases Index as Trade Deflator

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Decomposition of growth rate of Törnqvist version of CB GDP

Defining weights (sD,sX,sM) as 2-period average shares of

GDP, sD + sX – sM = 1, or sD = 1 – sX + sM .

Then Törnqvist price index for GDP is:

PDsD PX

sx PM-sM = PD(PX/PD)sx (PM/PD)-sM.

So Törnqvist implicit quantity index for CB GDP is:

CB GDP = (real GDP)(PX/PD)sx (PM/PD)-sM.

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Decomposition of Törnqvist CB GDP

CB GDP = real GDP × (PX/PD)sx (PM/PD)-sM

(PX/PD)sx (PM/PD)-sM

= (PX/PM)(sx + sM)/2 [(PXPM)½/PD](sx-sM)

= (Terms of Trade)(share of trade in GDP) × (Relative price of tradables)(shr of trade bal in GDP)

.

With PM as deflator had CB GDP = Real GDP × (Terms of Trade)(2-period average share of X in GDP).

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Contributions of Trade Prices to Fisher Framework National Income

Contribution to Fisher quantity index for GNP:

CX = PXAve. QX / GNP(PAve.,Q0)

where PXAve. = (PX0 + PX1/PGNP)/2.

Contribution to command-basis GNP:

CXCB = [PX

Ave.D QX + QXAve. PX ]/GNP(P0,Q0)

where PXAve.D = (PX0 + PX1/PD)/2 and

PX = (PX1/PD – PX0).

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Calculation as Difference of Contributions

QX terms approximately cancel, leaving:

CXCB – CX

QXAve. PX / GNP0.

A similar decomposition of the growth rate difference between CB GNP and real GNP simply rescales the standard decomposition of the Fisher price index.

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Calculation as Rescaled Decomposition of Price Index

QGNPCB – QGNP = QGNP

PGNP /PD – QGNP

= QGNP(PGNP – PD)/PD

= (QGNP/PD)[s*X(PX – PD) – s*M(PM – PD)]

where s*X = PXAve. QX0 / GNP(PAve.,Q0).

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Real Gross National Income, Qty Indexes

Line 2003 2004 1 Gross national product 105.067 109.031 2 LESS: Exports of goods and services and income receipts from the rest of the world 90.888 103.375 3 PLUS: Imports of goods and services and income payments to the rest of the world 99.269 112.627 4 EQUALS: Gross domestic purchases 106.071 110.444 2 PLUS: Exports of goods and services and income receipts from rest of the world, command-basis\1\ 87.906 100.27 3 LESS: Imports of goods and services and income payments to rest of the world, command-basis \1\ 94.406 108.63 4 EQUALS: Real gross national income\1\ 105.493 109.25

Addendum: 5 Percent change from preceding period in real gross national product 2.7 3.8

PLUS: Contributions to difference from gross national income -0.2 -0.2 7 Exports of Goods -0.02 0.04 8 Exports of services and income receipts from ROW 0.00 0.00 9 Imports of Goods -0.07 -0.22

10 Petroleum and Products -0.18 -0.29 11 Nonpetroleum 0.11 0.07 12 Imports of services and income payments to ROW -0.09 -0.03 13 EQUALS: Percent change from preceding period in real gross national income 2.6 3.6

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Figure 3: Contributions to Change in Trading Gains

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Exports of goods Petroleum and products

Imports of nonpetroleum goodsCB GNP – Real GNP

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Useful Detail on Terms of Trade

▪ Traditionally interest in terms of trade effects focused only on crude commodities.

▪ But explosive growth of manufactured imports has raised new questions.

▪ Price swings of petroleum obscure behavior of other prices in overall Terms of Trade.

▪ A non-petroleum Terms of Trade is needed.

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Real Gross National Income

Line 2003 2004 2005 2006 2007

1 Gross national product 10355.3 10746.0 11064.7 11370.1 11647.6 2 LESS: Exports of goods and services and income

receipts from the rest of the world 1344.2 1528.9 1688.9 1904.1 2101.8 3 PLUS: Imports of goods and services and income

payments to the rest of the world 1806.2 2049.3 2242.4 2473.2 2570.9 4 EQUALS: Gross Domestic Purchases 10815.0 11261.3 11612.7 11937.0 12117.8 5 PLUS: Command-basis exports of goods and services

and income receipts from the rest of the world\1\ 1300.0 1482.9 1637.0 1846.6 2049.3 6 LESS: Command-basis imports of goods and services

and income payments to the rest of the world\1\ 1717.7 1976.6 2207.6 2448.7 2559.2 7 EQUALS: Real gross national income \1\ 10397.3 10767.7 11042.1 11334.8 11607.7

Addendum: 8 Trading Gains\2\ 100.411 100.202 99.800 99.690 99.659 9 Terms of trade\3\ 101.699 100.565 98.457 97.951 97.947

10 Terms of trade, goods\4\ 102.628 101.368 98.154 97.320 97.373

11 Terms of trade, nonpetroleum goods \5\ 103.154 104.394 105.030 107.265 108.914

1. Uses gross domestic purchases price index as deflator. 2. Ratio (multiplied by 100) of price index for gross national product to price index for gross domestic purchases. 3. Ratio (multiplied by 100) of the implicit price deflator for exports of goods and services and income receipts to the

corresponding implicit price deflator for imports payments of income. 4. Ratio (multiplied by 100) of the price index for goods exports to price index for goods imports. 5. Ratio (multiplied by 100) of the price index for goods exports to price index for nonpetroleum goods imports.

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Figure 2: Indexes of Real Production, Real Purchases, and Real Income

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1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007

Gross national product

Equals: Gross domestic purchases

Equals: Real gross national income

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Nonpetroleum Terms of Trade (1995=100)

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