Measuring the Effects of Terms of Trade in National Accounts

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Measuring the Effects of Terms of Trade in
National Accounts

• Marshall Reinsdorf
• Presentation for PWT Workshop
• University of Pennsylvania
• May 11, 2008

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Real Income depends on Production and Gains from
Trade

• Current-dollar GDP D X M,
• where D CIG, 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 Mahdavys (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 l lt
  1.
• 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 l 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, well 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

• From a theoretical point of view, reasonable
  assumptions justify use of PD.
• To find influence of PX and PM just omit them
  from basket. This gives PD.
• Use of PD results in a simple decomposition and
  in CB GNP (Real D)(GNP/Nominal D).
• PM results in understatement of effects of import
  prices, given trade deficit.

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Problem of Presence of Investment Goods in PD

• Does a fall in price of future consumption count
  as a rise in current income?
• Weitzman (1976) current consumption and
  investment equals annuitized value of future
  consumption stream, so investment is OK to
  include in real income measure.
• But need RoR on investment to exceed rate of time
  preference for positive net investment.

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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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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 PXsx
  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 D Fisher quantity index for GNP
  CX PXAve. DQX / GNP(PAve.,Q0)
• where PXAve. (PX0 PX1/PGNP)/2.
• Contribution to D command-basis GNPCXCB
  PXAve.D DQX QXAve. DPX /GNP(P0,Q0)
• where PXAve.D (PX0 PX1/PD)/2 and
  DPX (PX1/PD PX0).

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Calculation as Difference of Contributions

• DQX terms approximately cancel, leaving
• CXCB CX ? QXAve. DPX / 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)sX(PX PD) sM(PM PD)
• where sX PXAve. QX0 / GNP(PAve.,Q0).

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Real Gross National Income, Qty Indexes
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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
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