Measuring the Effects of Terms of Trade in National Accounts

1. Measuring the Effects of Terms of Trade in National Accounts Marshall Reinsdorf Presentation for PWT Workshop University of Pennsylvania May 11, 2008

2. 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 PXand PMhave 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.

3. 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

4. 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 = Msince CB GDP becomes equal to D/PD+(X–M)/P*. • P*is deflator for net exports.

5. 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.

6. 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.”

7. 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 somel < 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 eliminatesthe trade deficit.

8. 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 )

9. Lasp & Paasche Agree if P* = PD • In general, for Laspeyres and Paasche to agree we must let P* = PD. • Otherwise, we’ll have to calculateLaspeyres and Paasche versions of CB GDP using Paasche and Laspeyres deflators, then find Fisher. • Simplicity is advantage in national accounts.

10. “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.

11. 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.

12. 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).

14. 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.

15. 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).

17. 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 GNP:CXCB =[PXAve.D DQX + QXAve. DPX ]/GNP(P0,Q0) where PXAve.D = (PX0+ PX1/PD)/2 and DPX = (PX1/PD – PX0).

18. 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.

19. Calculation as Rescaled Decomposition of Price Index QGNPCB– QGNP = QGNPPGNP/PD – QGNP = QGNP(PGNP – PD)/PD =(QGNP/PD)[s*X(PX – PD) – s*M(PM– PD)] where s*X = PXAve. QX0/ GNP(PAve.,Q0).

20. Real Gross National Income, Qty Indexes

23. 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.

24. Real Gross National Income

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