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

2. www.bea.gov 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: P GDP  s D P D + s X P x – s M P M ▪Though P X and P M 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.

3. www.bea.gov 3 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

4. www.bea.gov 4 Common Deflator for X and M required for Command-Basis GDP ▪If trade is always balanced, so that income = expenditures, D/P D is correct measure of real gross domestic income. ▪Real GDP = D/P D + X/P X – M/P M. ▪Same deflator P* for X and M ensures that CB GDP = D/P D if X = M since CB GDP becomes equal to D/P D + (X – M)/P*. ▪ P* is deflator for net exports.

5. www.bea.gov Disagreement on Choice of Deflator for the Current Account Balance ▪NIPAs deflate exports by imports index P M 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. www.bea.gov 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. www.bea.gov 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 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.

8. www.bea.gov Dilemma avoided if we let P* = P D Laspeyres-perspective index of CB GDP is: D 1 /P D + (X 1 – M 1 )/P* ——————————. D 0 + X 0 – M 0 Paasche-perspective quantity index is: D 1 + X 1 – M 1 —————————– P D D 0 + P*(X 0 – M 0 )

9. www.bea.gov Lasp & Paasche Agree if P* = P D  In general, for Laspeyres and Paasche to agree we must let P* = P D.  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.

10. www.bea.gov “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(b 1,b 2,b 3,b 4 )max(b 1,b 2,b 3,b 4 ) ] 0.5. ▪In case of incomplete pass-through, P D may understate effect of rise in P M so Fisher approach may be more reliable than P D approach.

11. www.bea.gov Why P D is a better choice for the net exports deflator than P M 1.From a theoretical point of view, reasonable assumptions justify use of P D. 2.To find influence of P X and P M just omit them from basket. This gives P D. 3.Use of P D results in a simple decomposition and in CB GNP = (Real D)(GNP /Nominal D). 4.P M results in understatement of effects of import prices, given trade deficit.

12. www.bea.gov Problem of Presence of Investment Goods in P D 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. 12

13. www.bea.gov 13 Given Negative Net Exports, Measure of CB GDP is High if P M Rises and X Deflated by P M ▪With P M 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 P M. ▪Terms of trade is defined as P X / P M. ▪With P M, 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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15. 15 Decomposition of growth rate of Törnqvist version of CB GDP Defining weights (s D,s X,s M ) as 2-period average shares of GDP, s D + s X – s M = 1, or s D = 1 – s X + s M. Then Törnqvist price index for GDP is: P D s D P X s x P M - s M = P D (P X /P D ) s x (P M /P D ) - s M. So Törnqvist implicit quantity index for CB GDP is: CB GDP = (real GDP)(P X /P D ) s x (P M /P D ) - s M.

16. www.bea.gov Decomposition of Törnqvist CB GDP CB GDP = real GDP × (P X /P D ) s x (P M /P D ) - s M (P X /P D ) s x (P M /P D ) - s M = (P X /P M ) (s x + s M )/ 2 [(P X P M ) ½ / P D ] (s x - s M ) = ( Terms of Trade ) (share of trade in GDP) × ( Relative price of tradables ) (shr of trade bal in GDP). With P M as deflator had CB GDP = Real GDP × (Terms of Trade) (2-period average share of X in GDP). 16

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18. www.bea.gov Contributions of Trade Prices to Fisher Framework National Income Contribution to  Fisher quantity index for GNP: C X = P X Ave.  Q X / GNP(P Ave.,Q 0 ) where P X Ave. = ( P X0 + P X1 / P GNP )/ 2. Contribution to  command-basis GNP: C X CB = [ P X Ave.D  Q X + Q X Ave.  P X ]/ GNP(P 0,Q 0 ) where P X Ave.D = ( P X0 + P X1 / P D )/ 2 and  P X = ( P X1 / P D – P X0 ).

19. www.bea.gov Calculation as Difference of Contributions  Q X terms approximately cancel, leaving: C X CB – C X  Q X Ave.  P X / GNP 0. A similar decomposition of the growth rate difference between CB GNP and real GNP simply rescales the standard decomposition of the Fisher price index.

20. www.bea.gov Calculation as Rescaled Decomposition of Price Index Q GNP CB – Q GNP = Q GNP P GNP / P D – Q GNP = Q GNP ( P GNP – P D )/ P D = ( Q GNP / P D ) [ s * X ( P X – P D ) – s * M ( P M – P D ) ] where s* X = P X Ave. Q X0 / GNP(P Ave.,Q 0 ). 20

21. www.bea.gov Real Gross National Income, Qty Indexes

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24. www.bea.gov 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

25. www.bea.gov Real Gross National Income

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