This section provides a detailed description of the trade-equation model discussed in Section II and used to estimate underlying current account balances. The basic analytical framework derives from standard models that relate trade flows to movements in domestic and foreign economic activity and changes in international relative prices. Within this framework, the effects of relative cyclical positions (i.e., output gaps) and the lagged effects of past exchange rate changes can be accounted for in obtaining an underlying measure of the current account. By summarizing the effects of the exchange rate on the external position, the model also describes the potential equilibrating role of the exchange rate in adjusting toward a position of macroeconomic balance. Specifically, based on the relative price elasticities that are specified, the model determines the magnitude of the exchange rate adjustment necessary to equate the underlying and equilibrium current account balances.

## The Framework for Industrial Countries

The model has a common structure for each country, consisting of a single equation for the aggregate volume of exports (of goods and nonfactor services), another equation for the aggregate volume of imports, and assumptions about the impacts of exchange rate changes on relative prices. More specifically, the volumes of exports and imports are assumed to depend upon the real exchange rate and on the domestic output gap (for imports) and a weighted average of foreign output gaps (for exports). The absolute values of the long-run elasticities with respect to the real exchange rate, which are assumed to be equal across the industrial countries, are 0.71 for exports and 0.92 for imports.^{1} These parameter values broadly reflect those in the existing estimated MULTIMOD equations.^{2} The full impact of an exchange rate change on trade volumes is assumed to be spread over three years, with 60 percent of the long-run effect occurring during the first year, a further 25 percent during the second year, and the remaining 15 percent in year three. This distributed lag pattern is similar to those derived from the MULTIMOD trade volume equations and corresponds as well to the stylized facts discussed in surveys of empirical trade equations.^{3}

In estimating underlying current account positions, account also needs to be taken of the prices of exports and imports in domestic currency. Export prices are assumed to be unaffected by changes in the real exchange rate. Import prices are assumed to immediately reflect any change in relative costs; that is, passthrough is immediate and complete (as is also assumed in MULTIMOD).

Table 5.1 shows the implications of the above assumptions for the absolute values of trade elasticities with respect to the real exchange rate. As can be seen, the Marshall-Lerner condition—that the sum of the elasticities of export and import volumes exceeds unity—is satisfied in the long run. In the short run, the condition fails very marginally.

**Absolute Values of Trade Elasticities with Respect to the Real Exchange Rate**

**Absolute Values of Trade Elasticities with Respect to the Real Exchange Rate**

Year | Year 1 | Year 2 | Year 3 |
---|---|---|---|

Export volume | 0.43 | 0.60 | 0.71 |

Import volume | 0.55 | 0.78 | 0.92 |

Price of exports | 0.00 | 0.00 | 0.00 |

Price of imports | 1.00 | 1.00 | 1.00 |

**Absolute Values of Trade Elasticities with Respect to the Real Exchange Rate**

Year | Year 1 | Year 2 | Year 3 |
---|---|---|---|

Export volume | 0.43 | 0.60 | 0.71 |

Import volume | 0.55 | 0.78 | 0.92 |

Price of exports | 0.00 | 0.00 | 0.00 |

Price of imports | 1.00 | 1.00 | 1.00 |

Changes in real output also affect the trade balance. The elasticity of exports with respect to a trade-weighted average of foreign GDPs and of imports with respect to domestic GDP are both assumed to be 1.5. The Goldstein and Kahn (1985) survey finds that estimated activity elasticities tend to lie in the range from 1 to 2 in both the short run and the long run, and 1.5 is the midpoint of that range. It is also similar to the estimated short-run real output elasticities for the export volume relationships in MULTIMOD, although somewhat less than the estimated elasticity of around 2 in the pooled import volume equation. The MULTIMOD equations impose a long-run elasticity of 1 for both export and import volumes, partly to produce a well-defined long-run steady state.

Putting the above assumptions together produces the following reduced-form equation for the ratio of the current account to nominal GDP:

where: *M, X*, and *Y* represent the nominal domestic-currency values of imports, exports, and GDP, respectively; *YGAP* is the logarithm of the ratio of real output to potential output for the economy in question; *YGAPF* is a trade-weighted average of such gaps for competitors; *R* is the logarithm of the real multilateral exchange rate (defined so that an increase is an appreciation); α is a constant term reflecting initial conditions; (β_{m} is the long-run exchange rate elasticity for imports (set at 0.92); (β_{x} is the equivalent value for exports (set at 0.71); and Ψ_{x} and Ψ_{x} are the elasticities of real imports and real exports with respect to activity (both set at 1.5).

The reduced-form equation is applied to annual data, consistent with the databases of the World Economic Outlook and MULTIMOD. The first few terms of equation (5.1) show the relationship of the nominal balance to current and past-year averages of the real exchange rate. A real exchange rate appreciation leads to an increase in the volume of imports and a decrease in the volume of exports, with the effects being averaged over several years. In addition, an appreciation tends to improve the current account by lowering domestic-currency prices of imported goods. The last two terms show the impact of changes in domestic and foreign output. A rise in domestic output (compared to potential) reduces the current account, while an increase in foreign output increases it.

The underlying current account is defined as the value that the current account would take if output was at potential at home and abroad and if trade volumes and prices had responded fully to the exchange rate prevailing at the time of the exercise *(RCUR)*. This is derived from equation (5.1) by setting domestic and foreign output gaps to zero and setting the average exchange rates for the current and previous two years to *RCUR*. Thus,

Subtraction of equation (5.2) from equation (5.1), with a slight manipulation of the exchange rate term, gives the following relationship between the underlying and actual current accounts:^{4}

The difference between the underlying current account and the base period (or present year) current account depends upon the difference between the current exchange rate and the average exchange rate for the base year, changes in the exchange rate over each of the last two years, and current deviations of output from potential.

To illustrate the application of this formula, recall the examples presented in Section II, Table 2.1. For countries 2 and 3, which have identical trade-to-GDP ratios (i.e., values of *M/Y* and *X/Y*) of .25, domestic output gaps of -3 percent, and foreign output gaps of -2 percent, the closing of domestic output gaps would change the current account by -1.125 [=.25 × 1.5 × (-3)] percent of GDP (column 8 of Table 2.1, which reflects rounding), while the closing of foreign output gaps would increase the current account by .75 [=.25 × 1.5 × 2] percent of GDP (column 9). For each of these countries, the value of [(*M/Y*)β_{m} + (*X/F*)β_{x}], the term that governs the longrun volume effects of exchange rate changes, is .4075 [= .25(.92 + .71)]; accordingly, a 10 percent depreciation, other things equal, has a positive volume effect of 4.1 percent of GDP spread over three years and a negative price effect of 2.5 percent of GDP in the first year. Thus, for country 2, the 10 percent depreciation during the current year^{5} would raise the underlying current account by 1.6 percent of GDP relative to the base-year current account -(column 10). By contrast, for country 3, the full price effect and 85 percent of the volume effect of the 10 percent depreciation would already be reflected in the base-year current account, leaving a remaining volume effect of .6 percent of GDP.

The calculation of the underlying current account is a comparative static exercise, best seen as a calculation of where the base-year current account would be if all economies were operating at potential and the exchange rate had been at its current value over the past two years. It takes no account of the impact of future accumulations or decumulations of net foreign assets on the net income balance, or of trends in output and real exchange rates on the future path of the current account. The impact of changes in net foreign assets on the current account could clearly be incorporated in the model, although it would require defining a dynamic path for the current account over the future. Similarly, to the extent that current accounts exhibited long-term trends over and above the effects of underlying trends in output and real exchange rates, such trends could also be incorporated into the model. In this respect, however, it may be noted that despite significant differences across countries in long-term growth rates of real output and trends in some real exchange rates (most particularly, the yen), there is little evidence that current accounts have exhibited trends over time.

## Treatment of the Rest of the World

To achieve full global coverage, the current account model described in the previous subsection has been extended to six regional groups of developing and transition economies. This extension rests on the premise that it is appropriate to apply the standard trade model to developing countries.^{6} The trade elasticities used for developing countries differ, however, from those for industrial countries in accordance with recent empirical evidence. In particular, the long-run elasticities of export and import volumes with respect to real exchange rate assumed to be 0.53 and 0.69, respectively, in absolute value terms.^{7} These long-run elasticities sum to 1.2, compared with 1.6 for the industrial countries. Hence, although the Marshall-Lerner condition is still satisfied, the trade balance is less sensitive to real exchange rate changes in developing countries.

At a practical level, data on domestic output gaps necessary for the calculation of underlying current accounts are not available for many developing countries. Consequently, for each developing country group, domestic output gaps are derived using the Hodrick-Prescott filter.

^{}1

As discussed below, different elasticity parameters are assumed for the developing and transition economies.

^{}4

Note that *R*, the average exchange rate over the year, can differ from *RCUR*, the exchange rate that is assumed to be maintained over the future.

^{}5

Strictly speaking, *RCUR-R* is appropriately measured as the current exchange rate minus the (projected) average exchange rate for the base year. Hence, if the value of *R* midway through the base year is constructed from the observed average for the first half of the year and a projection that the exchange rate will remain constant at *RCUR* during the second half of the year, the exchange rate would need to depreciate by 20 percent at midyear (relative to the average for the first half year) to make *RCUR* 10 percent lower than *R*.

^{}6

See Reinhart (1995) and Senhadji (1997) for cross-country evidence for developing countries supporting the (traditional) view that income and the real exchange rate are important determinants of trade flows.

^{}7

These estimates are broadly in line with the country estimates obtained in Reinhart (1995).

## References

Goldstein Morris & Khan Mohsin Jones Ronald W. & Kenen Peter B. 1985, “

*Income and Price Effects in Foreign Trade,” Chap. 20 in*Vol. 2, ed. by (New York: North Holland Press), pp. 1041–105.*Hand-book of International Economics*,Masson Paul, Symansky Steven & Meredith Guy 1990,

(Washington: International Monetary Fund).*MULTIMOD Mark II: A Revised and Extended Model*, IMF Occasional Paper No. 71Reinhart Carmen M. 1995, “Devaluation, Relative Prices, and International Trade,”

, Vol. 42, pp. 290–312.*Staff Papers*, International Monetary FundSenhadji Abdelhak 1997, “Time-Series Estimation of Structural Import Demand Equations: A Cross-Country Analysis,”

*IMF Working Paper 97/132*(Washington: International Monetary Fund).