RDP 9508: Are Terms of Trade Rises Inflationary? 3. A Model

Our model is an extension of the model presented by Gruen and Shuetrim (1994). The aim is to discover the ‘impact effect’ of a terms of trade shock on the domestic inflation rate and no allowance is made for policy reaction to the shock (that is, we assume that short-term real interest rates are kept constant). We assume a small open economy in which there are three types of goods: exportables, importables and non-traded goods.^[8] The domestic prices of these goods, expressed as logs, are p_x, p_m and p_n respectively. The domestic log price level, p, is a linear combination of these three prices and hence domestic inflation, Δp, is given by:

where α+β+γ=1. The prices of importables and exportables are determined in world markets, and the law of one price is assumed to hold. Hence, their first differences are:

where world prices are distinguished by an asterisk and Δe is the change in the nominal exchange rate index (expressed in units of foreign currency per unit of domestic currency).

The world price of domestic importables is assumed to rise at the world inflation rate, π*.^[9] However, in general, the world price of domestic exportables is assumed to rise at a different rate:

This difference results from the fact that the change in the log of the domestic terms of trade, ΔTOT, is , given the law of one price. ^[10] The implication is that the terms of trade shock arises from a change in the world price of exportables.

Non-traded goods price inflation, Δp_n , is assumed to be a function of ‘core’ domestic inflation, π, and a Phillips curve relation of the deviation of log output, y, from its natural rate, y_N. In the absence of the terms of trade shock, output is assumed to be at y_N. Note, however, that a change in the relative price of exportables (importables) has a substitution effect that also induces a change in the price of non-traded goods.^[11] Thus the change in the price of non-traded goods is given by:

The above expressions for changes in p_x, p_m and p_n can now be combined to form expressions for the change in the general price level, assuming both fixed and floating nominal exchange rates regimes.

With a fixed nominal exchange rate (Δe=0) that has been operating for long enough that domestic core inflation is equal to world inflation (π=π^*), domestic inflation is given by:

where χ=(1+σ+µ)⁻¹. From equation (5) the inflationary impact of an increase in the terms of trade can be seen to comprise three effects.

• First, there is a direct price effect. Provided α > 0 an increase in exportable prices will contribute directly to domestic inflation.
• Second, there is an income effect. A terms of trade rise increases domestic income. Some of this extra income is spent in the domestic non-traded sector, driving up the prices of non-traded goods and again adding to domestic inflation by a proportion γϕχ.
• Third, there is a substitution effect. An increase in the relative price of exportables induces substitution in consumption towards non-traded goods and substitution in production away from them, increasing domestic inflation by a proportions γσχ.

With a fixed exchange rate, all effects are positive and imply that an increase in the terms of trade is unambiguously inflationary. ^[12] Given the symmetry of the model, a fall in the terms of trade is unambiguously disinflationary.^[13]

A floating exchange rate will, however, alter this relationship. To derive the new expression, we introduce the change in the real exchange rate, Δq=Δe+Δp−π*, which measures deviations from purchasing power parity. We note the well-established relationship between the real exchange rate and the terms of trade:^[14]

With a floating nominal exchange rate, domestic core inflation need not equal world inflation (π ≠ π^*). As shown in Appendix 2, domestic inflation is now given by:

A rise in the terms of trade induces a real appreciation of the domestic currency. But with a floating exchange rate, this real appreciation occurs via nominal appreciation. This nominal appreciation has four consequences.

• First, it substantially modifies the direct price effect of exportables on the domestic price index. This direct price effect is now ΔTOT(α(1−δ)/χγ) which, for most plausible values of δ and γ (see later), is now less than when the exchange rate was fixed.^[15]
• Second, the rise in the terms of trade leads to a smaller rise in output, (y−y_N), because with cheaper imports, the proportion of domestic income spent on non-traded goods falls.
• Third, it reduces, and may reverse, the inflationary impact of the substitution effects because, with cheaper imports, demand switches away from non-traded goods while supply switches towards them.
• Fourth, and most importantly, it introduces a direct price effect of importables, −ΔTOT(βδ/χγ ), which acts to reduce domestic inflation.

Thus a floating exchange rate has insulating properties that reduce the direct price effect, substitution effect and income effect of the higher price of exportables. Other things being constant, a rise in the terms of trade is less inflationary than when the exchange rate is fixed. However, a floating exchange rate also introduces a role for the price of importables. If this direct price effect of importables exceeds the combination of other effects, an increase in the terms of trade will reduce inflation. Again, given the symmetry in the model, it follows that under such circumstances a terms of trade fall will be inflationary. In other words, with a floating exchange rate, there is no general theoretical result for the relationship between the terms of trade and inflation. The relationship is conditional upon the size of the importables price effect relative to other effects.

Footnotes

Exportables refer to actual exports plus the output of export-oriented industries. It is assumed that a single price exists for these goods. Importables refer to actual imports plus import replacements and, again, a single price is assumed to exist. Exportables and importables may comprise final or intermediate goods. [8]

The analysis implicitly assumes a small commodity exporting country (like Australia) which imports mainly manufactures, the prices of which are assumed to rise at the same rate as world consumer prices. [9]

In practice, passthrough to domestic traded prices is not instantaneous, and its rate differs between importables and exportables. This effect has been ignored here as it appears to be small in magnitude (Dwyer, Kent and Pease 1993). [10]

An increase in the domestic price of exportables (or importables) encourages a shift in demand towards the relatively cheaper non-traded goods. At the same time, there is a shift of supply away from the non-traded goods sector. The resulting excess demand places upward pressure on the price of non-traded goods so that σ and µ are unambiguously positive. For further discussion see Dornbusch (1980) and Edwards and van Wijnbergen (1987). [11]

That is, assuming that the increase in the terms of trade stems from an increase in export prices. Should the increase in the terms of trade result from a fall in import prices, given a fixed exchange rate, a different result would be found. Whilst the income effect would be of the same positive sign, the substitution effect would be negative as the lower price of importables encourages a shift in demand away from non-tradeables towards the relatively cheaper importables. Importantly, when the exchange rate floats, whether the shock arises from changes in the world price of exportables or importables is immaterial. This is the result of our assumption that purchasing power parity holds: following a change in the world price of exportables or importables, the resultant movement of the nominal exchange rate delivers an identical change in domestic prices. Consequently, there are identical income and substitution effects, whatever the source of change in the terms of trade. [12]

Of course, these are short-run effects. With a fixed nominal exchange rate, domestic inflation, π, must return to the world rate, π*, in the longer run. In this case, domestic monetary policy is subservient to the monetary policy of the anchor country. [13]

This accords with analyses of the equilibrium value of the exchange rate. See Neary (1988), Warr (1986), O'Mara et al. (1987), Gruen and Wilkinson (1991) and Blundell-Wignall et al. (1993). [14]

For a detailed analysis of the insulation properties of a floating exchange rate see Blundell-Wignall and Gregory (1990) and Pitchford (1993). Note that the direct price effect is now also influenced by the size of the substitution effects. [15]