RDP 9201: The Impact of Real and Nominal Shocks on Australian Real Exchange Rates 3. Real Exchange Rate Dynamics in Response to Real and Nominal Shocks: Theory and Identification

In the previous section, questions of price flexibility were ignored as they should make little difference to net exchange rate changes over periods of decades. In the short run, however, price rigidities can have important implications for exchange rate and unemployment dynamics. There is considerable evidence that many prices are sticky in the short run.^[9]Substantial research effort has recently been devoted to understanding the causes of these rigidities and their implications for output and employment, particularly in a closed economy (for a survey of this literature see Blanchard and Fischer (1989)).

The seminal work on the implications of price stickiness in an open economy is that of Dornbusch (1976). His model is essentially monetary in nature with its central focus being on the impact of monetary shocks on the exchange rate and output (and thus indirectly on unemployment). Given sticky prices in the short run, an increase in the money supply results in an immediate real depreciation. This real depreciation is the result of the nominal depreciation needed to sustain money market equilibrium. With an increase in money and with sticky prices, real balances increase and interest rates fall. To equalise the return on domestic and foreign assets the nominal exchange rate must thus be expected to appreciate. In a perfect foresight equilibrium this expectation is realised. The initial nominal depreciation followed by the appreciation implies that the nominal exchange rate initially overshoots its new equilibrium value. After the initial real depreciation, an increasing price level and the nominal appreciation work to restore the original level of the real exchange rate.^[10] During the exchange rate adjustment process, the depreciated real exchange rate and lower interest rates stimulate demand and reduce unemployment. This creates inflationary pressures which gradually erode the decline in unemployment. In the new equilibrium, unemployment returns to its level in the initial equilibrium.

So far two types of models of exchange rate determination have been discussed: a real model in Section 2 and the above monetary model. Mussa (1984) combines these two approaches to derive a model which is capable of answering questions concerning the dynamic impact of both nominal and real shocks on the exchange rate and unemployment when price adjustment is sluggish.

The real side of the model is simple. There is no modelling of production technologies or factor markets. All real shocks operate through shift parameters in the excess demand functions for domestic and foreign goods. Changes in these parameters lead to changes in relative prices and thus the real exchange rate. The domestic money price of domestic goods is assumed sticky. Equilibrium is defined as that combination of the real exchange rate and domestic residents holdings of foreign bonds which is consistent with rational expectations of a constant exchange rate and constant asset holdings.

The model delivers real exchange rate and unemployment responses to monetary shocks very similar to those in the Dornbusch model. Changes in the equilibrium price of non-traded goods have the same equilibrium effects on the real exchange rate as in the dependent economy model. However, in the face of sluggish adjustment in the prices of non-traded goods, the short run dynamics differ from those in the long run. Mussa shows that if the conditions guaranteeing overshooting of the nominal exchange rate in response to a nominal shock are satisfied then the real exchange rate will undershoot in response to the real shock. If the price of non-tradeables is below its long run equilibrium level, output (and thus implicitly employment) will be above its equilibrium level. Real shocks such as a favourable productivity shock in the traded goods sector or an increase in the real price of exports leads to excess demand for non-traded goods at constant prices and thus to a short-run fall in unemployment. As the price of non-traded goods gradually adjusts unemployment returns to its natural level.

To summarise, this model of real exchange rate determination makes a number of predictions about the response of the economy to various shocks. Specifically, nominal shocks are neutral in the long run but alter the real exchange rate and unemployment in the short run. In contrast, sustained real shocks have a permanent effect on the real exchange rate. As is the case with nominal shocks, price sluggishness allows these real shocks to have an effect on unemployment in the short run but not in the long run. These restrictions are used to examine the relative importance and dynamic effects of shocks to the two Australian dollar real exchange rates.

Consider three types of uncorrelated shocks.^[11] The first shock is permitted to have a long-run effect on the real exchange rate and assumed to have no long-run employment effect. This is interpreted as a real shock. The second and third shocks are constrained to have no long-run effect on the real exchange rate and as with the first shock are assumed to have no long-run employment effects. These two shocks are interpreted as nominal shocks, one originating in each country. The assumption on the long-run employment effects of the various shocks ensure that the unemployment rates are stationary. The only additional restriction that is imposed on the nominal shocks is that the Australian nominal shock has no instantaneous effect on foreign unemployment. Given the small size of the Australian economy and the lags in the international transmission of shocks this assumption is reasonable.

Define the vector χ' ≡ (ΔR,U,U^*) where R is the real exchange rate, U the Australian unemployment rate and U^* the foreign unemployment rate. Given the above assumptions χ has a vector Wold moving-average representation given by:

where C(j) is a 3×3 matrix and v is a 3×1 vector of innovations.

Further, define the vector of economic shocks as ε ≡ (ε_r,ε_a,ε_f) where ε_r is the real shock, ε_a is the Australian nominal shock and ε_f is the foreign nominal shock. Given the orthogonality/normalisation conditions, E εε'=I. The assumptions made above concerning these shocks imply that χ follows a stationary process given by:

The impact effect of shock i on the level of the real exchange rate is given by A_1i(0)^[12] while the long-run effect is given by . In contrast, the long run effect of the ith shock on the Australian unemployment rate is simply A_2i(∞). Our interest is in estimating the sequence of matrices {A(j)}.

The assumptions made above imply certain restrictions on the elements of A(j). The assumption that the long-run effect of an Australian nominal shock on the real exchange rate is zero translates into the restriction that . Similarly, the equivalent assumption for the foreign nominal shock implies that . Finally, the assumption that a nominal shock in Australia has no contemporaneous effect on foreign unemployment implies that A₃₂(0) = 0.

To recover the elements of A(j), note that the vector of innovations in the Wold decomposition (v) and the vector of economic shocks (ε) are related by the following:

and that

The elements of the sequence of matrices {C(j)} can be obtained by estimating and then inverting the vector autoregression of (ΔR,U,U^*) .Thus, given (7) the sequence of matrices {A(j)} can be obtained by identifying the elements of A(0) . This matrix has 9 elements and thus 9 restrictions are needed for identification.

From (4), (5), and (6) note that :

Equation (8) provides 6 non-linear restrictions on the elements of A(0) as Ω has 6 unique elements. Above it was noted that the long-run restrictions on the impact of the nominal shocks on the real exchange rate imply restrictions on the sum of the A₁₂(j) elements and on the sum of the A₁₃(j) elements. Using (7) these restrictions translate into the following restrictions on A(0):

Finally, recall that the restriction that the Australian nominal shock has no effect on contemporaneous foreign unemployment implies that A₃₂(0) = 0. These nine restrictions allow the identification of A(0) and thus A(j) .^[13]

To obtain the sequence of matrices C(j) a VAR system consisting of changes in the real exchange rate and the two countries' unemployment rates is estimated using monthly data. Twelve lags are used in the VAR. Separate systems are estimated for the AUD/USD and the AUD/YEN exchange rates.

In order to obtain some measure of the dispersion of the point estimates of the elements of A(j) matrices Efron's (1979) bootstrap procedure is used. A pseudo history for each of the three variables is created by randomly drawing (with replacement) N disturbances from the residuals of the vector autoregression and then adding these residuals to the predicted values from the vector autoregression. With this “new” data set the A(j) matrices are re-estimated. This procedure is repeated 500 times and the standard deviation of each element of the A(j) matrices is calculated. These standard deviations are reported in the Appendix for selected lags.

Footnotes

For evidence on specific prices see Cecchetti (1986) and Kashyap (1988). For more general but less direct evidence see Gali (1989) and Fahrer (1990). [9]

Nominal exchange rate overshooting is not a necessary implication of this model. If the output elasticity with respect to the real exchange rate and the money demand elasticity with respect to output are both large the demand for money may increase sufficiently so that interest rates actually increase in the short run. In such a case the initial nominal depreciation would be followed by further depreciation. The real exchange rate would, however, follow much the same pattern as before: an initial depreciation followed by real appreciation to reestablish the original equilibrium. [10]

The dimensionality of the system is intentionally kept low. Adding additional variables increases the number of restrictions needed for identification making it difficult to identify systems with more than three variables. There is clearly more than one type of real shock. Above we have discussed both productivity and terms of trade shocks. Blanchard and Quah (1989) provide necessary and sufficient conditions for the interpretation of the shocks to be valid when there are multiple real and nominal shocks. They show that correct identification is possible if and only if the individual lag responses of the different shocks within a certain class (e.g. real shocks) are sufficiently similar. While there is no way to verify whether this condition holds the Mussa model does predict similar responses to the two principal real shocks. [11]

The first subscript refers to the row of the matrix denoted by A, while the second refers to the column of the matrix. [12]

These restrictions do not provide an unique solution for A₁₂(0) and A₂₂(0) as both {(A₁₂(0),−A₂₂(0)} and {−A₁₂(0),A₂₂(0)} are solutions. This failure of uniqueness is, however, unimportant as the sign of all elements in any column of A(0) can be changed without altering the results. A column sign change simply alters the interpretation of the shock from a positive to a negative shock (or visa versa). [13]