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  • 1 https://isni.org/isni/0000000404811396, International Monetary Fund

APPENDIX

The point of departure for our econometric analysis is the aggregate-supply-aggregate-demand diagram appearing above as Figure 1. We estimate this model using a procedure proposed by Blanchard and Quah (1989), for distinguishing temporary from permanent shocks to a pair of time-series variables. Consider a system where the true model can be represented by an infinite moving average representation of a (vector) of variables, Xt, and an equal number of shocks, εt. Using the lag operator L, this can be written as:

Xt=A0єt+A1єt1+A2єt2+A3єt3.=Σi=0LiAiєt(3.1)

where the matrices Ai represent the impulse response functions of the shocks to the elements of X.

Let Xt be made up of change in output and the change in prices, and let εt be demand and supply shocks. Then the model becomes:

[ΔytΔpt]=Σi0Li[a11ia12ia21ia22i][єdtєst](3.2)

where yt and pt represent the logarithm of output and prices, εdt and εst are independent supply and demand shocks, and a11i represents element a11 in the matrix Ai.

The framework implies that while supply shocks have permanent effects, on the level of output, demand shocks only have temporary effects. (Both have permanent effects upon the level of prices). Since output is written in first difference form, this implies that the cumulative effect of demand shocks on the change in output (Δyt) must be zero. This implies the restriction:

Σi=0a11i=0.(3.3)

The model defined by equations (A.2) and (A.3) can be estimated using a vector autoregression. Each element of Xt can be regressed on lagged values of all the elements of X. Using B to represent these estimated coefficients, the estimating equation becomes,

Xt=B1Xt1+B2Xt2++BnXtn+et=(IB(L))1et=(I+B(L)+B(L)2+)et=et+D1et1+D2et2+D3et3+(3.4)

where et represents the residuals from the equations in the vector autoregression. In the case being considered, et is comprised of the residuals of a regression of lagged values of Δyt and Δpt on current values of each in turn; these residuals are labeled eyt and ept, respectively.

To convert (A.4) into the model defined by (A.2) and (A.3), the residuals from the VAR, et, must be transformed into demand and supply shocks, εt. Writing et = Cεt, four restrictions are required to define the four elements of the matrix C in the two-by-two case considered. Two are simple normalizations, which define the variance of the shocks εdt and εst. A third comes from assuming that demand and supply shocks are orthogonal.

The final restriction, which uniquely defines the matrix C, is that demand shocks have only temporary effects on output. This implies equation (A.3). In terms of the VAR:

Σi=0[d11id12id21id22i][c11c12c21c22]=[0](3.5)

This allows C to be uniquely defined and the demand and supply shocks to identified. Note from equation (A.4) that the long run impact of the shocks on output and prices is equal to (I-B(l))-1. The restriction that the long-run effect of demand shocks on output is zero implies a simple linear restriction on the coefficients of this matrix.

This is where our analysis, based on Blanchard and Quah (1989), differs from other VAR models. The usual decomposition assumes that the variables in the VAR can be ordered such that all the effects which could be attributed to (say) either at or bt are attributed to whichever comes first in the ordering, which is achieved by a Choleski decomposition.

Interpreting shocks with a permanent impact on output as supply disturbances and shocks with only a temporary impact on output as demand disturbances is controversial. Doing so requires adopting the battery of restrictions incorporated into the aggregate-supply-aggregate-demand model. One can think of frameworks other than the standard aggregate-supply-aggregate -demand model in which that association might break down. Moreover, it is conceivable that temporary supply shocks (for example, an oil price increase that is reversed subsequently) or permanent demand shocks (for, example, a permanent increase in government spending which affects real interest rates and related variables) dominate our data. But here a critical feature of our methodology comes into play. While restriction (A.5) affects the response of output to the two shocks, it says nothing about their impact on prices. The aggregate-supply-aggregate-demand model implies that demand shocks should raise prices while supply shocks should lower them. However, these responses are not imposed on the estimation, and hence can be used as an over-identifying restriction to see how well the responses corresponds to those expected from the underlying model.

The Blanchard-Quah procedure has also come in for more general criticism. Lippi and Reichlin (1993), in a comment on the Blanchard-Quah paper, point out that the procedure includes the assumption that the error terms in the model are fundamental, and that nonfundamental representations can give different results. As noted by Blanchard and Quah (1993), in their reply, however, this is a very general issue which is not specific to VAR representations, but covers virtually all dynamic analysis. Hence, while acknowledging that the assumption that the errors are fundamental is important to our procedure, we would note that this is a very general assumption in applied time-series work. On a different tack, Faust and Leeper (1994), discuss the identifying restrictions required for long-run restrictions to provide reliable results, involving the relationship between the long-run behavior and finite horizon data, aggregation across disturbances, and aggregation over time. These issues are clearly important, however, as in the case of Lippi and Reichlin, it remains unclear to us that these problems are peculiar to the structural VAR methodology. Overall, while we agree that it is important to understand the underlying assumptions required to implement a technique, these papers do not convince us that the identifying assumptions required by the Blanchard-Quah approach are significantly different from those used most other applied work.

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1/

International Monetary Fund and University of California at Berkeley, respectively. This paper is forthcoming in Modern Perspectives on the Classical Gold Standard.

2/

Experience was very different in Latin America and other parts of the “periphery,” as emphasized by Ford (1962), de Cecco (1984), and Bordo and Schwartz (1994).

3/

Cooperation was repeated subsequently. In 1895 a consortium of European banks, with the encouragement of their governments, defended the U.S. gold standard. In 1898 the Reichsbank and German commercial banks obtained assistance from the Bank of England and the Bank of France. In 1906 and 1907 the Bank of England, confronted by another financial crisis, again obtained support from the Bank of France and from the Reichsbank. The Russian State Bank shipped gold to Berlin to replenish the Reichsbank’s reserves. In 1909 and 1910 the Bank of France again discounted English bills, making gold available to London. Smaller European countries such as Belgium, Norway and Sweden also borrowed reserves from foreign central banks and governments.

4/

On the concept of escape clauses and for applications to exchange rates, see Canzoneri (1985), Obstfeld (1992), Flood and Isard (1989), and de Kock and Grilli (1989).

5/

For instance, there is Bloomfield’s (1959), seminal article emphasizing central banks’ violations of the rules of the gold standard game.

6/

Blanchard and Quah themselves formulated the model in terms of output and unemployment rather than output and prices. Keating and Nye estimate both variants of the model.

7/

Aside for Australia, for which our data come from Butlin (1984), and the United States, for which they are drawn from Romer (1989), the source of these time series is Mitchell (1976).

8/

Using the decomposition suggested in Bayoumi (1991).

9/

Results using a decomposition from aggregate data are similar (Bayoumi and Eichengreen, 1995).

10/

Breaks in wartime and during the postwar hyperinflation prevented us from constructing comparable estimates for Denmark and Germany, respectively.

11/

Global gold production rose and fell with the relative price of gold, particularly in the 1930s, and the supply response of the Australian mining industry contributed significantly to this variation.

12/

For additional discussion of the data and results for the post-World War II period, see Bayoumi and Eichengreen (1994).

13/

The aggregate supply and aggregate demand schedules traced out by the impulse-response functions generally accorded with the predictions of the standard model. One exception was France in the post-1972 period, for which neither response had converged toward a new long-run equilibrium level even after 20 years. We therefore exclude France from the post-1972 aggregate plotted below.

15/

Other writers, however, have failed to find increasing wage flexibility over time. For further discussion of the literature surrounding this point, see the chapter by Barry Eichengreen 1995.

16/

These results dissolve the paradox offered by Neumann (1993), since we generate the slopes of the relevant schedules directly on the basis of impulse response functions, rather than inferring them from the variance of output and prices and some auxiliary assumptions.

17/

We intend this story to apply only to the industrial countries whose experience is analyzed above.

The Stability of the Gold Standard and the Evolution of the International Monetary System
Author: Mr. Tamim Bayoumi and Mr. Barry J. Eichengreen