Back Matter

## Appendix A Variable Definitions

Table A-1The 13 industrial countries that make up these indices are: Canada, Japan, Austria, Denmark, France, Germany, Italy, Netherlands, Norway, Sweden, United Kingdom, Switzerland, and Belgium. A 4 at the end of quarterly data denotes a 4-quarter moving average; a 12 at the end of monthly data denotes a 12-month moving average.

## Appendix B: The Time-Series Properties of the Left-Hand-Side Variables

The models estimated in the main text use the first difference of the logs of various measures of real commodity prices and the real exchange rate as left-hand-side variables. This appendix explains why that specification was chosen. As the literature on money/income causality has taught, this decision on the treatment of apparently nonstationary economic time series can have important implications for the qualitative results (as in Stock and Watson, 1987).

Following Stock and Watson’s advice, we first subject our potential dependent variables to a battery of tests. First, using the monthly observations available from 1973:8 to 1987:6, we tested if the log levels of the series had one or two unit roots. As in Engle and Granger, 1987, the following test statistics were calculated (and appear as the column headings in Table A-2a):

Table A-2a

The Time-Series Behavior of Commodity Prices and The Real Exchange Rate

• Dickey-Fuller test, which is a “t-test” of the coefficient of the lagged level variable in the regression

$\text{D}\text{x}\left(\text{t}\right)=\text{a}+\text{b}\phantom{\rule{0.5em}{0ex}}\text{x}\left(\text{t-1}\right);$
• Augmented Dickey-Fuller test, which is a “t-test” of the coefficient on the lagged level variable in the regression:

$\text{D}\text{x}\left(\text{t}\right)=\text{a}+\text{b}\phantom{\rule{0.5em}{0ex}}\text{x}\left(\text{t-1}\right)+\begin{array}{c}4\\ \text{i}-1\end{array}{\text{c}}_{\text{i}}\phantom{\rule{0.8em}{0ex}}\text{D}\text{x}\left(\text{t-}\text{i}\right)$
• Durbin-Watson test, which is the standard Durbin-Watson statistic of the demeaned variable.

In all cases, for all potential dependent variables, the hypothesis of one unit root is not rejected while the hypothesis of two unit roots is rejected. The presence of a unit root in the real exchange rate is unsurprising and merely replicated Mussa’s more qualitative assessment (Mussa, 1986). The similar behavior of all the measures of real commodity prices supports the main contention of this paper: real commodity prices, similarly to the real exchange rate, are relative prices determined in a general equilibrium system. It would be disturbing to find sets of relative prices with differing time-series properties. (The presence of a unit root in these relative prices also tells us that nominal prices are not cointegrated--as in the Engle and Granger sense.)

Second, we examined if the differenced variable exhibits a time trend. For each potential left-hand-side variable, the first difference of the logs was regressed against a constant and a time trend and, alternatively, a constant, a time trend, and 4 lags of the dependent variable (to tighten the standard errors). As shown in Table A-2b, in no case was the time trend significant.

Table A-2b

The Trend in the Change in Commodity Prices and the Real Exchange Rate

These tests determined the basic unit of observation in the main text: first differences of the logs of all relative prices. They also suggest that any contemporaneous correlation is not an artifact of movements in nonstationary variables but a properly identified relationship of economic (as well as statistical) significance.

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