THE CYCLICAL BEHAVIOR OF PRICES AND RELATIVE PRICES

I. INTRODUCTION Correlations between shocks to prices and output provide evidence on the source of macroeconomic shocks. For example, Den Haan (2000) found positive correlations at short forecast horizons and negative correlations at longer forecast horizons for the consumer price index (CPI) and the index of industrial production (IP). (1) He interpreted these results to mean that demand shocks dominate in the short run while supply shocks dominate in the long run. Several other papers confirm the positive correlation between the CPI and the IP at short forecast horizons. On the other hand, some of these same authors have found a negative correlation between real gross domestic product (GDP) and the GDP deflator at short forecast horizons. (2) This difference is disappointing since the results provide conflicting evidence on the nature of shocks at short horizons and puzzling since the CPI and the deflator are positively correlated as are IP and GDP. An important distinction between pairing GDP with its deflator and pairing IP with the CPI is the extent to which products in the output index are matched to products in the price index. GDP and the GDP deflator are based on the same set of goods and services. On the other hand, IP contains products, such as those produced by mining, whose prices are not included in the CPI, and the CPI includes products, such as housing services, that are not included in IP. In this paper, we argue that the correlation between mismatched price and output indexes such at the CPI and IP can be, and often is, misleading. The explanation for why it is important to use matched indexes of price and output is simple. Suppose that you are interested in the correlation between the price and the quantity of apples. If instead you compute the correlation between the price of oranges and the quantity of apples, the correlation is correct only if the relative price of oranges to apples does not vary with the quantity of apples. If the relative price varies, then the mismatched correlation differs in magnitude from and may even have the opposite sign of the matched one. Correlations between both matched and mismatched pairs are mostly negative. Positive correlations are rare and small for matched pairs but more frequent for mismatched pairs. For example, investment and the investment deflator are negatively correlated, while investment and the consumption deflator are positively correlated. Our analysis below shows that these correlations imply that the relative price of consumption to investment may be positively correlated with investment. Previous authors have noted that the relative price of nondurables is procyclical, which is consistent with the bias we find for mismatches. These previous results are based on correlations between detrended variables. We confirm that these findings hold when considering the correlation between forecast errors of the relative price of nondurables to durables and output measures. (3) Because there is no price index that matches IP, and because correlations between mismatched price and output measures likely differ in size and may have the opposite sign of the correlation for matched pairs, there is no way to be certain of the cyclical nature of the prices of goods included in the index of IP. An examination of GDP components and price deflators provides reasons to be skeptical of the positive correlation between the CPI and the IP. First, matched pairs of price indexes and GDP components have small or negative correlations. Second, correlations between mismatched price indexes and GDP components show that the bias created by mismatches is sometimes substantial. Further, this bias tends to be positive when prices of nondurable goods, such as the CPI or consumption deflator, are mismatched with GDP components composed mostly of durable goods. Finally, when IP is paired with deflators for durables, investments, or goods, the correlation is either small or negative at short forecast horizons. …