The pre- and postwar price-output paradox revisited.

1. Introduction

Past studies relating changes in the overall price level to changes in real output show a positive correlation between these variables in the years before World War II (WWII) and a negative correlation in the years since the war. The empirical implications of these findings on the efficacy of price stability are unclear. Prima facie, it would appear this analysis shows that certain price level movements may be helpful sometimes and harmful other times. In their international study of the historical properties of business cycles, Backus and Kehoe (1992, p. 880) assert that, "Changes ... in the sign of the correlation between price and output fluctuations are the most striking differences between periods in the variables we have studied."

Interestingly, the pre-WWII period consisted largely of deflation, whereas the postwar era has consisted almost exclusively of inflation. In the United States, for example, in only one postwar year, 1949, did the price level fall, and this drop was under 1%. Conversely, the price level in 1913 was 16% below its 1869 level and the price level in 1940 was 32% below its 1920 level. Many other countries underwent relatively similar price movement experiences prior to and after WWII. Taking these price level movements into account, past studies on the price-output correlation suggest that, on average, the less prices fell in the deflationary period before 1940, the higher the growth in real output (a positive price-output relationship), and that the less prices have risen in the inflationary postwar era, again, the higher the growth in real output (a negative price-output relationship). Taken together, this implies that any change in the price level, regardless of the direction, is negatively correlated with the growth in real output: A stable empirical relationship may exist between these variables after all.

We use an international data set to see whether the price-output correlation disparity before and after WWII can be reconciled empirically by looking at the absolute value of changes in the price level. We find that the conflicting pre- and postwar findings can be resolved: Any change in the price level, positive or negative, has historically been associated with slower growth in real output. Our empirical findings support theories espousing the economic benefits of price stability.

2. Past Studies of the Price-Output Correlation

Many studies have examined the historical relationship between the rates of change in the price level and real output, both in the United States and across countries. International analyses such as Kormendi and Meguire (1985), Fischer (1991), DeGregario (1992), Gomme (1993), Wynne (1993), Bruno and Easterly (1998), Haslag (1998), and others consistently find a negative relationship between inflation rates and rates of output growth. (1) These analyses are, however, restricted to postwar years, which have been almost exclusively inflationary for the sampled countries. This implies that the less price levels have risen in the postwar era, the higher the rate of economic growth.

Whereas most international data sets contain 20 to 40 years of recent data for each country, price-output correlation studies of the United States have been able to take advantage of the availability of data to expand samples back to 1870. For example, Cooley and Ohanian (1991) estimate, among other relationships, the correlation between the rate of inflation and the rate of output growth and find that whereas this relationship is negative between 1949 and 1975, it is positive between 1870 and 1900.

Fortunately, the United States is not the only country for which significant amounts of pre-war data are available. Backus and Kehoe (1992) compile an international data set of 10 countries, including the United States, for which at least a century of data is available. Among other things, they analyze the relationship between percentage changes in the price level and percentage changes in output and find, consistent with the aforementioned postwar international studies, a negative price--output relationship in each of the 10 sampled countries after WWII. On the contrary, however, the pre- and interwar eras reveal a positive price-output relationship for the majority of countries observed. The authors speculate briefly on a few potential sources of these conflicting findings. One possibility, they note, is that a structural change has taken place in the way prices and real output have interacted since WWII. Another is that business cycle movements were driven by demand shocks before and supply shocks after the war. Additionally, there have been major differences in monetary policy with and without the gold standard, which has been largely abandoned in the postwar era. (2)

The purpose of this article is to offer and empirically support an additional hypothesis: The conflicting empirical findings are largely a result of the changing direction of price movements. When price movements are examined in absolute value, the pre- and postwar price-output correlation is consistently negative. Our hypothesis is complementary to the preceding explanation concerning changes in monetary policy.

3. Visual Abstraction 

Figure 1 shows a positive relationship between two variables, X and Y, when X is positive and Y is negative. Figure 2, on the other hand, shows a negative relationship between these same variables when both variables are positive. Added together, an analysis of the data points of Figures 1 and 2 would find no significant correlation between X and Y. In fact, a clear relationship does exist: The closer Y is to zero, the larger the value of X. Figures 1 and 2 are, in essence, mirror images of each other so that the absolute value of the variable Y in Figure 1 would overlap the line in Figure 2, suggesting a negative relationship between X and the absolute value of Y.

[FIGURES 1-2 OMITTED]

This abstraction may be useful for understanding the relationship between the rates of change in the price level and real output in the pre- and post-WWII eras. The X variable can be thought of as representing the rate of change in output and the Y variable as the rate of change in the price level. As with the abstraction, the fact that most economies have experienced both inflationary and deflationary periods since the 19th century may explain why a statistical analysis of these variables over long time periods yields no significant correlation. Perhaps only the fact that pre-WWII years were largely deflationary and postwar years largely inflationary have yielded the significant, but conflicting, pre- and postwar correlations between rates of change in the price level and real output.

4. Empirical Analysis and Results

Following most other studies on price-output correlations, we measure the historical correlation between the rate of change (log differences) in the overall price level (implicit Gross National Product [GNP] deflators) and the rate of change (log differences) in real output across countries. We use Backus and Kehoe's 0992) data set of 10 countries--Australia, Canada, Denmark, Germany, Italy, Japan, Norway, Sweden, the United Kingdom, and the United States--for which at least 100 years of price and output data are available. (3) Table 1 reports three sets of analysis: The mean and standard deviation of the percentage price change, the inflation-output growth correlation, and the same correlation using the absolute value of changes in the price level. These data are reported for the pre- and post-WWII eras as well as across the full sample (excluding the years of the two World Wars). The first column shows that, prior to WWII, only two countries, Japan and Italy, had inflation rates average above one half of 1%. In five of the remaining eight countries, the average rate of change in the price level was negative. In all 10 countries, the standard deviation of price movements was greater than the absolute value of the mean suggesting that both inflation and deflation were common. By contrast, in the postwar era, the mean change in the price level is positive in each country, and in each case the mean inflation rate is greater than the standard deviation, suggesting that deflation was relatively rare. Clearly, the pre- and post-WWII eras differ substantially in terms of aggregate price movements.

With respect to the price-output correlation, all 10 countries experienced a negative relationship between price and output percentage changes in the largely inflationary years after WWII. This result is consistent with the existing body of research on the postwar price-output correlation--the lower the rate of inflation, the higher the rate of economic growth. During the pre-WWII era, when both inflation and deflation were common, the price-output correlation results are mixed. A slight majority, 6 out of the 10 countries sampled, experienced a positive relationship between percentage changes in price and output levels. To the extent that many of these economies regularly experienced episodes of deflation prior to WWII, a positive relationship between price and output changes would suggest that the less prices fell, the more economic growth these countries experienced. (4)

Following through on the previous section's visual abstraction, we convert price level changes to absolute values to see if a consistent price-output relationship emerges in the pre- and postwar eras and hence across the entire time period. The results are reported in the third column of Table 1. During the pre-WWII era, when inflation and deflation were equally common, 9 out of the 10 observed countries experienced a negative relationship between absolute movements in the price level and changes in output. In the one outlier, Italy, the relationship was basically zero. Generally, the less price levels moved, in either direction, the higher the rate of economic growth. During the postwar era, when inflation was the norm, all 10 countries report a negative relationship between the absolute value of the price level change and the change in output. Changes in output, then, were negatively correlated with the absolute value of changes in the price level in both the pre- and postwar eras. Finally, when the analysis is expanded to include the entire sample (excluding the years of the First and Second World Wars) all 10 countries show a negative relationship between the absolute value of changes in the price level and changes in real output. (5) A consistent empirical relationship between the rate of change in price and output, then, does exist--any change in the price level, regardless of direction, is negatively correlated with the rate of change in real output.

5. Correlations between Price Level and Output Fluctuations Using Detrended Data

In addition to correlating percentage changes in the price level and output growth, past studies have also examined the correlation between cyclical fluctuations in the price and output levels. Backus and Kehoe (1992), among others, use a Hodrick-Prescott filter to detrend price and output data and find that, as is consistent with percentage changes in the raw data, fluctuations in the price level were generally correlated positively to fluctuations in output in the deflationary pre-war era and negatively correlated in the inflationary postwar era.

This is also consistent with the hypothesis that any movement in the price level is negatively correlated with movements in output. Suppose, for the sake of simplicity, that the previous price level and output are exactly at their trend level. The positive relationship between movements in the price and output levels relative to HP trend in the deflationary pre-war era generally means that when the price level fell less than trend (i.e., closer to price stability), output was above its HP trend. The negative relationship between fluctuations in price and output levels relative to HP trend in the inflationary postwar era generally means that when the price level rose less than trend (again closer to price stability), output was above its HP trend level. (6)

Incidentally, the use of an absolute value "correction" for price level deviations from HP trend (as opposed to deviations from price stability) would not be appropriate here. Doing so would cause similar movements in the price level above and below their HP trend to be considered empirically identical when correlating with output. Our hypothesis is that the direction of the deviation from HP trend is an important determinant of output when considered in samples that are broken into generally inflationary and deflationary time periods.

6. Price Stability and Economic Theory

In recent years, a new branch of macroeconomics involves the construction of dynamic stochastic general-equilibrium models in which monetary policy is an important determinant of real economic activity. Building micro foundations into such models is important not only to facilitate interpretation of outcomes, but also to provide a basis for welfare analysis of alternative policy rules. This recent literature has produced a growing consensus that price stability provides substantial gains to an economy. For example, King and Wolman (1999) and Rotemberg and Woodford (1999) conclude that the optimal monetary policy should achieve complete price stability. In a lecture summarizing the past 20 years of thinking about what central banks should do, Mishkin (2000) says that price stability is the first guiding principle for central banks. (7)

Among the economic costs of price volatility (particularly under the assumption that price movements cannot be fully anticipated) are an overexpansion of the financial system as economic actors devote resources to avoiding the effects of changes in the price level; poor functioning of product and labor markets as price level changes inject noise into the movements of relative prices; an increase in menu costs as firms have to re-price goods and monitor the prices of competitors and suppliers; distributional effects and the creation of winners and losers as the real value of savings and debts change, as well as the effects price level changes have on the real value of fixed contract payments. (8) Furthermore, Freedman (2001) notes that the entire legal, accounting, and tax framework of most modern economies is built on the assumption of a stable price level. Price level changes in either direction, even if fully anticipated, then, will create significant distortions on the incentives to work, save, and invest.

7. Conclusions

The purpose of this short article is to resolve past findings of a positive correlation between changes in the price level and changes in output prior to WWII and a negative correlation between movements in these variables since the war. We show that these conflicting findings, and the resultant noncorrelation of price and output changes over longer samples, are largely attributable to a change in the general direction of price movements between these two time periods. When analyzing the absolute value of the rate of change in price, our empirical analysis of 10 international economies, for which at least a century of data is available, shows that a consistent historical price-output correlation exists: The less the price level has moved, in either direction, the higher the rate of economic growth prior to WWII, after WWII, and across the entire sample. Though correlation does not imply causality, the empirical findings here are consistent with the surfeit of theories supporting the efficacy of price stability.

Table 1. Price Movements and Price-Output Correlation over Time

                    Percent Price
                     Change Mean
                 (Standard Deviation)

              Pre-
              WWII     Postwar    Total

Australia     0.11      6.78       2.29
             (4.72)    (5.11)     (5.76)
Canada        0.13      4.97       1.79
             (4.48)    (3.75)     (4.82)
Denmark      -0.20      6.36       2.18
             (5.46)    (2.87)     (5.64)
Germany       0.49      3.74       1.54
             (3.98)    (2.16)     (3.80)
Italy         1.23      7.84       3.40
             (7.27)    (5.76)     (7.47)
Japan         2.43      4.57       3.29
             (6.63)    (3.98)     (5.78)
Norway       -0.42      5.63       1.69
             (6.35)    (5.17)     (6.61)
Sweden       -0.27      6.27       1.91
             (6.17)    (3.81)     (6.29)
United       -0.14      6.76       2.36
  Kingdom    (4.37)    (5.07)     (5.69)
United       -0.59      4.15       1.02
  States     (5.01)    (2.55)     (4.87)

                  Correlation (Output
                   Growth, Inflation)
                       (p-Value)

               Pre-
               WWII      Postwar     Total

Australia     0.1017     -0.3081     0.0933
             (0.389)     (0.068)    (0.332)
Canada        0.2144     -0.3003     0.1469
             (0.086)     (0.084)    (0.147)
Denmark      -0.4410     -0.4003    -0.3101
             (0.000)     (0.016)    (0.002)
Germany       0.2315     -0.2243     0.2145
             (0.044)     (0.189)    (0.023)
Italy         0.1450     -0.5869     0.1423
             (0.218)     (0.000)    (0.138)
Japan        -0.2932     -0.2637    -0.1541
             (0.039)     (0.132)    (0.162)
Norway        0.2073     -0.5003     0.1956
             (0.087)     (0.002)    (0.044)
Sweden       -0.0535     -0.5593    -0.0938
             (0.651)     (0.000)    (0.328)
United       -0.0740     -0.5706    -0.0998
  Kingdom    (0.558)     (0.000)    (0.318)
United        0.2300     -0.2785     0.1636
  States     (0.063)     (0.111)    (0.104)

               Correlation (Output Growth,
                      Absolute Value
                 of Inflation) (p-Value)

               Pre
               WWII      Postwar     Total

Australia     -.01696    -0.2864    -0.1040
             (0.148)     (0.090)    (0.279)
Canada       -0.1634     -0.3005    -0.1533
             (0.193)     (0.084)    (0.130)
Denmark      -0.3240     -0.4003    -0.2816
             (0.010)     (0.016)    (0.005)
Germany      -0.1538     -0.2186    -0.1422
             (0.185)     (0.200)    (0.135)
Italy         0.0120     -0.5873    -0.0399
             (0.919)     (0.000)    (0.679)
Japan        -0.1709     -0.0676    -0.1604
             (0.236)     (0.704)    (0.145)
Norway       -0.0393     -0.3157    -0.0167
             (0.749)     (0.057)    (0.865)
Sweden       -0.0351     -0.5645    -0.1195
             (0.767)     (0.000)    (0.212)
United       -0.2799     -0.5706    -0.2591
  Kingdom    (0.024)     (0.000)    (0.009)
United       -0.2405     -0.2785    -0.2398
  States     (0.052)     (0.111)    (0.016)

Sample moments and calculations computed using log-differences of the
price level and real output. Pre-war generally refers to years prior to
1941, excluding the years of World War I (1915-1919), and postwar
generally refers to years after 1949. Total refers to all years except
those of 1915-1919 and 1941-1949. Missing data for some countries force
exceptions. Exact dates follow: Australia, 1862-1914, 1920-1940,
1950-1985; Canada, 1871-1914, 1920-1940, 1950-1983; Denmark, 1871-1914,
1922-1940, 1950-1985; Germany, 1851-1913, 1926-1938, 1951-1986; Italy,
1862-1914, 19201940, 1950-1985; Japan, 1886-1914, 1920-1940, 1953-1986;
Norway, 1866-1914, 1920-1939, 1950-1986; Sweden, 1862-1914, 1920-1940,
1950-1986; United Kingdom, 1871-1914, 1920-1940, 1950-1986; United
States, 1870-1914, 1920-1940, 1950-1983.

We thank Claire Hausman for able research assistance and David Backus and Patrick Kehoe for generously sharing their data. The views in this article are solely the responsibility of the authors and should not be interpreted as reflecting the view of the Board of Governors of the Federal Reserve System or any other person associated with the Federal Reserve System.

(1) Bruno and Easterly (1998) find a stong negative price--output correlation when examining discrete epiosodes of very high inflation across countries.

(2) See Backus and Kehoe (1992, pp. 882-3) for a brief review of some other hypotheses.

(3) For a detailed description of the data and its sources, see Backus and Kehoe (1992).

(4) Backus and Kehoe note that Japan, with the highest pre-WWII inflation average of the 10 countries sampled, is a significant outlier in terms of pre-war price movements and price-output correlations. The negative (and statistically significant) relationship in Japan's case means that the lower the inflation rate, the higher the growth in real output in Japan prior to 1940.

(5) Though statistical significance has not been a major focus of this or other studies on inflation-output growth correlations, Table 1 reports p-values for all correlation coefficients. In 6 countries, the negative inflation--output correlation over the entire sample is significant at the 15% confidence interval.

(6) Though this logic is easiest to see with the assumption of a simple linear trend, the principle still generally holds with the Hodrick-Prescott trending procedure.

(7) See also Goodfriend and King (2001), which argues the case for price stability.

(8) See Bemanke et al. (1999) for a general discussion of the benefits of stable prices.

References

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Jason E. Taylor * and Jinill Kim ([dagger])

* Department of Economics, Central Michigan University, 321 Sloan Hall, Mount Pleasant, MI 48859, USA; E-mail [e-mail]; corresponding author.

([dagger]) Division of Monetary Affairs, Federal Reserve Board, Mail Stop 70, Washington, DC 20551, USA; E-mail [e-mail].

Received September 2002; accepted November 2003.