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Stock returns during the German hyperinflation
The Quarterly Review of Economics and Finance 40 (2000) 375–386
Stock returns during the German hyperinflation S. R. Leea,*, D. P. Tangb, K. Matthew Wongc a
Division of Asian Studies, Dongguk University, Seoul, Korea Department of Economics, Division of Social Sciences, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, People’s Republic of China c Department of Economics and Finance, St. John’s University, Queens, NY 11439, USA
b
Abstract We examine the relationship between stock returns and inflation during the German hyperinflation period. As Cagan (1956) argues, hyperinflation is close to a pure monetary phenomenon, the monetary sector is almost isolated from the real sector of the economy. We can thus study the impact of inflation on common stock returns directly, unaffected by the potential interactions of other economic variables such as expected real output. The negative relationship between inflation and stock returns widely reported in the literature may be spurious because they have not made such a distinction. By using forward exchange rate premium as a proxy for expected inflation, we find that stock returns, inflation, expected inflation, and unexpected inflation are cointegrated during the German hyperinflation period. The results also indicate that the fundamental relationship between stock returns and both realized and expected inflation is highly positive. © 2000 Bureau of Economic and Business Research, University of Illinois. All rights reserved. JEL classification: E310; G120
1. Introduction The purpose of this article is to examine the relationship between stock returns and inflation during the German hyperinflation period in the early 1920s. During hyperinflation the increases in prices and money supply are so large that any potential changes in real economic variables are “small” compared to the monetary changes. The nearly controlled
* Corresponding author. Tel.: ⫹2-592-3265; fax: ⫹2-2260-3265. E-mail address: [email protected] (S.R. Lee). 1062-9769/00/$ – see front matter © 2000 Bureau of Economic and Business Research, University of Illinois. All rights reserved. PII: S 1 0 6 2 - 9 7 6 9 ( 0 0 ) 0 0 0 4 6 - 6
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experimental environment given by this unique experience provides an interesting opportunity to test directly the observed stock returns/inflation relationship. According to Irving Fisher (1930), the nominal interest rate includes an expected real return component plus an expected rate of inflation. Because real returns, as theorized by classical monetarists, are determined by real factors, inflationary expectations should have little influence on the real rate of return. Fama and Schwert (1977) argue that Fisher’s Hypothesis can be extended to any assets in an efficient market. Under this condition, the expected nominal return on any common stock from t-1 to t would simply be the sum of the expected real rate of return and expected inflation rate during the period. That is, E(RSt兩⌽t⫺1) ⫽ E(RRSt兩⌽t⫺1) ⫹ E(It兩⌽t⫺1)
(1)
where RS is the nominal stock return, RRS is the real return, I is the realized inflation rate, and ⌽t⫺1 denotes the information set available at time t⫺1. Consequently, expected nominal returns on common stocks contain two elements: an expected real rate of return and an expected rate of inflation. Because common stock returns should only be affected by real factors in the economy, the expected depreciation of purchasing power would have no effect on expected real stock returns. The following model can test such a hypothesis: RSt ⫽ ␣ ⫹ E(It兩⌽t⫺1) ⫹ ⑀t
(2)
Because the expected value of the dependent variable is conditional upon the regressor in Eq. (2), the model measures the ex ante relationship between nominal stock returns and inflation. If the  coefficient is equal to one, then common stock is said to be a perfect hedge against inflation, that is, the nominal stock returns exactly account for expected inflation. This also implies that real stock returns are independent of expected inflation. Most empirical research investigates the relationship between stock returns and inflation using a generalized Fisher equation framework as follows: (e.g., Gultekin, 1983a; Wahlroos and Berglund, 1986). RSt ⫽ ␣ ⫹ 1E(It兩⌽t⫺1) ⫹ 2[It ⫺ E(It兩⌽t⫺1)] ⫹ ⑀t
(3)
If common stocks are a perfect hedge against both expected and unexpected inflation, then the beta coefficients should not be significantly different from unity. Such a model assumes that the monetary sector and the real sector in the economy are completely independent. The real return, as Fisher contends, should only be determined by real factors such as productivity. In marked contradiction to traditional beliefs and the generalized Fisher Hypothesis, empirical research using post WWII data shows that common stocks are a poor inflation hedges in most industrialized economies. Since Fama and Schwert (1977) documented the inverse relationship between real stock returns and inflation, evidence has repeatedly indicated that real stock returns are negatively related to both expected inflation and unexpected inflation in the literature (see Lintner, 1975; Bodie, 1976; Jaffe and Mandelker, 1977;
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Nelson, 1976 for earlier contributions. Similar international results have been reported by Gultekin, 1983a; Solnik, 1983; Mandelker and Tandon, 1985; Kaul, 1987.) Fama (1981) attempts to explain the negative relationship between stock returns and expected inflation with a proxy hypothesis. Stock returns are expected to be positively related to expected future activity. On the other hand, an increase in future activity can cause a decline in inflation if money supply remains stable. This proxy effect therefore produces the apparent negative correlation between stock returns and inflation. Geske and Roll (1983) argue that the role of money is not merely passive. There would be reductions in government income during economic downturns due to a decline in tax receipts. The subsequent deficits then subvert monetary policy. In other words, the monetary authority simply monetizes government debts which is, presumably, inflationary. And a sudden decline in stock returns signals depressed future activity expectations. This chain of events thus explains the inverse relationship between inflation and stock returns. Kaul (1987) further generalizes the role of the monetary sector by surmising that a negative relationship between stock returns and inflation can exist, if the monetary authority simply follows a countercyclical policy during economic expansions. When a pro-cyclical policy is followed, the relationship should be positive. Although the hypothesized channels of influence are different under these theories, the authors essentially argue that the negative stock returns/inflation relationship simply reflects a negative relationship between inflation and output, and a positive relationship between stock returns and output in the real sector. Unfortunately, their tests cannot isolate the effect of inflation on stock returns from the effect of output on the same stock returns. However, in a paper by Boudoukh and Richardson (1993), they found that long-horizon stock returns are positively related to long-term inflation. Siegel (1998) also mentions that stocks will be, by far, the best-performing financial assets in the event of hyperinflation although he does not explicitly test his hypothesis. As previous studies shown, the role of real output is extremely important in the stock returns and its link with inflation. During hyperinflationary periods, however, real output is almost constant relative to inflation. Cagan (1956, p. 25), in his classic article, describes how hyperinflation is an unique situation where relations between the real and the monetary factors can be clarified: “Hyperinflations provide an unique opportunity to study monetary phenomena. The astronomical increases in prices and money dwarf the changes in real income and other real factors. Even a substantial fall in real income, which generally has not occurred in hyperinflations, would be small compared with the typical rise in prices. Relations between monetary factors can be studied, therefore, in what almost amounts to complete isolation from the real sector of the economy.“
By studying the stock returns/inflation relationship during hyperinflation, we avoid the concurrent effect of output on stock returns and we can then directly examine the effect of inflation on stock returns. In this paper, we hypothesize that the fundamental relationship between stock returns and inflation should be positive, and the observed anomaly of a negative relationship is spurious, caused by confusions between the real and monetary effects.
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2. Data and methodology The most popular method in the literature to extract inflationary expectations from an ex post data series is to model an ARIMA process from the data. However, such a modeling procedure would not be useful because of the extremely skewed nature of the data during the German hyperinflation. Following Frenkel (1977), 1979), we employ the monthly average forward premium on a one-month forward contract on foreign exchange between Reichmark and Pound Sterling as a proxy for expected inflation. In these two papers, Frenkel concludes that the foreign exchange market was efficient during the German hyperinflation period and the forward premium was a good proxy for expected inflation. The period studied, from January 1921 to September 1923, is dictated by data availability. Most of the economic literature on hyperinflation also focuses on the same period. Monthly data, except the forward premiums, are collected from Economics of Inflation (Bresciani– Turroni, 1937, p.452). Monthly average stock returns were used and the inflation rates were proxied by monthly average changes in wholesale price calculated by the Statistical Bureau of the Reich.1 The Statistical Bureau calculated the stock index based on 300 companies in the Berlin Bourse.2 The monthly average forward exchange rate premium series was obtained from Abel et al. (1979, p. 103). The standard ordinary least squares (OLS) regression analysis is used to investigate the relationship between stock returns and inflation. However, it is well known in the literature that if the economic series are not stationary, then regressing a nonstationary series on other nonstationary series leads to serious econometric problems and the results are devoid of meaning. A typical correction for this problem of nonstationarity is to regress the first differences of the series. However, Hendry (1986) shows that such a transformation eliminates all information about the possible equilibrium relationship between the series. Following Granger and Engle (1987), we perform a unit root test of the series as follows:
冘 ␦ (y k
yt ⫺ yt⫺1 ⫽ ␣ ⫹ yt⫺1 ⫹
n
t⫺n
⫺ yt⫺n⫺1) ⫹ 1t
(4)
n⫽1
where yt is an economic variable at time t, and ⑀ is the error term. The k differenced terms are used to control for possible autocorrelation problem. The null hypothesis is that  ⫽ 0, that is, the variable has a unit root and is nonstationary. One can use the t value from the Augmented Dickey–Fuller (ADF) test statistics table (Dickey and Fuller, 1976) to reject the hypothesis. If a first-order model is appropriate, then a Dickey–Fuller (DF) test on the above equation without the k differenced terms can be used. We then conduct a cointegration test to examine if there is any relationship between the variables. Cointegration implies that one or more linear combinations of random variables are stationary even though individually the variables are not. For example, if variables x and y are nonstationary, however, z ⫽ x ⫺ by is stationary where b is the parameter, then x and y are said to be cointegrated. Engle and Granger (1987) prove that such a cointegrating equation can be estimated consistently using OLS regression. In this paper, we perform the following regressions:
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RSt ⫽ ␣ ⫹ 1It ⫹ ⑀t
(5)
RSt ⫽ ␣ ⫹ 2E(It兩⌽t⫺1) ⫹ ⑀t
(6)
RSt ⫽ ␣ ⫹ 2E(It兩⌽t⫺1) ⫹ 3[It ⫺ E(It兩⌽t⫺1)] ⫹ ⑀t
(7)
Because most previous studies also employ real stock returns, equations using real stock returns (RRS) are examined in this paper, as follows: RRSt ⫽ ␣ ⫹ 1It ⫹ ⑀t
(8)
RRSt ⫽ ␣ ⫹ 2E(It兩⌽t⫺1) ⫹ ⑀t
(9)
RRSt ⫽ ␣ ⫹ 2E(It兩⌽t⫺1) ⫹ 3[It ⫺ E(It兩⌽t⫺1)] ⫹ ⑀t
(10)
Cointegration can then be tested by examining the stationarity of the residuals from the above equations:
冘 ␦ (⑀ k
⑀t ⫺ ⑀t⫺1 ⫽ ␥⑀t⫺1 ⫹
n
t⫺n
⫺ ⑀t⫺n⫺1) ⫹ t
(11)
n⫽1
DF and ADF tests are applied to Eq. (11) to examine for stationarity (see Engle and Yoo, 1987; Hall, 1986). Also, we examine the Durbin–Watson tests statistics (CRDW) from cointegration Eqs. (5) through (10). A low CRDW statistics implies that the residuals are not stationary, and the existence of a long run relationship between the variables can be rejected. 3. Empirical results In Fig. 1, we plot the ratio between the nominal stock price index and the wholesale price index for the January 1921 to September 1923 period.3 During this period, the mean monthly changes of the stock price index and the wholesale price index are 45% and 44%, respectively. The figure shows that until February 1922, the nominal stock price not only kept up with inflation but actually outpaced it. Then the stock price began to fall behind inflation from February to October 1922. The scope of the decline was very broad including many “important companies” whose financial conditions were excellent. Bresciani–Turroni speculates several reasons for the sharp decline of the stock price relative to inflation: First, after the sharp selloff of common stocks on December 1, 1921 (the so called “Black Thursday”), investor’s attitude toward stocks became much more cautious.4 And investors began to shift their attention to foreign exchanges and commodities to hedge against inflation. Firms also began to price their products in gold terms to preserve their purchasing power; Second, German banks restricted credits because they were losing deposits due to high inflation; Third, the German government imposed significant new taxes and tariffs to reduce its deficits. The decline of the stock market was short-lived. Toward the end of 1922, with the easing of money market conditions5 and investors’ realization that the stock market was greately undervalued6, stock price rose more rapidly than the value of the dollar and gold. For
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Fig. 1. The ratio of nominal stock price index to WPI.
example, the stock index in terms of gold had risen from 5.24 in January of 1923 to 16.03 in July. Results of the unit root test on the data series in Table 1 show that all series are integrated of order 2 (i.e., all series are stationary after differncing them twice). Therefore, their cointegrating relationships can be examined directly by testing the stationarity of the residuals in Eqs. (5) through (10). Table 2 presents the cointegration results between realized inflation and both nominal and real stock returns. The findings are inconclusive. Whereas the CRDW statistics are significant (i.e., the series are cointegrated), DF and ADF results are not. To further examine the relations, we conduct the cointegration tests employing the first difference of the variables. Results (also in Table 2) indicate that changes in realized inflation and changes in stock returns are cointegrated. To further the analysis, we examine the relationships between stock returns and both expected and unexpected inflation. Tables 3 and 4 shows that: (1) expected inflation and stock returns are cointegrated; and (2) both expected and unexpected inflation, and stock returns are cointegrated. Given these cointegration results, estimates from regressions on Eqs. (5) through (10) are consistent and the findings are meaningful. The evidence shows that nominal stock returns are positively correlated with inflation and more interestingly, with expected inflation. The results are displayed in Table 5. As expected, common stocks are an excellent hedge for realized inflation. The estimated  coefficient in Eq. (5) is greater than unity.7 The  coefficient is slightly greater than one probably because stock prices outpaced inflation during part of the period studied especially between November 1922 to September 1923. Moreover, the relationship between nominal stock returns and expected inflation is positive, in contrast to most other studies. Similarly, real stock returns are also positively related to expected inflation. The  coefficients in Eq. (6) and Eq. (9) are
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381
Table 1 Unit root tests Test statisitcsa Dep. Var.
ADF()
ADF()
RS ⌬RS ⌬2RS I ⌬I ⌬2I RRS ⌬RRS ⌬2RRS E(I) ⌬E(I) ⌬2E(I) I⫺E(I) ⌬(I⫺E(I)) ⌬2(I⫺E(I))
⫺0.36(1 lag) ⫺2.82(4 lags) ⫺4.89(2 lags) ⫺0.14(5 lags) ⫺2.58(7 lags) ⫺7.74(1 lag) ⫺1.96(3 lags) ⫺2.40(2 lags) ⫺4.91(3 lags) ⫺1.48(6 lags) ⫺1.90(6 lags) ⫺6.01(3 lags) ⫺0.62(3 lags)a ⫺2.98(7 lags) ⫺8.18(1 lag) b
⫺0.87(1 lag) ⫺3.02(4 lags) ⫺4.95(2 lags) ⫺2.86(4 lags) ⫺2.95(8 lags) ⫺8.11(1 lag) ⫺1.93(3 lags) ⫺2.33(4 lags) ⫺4.75(3 lags) ⫺0.38(6 lags) ⫺2.83(6 lags) ⫺5.63(3 lags) ⫺3.41(4 lags) ⫺2.69(7 lags) ⫺8.56(1 lag)
a
Critical values are Dickey and Fuller, Table 8.5.2. (1976). 1% 5% 10% () ⫺4.38 ⫺3.60 ⫺3.24 () ⫺3.75 ⫺3.00 ⫺2.63 and represent the critical values for the unit root test with and without a trend. b We chose the appropriate lags structure based on the highest R 2 . We tried up to nine lags. RS ⫽ nominal stock returns. RRS ⫽ real stock returns. I ⫽ realized inflation. E(I) ⫽ expected inflation. I⫺E(I) ⫽ unexpected inflation. ⌬ and ⌬2 denote the first and second differences.
9.04 and 1.83 respectively. Thus, it appears that common stocks are a “super hedge” against expected inflation.8 Such a highly positive correlation may imply that during hyperinflation there exists a time varying stock risk premium. In other words, investors simply demand a higher real return for taking the same risk. Gultekin (1983b) also raises such a possibility in his study of US stock returns and expected inflation in recent periods. He argues that the required real return probably increases with a higher expected rate of inflation. Another explanation for the positive stock returns/expected inflation relationship may be “speculative bubble.” During hyperinflation, investors hedge their wealth by accelerating the acquisition of goods and real assets. Because common stocks represent claims on real assets, an increasing number of people would participate in the stock market. Nominal prices of stocks should increase rapidly. Rational investors anticipate such market reactions, and the increase in expected real stock returns would outpace the increase in expected inflation. Common stocks then become a “super hedge” against expected inflation. This argument is partially supported by Bresciani–Turroni (1937, p. 259). He describes that in 1921 the German stock exchange experienced the “most violent fever of speculation.” Beginning in 1922, stock returns declined in Germany, but the share prices started to rise once again toward the end of October 1922. By 1923, even rural population in Germany was participating in the frenzied stock market speculation. “In 1923 the telephone lines that
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Table 2 Tests of cointegration using residuals from cointegration equations RSt, RRSt ⫽ ␣ ⫹ 1It ⫹ ⑀t ⌬RSt, ⌬RRSt ⫽ ␣ ⫹ 1⌬It ⫹ ⑀r
冘 k
⑀t ⫺ ⑀t⫺1 ⫽ ␥⑀t⫺1 ⫹
␦n 共⑀t⫺n ⫺ ⑀t⫺n⫺1 兲 ⫹ t
n⫽1
Test statisticsa Dep. Var.
CRDW
DF(␥)
ADF(␥)
RS RRSc ⌬RS ⌬RRS
1.350* 1.350* 2.115* 2.115*
⫺2.795 ⫺2.795 ⫺5.794* ⫺5.794*
⫺3.048(2 ⫺3.048(2 ⫺4.113(2 ⫺4.113(2
lags)b lags) lags)** lags)**
a
The critical values are from Hall (1986) and Engle and Yoo (1987). We chose the appropriate lags structure based on the highest R 2 . We tried up to nine lags. c Because RRS is computed by subtracting INF from RS, the residuals from both regressions would be identical. Therefore, the test statistics are the same. b
The null hypothesis is non-cointegration. * Denotes significance at the 1% level. ** Denotes significance at the 5% level.
connected Berlin with the agricultural districts were always congested at certain hours, because the country folk sought information on the latest dollar exchange rate and gave Stock Exchange orders to their bankers.” (Bresciani–Turroni, 1937, p. 271). Table 3 Tests of cointegration using residuals from cointegration equations RSt, RRSt ⫽ ␣ ⫹ 1E(It兩⌽t⫺1) ⫹ ⑀t ⌬RSt, ⌬RRSt ⫽ ␣ ⫹ 1⌬E(It兩⌽t⫺1) ⫹ ⑀t
冘 k
⑀t ⫺ ⑀t⫺1 ⫽ ␥⑀t⫺1 ⫹
␦n(⑀t⫺n ⫺ ⑀t⫺n⫺1) ⫹ t
n⫽1
Test statisticsa Dep. Var.
CRDW
DF(␥)
ADF(␥)
RS RRS ⌬RS ⌬RRS
0.93* 1.301* 1.746* 2.024*
⫺2.824 ⫺3.806** ⫺4.994* ⫺5.017*
⫺5.007*(4 lags)b ⫺4.352(1 lag)* ⫺2.654(4 lags)c ⫺5.751*(2 lags)
a
The critical values are from Hall (1986) and Engle and Yoo (1987). We chose the appropriate lags structure based on the highest R 2 . We tried up to nine lags. c 2 R for the DF test is 0.496, R2 for ADF test is 0.501. Thus, there is no advantage of imposing a lag structure in the unit root test of error terms. The DF test alone will suffice in this case. The null hypothesis is non-cointegration. * Denotes significance at the 1% level. ** Denotes significance at the 5% level. b
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Table 4 Tests of cointegration using residuals from cointegration equations RSt, RRSt ⫽ ␣ ⫹ 1E(It兩⌽t⫺1 2[It ⫺ E(It兩⌽t⫺1)] ⫹ ⑀t ⌬RSt, ⌬RRSt ⫽ ␣ ⫹ 1⌬E(It兩⌽t⫺1) ⫹ 2⌬[It ⫺ E(It兩⌽t⫺1)] ⫹ ⑀t
冘 k
⑀t ⫺ ⑀t⫺1 ⫽ ␥⑀t⫺1 ⫹
␦n 共⑀t⫺n ⫺ ⑀t⫺n⫺1 兲 ⫹ t
n⫽1
Test statisticsa Dep. Var.
CRDW
DF(␥)
ADF(␥)
RS RRS ⌬RS ⌬RRS
1.378* 1.378* 2.052* 2.052*
⫺3.948** ⫺3.948** ⫺5.262* ⫺5.262*
⫺4.671*(2 ⫺4.671*(1 ⫺5.902*(2 ⫺5.902*(2
lags)b lag)c lags) lags)
a
The critical values are from Hall (1986) and Engle and Yoo (1987). We chose the appropriate lags structure based on the highest R 2 . We tried up to nine lags. c Because RRS is computed by subtracting INF from RS, the residuals from both regressions would be identical. Therefore, the test statistics are the same. b
The null hypothesis is non-cointegration. * Denotes significance at the 1% level. ** Denotes significance at the 5% level.
In addition, Kaul (1987) argues that as a result of a pro-cyclical monetary policy, real activity and inflation could be positively related or unrelated. Stock returns therefore would be positively related to inflation. His argument is supported by evidence from the US and Canada using data during the Pre-WWII Period. During the studied period in this paper, there was evidence that output and inflation were positively linked in Germany. Money supply increased by 34% in 1921. It was 288% in 1922. Meanwhile, the unemployment rate declined from 2.8% in 1921 to 1.5% in 1922.9 Also, the results of this study show that common stock is a “partial hedge” against even unexpected inflation. The coefficient for unexpected inflation in Eq. (7) is less than unity (but positive). This result is further corroborated by the evidence from Eq. (10). Again, these results simply manifest the fact that increases in expected stock returns far outpaced increases in expected inflation during hyperinflation.10 The differential between expected real stock returns and expected inflation represents a form of insurance against unexpected inflation in a highly inflationary environment.
4. Conclusion In this paper, we examine the relationship between stock returns and inflation during the German hyperinflation period. As Cagan (1956) argues, hyperinflation is close to a pure monetary phenomenon, the monetary sector is almost isolated from the real sector of the economy. We can thus study the impact of inflation on common stock returns directly, unaffected by the potential interactions of other economic variables such as expected real
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Table 5 Estimations of the relationship between stock returns and inflation during the German hyperinflation (A) RSt ⫽ ␣ ⫹ 1It ⫹ 2E(It兩⌽t⫺1) ⫹ 3[It ⫺ E(It兩⌽t⫺1)] ⫹ ⑀t
␣
1
Eg. (5)
⫺0.02 (⫺0.52}
1.06 (19.88)
Eq. (6)
0.11 (1.16)
8.77 (7.43)
Eq. (7)
⫺0.03 (⫺0.35)
5.03 (4.53)
(B)
2
3
0.92 (5.29)
Adj. R 2
DW
0.93
1.35
0.65
0.91
0.82
1.55
RRSt ⫽ ␣ ⫹ 1It ⫹ 2E(It兩⌽t⫺1) ⫹ 3[It ⫺ E(It兩⌽t⫺1)] ⫹ ⑀t
␣
1
2
Eq. (8)
⫺0.02 (⫺0.52)
0.06 (1.19)
Eq. (9)
⫺0.006 (⫺1.68)
1.72 (3.80)
Eq. (10)
⫺0.04 (⫺0.99)
2.39 (4.23)
3
⫺0.16 (⫺1.86)
Adj. R 2
DW
0.04
1.35
0.33
1.29
0.40
1.45
Notes: t-Statistics are in parentheses. RS and RRS denote nominal stock returns and real stock returns respectively. I is the realized rate of inflation.
output. The negative relationship between inflation and stock returns widely reported in the literature may be spurious because they have not made such a distinction. This research demonstrates that stock returns, inflation, expected inflation and unexpected inflation are cointegrated during the German hyperinflation period. The results also indicate that the fundamental relationship between stock returns and both realized and expected inflation is highly positive. Common stocks appear to be a good hedge against inflation during the hyperinflation period.
Acknowledgments We want to thank comments from Philip Cagan, Rawley Thomas, and two anonymous referees.
Notes 1. 2.
We also used the consumer price index, the results are similar. See Economics of Inflation (Bresciani–Turroni, 1937, p. 254) for a more detailed description of data.
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3. 4. 5.
The ratio is computed as: Stock Price Index/Wholesale Price Index. Between November and December 1921 the stock market price declined by 22%. A proportional increase in money supply in the quarter October through December 1922 was the same as the increase in the first nine months of 1922. 6. For example, in November 1922 the capitalization of Daimler Motor Works was equivalent to that of 327 cars only. See Guttmann and Meehan (1975, p 148). 7. Also, the standard error of the estimate is small (0.0550), indicating that the actual stock price appreciation matched realized inflation closely. Perhaps investors and savers who used stocks as a store of value actually repriced stocks frequently (through buying and selling stocks) based on announced inflation rates. Under hyperinflation, such frequent repricing is a very rational behavior. Indeed, Bresciani–Turroni (1937, p.257) notes: “Because of the dearness of living which lowered real incomes, many classes of people were forced to try to supplement their incomes by speculation on the Bourse.” These speculations (or in effect, hedging), necessitated frequent tradings. 8. Following Fama and Schwert. (1977), when the beta coefficient is greater than unity, we describe common stocks as a super hedge against inflation. To maintain an investor’s purchasing power on an after tax basis, nominal stock returns cannot simply rise in parity with expected inflation (i.e., ⫽1), rising taxes on inflated nominal gains must also be considered. Therefore, the “super hedge” effect may also account for taxes on the substantial nominal gains during the hyperinflation period. However, taxes alone probably cannot explain the size of the coefficient. Because of a lack of precise data on German taxes during hyperinflation, we could not perform statistical tests on the proposition. 9. See Sommavira and Tullio (1987, p.134). The unemployment rate increased to 10.2% in 1923. However, most of the increase came from the last four months of that year because of the government’s currency reform and the total collapse of the economy. 10. The monthly data on the real output during hyperinflation were not available. However, in a paper by Michael et al. (1994), they used real wages as a proxy for real output in their study of the demand for money during the German hyperinflation. Thus, we have incorporated real wages as a proxy for real output. We ran regressions as in Table 5 except that we added the real wages into Eqs. (5) to (10). We found that the real wages coefficients were not significant and hardly changed the results in Table 5.
References Abel, A. R. Dornbusch, J. Huizinga, & Marcus, A. (1979). Money demand during hyperinflation. J Monetary Econ, 5, 97–104. Bodie, Z. (1976). Common stock as a hedge against inflation. J Finan, 31, 459 – 470. Boudoukh, J., & Richardson, M. (1993). Stock returns and inflation: a long-horizon perspectives. Am Econ Rev, 83, 1346 –1355.
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Bresciani–Turroni, C. (1937). Economics of Inflation. Britain: Augustus M. Kelly. Cagan, P. (1956). The monetary dynamics of hyperinflation. In M. Friedman (Ed.). Studies in the Quantity Theory of Money (25–117). Chicago, IL: University of Chicago Press. Dickey, D. A. & Fuller, W. A. (1976). Distribution of the estimators for autoregressive time series with a unit root. J Am Stat Assoc, 74, 427– 431. Engle, R. F. & Granger, C. W. J. (1987)., Co-integration and error correction: representation, estimation, and testing. Econometrica, 55, 251–276. Engle, R. F. & Yoo, B. S. (1987). Forecasting and testing in co-integrating system. J Econometrics, 35, 143–159. Fuller, W. A. (1976). Introduction to Statistical Time Series. New York: John Wiley and Sons. Fama, E. F. (1981). Stock returns, real activity, inflation and money. Am Econ Rev, 71, 545–565. Fama, E. F. & Schwert, G. (1977). Asset returns and inflation. J Finan Econ 5, 115–146. Frenkel, J. A. (1977). The forward exchange rate, expectations, and the demand for money: the German hyperinflation. Am Econ Rev, 67, 633– 670. Frenkel, J. A. (1979). Further evidence on expectations and the demand for money during the German hyperinflation. J Monetary Econ, 5, 81–96. Geske, R. & Roll, R. (1983). The fiscal and monetary linkage between stock returns and inflation. J Finan, 38, 1–33. Graham, F. D. (1930). Exchange, prices and production in hyper-inflation Germany, 1920 –23. Princeton: Princeton University Press. Gultekin, N. B. (1983a). Stock market returns and inflation: evidence from other countries. J Finan, 38, 49 – 65. Gultekin, N. B. (1983b). Stock market returns and inflation forecasts. J Finan, 38, 663– 673. Guttmann, W. & Meehan, P. (1975). The Great Inflation: Germany 1919 –23. Britain: Saxon House. Hall, S. G. (1986). An application of the Granger & Engle two-step estimation procedure to United Kingdom aggregate wage data. Oxford Bull Econ Stats, 48, 229 –239. Hendry, D. F. (1986). Econometric modelling with cointegrated variables: an overview. Oxford Bull Econ Stats, 48, 201–212. Jaffe, J. & Mandelker, G. (1977). The ‘Fisher effect’ for risky assets: an empirical investigation. J Finan, 31, 447– 458. Kaul, G. (1987). Stock returns and inflation: the role of the monetary sector. J Finan Econ, 18, 253–276. Lintner, J. (1975). Inflation and securities returns. J Finan, 30, 259 –280. Mandelker, G. & Tandon, K. (1985). Common stock returns, real activity, money and inflation: some international evidence. J Intl Money Finance, 4, 267–286. Michael, P, Nobay, A., & Peel, D. (1994). The German hyperinflation and the demand for money revisited. Intl Econ Rev, 35, 1–22. Nelson, C. (1976). Inflation and rates of returns on common stocks. J Finan, 31, 471– 483. Siegel, J. (1998). Stocks for the long run: the definitive guide to financial market returns and long-term investment strategies. New York: McGraw–Hill. Solnik, B. (1983). The relation between stock prices and inflationary expectations: the International evidence. J Finan, 38, 35– 48. Sommariva, A. & Tullio, G. (1987). German macroeconomic history, 1880 –1979. New York: St. Martin’s Press. Wahlroos, B. & Berglund, T. (1986). Stock returns, inflationary expectations and real activity. J Banking Finan, 10, 377–389.
Stock returns during the German hyperinflation S. R. Leea,*, D. P. Tangb, K. Matthew Wongc a
Division of Asian Studies, Dongguk University, Seoul, Korea Department of Economics, Division of Social Sciences, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, People’s Republic of China c Department of Economics and Finance, St. John’s University, Queens, NY 11439, USA
b
Abstract We examine the relationship between stock returns and inflation during the German hyperinflation period. As Cagan (1956) argues, hyperinflation is close to a pure monetary phenomenon, the monetary sector is almost isolated from the real sector of the economy. We can thus study the impact of inflation on common stock returns directly, unaffected by the potential interactions of other economic variables such as expected real output. The negative relationship between inflation and stock returns widely reported in the literature may be spurious because they have not made such a distinction. By using forward exchange rate premium as a proxy for expected inflation, we find that stock returns, inflation, expected inflation, and unexpected inflation are cointegrated during the German hyperinflation period. The results also indicate that the fundamental relationship between stock returns and both realized and expected inflation is highly positive. © 2000 Bureau of Economic and Business Research, University of Illinois. All rights reserved. JEL classification: E310; G120
1. Introduction The purpose of this article is to examine the relationship between stock returns and inflation during the German hyperinflation period in the early 1920s. During hyperinflation the increases in prices and money supply are so large that any potential changes in real economic variables are “small” compared to the monetary changes. The nearly controlled
* Corresponding author. Tel.: ⫹2-592-3265; fax: ⫹2-2260-3265. E-mail address: [email protected] (S.R. Lee). 1062-9769/00/$ – see front matter © 2000 Bureau of Economic and Business Research, University of Illinois. All rights reserved. PII: S 1 0 6 2 - 9 7 6 9 ( 0 0 ) 0 0 0 4 6 - 6
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experimental environment given by this unique experience provides an interesting opportunity to test directly the observed stock returns/inflation relationship. According to Irving Fisher (1930), the nominal interest rate includes an expected real return component plus an expected rate of inflation. Because real returns, as theorized by classical monetarists, are determined by real factors, inflationary expectations should have little influence on the real rate of return. Fama and Schwert (1977) argue that Fisher’s Hypothesis can be extended to any assets in an efficient market. Under this condition, the expected nominal return on any common stock from t-1 to t would simply be the sum of the expected real rate of return and expected inflation rate during the period. That is, E(RSt兩⌽t⫺1) ⫽ E(RRSt兩⌽t⫺1) ⫹ E(It兩⌽t⫺1)
(1)
where RS is the nominal stock return, RRS is the real return, I is the realized inflation rate, and ⌽t⫺1 denotes the information set available at time t⫺1. Consequently, expected nominal returns on common stocks contain two elements: an expected real rate of return and an expected rate of inflation. Because common stock returns should only be affected by real factors in the economy, the expected depreciation of purchasing power would have no effect on expected real stock returns. The following model can test such a hypothesis: RSt ⫽ ␣ ⫹ E(It兩⌽t⫺1) ⫹ ⑀t
(2)
Because the expected value of the dependent variable is conditional upon the regressor in Eq. (2), the model measures the ex ante relationship between nominal stock returns and inflation. If the  coefficient is equal to one, then common stock is said to be a perfect hedge against inflation, that is, the nominal stock returns exactly account for expected inflation. This also implies that real stock returns are independent of expected inflation. Most empirical research investigates the relationship between stock returns and inflation using a generalized Fisher equation framework as follows: (e.g., Gultekin, 1983a; Wahlroos and Berglund, 1986). RSt ⫽ ␣ ⫹ 1E(It兩⌽t⫺1) ⫹ 2[It ⫺ E(It兩⌽t⫺1)] ⫹ ⑀t
(3)
If common stocks are a perfect hedge against both expected and unexpected inflation, then the beta coefficients should not be significantly different from unity. Such a model assumes that the monetary sector and the real sector in the economy are completely independent. The real return, as Fisher contends, should only be determined by real factors such as productivity. In marked contradiction to traditional beliefs and the generalized Fisher Hypothesis, empirical research using post WWII data shows that common stocks are a poor inflation hedges in most industrialized economies. Since Fama and Schwert (1977) documented the inverse relationship between real stock returns and inflation, evidence has repeatedly indicated that real stock returns are negatively related to both expected inflation and unexpected inflation in the literature (see Lintner, 1975; Bodie, 1976; Jaffe and Mandelker, 1977;
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Nelson, 1976 for earlier contributions. Similar international results have been reported by Gultekin, 1983a; Solnik, 1983; Mandelker and Tandon, 1985; Kaul, 1987.) Fama (1981) attempts to explain the negative relationship between stock returns and expected inflation with a proxy hypothesis. Stock returns are expected to be positively related to expected future activity. On the other hand, an increase in future activity can cause a decline in inflation if money supply remains stable. This proxy effect therefore produces the apparent negative correlation between stock returns and inflation. Geske and Roll (1983) argue that the role of money is not merely passive. There would be reductions in government income during economic downturns due to a decline in tax receipts. The subsequent deficits then subvert monetary policy. In other words, the monetary authority simply monetizes government debts which is, presumably, inflationary. And a sudden decline in stock returns signals depressed future activity expectations. This chain of events thus explains the inverse relationship between inflation and stock returns. Kaul (1987) further generalizes the role of the monetary sector by surmising that a negative relationship between stock returns and inflation can exist, if the monetary authority simply follows a countercyclical policy during economic expansions. When a pro-cyclical policy is followed, the relationship should be positive. Although the hypothesized channels of influence are different under these theories, the authors essentially argue that the negative stock returns/inflation relationship simply reflects a negative relationship between inflation and output, and a positive relationship between stock returns and output in the real sector. Unfortunately, their tests cannot isolate the effect of inflation on stock returns from the effect of output on the same stock returns. However, in a paper by Boudoukh and Richardson (1993), they found that long-horizon stock returns are positively related to long-term inflation. Siegel (1998) also mentions that stocks will be, by far, the best-performing financial assets in the event of hyperinflation although he does not explicitly test his hypothesis. As previous studies shown, the role of real output is extremely important in the stock returns and its link with inflation. During hyperinflationary periods, however, real output is almost constant relative to inflation. Cagan (1956, p. 25), in his classic article, describes how hyperinflation is an unique situation where relations between the real and the monetary factors can be clarified: “Hyperinflations provide an unique opportunity to study monetary phenomena. The astronomical increases in prices and money dwarf the changes in real income and other real factors. Even a substantial fall in real income, which generally has not occurred in hyperinflations, would be small compared with the typical rise in prices. Relations between monetary factors can be studied, therefore, in what almost amounts to complete isolation from the real sector of the economy.“
By studying the stock returns/inflation relationship during hyperinflation, we avoid the concurrent effect of output on stock returns and we can then directly examine the effect of inflation on stock returns. In this paper, we hypothesize that the fundamental relationship between stock returns and inflation should be positive, and the observed anomaly of a negative relationship is spurious, caused by confusions between the real and monetary effects.
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2. Data and methodology The most popular method in the literature to extract inflationary expectations from an ex post data series is to model an ARIMA process from the data. However, such a modeling procedure would not be useful because of the extremely skewed nature of the data during the German hyperinflation. Following Frenkel (1977), 1979), we employ the monthly average forward premium on a one-month forward contract on foreign exchange between Reichmark and Pound Sterling as a proxy for expected inflation. In these two papers, Frenkel concludes that the foreign exchange market was efficient during the German hyperinflation period and the forward premium was a good proxy for expected inflation. The period studied, from January 1921 to September 1923, is dictated by data availability. Most of the economic literature on hyperinflation also focuses on the same period. Monthly data, except the forward premiums, are collected from Economics of Inflation (Bresciani– Turroni, 1937, p.452). Monthly average stock returns were used and the inflation rates were proxied by monthly average changes in wholesale price calculated by the Statistical Bureau of the Reich.1 The Statistical Bureau calculated the stock index based on 300 companies in the Berlin Bourse.2 The monthly average forward exchange rate premium series was obtained from Abel et al. (1979, p. 103). The standard ordinary least squares (OLS) regression analysis is used to investigate the relationship between stock returns and inflation. However, it is well known in the literature that if the economic series are not stationary, then regressing a nonstationary series on other nonstationary series leads to serious econometric problems and the results are devoid of meaning. A typical correction for this problem of nonstationarity is to regress the first differences of the series. However, Hendry (1986) shows that such a transformation eliminates all information about the possible equilibrium relationship between the series. Following Granger and Engle (1987), we perform a unit root test of the series as follows:
冘 ␦ (y k
yt ⫺ yt⫺1 ⫽ ␣ ⫹ yt⫺1 ⫹
n
t⫺n
⫺ yt⫺n⫺1) ⫹ 1t
(4)
n⫽1
where yt is an economic variable at time t, and ⑀ is the error term. The k differenced terms are used to control for possible autocorrelation problem. The null hypothesis is that  ⫽ 0, that is, the variable has a unit root and is nonstationary. One can use the t value from the Augmented Dickey–Fuller (ADF) test statistics table (Dickey and Fuller, 1976) to reject the hypothesis. If a first-order model is appropriate, then a Dickey–Fuller (DF) test on the above equation without the k differenced terms can be used. We then conduct a cointegration test to examine if there is any relationship between the variables. Cointegration implies that one or more linear combinations of random variables are stationary even though individually the variables are not. For example, if variables x and y are nonstationary, however, z ⫽ x ⫺ by is stationary where b is the parameter, then x and y are said to be cointegrated. Engle and Granger (1987) prove that such a cointegrating equation can be estimated consistently using OLS regression. In this paper, we perform the following regressions:
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379
RSt ⫽ ␣ ⫹ 1It ⫹ ⑀t
(5)
RSt ⫽ ␣ ⫹ 2E(It兩⌽t⫺1) ⫹ ⑀t
(6)
RSt ⫽ ␣ ⫹ 2E(It兩⌽t⫺1) ⫹ 3[It ⫺ E(It兩⌽t⫺1)] ⫹ ⑀t
(7)
Because most previous studies also employ real stock returns, equations using real stock returns (RRS) are examined in this paper, as follows: RRSt ⫽ ␣ ⫹ 1It ⫹ ⑀t
(8)
RRSt ⫽ ␣ ⫹ 2E(It兩⌽t⫺1) ⫹ ⑀t
(9)
RRSt ⫽ ␣ ⫹ 2E(It兩⌽t⫺1) ⫹ 3[It ⫺ E(It兩⌽t⫺1)] ⫹ ⑀t
(10)
Cointegration can then be tested by examining the stationarity of the residuals from the above equations:
冘 ␦ (⑀ k
⑀t ⫺ ⑀t⫺1 ⫽ ␥⑀t⫺1 ⫹
n
t⫺n
⫺ ⑀t⫺n⫺1) ⫹ t
(11)
n⫽1
DF and ADF tests are applied to Eq. (11) to examine for stationarity (see Engle and Yoo, 1987; Hall, 1986). Also, we examine the Durbin–Watson tests statistics (CRDW) from cointegration Eqs. (5) through (10). A low CRDW statistics implies that the residuals are not stationary, and the existence of a long run relationship between the variables can be rejected. 3. Empirical results In Fig. 1, we plot the ratio between the nominal stock price index and the wholesale price index for the January 1921 to September 1923 period.3 During this period, the mean monthly changes of the stock price index and the wholesale price index are 45% and 44%, respectively. The figure shows that until February 1922, the nominal stock price not only kept up with inflation but actually outpaced it. Then the stock price began to fall behind inflation from February to October 1922. The scope of the decline was very broad including many “important companies” whose financial conditions were excellent. Bresciani–Turroni speculates several reasons for the sharp decline of the stock price relative to inflation: First, after the sharp selloff of common stocks on December 1, 1921 (the so called “Black Thursday”), investor’s attitude toward stocks became much more cautious.4 And investors began to shift their attention to foreign exchanges and commodities to hedge against inflation. Firms also began to price their products in gold terms to preserve their purchasing power; Second, German banks restricted credits because they were losing deposits due to high inflation; Third, the German government imposed significant new taxes and tariffs to reduce its deficits. The decline of the stock market was short-lived. Toward the end of 1922, with the easing of money market conditions5 and investors’ realization that the stock market was greately undervalued6, stock price rose more rapidly than the value of the dollar and gold. For
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Fig. 1. The ratio of nominal stock price index to WPI.
example, the stock index in terms of gold had risen from 5.24 in January of 1923 to 16.03 in July. Results of the unit root test on the data series in Table 1 show that all series are integrated of order 2 (i.e., all series are stationary after differncing them twice). Therefore, their cointegrating relationships can be examined directly by testing the stationarity of the residuals in Eqs. (5) through (10). Table 2 presents the cointegration results between realized inflation and both nominal and real stock returns. The findings are inconclusive. Whereas the CRDW statistics are significant (i.e., the series are cointegrated), DF and ADF results are not. To further examine the relations, we conduct the cointegration tests employing the first difference of the variables. Results (also in Table 2) indicate that changes in realized inflation and changes in stock returns are cointegrated. To further the analysis, we examine the relationships between stock returns and both expected and unexpected inflation. Tables 3 and 4 shows that: (1) expected inflation and stock returns are cointegrated; and (2) both expected and unexpected inflation, and stock returns are cointegrated. Given these cointegration results, estimates from regressions on Eqs. (5) through (10) are consistent and the findings are meaningful. The evidence shows that nominal stock returns are positively correlated with inflation and more interestingly, with expected inflation. The results are displayed in Table 5. As expected, common stocks are an excellent hedge for realized inflation. The estimated  coefficient in Eq. (5) is greater than unity.7 The  coefficient is slightly greater than one probably because stock prices outpaced inflation during part of the period studied especially between November 1922 to September 1923. Moreover, the relationship between nominal stock returns and expected inflation is positive, in contrast to most other studies. Similarly, real stock returns are also positively related to expected inflation. The  coefficients in Eq. (6) and Eq. (9) are
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381
Table 1 Unit root tests Test statisitcsa Dep. Var.
ADF()
ADF()
RS ⌬RS ⌬2RS I ⌬I ⌬2I RRS ⌬RRS ⌬2RRS E(I) ⌬E(I) ⌬2E(I) I⫺E(I) ⌬(I⫺E(I)) ⌬2(I⫺E(I))
⫺0.36(1 lag) ⫺2.82(4 lags) ⫺4.89(2 lags) ⫺0.14(5 lags) ⫺2.58(7 lags) ⫺7.74(1 lag) ⫺1.96(3 lags) ⫺2.40(2 lags) ⫺4.91(3 lags) ⫺1.48(6 lags) ⫺1.90(6 lags) ⫺6.01(3 lags) ⫺0.62(3 lags)a ⫺2.98(7 lags) ⫺8.18(1 lag) b
⫺0.87(1 lag) ⫺3.02(4 lags) ⫺4.95(2 lags) ⫺2.86(4 lags) ⫺2.95(8 lags) ⫺8.11(1 lag) ⫺1.93(3 lags) ⫺2.33(4 lags) ⫺4.75(3 lags) ⫺0.38(6 lags) ⫺2.83(6 lags) ⫺5.63(3 lags) ⫺3.41(4 lags) ⫺2.69(7 lags) ⫺8.56(1 lag)
a
Critical values are Dickey and Fuller, Table 8.5.2. (1976). 1% 5% 10% () ⫺4.38 ⫺3.60 ⫺3.24 () ⫺3.75 ⫺3.00 ⫺2.63 and represent the critical values for the unit root test with and without a trend. b We chose the appropriate lags structure based on the highest R 2 . We tried up to nine lags. RS ⫽ nominal stock returns. RRS ⫽ real stock returns. I ⫽ realized inflation. E(I) ⫽ expected inflation. I⫺E(I) ⫽ unexpected inflation. ⌬ and ⌬2 denote the first and second differences.
9.04 and 1.83 respectively. Thus, it appears that common stocks are a “super hedge” against expected inflation.8 Such a highly positive correlation may imply that during hyperinflation there exists a time varying stock risk premium. In other words, investors simply demand a higher real return for taking the same risk. Gultekin (1983b) also raises such a possibility in his study of US stock returns and expected inflation in recent periods. He argues that the required real return probably increases with a higher expected rate of inflation. Another explanation for the positive stock returns/expected inflation relationship may be “speculative bubble.” During hyperinflation, investors hedge their wealth by accelerating the acquisition of goods and real assets. Because common stocks represent claims on real assets, an increasing number of people would participate in the stock market. Nominal prices of stocks should increase rapidly. Rational investors anticipate such market reactions, and the increase in expected real stock returns would outpace the increase in expected inflation. Common stocks then become a “super hedge” against expected inflation. This argument is partially supported by Bresciani–Turroni (1937, p. 259). He describes that in 1921 the German stock exchange experienced the “most violent fever of speculation.” Beginning in 1922, stock returns declined in Germany, but the share prices started to rise once again toward the end of October 1922. By 1923, even rural population in Germany was participating in the frenzied stock market speculation. “In 1923 the telephone lines that
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Table 2 Tests of cointegration using residuals from cointegration equations RSt, RRSt ⫽ ␣ ⫹ 1It ⫹ ⑀t ⌬RSt, ⌬RRSt ⫽ ␣ ⫹ 1⌬It ⫹ ⑀r
冘 k
⑀t ⫺ ⑀t⫺1 ⫽ ␥⑀t⫺1 ⫹
␦n 共⑀t⫺n ⫺ ⑀t⫺n⫺1 兲 ⫹ t
n⫽1
Test statisticsa Dep. Var.
CRDW
DF(␥)
ADF(␥)
RS RRSc ⌬RS ⌬RRS
1.350* 1.350* 2.115* 2.115*
⫺2.795 ⫺2.795 ⫺5.794* ⫺5.794*
⫺3.048(2 ⫺3.048(2 ⫺4.113(2 ⫺4.113(2
lags)b lags) lags)** lags)**
a
The critical values are from Hall (1986) and Engle and Yoo (1987). We chose the appropriate lags structure based on the highest R 2 . We tried up to nine lags. c Because RRS is computed by subtracting INF from RS, the residuals from both regressions would be identical. Therefore, the test statistics are the same. b
The null hypothesis is non-cointegration. * Denotes significance at the 1% level. ** Denotes significance at the 5% level.
connected Berlin with the agricultural districts were always congested at certain hours, because the country folk sought information on the latest dollar exchange rate and gave Stock Exchange orders to their bankers.” (Bresciani–Turroni, 1937, p. 271). Table 3 Tests of cointegration using residuals from cointegration equations RSt, RRSt ⫽ ␣ ⫹ 1E(It兩⌽t⫺1) ⫹ ⑀t ⌬RSt, ⌬RRSt ⫽ ␣ ⫹ 1⌬E(It兩⌽t⫺1) ⫹ ⑀t
冘 k
⑀t ⫺ ⑀t⫺1 ⫽ ␥⑀t⫺1 ⫹
␦n(⑀t⫺n ⫺ ⑀t⫺n⫺1) ⫹ t
n⫽1
Test statisticsa Dep. Var.
CRDW
DF(␥)
ADF(␥)
RS RRS ⌬RS ⌬RRS
0.93* 1.301* 1.746* 2.024*
⫺2.824 ⫺3.806** ⫺4.994* ⫺5.017*
⫺5.007*(4 lags)b ⫺4.352(1 lag)* ⫺2.654(4 lags)c ⫺5.751*(2 lags)
a
The critical values are from Hall (1986) and Engle and Yoo (1987). We chose the appropriate lags structure based on the highest R 2 . We tried up to nine lags. c 2 R for the DF test is 0.496, R2 for ADF test is 0.501. Thus, there is no advantage of imposing a lag structure in the unit root test of error terms. The DF test alone will suffice in this case. The null hypothesis is non-cointegration. * Denotes significance at the 1% level. ** Denotes significance at the 5% level. b
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Table 4 Tests of cointegration using residuals from cointegration equations RSt, RRSt ⫽ ␣ ⫹ 1E(It兩⌽t⫺1 2[It ⫺ E(It兩⌽t⫺1)] ⫹ ⑀t ⌬RSt, ⌬RRSt ⫽ ␣ ⫹ 1⌬E(It兩⌽t⫺1) ⫹ 2⌬[It ⫺ E(It兩⌽t⫺1)] ⫹ ⑀t
冘 k
⑀t ⫺ ⑀t⫺1 ⫽ ␥⑀t⫺1 ⫹
␦n 共⑀t⫺n ⫺ ⑀t⫺n⫺1 兲 ⫹ t
n⫽1
Test statisticsa Dep. Var.
CRDW
DF(␥)
ADF(␥)
RS RRS ⌬RS ⌬RRS
1.378* 1.378* 2.052* 2.052*
⫺3.948** ⫺3.948** ⫺5.262* ⫺5.262*
⫺4.671*(2 ⫺4.671*(1 ⫺5.902*(2 ⫺5.902*(2
lags)b lag)c lags) lags)
a
The critical values are from Hall (1986) and Engle and Yoo (1987). We chose the appropriate lags structure based on the highest R 2 . We tried up to nine lags. c Because RRS is computed by subtracting INF from RS, the residuals from both regressions would be identical. Therefore, the test statistics are the same. b
The null hypothesis is non-cointegration. * Denotes significance at the 1% level. ** Denotes significance at the 5% level.
In addition, Kaul (1987) argues that as a result of a pro-cyclical monetary policy, real activity and inflation could be positively related or unrelated. Stock returns therefore would be positively related to inflation. His argument is supported by evidence from the US and Canada using data during the Pre-WWII Period. During the studied period in this paper, there was evidence that output and inflation were positively linked in Germany. Money supply increased by 34% in 1921. It was 288% in 1922. Meanwhile, the unemployment rate declined from 2.8% in 1921 to 1.5% in 1922.9 Also, the results of this study show that common stock is a “partial hedge” against even unexpected inflation. The coefficient for unexpected inflation in Eq. (7) is less than unity (but positive). This result is further corroborated by the evidence from Eq. (10). Again, these results simply manifest the fact that increases in expected stock returns far outpaced increases in expected inflation during hyperinflation.10 The differential between expected real stock returns and expected inflation represents a form of insurance against unexpected inflation in a highly inflationary environment.
4. Conclusion In this paper, we examine the relationship between stock returns and inflation during the German hyperinflation period. As Cagan (1956) argues, hyperinflation is close to a pure monetary phenomenon, the monetary sector is almost isolated from the real sector of the economy. We can thus study the impact of inflation on common stock returns directly, unaffected by the potential interactions of other economic variables such as expected real
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Table 5 Estimations of the relationship between stock returns and inflation during the German hyperinflation (A) RSt ⫽ ␣ ⫹ 1It ⫹ 2E(It兩⌽t⫺1) ⫹ 3[It ⫺ E(It兩⌽t⫺1)] ⫹ ⑀t
␣
1
Eg. (5)
⫺0.02 (⫺0.52}
1.06 (19.88)
Eq. (6)
0.11 (1.16)
8.77 (7.43)
Eq. (7)
⫺0.03 (⫺0.35)
5.03 (4.53)
(B)
2
3
0.92 (5.29)
Adj. R 2
DW
0.93
1.35
0.65
0.91
0.82
1.55
RRSt ⫽ ␣ ⫹ 1It ⫹ 2E(It兩⌽t⫺1) ⫹ 3[It ⫺ E(It兩⌽t⫺1)] ⫹ ⑀t
␣
1
2
Eq. (8)
⫺0.02 (⫺0.52)
0.06 (1.19)
Eq. (9)
⫺0.006 (⫺1.68)
1.72 (3.80)
Eq. (10)
⫺0.04 (⫺0.99)
2.39 (4.23)
3
⫺0.16 (⫺1.86)
Adj. R 2
DW
0.04
1.35
0.33
1.29
0.40
1.45
Notes: t-Statistics are in parentheses. RS and RRS denote nominal stock returns and real stock returns respectively. I is the realized rate of inflation.
output. The negative relationship between inflation and stock returns widely reported in the literature may be spurious because they have not made such a distinction. This research demonstrates that stock returns, inflation, expected inflation and unexpected inflation are cointegrated during the German hyperinflation period. The results also indicate that the fundamental relationship between stock returns and both realized and expected inflation is highly positive. Common stocks appear to be a good hedge against inflation during the hyperinflation period.
Acknowledgments We want to thank comments from Philip Cagan, Rawley Thomas, and two anonymous referees.
Notes 1. 2.
We also used the consumer price index, the results are similar. See Economics of Inflation (Bresciani–Turroni, 1937, p. 254) for a more detailed description of data.
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3. 4. 5.
The ratio is computed as: Stock Price Index/Wholesale Price Index. Between November and December 1921 the stock market price declined by 22%. A proportional increase in money supply in the quarter October through December 1922 was the same as the increase in the first nine months of 1922. 6. For example, in November 1922 the capitalization of Daimler Motor Works was equivalent to that of 327 cars only. See Guttmann and Meehan (1975, p 148). 7. Also, the standard error of the estimate is small (0.0550), indicating that the actual stock price appreciation matched realized inflation closely. Perhaps investors and savers who used stocks as a store of value actually repriced stocks frequently (through buying and selling stocks) based on announced inflation rates. Under hyperinflation, such frequent repricing is a very rational behavior. Indeed, Bresciani–Turroni (1937, p.257) notes: “Because of the dearness of living which lowered real incomes, many classes of people were forced to try to supplement their incomes by speculation on the Bourse.” These speculations (or in effect, hedging), necessitated frequent tradings. 8. Following Fama and Schwert. (1977), when the beta coefficient is greater than unity, we describe common stocks as a super hedge against inflation. To maintain an investor’s purchasing power on an after tax basis, nominal stock returns cannot simply rise in parity with expected inflation (i.e., ⫽1), rising taxes on inflated nominal gains must also be considered. Therefore, the “super hedge” effect may also account for taxes on the substantial nominal gains during the hyperinflation period. However, taxes alone probably cannot explain the size of the coefficient. Because of a lack of precise data on German taxes during hyperinflation, we could not perform statistical tests on the proposition. 9. See Sommavira and Tullio (1987, p.134). The unemployment rate increased to 10.2% in 1923. However, most of the increase came from the last four months of that year because of the government’s currency reform and the total collapse of the economy. 10. The monthly data on the real output during hyperinflation were not available. However, in a paper by Michael et al. (1994), they used real wages as a proxy for real output in their study of the demand for money during the German hyperinflation. Thus, we have incorporated real wages as a proxy for real output. We ran regressions as in Table 5 except that we added the real wages into Eqs. (5) to (10). We found that the real wages coefficients were not significant and hardly changed the results in Table 5.
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