The Proxy hypothesis

The view that inflation and stocks are positively related as defined by the Fisher Hypothesis was questioned by Tobin (1969), Branch (1974) and Lintner (1974) but, more importantly, Nelson (1976), Jaffee and Mandelker (1976) and Bodie (1976) empirically ignited the contrary discussion. As noted earlier, economic theory before the 1970s held the position that there was a positive relationship between inflation and stock market prices, and this position drew its strength from the rationale that stocks ought to at least maintain their value during inflationary periods. However, contrary to the then held belief among economists on this stock value preservation rationale Bodie (1976), who looked at USA data and empirical work between 1953 and 1972, found that the real return on equity was negatively related to both anticipated and unanticipated inflation, in the short run. This result by Bodie was also confirmed by Fama and Schwert (1977), whose study considered both expected and unexpected components of inflation by looking at the variables’ relationship in the USA between 1953 and 1971. Their

empirical evidence demonstrated that common stocks were rather perverse as a hedge against inflation.

The justification of this empirical evidence was attributed to the Proxy effect by Fama (1981), who acknowledged that the negative relationship is puzzling given the accepted wisdom that common stock, representing ownership of the income generated real assets, should be a hedge against inflation. In accordance with the Proxy effect, the negative inflation and stock return relations are proxying for the positive relationship between stock returns and real variables which Fama (1981) argued are more fundamental determinants of equity values. The negative relations are induced by the negative relationship between the real economy and inflation, owing to both the money demand theory and the quantity theory of money (Fama, 1981). In his paper, which used monthly, quarterly and annual data from the USA between 1953 and 1977, Fama concluded that there was evidence that real stock returns positively related to measures of real activity like capital expenditure, average real return on capital and output, which reflected the variations in the quantity of capital investment with expected return in excess of costs of capital. Furthermore, he noted that the anomalous stock return and inflation relations are strongly related to measures of future real activity, and this is consistent with a rational expectations view in which markets for goods and securities set current prices on the basis of forecasts of relevant real variables. Ram and Spencer (1983) note that the Proxy hypothesis is a three–step procedure. First there is the need to estimate two sets of the inflation regression to show the negative inflation and real activity relations. One of the regressions is derived from the money demand equation and the other is based on the rational

expectations theory in the same form as the Fisher-type equation. The objective of the second step is to show the positive relationship between stock returns and real activity; thus it estimates the regressions on capital expenditure functions and real stock returns. For the third step, the intention is to demonstrate that inflation is not negatively related with stock returns, and this is achieved by holding real activity constant in a stock return regression, with inflation and real activity as variables. The result is a demonstration of the inference in the expected inflation and stocks returns relations. This has led to a new school of thought about the interaction of these variables which is now commonly known as the Proxy hypothesis.

In an economy with a long–run vertical supply curve, demand shocks have little or no impact on the future of output growth, while the inverse is also true for supply shocks (Gallagher and Taylor, 2002). Given this economic reality, Gallagher and Taylor argue that only inflation which is induced by supply shocks should act as a proxy for expected future movements in real activity. This observation thus calls for the decomposition of the inflation data to reflect its drivers. Thus, inflation is broken down to reflect the drivers generated by supply shocks or those from demand shocks. Using multivariate innovation decomposition and quarterly data between 1957 and 1997, Gallagher and Taylor confirmed the Proxy hypothesis, but based on the evidence that only the component due to supply shocks is negative and significantly correlated with stock returns. The evidence also showed that stock returns were insignificantly correlated with the inflation rate which is purely derived from demand innovations.

Geske and Roll (1983), who subscribe to the Proxy hypothesis, strengthen the Proxy hypothesis by showing that the spurious negative relationship between stocks and inflation is driven by a chain of macroeconomic events which result in a higher rate of monetary expansion. Geske and Roll state that this chain starts with a random negative real shock which affects stock returns. This in turn this signals higher unemployment and low corporate earnings. The low corporate earnings and unemployment induce a fall in personal and corporate tax revenues and this happens without an adjustment in the government expenditure, hence an increase in treasury deficit. To cover this deficit, an increase in the borrowings by treasury becomes imminent, as well as an expansion in money supply, which ultimately induces a rise in the inflation rate. The analysis implies that a decrease in economic activity will result in expected growth in money supply and thus large increases in inflation (Stulz, 1986). According to Chang and Pinegar (1987), Fama (1981) and Geske and Roll (1983), models suggest that the stock and inflation relation varies systematically with security risk, and they support this notion through the analysis of American data from 1952 to 1982. James, Koreisha and Partch (1985) find support for the Geske and Roll money supply explanation when they examined the causality links between stocks, real activity, inflation and money supply using a vector autoregressive-moving average (VARMA) model. They found evidence that stocks signal both changes in real activity and changes in the monetary base, which suggests a link between money supply and real activity (Lee, 1992). However, Lee (1992) noted that, as observed by Mehra (1978) and Sims (1980), the causality relations used by Geske and Roll (1983) are based on a bivariate causality test and may not be robust when other variables are introduced into the vector autoregressive (VAR) system. Thus James, Koreisha and Partch’s (1985) VARMA model might be more appropriate.

Kaul (1987) also argued that Geske and Roll (1983) did not analyse the money supply process completely because a procyclical monetary policy is either positively related to or has no relation with inflation. Thus, the explanations contained in Geske and Roll (1983) would be relevant when the government embarks on a reactive monetary policy which either addresses unemployment, foreign currency shortages or a deficit in the treasury; hence a shortcoming of the Geske and Roll explanations of the proxy relation between inflation and stocks. To give a more robust explanation to the Proxy hypothesis relationship, Kaul (1987) argued that it depends on the equilibrium process in the monetary sector, thus placing the importance of demand and supply factors of money in the relationship. While this seems to suggest that Kaul’s conclusions reflect a negative relationship between stocks and inflation, the inference is that it could either be positive or negative depending on money demand and the cyclical nature of the monetary policy. In this regard, Kaul hypothesised that if money demand effects were coupled with monetary responses that are procyclical, stock return and inflation relations would be either insignificant or positive. In this empirical analysis, growth of money was related to government deficit, unemployment rate and lags of money growth, with deficit said to induce countercyclical monetary policy hence a negative relationship. Kaul (1990) reinforced this reasoning to the Proxy hypothesis by concluding that countercyclical monetary policy induces stronger negative relationships than procyclical and neutral monetary regimes. Ely and Robinson (1992), however, found no evidence to support these various policy regimes to explain the relationship between stocks and inflation.

Apart from Kaul’s research, most of the Proxy hypothesis findings contained above are based on USA evidence. Thus Spyrou (2001) investigated the relationship in an emerging market using the regression models as well as cointegration techniques to arrive at his conclusions. His findings, based on data from the emerging market of Greece between 1990 and 2000, were that the stock–inflation relations in the first half of the decade were a strong negative relationship, and in the second half statistically insignificant figures were noted. The reason for this difference is attributed to the role of monetary fluctuations (rather than real activity) influencing inflation levels. In order to examine the relationship between stock prices and inflation, Spyrou’s study tested for cointegration among the variables using the Johansen technique, and tests showed that the first difference was stationary and thus the series were candidates for cointegration. Spyrou (2001) noted that the results of this study were consistent with conclusions made by Marshal (1992) which showed that the negative relationship between stock and inflation is influenced by monetary fluctuations. While this research confirms the earlier submission about the influences of monetary policy on the relationship between the variables, conclusions from one country represent a bias and cannot be used with confidence to infer the relationship in all emerging markets, nor, indeed, in the world generally.

Guitekin (1983) investigated twenty–six countries over thirty–two years from January 1947, using data from International Financial Statistic (IFS) and Capital International Perspective (CIP). He employed regression models estimated by using contemporaneous rates as proxies for expected inflation, autoregressive integrated moving average (ARIMA) models to derive expected inflation and short-term interest rates as predictors of inflation. Cross–sectional data

Using time series regressions, Guitekin (1983) concluded that there was no reliable positive relation between nominal stock returns and inflation rates for the period between 1947 and 1979, with evidence showing a negative relationship between stocks and inflation in most countries except for the United Kingdom. While he found the regression coefficients to be negative, the stock returns–inflation relation was discovered not to be stable over time and was different between countries, with results from the UK continuously positive and different from the rest. Graham (1996) also found the relationship between stocks and inflation to be unstable throughout the post–World War II era, in the sense that it was negative before 1976 and after 1982, but positive in between these years. “Real stock return-inflation relation should be negative only when variation in money demanded is not accommodated by offsetting variation in nominal money growth i.e. procyclical monetary policy,” (Graham, 1996 p. 29). This finding raises questions about the effect of economic or monetary regimes on the relationship, and adds the dimension that the stock–inflation relations could be cyclical and induced the changes in monetary policy.

Partial confirmation of and modification to the Proxy hypothesis are documented by Ram and Spencer (1983), Hasbrouck (1984), Stulz (1986), Lee (1992) and Lee and Ni (1986). Ram and Spencer (1983) question the rationale of the view that inflation and real activity are negatively related in the Proxy hypothesis, given the Phillips curve, which hypothesises positive relations. In this context, Ram and Spencer show that inflation and stock relations instead proxy a reverse of Fama’s hypothesis and explanation of the inferred relations. They suggest that the negative relationship is a result of the relations in the Phillips curve and the negative relations between stocks and output which is in line with the Mundell–Tobin effect. However, Lee

(1992) states that the measure of real activity adopted by Ram and Spencer (1983) is current output, whereas Fama’s theory is based on future output. In addition to the above limitation to Ram and Spencer explanation of the Proxy Hypothesis, output is not the only measure of economic activity, as demonstrated above by Geske and Roll (1983), who propose that government deficit plays a role in the chain (Lee, 1992).

Research findings from the Proxy hypothesis and, indeed, most confirmations thereof, use ex

post data for their evidence, in particular proxy variables to infer expected inflation levels.

However, Hasbrouck (1984) noted that the strength of such findings were in part due to the proxy used, and thus propose the use of Livingstone Surveys as the measure for expected inflation. Gultekin (1983a) also used Livingstone Surveys and found a negative relationship between expected inflation and actual stock returns, though these findings were insignificant. Hasbrouck (1984) found a slight negative relationship between expected economic activity and expected inflation in quantity theory estimation; however, there is no significant simple bivariate relationship. For the stock–economic activity relations, a positive sign in the coefficient of the dependable variable is noted. The conclusion from this evidence, therefore, is that Fama’s Hypothesis is less strong when survey data is used to determine expected variables of this stock–inflation puzzle. Having noted these findings, it is important to mention that the use of data from the Livingstone Survey, however, has been criticised by Lakonishok (1980) and this questions the robustness of these results.

inflation and money growth. The evidence is in support of the Fama hypothesis as well as the findings presented by Geske and Roll’s (1983) view of the negative relationship between stock returns and inflation. Stulz provides a theoretic framework explaining these relations by noting that an increase in expected inflation, irrespective of its origin, results in the fall of real wealth of households because of the increased opportunity cost of real balances and the decrease in households’ holdings in real balances. To keep the stock capital invested in production, which Stulz equates to households’ desired holdings of nominal assets, the default-free nominal interest rate and cash must fall by the same margin as the desire by households to hold real balances, and this can be achieved though a decrease in real rate of interest. The fall in interest rates thus makes the investment in nominal assets less attractive to invest in compared to investment in production (Stulz, 1986). The result, according to Stulz, is that the decrease in real wealth caused by a rise in expected inflation results in households choosing a portfolio of investments in production with a lower mean and a variance of return. The model thus predicts a negative correlation between expected inflation and ex ante real stock returns, but Marshall (1992) stated that the model does not provide evidence as to whether the predicted negative correlation is large enough to match the data. Moreover, it fails to reconcile the negative relationship between stock returns and inflation with the positive correlation between returns and money growth.

The final weak support for the Proxy hypothesis provided herein is by Lee (1992) and Lee and Ni (1996). Lee (1992) used multivariate VAR on post–war USA data between June 1947 and December 1987 to determine the causal relations among stock returns, interest rates, real activity and inflation. The findings show that stock returns help explain significant movements

in real activity which respond positively to stock return shocks, but with interest rates in the VAR, stock returns explain little variations in inflation rate, contrary to findings by James, Koreisha and Partch (1985) which are compatible with the original Proxy hypothesis (Lee, 1992). Furthermore, Lee finds no support for the inflation–economic activity hypothesis, given that inflation explained little variations in real activity movements which, however, responded negatively to inflation shocks. These results question the reliability of the negative inflation– stock relations findings,, given the weak evidence of the causal interactions. In a subsequent paper with Ni, Lee further examined the Fama hypothesis and noted that persistent inflation has a stronger effect on future output than temporary inflation. The decomposition of inflation into persistent and temporary elements, using a filter model, was based on the intuition that future economic activity can be more sensitive to persistent movements on inflation than to temporary ones, as an increase in persistent inflation predicts slower future real activity and a consequent fall in stock returns (Lee and Ni, 1996). Moreover, Lee and Ni (1996) state that an increase in temporary inflation induces investors to shift portfolios from stocks to interest–bearing liquid assets because a rise in temporary inflation decreases the relative attractiveness of stocks even though market present value of future cash flows is unchanged. The findings of this research show that both persistent and temporary inflation are negatively correlated with stock returns, though with different patterns. However, the inclusion of output does not suggest the presence of a proxy relation, especially when temporary inflation is considered. These results further bring into question the reliability of the Fama hypothesis which is based on the significance of the relationship between inflation and future output.