Inflation, Inflation Variability, and Stock Returns: The Inflation Irrelevance Proposition

The book is an empirical investigation of the irrelevance proposition of inflation and of inflation variability for stock prices and returns.

Chapter 1 begins by presenting the statistical evidence on the usual statistically significant and negative bivariate relation between inflation and stock returns. The chapter argues and proves that this negative relation is spurious and disappears when a supplementary fundamental variable is added to the regression. The inflation variable is constructed so as to take one of the following: actual, expected, unexpected, positive unexpected, negative unexpected, unexpected positive inflation rate in periods of positive growth, unexpected positive inflation rate in periods of negative growth, unexpected negative inflation rate in periods of positive growth, and unexpected negative inflation rate in periods of positive growth. Stock returns are calculated from the log returns of the Dow Jones Industrial Average, and from the S&P 500 stock market index.

Chapter 2 studies the effect of inflation variability on stock returns. Inflation variability is measured either by absolute inflation or by the square of inflation. A negative and statistically significant relation between inflation variability and stock returns is documented in bivariate regressions. When both inflation and inflation variability are included as regressors, the coefficient on the inflation variable turns out to be statistically insignificant while the coefficient on inflation variability stays statistically significant and negative. Hence the influence of the variability of inflation dominates the empirical scene. However, by adding a fundamental variable, which is the change in the cost of equity, the coefficients of both the inflation and inflation variability variables become statistically insignificant. This is further evidence on inflation irrelevance.

The goal of Chapter 3 is to re-estimate the effect of inflation on stock returns, allowing for an endogenous calendar break, and for the existence of two Markov switching regimes. The results show the presence of an endogenous calendar break, and the existence of two regimes. In one subsample, and in one regime, the relation between inflation and stock returns is statistically negative and significant, whereas in the other subsample, or the other regime, there is no statistical relation. Further scrutiny finds that the statistically significant results are driven by conditional heteroscedasticity, and by a non-stationary probability distribution of the inflation variable. A simple theoretical stock market model, that includes the same fundamental variable as in Chapters 1 and 2, is strongly supported.

Chapter 4 relies on the same simple stock model, which is the constant growth in dividends, and is known as the Gordon dividend discount model. This model predicts that stock returns are explained by three fundamental variables, which are the change in the cost of equity, the change in the US dollar exchange rate, and the change in aggregate demand, with no explanatory power left for inflation and inflation uncertainty. The approach is based on GARCH models, endogenous calendar breakpoints, and least squares regressions. The inflation and inflation uncertainty variables are found to be statistically insignificant. The US dollar has a statistically significant effect in only one subsample, the recent one, the break being in July 1998. It is estimated that after this date a 1% depreciation of the US dollar increases stock prices by 1.6%.

The goal of Chapter 5 is to estimate the effect of inflation, on nominal, and real stock returns, and on the equity premium. The null hypothesis is for a lack of an association of inflation with stock returns, and for a negative unitary effect of inflation on real stock returns, and on the equity premium. These last two effects come about from the existence of the inflation variable, or its proxy, on both sides of the regression. The reader is referred to the appendix which tackles this issue. The approach in Chapter 5 is based on EGARCH models, Markov switching regimes, robust least squares, quantile regressions, and least squares regressions with HAC robust standard errors. The inflation and the T-bill variables are found to be statistically insignificant. The equity premium is negatively related to inflation with a unitary coefficient. This is due to the fact that the T-bill rate is an unbiased predictor of the inflation rate.

The goal of Chapter 6 is to re-estimate the effect of inflation on stock returns by considering separate and joint relations of the 30 stocks included in the Dow Jones Industrial Average market stock index. Both consumer price index inflation and core inflation are studied. The model predicts that stock returns are explained by one fundamental variable, which is the change in the cost of equity, with no explanatory power left for inflation. Besides taking different inflation index estimates, the chapter applies linear regressions, constrained and unconstrained system regressions, and panel least squares. The results show that the hypothesis of inflation irrelevance is strongly supported, especially when core inflation is used in the analysis. Whatever the stock, and whatever the econometric procedure, inflation is found not to be related to stock returns. The chapter is original for at least three reasons. The first is to test for irrelevance of the 30 Dow individual stocks, instead of considering market indices, as is usually done in the literature. The second is to apply more than one econometric procedure, with unconstrained and constrained system regressions that preserve cross equation dependencies. And the third is to conduct panel least squares.

The goal of Chapter 7 is to re-estimate the effect of inflation on stock returns by considering separate and joint relations of the following six US market stock indices: AMEX, DJIA, NASDAQ, NYSE, RUSSEL, and S&P 500. The null hypothesis is for a lack of an association. Core inflation is chosen to be the price variable. The chapter develops a market stock model that assumes constant growth in dividends. This model predicts that stock returns are explained by four fundamental variables, which are the change in the cost of equity, domestic aggregate demand, the VIX volatility index, and the US dollar, with no explanatory power left for inflation. The chapter applies linear regressions, constrained and unconstrained system regressions, and panel least squares. The results show that the hypothesis of inflation irrelevance is strongly supported. Whatever the stock index, and whatever the econometric procedure, inflation is found not to be related to stock returns. The chapter is original for at least three reasons, which are similar to those for Chapter 6.

The goal of Chapter 8 is to re-estimate the effect of inflation on stock returns by considering separate and joint relations on the 20 Fama-French stocks. The chapter develops a market stock model that assumes constant growth in dividends. The model predicts that stock returns are explained by four fundamental variables, which are the change in the cost of equity, domestic aggregate demand, the VIX volatility index, and the US dollar, with no explanatory power left for inflation. Proper concern is given for the presence of outliers. Two econometric procedures that are resistant to outliers are implemented. The results show that the hypothesis of inflation irrelevance is strongly supported. Whatever the stock portfolio, and whatever the econometric procedure, inflation is found not to be related to stock returns. The chapter is original for at least one reason, which is by applying two econometric procedures, robust least squares and quantile regressions, that are resistant to the presence of outliers.

Chapter 9 has an international flavor, and tests for inflation irrelevance the stock indices of 17 countries. The chapter develops a theoretical stock model and applies correlation and least squares analysis, including robust least squares and quantile regressions, on 17 independent international stock indices. A non-linear effect of positive and negative inflation rates is also studied. The chapter shows that inflation irrelevance is solidly supported internationally, and that there are no non-linearities present.

Chapter 10 tests for inflation irrelevance a panel of the 16 countries covered in Chapter 9. Turkey, which is the 17th country in Chapter 9, is kept excluded for being a noticeable outlier. The chapter develops a theoretical stock model and applies panel least squares analysis on these 16 international stock indices. In addition, robust least squares, quantile regressions, and Full Information Maximum Likelihood procedures are conducted. Both a linear and a non-linear specification of the inflation variable are carried out. The chapter shows that inflation irrelevance is solidly supported, and that there are no non-linearities in the inflation/stock returns relation. One caveat is that the change in the inflation rate carries a negative and statistically significant coefficient. However, this change variable picks up the duration effect, which is the same duration effect as for the change in real interest rates. One is reminded about the Fisher hypothesis, in first-differences, which separates the change in the nominal interest rates into the change in real interest rates and the change in the inflation rate.

The goal of Chapter 11 is to estimate the relation between inflation variability and inflation. The null hypothesis, which is held and tested, is for a lack of an association. The major innovation is by setting up a full-fledged macroeconomic model of the inflation rate (the mean equation), instead of reverting to an ad hoc ARMA model, and by formulating a GARCH specification (the conditional variance equation). The inflation rate is included in the variance equation and the GARCH variable is included in the mean equation. There is strong support for the macro model, and by carrying out Monte Carlo bootstrapping, this strong support is further confirmed. In addition, there is strong support for a causality running from inflation variability to inflation.

The goal of Chapter 12 is to estimate the effect of inflation on stock returns, taking into consideration the eventual presence of calendar breakpoints due to structural changes in a given economy, or due to varying political and policy regimes, or even to international circumstances and global spillovers. The analysis covers the five developing countries that were not tested by the author in Chapters 9 and 10. The null hypothesis is for a lack of an association even when breaks are allowed. The chapter applies standard linear and multiple regression analysis. It looks for statistical breaks, which, if present, may undermine the sampling procedure and the econometric results. These breaks are endogenously determined. The chapter considers two models of regression analysis, one constrained with inflation only, and the other unconstrained which includes five independent variables, chosen from a theoretical model. The chapter finds statistical breaks for Brazil, Indonesia, and Mexico. They are in 1988M05, 1998M11, 2000M08, and 2003M07. In case of Chile and Colombia no break is featured. The breaks produce a strong association only in the Brazilian sample and only for the small subsample before the break. Otherwise, inflation irrelevance is supported for the other four developing countries: Chile, Colombia, Indonesia, and Mexico. The association is robustly null and void, despite the presence of breaks. One criticism of the evidence on the inexistence of a relation between stock returns and inflation is that the sample study suffers from calendar breaks which are the result of the institutional setting of each country. This chapter serves to dispel such a notion, and to augment the already sizeable literature of inflation irrelevance.

Finally, the appendix attracts the attention of the researcher on the econometric pitfall of including the same variable on both sides of the regression equation. The paper considers both a theoretical proof and an empirical one. In both cases the estimation results are supportive of an important bias in the regression slope estimate. Moreover statistical evidence can be found where none is warranted. This econometric problem surfaces in many parts of the book, which is why it is included as an appendix.