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

In this book, the relevance of inflation and the impact of inflation variability on stock prices and returns are empirically investigated.

The statistical evidence for the common statistically significant and negative bivariate relationship between inflation and stock returns is presented at the beginning of Chapter 1. This chapter makes the case and provides evidence that the presence of a supplemental basic variable makes the ostensibly negative relationship disappear. 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 are all possible values for the inflation variable. The Dow Jones Industrial Average’s log returns and the S&P 500 stock market index are used to compute stock returns.

The impact of inflation fluctuation on stock returns is examined in Chapter 2. Either absolute inflation or the square of inflation can be used to determine inflation variability. Bivariate regressions show a negative and statistically significant relationship between inflation variability and stock returns. The coefficient on the inflation variable becomes statistically negligible when both inflation and inflation variability are included as regressors, but the coefficient on inflation variability remains statistically significant and negative. As a result, the impact of inflation’s fluctuation rules the empirical landscape. The coefficients of both inflation and inflation variability become statistically irrelevant when a basic variable is included, namely the change in the cost of equity. This provides more proof why inflation is irrelevant.

In Chapter 3, the impact of inflation on stock returns is recalculated while accounting for an endogenous calendar break and the existence of two Markov switching regimes. The findings demonstrate the existence of two regimes and an endogenous calendar break. The relationship between inflation and stock returns is statistically significant and negative in one subsample and one regime, but there is no statistical relationship in the other subsample or the other regime. Further investigation reveals that conditional heteroscedasticity and a non-stationary probability distribution of the inflation variable are what are responsible for the statistically significant results. Strong evidence is shown in favour of a straightforward theoretical stock market model that includes the same fundamental variable as in Chapters 1 and 2.

The Gordon dividend discount model, which is used in Chapter 4, is based on the same basic stock model of dividend growth. According to this model, changes in the cost of equity, the exchange rate of the US dollar, and changes in aggregate demand account for all stock return explanations; inflation and inflation uncertainty have no further explanatory power. The strategy is based on least squares regressions, endogenous calendar breakpoints, and GARCH models. It is discovered that both the inflation and inflation uncertainty variables are statistically negligible. Only one subsample—the most recent one—shows a statistically significant impact of the US dollar; the break occurred in July 1998. After this date, it is predicted that a 1% decline in the value of the US dollar will result in a 1.6% rise in stock prices.

Estimating the impact of inflation on nominal and real stock returns as well as the equity premium is the aim of Chapter 5. The null hypothesis holds that there is no correlation between inflation and stock returns and that inflation has a detrimental unitary impact on both real stock returns and the equity premium. These final two effects are a result of the inflation variable—or a substitute for it—existing on both sides of the regression. The appendix, which addresses this topic, is recommended to the reader. EGARCH models, Markov switching regimes, resilient least squares, quantile regressions, and least squares regressions with HAC robust standard errors form the foundation of the method in Chapter 5. The variables for inflation and T-bills are discovered to be statistically insignificant. With a unitary coefficient, the equity premium is inversely correlated with inflation. This is as a result of the T-bill rate’s independence as a gauge of inflation.

By taking into account the independent and combined relationships of the 30 stocks that make up the Dow Jones Industrial Average market stock index, Chapter 6 seeks to re-estimate the impact of inflation on stock returns. Both core inflation and consumer price index inflation are looked at. According to the model, the change in the cost of equity is the only fundamental variable that can adequately explain stock returns; inflation has no remaining explanatory ability. The chapter uses panel least squares, limited and unconstrained system regressions, and other inflation index estimations in addition to linear regressions. The findings demonstrate that the inflation irrelevance hypothesis is well-supported, particularly when core inflation is included in the research. Inflation is proven to be unrelated to stock returns, regardless of the stock or econometric method. There are at least three reasons why this chapter is unique. The first is to examine the 30 Dow individual stocks for relevance rather than using market indexes as is customary in the literature. The second is to use multiple econometric techniques, including cross equation dependencies in both unconstrained and limited system regressions. The third step is to perform panel least squares analysis.

By taking into account the independent and combined relationships of the following six US market stock indices: AMEX, DJIA, NASDAQ, NYSE, RUSSEL, and S&P 500, Chapter 7 aims to re-estimate the impact of inflation on stock returns. The null hypothesis assumes that there is no correlation. The price variable is decided to be core inflation. The chapter creates a market stock model that takes dividend growth to be constant. The four basic variables that make up this model’s prediction that stock returns can be explained by changes in the cost of equity, There is no longer any ability to explain inflation using domestic aggregate demand, the VIX volatility index, or the US dollar. Panel least squares, limited and unconstrained system regressions, and linear regressions are all used in this chapter. The findings demonstrate that the inflation irrelevance hypothesis is well supported. Inflation is determined to be unrelated to stock returns, regardless of stock index or econometric method. At least three reasons—similar to those for Chapter 6—make this chapter unique.

In Chapter 8, the 20 Fama-French stocks are used to re-estimate the impact of inflation on stock returns by taking independent and combined relations into account. The chapter provides a market stock model that accounts for dividend increase that is constant across time. The model predicts that four basic variables—the change in the cost of equity, domestic aggregate demand, the VIX volatility index, and the US dollar—explain stock return trends, leaving inflation out of the picture. The existence of outliers is properly taken into consideration. Implemented are two outlier-resistant econometric techniques. The findings demonstrate that the inflation irrelevance hypothesis is well supported. Inflation is determined to be unrelated to stock returns regardless of the stock portfolio or the econometric method. The application of two robust least squares and quantile regressions, which are robust to the presence of outliers, makes the chapter unique for at least one reason.

The stock indices of 17 different nations are tested in Chapter 9 for their relevance to inflation. On 17 distinct international stock indexes, the chapter creates a theoretical stock model and uses correlation and least squares analysis, including robust least squares and quantile regressions. Positive and negative inflation rates both have a non-linear impact, which is also researched. The chapter demonstrates that there are no non-linearities and that inflation irrelevance has strong international backing. A panel of the 16 nations studied in Chapter 9 is used in Chapter 10 to examine the relevance of inflation. Turkey, the 17th nation in Chapter 9, is left out because it stands out as an obvious exception. On these 16 worldwide market indexes, the chapter performs panel least squares analysis and creates a theoretical stock model. Additional techniques include robust least squares, quantile regressions, and full information maximum likelihood. The inflation variable is specified in both a linear and a non-linear manner. The chapter demonstrates that the inflation/stock return relationship is linear and that inflation irrelevance is well supported. It should be noted that the change in the inflation rate has a statistically significant negative coefficient. But the duration effect, which is the same duration effect as for the change in real interest rates, is captured by this change variable. It brings to mind the Fisher hypothesis, which divides changes in nominal interest rates into changes in real interest rates and changes in the rate of inflation.

Estimating the relationship between inflation variability and inflation is the aim of Chapter 11. The absence of an association is the null hypothesis, which is accepted and put to the test. The main innovation involves developing a GARCH specification and setting up a full-fledged macroeconomic model of the inflation rate (the mean equation) rather than reverting to an ad hoc ARMA model (the conditional variance equation). The variance equation contains the inflation rate, and the mean equation contains the GARCH variable. The macro model has strong support, and this strong support is further confirmed by using Monte Carlo bootstrapping. Furthermore, a causal relationship between inflation variability and inflation has a lot of evidence to back it up.

The purpose of Chapter 12 is to estimate the impact of inflation on stock returns while taking into account the potential occurrence of calendar breakpoints brought on by structural changes in a particular economy, varying political and policy regimes, or even global events and spillovers from other countries. The five emerging nations that the author did not test in Chapters 9 and 10 are included in the analysis. Even when breaks are permitted, there is no relationship, according to the null hypothesis. Standard linear and multiple regression analyses are used in this chapter. It searches for statistical anomalies that, if they exist, could cast doubt on both the sampling process and the econometric findings. These fractures are determined endogenously. The chapter examines two regression analysis models, one that is merely bound by inflation and the other that is unconstrained and takes five independent variables taken from a theoretical model into account. For Brazil, Indonesia, and Mexico, statistical breaks are discovered in this chapter. 1988M05, 1998M11, 2000M08, and 2003M07 are the relevant years. No break is present for Chile and Colombia. Only the Brazilian sample and the small subsample prior to the break show a significant connection with the breaks. For the other four emerging nations—Chile, Colombia, Indonesia, and Mexico—inflation is supported as irrelevant. Despite the breaks, the relationship is clearly null and void. One criticism of the data showing there is no correlation between stock returns and inflation is that the sample study has calendar breaks due to institutional differences between the various nations. This chapter attempts to refute this claim and to add to the substantial body of scholarship on inflation’s lack of relevance.

The researcher is then drawn to the appendix’s discussion of the econometric error of using the same variable on both sides of the regression equation. The work takes into account both a theoretical and an empirical proof. The estimated outcomes in both situations are consistent with a significant bias in the regression slope estimate. Furthermore, statistical support can be obtained in cases where it is not necessary. This econometric issue appears frequently throughout the text, which is why it is appended.

**Author (s) Details**

**Samih Antoine Azar**

Faculty of Business Administration & Economics, Haigazian University, Lebanon.

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**Keywords – **Inflation, inflation variability, stock returns, Gordon dividend discount model, advanced financial econometrics, irrelevance proposition.