{'fraction_non_alphanumeric': 0.01818181818181818, 'fraction_numerical': 0.0005865102639296188, 'mean_word_length': 5.53639846743295, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Nonlinearity and Endogeneity in Macro-Asset Pricing 1

Linear asset-pricing relations, with macroeconomic factors as state variables, have found wide use in empirical finance. Applications of such relations range from academic studies of market efficiency and market anomalies to practical uses such as risk management and estimation of the cost of capital. These applications make two key assumptions: that the relationship is exclusively linear, and that the macroeconomic factors are exogenous to returns. For the set of macrofactors commonly used in these applications, both assumptions run counter to economic intuition. We set out to demonstrate that they are also counter to empirical evidence. We carry out this task using tests for linear and nonlinear Granger causality. We find linear and nonlinear feedback between stock returns and commonly used macroeconomic pricing factors. We also find linear and nonlinear feedback between residuals from linear pricing relations and returns. In addition, there is little evidence to suggest that neglected autoregressive or autoregressive conditionally heteroskedastic dynamics are responsible for these findings, implying that the underlying dynamics are complicated. Thus, linear asset-pricing relations omit interesting and potentially useful aspects of the relationship between stock returns and the macroeconomy. Acknowledgments. We wish to thank the participants at earlier presentations of this paper for their helpful comments. We also wish to thank Pedro de Lima, Robert Flood, Ted Jaditz, Jonathan Jones, Francis Longstaff, Bruce Mizrach, and anonymous referees for comments. We also thank Janet Shelley for her assistance with the manuscript.