In long-term US data the stock market dividend yield is a strong predictor of long-horizon inflation with a negative slope coefficient. This finding is puzzling in light of the traditional Modigliani-Cohn money illusion hypothesis according to which the dividend yield varies positively with expected inflation. To rationalize the finding we develop a consumption-based model with recursive preferences and money illusion. The model with reasonable values of risk aversion and intertemporal elasticity of substitution, and either rational or adaptive expectations, implies significantly negative slope coefficients that increase numerically with the horizon in regressions of future inflation onto the dividend yield, in accordance with the data. A purely rational version of the model with no money illusion, but with a link from expected inflation to real consumption growth, also generates a negative inflation-dividend yield relationship.