This paper examines the role of money in understanding the behavior of asset prices and whether and how monetary policy should react to asset prices such as stock prices and equity premiums. To do so, I introduce money via the form of transaction cost into a production economy with limited stock market participation where agents with lower inter-temporal elasticity of substitution (IES), called non-stockholders, have no access to stock market. In addition to facilitating transactions of consumption goods, money also redistributes wealth by countercyclically transferring resources from stockholders to non-stockholders, the main role of non-state contingent bonds. The benchmark model resolves quantitatively the risk premium puzzle and the risk-free return puzzle, matches macroeconomic behavior such as volatilities of output, consumption and investment, and is in line with empirically documented facts about money growth, inflation and asset prices in literature. This model is then used to evaluate alternative policies for money growth rates. I find that monetary policies are welfare improving for both stockholders and non-stockholders if they reduce equity premiums in the economy. These policies include a lower expected money growth, a pro-cyclical money growth rate, and growth rates of money being positively reacting to equity prices or equity premiums, all of which enhance the precautionary saving role of money.
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