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Estimating the Expected Marginal Rate of Substitution

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Estimating the Expected Marginal Rate of Substitution: A Systematic Exploitation of Idiosyncratic Risk Robert P. Flood and Andrew K. Rose* Revised: March 9, 2005 Robert P. Flood Andrew K. Rose (correspondence) Research Dept, IMF Haas School of Business 700 19th St., NW University of California Washington, DC 20431 Berkeley, CA 94720-1900 Tel: (202) 623-7667 Tel: (510) 642-6609 Fax: (202) 589-7667 Fax: (510) 642-4700 E-mail: [email protected] E-mail: [email protected] Abstract We develop a methodology to estimate the shadow risk free rate or expected intertemporal marginal rate of substitution, “EMRS”. Our technique relies upon exploiting idiosyncratic risk, since theory dictates that idiosyncratic shocks earn the EMRS. We apply our methodology to recent monthly and daily data sets for the New York and Toronto Stock Exchanges. We estimate EMRS with precision and considerable time-series volatility, subject to an identification assumption. Both markets seem to be internally integrated; different assets traded on a given market share the same EMRS. We reject integration between the stock markets, and between stock and money markets. JEL Classification Numbers: G14 Keywords: integration, asset, market, discount, stock. * Flood is Senior Economist, Research Department, International Monetary Fund. Rose is B.T. Rocca Jr. Professor of International Business, Haas School of Business at the University of California, Berkeley, NBER Research Associate, and CEPR Research Fellow. This is a heavily revised version of a working paper with the same title. For comments, we thank workshop participants at the Carnegie-Rochester conference, Dartmouth, the Federal Reserve Board, Minnesota, Princeton, SMU, and Wisconsin as well as Jon Faust, Marvin Goodfriend, Rich Lyons, Mark Watson, Chris Sims, Ken West, Yangru Wu, and especially David Marshall and an anonymous referee. Rose thanks INSEAD and SMU for hospitality during the course of this research. The data set, sample output, and a current version of this paper are available at http://faculty.haas.berkeley.edu/arose.11 Introduction In this paper, we develop and apply a simple methodology to estimate the shadow risk-free rate or expected intertemporal marginal rate of substitution (hereafter “EMRS”). We do this for two reasons. First, it is of intrinsic interest. Second, when different series for the EMRS are estimated for different markets, comparing these estimates provides a natural test for integration between markets. Our method is novel in that it exploits information in asset-idiosyncratic shocks. While the primary objective of this paper is methodological, we illustrate our technique by applying it to monthly and daily data covering firms from large American and Canadian stock exchanges. Our method delivers EMRS estimates with precision and striking volatility. Estimates from different markets can be distinguished from each other and from the Treasury bill equivalent. Section 2 motivates our measurement by providing a number of macroeconomic applications. We then present our methodology; implementation details are discussed in the following section. Our empirical results are presented in section 5, while the paper ends with a brief conclusion. 2 Why Should Macroeconomists Care About Asset Market Integration? We begin with a conventional intertemporal asset pricing condition: )(11jtttjtxmEp++= (1)2where: jtp is the price at time t of asset j, Et() is the expectations operator conditional on information available at t, 1+tm is the time-varying intertemporal marginal rate of substitution (MRS), used to discount income accruing in period t+1 (also known as the stochastic discount factor, marginal utility growth, or pricing kernel), and jtx1+ is income received at t+1 by owners of asset j at time t (the future value of the asset plus any dividends or other income). We adopt the standard definition of asset integration – two assets are said to be integrated when the systemic and idiosyncratic risks in those assets are priced identically. Here “priced” means that equation (1) holds for the assets in question. Equation (1) involves the moments of 1+tm andjtx1+, not the realized values of those variables. Although many moments of 1+tm are involved in asset market integration, the object of interest to us in this study is 1+ttmE the time t expectation of the intertemporal marginal rate of substitution (EMRS). We concentrate on the first moment for three reasons. First, the expectation of the MRS, 1+ttmE, is intrinsically important; it lies at the heart of much intertemporal macroeconomic and financial economics and is virtually the DNA of modern aggregate economics. Second, it is simple to measure, subject to certain caveats discussed below. Third, cross-market differences in estimated values of 1+ttmE are statistically distinguishable, providing powerful evidence concerning market integration. We are testing only for first-moment equality when many additional moments are used in asset pricing; thus, ours it a test of a necessary condition for integration. If we reject equality of the first moment, we can reject integration, but failing to reject first-moment equality is consistent with (but does not imply) complete integration. 2.1 Motivation3Asset market integration is a topic of continuing interest in international finance, see e.g., Adam et. al. (2002). It is of special interest in Europe where continuing monetary and institutional integration have lead to lower barriers to asset trade inside the EU. But there are a number of compelling reasons why most policy-oriented macroeconomists should be interested in asset market integration. When macroeconomic modeling was based on descriptive structure a generation ago, market integration was not very relevant to macro. Modern macroeconomic models, however, are usually built on the assumption that agents maximize an intertemporal utility function in a stochastic setting (e.g., King and Rebelo, 2000, and Clarida, Gali and Gertler, 1999). In such macro models our equation (1) could be used to characterize bond holdings and might look like: )*)(*)(()1(111++=+ttcttcttqcuqcuEiρ. (2) The corresponding equation for stock holding or to value firm revenues would be: )**)(*)((111+++=tttcttcttxqcuqcuEpρ. (3) In equations (2) and (3), 01ρ<< is a


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