introduce transaction costs to trading. Introducing transaction costs means that investor/consumers will not invest at the theoretically optimal level without receiving an additional compensation. An example of this type of research is shown in Aiyagari and Gertler (1991). A second way to introduce frictions is by changing the nature of the optimization problem that our investor/consumer faces. In particular, a number of researchers have suggested the existence of "habit persistence" in modeling investor/consumer behavior. Equation (5.2) is modified so that an investor's well-being depends not only on the path of current and future consumption, but on the path of past consumption as well. The path of past consumption sets a "habit" level of consumption that investors do not want to fall below. Because investing necessarily means taking on risk, the investor must be compensated by an extraordinary return on equity to compensate for the possibility that consumption will fall below its habit level: At higher habit levels, the impact of potential declines in consumption is more significant than at lower habit levels. Constantinides and Ferson (1991) first develop such a model, and Campbell and Cochrane (1999) provide an example of further research in this direction. The third way that frictions can be introduced is through the institutional environment. Institutional constraints operate in the same spirit as transaction costs, in the sense that they prevent investors from reaching their theoretically optimal allocations. Examples of institutional barriers include taxes, foreign content legislation, and laws increasing the liability to investment providers. An example of this type of research is given by McGrattan and Prescott (2001), which is discussed in more detail later. These lines of research suggest a natural resolution between the theoretical value of the equity premium and the observed performance of the U.S. equity market. In particular, these lines of research suggest that the ex post behavior of the U.S. equity market can be viewed as the result of a transition between high and low equity premium regimes. Differences between the regimes are produced by declines in transaction costs, taxes, and the regulatory environment (as it relates to equity holdings). Suppose we assume that markets are fairly priced before and after the transition between the two regimes. Since the second regime embeds a lower equity premium than the first, valuations must be higher (but expected returns lower). Consequently, during the transition period between the two regimes, equity prices must increase, thereby producing ex post equity returns that are in excess of the ex ante returns in the new regime. For example, McGrattan and Prescott offer an explanation for P/E expansion that does not rely on market disequilibrium: taxes. Most previous research- including Prescott's previously referenced paper on the equity premium puzzle-ignores taxes, but in reality investors consume only after-tax wealth. McGrattan and Prescott point out that the effective dividend tax rate has more than halved over the past 50 years, from around 44 percent in 1950 to about 18 percent today. By their calculations, the change in effective tax rates completely explains the observed shift in price-dividend ratios. Two primary explanations for the lower effective dividend tax rates are the decrease in the highest marginal corporate and personal income taxes and the significantly larger proportion of stocks held by nontaxable entities like pension plans and individual retirement accounts (IRAs).