This thesis studies the field of asset price bubbles. It is comprised ofthree independent chapters. Each of these chapters either directly orindirectly analyse the existence or implications of asset price bubbles.The type of bubbles assumed in each of these chapters is consistentwith rational expectations. Thus, the kind of price bubbles investigated here are known as rational bubbles in the literature. Thefollowing describes the three chapters.Chapter 1: This chapter attempts to explain the recent US housingprice bubble by developing a heterogeneous agent endowment economy asset pricing model with risky housing, endogenous collateraland defaults. Investment in housing is subject to an idiosyncratic riskand some mortgages are defaulted in equilibrium. We analytically derive the leverage or the endogenous loan to value ratio. This variablecomes from a limited participation constraint in a one period mortgage contract with monitoring costs. Our results show that low valuesof housing investment risk produces a credit easing effect encouragingexcess leverage and generates credit driven rational price bubbles inthe housing good. Conversely, high values of housing investment riskproduces a credit crunch characterized by tight borrowing constraints,low leverage and low house prices. Furthermore, the leverage ratio wasfound to be procyclical and the rate of defaults countercyclical consistent with empirical evidence.Chapter 2: It is widely believed that financial assets have considerablepersistence and are susceptible to bubbles. However, identification ofthis persistence and potential bubbles is not straightforward. Thischapter tests for price bubbles in the United States housing marketaccounting for long memory and structural breaks. The intuition isthat the presence of long memory negates price bubbles while thepresence of breaks could artificially induce bubble behaviour. Hence,we use procedures namely semi-parametric Whittle and parametricARFIMA procedures that are consistent for a variety of residual biases to estimate the value of the long memory parameter, d, of thelog rent-price ratio. We find that the semi-parametric estimation procedures robust to non-normality and heteroskedasticity errors foundfar more bubble regions than parametric ones. A structural break wasidentified in the mean and trend of all the series which when accountedfor removed bubble behaviour in a number of regions. Importantly, theUnited States housing market showed evidence for rational bubbles atboth the aggregate and regional levels.In the third and final chapter, we attempt to answer the followingquestion: To what extend should individuals participate in the stockmarket and hold risky assets over their lifecycle? We answer this question by employing a lifecycle consumption-portfolio choice model withhousing, labour income and time varying predictable returns wherethe agents are constrained in the level of their borrowing. We firstanalytically characterize and then numerically solve for the optimalasset allocation on the risky asset comparing the return predictability case with that of IID returns. We successfully resolve the puzzlesand find equity holding and participation rates close to the data. Wealso find that return predictability substantially alter both the level ofrisky portfolio allocation and the rate of stock market participation.High factor (dividend-price ratio) realization and high persistence offactor process indicative of stock market bubbles raise the amount ofwealth invested in risky assets and the level of stock market participation, respectively. Conversely, rare disasters were found to bringdown these rates, the change being severe for investors in the lateryears of the life-cycle. Furthermore, investors following time varyingreturns (return predictability) hedged background risks significantlybetter than the IID ones.