Essays on annuitization and housing choice

Abstract

Chapter 1 For most US households, labor income is the most important source of wealth and housing is the most important risky asset. A natural intuition is thus that households whose incomes covary relatively strongly with housing prices should own relatively little housing. Under plausible assumptions on preferences and distributions, this result holds theoretically. Empirically, I find a significant effect: among US households, a one standard deviation increase in income-house price covariance is associated with a decrease of approximately $25,000 in the value of owner occupied housing. This empirical result implies greater cognizance of the interaction between labor income and asset risk on the part of households than suggested by most analyses of stock market behavior. The analysis also suggests that many homeowners enter financial markets in a riskier position than typically thought, and reinforces the intuitive appeal of proposals for market- or tax-based risk sharing in housing prices. Chapter 2 extends the theory of annuitization with no bequest motive in two directions. First, we derive sufficient conditions, in a more general setting than Yaari (1965), under which complete annuitization is optimal, and weaker conditions under which partial annuitization is better than zero annuitization. Second, we explore how incremental and complete annuitization affect consumer welfare in these more general conditions. When markets are complete, all savings are optimally annuitized as long as there is no bequest motive and annuitized assets have greater returns than conventional assets.

(cont.) Consumers' utility need not satisfy intertemporal additive separability nor the expected utility axioms, and annuities need not be actuarially fair. The result is weakened if annuities markets are incomplete, so that there are some assets which do not exist in annuitized form: as long as trade occurs all at once and consumption is positive in every state of nature, a small degree of annuitization is better than no annuitization. When conventional asset markets are incomplete, if annuities are illiquid, then it is possible that no savings are annuitized. We present numerical calculations of the financial benefit and optimal degree of annuitization for consumers with standard CRRA preferences, and compare these results to results where otherwise identical consumers have utility that depends both on present consumption and a standard of living to which they have grown accustomed. In our specification, the effect of adding intertemporal dependence hinges on the size of initial standard of living relative to resources. Chapter 3 addresses the measurement of income sorting and the attribution of observed sorting to different causes. In terms of measurement, I show that a standard decomposition of variance of household income into within jurisdiction and between jurisdiction components understates sorting in the presence of measurement error. Using 1990 US Census data, I find that adjusting for this error approximately doubles the estimated extent of sorting. On average, across all US metropolitan areas (MSAs) I find that approximately ten percent of the variation in household income can be explained by differences across jurisdictions ...