Isotone Recursive Methods for Overlapping Generation Models with Stochastic Nonclassical Production

Based on an order-theoretic approach, we derive sufficient conditions for the existence, characterization, and computation of Markovian equilibrium decision processes and stationary Markov equilibrium on minimal state spaces for a large class of stochastic overlapping generations models. In contrast to all previous work, we consider reduced-form stochastic production technologies that allow for a broad set of equilibrium distortions such as public policy distortions, social security, monetary equilibrium, and production nonconvexities. Our order-based methods are constructive, and we provide monotone iterative algorithms for computing extremal stationary Markov equilibrium decision processes and equilibrium invariant distributions, while avoiding many of the problems associated with the existence of indeterminacies that have been well-documented in previous work. We provide important results for existence of Markov equilibria for the case where capital income is not increasing in the aggregate stock. Finally, we conclude with examples common in macroeconomics such as models with fiat money and social security. We also show how some of our results extend to settings with unbounded state spaces.

The Time-Series Properties on Housing Prices: A Case Study of the Southern California Market

We examine the time-series relationship between housing prices in eight Southern California metropolitan statistical areas (MSAs). First, we perform cointegration tests of the housing price indexes for the MSAs, finding seven cointegrating vectors. Thus, the evidence suggests that one common trend links the housing prices in these eight MSAs, a purchasing power parity finding for the housing prices in Southern California. Second, we perform temporal Granger causality tests revealing intertwined temporal relationships. The Santa Anna MSA leads the pack in temporally causing housing prices in six of the other seven MSAs, excluding only the San Luis Obispo MSA. The Oxnard MSA experienced the largest number of temporal effects from other MSAs, six of the seven, excluding only Los Angeles. The Santa Barbara MSA proved the most isolated in that it temporally caused housing prices in only two other MSAs (Los Angels and Oxnard) and housing prices in the Santa Anna MSA temporally caused prices in Santa Barbara. Third, we calculate out-of-sample forecasts in each MSA, using various vector autoregressive (VAR) and vector error-correction (VEC) models, as well as Bayesian, spatial, and causality versions of these models with various priors. Different specifications provide superior forecasts in the different MSAs. Finally, we consider the ability of theses time-series models to provide accurate out-of-sample predictions of turning points in housing prices that occurred in 2006:Q4. Recursive forecasts, where the sample is updated each quarter, provide reasonably good forecasts of turning points.

"Ripple Effects" and Forecasting Home Prices in Los Angeles, Las Vegas, and Phoenix

We examine the time-series relationship between housing prices in Los Angeles, Las Vegas, and Phoenix. First, temporal Granger causality tests reveal that Los Angeles housing prices cause housing prices in Las Vegas (directly) and Phoenix (indirectly). In addition, Las Vegas housing prices cause housing prices in Phoenix. Los Angeles housing prices prove exogenous in a temporal sense and Phoenix housing prices do not cause prices in the other two markets. Second, we calculate out-of-sample forecasts in each market, using various vector autoregessive (VAR) and vector error-correction (VEC) models, as well as Bayesian, spatial, and causality versions of these models with various priors. Different specifications provide superior forecasts in the different cities. Finally, we consider the ability of theses time-series models to provide accurate out-of-sample predictions of turning points in housing prices that occurred in 2006:Q4. Recursive forecasts, where the sample is updated each quarter, provide reasonably good forecasts of turning points.

Is Menopause Optimal?

Various theories have been put forward to explain the fact that humans experience menopause while virtually no animals do. This paper aims to investigate one such theory: children provide a savings technology into old age, but as human babies are usually large and have long gestation periods, a substantial risk of death exists for the mother as she bears children. It seems therefore appropriate to impose a stopping rule for fertility. Given an objective (support for old age) and demographics (mortality of mother and children), an optimal age for menopause can be calculated. Using demographic data from populations that have seen little influence from modern medicine, this optimal age is compared to empirical evidence.