Econometrics

A Variational Model for Urban Planning with Traffic Congestion

An entrepreneur with limited liability needs to finance an infinite horizon investment
project. An agency problem arises because she can divert operating cash-flows before
reporting them to the financiers. We first study the optimal contract in discrete time. This contract can be implemented by cash reserves, debt and equity. The latter is split between the financiers and the entrepreneur, and pays dividends when retained earnings reach a threshold. To provide appropriate incentives to the entrepreneur, the firm is downsized when it runs short of cash. We then study the continuous-time limit of the model. We prove the convergence of the discrete-time value functions and optimal contracts. Our analysis yields rich implications for the dynamics of security prices. Stock prices follow a diffusion reflected at the dividend barrier and absorbed at zero. Their volatility, as well as the leverage ratio of the firm, increase after bad performance. Stock prices and book-to-market ratios are in a non-monotonic relationship. A more severe agency problem entails lower price earning ratios and firm liquidity, and higher default risk.

Despite its large sample efficiency, the truncated flat (TF) kernel estimator of long-run covariance matrices is seldom used, because it lacks the guaranteed positive semidefiniteness and sometimes performs poorly in small samples, compared to other familiar kernel estimators. This paper proposes simple modifications to the TF estimator to enforce the positive definiteness without sacrificing the large sample efficiency and make the estimator more reliable in small samples through better utilization of the bias-variance tradeoff. We study the large sample properties of the modified TF estimators and verify their improved small-sample performances by Monte Carlo simulations.

The ‘oil’igopoly theory of oil production with fixed reserves predicts that firms with larger reserves will extract a larger quantity but a smaller proportion of their reserves. While this theory is supported when looking at production data, it is not supported when looking at changes in proven reserves data. This paper develops a theory of ‘oil’igopolistic oil exploration to explain trends observed in the world oil industry over the past fifty years. The ‘oil’igopoly theory of oil exploration predicts that firms with smaller proven reserves will do more exploration than firms with larger proven reserves, as well as reproducing the predictions of the ‘oil’igopoly oil production model. These predictions are consistent with international production and reserve data in the post-World War II era.