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Countries with strict immigration policies often resort to deportation measures to reduce their stocks of illegal immigrants. Many of their undocumented foreign workers, however, are not deported but rather choose to return home voluntarily. This paper studies the optimizing behavior of undocumented immigrants who continuously face the risk of deportation, modeled by a stochastic process, and must decide how long to remain in the host country. It is found that the presence of uncertainty with respect to the length of stay abroad unambiguously reduces the desired migration duration and may trigger a voluntary return when a permanent stay would otherwise be optimal. Voluntary return is motivated by both economic and psychological factors. Calibration of the model to match the evidence on undocumented Thai migrants in Japan suggests that the psychological impact of being abroad as an illegal alien may be equivalent to as large as a 68 % cut in the consumption rate at the point of return., Journal of Population Economics, 29 (3), ISSN:0933-1433, ISSN:1432-1475

This paper considers the portfolio problem for high dimensional data when the dimension and size are both large.We analyze the traditional Markowitz mean-variance (MV) portfolio by large dimension matrix theory, and find the spectral distribution of the sample covariance is the main factor to make the expected return of the traditional MV portfolio overestimate the theoretical MV portfolio. A correction is suggested to the spectral construction of the sample covariances to be the sample spectrally corrected covariance, and to improve the traditional MV portfolio to be spectrally corrected. In the expressions of the expected return and risk on the MV portfolio, the population covariance matrix is always a quadratic form, which will direct MV portfolio estimation. We provide the limiting behavior of the quadratic form with the sample spectrally-corrected covariance matrix, and explain the superior performance to the sample covariance as the dimension increases to infinity proportionally with the sample size. Moreover, this paper deduces the limiting behavior of the expected return and risk on the spectrally-corrected MV portfolio, and illustrates the superior properties of the spectrally-corrected MV portfolio. In simulations, we compare the spectrally-corrected estimates with the traditional and bootstrap-corrected estimates, and show the performance of the spectrally-corrected estimates are the best in portfolio returns and portfolio risk. We also compare the performance of the new proposed estimation with different optimal portfolio estimates for real data from S&P 500. The empirical findings are consistent with the theory developed in the paper.

Countries with strict immigration policies often resort to deportation measures to reduce their stocks of illegal immigrants. Many of their undocumented foreign workers, however, are not deported but rather choose to return home voluntarily. This paper studies the optimizing behavior of undocumented immigrants who continuously face the risk of deportation, modeled by a stochastic process, and must decide how long to remain in the host country. It is found that the presence of uncertainty with respect to the length of stay abroad unambiguously reduces the desired migration duration and may trigger a voluntary return when a permanent stay would otherwise be optimal. Voluntary return is motivated by both economic and psychological factors. Calibration of the model to match the evidence on undocumented Thai migrants in Japan suggests that the psychological impact of being abroad as an illegal alien may be equivalent to as large as a 68% cut in the consumption rate at the point of return., Economics Working Paper Series, 15/218

This paper analyzes how banks' funding constraints impact the access and cost of capital of small firms. Banks raise external finance from a large number of small investors who face co-ordination problems and invest in small, risky businesses. When investors observe noisy signals about the true implementation cost of real sector projects, the model can be solved for a threshold equilibrium in the classical global games approach. We show that a "socially optimal" interest rate that maximizes the probability of success of the small firm is higher than the risk-free rate, because higher interest rates relax the bank's funding constraint. However, banks will generally set an interest rate higher than this socially optimal one. This gives rise to a built-in inefficiency of banking intermediation activity that can be corrected by various policy measures.