Least squares and stochastic difference equations

In this paper we study the asymptotic properties of least squares estimates of parameters in a stochastic difference equation. The difference equation is assumed to be linear with constant real coefficients. Moreover, the roots of the associated characteristic polynomial are all assumed to have absolute value different from one. Finally, the difference equation is assumed to be non-homogeneous with fixed (i.e., non-random) initial values, and to have ‘error terms’ that are independently and identically distributed with mean zero and finite variance. We show that under these conditions the least squares estimates of the coefficients of the difference equation converge with probability one to the true values.     

Portfolio optimization under model uncertainty and BSDE games

We consider robust optimal portfolio problems for markets modeled by (possibly non-Markovian) Itô–Lévy processes. Mathematically, the situation can be described as a stochastic differential game, where one of the players (the agent) is trying to find the portfolio that maximizes the utility of her terminal wealth, while the other player (“the market”) is controlling some of the unknown parameters of the market (e.g., the underlying probability measure, representing a model uncertainty problem) and is trying to minimize this maximal utility of the agent. This leads to a worst case scenario control problem for the agent. In the Markovian case, such problems can be studied using the Hamilton–Jacobi–Bellman–Isaacs (HJBI) equation, but these methods do not work in the non-Markovian case. We approach the problem by transforming it into a stochastic differential game for backward stochastic differential equations (a BSDE game). Using comparison theorems for BSDEs with jumps we arrive at criteria for the solution of such games in the form of a kind of non-Markovian analogue of the HJBI equation. The results are illustrated by examples.     

Legal versus illegal U.S. immigration and source country characteristics

"Based on micro data from the Immigration and Naturalization Service (INS) on legal immigrants as well as on legalization applications that followed the passage of IRCA [the Immigration Reform and Control Act of 1986], this study exploits the variation in legal and illegal immigration flows across seventy source countries to examine the sensitivity of immigration flows to underlying source country characteristics. The study finds that earnings in the source country and the distance from the United States form significant deterrents of both legal and illegal immigration flows. We also find that illegal immigration is more sensitive to such factors than is legal immigration." The impact of the North American Free Trade Agreement on U.S. immigration from Mexico is also assessed.     

RISK INDIFFERENCE PRICING IN JUMP DIFFUSION MARKETS

We study the risk indifference pricing principle in incomplete markets: The (seller's)  risk indifference price        is the initial payment that makes the  risk  involved for the seller of a contract equal to the risk involved if the contract is not sold, with no initial payment. We use stochastic control theory and PDE methods to find a formula for       and similarly for      . In particular, we prove that  where    p _low   and    p _up   are the lower and upper hedging prices, respectively.     

The diversification cost of large,concentrated equity stakes. How big is it? Is it justified?

While the hypothesis that ownership concentration can affect the value of a company has seen a lot of empirical study, little light has been shed on a complementary problem, that these concentrated owners have a cost of their position due to an undiversified portfolio. Using a unique data set of the actual diversification of all Norwegian equity owners, we show that the largest owners of a corporation in fact have very undiversified equity portfolios, and that such owners have significant costs to their concentrated portfolios. At the level of risk of a benchmark portfolio, if they were to move from their present portfolio composition in risky assets to a well diversified portfolio, their returns would have increased by about 13 percentage points in annual terms. We ask whether this cost can be explained by estimated benefits of ownership concentration (private benefits), and show that extant estimates of private benefits are too low to offset our cost estimates.     

Earnings inequality narrows for young workers despite a widening wage structure

Inequality of wage rates has widened in the United States. But inequality of earnings also depends on the distribution of hour's worked. If the distribution of hours contracts sufficiently, earnings inequality may narrow despite a widening wage structure. The present study examines recent trends in inequality for young workers and, consistent with the preceding scenario, finds that rising inequality of wage rates has been overwhelmed by declining inequality of hours worked. As a consequence, earnings inequality of young workers declined during the 1980s.     

A UNIVERSAL OPTIMAL CONSUMPTION RATE FOR AN INSIDER

We consider a cash flow   X ^{( c )} ( t )  modeled by the stochastic equation where B (·) and     are a Brownian motion and a Poissonian random measure, respectively, and   c ( t ) ≥ 0  is the consumption/dividend rate. No assumptions are made on adaptedness of the coefficients  μ, σ, θ  , and c , and the (possibly anticipating) integrals are interpreted in the forward integral sense. We solve the problem to find the consumption rate c (·), which maximizes the expected discounted utility given by Here  δ( t ) ≥ 0  is a given measurable stochastic process representing a discounting exponent and τ is a random time with values in (0, ∞), representing a terminal/default time, while  γ≥ 0  is a known constant.     

Price differences between equity classes. Corporate control,foreign ownership or liquidity?

This paper is the first comprehensive study of price differences for dual class equity at the Oslo Stock Exchange. It analyzes the relative importance of corporate control, foreign ownership restrictions and stock market liquidity for the price differences. The Norwegian market has the peculiar feature that in part of the sample period non-voting shares were trading at a premium to voting shares, i.e., what is usually termed the “voting premium” was negative. This result can be rationalized by restrictions on foreign ownership. In the later part of the period, with no regulatory restrictions on foreign ownership, the voting premium is positive, and related to corporate governance and liquidity.     

Identifying Earnings Assimilation of Immigrants under Changing Macroeconomic Conditions

Failure to account for differences between immigrants and natives in their responsiveness to changes in macroeconomic conditions may bias estimates of assimilation effects on immigrant earnings. Using Norwegian register data from 1980 to 1996, we first establish that earnings of immigrants from non‐OECD countries exhibit greater sensitivity to local unemployment than do earnings of natives. The empirical analysis further reveals that standard methods of estimation—which fail to consider differential immigrant and native responsiveness—understate earnings growth and overstate cohort differentials among non‐OECD immigrants. These biases are attributable to trends in macroeconomic conditions over the sample period.