"A New Light from Old Wisdoms : Alternative Estimation Methods of Simultaneous Equations with Possibly Many Instruments"

We compare four dffierent estimation methods for a coefficient of a linear structural equation with instrumental variables. As the classical methods we consider the limited information maximum likelihood (LIML) estimator and the two-stage least squares (TSLS) estimator, and as the semi-parametric estimation methods we consider the maximum emirical likelihood (MEL) estimator and the generalized method of moments (GMM) (or the estimating equation) estimator. We prove several theorems on the asymptotic optimality of the LIML estimator when the number of instruments is large, which are new as well as old, and we relate them to the results in some recent studies. Tables and figures of the distribution functions of four estimators are given for enough values of the parameters to cover most of interest. We have found that the LIML estimator has good performance when the number of instruments is large, that is, the micro-econometric models with many instruments in the terminology of recent econometric literature.

Variation of Molecular Cloud Properties across the Spiral Arm in M 51

We present the results of high-resolution 13CO(1-0) mapping observations with the NRO 45m telescope of the area toward the southern bright arm region of M51, including the galactic center. The obtained map shows the central depression of the the circumnuclear ring and the spiral arm structure.The arm-to-interarm ratio of the 13CO(1-0) integrated intensity is 2-4. We also have found a feature different from that found in the 12CO results. The 12CO/13CO ratio spatially varies, and shows high values (~20) for the interarm and the central region, but low values(~10) for the arm. These indicate that there is a denser gas in the spiral arm than in the interarm. The distribution of the 13CO shows a better correspondence with that of the H\alpha emission than with the 12CO in the disk region, except for the central region. We found that the 13CO emission is located on the downstream side of the 12CO arm, namely there is an offset between the 12CO and the 13CO as well as the H\alpha emission. This suggests that there is a time delay between the accumulation of gas caused by the density wave and dense gas formation, accordingly star formation. This time delay is estimated to be ~10^7 yr based on the assumption of galactic rotation derived by the rotation curve and the pattern speed of M51. It is similar to the growth timescale of a gravitational instability in the spiral arm of M51, suggesting that the gravitational instability plays an important role for dense gas formation.Comment: 23 pages, 10 figures, PASJ Vol.54, No.2 (2002), in pres

Simultaneous Superconducting and Antiferroquadrupolar Transitions in PrRh2_{2}Zn20_{20}

Superconducting and antiferroquadrupolar (AFQ) transitions in a Pr-based compound PrRh2Zn20 have been found to occur simultaneously at Tc=TQ=0.06 K. The superconducting transition manifests itself by zero resistance and large diamagnetic susceptibility. The specific heat exhibits a Schottky anomaly peaking at 14 K and magnetization curves measured at 2 K show anisotropic behaviors. The analysis of these data indicates that the crystalline electric field (CEF) ground state of the trivalent Pr ion is the non-Kramers Gamma3 doublet with the quadrupolar degrees of freedom. A sharp peak in the specific heat at 0.06 K has been attributed not to the superconducting transition but to the AFQ transition because the ordering temperature TQ decreases in B || [100] but increases in B || [110] and B || [111] with increasing B up to 6 T. This anisotropic behavior of TQ(B) can be well explained by a two-sublattice mean-field calculation, which corroborates the AFQ ordered state below TQ. The entropy release at TQ is only 10% of Rln2 expected for the Gamma3 doublet, suggesting possible interplay between the quadrupolar degrees of freedom and the superconductivity.Comment: 18 page, 6 figures, accepted for publication in Phys. Rev.

Ordered magnetic and quadrupolar states under hydrostatic pressure in orthorhombic PrCu2

We report magnetic susceptibility and electrical resistivity measurements on single-crystalline PrCu2 under hydrostatic pressure, up to 2 GPa, which pressure range covers the pressure-induced Van Vleck paramagnet-to-antiferromagnet transition at 1.2 GPa. The measured anisotropy in the susceptibility shows that in the pressure-induced magnetic state the ordered 4f-moments lie in the ac-plane. We propose that remarkable pressure effects on the susceptibility and resistivity are due to changes in the quadrupolar state of O22 and/or O20 under pressure. We present a simple analysis in terms of the singlet-singlet model.Comment: 14 pages, 9 figures submitted to Phys. Rev.

"On the Asymptotic Optimality of the LIML Estimator with Possibly Many Instruments"

We consider the estimation of the coefficients of a linear structural equation in a simultaneous equation system when there are many instrumental variables. We derive some asymptotic properties of the limited information maximum likelihood (LIML) estimator when the number of instruments is large; some of these results are new and we relate them to results in some recent studies. We have found that the variance of the LIML estimator and its modifications often attain the asymptotic lower bound when the number of instruments is large and the disturbance terms are not necessarily normally distributed, that is, for the micro-econometric models with many instruments.