Jeffreys Prior Analysis of the Simultaneous Equations Model in the Case with n+1 Endogenous Variables

This paper analyzes the behavior of posterior distributions under the Jeffreys prior in a simultaneous equations model. The case under study is that of a general limited information setup with n + 1 endogenous variables. The Jeffreys prior is shown to give rise to a marginal posterior density which has Cauchy-like tails similar to that exhibited by the exact finite sample distribution of the corresponding LIML estimator. A stronger correspondence is established in the special case of a just-identified orthonormal canonical model, where the posterior density under the Jeffreys prior is shown to have the same functional form as the density of the finite sample distribution of the LIML estimator. The work here generalizes that of Chao and Phillips (1997), which gives analogous results for the special case of two endogenous variables.Cauchy tails, exact finite sample distributions, Jeffreys prior, just identification, limited information, posterior density, simultaneous equations model

New South Wales Vegetation Classification and Assessment : part 1, plant communities of the NSW Western Plains

For the Western Plains of New South Wales, 213 plant communities are classified and described and their protected area and threat status assessed. The communities are listed on the NSW Vegetation Classification and Assessment database (NSWVCA). The full description of the communities is placed on an accompanying CD together with a read-only version of the NSWVCA database. The NSW Western Plains is 45.5 million hectares in size and covers 57% of NSW. The vegetation descriptions are based on over 250 published and unpublished vegetation surveys and maps produced over the last 50 years (listed in a bibliography), rapid field checks and the expert knowledge on the vegetation. The 213 communities occur over eight Australian bioregions and eight NSW Catchment Management Authority areas. As of December 2005, 3.7% of the Western Plains was protected in 83 protected areas comprising 62 public conservation reserves and 21 secure property agreements. Only one of the eight bioregions has greater than 10% of its area represented in protected areas. 31 or 15% of the communities are not recorded from protected areas. 136 or 64% have less than 5% of their pre-European extent in protected areas. Only 52 or 24% of the communities have greater than 10% of their original extent protected, thus meeting international guidelines for representation in protected areas. 71 or 33% of the plant communities are threatened, that is, judged as being ‘critically endangered’, ‘endangered’ or ‘vulnerable’. While 80 communities are recorded as being of ‘least concern’ most of these are degraded by lack of regeneration of key species due to grazing pressure and loss of top soil and some may be reassessed as being threatened in the future. Threatening processes include vegetation clearing on higher nutrient soils in wetter regions, altered hydrological regimes due to draw-off of water from river systems and aquifers, high continuous grazing pressure by domestic stock, feral goats and rabbits, and in some places native herbivores — preventing regeneration of key plant species, exotic weed invasion along rivers and in fragmented vegetation, increased salinity, and over the long term, climate change. To address these threats, more public reserves and secure property agreements are required, vegetation clearing should cease, re-vegetation is required to increase habitat corridors and improve the condition of native vegetation, environmental flows to regulated river systems are required to protect inland wetlands, over-grazing by domestic stock should be avoided and goat and rabbit numbers should be controlled and reduced. Conservation action should concentrate on protecting plant communities that are threatened or are poorly represented in protected areas

Bayesian Posterior Distributions in Limited Information Analysis of the Simultaneous Equations Model Using the Jeffreys’ Prior

This paper studies the use of the Jeffreys’ prior in Bayesian analysis of the simultaneous equations model (SEM). Exact representations are obtained for the posterior density of the structural coefficient beta in canonical SEM’s with two endogenous variables. For the general case with m endogenous variables and an unknown covariance matrix, the Laplace approximation is used to derive an analytic formula for the same posterior density. Both the exact and the approximate formulas we derive are found to exhibit Cauchy-like tails analogous to comparable results in the classical literature on LIML estimation. Moreover, in the special case of a two-equation, just-identified SEM in canonical form, the posterior density of beta is shown to have the same infinite series representation as the density of the finite sample distribution of the corresponding LIML estimator. This paper also examines the occurrence of a nonintegrable asymptotic cusp in the posterior distribution of the reduced form parameter Pi, first documented in Kleibergen and van Dijk (1994). This phenomenon is explained in terms of the jacobian of the mapping from the structural model to the reduced form. This interpretation assists in understanding the success of the Jeffreys’ prior in resolving this proble

Model Selection in Partially Nonstationary Vector Autoregressive Processes with Reduced Rank Structure

The current practice for determining the number of cointegrating vectors, or the cointegrating rank, in a vector autoregression (VAR) requires the investigator to perform a sequence of cointegration tests. However, as was shown in Johansen (1992), this type of sequential procedure does not lead to consistent estimation of the cointegrating rank. Moreover, these methods take as given the correct specification of the lag order of the VAR, though in actual applications the true lag length is rarely known, Simulation studies by Toda and Phillips (1994) and Chao (1993), on the other hand, have shown that test performance of these procedures can be adversely affected by lag misspecification. This paper addresses these issues by extending the analysis of Phillips and Ploberger (1996) on the Posterior Information Criterion (PIC) to a partially nonstationary vector autoregressive process with reduced rank structure. This extension allows lag length and cointegrating rank to be jointly selected by the criterion, and it leads to the consistent estimation of both. In addition, we also evaluate the finite sample performance of PIC relative to existing model selection procedures, BIC and AIC, through a Monte Carlo study. Results here show PIC to perform at least as well and sometimes better than the other two methods in all the cases examined

Uniform Inference in Panel Autoregression

This paper considers estimation and inference concerning the autoregressive coefficient (ρ) in a panel autoregression for which the degree of persistence in the time dimension is unknown. The main objective is to construct confidence intervals for ρ that are asymptotically valid, having asymptotic coverage probability at least that of the nominal level uniformly over the parameter space. It is shown that a properly normalized statistic based on the Anderson-Hsiao IV procedure, which we call the M statistic, is uniformly convergent and can be inverted to obtain asymptotically valid interval estimates. In the unit root case confidence intervals based on this procedure are unsatisfactorily wide and uninformative. To sharpen the intervals a new procedure is developed using information from unit root pretests to select alternative confidence intervals. Two sequential tests are used to assess how close ρ is to unity and to correspondingly tailor intervals near the unit root region. When ρ is close to unity, the width of these intervals shrinks to zero at a faster rate than that of the confidence interval based on the M statistic. Only when both tests reject the unit root hypothesis does the construction revert to the M statistic intervals, whose width has the optimal N^{-1/2}T^{-1/2} rate of shrinkage when the underlying process is stable. The asymptotic properties of this pretest-based procedure show that it produces confidence intervals with at least the prescribed coverage probability in large samples. Simulations confirm that the proposed interval estimation methods perform well in finite samples and are easy to implement in practice. A supplement to the paper provides an extensive set of new results on the asymptotic behavior of panel IV estimators in weak instrument settings

Model Selection in Partially Nonstationary Vector Autoregressive Processes with Reduced Rank Structure

The current practice for determining the number of cointegrating vectors, or the cointegrating rank, in a vector autoregression (VAR) requires the investigator to perform a sequence of cointegration tests. However, as was shown in Johansen (1992), this type of sequential procedure does not lead to consistent estimation of the cointegrating rank. Moreover, these methods take as given the correct specification of the lag order of the VAR, though in actual applications the true lag length is rarely known, Simulation studies by Toda and Phillips (1994) and Chao (1993), on the other hand, have shown that test performance of these procedures can be adversely affected by lag misspecification. This paper addresses these issues by extending the analysis of Phillips and Ploberger (1996) on the Posterior Information Criterion (PIC) to a partially nonstationary vector autoregressive process with reduced rank structure. This extension allows lag length and cointegrating rank to be jointly selected by the criterion, and it leads to the consistent estimation of both. In addition, we also evaluate the finite sample performance of PIC relative to existing model selection procedures, BIC and AIC, through a Monte Carlo study. Results here show PIC to perform at least as well and sometimes better than the other two methods in all the cases examined.Cointegrating rank, information criterion, order selection, PIC, reduced rank regression, vector autoregression

Jeffreys Prior Analysis of the Simultaneous Equations Model in the Case with n + 1 Endogenous Variables

This paper analyzes the behavior of posterior distributions under the Jeffreys prior in a simultaneous equations model. The case under study is that of a general limited information setup with n +1 endogenous variables. The Jeffreys prior is shown to give rise to a marginal posterior density which has Cauchy-like tails similar to that exhibited by the exact finite sample distribution of the corresponding LIML estimator. A stronger correspondence is established in the special case of a just-identified orthonormal canonical model, where the posterior density under the Jeffreys prior is shown to have the same functional form as the density of the finite sample distribution of the LIML estimator. The work here generalizes that of Chao and Phillips (1997), which gives analogous results for the special case of two endogenous variables

Fish passage hydrodynamics New Zealand context

New Zealand is home to 57 native freshwater fish species, of which a considerable number are diadromous, having to move between freshwater and saltwater at least once during their lifecycle. The economic utilisation of New Zealand rivers has largely been carried out without fish migration behaviour in mind, resulting in thousands of structures that prevent fish migration up- and downriver. Remediation of existing structures, especially culverts, and construction of new, more fish friendly, structures requires in-depth knowledge of the needs of the target fish species. In April 2018, the New Zealand Fish Passage Guidelines were released, providing a design framework to enable fish passage in new and existing structures. In support of the new guidance, our project aims to gain insight into the swimming behaviour and performance of inanga (Galaxias maculatus) under various hydraulic conditions, in particular when swimming upstream, which is not well understood. For this purpose, we are designing a new experimental setup in a 600 mm wide flume at the Water Engineering Laboratory at the University of Auckland. We will study hydrodynamics of fish passes with roughened surfaces, baffles and energy dissipators. We will evaluate sensor equipment used to enable flow and fish tracking, with the intention of tracking individual inanga at critical cross sections. This will allow us to study fish response to turbulence, boundary layers, resting zones and wetted margins. We aim to gain valuable insight into design methods and materials that best help inanga, and potentially other members of the family Galaxiidae, with their migration. Eventually, the project aims to provide guidelines suitable for retrofitting existing and building new structures

Tracing the String: BMN correspondence at Finite J^2/N

Employing the string bit formalism of hep-th/0209215, we identify the basis transformation that relates BMN operators in N=4 gauge theory to string states in the dual string field theory at finite g_2=J^2/N. In this basis, the supercharge truncates at linear order in g_2, and the mixing amplitude between 1 and 2-string states precisely matches with the (corrected) answer of hep-th/0206073 for the 3-string amplitude in light-cone string field theory. Supersymmetry then predicts the order g_2^2 contact term in the string bit Hamiltonian. The resulting leading order mass renormalization of string states agrees with the recently computed shift in conformal dimension of BMN operators in the gauge theory.Comment: 11 pages, 1 figur