Polytomies and bayesian phylogenetic inference

Bayesian phylogenetic analyses are now very popular in systematics and molecular evolution because they allow the use of much more realistic models than currently possible with maximum likelihood methods. There are, however, a growing number of examples in which large Bayesian posterior clade probabilities are associated with very short edge lengths and low values for non-Bayesian measures of support such as nonparametric bootstrapping. For the four-taxon case when the true tree is the star phylogeny, Bayesian analyses become increasingly unpredictable in their preference for one of the three possible resolved tree topologies as data set size increases. This leads to the prediction that hard (or near-hard) polytomies in nature will cause unpredictable behavior in Bayesian analyses, with arbitrary resolutions of the polytomy receiving very high posterior probabilities in some cases. We present a simple solution to this problem involving a reversible-jump Markov chain Monte Carlo (MCMC) algorithm that allows exploration of all of tree space, including unresolved tree topologies with one or more polytomies. The reversible-jump MCMC approach allows prior distributions to place some weight on less-resolved tree topologies, which eliminates misleadingly high posteriors associated with arbitrary resolutions of hard polytomies. Fortunately, assigning some prior probability to polytomous tree topologies does not appear to come with a significant cost in terms of the ability to assess the level of support for edges that do exist in the true tree. Methods are discussed for applying arbitrary prior distributions to tree topologies of varying resolution, and an empirical example showing evidence of polytomies is analyzed and discussed.

Polytomies and bayesian phylogenetic inference

Bayesian phylogenetic analyses are now very popular in systematics and molecular evolution because they allow the use of much more realistic models than currently possible with maximum likelihood methods. There are, however, a growing number of examples in which large Bayesian posterior clade probabilities are associated with very short edge lengths and low values for non-Bayesian measures of support such as nonparametric bootstrapping. For the four-taxon case when the true tree is the star phylogeny, Bayesian analyses become increasingly unpredictable in their preference for one of the three possible resolved tree topologies as data set size increases. This leads to the prediction that hard (or near-hard) polytomies in nature will cause unpredictable behavior in Bayesian analyses, with arbitrary resolutions of the polytomy receiving very high posterior probabilities in some cases. We present a simple solution to this problem involving a reversible-jump Markov chain Monte Carlo (MCMC) algorithm that allows exploration of all of tree space, including unresolved tree topologies with one or more polytomies. The reversible-jump MCMC approach allows prior distributions to place some weight on less-resolved tree topologies, which eliminates misleadingly high posteriors associated with arbitrary resolutions of hard polytomies. Fortunately, assigning some prior probability to polytomous tree topologies does not appear to come with a significant cost in terms of the ability to assess the level of support for edges that do exist in the true tree. Methods are discussed for applying arbitrary prior distributions to tree topologies of varying resolution, and an empirical example showing evidence of polytomies is analyzed and discussed.

Some Identification Issues in Nonparametric Linear Models with Endogenous Regressors

In applied work economists often seek to relate a given response variable y to some causal parameter mu* associated with it. This parameter usually represents a summarization based on some explanatory variables of the distribution of y, such as a regression function, and treating it as a conditional expectation is central to its identification and estimation. However, the interpretation of mu* as a conditional expectation breaks down if some or all of the explanatory variables are endogenous. This is not a problem when mu* is modelled as a parametric function of explanatory variables because it is well known how instrumental variables techniques can be used to identify and estimate mu*. In contrast, handling endogenous regressors in nonparametric models, where mu* is regarded as fully unknown, presents di±cult theoretical and practical challenges. In this paper we consider an endogenous nonparametric model based on a conditional moment restriction. We investigate identification related properties of this model when the unknown function mu* belongs to a linear space. We also investigate underidentification of mu* along with the identification of its linear functionals. Several examples are provided in order to develop intuition about identification and estimation for endogenous nonparametric regression and related models.

Direct and Indirect Measures of Capacity Utilization: A Nonparametric Analysis of U.S. Manufacturing

We measure the capacity output of a firm as the maximum amount producible by a firm given a specific quantity of the quasi-fixed input and an overall expenditure constraint for its choice of variable inputs. We compute this indirect capacity utilization measure for the total manufacturing sector in the US as well as for a number of disaggregated industries, for the period 1970-2001. We find considerable variation in capacity utilization rates both across industries and over years within industries. Our results suggest that the expenditure constraint was binding, especially in periods of high interest rates.

GMM Based Inference with Standard Stratified Samples when the Aggregate Shares are Known

We show how to do efficient moment based inference using the generalized method of moments (GMM) when data is collected by standard stratified sampling and the maintained assumption is that the aggregate shares are known.

Efficiency Bounds for Estimating Linear Functionals of Nonparametric Regression Models with Endogenous Regressors

Consider a nonparametric regression model Y=mu*(X) + e, where the explanatory variables X are endogenous and e satisfies the conditional moment restriction E[e|W]=0 w.p.1 for instrumental variables W. It is well known that in these models the structural parameter mu* is 'ill-posed' in the sense that the function mapping the data to mu* is not continuous. In this paper, we derive the efficiency bounds for estimating linear functionals E[p(X)mu*(X)] and int_{supp(X)}p(x)mu*(x)dx, where p is a known weight function and supp(X) the support of X, without assuming mu* to be well-posed or even identified.

Moment Based Inference with Stratified Data

Many datasets used by economists and other social scientists are collected by stratified sampling. The sampling scheme used to collect the data induces a probability distribution on the observed sample that differs from the target or underlying distribution for which inference is to be made. If this effect is not taken into account, subsequent statistical inference can be seriously biased. This paper shows how to do efficient semiparametric inference in moment restriction models when data from the target population is collected by three widely used sampling schemes: variable probability sampling, multinomial sampling, and standard stratified sampling.

Liberalization, Ownership, and Efficiency in Indian Banking: A Nonparametric Approach

This paper empirically estimates and analyzes various efficiency scores of Indian banks during 1997-2003 using data envelopment analysis (DEA). During the 1990s India's financial sector underwent a process of gradual liberalization aimed at strengthening and improving the operational efficiency of the financial system. It is observed, none the less, that Indian banks are still not much differentiated in terms of input or output oriented technical efficiency and cost efficiency. However, they differ sharply in respect of revenue and profit efficiencies. The results provide interesting insight into the empirical correlates of efficiency scores of Indian banks. Bank size, ownership, and the fact of its being listed on the stock exchange are some of the factors that are found to have positive impact on the average profit efficiency and to some extent revenue efficiency scores are. Finally, we observe that the median efficiency scores of Indian banks in general and of bigger banks in particular have improved considerably during the post-reform period.

Are Indian Firms too Small? A Nonparametric Analysis of Cost Efficiency and Industry Structure of Indian Manufacturing

In this paper we use the 2004-05 Annual Survey of Industries data to estimate the levels of cost efficiency of Indian manufacturing firms in the various states and also get state level measures of industrial organization (IO) efficiency. The empirical results show the presence of considerable cost inefficiency in a majority of the states. Further, we also find that, on average, Indian firms are too small. Consolidating them to attain the optimal scale would further enhance efficiency and lower average cost.

Technical Efficiency in the Indian Textiles Industry: A Nonparametric Analysis of Firm-Level Data

The Indian textiles industry is now at the crossroads with the phasing out of quota regime that prevailed under the Multi-Fiber Agreement (MFA) until the end of 2004. In the face of a full integration of the textiles sector in the WTO, maintaining and enhancing productive efficiency is a precondition for competitiveness of the Indian firms in the new liberalized world market. In this paper we use data obtained from the Annual Survey of Industries for a number of years to measure the levels of technical efficiency in the Indian textiles industry at the firm level. We use both a grand frontier applicable to all firms and a group frontier specific to firms from any individual state, ownership, or organization type in order to evaluate their efficiencies. This permits us to separately identify how locational, proprietary, and organizational characteristics of a firm affect its performance.

Reputation and Efficiency: A Nonparametric Assessment of America's Top-Rated MBA Programs

Widely publicized reports of fresh MBAs getting multiple job offers with six-figure annual salaries leave a long-lasting general impression about the high quality of selected business schools. While such spectacular achievement in job placement rightly deserves recognition, one should not lose sight of the resources expended in order to accomplish this result. In this study, we employ a measure of Pareto-Koopmans global efficiency to evaluate the efficiency levels of the MBA programs in Business Week's top-rated list. We compute input- and output-oriented radial and non-radial efficiency measures for comparison. Among three tier groups, the schools from a higher tier group on average are more efficient than those from lower tiers, although variations in efficiency levels do occur within the same tier, which exist over different measures of efficiency.

Nonparametric Measures of Capacity Utilization: A Dual Approach

This paper develops a nonparametric method of obtaining the minimum of the long run average cost curve of a firm to define its capacity output. This provides a benchmark for measuring of capacity utilization at the observed output level of the firm. In the case of long run constant returns to scale, the minimum of the short run average cost curve is determined to measure short run capacity utilization. An empirical application measures yearly rates of capacity utilization in U.S. manufacturing over the period 1968-1998. Nonparametric determination of the short run average cost curve under variable returns to scale using an iterative search procedure is described in an appendix to this paper.