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Protein-coding genetic variants that strongly affect disease risk can provide important clues into disease pathogenesis. Here we report an exome sequence analysis of 20,791 type 2 diabetes (T2D) cases and 24,440 controls from five ancestries. We identify rare (minor allele frequency30 SLC30A8 alleles, and (b) within 12 gene sets, including those corresponding to T2D drug targets (p=6.1×10−3) and candidate genes from knockout mice (p=5.2×10−3). Within our study, the strongest T2D rare variant gene-level signals explain at most 25% of the heritability of the strongest common single-variant signals, and the rare variant gene-level effect sizes we observe in established T2D drug targets will require 110K-180K sequenced cases to exceed exome-wide significance. To help prioritize genes using associations from current smaller sample sizes, we present a Bayesian framework to recalibrate association p-values as posterior probabilities of association, estimating that reaching ppwww.type2diabetesgenetics.org.

We screened DNA sequence variants on an exome-focused genotyping array in >300,000 participants with replication in >280,000 participants and identified 444 independent variants in 250 loci significantly associated with total cholesterol (TC), high-density lipoprotein cholesterol (HDL-C), low-density lipoprotein cholesterol (LDL-C), and/or triglycerides (TG). At two loci (JAK2 and A1CF), experimental analysis in mice revealed lipid changes consistent with the human data. We utilized mapped variants to address four clinically relevant questions and found the following: (1) beta-thalassemia trait carriers displayed lower TC and were protected from coronary artery disease; (2) outside of the CETP locus, there was not a predictable relationship between plasma HDL-C and risk for age-related macular degeneration; (3) only some mechanisms of lowering LDL-C seemed to increase risk for type 2 diabetes; and (4) TG-lowering alleles involved in hepatic production of TG-rich lipoproteins (e.g., TM6SF2, PNPLA3) tracked with higher liver fat, higher risk for type 2 diabetes, and lower risk for coronary artery disease whereas TG-lowering alleles involved in peripheral lipolysis (e.g., LPL, ANGPTL4) had no effect on liver fat but lowered risks for both type 2 diabetes and coronary artery disease.

The meta-frontier framework has been used extensively for evaluating the technical efficiency of heterogeneous production units that can be classified into different groups. This paper shows how the framework can also be used to make total factor productivity (TFP) comparisons within and across groups. The paper develops a new measure of the distance between a group frontier and the meta-frontier (the so-called ‘technology gap’). It then shows how a spatially- and temporally-transitive TFP index can be decomposed into measures of global technical change (measuring movements in the metafrontier), local technical change (measuring movements in the group frontiers) and efficiency change (measuring movements towards or around the group frontiers). To illustrate the methodology, the paper examines the productive performance of road authorities responsible for maintaining interstate highways in the US state of Virginia.

The Bureau of Labor Statistics measures productivity change using an index formula that fails a transitivity test. This means the Bureau is likely to report productivity changes even when outputs and inputs in different (non-adjacent) periods are identical. I use alternative formulas that i) satisfy all economically-relevant tests from index theory, and ii) can be decomposed into measures of technical change and efficiency change. I find the main sources of productivity change are scale and mix efficiency change. This supports the view that firms are technically efficient and rationally change their production plans in response to changes in (expected) prices.

The economically-relevant characteristics of multi-input multi-output production technologies can be represented using distance functions. The econometric approach to estimating these functions typically involves factoring out one of the outputs or inputs and estimating the resulting equation using maximum likelihood methods. A problem with this approach is that the outputs or inputs that are not factored out may be correlated with the composite error term. Fernandez, Koop and Steel (2000, p. 58) have developed a Bayesian solution to this so-called ‘endogeneity’ problem. O'Donnell (2007) has adapted the approach to the estimation of directional distance functions. This paper shows how the approach can be used to estimate Shephard (1953) distance functions and an associated index of total factor productivity (TFP) change. The TFP index is a new multiplicatively-complete index that satisfies most, if not all, economically-relevant tests and axioms from index number theory. The fact that it is multiplicatively-complete means it can be exhaustively decomposed into a measure of technical change and various measures of efficiency change. The decomposition can be implemented without the use of price data and without making any assumptions concerning either the optimising behaviour of firms or the degree of competition in product markets. The methodology is illustrated using state-level quantity data on U.S. agricultural inputs and outputs over the period 1960-2004. Results are summarised in terms of the characteristics (e.g., means) of estimated probability densities for measures of TFP change, technical change and output-oriented measures of efficiency change.

In industry sectors where market prices are unavailable it is common to represent multiple-input multiple-output production technologies using distance functions. Econometric estimation of such functions is complicated by the fact that more than one variable in the function may be endogenous. In such cases, maximum likelihood estimation can lead to biased and inconsistent estimates of the model parameters and associated measures of firm performance. We solve the problem by using linear programming to construct a quantity index. The distance function is then written in the form of a conventional stochastic frontier model where the explanatory variables are unambiguously exogenous. We use this approach to estimate productivity indexes and support (or shadow) prices for a sample of Australian public hospitals. We decompose the productivity index into several measures of environmental change and efficiency change. We find that the productivity effects of improvements in input-oriented technical efficiency have been largely offset by the effects of deteriorations in the production environment over time.

Chambers and Quiggin (2000) have used state-contingent production theory to establish important results concerning economic behaviour in the presence of uncertainty, including problems of consumer choice, the theory of the firm, and principal-agent relationships. Empirical application of the state contingent approach has proved difficult, not least because most of the data needed for applying standard econometric methods are lost in unrealized states of the world. O’Donnell and Griffiths (2006) show how a restrictive type of state-contingent technology can be estimated in a finite mixtures framework. This paper shows how Bayesian methodology can be used to estimate more flexible types of state-contingent technologies.

Profitability change can be decomposed into the product of a total factor productivity (TFP) index and an index of relative price change. O’Donnell (2008) shows that the TFP index can be further decomposed into an index of technical change and various indexes of efficiency change – these indexes measure changes in productivity resulting from movements in the production frontier, movements by firms towards the frontier, and movements by firms around the frontier to capture economies of scale and scope. The O’Donnell decomposition methodology can be applied in any multiple-input multiple-output setting, it makes no assumptions concerning the optimising behaviour of firms or the degree of competition in product markets, and it only involves components that can be unambiguously interpreted as measures of either technical change or efficiency change. This paper uses the methodology to decompose spatially - and temporally-transitive Lowe indexes of TFP change in U.S. agriculture for the period 1960-2004. To implement the methodology, data envelopment analysis (DEA) is used to estimate separate production frontiers for each of the ten farm production regions identified by the USDA Economic Research Service (ERS). California and Florida are found to be the most profitable and productive states. In most states, the main drivers of TFP change over the 45-year study period appear to have been technical change and scale and mix efficiency change. For example, Texas is found to have experienced a 40% increase in productivity due to technical change and a 32% increase in productivity due to economies of scale and scope, resulting in an overall productivity increase of 1.40 ! 1.32 – 1 = 85%; in Tennessee, the combined effects of technical progress (122%), technical efficiency improvement (1%) and diseconomies of scale and scope (-24%) resulted in an net productivity increase of 2.22 ! 1.01 ! 0.76 – 1 = 70%.

DPIN Version 1.0 is a fast user†friendly program for computing and Decomposing Productivity Index Numbers. The program uses the conceptual framework developed by O'Donnell (2008) and the data envelopment analysis (DEA) programs developed by O'Donnell (2009). This paper describes the conceptual framework and the main features of the software.