Convergence of the mass-transport steepest descent scheme for the sub-critical Patlak-Keller-Segel model

Variational steepest descent approximation schemes for the modified Patlak-Keller-Segel equation with a logarithmic interaction kernel in any dimension are considered. We prove the convergence of the suitably interpolated in time implicit Euler scheme, defined in terms of the Euclidean Wasserstein distance, associated to this equation for sub-critical masses. As a consequence, we recover the recent result about the global in time existence of weak-solutions to the modified Patlak-Keller-Segel equation for the logarithmic interaction kernel in any dimension in the sub-critical case. Moreover, we show how this method performs numerically in one dimension. In this particular case, this numerical scheme corresponds to a standard implicit Euler method for the pseudo-inverse of the cumulative distribution function. We demonstrate its capabilities to reproduce easily without the need of mesh-refinement the blow-up of solutions for super-critical masses.

Do institutions matter for economic fluctuations? Weak property rights in a business cycle model for Mexico

This paper shows that introducing weak property rights in the standard real business cycle (RBC) model can help to explain economic fluctuations. This is motivated by the empirical observation that changes in institutions in emerging markets are related to the evolution of the main macroeconomic variables. In particular, in Mexico, the movements in productivity in the data are associated with changes in institutions, so that we can explain productivity shocks to a large extent as shocks to the quality of institutions. We find that the model with shocks to the degree of protection of property rights only - without technology shocks - can match the second moments in the data for Mexico well. In particular, the fit is better than that of the standard neoclassical model with full protection of property rights regarding the auto-correlations and cross-correlations in the data, especially those related to labor. Viewing productivity shocks as shocks to institutions is also consistent with the stylized fact of falling productivity and non-decreasing labor hours in Mexico over 1980-1994, which is a feature that the neoclassical model cannot match.

Technology shocks and aggregate fluctuations in an estimated hybrid RBC model

This paper contributes to the on-going empirical debate regarding the role of the RBC model and in particular of technology shocks in explaining aggregate fluctuations. To this end we estimate the model’s posterior density using Markov-Chain Monte-Carlo (MCMC) methods. Within this framework we extend Ireland’s (2001, 2004) hybrid estimation approach to allow for a vector autoregressive moving average (VARMA) process to describe the movements and co-movements of the model’s errors not explained by the basic RBC model. The results of marginal likelihood ratio tests reveal that the more general model of the errors significantly improves the model’s fit relative to the VAR and AR alternatives. Moreover, despite setting the RBC model a more difficult task under the VARMA specification, our analysis, based on forecast error and spectral decompositions, suggests that the RBC model is still capable of explaining a significant fraction of the observed variation in macroeconomic aggregates in the post-war U.S. economy.

Stochastic Search Variable Selection in Vector Error Correction Models with an Application to a Model of the UK Macroeconomy

This paper develops methods for Stochastic Search Variable Selection (currently popular with regression and Vector Autoregressive models) for Vector Error Correction models where there are many possible restrictions on the cointegration space. We show how this allows the researcher to begin with a single unrestricted model and either do model selection or model averaging in an automatic and computationally efficient manner. We apply our methods to a large UK macroeconomic model.

Productivity shocks and aggregate fluctuations in an estimated endogenous growth model with human capital

Employing an endogenous growth model with human capital, this paper explores how productivity shocks in the goods and human capital producing sectors contribute to explaining aggregate fluctuations in output, consumption, investment and hours. Given the importance of accounting for both the dynamics and the trends in the data not captured by the theoretical growth model, we introduce a vector error correction model (VECM) of the measurement errors and estimate the model’s posterior density function using Bayesian methods. To contextualize our findings with those in the literature, we also assess whether the endogenous growth model or the standard real business cycle model better explains the observed variation in these aggregates. In addressing these issues we contribute to both the methods of analysis and the ongoing debate regarding the effects of innovations to productivity on macroeconomic activity.

A general model to predict individual exposure to solar UV by using ambient irradiance data

Excessive exposure to solar ultraviolet (UV) is the main cause of skin cancer. Specific prevention should be further developed to target overexposed or highly vulnerable populations. A better characterisation of anatomical UV exposure patterns is however needed for specific prevention. To develop a regression model for predicting the UV exposure ratio (ER, ratio between the anatomical dose and the corresponding ground level dose) for each body site without requiring individual measurements. A 3D numeric model (SimUVEx) was used to compute ER for various body sites and postures. A multiple fractional polynomial regression analysis was performed to identify predictors of ER. The regression model used simulation data and its performance was tested on an independent data set. Two input variables were sufficient to explain ER: the cosine of the maximal daily solar zenith angle and the fraction of the sky visible from the body site. The regression model was in good agreement with the simulated data ER (R(2)=0.988). Relative errors up to +20% and -10% were found in daily doses predictions, whereas an average relative error of only 2.4% (-0.03% to 5.4%) was found in yearly dose predictions. The regression model predicts accurately ER and UV doses on the basis of readily available data such as global UV erythemal irradiance measured at ground surface stations or inferred from satellite information. It renders the development of exposure data on a wide temporal and geographical scale possible and opens broad perspectives for epidemiological studies and skin cancer prevention.

Blow-up, concentration phenomenon and global existence for the Keller-Segel model in high dimension

"Vegeu el resum a l'inici del document del fitxer adjunt."

National, regional, and global trends in fasting plasma glucose and diabetes prevalence since 1980: systematic analysis of health examination surveys and epidemiological studies with 370 country-years and 2·7 million participants.

BACKGROUND: Data for trends in glycaemia and diabetes prevalence are needed to understand the effects of diet and lifestyle within populations, assess the performance of interventions, and plan health services. No consistent and comparable global analysis of trends has been done. We estimated trends and their uncertainties in mean fasting plasma glucose (FPG) and diabetes prevalence for adults aged 25 years and older in 199 countries and territories. METHODS: We obtained data from health examination surveys and epidemiological studies (370 country-years and 2·7 million participants). We converted systematically between different glycaemic metrics. For each sex, we used a Bayesian hierarchical model to estimate mean FPG and its uncertainty by age, country, and year, accounting for whether a study was nationally, subnationally, or community representative. FINDINGS: In 2008, global age-standardised mean FPG was 5·50 mmol/L (95% uncertainty interval 5·37-5·63) for men and 5·42 mmol/L (5·29-5·54) for women, having risen by 0·07 mmol/L and 0·09 mmol/L per decade, respectively. Age-standardised adult diabetes prevalence was 9·8% (8·6-11·2) in men and 9·2% (8·0-10·5) in women in 2008, up from 8·3% (6·5-10·4) and 7·5% (5·8-9·6) in 1980. The number of people with diabetes increased from 153 (127-182) million in 1980, to 347 (314-382) million in 2008. We recorded almost no change in mean FPG in east and southeast Asia and central and eastern Europe. Oceania had the largest rise, and the highest mean FPG (6·09 mmol/L, 5·73-6·49 for men; 6·08 mmol/L, 5·72-6·46 for women) and diabetes prevalence (15·5%, 11·6-20·1 for men; and 15·9%, 12·1-20·5 for women) in 2008. Mean FPG and diabetes prevalence in 2008 were also high in south Asia, Latin America and the Caribbean, and central Asia, north Africa, and the Middle East. Mean FPG in 2008 was lowest in sub-Saharan Africa, east and southeast Asia, and high-income Asia-Pacific. In high-income subregions, western Europe had the smallest rise, 0·07 mmol/L per decade for men and 0·03 mmol/L per decade for women; North America had the largest rise, 0·18 mmol/L per decade for men and 0·14 mmol/L per decade for women. INTERPRETATION: Glycaemia and diabetes are rising globally, driven both by population growth and ageing and by increasing age-specific prevalences. Effective preventive interventions are needed, and health systems should prepare to detect and manage diabetes and its sequelae. FUNDING: Bill & Melinda Gates Foundation and WHO.

Correcting Measurement Error Bias in Interaction Models with Small Samples

Several methods have been suggested to estimate non-linear models with interaction terms in the presence of measurement error. Structural equation models eliminate measurement error bias, but require large samples. Ordinary least squares regression on summated scales, regression on factor scores and partial least squares are appropriate for small samples but do not correct measurement error bias. Two stage least squares regression does correct measurement error bias but the results strongly depend on the instrumental variable choice. This article discusses the old disattenuated regression method as an alternative for correcting measurement error in small samples. The method is extended to the case of interaction terms and is illustrated on a model that examines the interaction effect of innovation and style of use of budgets on business performance. Alternative reliability estimates that can be used to disattenuate the estimates are discussed. A comparison is made with the alternative methods. Methods that do not correct for measurement error bias perform very similarly and considerably worse than disattenuated regression

Use of Two-Part Regression Calibration Model to Correct for Measurement Error in Episodically Consumed Foods in a Single-Replicate Study Design: EPIC Case Study.

In epidemiologic studies, measurement error in dietary variables often attenuates association between dietary intake and disease occurrence. To adjust for the attenuation caused by error in dietary intake, regression calibration is commonly used. To apply regression calibration, unbiased reference measurements are required. Short-term reference measurements for foods that are not consumed daily contain excess zeroes that pose challenges in the calibration model. We adapted two-part regression calibration model, initially developed for multiple replicates of reference measurements per individual to a single-replicate setting. We showed how to handle excess zero reference measurements by two-step modeling approach, how to explore heteroscedasticity in the consumed amount with variance-mean graph, how to explore nonlinearity with the generalized additive modeling (GAM) and the empirical logit approaches, and how to select covariates in the calibration model. The performance of two-part calibration model was compared with the one-part counterpart. We used vegetable intake and mortality data from European Prospective Investigation on Cancer and Nutrition (EPIC) study. In the EPIC, reference measurements were taken with 24-hour recalls. For each of the three vegetable subgroups assessed separately, correcting for error with an appropriately specified two-part calibration model resulted in about three fold increase in the strength of association with all-cause mortality, as measured by the log hazard ratio. Further found is that the standard way of including covariates in the calibration model can lead to over fitting the two-part calibration model. Moreover, the extent of adjusting for error is influenced by the number and forms of covariates in the calibration model. For episodically consumed foods, we advise researchers to pay special attention to response distribution, nonlinearity, and covariate inclusion in specifying the calibration model.

Selected configuration interaction with truncation energy error and application to the Ne atom

Selected configuration interaction (SCI) for atomic and molecular electronic structure calculations is reformulated in a general framework encompassing all CI methods. The linked cluster expansion is used as an intermediate device to approximate CI coefficients BK of disconnected configurations (those that can be expressed as products of combinations of singly and doubly excited ones) in terms of CI coefficients of lower-excited configurations where each K is a linear combination of configuration-state-functions (CSFs) over all degenerate elements of K. Disconnected configurations up to sextuply excited ones are selected by Brown's energy formula, ΔEK=(E-HKK)BK2/(1-BK2), with BK determined from coefficients of singly and doubly excited configurations. The truncation energy error from disconnected configurations, Δdis, is approximated by the sum of ΔEKS of all discarded Ks. The remaining (connected) configurations are selected by thresholds based on natural orbital concepts. Given a model CI space M, a usual upper bound ES is computed by CI in a selected space S, and EM=E S+ΔEdis+δE, where δE is a residual error which can be calculated by well-defined sensitivity analyses. An SCI calculation on Ne ground state featuring 1077 orbitals is presented. Convergence to within near spectroscopic accuracy (0.5 cm-1) is achieved in a model space M of 1.4× 109 CSFs (1.1 × 1012 determinants) containing up to quadruply excited CSFs. Accurate energy contributions of quintuples and sextuples in a model space of 6.5 × 1012 CSFs are obtained. The impact of SCI on various orbital methods is discussed. Since ΔEdis can readily be calculated for very large basis sets without the need of a CI calculation, it can be used to estimate the orbital basis incompleteness error. A method for precise and efficient evaluation of ES is taken up in a companion paper

Intramolecular basis set superposition error effects on the planarity of benzene and other aromatic molecules: A solution to the problem

Recently, the surprising result that ab initio calculations on benzene and other planar arenes at correlated MP2, MP3, configuration interaction with singles and doubles (CISD), and coupled cluster with singles and doubles levels of theory using standard Pople’s basis sets yield nonplanar minima has been reported. The planar optimized structures turn out to be transition states presenting one or more large imaginary frequencies, whereas single-determinant-based methods lead to the expected planar minima and no imaginary frequencies. It has been suggested that such anomalous behavior can be originated by two-electron basis set incompleteness error. In this work, we show that the reported pitfalls can be interpreted in terms of intramolecular basis set superposition error (BSSE) effects, mostly between the C–H moieties constituting the arenes. We have carried out counterpoise-corrected optimizations and frequency calculations at the Hartree–Fock, B3LYP, MP2, and CISD levels of theory with several basis sets for a number of arenes. In all cases, correcting for intramolecular BSSE fixes the anomalous behavior of the correlated methods, whereas no significant differences are observed in the single-determinant case. Consequently, all systems studied are planar at all levels of theory. The effect of different intramolecular fragment definitions and the particular case of charged species, namely, cyclopentadienyl and indenyl anions, respectively, are also discussed

Global Prospects for Dairy in Argentina and Chile: Evidence from Field Visits and Model Simulations, August 2006

We assess the international competitiveness of the dairy industries in Argentina and Chile, combining recent market intelligence gathered from field visits with quantitative simulations of global policy reform scenarios. Both countries exhibit strong potential for export growth but face significant internal and external barriers to expanding their dairy industries. Global policy reforms would resolve some of the international obstacles to their expansion. Argentina has great potential, but it is handicapped by its current macroeconomic policies, trade policy distortions, and the uncertainty associated with policy implementation. Chile is more limited in terms of natural capacity for expansion, but it has a positive trade and investment environment.

Adaptive model selection using empirical complexities

Given $n$ independent replicates of a jointly distributed pair $(X,Y)\in {\cal R}^d \times {\cal R}$, we wish to select from a fixed sequence of model classes ${\cal F}_1, {\cal F}_2, \ldots$ a deterministic prediction rule $f: {\cal R}^d \to {\cal R}$ whose risk is small. We investigate the possibility of empirically assessingthe {\em complexity} of each model class, that is, the actual difficulty of the estimation problem within each class. The estimated complexities are in turn used to define an adaptive model selection procedure, which is based on complexity penalized empirical risk.The available data are divided into two parts. The first is used to form an empirical cover of each model class, and the second is used to select a candidate rule from each cover based on empirical risk. The covering radii are determined empirically to optimize a tight upper bound on the estimation error. An estimate is chosen from the list of candidates in order to minimize the sum of class complexity and empirical risk. A distinguishing feature of the approach is that the complexity of each model class is assessed empirically, based on the size of its empirical cover.Finite sample performance bounds are established for the estimates, and these bounds are applied to several non-parametric estimation problems. The estimates are shown to achieve a favorable tradeoff between approximation and estimation error, and to perform as well as if the distribution-dependent complexities of the model classes were known beforehand. In addition, it is shown that the estimate can be consistent,and even possess near optimal rates of convergence, when each model class has an infinite VC or pseudo dimension.For regression estimation with squared loss we modify our estimate to achieve a faster rate of convergence.

Comment to "Weak instruments robust tests in GMM and the New Keynesian Phillips curve" by Frank Kleibergen and Sophocles Mavroeidis

I discuss the identifiability of a structural New Keynesian Phillips curve when it is embedded in a small scale dynamic stochastic general equilibrium model. Identification problems emerge because not all the structural parameters are recoverable from the semi-structural ones and because the objective functions I consider are poorly behaved. The solution and the moment mappings are responsible for the problems.