Trends in COVID-19 Infected Cases and Deaths Based on Parametric and Nonparametric Regression Models

The present investigation was carried out to study the trends in COVID-19 infected cases and deaths based on the parametric, exponential smoothing and non-parametric regression models by using COVID-19 cumulative infected cases and deaths due to infections The statistically most suited parametric models are selected based on the highest adjusted R2, significant regression co-efficient and co-efficient of determination (R2). Appropriate model is selected based on the model performance measures such as, Root Mean Square Error, Mean Absolute Error, Mean Absolute Percentage Error, assumptions of normality and independence of residuals. Nonparametric estimates of underlying growth functions are computed at each and every time points.

Effectiveness of Auctions in Securing Price Support for Farmers: The Case of a Grain Market in India

This paper reviews rice procurement operations of Government of India from the standpoints of cost of procurement as well as effectiveness in supporting farmers’ incomes. The two channels in use for procuring rice till 2015, were custom milling of rice and levy. In the first, the government bought paddy directly from farmers at the minimum support price (MSP) and got it milled from private millers; while in the second, it purchased rice from private millers at a pre-announced levy price thus providing indirect price support to farmers. Secondary data reveal that levy, despite implying lower cost of procurement was discriminated against till about a decade back and eventually abolished in 2015 in favor of custom milling, better trusted to provide minimum price support. We analyze data from auctions of paddy from a year when levy was still important to investigate its impact on farmers’ revenues. We use semi-nonparametric estimates of millers’ values to simulate farmers’ expected revenues and find these to be rather close to the MSP; a closer analysis shows that bidder competition is critical to this result. Finally, we use our estimates to quantify the impact of change in levy price on farmers’ revenues and use this to discuss ways to revive the levy channel.

A Nonparametric Hawkes Model for Forecasting California Seismicity

ABSTRACT A variety of nonparametric models have been proposed for estimating earthquake triggering. We investigate the ability of the model-independent stochastic declustering method developed by Marsan and Lengliné (2008) to estimate variable spatial triggering that can vary with direction, magnitude, and region. We develop an approach for local fault estimation and demonstrate forecasting methods that use the nonparametric estimates. Simulation studies are conducted to verify the effectiveness of the method, and the nonparametric estimates are applied to a California earthquake catalog. Model forecast performance is evaluated retrospectively by comparing our models with the long-term forecast of Helmstetter et al. (2007), using both deviance and Voronoi residuals. We show improved performance compared with Helmstetter et al. (2007) in various regions while using a full nonparametric estimation and forecasting approach.

Theoretical and empirical Lorenz functions, Gini indices, and their properties

The issues of assessing the fairness and efficiency of the distribution of the total income of society between different groups of the population have attracted attention of scientists for a long time. They became most relevant at the end of the 19th – beginning of the 20th centuries in connection with the intensive stratification of countries with various political and social systems caused by the intensive development of the economy, science and technology. The Lorenz function and the Lorenz curve, as well as the Gini index, are commonly used for theoretical research and applications in the economic and social sciences. These tools were originally introduced to describe and study the inequality in the incomes and wealth distribution among a given population. Nowadays they have found wide application in such fields as demography, insurance, healthcare, the risk and reliability theory, as well as in other areas of human activities. In this paper we present the properties of the Lorentz function and various representations of the Gini index, systematize the analytical results for uniform, exponential, power-law (types I and II) and lognormal distributions, as well as for the Pareto distribution (types I and II). Additionally, the issue of estimating inequality based on the Pietra index and its relationship with the Lorentz function was studied. Nonparametric estimates of the Lorentz function and the Gini index based on a sample from the corresponding distribution are considered. Strict consistency and asymptotic unbiasedness of these estimates are shown under certain conditions for the initial distribution with an increase in the sample size. On the basis of the method of linearization of estimates, the asymptotic normality of the empirical Lorentz function and the empirical Gini index is determined.

Nonparametric estimation of a primary care production function in urban Brazil

Background The Brazilian public health system is one of the largest health systems in the world, with a mandate to deliver medical care to more than 200 million Brazilians. The objective of this study is to estimate a production function for primary care in urban Brazil. Our goal is to use flexible estimates to identify heterogeneous returns and complementarities between medical capital and labor. Methods We use a large dataset from 2012 to 2016 (with more than 400 million consultations, 270 thousand physicians, and 11 thousand clinics) to nonparametrically estimate a primary care production function and calculate the elasticity of doctors’ visits (output) to two inputs: capital stock (number of clinics) and labor (number of physicians). We benchmark our nonparametric estimates against estimates of a Cobb-Douglas (CD) production function. The CD model was chosen as a baseline because it is arguably the most popular parametric production function model. By comparing our nonparametric results with those from the CD model, our paper shed some light on the limitations of the parametric approach, and on the novelty of nonparametric insights. Results The nonparametric results show significantly heterogeneity of returns to both capital and labor, depending on the scale of operation. We find that diseconomies of scale, diminishing returns to scale, and increasing returns to scale are possible, depending on the input range. Conclusions The nonparametric model identifies complementarities between capital and labor, which is essential in designing efficient policy interventions. For example, we find that the response of primary care consultations to labor is steeper when capital level is high. This means that, if the goal is to allocate labor to maximize increases in consultations, adding physicians in cities with a high number of clinics is preferred to allocating physicians to low medical infrastructure municipalities. The results highlight how the CD model hides useful policy information by not accounting for the heterogeneity in the data.

A Consistent Nonparametric Test for Granger Non-Causality Based on the Transfer Entropy

To date, testing for Granger non-causality using kernel density-based nonparametric estimates of the transfer entropy has been hindered by the intractability of the asymptotic distribution of the estimators. We overcome this by shifting from the transfer entropy to its first-order Taylor expansion near the null hypothesis, which is also non-negative and zero if and only if Granger causality is absent. The estimated Taylor expansion can be expressed in terms of a U-statistic, demonstrating asymptotic normality. After studying its size and power properties numerically, the resulting test is illustrated empirically with applications to stock indices and exchange rates.

Testing exogeneity in nonparametric instrumental variables models identified by conditional quantile restrictions

Summary This paper presents a test for exogeneity of explanatory variables in a nonparametric instrumental variables (IV) model whose structural function is identified through a conditional quantile restriction. Quantile regression models are increasingly important in applied econometrics. As with mean-regression models, an erroneous assumption that the explanatory variables in a quantile regression model are exogenous can lead to highly misleading results. In addition, a test of exogeneity based on an incorrectly specified parametric model can produce misleading results. This paper presents a test of exogeneity that does not assume that the structural function belongs to a known finite-dimensional parametric family and does not require estimation of this function. The latter property is important because nonparametric estimates of the structural function are unavoidably imprecise. The test presented here is consistent whenever the structural function differs from the conditional quantile function on a set of nonzero probability. The test has nontrivial power uniformly over a large class of structural functions that differ from the conditional quantile function by $O({n^{ - 1/2}})$. The results of Monte Carlo experiments and an empirical application illustrate the performance of the test.

LIKELIHOOD INFERENCE ON SEMIPARAMETRIC MODELS WITH GENERATED REGRESSORS

Hahn and Ridder (2013, Econometrica 81, 315–340) formulated influence functions of semiparametric three-step estimators where generated regressors are computed in the first step. This class of estimators covers several important examples for empirical analysis, such as production function estimators by Olley and Pakes (1996, Econometrica 64, 1263–1297) and propensity score matching estimators for treatment effects by Heckman, Ichimura, and Todd (1998, Review of Economic Studies 65, 261–294). The present article studies a nonparametric likelihood-based inference method for the parameters in such three-step estimation problems. In particular, we apply the general empirical likelihood theory of Bravo, Escanciano, and van Keilegom (2018, Annals of Statistics, forthcoming) to modify semiparametric moment functions to account for influences from plug-in estimates into the above important setup, and show that the resulting likelihood ratio statistic becomes asymptotically pivotal without undersmoothing in the first and second step nonparametric estimates.