Ratios of Parameters: Some Econometric Examples (original) (raw)
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Confidence Intervals for Ratios: Econometric Examples with Stata
Social Science Research Network, 2018
Ratios of parameter estimates are often used in econometric applications. However, the test of these ratios when estimated can cause difficulties since the ratio of asymptotically normally distributed random variables have a Cauchy distribution for which there are no finite moments. This paper presents a method for the estimation of confidence intervals based on the Fieller approach that has been shown to be preferable to the usual Delta method. Using example applications in both Stata and R, we demonstrate that a few extra steps in the examination of the estimate of the ratio may provide a confidence interval with superior coverage.
This chapter presents the econometric methods that are used in health economics to model individuals health care costs. These methods are used for prediction, projection and forecasting, in the context of risk adjustment, resource allocation, technology assessment and policy evaluation. The chapter reviews the literature on the comparative performance of the methods, especially in the context of forecasting individual health care costs, and concludes with an empirical case study.
Providing Intuition to the Fieller Method with Two Geometric Representations using STATA and EVIEWS
SSRN Electronic Journal, 2000
The Fieller Method for the construction of confidence intervals for ratios of the expected value of two normally distributed random variables has been shown by a number of authors to be a superior method to the delta approximation. However, it is not widely used due in part, to the tendency to present the intervals only in a formula context. In addition, potential users have been deterred by the potential difficulty in interpreting non-finite confidence intervals when the confidence level is less than 100%. In this paper we present two graphical methods which can be easily constructed using two widely used statistical software packages (Eviews and Stata) for the representation of the Fieller intervals. An application is presented to assess the results of a model of the non-accelerating inflation rate of unemployment (NAIRU).
Non-Standard Confidence Sets for Ratios and Tipping Points with Applications to Dynamic Panel Data
Annals of Economics and Statistics, 2019
We study estimation uncertainty when the object of interest contains one or more ratios of parameters. The ratio of parameters is a discontinuous parameter transformation; it has been shown that traditional confidence intervals often fail to cover this true ratio with very high probability. Constructing confidence sets for ratios using Fieller's method is a viable solution as the method can avoid the discontinuity problem. This paper proposes an extension of the multivariate Fieller method beyond standard estimators, focusing on asymptotically mixed normal estimators that commonly arise in dynamic panel polynomial regression with persistent covariates. We discuss the cases where the underlying estimators converge to various distributions, depending on the persistence level of the covariates. We show that the asymptotic distribution of the pivotal statistic used for constructing a Fieller's confidence set remains a standard Chi-squared distribution regardless of rates of convergence, thus the rates are being 'self-normalized' and can be unknown. A simulation study illustrates the finite sample properties of the proposed method in a dynamic polynomial panel. Our method is demonstrated to work well in small samples, even when the persistence coefficient is unity.
Comparison of Regression Estimator and Ratio Estimator: A Simulation Study
2017
We compared ratio and regression estimators empirically based on bias and coefficient of variation. Simulation studies accounting for sampling rate, population size, heterogeneity of the auxiliary variable x, deviation from linearity and model misspecification were conducted. The study shows that ratio estimator is better than regression estimators when regression line is close to the origin. Ratio and regression estimators still work even if there is a weak linear relationship between x and y, provided that there is minimal, if not absent, model misspecification. When the relationship between the target variable and the auxiliary variable is very weak, bootstrap estimates yield lower bias. Regression estimator is generally more efficient than ratio estimator.
COMPARATIVE ANALYSIS OF SOME SELECTED CLASSES OF RATIO ESTIMATORS
Many ratio type estimators for population mean have come into play in the past. Researchers over the years have been making efforts to improve the efficiency of thee estimators. There has been a lot of modification of some of these estimators. Some forms of comparison have been done in the literature. There is need to further compare these estimators with other existing estimators at varying sample sizes and also considering discrete and continuous distribution. Thirty-eight estimators, five different sample sizes and seven distributions were considered. The population mean estimates and their Bias were computed for the thirty-eight estimators at varying sample sizes under various distribution. The efficiency of the estimator was computed using Mean Square Error (MSE). Using simulation study, it was observed that the efficiency of the estimators increase as sample sizes increases and the estimator performed alike in most distributions.
Likelihood-based Inference for the Ratios of Regression Coefficients in Linear Models
Annals of the Institute of Statistical Mathematics, 2006
We consider the standard linear multiple regression model in which the parameter of interest is the ratio of two regression coefficients. Our setup includes a broad range of applications. We show that the 1 − α confidence interval for the interest parameter based on the profile, conditional profile, modified profile or adjusted profile likelihood can potentially become the entire real line, while appropriately chosen integrated likelihoods do not suffer from this drawback. We further explore the asymptotic length of confidence intervals in order to compare integrated likelihood-based proposals. The analysis is facilitated by an orthogonal parameterization.
Comparison of Two Ratio Estimators Using Auxiliary Information
IOSR Journal of Mathematics, 2016
This study is conducted to compare two ratio estimators that use auxiliary information. The estimators are Olkin average ratio estimator and Kadilar-Cingi estimator. Efficiencies of the estimators are investigated theoretically and using data from Federal Inland Revenue Service Revenue House Store. The result shows Kadilar-Cingi estimator is more efficient than Olkin estimator.
2014
The present study proposes improved ratio estimator by utilizing the estimator of Ray and Singh (1981) in simple random sampling. We calculate Mean square error (MSE) and compared it with other existing estimators. Theoretical result is supported by a numerical illustration .