A Study About The Modification And Sampling-based Estimation Of Engel Coefficient

As an important criterion to measure the wealth of a country or region, it has been widely used since its introduction. However, it shows a great inadaptability when the engel coefficient is used to judge the residents' living standards of our country. The engel coefficient does not adequately measure the level the residents' living standards of our country.At first, this paper describes a series of inadaptability to our country's economic. It descends too quickly in vertical comparison, it overrates the residents'living standards of our country. And engel coefficient does not correspond to the wealth of different regions in horizontal comparison. And this paper also analyses the reason of its inadaptability.Then through summarizing previous research results, aiming at the reasons of inadaptability to the economic of our country, this paper brings forward the modified formula. According to the different functions of different kinds of food, this paper brings forward two kinds of engel coefficients. In general, the disposable income is high in rich regions and with disposable income low in poor regions. So this paper analyses the different function of two kinds of engel coefficient based on the Mutual relations of disposable income and two kinds of engel coefficients, and then brings forward the modified formula. Besides that, this paper also provides an instance to prove that the modified engel coefficient is more suitable, and it can reflect the residents'living level of our country more efficiently.At last, this paper proposes the method of sampling-based estimation of engel coefficient. As engel coefficient is ratio of food payout and consumption payout, food payout is part of consumption payout. This paper gives the general ratio estimator of engel coefficient and the statistical properties of the estimator which are bias of the estimator, mean square error of the estimator and estimation of mean square error of the estimator, then does interval estimation and hypothesis test. This paper also gives the method of comparing the engel coefficient of different regions in the same stages or different stages in the same regions, and in the end of the paper, it gives an instance to prove.