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Words 5119

Pages 21

Nonparametric Estimation and Hypothesis Testing in Econometric Models

By A. Ullah ~

Abstract: In this paper we systematically review and develop nonparametric estimation and testing techniques in the context of econometric models. The results are discussed under the settings of regression model and kernel estimation, although as indicated in the paper these results can go through for other econometric models and for the nearest neighbor estimation. A nontechnical survey of the asymptotic properties of kernel regression estimation is also presented. The technique described in the paper are useful for the empirical analysis of the economic relations whose true functional forms are usually unknown.

1 Introduction

Consider an economic model

y =R(x)+u where y is a dependent variable, x is a vector o f regressors, u is the disturbance and

R(x) = E ( y l x ) . Often, in practice, the estimation o f the derivatives o f R(x)are o f interest. For example, the first derivative indicates the response coefficient (regression coefficient) o f y with respect to x, and the second derivauve indicates the curvature o f

R(x). In the parametric econometrics the estimation o f these derivatives and testing

1 Aman Ullah, Department of Economics, University of Western Ontario, London, Ontario, N6A 5C2, Canada. I thank L Ahmad, A. Bera, A. Pagan, C. Robinson, A. Zellner, and the participants of the workshops at the Universities of Chicago, Northern Illinois, Stanford, Riverside and Santa Barbara, for their comments on the subject matter of this paper. The work on this paper was done when the author was a vising scholar at the Stanford University. The SSHRC research grant and research facilities at the Stanford University are gratefully acknowledged.

0377-7332/88/3-4/223-249 $2.50 9 1988 Physica-Verlag, Heidelberg

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...Hypothesis Testing: One Population Hypothesis testing is used to make decisions about a population based on the analysis of sample statistics. There are always two hypothesis statements which are mutually exclusive and complementary statements concerning the value of the population parameter of interest: Null Hypothesis (H0): An assumption regarding a population parameter of interest. This hypothesis always includes the equal sign as the null hypothesis is assumed to be true unless sample data produces evidence to the contrary. Alternative Hypothesis (H1): The alternative option available when the null hypothesis is rejected. Three Types of Hypothesis Tests: Lower-Tail Test Upper-Tail Test Two-Tailed Test H0: ( ( (0 H0: ( ( (0 H0: ( = (0 H1: ( < (0 H1: ( > (0 H1: ( ( (0 Two-Sided Tests: A Two-Tailed Test (TTT) is designed to detect a change in the population parameter of interest from some hypothesized value to some different value. One-Sided Tests: A Lower-Tail Test (LTT) is designed to detect a change in the population parameter of interest from some hypothesized value to some lower value. An Upper-Tail Test (UTT) is designed to detect a change in the population parameter of interest from some hypothesized value to some greater value. Test Statistics and Action Limits: A test statistic is a sample statistic corresponding to the population parameter being tested. For example, when testing a......

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...the lack of monthly data. Specification of the Theoretical Model: The theoretical model of estimated function of rice paddy is: QS =α₀+α1RPSt+α2RSYt+α3RIAt +α4FSt +α5PRt +εt Where, QS is quantity supplied at current year (kg/capita/year), RPt is Rice Production (Seasonal), RSY t is the rice seasonal yield, RIA t is rice irrigated area, FS t is fertilizer sales, PR t is the price of rice of the wholesalers. 1 Identification of the variables: Economic theory suggests that the supply for food grain (rice) depends on various factors. The supply of rice paddy is totally depended on production, fertilizers wholesalers pricing area of irrigation. Without these variables quantity supplied amount will not be definable. Collection of Data: Secondary data have been used mostly for the estimation. We have used years of 1980-2005, which is 25 years to see the pattern of the supply of rice and what factors are affecting the supply of rice in these whole years. Data are in the Appendix section. Estimation of the Parameter of the Model: Estimated Relationship between Rice production in the country and Quantity Supplied: Rice production in the county is the major factor in estimating the supply function of rice because production quantity of rice determines how much rice will be supplied from the country and how much will be imported from the foreign country. Therefore, in this context the hypothesis will be: H0: Production of Rice has no impact on quantity......

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...Hypothesis Testing Hypothesis testing is basically a process that uses statistical inference to test claims about population parameters. In hypothesis testing we begin by making a tentative assumption about a population parameter. This assumption is called the null hypothesis and is denoted by Ho. We then define another hypothesis, called the alternative hypothesis, which is the opposite of what is stated is the null hypothesis. The alternative hypothesis is denoted by Ha. The hypothesis testing procedure involves using data from a sample to test the competing claims indicated by the null and alternate hypotheses. Testing the hypothesis is similar to a criminal trail. Ho: The defendant is innocent Ha: The defendant is guilty Just as the defendant in a criminal trial is assumed to be innocent, the null hypothesis is assumed to be true and given the benefit of the doubt. The testimony and evidence obtained during the trial provide the sample information. If the sample information is consistent with the assumption of innocence, the null hypothesis that the defendant is innocent cannot be rejected. On the other hand, if the sample information is inconsistent with the assumption of innocence, the null hypothesis is rejected and action is taken based on the alternative hypothesis that the defendant is guilty. Developing Null and Alternative Hypotheses In some applications it may not be obvious how the null and alternative hypotheses should be......

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...able to fully understand hypothesis testing and the five steps involved in the complete process, one must first understand what a hypothesis and a hypothesis test is and why it is used. To begin with, a hypothesis, when involved in statistics, is an idea which could be set in the form of an assumption or a theory that shows the characteristics of a single or even multiple variables of a single or group of populations (Aron, Aron & Coups, 2009). These ideas or predictions need to be explored so as to give them validation, possibly creating further research, or these ideas need to be shown to be invalid, thus saving time by not putting more research into an idea that shows itself to be incorrect, however, sometimes an invalid result can create further research of another facet of the original idea set forth. Hypothesis testing is a process that uses statistical data in order to determine if an idea is able to be supported or warrants further research within a certain population that the idea or prediction seems to apply to, and is used by researchers (Aron et. al., 2009). There are five steps involved in this research process. The first step is to pose the question related to the idea or prediction as a logically formed statement called a research hypothesis. In addition to this statement, there is also a statement that is the complete opposite of the research hypothesis statement, called a null hypothesis statement (Aron et. al., 2009). Both these hypothesis statements are......

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...Unit 4 – Hypothesis Testing & Variance Abstract There are two tests that are preformed following a two-tailed hypothesis test, using a .05 significance level. The first test is intrinsic by gender and the second is extrinsic variable by position type. This section will be taking a closer look at intrinsic satisfaction by gender and extrinsic satisfaction by position. Separate hypothesis test will be performed on both variances with the outcomes. Hypothesis Test #1 Looking at Intrinsic Satisfaction by Gender H0:Males= μ Females H1:Males= μ Females ∝ = .05 Significance level: 0.05 T statistic: 2.05 Critical T values: -1.98 and 1.98 P value: 0.04 Since the test statistics of 2.05 is greater than critical value of 1.98 we reject to reject the Ho. The decision made for the intrinsic job satisfaction survey, which intrinsic is when one does it for one’s satisfaction. The data says that it does not support the intrinsic Ho. The p value is less than the alpha. Managers for this business could use this information specifically to help drive the motivation of their employees. This information could show value in the growth of the company with having employees that enjoy their job and complete for their own satisfaction not for reasons such as outside rewards could say a lot about working for this company. If employees first enjoy their job this could mean greatness for the company, employees will strive to better the company and their......

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...Hypothesis Testing Opinions of Social Security System Probability and statistics August 1 2013 1. The Problem In an effort to design better advertising campaigns, the public relations department of the Social Security Administration conducted a survey to find out the opinions people in the United States have about the Social Security System. The public relations department collected and analyzed the survey data and claims that 40% of people in the United States think the Social Security system will have money available to provide the benefits they expect for their retirement. Also, they claim that the average age of people in the United States who would say yes to this question when asked is 60 years or older. The purpose of this study is therefore to examine and test the hypothesis of these claims and determine whether they can be supported or rejected for advertising purposes. 2. The Research Design and Hypothesis To test the hypothesis, a data table was collected from a survey adapted from Newsweek, by the public relations department of the Social Security Administration. The survey consisted of data from 32 adults ranging in age from 18 to 83. The study examines the two hypothesis by utilizing the classical method to construct a condition for testing the hypothesis claimed by the public relations department of the Social Security Administration. In this case, the null hypothesis is 40% of the people in the United States think the Social......

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...Hypothesis Testing Paper Hypothesis testing in statistics goes beyond the traditional acceptances of trying to prove a hypothesis correct. Hypothesis testing is matter of accepting what has already been proven until another hypothesis is verified to be true. In the essay, an overview of the hypothesis testing process is described using a fictional example and numerical values to detail the process. The idea formed by the hypothesis, “online students have more stress than traditional on campus students”, is to reject the hypothesis that online college students experience less stress than on campus college students. This is in no way true findings; it is a fictional example to help walk the reader through the steps of hypothesis testing. Hypothesis testing is a king of research used to say how a certain topic of interest will end or how researchers think it will end in the environment. The testing will show that just because one forms an answer it does not prove that the answer is correct for there are many factors that could change the outcome, which is why researchers use probability rates of five or one percent. The null hypothesis endeavors to show that there is no variation between variables, or a single variable is no different from zero. It is surmised to be true until statistical evidence nullifies it for an alternative hypothesis. Null hypothesis is a hypothesis that the researcher endeavors to confute, reject, or nullify. The research hypothesis is the......

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...Nonparametric Hypothesis Test:. Research can be focused in a number of ways, to help refine our topic to a point where we have clear hypotheses statements. If the housing industry was determined to be doing better than the rest of the economy, a hypothesis test might be in order, with mean prices greater than other housing industries. The test to determine the difference is the one sample run (Wald- Wolfowitz test to determine the mean prices to be equal to each home cost (Doane & Seward, 2007). However, March home sales were higher than expected. Our Presidents recent trip aboard has secured enough raw material and additional energy products to secure the USA zone of growth for 100 years. We believe America remains at the top of the economic world and by far the most secure in the housing industry recovery (Dohrmann B, 2011). More often than not, homeowners has maximize their time and search for the best sales for homes by searching information about homes sales and choices(Rosales L. 2011). The housing industry can also find the best buyer’s options that are available to him or her in a similar way that real estate agencies can seek the best sales on homes. However, the homes of the homeowners in the housing industry are set by the regional, state, and local expectations of the buyers and not so much by differences in qualifications of the homeowners. There are still a bright light in our housing futures across the nation (Rosales L, 2011) When the housing......

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...Basic Econometrics, Fourth Edition Front Matter Preface © The McGraw−Hill Companies, 2004 PREFACE BACKGROUND AND PURPOSE As in the previous three editions, the primary objective of the fourth edition of Basic Econometrics is to provide an elementary but comprehensive introduction to econometrics without resorting to matrix algebra, calculus, or statistics beyond the elementary level. In this edition I have attempted to incorporate some of the developments in the theory and practice of econometrics that have taken place since the publication of the third edition in 1995. With the availability of sophisticated and user-friendly statistical packages, such as Eviews, Limdep, Microﬁt, Minitab, PcGive, SAS, Shazam, and Stata, it is now possible to discuss several econometric techniques that could not be included in the previous editions of the book. I have taken full advantage of these statistical packages in illustrating several examples and exercises in this edition. I was pleasantly surprised to ﬁnd that my book is used not only by economics and business students but also by students and researchers in several other disciplines, such as politics, international relations, agriculture, and health sciences. Students in these disciplines will ﬁnd the expanded discussion of several topics very useful. THE FOURTH EDITION The major changes in this edition are as follows: 1. In the introductory chapter, after discussing the steps involved in traditional econometric......

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... Econometrics of Random Walk Hypothesis ABSTRACT The random walk hypothesis is a key instrument used in the analysis of forecasting in the economic and financial market. It is used primarily in the forecasting of the prices of stocks. This is useful to determine and forecast the prices of stocks given previous stock prices. This paper discusses the basis of the hypothesis, the two types of random walk hypothesis, its framework, methodologies and the analysis of its repercussions. INTRODUCTION The random walk hypothesis states that stock price changes have the same distribution and are independent of one another, so the past movement or trend of a stock price or of the market as a whole cannot be used to predict its future price or any possible future trends. The concept originated in the late 1800s from Jules Regnault, a French broker, and Louis Bachelier, a French mathematician, whose Ph.D. dissertation titled "The Theory of Speculation". The same ideas were later developed and studied further by Paul Cootner, an MIT Sloan School of Management professor, in his 1964 book The Random Character of Stock Market Prices. The term was popularized by the 1973 book, A Random Walk Down Wall Street, by Burton Malkiel, a professor of economics at Princeton University, and was used earlier in Eugene Fama's 1965 article "Random Walks In Stock Market Prices”. The theory that stock prices move randomly was earlier proposed by Maurice Kendall in his 1953 paper, “The Analytics of......

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...The steps in testing a research hypothesis There are a total of five steps that are used in testing a hypothesis and they are: “(1) Making assumptions, (2) Stating the research and null hypotheses and selecting (setting) alpha, (3) Selecting the sampling distribution and specifying the test statistic, (4) Computing the test statistic, and (5) Making a decision and interpreting the results.” (Boston University Metropolitan College, n.d., Para. 1). When beginning the process of creating a hypothesis to test, the first thing that must be done is to make assumptions about the type of sampling method that would be used, the level of measurement for the variable, including the sample size. The second step is then to state the research and null hypotheses and selecting the alpha. “We always state research hypotheses in terms of population parameters because we want to use sample statistics to estimate population parameters.” (Boston University Metropolitan College, n.d., Para. 5). After the research has been stated, then the next step is to complete the null hypothesis, which will contradict the research hypothesis. The third step in testing a hypothesis is to select the sampling distribution and to specify the test statistic. The fourth step is to compute the test statistic following the specified formula to be able to test the statistic. The fifth and final step is to make a decision and to interpret the results. This simply means that we are looking over the results and......

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...RES 342 Week 4 Team Assignment Nonparametric Hypothesis Testing Paper Get Tutorial by Clicking on the link below or Copy Paste Link in Your Browser http://hwguiders.com/downloads/res-342-week-4-team-assignment-nonparametric-hypothesis-testing-paper/ For More Courses and Exams use this form ( http://hwguiders.com/contact-us/ ) Feel Free to Search your Class through Our Product Categories or From Our Search Bar (http://hwguiders.com/ ) Use the same research question and data from the Learning Team Meeting Two assignment. Conduct the equivalent, nonparametric test of hypothesis using the five-step process. Prepare a 1,050- to 1,750-word paper describing the results of the nonparametric hypothesis test. Include the following in your paper: • Formulate a hypothesis statement regarding your research issue. • Perform the five-step hypothesis test on the data. • Explain which nonparametric test you used to analyze your data and why you chose that test. • Interpret the results of your test, and explain the differences, if any, that you observe from your Week Three paper. Include your raw data tables and the results of your computations in your paper, using graphical and tabular methods of displaying data and results. Format your paper consistent with APA guidelines. RES 342 Week 4 Team Assignment Nonparametric Hypothesis Testing Paper Get Tutorial by Clicking on the link below or Copy Paste Link in Your......

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...Hypothesis Testing Paper Michelle Ware Psy 315 July 6, 2015 Nancy Walker Hypothesis Testing Paper Criminal acts stemming from prejudice based on race, religion, sexual orientation, or ethnicity-frequently referred to as “hate violence”- have increased during recent years. (Barnes & Ephross, 1994) My hypothesis is the nature of hate attacks and victim’s responses. We can date back in American history the major importance of crime as a social problem. Society in America has been increasingly concerned about this problem and the victims experience with hate. This type of crime has generated the development of a numerous variety of victim service programs and research that will focus on victims instead of giving the criminals their five seconds of fame. “Hate violence crimes are those directed against persons, families, groups, or organizations because of their racial, ethnic, religious, or sexual identities or their sexual orientation or condition of disabilities. These crimes include arson of homes, businesses, and harassment, destruction of religious property, cross burnings, personal assaults, and homicides.” (Barnes & Ephross, 1994) It could be a difficult task to estimate the current prevalence of hate violence in the United States. With the help of media sources, there is a way to keep track and be more aware of these types of crimes. Focus group meetings, individual interviews, and questionnaires would be a way of sampling victims. Victims should...

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...Hypothesis Testing Tricia Gifford PSY/315 May 4, 2015 Karen Hoeve Hypothesis Testing Before a hypothesis test can be performed, it would be beneficial to have an understanding of what a hypothesis test is inclusive. A hypothesis is a declaration made in advance based on informal observation, a theory, or previous research, which is tested in a study. When this hypothesis declaration has been made, the hypothesis test can then be performed, which is a process for making a decision as to the outcome of a study supporting a particular theory or realistic innovation primarily thought to pertain to a population. In this hypothesis-testing scenario presented, a chosen research topic will be described along with its hypothesis statement concerning the topic. A population and its description will be determined and how the sampling method was obtained. The statistical technique will also be analyzed determining of the data. Research Issue The hypothesis test always starts out with a question regarding a subject of interest. The subject of interest is to determine if the suicide rate in the Pacific Northwest population is higher than the suicide rate in the South Midwest population. The states included in the Pacific Northwest are Idaho, Oregon, and Washington, and the states inclusive in the South Midwest are Arizona, New Mexico, and Texas. The populations are: 1) residents in the Pacific Northwest, and 2) residents in the South Midwest. ......

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...Nonparametric Hypothesis Testing RES/342 Nonparametric Hypothesis Testing During the course of the last three weeks, the team explored the hypothesis testing segment of statistics research. The first part of this assignment was the one sample hypothesis testing. The second was the two or more sample hypothesis testing, and finally in this third week, we will look at nonparametric hypothesis testing. This week’s project is a continuation of the previous projects and entails to build on the identical research question that we will frame a research hypothesis from the same provided data sets (Wage and Wage Earners) using ratio or interval numerical data; however, this week we will use a nonparametric hypothesis test to find our answer. In the next following paragraphs, the team will clearly affirm a hypothesis statement that will provide the base for our survey, perform a five-step hypothesis test on information concerning our choice and apply the concepts of nonparametric testing learned in this course, and describe how the results of our findings answer our research question. Finally, we will conclude this study with a brief summary that will examine the main points, the purpose, and conclusions of this final third week’s study on nonparametric testing. Perform the five-step hypothesis test on the data Nonparametric tests are statistical tests that analyze data that does not require assumptions about the distribution of shape of the population from......

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