Applied Economic Analysis

Slides:



Advertisements
Similar presentations
Multiple Regression and Model Building
Advertisements

Welcome to Econ 420 Applied Regression Analysis Study Guide Week Nine.
Irwin/McGraw-Hill © Andrew F. Siegel, 1997 and l Chapter 12 l Multiple Regression: Predicting One Factor from Several Others.
Econ 140 Lecture 151 Multiple Regression Applications Lecture 15.
QUALITATIVE AND LIMITED DEPENDENT VARIABLE MODELS.
Multiple Regression Involves the use of more than one independent variable. Multivariate analysis involves more than one dependent variable - OMS 633 Adding.
Multiple Regression Models
Econ 140 Lecture 171 Multiple Regression Applications II &III Lecture 17.
So far, we have considered regression models with dummy variables of independent variables. In this lecture, we will study regression models whose dependent.
Statistical Analysis SC504/HS927 Spring Term 2008 Session 7: Week 23: 7 th March 2008 Complex independent variables and regression diagnostics.
1 Simple Linear Regression Chapter Introduction In this chapter we examine the relationship among interval variables via a mathematical equation.
Topic 3: Regression.
Simple Linear Regression. Introduction In Chapters 17 to 19, we examine the relationship between interval variables via a mathematical equation. The motivation.
Multiple Regression. In the previous section, we examined simple regression, which has just one independent variable on the right side of the equation.
Understanding Multivariate Research Berry & Sanders.
Modeling Possibilities
1 Research Method Lecture 6 (Ch7) Multiple regression with qualitative variables ©
Chapter 14 Introduction to Multiple Regression
Specification Error I.
1 1 Slide © 2008 Thomson South-Western. All Rights Reserved Chapter 15 Multiple Regression n Multiple Regression Model n Least Squares Method n Multiple.
CHAPTER 14 MULTIPLE REGRESSION
Production Planning and Control. A correlation is a relationship between two variables. The data can be represented by the ordered pairs (x, y) where.
Statistics and Econometrics for Business II Fall 2014 Instructor: Maksym Obrizan Lecture notes III # 2. Advanced topics in OLS regression # 3. Working.
Welcome to Econ 420 Applied Regression Analysis Study Guide Week Seven.
1 MGT 511: Hypothesis Testing and Regression Lecture 8: Framework for Multiple Regression Analysis K. Sudhir Yale SOM-EMBA.
Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 14-1 Chapter 14 Multiple Regression Model Building Statistics for Managers.
Regression Analysis: Part 2 Inference Dummies / Interactions Multicollinearity / Heteroscedasticity Residual Analysis / Outliers.
Chapter 8: Simple Linear Regression Yang Zhenlin.
Copyright ©2011 Pearson Education, Inc. publishing as Prentice Hall 14-1 Chapter 14 Introduction to Multiple Regression Statistics for Managers using Microsoft.
Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice- Hall, Inc. Chap 14-1 Business Statistics: A Decision-Making Approach 6 th Edition.
11 Chapter 5 The Research Process – Hypothesis Development – (Stage 4 in Research Process) © 2009 John Wiley & Sons Ltd.
Introduction to Multiple Regression Lecture 11. The Multiple Regression Model Idea: Examine the linear relationship between 1 dependent (Y) & 2 or more.
PO 141: INTRODUCTION TO PUBLIC POLICY Summer I (2015) Claire Leavitt Boston University.
Stats Methods at IC Lecture 3: Regression.
Correlation and Linear Regression
Scatter Plots and Correlation
Chapter 14 Introduction to Multiple Regression
Multiple Regression Analysis with Qualitative Information
Correlation and Regression analysis
Chapter 15 Multiple Regression and Model Building
Inference for Least Squares Lines
26134 Business Statistics Week 5 Tutorial
Inference and Tests of Hypotheses
Political Science 30: Political Inquiry
Multiple Regression Analysis and Model Building
Multiple Regression Analysis with Qualitative Information
Multiple Regression.
Elementary Statistics
Spearman’s rho Chi-square (χ2)
Instrumental Variables and Two Stage Least Squares
Multiple logistic regression
Multiple Regression Analysis with Qualitative Information
Prepared by Lee Revere and John Large
Multiple Regression Models
Instrumental Variables and Two Stage Least Squares
24/02/11 Tutorial 3 Inferential Statistics, Statistical Modelling & Survey Methods (BS2506) Pairach Piboonrungroj (Champ)
PUBLIC FINANCE AND TAX POLICY
Instrumental Variables and Two Stage Least Squares
SIMPLE LINEAR REGRESSION
Korelasi Parsial dan Pengontrolan Parsial Pertemuan 14
Chapter 7: The Normality Assumption and Inference with OLS
Seminar in Economics Econ. 470
Product moment correlation
SIMPLE LINEAR REGRESSION
Multiple Regression Analysis with Qualitative Information
Chapter 9 Dummy Variables Undergraduated Econometrics Page 1
TEST FOR RANDOMNESS: THE RUNS TEST
Introduction to Regression
Inferential testing.
Presentation transcript:

Applied Economic Analysis Lecture 18 Working through examples

Example 1 A researcher has been provided with a data set comprising a random sample of 1500 individuals aged between 16 and 64 years. The following information is recorded for each individual: Pay: Gross hourly pay in pounds. Gender: One if male, zero if female Tenure: Number of years working for current employer Highest Educational Qualification: Degree level: one if degree or equivalent, zero otherwise A level: one if A level or equivalent, zero otherwise GCSE: one if GCSE or equivalent, zero otherwise No qualifications: one if no qualifications, zero otherwise

The researcher has used the data set to estimate two regression models The researcher has used the data set to estimate two regression models. The results are shown in the following table (standard errors in brackets):

(i) Interpret the results in model one (i) Interpret the results in model one. Do you think this is a good model? The constant represents the starting hourly pay for females. This is predicted to be £4.62 per hour. The model predicts that the starting hourly for men is £2.43 higher than for females, ceteris paribus. Tenure – Each additional year in the current job is predicted to increase hourly pay by 52p, ceteris paribus.

Tests for individual significance (t-tests): Test H0: β0 = 0 Against H1: β0 > 0 (a one-tailed test as we expect starting hourly pay to be positive). t = 4.62/1.55 = 2.98 > critical value t1497,0.05 = 1.64 There is evidence that the starting hourly pay is positive.

t-tests Test H0: β1 = 0 Against H1: β1 > 0 (a one-tailed test if you have a prior belief that hourly pay is higher for males). t = 2.43/0.96 = 2.53 > critical value of 1.64. There is evidence that starting hourly pay is higher for males.

t-tests Test H0: β2 = 0 Against H1: β2 > 0 You would expect that pay would rise with tenure so this could be a one-tailed test: t = 0.52/0.19 = 2.74 > 1.64 There is evidence that pay rises with tenure.

R2 R2 is not very high – it indicates that only 25% of the variation in hourly pay is explained by the model. (Adjusted R2 is not reported in the results). However, the explanatory variables are individually significant.

F-test for overall significance: Test H0: β1= 0, β2 = 0 Against H1: β1 ≠ 0, β2 ≠ 0 Fcrit = F 2,1497 = 3 249.5 > 3 so we reject the null hypothesis. We have evidence that gender and tenure jointly affect hourly pay. Overall this is a satisfactory model.

(ii) The researcher is not satisfied with her results in Model 1 and thinks that the relationship between tenure and hourly pay might be non-linear. What would be a plausible specification for the non-linearity? Sketch the suggested relationship and explain how you would estimate it.

Might expect this relationship – pay rises with tenure but at a decreasing rate. Hourly Pay Tenure (yrs)

To build non-linearity into the model could add a new variable tenure2 To build non-linearity into the model could add a new variable tenure2. If the relationship is as shown in the diagram, the sign on the tenure variable would be positive and the sign on tenure2 would be negative. Also we would to carry out t-tests to see whether there is evidence of the suggested relationship.

(iii) Interpret the coefficients on the educational qualification variables in Model 2 and test their individual significance. Explain why you have chosen each test. The base case here is ‘no qualifications’ so the interpretations are as follows: Individuals with a degree are predicted to earn £4.98 per hour more than those with no qualifications, ceteris paribus.

Individuals educated to A level standard are predicted to earn £2 Individuals educated to A level standard are predicted to earn £2.02 per hour more than those with no qualifications, ceteris paribus. Individuals educated to GCSE standard are predicted to earn £1.35 per hour more than those with no qualifications, ceteris paribus

t-tests The t-statistics are: tβ3 = 5.03 t β4 = 3.11 t β5 = 2.33 One-tailed tests would be suitable as we expect those with qualifications to earn more that those without (human capital theory). Critical value = 1.64

Therefore we have evidence that: Hourly pay is higher for individuals with a GCSE, than for those with no qualifications. Hourly pay is higher for individuals with an A-level than for those with no qualifications. Hourly pay is higher for individuals with a degree than for those with no qualifications.

(iv) Why has the researcher excluded the ‘no qualifications’ variable from her model? To avoid the dummy variable trap – if all the dummy variables were included there would be a problem of perfect multicollinearity and a violation of MLR3. One of the educational qualification groups is omitted and used as a reference group, the other coefficients are interpreted in relation to the reference category.

Example 2: Logit Model example High prices in the housing market could result in young people or those on low incomes being unable to afford to buy their own homes and, therefore, being more likely to live in rented accommodation. An econometrician has been hired to identify the key factors that determine whether an individual will choose to buy their own home. She has been provided with data containing the following information on 3,000 randomly selected individuals aged between 20 and 64:

Yi: One if the individual is a homeowner; zero if they rent Agei: Age of individual in years Incomei: Weekly Income (£) Labour market status: One if working, zero if unemployed or out of the labour market Marital Statusi: Single   Married or Living as Married Separated Divorced Widowed

Logit Model example (a) Explain why logit is a suitable choice of model. Would a different model also be suitable? (b) Using Model 2, interpret the results and comment on the individual significance of the explanatory variables.

Logit Model example (c) The econometrician had a prior belief that marital status has an impact on the probability of home ownership. Do her results confirm this? Use a LR test to answer this question. (d) Using Model 2, estimate the probability of a 45-year-old individual who is married, employed and earning £280 per week owning his/her own home.  

Solutions a) The logit model is suitable model because it gives the required sigmoid shape - probabilities will be between zero and one. The linear probability model may yield probabilities that are greater than one or less than zero.

Part (b) The positive coefficients for age and income suggest that the probability of home ownership rises with age and income, ceteris paribus. We also see that an individual who is working is more likely to own their own home than an individual who is not in work, ceteris paribus.

Marital status – here we see that married/living as married and widowed people are more likely to own their own homes than single people, ceteris paribus. Separated and divorced people are less likely to own their own home than single people, ceteris paribus.

Whether you carry out a one or two tailed test depends on your prior belief – I will carry out one-tailed tests. Asymptotic t-stats are: tAge = 0.0003/0.0001 = 3 tIncome = 0.001/0.0004 = 2.5 tLabour market status = 0.058/0.02 = 2.9 tMarried/LAM = 0.015/0.007= 2.14 tSeparated= - 0.006/0.0025= -2.4 tDivorced= - 0.007/.0.002= -3.5 tWidowed = 0.068/0.25 = 0.272

One-tailed asymptotic t-tests Comparing the t-stats with the critical value of 1.64 we see that there is evidence of a positive relationship between age, income and labour market status (working) and home ownership. There is evidence that married/LAM individuals are more likely to own their own home that those who are single.

Comparing the t-stats with -1 Comparing the t-stats with -1.64, we find that separated and divorced individuals are less likely to own their own homes than those who are single. Comparing t-stats with 1.64 we find no evidence that widowed individuals are more likely to own their own homes than those who are single.