Lecture 3 Learning to Use Regression Analysis اقتصادسنجيا © Dr. Yoke Muelgini, M.Sc. FEB Unila, 2012 Department of Economics and Development Studies, Faculty of Economics and Business, University of Lampung 1

Steps in Applied Regression Analysis The first step is choosing the dependent variable – this step is determined by the purpose of the research (see Chapter 11 for details) After choosing the dependent variable, its logical to follow the following sequence: 1. Review the literature and develop the theoretical model 2. Specify the model: Select the independent variables and the functional form 3. Hypothesize the expected signs of the coefficients 4. Collect the data. Inspect and clean the data 5. Estimate and evaluate the equation 6. Document the results © Dr. Yoke Muelgini, M.Sc. FEB Unila, 2012 Department of Economics and Development Studies, Faculty of Economics and Business, University of Lampung 2

Step 1: Review the Literature and Develop the Theoretical Model Perhaps counter intuitively, a strong theoretical foundation is the best start for any empirical project Reason: main econometric decisions are determined by the underlying theoretical model Useful starting points: – Journal of Economic Literature or a business oriented publication of abstracts – Internet search, including Google Scholar – EconLit, an electronic bibliography of economics literature (for more details go to © Dr. Yoke Muelgini, M.Sc. FEB Unila, 2012 Department of Economics and Development Studies, Faculty of Economics and Business, University of Lampung 3

Step 2: Specify the Model: Independent Variables and Functional Form After selecting the dependent variable, the specification of a model involves choosing the following components: 1. the independent variables and how they should be measured, 2. the functional (mathematical) form of the variables, and 3. the properties of the stochastic error term © Dr. Yoke Muelgini, M.Sc. FEB Unila, 2012 Department of Economics and Development Studies, Faculty of Economics and Business, University of Lampung 4

Step 2: Specify the Model: Independent Variables and Functional Form (cont.) A mistake in any of the three elements results in a specification error For example, only theoretically relevant explanatory variables should be included Even so, researchers frequently have to make choices –also denoted imposing their priors Example: when estimating a demand equation, theory informs us that prices of complements and substitutes of the good in question are important explanatory variables But which complementsand which substitutes? © Dr. Yoke Muelgini, M.Sc. FEB Unila, 2012 Department of Economics and Development Studies, Faculty of Economics and Business, University of Lampung 5

Step 2: Specify the Model: Independent Variables and Functional Form (cont.) Once the variables are selected, its important to hypothesize the expected signs of the regression coefficients Example: demand equation for a final consumption good First, state the demand equation as a general function: (3.2) The signs above the variables indicate the hypothesized sign of the respective regression coefficient in a linear model. © Dr. Yoke Muelgini, M.Sc. FEB Unila, 2012 Department of Economics and Development Studies, Faculty of Economics and Business, University of Lampung 6

Step 4: Collect the Data & Inspect and Clean the Data A general rule regarding sample size is the more observations the better as long as the observations are from the same general population! The reason for this goes back to notion of degrees of freedom (mentioned first in Section 2.4) When there are more degrees of freedom: Every positive error is likely to be balanced by a negative error (see Figure 3.2) The estimated regression coefficients are estimated with a Precision © Dr. Yoke Muelgini, M.Sc. FEB Unila, 2012 Department of Economics and Development Studies, Faculty of Economics and Business, University of Lampung 7

Figure 3.1 Mathematical Fit of a Line to Two Points © Dr. Yoke Muelgini, M.Sc. FEB Unila, 2012 Department of Economics and Development Studies, Faculty of Economics and Business, University of Lampung 8

Figure 3.2 Statistical Fit of a Line to Three Points © Dr. Yoke Muelgini, M.Sc. FEB Unila, 2012 Department of Economics and Development Studies, Faculty of Economics and Business, University of Lampung 9

Step 4: Collect the Data & Inspect and Clean the Data (vcont.) Estimate model using the data in Table 2.2 to get: Inspecting the dataobtain a printout or plot (graph) of the data Reason: to look for outliers – An outlier is an observation that lies outside the range of the rest of the observations Examples: – Does a student have a 7.0 GPA on a 4.0 scale? – Is consumption negative? © Dr. Yoke Muelgini, M.Sc. FEB Unila, 2012 Department of Economics and Development Studies, Faculty of Economics and Business, University of Lampung 10

Step 5: Estimate and Evaluate the Equation Once steps 1–4 have been completed, the estimation part is quick – using Eviews or Stata to estimate an OLS regression takes less than a second! The evaluation part is more tricky, however, involving answering the following questions: – How well did the equation fit the data? – Were the signs and magnitudes of the estimated coefficients as expected? Afterwards may add sensitivity analysis (see Section 6.4 for details) © Dr. Yoke Muelgini, M.Sc. FEB Unila, 2012 Department of Economics and Development Studies, Faculty of Economics and Business, University of Lampung 11

Step 6: Document the Results A standard format usually is used to present estimated regression results: (3.3) The number in parentheses under the estimated coefficient is the estimated standard error of the estimated coefficient, and the t-value is the one used to test the hypothesis that the true value of the coefficient is different from zero on (more this later!) © Dr. Yoke Muelgini, M.Sc. FEB Unila, 2012 Department of Economics and Development Studies, Faculty of Economics and Business, University of Lampung 12

Case Study: Using Regression Analysis to Pick Restaurant Locations Background: You have been hired to determine the best location for the next Woodys restaurant (a moderately priced, 24- hour, family restaurant chain) Objective: How to decide location using the six basic steps of applied regression analysis, discussed earlier? © Dr. Yoke Muelgini, M.Sc. FEB Unila, 2012 Department of Economics and Development Studies, Faculty of Economics and Business, University of Lampung 13

Step 1: Review the Literature and Develop the Theoretical Model Background reading about the restaurant industry Talking to various experts within the firm – All the chains restaurants are identical and located in suburban, retail, or residential environments – So, lack of variation in potential explanatory variables to help determine location – Number of customers most important for locational decision Dependent variable: number of customers (measured by the number of checks or bills) © Dr. Yoke Muelgini, M.Sc. FEB Unila, 2012 Department of Economics and Development Studies, Faculty of Economics and Business, University of Lampung 14

Step 2: Specify the Model: Independent Variables and Functional Form More discussions with in-house experts reveal three major determinants of sales: – Number of people living near the location – General income level of the location – Number of direct competitors near the location © Dr. Yoke Muelgini, M.Sc. FEB Unila, 2012 Department of Economics and Development Studies, Faculty of Economics and Business, University of Lampung 15

Step 2: Specify the Model: Independent Variables and Functional Form Based on this, the exact definitions of the independent variables you decide to include are: – N = Competition: the number of direct competitors within a two mile radius of the Woodys location – P = Population: the number of people living within a three-mile radius of the location – I = Income: the average household income of the population measured in variable P With no reason to suspect anything other than linear functional form and a typical stochastic error term, thats what you decide to use © Dr. Yoke Muelgini, M.Sc. FEB Unila, 2012 Department of Economics and Development Studies, Faculty of Economics and Business, University of Lampung 16

Step 3: Hypothesize the Expected Signs of the Coefficients After talking some more with the in-house experts and thinking some more, you come up with the following: (3.4) © Dr. Yoke Muelgini, M.Sc. FEB Unila, 2012 Department of Economics and Development Studies, Faculty of Economics and Business, University of Lampung 17

Step 4: Collect the Data & Inspect and Clean the Data You manage to obtain data on the dependent and independent variables for all 33 Woodys restaurants Next, you inspect the data The data quality is judged as excellent because: Each manager measures each variable identically All restaurants are included in the sample All information is from the same year The resulting data is as given in Tables 3.1 and 3.3 in the book ( using Eviews and Stata, respectively) © Dr. Yoke Muelgini, M.Sc. FEB Unila, 2012 Department of Economics and Development Studies, Faculty of Economics and Business, University of Lampung 18

Step 5: Estimate and Evaluate the Equation You take the data set and enter it into the computer You then run an OLS regression (after thinking the model over one last time!) The resulting model is: (3.5) Estimated coefficients are as expected and the fit is reasonable Values for N, P, and I for each potential new location are then obtained and plugged into (3.5) to predict Y © Dr. Yoke Muelgini, M.Sc. FEB Unila, 2012 Department of Economics and Development Studies, Faculty of Economics and Business, University of Lampung 19

Step 6: Document the Results The results summarized in Equation 3.5 meet our documentation requirements Hence, you decide that theres no need to take this step any further © Dr. Yoke Muelgini, M.Sc. FEB Unila, 2012 Department of Economics and Development Studies, Faculty of Economics and Business, University of Lampung 20

Table 3.1a Data for the Woodys Restaurants Example (Using the Eviews Program) © Dr. Yoke Muelgini, M.Sc. FEB Unila, 2012 Department of Economics and Development Studies, Faculty of Economics and Business, University of Lampung 21

Table 3.1b Data for the Woodys Restaurants Example (Using the Eviews Program) © Dr. Yoke Muelgini, M.Sc. FEB Unila, 2012 Department of Economics and Development Studies, Faculty of Economics and Business, University of Lampung 22

Table 3.1a Data for the Woodys Restaurants Example (Using the Eviews Program) © Dr. Yoke Muelgini, M.Sc. FEB Unila, 2012 Department of Economics and Development Studies, Faculty of Economics and Business, University of Lampung 23

Table 3.2a Data for the Woodys Restaurants Example (Using the Eviews Program) © Dr. Yoke Muelgini, M.Sc. FEB Unila, 2012 Department of Economics and Development Studies, Faculty of Economics and Business, University of Lampung 24

Table 3.2b Data for the Woodys Restaurants Example (Using the Eviews Program) © Dr. Yoke Muelgini, M.Sc. FEB Unila, 2012 Department of Economics and Development Studies, Faculty of Economics and Business, University of Lampung 25

Table 3.3 Data for the Woodys Restaurants Example (Using the Eviews Program) © Dr. Yoke Muelgini, M.Sc. FEB Unila, 2012 Department of Economics and Development Studies, Faculty of Economics and Business, University of Lampung 26

Table 3.3b Data for the Woodys Restaurants Example (Using the Eviews Program) © Dr. Yoke Muelgini, M.Sc. FEB Unila, 2012 Department of Economics and Development Studies, Faculty of Economics and Business, University of Lampung 27

Table 3.4a Data for the Woodys Restaurants Example (Using the Eviews Program) © Dr. Yoke Muelgini, M.Sc. FEB Unila, 2012 Department of Economics and Development Studies, Faculty of Economics and Business, University of Lampung 28

Table 3.4b Data for the Woodys Restaurants Example (Using the Eviews Program) © Dr. Yoke Muelgini, M.Sc. FEB Unila, 2012 Department of Economics and Development Studies, Faculty of Economics and Business, University of Lampung 29

Key Terms from Lecture 04 The six steps in applied regression analysis Dummy variable Cross-sectional data set Specification error Degrees of freedom © Dr. Yoke Muelgini, M.Sc. FEB Unila, 2012 Department of Economics and Development Studies, Faculty of Economics and Business, University of Lampung 30

The End of Lecture 3 Practice Makes Perfect: Learning to Use Regression Analysis © Dr. Yoke Muelgini, M.Sc. FEB Unila, 2012 Department of Economics and Development Studies, Faculty of Economics and Business, University of Lampung 31