1. Seminar in Economics Econ. 470
Chapter 6:
Research Process
Stage 4: Hypothesis Development

2. Recall the Research process:
Broad problem area
Problem statement
Theoretical Framework
Generation of hypotheses
Data collection:
Data analysis:
Report Writing( Interpretation of results)
© 2009 John Wiley & Sons Ltd.

3. Stage 4 : Hypothesis
A proposition that is empirically testable. It is an empirical statement concerned with the relationship among variables.
Good hypothesis:
Must be adequate for its purpose
Must be testable
Must be better than its rivals
© 2009 John Wiley & Sons Ltd.

4. The Simple Regression Model
Regression analysis is a statistical tool for the investigation of relationships between variables.
Usually, the investigator seeks to determine the causal effect of one variable upon another.
To explore such issues, the investigator assembles data on the underlying variables of interest and employs regression to estimate the quantitative effect of the causal variables upon the variable that they influence. The investigator also typically assesses the “statistical significance” of

5. The Simple Regression Model
The investigator also typically assesses the “statistical significance” of the estimated relationships, that is, the degree of confidence that the true relationship is close to the estimated relationship.
Regression techniques have long been central to the field of economic statistics (“econometrics”).

6. The Simple Regression Model
Definition of the simple linear regression model
"Explains variable in terms of variable "
Intercept
Slope parameter
Dependent variable,
explained variable,
response variable,…
Error term,
disturbance,
unobservables,…
Independent variable,
explanatory variable,
regressor,…

7. The Simple Regression Model
Example: Soybean yield and fertilizer
Example: A simple wage equation
Rainfall,
land quality,
presence of parasites, …
Measures the effect of fertilizer on
yield, holding all other factors fixed
Labor force experience,
tenure with current employer,
work ethic, intelligence …
Measures the change in hourly wage
given another year of education,
holding all other factors fixed

8. The Simple Regression Model
In order to estimate the regression model one needs data
A random sample of observations
First observation
Second observation
Third observation
Value of dependent
variable of the i-th observation
Value of the explanatory variable of the i-th observation
n-th observation

9. The Simple Regression Model
Fit as good as possible a regression line through the data points:
Fitted regression line
For example, the i-th
data point

10. The Simple Regression Model
What does "as good as possible" mean?
Regression residuals
Minimize sum of squared regression residuals
Ordinary Least Squares (OLS) estimates

11. The Simple Regression Model
CEO Salary and return on equity
Fitted regression
Causal interpretation?
Salary in thousands of dollars
Return on equity of the CEO‘s firm
Intercept
If the return on equity increases by 1 percent,
then salary is predicted to change by 18,501 $

12. The Simple Regression Model
Wage and education
Fitted regression
Hourly wage in dollars
Years of education
Intercept
In the sample, one more year of education was
associated with an increase in hourly wage by 0.54 $

13. The Simple Regression Model
CEO Salary and return on equity
The regression explains only 1.3 %
of the total variation in salaries

14. Multiple Regression Analysis: Estimation
Definition of the multiple linear regression model
"Explains variable in terms of variables "
Intercept
Slope parameters
Dependent variable,
explained variable,
response variable,…
Error term,
disturbance,
unobservables,…
Independent variables,
explanatory variables,
regressors,…

15. Multiple Regression Analysis: Estimation
Motivation for multiple regression
Incorporate more explanatory factors into the model
Explicitly hold fixed other factors that otherwise would be in
Allow for more flexible functional forms
Example: Wage equation
Now measures effect of education explicitly holding experience fixed
All other factors…
Hourly wage
Years of education
Labor market experience

16. Multiple Regression Analysis: Inference
Example: Wage equation
Test whether, after controlling for education and tenure, higher work experience leads to higher hourly wages
Standard errors
Test against
One would either expect a positive effect of experience on hourly wage or no effect at all.

17. Multiple Regression Analysis: Inference
Example: Wage equation (cont.)
t-statistic
Degrees of freedom;
here the standard normal
approximation applies
Critical values for the 5% and the 1% significance level (these are conventional significance levels).
The null hypothesis is rejected because the t-statistic exceeds the critical value.
"The effect of experience on hourly wage is statistically greater than zero at the 5% (and even at the 1%) significance level."

18. Multiple Regression Analysis: Inference
Testing against two-sided alternatives
Test agai nst
Reject the null hypothesis in favour of the alternative hypothesis if the absolute value
of the estimated coefficient is too large.
Construct the critical value so that, if the
null hypothesis is true, it is rejected in,
for example, 5% of the cases.
In the given example, these are the points
of the t-distribution so that 5% of the cases
lie in the two tails.
! Reject if absolute value of t-statistic is less than or greater than 2.06

19. Multiple Regression Analysis: Inference
Guidelines for discussing economic and statistical significance
If a variable is statistically significant, discuss the magnitude of the coefficient to get an idea of its economic or practical importance
The fact that a coefficient is statistically significant does not necessa-rily mean it is economically or practically significant!
If a variable is statistically and economically important but has the "wrong“ sign, the regression model might be misspecified
If a variable is statistically insignificant at the usual levels (10%, 5%, 1%), one may think of dropping it from the regression
If the sample size is small, effects might be imprecisely estimated so that the case for dropping insignificant variables is less strong

20. Multiple Regression Analysis: Inference
Computing p-values for t-tests
If the significance level is made smaller and smaller, there will be a point where the null hypothesis cannot be rejected anymore
The reason is that, by lowering the significance level, one wants to avoid more and more to make the error of rejecting a correct H0
The smallest significance level at which the null hypothesis is still rejected, is called the p-value of the hypothesis test
A small p-value is evidence against the null hypothesis because one would reject the null hypothesis even at small significance levels
A large p-value is evidence in favor of the null hypothesis
P-values are more informative than tests at fixed significance levels