OSU Economics 444: Elementary Econometrics Ch.3 Use ...

OSU Economics 444: Elementary Econometrics
Ch.3 Use Regression Analysis (in an empirical project)
•• Steps in Applied Regression Analysis
• Step 0: There is a purpose of doing an empirical project. The choice of the dependent variable in
regression analysis is determined by the purpose of the project.
• Step 1: Review the literature and develope the theoretical model.
1) understand the topic you are studying;
2) review the existing literature on the topic;
3) Þnd out what other researchers have learned (if any);
–- may follow their footsteps;
–— or, develope a different approach (if not be convinced).
• Step 2: Model (regression equation) speciÞcation: Select the independent variables and
the functional form of the equation.
1) The elements of speciÞcation shall be determined on the basis of economic theory (or reasoning).
2) Select independent variables based on economic theory. An explanatory variable is selected because it
is a theoretical determinant of the dependent variable.
3) Explanatory variables that are suspected of having little effect shall not be included (except if they are
in the center stage of an inquiry).
For example, in a model that explains the demand of a consumption good, economic theory indicates
that the price of the good, consumer income, as well as prices of complements and substitutes are important
explanatory variables. The list of possible complements and substitutes may be determined by intuition,
common sense, and experience. But the Þnal selection should be explained and justiÞed (and debated).
• Step 3: Hypothesize the (expected) signs of the coefficients.
1) Hypothesize the expected effects of expanatory variables based on the underlying theory.
For example, the own price and the prices of completmentary goods are expected to be negative in
a demand equation. Consumer income and the prices of substitute goods are expected to have positive
coefficients.
• Step 4: Obtain the needed data.
1) The more observations are better. The excess of the number of observations over the number of parameters
is called the degrees of freedom. More data provide more information.
2) The units of measurement of the variables are unimportant because the coefficients will compensate for
the change of the units of measurement. However, it is recommended to select units of measurement
such that magnitudes of variables are similar (because of rounding error in computing).
• Step 5: Estimate and Evaluate the Equation
1) Choose the appropriate estimation method.
2) The results should be checked for possible errors (e.g., due to data errors, theoretical reasoning, etc.)!
• Step 6: Document (report) the Results
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1) For regression analysis, the estimated equation can be reported with the following format:
Ŷ i =103.40+6.38x i
(0.88)
n=20, ¯R2 =0.73.
The number in parenthesis is either the estimated standard error of the estimated coefficient or the
t-statistics. n isthesamplesizeusedforestimation.
2) Explain the model, the assumptions, the data used, and the estimation procedures. In principle, the
reported results shall be replicated by readers or other researchers.
•• Different types of independent variables
There are many different types of independent variables. The following types are common.
1) Instantaneous independent variables
An independent variable x t that comes from the same time period of the dependent variable y t is an
instantaneous independent variable.
2) Lagged independent variables
It is possible that an independent variable may take time in order to have effect on the dependent
variable. For example, the supply of an agricultural product might be determined by its price in the previous
period.
3) For example,
C t = β 0 + β 1 PC t−1 + β 2 PL t + ² t ,
where C t = the quantity of cotton supplied in year t, PC t−1 = the price of cotton in year t − 1, and
PL t = the price of farm labor in year t.
Here PL t , the price of farm labor, is an instantaneous independent variable. PC t−1 is a lagged independent
variable. If cotton prices change, farmers won’t be able to react immediately because it takes a while
for cotton to be planned and to grow.
4) Dummy variables
Some variables can be expressed only in a qualitative manner.
a) A dummy variable takes on the values one or zero depending on whether some condition holds or
not.
For example,
Y i = β o + β 1 X 1i + β 2 X 2i + ² i
where X 1i = the number of years teaching experience of the ith teacher (high school teacher), and
n 1 if the ith teacher has an M.A.,
X 2i =
0 otherwise.
Here X 2i is a dummy variable.
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) When a dummy variable can only change the intercept of the regression, it is an intercept dummy
variable.
(Figure 3.3 here)
c) One fewer dummy variable shall be constructed than conditions. An omitted condition shall form
the basis against which the included conditions are compared. (avoid the dummy variables trap!)
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