Dummy variables代写
Lecture 2: Dummy variables and quarterly data
Dummy variables代写 Qualitative factors often come in the form of binary information. In econometrics, binary variables are most…
Qualitative factors often come in the form of binary information. In econometrics, binary variables are most commonly called DUMMY VARIABLES.
In defining a dummy variable, we must decide which event is assigned to the value of one and which is assigned to the value of zero.
How do we incorporate binary information into regression models? In the simplest case with only a single dummy, we just add it as an independent variable in the equation. Note: Redundant dummy
Where d=1 if a event happens (e.g., bankrupt, buy a car) and 0 otherwise.
Interpreting coefficients on dummy when the dependent variable is log(y)?
Answer: it can be interpreted as the percentage difference in y, holding all other factors fixed.
Now let’s focus on the problem of allowing for seasonal behaviour in quarterly time series data, so the qualitative variable is ‘quarter’, i.e, seasonal effect.
The basic equation is:
How do we test the seasonal effect?
Suppose we wish to consider the possibility that 
and
both vary from quarter to quarter. To allow for this, the variables
would be added to above equation
And then least squares applied to this model would give S with T-(4+6) degrees of freedom. Under the null hypothesis of no seasonal difference in both
and
, least squares would give Sr with T-4 degrees of freedom. So we can apply F-test to conduct the null hypothesis testing.
Where Sr is the residual sum of squares obtained from the restricted regression (Note: most commercial software packages will generate this value for you, often denoted as RSS or Residual SS) and S is the residual sum of squares from the unrestricted regression. Under the null, it will have an F distribution with g and T-k degrees of freedom.
Assuming a 5% significant level, if the value of F_test is greater than
We reject of the null that at least one of the parameters and change at least one quarter.
