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Lecture20 - Lecture 21 Lags and Dummy Variables Lagged...

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Lecture 21 – Lags and Dummy Variables Lagged variables -up until now we have given all of our variables the same time subscript, t. When we do this we are saying that a change in an independent variable at one point in time affects the dependent variable at the same point in time. In other words, the change is contemporaneous. In many cases, however, a change in the independent variable will take sometime before it affects the dependent variable. When this occurs, we say that there is a lag between the time the independent variable changes and the time when this affects the dependent variable. Right now, we are going to look at the simplest type of lag, which is a one-period lag. This means that a change in X that takes place at time t-1 will lead to a change in the dependent variable at time t. An example of where a lag might arise is given by the inflation example we looked at in the last class. It may be the case that a change in the money supply takes some time before it affects inflation. Let us say it takes one year for the change in money supply to affect inflation. We would write the regression equation as follows: & P B B M B AD t t = + + + 0 1 1 2 ε t t Note that in the equation aggregate demand affects the rate of inflation in the same time period, whereas there is a one period lag before a change in the money supply affects inflation. So it is perfectly ok to have some variables Lagged and others contemporaneous. We interpret B 1 as follows: a one unit change in the independent variable M at time t-1, holding all other independent variables constant, leads to a B unit change in the dependent variable at time t. 1 Including a lagged independent variable in your regression equation is simple. Simply generate a new variable, such as Xlag as follows: gen xlag = x[_n-1] Note you are using braces here, not parentheses Example: suppose you're given the following data : quantity price per pound Ad expend 30 100 5.5 55 90 6.3 100 80 7.2 105 70 6.3 115 70 7.35 110 70 5.6 85 70 7.15 120 65 7.5 135 60 6.9 130 60 7.15 140 55 7 150 50 6.5 Here price is measured in cents, and advertising expenditure in thousands of dollars. Using STATA to run the regression, we find the following results.
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----------------------------------------------------------------------------- -- log: C:\DATA\ECO230\Lag exercise.log log type: text opened on: 24 Feb 2003, 16:35:21 . summarize Variable | Obs Mean Std. Dev. Min Max -------------+----------------------------------------------------- Q | 12 106.25 35.2346 30 150 P | 12 70 14.30194 50 100 AD | 12 6.704167 .6645088 5.5 7.5 . *Let's look at the data to make sure it was entered correctly . list Q P AD 1. 30 100 5.5 2. 55 90 6.3 3. 100
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