Run Q on the regressors: P (price), I (income), other variables and lagged Q to capture habit forming. Skip the first row because of the empty cell in this row.
From the regression output, write down the estimated linear demand equation with t-statistics under the estimated coefficients. In addition, write down the R-square? Statistical significance of T-statistics is given by the P-values. There are three levels of significance: 1%, 5% and 10%. Ignore the P-values given in this output because the sample period is very small. Instead, use the following standard significance levels
If t-statistics > 2.54, there is statistical significance at the 1% level.
Calculate the short run and long run price and income elasticities of demand from the estimated coefficients in the regression equation, using the averages for the quantity, price and income (skip the first row when you calculate the averages)
Short Run P-elasticity for a linear Eq. = slope of price*(average price/average quantity)
long run P -elasticity for a linear Eq. = [slope of price / (1- slope of the lagged variable)]*(average Price/average quantity).
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Short Run I- elasticity for a linear Eq. = slope of income*(average income/average quantity)
Long Run P- elasticity for a linear Eq. = [slope of income / (1- slope of the lagged variable)]*(average income/average quantity).
Average = sum/n (skip first row).
The short-run and long run income elasticities are calculated the same way. Here the slope is for income.
Can you think of another independent variable that you may add to the above equation? What will the sign of this variable be? Specify the name of this variable. Do not include Weather in the demand equation.
STEPS TO DO REGRESSIONS
We will estimate a demand function using linear regressions.
• Linear Regression: The following demand function has four variables.
Qt = a1 + a2Pt + a3It + a4Qt-1
where: Q is the Quantity of good X,
P is the Price,
I is the Income,
Qt-1 is the lagged Q, and
t is the time period
• Input or copy the data on an EXCEL sheet, clearly specifying the dependent Y variable to be the quantity (Qt), and the independent X variables to be the price of good X (Pt), income (It), and the lagged Qxt-1.
• To enter values for the lagged Qt-1, you may copy the whole data under Qt and paste it in a new column added to the given sheet under the lagged Qt-1. Pasting should start such that the first observation under Qt will be the first observation under the lagged Qt-1 starting with the second row.
• Go to TOOLS menu and click DATA ANALYSIS. Pick up REGRESSION from the ANALYSIS TOOLS presented in the pop up menu and click OK.
• First highlight the dependent variable cell range from the spreadsheet starting from the second row (skip the row with the empty cell), and click OK on the REGRESSION pop up menu to insert the selected data range in the Input Y range box. Similarly select the relevant data range for all the independent variables together including lagged Q and insert the selected data range in the Input X range box. Double check your cell ranges.
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• In the OUTPUT OPTIONS, click New Worksheet Ply and say OK. The Regression output will be available to you on a newly created worksheet.
How to add DATA ANALYSIS to your TOOLS menu if your computer doesn’t have it?
• If the TOOLS menu does not have DATA ANALYSIS, you can add it by doing the following.
• Open TOOLS
• Click on ADD-INS
• Include ANALYSIS TOOLPACK from the pop up menu dialog box and click OK.
• Go back to TOOLS and you will find DATA ANALYSIS at the bottom of the menu.
(DATABASE IS BELOW)
Paste the following database into an excel spreadsheet.
Demand for Raspberries (skip the first row)
|Year |Qx |Px |M | Py |Lagged Q |
|1984 |4 |30 | 5 |15 | |
|1985 |5 |27 |8 |16 |4 |
|1986 |5 |26 |8 |18 |5 |
|1987 |6 |26 |9 |18 |5 |
|1988 |7 |25 |10 |19 |6 |
|1989 |11 |23 |10 |22 |7 |
|1990 |13 |20 |11 |24 |11 |
|1991 |16 |14 |15 |24 |13 |
|1992 |21 |11 |15 |25 |16 |
|1993 |24 |9 |18 |27 |21 |
|1994 |28 |7 |20 |27 |24 |
|1995 |33 |5 |22 |27.5 |28 |
|1996 |36 |4 |25 |27.5 |33 |
|1997 |36.5 |3.8 |26 |27.5 |36 |
|1998 |39 |3 |30 |27.5 |36.5 |
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|1999 |40 |2.9 |31 |28 |39 |
|2000 |42 |2.4 |33 |28 |40 |
|2001 |45 |2.1 |36 |28.5 |42 |
|2002 |46 |2.00 |40 |28.5 |45 |