Econ 101 – Summer 2009

Assignment 1 – An Introduction to Consumption Functions

Your assignment will be to estimate six different consumption functions (4 with income only and 2 with income and interest rates) as discussed in class, the textbook, and in the article Going Empirical by Blanchard, found in RBR, under eRES. The focus box page 69 of Blanchard's article is very important for all definitions of statistical terms which you must use correctly in your analysis. Familiarize yourself with the E-views program by attending the E-views training sessions scheduled the second week. Additional practice on your own is often useful. Read and reread the handouts under Resources at the top of the class page. You can do this prior to your E-views section meeting in the labs during week 2. The second section meeting for this class reviews regression analysis (remember PStat 5). The procedure used for this analysis is called least-squares (LS).

The ground rules are:

All papers must be typed, double spaced, one side. The analyses must be your own (see plagiarism statement on course syllabus). You cannot sit side-by-side in the lab doing the project. English structure is important.

All graphs and regression results (printouts) must be included, labeled (if they are not labeled no one can follow your analysis) and referenced as you use them in the paper.

Set the sample period from 1960.1 to 1995.1 for estimation. You may want to use a longer sample to obtain necessary consumption and income values outside this sample period for forecasting, discussed below. This is important, don't say you can't find the income and consumption values outside the sample periods.

For each equation estimated, discuss the economics of your results, including an evaluation of the R², t-statistics, and the interpretation of all coefficients, i.e., what do they mean and why? (Note the subtitle of Blanchard’s article.) – The coefficients are the most important item but don't forget the rest. Use the actual values your data is measured in, billions constant dollars to interpret all slopes.

All equations will use an intercept value or constant term, designated “c” in the E-views program.

Real total consumption and real disposable income are the only variables used in the first four equations of this exercise. You should know the reason why only real variables are used, and must tell me in your paper why you are doing this.

Use a graph to plot, over time, each of your variables (use line graph option). You must tell me what you observe. Next, go to graph option and choose “scatter” and plot the data points for the LR (eq.1) and SR (eq. 2) variables. (Lagged variables do NOT have to be plotted.) Using your scatter plots with consumption on the vertical axis and disposable income on the horizontal (this depends on the order you enter the variables in the scatter graph program) from the scatter plots guesstimate the relationships between consumption and disposable income. This means "draw" your best estimate of a straight line through the points. Using the values on the axis, hand calculate the slope you have estimated. Show work in your presentation. Compare and report your hand estimated results with the actual values from the regression estimates. Explain why there are differences. Include your LS printouts (4), the two scatter plots and the two line graphs (both consumption and income on same graph) in your paper (properly referenced to text; no references, lower grade). Explain your scatter plot results with respect to R² values from equations 1 and 2.

In class, the general consumption function included b₅Y_D(-1) as one of the arguments. Using your short run results, compare the numerical values of c₁ and b₅. Explain why the results appear economically reasonable.

The first estimation is a long run consumption function. It is estimated using the level values (found in the data set) of the variables. No time trend is removed. (Explain what this means in your paper analysis.)

The LR equation is: (1) CON = C + c₁Y_D using your own named variables. Estimate using E-views, evaluate and interpret your results for both intercept and slope. Are the values consistent with the textbook presentation in Chs. 3 and 15? Explain why or why not. You must provide a textbook page(s) reference(s) and quotations to verify your long run MPC and intercept values If they are different from text, explain why in your paper.

The last three consumption functions are short run as discussed in Blanchard. To take the trend out of the variables we will use first differences, i.e., FD VARX = VARX – VARX(-1). Explain in your paper why FD removes the trend. The lag operator (-1) added to any variable will lag any variable by one period, (-2) lags the variable two quarters, etc. You must provide your own name for any variable you generate in an equation, such as first differences, real interest rates, or real profits. Use your initials on any variable you generate, i.e., John’s FD of Consumption = JFDCON. See the E-Views Quick Reference under “resources” in the 101 Outline.

The short run equations to be estimated are: (where D means FD)

(2) DCON = C + c₁DY_D

(3) DCON = C + c₁DY_D + c₂DY_D(-1)

(4) DCON = C + c₁DY_D + c₂DY_D(-1) + c₃DY_D(-2)

Analyze what happens to each coefficient as you add more lagged disposable income variables. This includes the constant term.

Compare your results for equations 2 and 4 to Blanchard’s equations 4.5 and 4.6 in his article. Analyze the differences. Are the results for MPC similar or different? Explain the total MPC. Explain why his results might be different than yours. Explain why his equation structure is the same as or different from yours. Include an analysis of your scatter plot compared to Blanchard’s scatter plots.

Forecasting:

Take your results in equation 4 and forecast total consumption expenditures two quarters ahead, (beyond the sample period) 1995.2 and 1995.3 using the actual values of disposable income from the data set. Do this on your hand calculator. Evaluate your forecasted results of consumption changes with the actual consumption changes, which can be calculated from the E-views data set. Show all work. Now, forecast for the same two quarters using the long run consumption function equation. Explain which forecast, short run or long run, are closer to the actual values of consumption. Explain why they are different.

While our results using income were consistent with theory, theory also suggests that other variables (interest rate, value of real assets, debt to income ratio, and consumer expectations to name a few) play a role in household spending behavior. For the last part of this exercise take the structure of equation 3 (DCON=C + c₁ DY_D + c₂ DY_D(-1)) and add the value of the real interest rate. Calculate the real rate by using an appropriate (to households) nominal rate (found in the data set) and subtract the actual rate of inflation calculated from an appropriate household price index in data set. (Remember, interest rates are measured on an annual basis as percents, and your inflation measure has to have the same units. The price indexes in the data set are quarterly, and your final inflation measure must be annual percents, not a decimal fraction.)

Keep in mind the difference between quarterly and annual values.

For Equation 5, add the real rate to Equation 3 using same sample period. Interest rates do not have to be first-differenced because there is no time trend in the interest rate series. Graph on one printout page your calculation of the real rate and the nominal rate (you used) and describe your results.

Compare your results of this equation (5) with your results from the estimation of Equation 3. Compare coefficients, t-values, and adjusted R². Which equation is "better"? Explain why? Interpret the sign and size of the coefficient on the real rate. What does it say about the change in consumption for a 1% increase in the real rate?

There is some debate among economists whether households use the real rate or the nominal rate in their decision to spend. To test this hypothesis, re-estimate your Equation 5 above using the nominal rate in place of the real rate and call it Equation 6. Evaluate the results with respect to coefficient values, t-values, adjusted R². What does the equation say about consumption changes for a 1% increase in the nominal interest rate? Finally, which interest rate (real or nominal) explains consumption expenditures best? Offer some reasons for your conclusion.