YOUR NAME HERE
College of Business
Western Carolina University
The abstract is a one paragraph executive summary which should be 100-200 words long, saying what you are forecasting, what theoretical approach you took, what explanatory variables you used, and provides a brief summary of your findings, (e.g. "Real GDP is projected to increase approximately four percent for each of the next two years,") and policy conclusions. Write this part of your paper last. Submit one copy of your paper on 8.5" x 11" white paper and one copy as a file posted on your website, and provide me with the website address. Feel free to use a home page supported by your ISP if you don't want to use your VMS home page. Use MS Word for word processing. Be sure to keep your own copy of the files on disk, in whatever software you prefer to use. Use 14 point Times New Roman bold for the title. Everything else should be in 10 point Times New Roman. Single space inside each paragraph. Space between paragraphs. Do not indent. Follow the format for the proposal for listing authors and institutional affiliations. Use passive voice and third person throughout: (e.g., "It seems…" or "It appears…" rather than "We found …" or "I used ….") Your abstract should end with at least one, but no more than three, JEL codes from the Journal of Economic Literature, listed in parentheses as follows. (JEL: E22, E66)
Part 1. Introduction
The first part of your paper should be headed as shown above, centered in bold. Very briefly explain the importance of the forecast target, and the value of having a good forecast of this variable over the forecasting horizon you have chosen. Discuss the probably accuracy of the forecast. (Further into the future = less accurate.) You may also state the kind of model being used and argue for its appropriateness to your use of it. (Emphasize simplicity.) The introduction should end with a sentence which reads something like: "The rest of this paper is organized as follows: part 2. presents the data used to forecast variable X (and whatever else you might use data for in your paper); part 3. explains the theoretical basis for the approach adopted in forecasting variable X; part 4. presents the forecast(s) of variable X (conditional on various values of variable(s) Z, if relevant) (and empirical estimates of any equations or quantities needed to provide a forecast of variable X, if relevant); part 5. evaluates the importance of the forecast(s) for the economy, and part 6. discusses conclusions for economic policy." This must be the last sentence in part 1., which may be no more than three paragraphs long, and in most cases can be just one paragraph.
Part 2. Data
This part should describe the data you will be using. Identify the source, observation interval, and sample period for each variable. Be sure to list the data source(s) in your references. If you use a secondary source like the Federal Reserve Bank of St. Louis's Federal Reserve Economic Data (FRED) database, mention the primary source, (e.g., U.S. Real GDP, measured in billions of chained 1992 dollars, seasonally adjusted annual rates (SAAR), FRED quarterly variable GDPC92 for 1992.1-1998.3, from the Department of Commerce Bureau of Economic Analysis.) Be sure to state whether you are using one variable to proxy another, e.g., in analyses using monthly data, the Index of Industrial Production, which is measured monthly, is often used as a proxy for real GDP, which is only observed quarterly. State whether you transformed your data by forming indices, taking logarithms, or taking first-differences, and explain why this was necessary. State if you transformed data with one period of observation to another frequency, e.g., monthly to quarterly, and explain why and how you did the transformation. You will be free to change your data transformations later, if it helps your results. State your forecast horizon, e.g., one year, two years, five years, or ten years into the future. Discuss the appropriateness of the data you have chosen, including availability, ease of access (both for yourself and others), and why this data is best for your purpose. (You may take a pro-and-con approach here: e.g., "Real GNP was used as a measure of national output and income. Alternative measures were considered, including real GDP, real net private income, and real disposable income, and any could have been used in this case.")
If you want to present any graphs of the original data, import the graph files from MS Excel 97 and put them right in the text. Include graphs only if they are especially interesting. Do not make them any bigger than they have to be to show what you think is of special interest.
Part 3. Economic Theory
Try to come up with a catchier, more descriptive title for part 3., like "The New Classical Phillips Curve as a Forecasting Instrument," or "Forecasting with the Keynesian Aggregate Expenditures Model," but if all else fails, just call it "Economic Theory."
Explain why your forecasting approach, including theoretical model and choice of explanatory variables, is appropriate to the forecast horizon you have chosen. You do not have to repeat the derivation of a well-known model, but give any theoretical equations your forecasting approach depends on. If you adopt a particular theoretical approach, but your forecasting equation will be different because it will include lagged values of certain variables, give your forecasting equation, and discuss its relationship to the theoretical model.
If you were taking a Keynesian approach to forecasting consumption expenditures, you might present the theory like this:
"The Keynesian consumption function can be written as:
where C0 is autonomous consumption and MPCxYt is induced consumption. Yt is real GDP. Since real GDP equals real aggregate expenditures (AE) in equilibrium, the AE function can be written as:
Solving this accounting identity for C:
suggesting the following short-term forecasting equation for use with quarterly data:
where IM is total or gross real imports. The greater the sum of the two coefficients on IM, the more Americans buy foreign products to satisfy their wants. An estimate of equation 1 and forecasts based on the regression are presented in part. 4."
Number any equations that are referred to anyplace else in the text. This is especially important for equations you will be estimating by regression.
Explain any relevant assumptions, e.g., f you are using a Keynesian model and need to assume a certain value for the marginal propensity to consume (MPC), you can adopt someone else's estimate, estimate it yourself by regression using the appropriate data, or calculate several conditional forecasts based on a range plausible values for the explanatory variable(s). Say which of these three approaches you have adopted.
If you use someone's published estimate, give the value, and refer to the author's last name with the year of publication, and refer to the exact pages in parentheses, e.g., "Dornbusch and Fischer (1978, p. 143) estimated an MPC of 0.88." If you don't mention the authors by name in a sentence, put the names in the parentheses like this: "Estimates range from 0.55 in the short run to 0.72 in the long run (Dornbusch and Fischer, 1978, p. 152)." If you are using a monetarist or new classical LRPC, state what value or values you are assuming for the natural rate of unemployment. Justify your assumptions as appropriate. If you need any equations to explain the theoretical approach, or derive the equations you will be estimating as regressions, center, bold, and italicize them.
Part 4. Empirical Results
Try to provide a descriptive title, like "A Long-term Forecast of North Carolina Tourism Revenues, 2000-2010," or "U.S. Consumption: a Short-term Projection 1999-2000." "The X Variable: an Estimate(s) and/or Forecast(s)" or just "Empirical Results" is fine, if a bit dull. If you are doing conditional forecasts, mention that in the title. If you estimate a regression, report the R-squared or Adjusted-R-squared (your choice), the F-statistic and its probability level, and each estimated coefficient with either its t-statistic or the probability level of the t-statistic (your choice). You can use either an equation format (best for short equations with few variables,) or a table format (best for long equations with too many variables).
An example of each is given below:
Forecasting equation 1 was estimated by an ordinary least squares regression for the period 1992.1-1998.3. The R-squared of the estimate is 0.8995. The F-statistic for the joint null hypothesis of zero slopes is 17.83, with a probability level of 0.038 = 4%, supporting rejection of the null. The estimate of the equation is (with t-statistics in parentheses):
Do not report the F-statistic if there is only one RHS variable. Report the Durbin-Watson statistic if your software provides it.
Regression Estimate of Consumption Forecasting Equation 1: 1992.1-1998.3
|Explanatory variable||Estimated coefficient||t-ratio probability level|
|R2 = 0.8995||F (zero slopes) = 17.83||Prob F = 0.038|
Label your first table "Table 1" even if there are no others. Choose an attractive color for your table or leave it white. Whenever you present regression results, discuss the validity of the estimate based on the closeness of the R-squared to one, and the low probability level of the F-statistic. Make any excuses you can if these values are not a good as you wanted. Discuss the validity of your coefficient estimates. Here I would need to discuss why I left the coefficient on Yt-4 in the equation, even though the probability level of the t-statistic is greater than 10% - this means it is not statistically significant and should have been deleted from the model. (One thing in its favor is that the probability value is not much more than 10%.) Discuss the meaning of the estimated coefficients, and interpret their relative magnitudes and signs. Does it make any sense that consumption spending should go down a year after imports go up? Or vice versa? (That is what the negative coefficient tells us.)
Use your regression equation or other mathematical relationship to calculate a forecast of the target. If you were using annual data and forecasting one year into the future, you might show the calculation like this:
If you are forecasting several quarters or months into the future present the results of your calculations in a table:
Forecasts of U.S. Consumption Spending 1998.4-2000-4
(Billions of Chained 1992 dollars, SAAR)
If you are providing a conditional forecast, use a table
Forecasts of Real Net Private Investment Expenditures
Conditional on the Secondary Market T-bill Rate
(Billions of Chained 1992 Dollars, SAAR)
Choose a title for part 5. which encapsulates the results of your forecast predictions, like "A Rosy Outlook," "Steady as She Goes," or "Armageddon: the Sequel," in the case of a particularly unfavorable projection. Explain whether your forecast is favorable or not, and to which groups of people. If you have predicted a 1% increase in unemployment, explain what this means in terms of the number of workers thrown out of work. Estimate how much more state and federal governments will have to pay in unemployment benefits. If you predict lower unemployment, estimate how much will be saved. Be sure to point out how different assumptions from the ones on which you based the forecast might have changed things. Suggest recommended courses of action for particular groups: if you forecast high demand for particular kinds of jobs, let the reader know what they are and how people can qualify; if you forecast expansion of a particular industry, give the reader some stock picks so they can get in on this growth (or unload some dogs if you forecast contraction.)
Part 6. Policy Conclusions
Here you will briefly review your findings in no more than one paragraph. Be as precise as possible, e.g., "private investment is projected to rise 5% per year for the next five years, fueling 7% GDP growth." Then you have to address two issues:
1. What should affected industries do if what your forecast comes to pass? If you have any suggestion to help them through their hard times, or help them better enjoy their good times, explain what that is. If they have to live through events passively, note that, and describe what they have in store.
2. What can and should the government, (at various levels, local, state, federal,) and the Federal Reserve, do in response to forecast events? If the government can make things better, explain how. If the government can take advantage of the situation, explain how. If the government should not change anything, note that and explain why. Do the same for the Fed.
Follow these examples. Use hanging indentation in your word processing file, but understand that the web page may not support hanging indentation. Give references only for sources mentioned in the text of your paper. Make sure you refer to all your data sources. The reference for a journal article should include the volume number and the date of the issue the article appeared in. Indent the second and each following line for each citation. (This is impossible to show in a web document.) You may not cite on-line periodicals or newsletters, but you may give the website address in addition to the complete citation for the paper version. You may cite on-line datasources. All variable descriptors must be given in the text of your paper, or in the citation. WWW citations must always include two dates in parentheses: the date of the website's publication or last revision, and the date you accessed the website, which is always given last.
Federal Reserve Bank of St. Louis, Federal Reserve Economic Data (FRED) (12-31-98), http://www.stls.frb.org/fred/ (2-29-99).
Friedman, Milton, and Schwartz, Anna Jacobson, A Monetary History of the United States, 1867-1960, Princeton NJ: Princeton University Press, 1963.
Mandelbrot, Benoit, "A Multifractal Walk Down Wall Street," Scientific American, 280:2, February 1999, pp. 70-73.
Mussa, Michael, "The Theory of Exchange Rate Determination,"
in Bilson, John F.O., and Marston, Richard C., eds., Exchange Rate Theory
and Practice, Chicago: University of Chicago Press, 1984, pp. 13-78.
ROBERT F. MULLIGAN
College of Business
Western Carolina University
U.S. real GDP is forecast to grow approximately 3% per year throughout 1999 and 2000. The forecast is based on a Keynesian aggregate expenditures model which assumed fixed interest rates, consumption spending, government spending, and net exports. The MPC and MPI are 56% and 23% estimated from 1992.1-1998.3 quarterly data. This implies an historically low Keynesian autonomous expenditures multiplier of 1.52. The interest elasticity of investment is (positive)16%, also estimated from 1992.1-1998.3 data. Investment spending is projected into the future with a linear time trend as all the other components of aggregate expenditures are held constant. GDP growth will moderate slightly over the next two years, alleviating the current labor shortage without creating significant new unemployment. The government and private firms should avoid measures to substitute capital and other factors for labor. The Federal Reserve should attempt to keep prices and interest rates as stable as possible. (JEL: E22, E66)
Part 1. Introduction
This paper forecasts U.S. gross domestic product (GDP) for the years 1999 and 2000. The explanatory variable is real private nonresidential fixed investment. The approach is based on the Keynesian aggregate expenditure model using new estimates of the marginal propensity to consume (MPC) and import (MPI) based on data for 1992-1998. A Keynesian investment function is also estimated, providing an estimate of the interest elasticity of investment. The Keynesian approach benefits from simplicity of implementation, and exploits the role of private investment expenditures in driving aggregate economic activity.
Real GDP is the most comprehensive measure of national income and output. Continued growth of real GDP is necessary to sustain low unemployment and a rising standard of living. A forecast downturn of GDP would predict a recession. The forecast horizon of two years was chosen to minimize the possibility of external factors impacting the economy in an unforeseen way. The forecast horizon is short enough to avoid seriously overstating or understating future GDP.
The rest of this paper is organized as follows: part 2. presents the data used to forecast GDP, estimate MPC and MPI, and estimate the investment function; part 3. presents the theoretical basis for the approach adopted in forecasting GDP; part 4. presents forecasts of GDP for 1999 and 2000; part 5. evaluates the importance of the forecast for the economy; and part 6. discusses conclusions for economic policy.
Part 2. Data
All variables are taken from the Federal Reserve Bank of St. Louis Federal Reserve Economic Data (FRED). The measures of GDP, Private Consumption Expenditures, Imports of Goods and Services, and Gross Private Domestic Investment are FRED variables GDPC92, PCEC92, IMPGSC92, and GPDIC92, are all real variables, and are given in billions of chained 1992 dollars at seasonally adjusted annual rates (SAAR). The primary source is the U.S. Department of Commerce Bureau of Economic Analysis. The interest rate data are the secondary market 3-month T-bill rates given in FRED variable TB3MS, which is given as a percent discount. The primary source is the Board of Governors, U.S. Federal Reserve System. These are quarterly variables except for consumption (PCEC92) and the T-bill rate (TB3MS), which are monthly. The value given for the first month of each quarter (January, April, July, and October) was taken as the value for that quarter. The sample period for the data used is from the first quarter of 1992 to the third quarter of 1998. This sample period runs from the end of the 1990-91 recession to the end of the available data. The forecast horizon is two years into the future. The data was first-differenced to estimate the MPC and MPI. The regression of interest rates on investment was done in logarithms because the relationship is probably nonlinear, and to estimate the interest elasticity of investment.
Real GDP was used as a measure of national output and income because it is the most encompassing and most commonly used measure. Alternative measures were considered, including real GNP, real net private income, and real disposable income, and any could have been used in this case, though they may not have provided equally good results. Alternative measures of consumption, investment, imports, and interest rates were also available. Private Consumption Expenditures and Private Domestic Investment, which exclude government investment and purchases of consumption goods, were used because the Keynesian model depends strongly on the consumption behavior of households and the investment behavior of private firms. Although government spending also plays a major role in the Keynesian model, it is considered independent of GDP. (Gross) Imports of Goods and Services was used instead of Net Exports, because Gross Imports should respond more clearly to changes in U.S. GDP. The 3-month T-bill rate was used because it is the one interest rate the Federal Reserve System exerts very much control over, since the Fed is the primary buyer and holder of U.S. Treasury securities, and which also strongly influences market interest rates. For example, the Fed also controls the discount rate, but that has less direct influence on market interest rates.
Part 3. Economic Theory:
the Aggregate Expenditures Function
as a Forecasting Instrument
This forecast assumes the interest rate will remain constant for the next two years and will have no impact on investment spending or GDP. The annual growth rates for investment spending will be calculated over the sample period of the data. The average annual growth rate will be used to project investment spending into the future for the eight quarters of 1999 and 2000 to provide a short-term projection of investment. The values for projected future investment will be used to calculate GDP forecasts for each future quarter using the Keynesian autonomous expenditures multiplier:
This is a simple model appropriate for forecasting short-term GDP growth. The forecast should be interpreted as trend GDP in the absence of a recession. This model is probably not adequate to forecast a recession, especially one caused by unanticipated real aggregate supply shocks.
The marginal propensity to save (MPS) is 0.43, from a Keynesian consumption function estimated with 1992.1-1998.3 quarterly data. The Keynesian consumption function is written as:
Ct = C0 + MPC x Yt,
where C is real aggregate consumption expenditures and Y is real GDP. The consumption function was estimated in first-differences to address the effects of serial correlation of the data:
(Ct - Ct-1) = MPC x (Yt - Yt-1), (2.
This equation was estimated with a constant or intercept to avoid the unrealistic restriction that the regression line passed through the origin. The MPS = 1 - MPC.
The marginal propensity to import (MPI) is 0.23, from a Keynesian net export function estimated with 1992.1-1998.3 quarterly data. The Keynesian net export function is written as:
Xt = EXt - IMt = EXt - MPI x Yt,
where X is real net exports, EX is real gross exports, IM is real gross imports and is assumed to be a function of real GDP, and Y is real GDP. The gross import function is written as:
IMt = MPI x Yt,
(IMt - IMt-1) = MPI x (Yt - Yt -1), (3.
The MPI in the gross import function is the same as in the net export function. Like the consumption function, the first-differenced gross import function was estimated with an intercept to avoid the unrealistic restriction that the regression line passes through the origin.
The investment function is assumed to be nonlinear in a time index (t), which starts at zero for 1992.1 quarter and counts up by one for each subsequent quarter, and the secondary market three-month treasury bill interest rate (i):
It = atbitc,
which is written as it will be estimated in logarithms as:
ln(It) = ln(a) + b x ln(t) + c x ln(it), (4.
The coefficient c is the interest elasticity of investment and shows the percentage change in total real investment spending for every one percent change in the interest rate.
One of the shortcomings of this paper's approach is that investment spending is known to be highly volatile and responds to changes in interest rates and other factors which are particularly difficult to predict. Thus, the GDP forecasts here are best interpreted as long-term trend real GDP, that is, what GDP should be in the absence of a recession. Actual GDP may deviate from its long-term trend. Since investment may not grow at a constant rate, and since the MPS and MPI may not be constant over long periods of time, a relatively short forecast horizon, here two years, is the most appropriate use of this model.
Dornbusch and Fischer (1978, p. 143) estimated an MPS of 12% = 0.12. They cite estimates ranging from 65% = 0.65 in the short run to 28% = 0.28 in the long run (Dornbusch and Fischer, 1978, p. 152), based on data for the 1960s and 1970s. This should make it clear that it is very difficult to estimate the MPS, MPC, and MPI.
Part 4. Estimates of Investment, Consumption,
and Net Export Functions, and Forecast GDP
The consumption function, equation 2, was estimated with 1992.1-1998.3 quarterly data. The regression estimate is (t-statistics in parentheses):
(Ct - Ct-1) = 7.729(0.82) + 0.5653(3.51) x (Yt - Yt-1).
The estimated MPC is the coefficient on Y, indicating a value of 43% = 0.43 for the MPS. The adjusted R-square of the estimate is 0.312, indicating approximately 30% of the variation of C is explained by variation in Y. Low R-squares are not surprising for regressions with first-differenced data, which tend to amplify the impact of noise in the data. The t-statistic of the MPC is greater than three, indicating strong rejection of the null hypothesis that the MPC = 0. The t-statistic of the intercept is less than one, indicating failure to reject the null hypothesis that the intercept equals zero.
The gross import function, equation 3, was also estimated with 1992.1-1998.3 quarterly data. The regression estimate is (t-statistics in parentheses):
(IMt - IMt-1) = 9.648(1.92) + 0.23415(2.75) x (Yt - Yt-1).
The estimated MPI of 23% = 0.23 is the coefficient on Y. The adjusted R-square of the estimate is 0.207, indicating approximately 20% of the variation of gross imports is explained by variation in real GDP. As with the consumption function, low R-squares are not surprising for regressions with first-differenced data. The t-statistic of the MPI is nearly three, indicating strong rejection of the null hypothesis that the MPI = 0. The t-statistic of the intercept is nearly two, indicating rejection of the null hypothesis that the intercept equals zero. One interpretation of this non-zero intercept is that the first-differenced gross import function is misspecified, which would mean our MPI estimate is biased upward. Note this was not the case for the consumption function.
Based on the estimates of equations 2 and 3, MPS = 0.43 and MPI = 0.23. The Keynesian autonomous spending multiplier 1/[MPS + MPC] = 1.52.
The investment function, equation 4, was also estimated with 1992.1-1998.3 quarterly data. The regression estimate is (t-statistics in parentheses):
ln(It) = 6.375(76.7) + 0.110(1.48) x ln(t) + 0.159(7.44) x ln(it).
The estimated interest elasticity of investment is 16% = 0.16 indicates raising the interest rate by one percentage point causes investment spending to rise by 16%. Theoretically, the interest elasticity should be negative, so this estimate will not be used for forecasting investment spending conditional on different choices of the rate of interest. White (1956) cites survey data suggesting very low interest elasticity of investment, which may explain a positive estimate.
The investment function will only be used to project investment spending into the future assuming no change in interest rates. The t-statistic for the constant and the interest elasticity of investment indicate strong rejection of the null hypotheses that the coefficients equal zero. The t-statistic for the time index coefficient rejects the null hypothesis that the coefficient equals zero only at the 15% significance level or higher.
The adjusted R-square is 0.8399, indicating 84% of the variation in investment spending is explained by variation in interest rates and a linear time trend. The F-statistic is 69.2, indicating strong rejection of the null hypothesis of zero slopes.Equation 4 is used to project investment spending into the future for 1998.4-2000.4. Real investment spending is projected to increase each quarter by an amount equal to the coefficient on the time index. Changes in projected investment spending are multiplied by the Keynesian autonomous expenditures multiplier , as in equation 1, to get changes in real GDP:
DY = DI/[MPS + MPI] = 1.52 x DI,
which are added cumulatively to real GDP for 1998.3 quarter
to get projected real GDP. Results of this calculation are given
in table 1. All numbers are given in billions of chained 1992 dollars.
Forecast Real GDP and Investment, 1998.4-2000.4
|Quarter||Projected Real Investment (I)||Projected DI||Projected Change in Real GDP (Y)||Projected Real GDP|
Part 5. Forecast Implications: Steady Growth in the Short Term
GDP forecasts are interesting to a broad range of people because GDP is the most comprehensive and encompassing measure of economic activity. Because the forecast presented here can be interpreted as trend GDP, it could be compared to the U.S. Department of Commerce's projected GDP data to provide early warning of a recession. The forecast predicts a mild slowdown in the growth of real GDP and investment, but nothing too drastic. The forecast suggests little possibility that the continued low unemployment of the current expansion can rise to the level where output prices are driven up. Slightly higher unemployment levels seem to be indicated for the next two years, making it easier for employers to find employees, probably without creating much involuntary unemployment.
Part 6. Policy Conclusions
Real GDP is forecast to rise at approximately 3% per year, with real investment spending rising approximately 13-14%, for the next two years.
Assuming the forecast turns out to be correct, the many firms seeking to fill vacant job positions face some relief. The situation is not going to get worse, at least not over the next two years. It probably will become at least a little easier to fill job vacancies in the near future. No very dramatic change is forecast. Because of the shortage of workers, some firms are desperate to hire, and some have abandoned job searches. Firms are well advised to avoid or delay extreme measures to substitute other resources for labor, such as capital. The current labor shortage may be a persistent, long-term problem, but it is not going to get worse in the next two years.
Workers may not be able to continue to command such high wage increases, starting salaries, and signing bonuses, but the outlook for labor is similarly rosy. Unemployment should not increase above, and perhaps not even up to, the natural rate of approximately 6%. Although upward wage pressures should moderate compared to the past three years, the economic expansion and favorable job market appear far from over.
The forecast assumes no significant change in government spending over the next two years, which seems likely given projected budget surpluses. The government is not likely to increase spending dramatically, which would cause the expansion to overheat, or decrease it, which could cause a recession.
The forecast assumes no change in interest rates over the next two years. The Federal Reserve should be extremely careful not to change the interest rate unless it is clearly justified, and any change should be extremely moderate. The interest rate is currently very low, and lowering farther would promote more investment, lower unemployment, and threaten inflationary pressures. Raising the interest rate would also have negative effects of choking off the investment-fueled expansion, and raise unemployment, perhaps above the natural rate.
Federal Reserve Bank of St. Louis, Federal Reserve Economic Data (FRED), http://www.stls.frb.org/fred/
Dornbusch, Rudiger, and Fischer, Stanley, Macroeconomics, New York: McGraw-Hill, 1978.
White, William H., "Interest Inelasticity of Investment Demand - The Case from Business Attitude Surveys Re-examined," American Economic Review, 46, September 1956, pp. 565-587, reprinted in Mueller, M.G., Readings in Macroeconomics, New York: Holt, Rinehart and Winston, 1966, pp. 95-113.