Some Economic Theory and Possible Paper Topics

Robert F. Mulligan, Ph.D.
Department of Economics, Finance, & International Business

Journal of Economic Literature Classification Codes

The Keynesian Aggregate Expenditure (AE) Model

This model is a.) highly oversimplified (like any really good model) and b.) can be considered ideologically biased (particularly by people who find its policy implications unattractive.) It is especially useful for macroeconomic forecasting and policy analysis because it is simple and relatively easy to use, because its parts correspond well to the National Income and Product Accounts (NIPA), and because it includes many of the most important variables used to track economic progress.

Aggregate expenditure (AE) is equal to the sum of consumption (C), investment (I), government spending (G), and net exports (X). Net exports equal total (gross) exports minus total (gross) imports. In equilibrium, nominal AE equals nominal gross domestic product (GDP) and real AE equals real GDP, over any time period. Our focus is normally on real, rather than nominal, variables.

C consists of autonomous consumption, which does not depend on real GDP or disposable income, and induced consumption, which depends on real GDP and disposable income. Autonomous consumption is the intercept of the consumption function. The slope of the consumption function is called the Marginal Propensity to Consume (MPC). Since any disposable income not consumed is saved, the MPC and the marginal propensity to save (MPS), or savings rate, always sum to one. Therefore, an estimate of the MPS gives an estimate of the MPC, and vice versa. The consumption function can be written as:

C = C0 + MPCxY,
where C0 is autonomous consumption and MPCxY is induced consumption. Y is real GDP or disposable income. Disposable income is income after taxes. Real GDP and disposable income are not the same, but have a constant relationship unless the tax rate is changed.

I and G do not depend on GDP or disposable income, and are autonomous in the same sense as autonomous consumption. The same is true of total (gross) exports, which depend on foreign income, not U.S. income. I, G, autonomous consumption, and total (gross) exports add up to autonomous expenditures, the intercept of the AE. I is the most volatile component of AE, and depends on the interest rate (r). The higher r, the lower I.

The last part of the AE, total (gross) imports, depends on U.S. GDP and disposable income. Total imports rise as U.S. GDP and disposable income rise. The percentage of every dollar in disposable income spent on imports is called the marginal propensity to import (MPI). Since total imports contribute negatively to AE (which is aggregate spending on U.S. GDP), the MPI is a negative component of the slope of the AE.

If the investment function is written as:

I = I(r),
showing investment is a function of the interest rate; G is a constant arbitrarily determined by the government; and the net export function is written as:
X = EX - MPIxY,
where EX is total (gross) exports, and the second term (MPIxY) is total (gross) imports, which depends on the level of real GDP and is subtracted from AE; then AE is written as:
AE = C+I+G+X = (C0 + MPCxY) + I(r) + G + (EX - MPIxY),
or, gathering terms:
AE = [C0+I(r)+G+EX] + [MPCxY - MPIxY] = autonomous expenditures + [MPC-MPI]xY,
the sum of autonomous and induced expenditures.

In equilibrium AE = Y (planned aggregate expenditures on U.S. GDP equal actual aggregate expenditures on U.S. GDP), so we can substitute Y for AE:

Y = autonomous expenditures + [MPC-MPI]xY.

Solving for equilibrium real GDP and recalling that MPC + MPS = 1, we find

Y = autonomous expenditures/[1-MPC+MPI] = autonomous expenditures/[MPS+MPI].

This expression for real GDP shows us the Keynesian autonomous spending multiplier 1/(MPS+MPI), often called the government spending multiplier or just the multiplier.

If one knows MPS (or MPC) and MPI, (or estimates them, or borrows someone else's estimates,) then one can determine the change in real GDP which will be caused by a change in any component of autonomous spending, including G or I. Since government spending is a.) largely non-discretionary, and b.) not easy to change in the short run (given a two-year or longer government budget cycle,) today, most use of the AE centers around how changes in the consumption, investment, or net export functions impact real GDP. The traditional Keynesian use of the AE was to calculate the amount G needed to be increased during a recession to raise GDP to the pre-recession level.

A good forecasting project would be to estimate the investment function, using NIPA investment data, and actual interest rates for bonds or other instruments of appropriate time-to-maturity. This would provide the relationship between I and r. Other variables could be included to improve the estimate. Then the AE could be used to forecast GDP given different possible future interest rates.

Another good forecasting project would be an evaluation of the Japanese recovery program. Based on Japanese MPS and MPI, and the planned increase in government spending, how much should Japanese GDP increase? Is this amount sufficient to end the recession, and if not, how much is required? How much will the increase in government spending cause the interest rate to rise? To what extent will crowding out of investment prevent GDP from increasing?

Another project would be an assessment of the impact of German unification on the German (and possibly the European) macroeconomy. To finance massive investment in East German infrastructure, the German government greatly increased government spending, raising both German nominal interest rates and inflation. To what extent has this crowded out private investment, and how has it impacted German GDP?

Another project would be a similar preliminary assessment of the probable impact of Korean unification on the Korean economy. How much would need to be spent, from a Keynesian perspective, to raise North Korean per capita GDP to the same level as South Korea? How many years should be allowed? What impact would the increase in spending have on the South Korean economy?

European monetary unification provides a large range of possible topics. One would be an examination of the trade-off between the need for European central bank intervention to maintain fixed exchange rates and the behavior of the member countries' governments and central banks to minimize the need and cost of such intervention.

Speculative attack against EMU currencies, using spot and forward foreign exchange contracts, delayed implementation of the Maastrich agreement. A possible project would be to evaluate the possibility of future speculative attack, both in terms of assessing its likelihood, profitability to speculators, and cost to other investors, and the possibility of defending against or deterring it (by raising interest rates).

Another project would be to estimate consumption functions using demographic data (as well as GDP), and forecasting GDP for a variety of different demographic outcomes. For example, estimate the relationship between consumption spending and the number of U.S. residents under 40. Project different consumption levels for a range of different outcomes for this explanatory variable (holding any others constant.) Then project GDP based on the range of estimated consumption functions.

A further project would be to estimate the net export function (including the MPI), based on different scenarios about future economic growth in Canada, Europe, or Japan. What impact is the recession in Japan having on our economy? What would happen to U.S. GDP if Japan were to recover? What if Europe and/or Canada were to have recessions also? What about our next largest trading partner, Mexico? The impact of the economic crises in Thailand, Hong Kong, Singapore, Malaysia, Indonesia, Brazil, and Russia has been minor so far, but could be analyzed the same way. How much should the U.S. be willing to spend to fix these problems?

Changing the tax rate also changes the consumption, investment, and net export functions, so the Keynesian AE model can also be used to evaluate the impact of a tax increase or decrease.

The AE is used to derive the aggregate demand (AD) function, which relates the level of equilibrium real GDP to the price level. The traditional Keynesian AS was horizontal, and suggested any increase in G resulted in an increase in real GDP, without any increase in the price level. This model explained reality very well for the severe post World War I recession, and the Great Depression, when economies faced high unemployment and low capacity utilization.

The traditional classical AS was vertical, which has some plausibility in explaining an environment with low unemployment and high capacity utilization. The neoclassical SRAS is horizontal at low employment and capacity utilization levels, and vertical at the physical limit region, when the economy operates at full capacity and above natural employment (below natural unemployment, also called natural output.) The economy operates most of the time in the intermediate upward-sloping region of the SRAS where it crosses the LRAS.

Monetarism: The Quantity Theory of Money and the Monetarist Interpretation of the Phillips Curve

The Quantity Theory of Money is defined by the equation of exchange:

where M is a measure of the money supply such as M1, M2, M3, etc., P is the price level, which can be measured by the real GDP deflator or the consumer price index, Q is real GDP (sometimes called Y for income rather than Q for output), and VQ (or VY) the income velocity of money, often assumed to be a constant which evolves slowly as banking practice and technology for facilitating transactions improve. There is a different, special V for each measure of the money supply (e.g., M3 velocity.)

If Q is replaced by T, the total amount of money transactions, the equation of exchange becomes:

and the new VT is called the transactions velocity. Solving either of these equations for P gives an explanation of the price level and a way to forecast or analyze the rate of inflation:
P = MVQ/Q = MVT/T.

After the Phillips curve was discovered, it was adopted by the Keynesians as proof that raising government spending (which would eventually bid up product prices) would lead to more GDP being produced and therefore lower unemployment. The starkly contrasting monetarist view is that unemployment is always fixed at the natural rate in the long run and therefore the long-run Phillips curve (LRPC) is vertical at natural rate of unemployment (approximately 6%).

The New Classical School: the Supply Side and the Expectations-augmented Phillips Curve

In the late sixties the U.S. faced both high inflation and high unemployment. It appeared that the traditional Keynesian interpretation that the Phillips curve, which indicated a clear trade-off between inflation and unemployment, had failed. The New Classical economists suggested money and price-related variables could not affect real output. They looked to real supply-side shocks like the OPEC oil embargo to explain business-cycle output and employment fluctuations. They also provided an explanation of the short-run relationship between inflation and unemployment.

The New Classical interpretation of the Phillips curve is that it is vertical in the long run, but upward-sloping in the short run. This provides the inflation-unemployment trade-off Phillips identified. The location of the short-run Phillips curve (SRPC) is determined by what people expect the inflation rate will be in the future (i.e., how fast they expect the price level to rise.) The SRPC intersects the LRPC at the expected inflation rate.

If the government takes advantage of the SRPC trade-off, it can lower unemployment by raising the price level faster than workers expect. Workers require relatively low wage increases because they expect low inflation. If the government or central bank delivers a higher inflation rate than workers expect, the price of output increases faster than workers' wages, and more workers are hired to produce higher-priced output.

But workers eventually respond by revising their expectations upward, shifting the Phillips curve upward. If the government takes advantage of this once, the trade-off breaks down, because the SRPC shifts up. A possible project would be to graph U.S. inflation and unemployment from 1980 to 1999, assuming a natural rate of unemployment of 6%, to show what the expected inflation rates were at each time.

The Forecasting Project

(This is mostly copied from the syllabus.)

Each student or team will contribute a 4-5 page article to a comprehensive survey and projection of economic conditions. Variables you may choose to forecast include: real GDP or any significant component of real GDP, real consumption spending, real investment spending, the real capital stock, real net exports, unemployment, employment, inflation, the money supply velocity of exchange, interest rate(s), or the shape of the yield curve. Your forecast may discuss the behavior of a variable at the national, regional, or state level. "Regional forecasting projects" may focus on regions consisting of more than one state, such as the Southeast, or the Richmond Federal Reserve District, or regions of a particular state, such as Western North Carolina, or Jackson County. Industry analysis and outlook articles will also be acceptable.

You will be required to submit two, different 1-2 page proposals, to avoid duplication of topics. It will be OK if two papers forecast GDP if the forecasts take different ideological approaches (i.e., Keynesian, new classical, or monetarist), or if they use different approaches (e.g., Keynesian GDP forecast based on projected government spending v. based on projected consumption spending, investment spending, or net exports,) or forecast horizons (e.g., one-year GDP forecast based on investment spending v. ten- year forecast based on census projections.) You may work as individuals or in teams of two. Teams of three or more will not be permitted.

Your proposals must identify the subject of your forecast and analysis. You must discuss the importance of forecasting this particular variable, explain the theoretical basis for your forecast (e.g., Keynesian, new classical, monetarist, etc.), and identify the data you will use. You must identify the source of your data in your proposal and you must be certain the data is really available from that source. I will take your proposals to indicate you have ensured you have access to the data you need, and I will hold you to that. You must indicate the forecast horizon and explain why your approach and explanatory variables are appropriate to the horizon you have chosen.

Be sure to include an introduction and conclusion in your paper. The introduction should explain the overall plan of the paper so the reader knows what to expect and where to look for parts of special interest. Indicate your data sources, a bibliography, and footnotes or endnotes. The Wall Street Journal is an excellent source of information and relevant articles.

I will provide further instructions and a sample format for the paper.

Do not attempt a project that is very data intensive. Limit the number of explanatory variables to one if possible, and no more than three or four at a maximum. Do not go back beyond 1990 for data. Consider the fact that you may have to enter each observation in an MS Excel spreadsheet.


Proposal Format

College of Business
Western Carolina University

Use MS Word if possible. Use 14 point Times New Roman bold for the title. Make a descriptive title which you intend to be the same for the final paper, though you will be free to change the title. If you are stuck for a good title, use something like: "A Ten Year Forecast of U.S. Consumption Spending," or "North Carolina Domestic Product: Year 2000 Outlook." Everything else should be in 10 point Times New Roman. Single space inside each paragraph. Space between paragraphs. Leave one-inch margins throughout.

Your name(s) should be all caps and bold. Your primary institutional affiliation should be exactly as shown, but do not leave any blank lines between your name and institutional affiliation. You may list a secondary institutional affiliation (e.g., your employer) below the first, separated by one line with an ampersand (&). If there are two co-authors, list both on the same line: "JANE DOE and JOE DOAKS" as long as the institutional affiliations are the same for both authors. For two co-authors with different institutional affiliations, list one above the other, separated by "and" with a blank line before and after the "and."

The first paragraph of your proposal should state the variable to be forecast and the explanatory variables to be used as the basis for the forecast. State what model you are using. You may discuss the benefits/shortcomings of using such a simple model as long as it will not make your proposal exceed one page.

The second paragraph should describe the data you will be using. Identify the source, observation interval, and sample period for each variable. If you can find all the data in a single source, like the Federal Reserve Bank of St. Louis's FRED database, that is a big plus. The National Income and Product Accounts (NIPA) are your best source for most non-financial macroeconomic data for the U.S. Make sure your forecasting approach is based on a theoretical relationship, and not an accounting identity (e.g., AE = GDP = C+I+G+X is an accounting identity.) State whether you are using one variable to proxy another. 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 will transform your data by forming indices, taking logarithms, taking first-differences, and explain why you feel this may be helpful. 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.

The third paragraph should explain any relevant assumptions. If 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). If you use someone's published estimate, state who it is, and give the value. 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.

The fourth paragraph should explain why your forecasting approach, including theoretical model and choice of explanatory variables, is appropriate to the forecast horizon you have chosen.

The fifth paragraph should explain why the variable you have chosen to forecast is interesting and important to forecast. Explain who might be interested in your forecast and what it might be useful for.

If you have any equations, center, bold, and italicize them. References are not required for the proposal. See the sample proposal on the next page.


U.S. Gross Domestic Product: a Year 2000 Forecast
from a Simple Aggregate Expenditures Perspective

College of Business
Western Carolina University

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 Simon Kuznet's estimates of the marginal propensity to save (MPS) and import (MPI).

Both variables are taken from the Federal Reserve Bank of St. Louis Federal Reserve Economic Data (FRED). Both are observed quarterly. The sample period for the data used will be from the first quarter of 1992 to the fourth quarter of 1998. The measure of GDP used is FRED variable GDPC92, real GDP measured in chained 1992 dollars, seasonally adjusted annual rates. The measure of investment spending is FRED variable GPDIC92, real gross private domestic investment measured in billions of chained 1992 dollars, seasonally adjusted annual rates. The forecast horizon is two years into the future. No data transformations will be performed.

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:

D Y = D I/[MPS+MPI].

The values of the marginal propensity to save (MPS) and the marginal propensity to import (MPI) are 10% and 7% estimated by Kuznets (1946).

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.

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.