November 14, 2002
A Spreadsheet for Rapid Solow Growth Model Calculations

The purpose of this spreadsheet is to give you a framework that you can use to calculate your own scenarios for the Solow growth model--the workhorse model for the modern neoclassical theory of economic growth. The equations just sit there on the page. To get an idea of how the model works and what the model means, you need to look at scenarios: at sample toy economies that behave according to the model, and on how their behavior changes in response to different kinds of shocks that might affect the economy through changing the parameters of the growth model.

Download this spreadsheet and play with it. Set up your own baseline scenarios, and see how different parameters in the pre-shock baseline affect the pattern of economic growth for an economy growing along its balanced-growth path. Then settle on a baseline scenario, play with different kinds and magnitudes of shocks, and examine the dynamic response of the scenarios' economies to these shocks over time.

Scenario 1: Permanent Changes in Fiscal Policy

(a) Begin with a typical baseline scenario: In the shaded "initial values" boxes, set the economy's savings-investment rate s to 21% of output, set the depreciation rate delta to 4% per year, set the rate of technological progress in labor efficiency g to 2% per year, and set the population growth rate n to 1% per year. Set the production-function parameter alpha set equal to 1/3, and with the year-zero (that is, the shock year) level of the efficiency of labor E set equal to \$46,188 to give a year-zero output per worker level of \$80,000.

Now suppose that a president who ran on a program of tax cuts changes the tone in Washington, and so permanently changes the government's budget balance from an average surplus of 2% of output per year to a small deficit of 1.5% of output per year. Suppose that this shift in fiscal policy triggers no countervailing or reinforcing shifts in private savings or in net investment by foreigners, so that the effect of this policy change on the parameters of the growth model is to reduce the savings-investment rate s by 3.5%. So add a "-3.5%" to the shaded box in the "shocks" column in the line of the spreadsheet that sets the value of the savings-investment rate s. Look at the calculated numbers for the economy's growth path before and after this fiscal policy shock. Look at the graphs showing output per worker and the capital-output ratio. What is the effect of the shift in fiscal policy on the location and slope of the economy's balanced-growth path? How fast does the economy converge to its new balanced-growth path? How would you summarize the effects of the policy change on economic growth?

Extra Credit: If there is no monopoly or increasing returns in an economy, the gross earnings--interest, dividends, retained earnings, and other gross profits--of owners of capital can be calculated easily: simply divide the production-function parameter alpha by the capital-output ratio. That gives you the contemporaneous rate of gross profit. Calculate--for whatever sample years you wish--the effect of this shift in fiscal policy on the gross rate of profit. Recall that the net rate of profit is simply the gross rate of profit minus the rate of depreciation. Calculate the effect of this shift in fiscal policy on the net rate of profit. Suppose further that there is a risk premium of four percent that drives a wedge between the rate of profit earned by owners of capital (who bear a lot of risk) and the rate of interest earned by owners of (safe) Treasury bonds. What then is the real rate of interest on Treasury bonds before the change in fiscal policy? What happens to the real rate of interest over time?

(b) In response to the change in fiscal policy, Harvard economist Robert Barro goes on a nationwide speaking tour, pointing out that taxes have been cut--not spending--that as a result the government is going to have to raise taxes far and fast in the future, and that people need to increase their savings so as not to be impoverished when the tax increases do come. People listen, and believe: private savings increases by 2.5 percent of GDP, so that the net effect of the change in fiscal policy is not a 3.5% but a 1% decline in the savings-investment rate s. How are the answers you get from evaluating the effect of this shock--deficit increase plus partial savings offset--different from the answers you got in part (a)?

(c) Return to the situation of part (a), and make a different set of assumptions about the ramifications of the change in fiscal policy. In response to the change in fiscal policy, New York University economist Thomas Sargent goes on a nationwide speaking tour, pointing out that a government with a chronic deficit is going to be under a large temptation to repudiate its debt by resorting to high inflation at some point in the future. People listen, and believe: Americans take 3.5% percent of GDP that they had devoted to domestic savings and, worried about the consequences for wealth holders of high future inflation, invest it abroad instead. Thus the net effect of the change in fiscal policy is not a 3.5% but a 7% decline in the savings-investment rate s. How are the answers you get from evaluating the effect of this shock--deficit increase and savings amplification--different from the answers you got in part (a)?

(d) Return to the situation of part (a), and make a different set of assumptions about the ramifications of the change in fiscal policy. Suppose that part of the increase--2.0% of output--in the federal deficit is financed by foreigners, so that the net effect of the fiscal policy is a decline of 1.5% in the savings-investment parameter s. How are the answers you get from evaluating the effect of this shock--deficit increase partly offset by a capital inflow--different from the answers you got in part (a)?

(e) Return to the situation of part (a), and make a different set of assumptions about the ramifications of the change in fiscal policy. Suppose that the higher deficit causes foreigners to fear monetary instability in the U.S. at some point in the future, and leads them to pull investments out of the United States. Thus the decline in the savings-investment parameter is amplified by this capital outflow, and the total amount that s declines by is 5.0%. How are the answers you get from evaluating the effect of this shock--deficit increase plus capital outflow--different from the answers you got in part (a)?

Now think of your own scenarios: changes in population growth rates, in the growth rate of technical progress, and so on. And think of changing more than one parameter at a time. What effect does a budget deficit have if the production-function parameter alpha is larger? Smaller? There is lots to do...

Posted by DeLong at November 14, 2002 05:03 PM | Trackback

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"...Thomas Sargent goes on a nationwide speaking tour, pointing out that a government with a chronic deficit is going to be under a large temptation to repudiate its debt by resorting to high inflation at some point in the future."

The temptation might be there, but I doubt that this can occur in today's instant communication era. Governments try at least to be discrete, if not downright sneaky when attempting to increase the inflation rate to cover their debts. In the United States, the stock market would take a nose dive at the first hint that the politicians were planning to pull such a stunt.

Posted by: David Thomson on November 14, 2002 05:43 PM

So we get a deficit and then inflation...the bond market goes sour for now and and the stock market picks up. At some point the inflation premium will be factored into bond prices. It was said that many new technology companies benefited from the low cost of capital, so inflation and a higher cost of capital, will dampen technology start ups. But technology was one of the things stimulating the economy.

Posted by: on December 10, 2002 02:47 AM