The Tax Foundation Small Comparative Statics Model of the U.S. Economy

The Tax Foundation’s Taxes and Growth Model is a dynamic tax simulation model that simulates the impact of tax policy changes on the U.S. economy, drawing its key data from the Internal Revenue Service, the U.S. Bureau of Economic Analysis and the Federal Reserve. It is comprised of two interactive components to capture the interaction between the tax system and economic growth:

A Tax Simulator: This simulator, or tax calculator, can be thought of as “TurboTax” for the entire country. Unlike TurboTax, which performs calculations for one taxpayer at a time, our model calculates the effects on taxpayers across the income spectrum based on a large dataset made available by the IRS that contains roughly 150,000 statistically representative tax returns. The calculator generates average and marginal income tax rates, after-tax incomes, and the familiar “distributional tables” that display the after-tax effects of policy changes by AGI ranges and deciles. The results flow into the Tax Foundation’s Dynamic Macroeconomic model.

A Dynamic Macroeconomic Model: This is a “neoclassical” open-economy model that is driven by changes in the cost of labor and the cost of capital. Unlike some macroeconomic models, the Tax Foundation model holds Federal Reserve policy constant so that we can focus on the effects of tax changes, not the combination of monetary policy and tax policy. The model estimates the effect of tax changes on GDP, the cost of capital, wages, and federal tax revenues.

The Tax Foundation's Taxes and Growth Model is a small comparative statics model of the US economy.  It is based on empirical observations of the behavior of the economy over the post-world-war period.The underlying assumptions of the are straightforward:

  • The long run real aftertax rate of return to physical capital is virtually constant,
  • Labor’s share of factor income is virtually constant as well,
  • The supply of labor is somewhat inelastic (unresponsive) to its aftertax compensation.

These three assumptions define a set of five basic equations that when solved describe a baseline picture of the economy at a point in time as well as allowing changes in government taxes and spending to yield an alternative description.

The first assumption says that real interest rates tend to be constant when viewed over long periods.  It doesn’t have to be completely stationary; it merely requires that deviations tend to return toward the average.  Observations by economists as early as 1800 suggest this fact as they found that the level of interest rates in England tended toward its average.  Our own analysis shows the same result in the US over the past 60 years.  Deviations tend to return to the long run average within 5 years.  The mechanics are simple – deviations above the long run average encourage extra investment which drives the return down, and deviations below the long run discourage investment raising the return over time.

Looking at shares of factor income in businesses we find a second virtual constant.  The shares of factor incomes going to labor and capital are so constant that more sophisticated alternative explanations are statistically rejected.  The implication of this observation is that output can be predicted by a simple relationship that is linear in the logs of output and factor inputs (capital and labor).  Further the compensation paid labor and capital can be predicted as a constant percentage of net revenues.  Many have tried to estimate alternative models of production but none have overcome the empirical fact of the constancy of the shares.

Where the first assumption implies that capital is highly responsive to its return, labor is much less responsive to changes in compensation.  Dividing the labor force into primary and secondary pools finds that the primary pool (males 15 to 64) is extremely insensitive to compensation (an elasticity of about .1) with the secondary pool (primarily women) much more responsive (elasticities approaching 1).  We generally use an assumed elasticity of labor supply of .3; that is a 10% increase in real aftertax compensation gives rise to a 3% increase in labor.  Since we are less confident about this assumption we have constructed our model in a way that allows us to easily change this assumption.

The model is constructed by separating the economy into production sectors: corporate and noncorporate private business, households and institutions, government enterprises, and general government.  This aligns output according to how products are distributed and how the income generated is taxed.  General government does not sell its product in the market place while government enterprises do.  Institutions and households don’t actually sell their products but can be loosely construed as indirectly doing so.  All four of these sectors do have employees that pay taxes through the individual income tax.  Private businesses produce the lion’s share of output. They pay taxes on their capital income and their employees pay individual taxes as well.  This division into four sectors provides enough detail to construct tax bases for most taxes.

Each sector is constructed applying the three assumptions outlined above.  This provides us with estimates of output and the compensation of capital and labor for the sector.  Labor from all sectors is aggregated and the overall wage rate for labor is determined by our assumed response to changes in real aftertax compensation.

We make one final assumption to round out the model -- the Federal Reserve changes its policy to maintain the price level at its baseline values.  This allows us to focus on the effect of the spending or tax change rather than some combination of fiscal policy change with an accompanying monetary change.  The secondary benefit is that we don’t have to adjust for price changes in determining real compensation for capital and labor.

Using the structure we have outlined we can calibrate the model to the chosen baseline.  An alternative fiscal mix of taxes and spending can be entered into the framework.  The baseline aftertax rate of return can be used to calculate what the pretax return must be under the new tax system.  This rate of return implies the wage rate that must prevail to satisfy the existing production technology.  Removing the taxes on labor tells us the change in the aftertax rate of compensation.  Using our assumed elasticity of labor supply tells us how much labor will be supplied in the economy.  This then will tell us how much capital will be employed and finally what the level of output will be.

Since we have split our income in a manner that will allow us to calculate the various tax bases needed to estimate taxes, we can calibrate tax revenue parameters using the baseline and use them to calculate a detailed set of revenue accounts for federal, state and local governments.  Personal income taxes and effective marginal rates are calculated using a large weighted sample of tax returns that represent the base year.  The impact of cost recovery (depreciation) changes is simulated using a detailed breakdown of over 1,000 types of business capital for the base year.  A spending account is added to allow us to calculate deficits as well.