The economic effects of the fair tax: analysis of results of a dynamic CGE model of the US economy

By replacing the current income tax with a national sales tax, the FairTax proposal would end the double taxation of saving inherent in the existing tax code and, by doing so, raise output, employment, investment and capital stock relative to the benchmark economy. While these positive effects would be felt almost immediately, the FairTax is very much an investment in the future. Its full benefits would be realized only after the economy achieved a new “steady state,” some 20–25 years into implementation. Only by that point, will the effects on growth have been fully absorbed into the economy and the wellbeing of most households across most income groups improved. The policy choice, then, is between the status quo, and a new policy that would inflict some short-run pain as the price of a permanently expanded economy.

and exchange rates. The most appropriate tool for quantifying these effects is a computable general equilibrium (CGE) model. Since their beginnings in the 1970s, CGE models have been used to address tax issues, and are routinely used by government agencies such as the U.S. Treasury, the Congressional Budget Office, and International Trade Commission for policy analysis. A very clear early exposition is provided in Shoven andWhalley (1984, 1992).
We have constructed a large, 15,000-variable, disaggregated dynamic national CGE model of the United States economy. The essence of our model is shown in Fig. 1, which is heavily inspired by Berck et al. (1996), and where arrows represent flows of money (for instance, households buying goods and services) and goods (for instance, households supplying their labor to firms).
Households own the factors of productionland and capitaland are assumed to maximize their lifetime Butility^, which they derive from consumption (paid for out of after-tax income) and leisure, both now and in the future. Households must decide how much to work, and how much to save. They are also forward-looking, so that if they see a tax change in the future, they may react by changing their decisions even now. By eliminating the personal income tax, corporate income tax, payroll taxes and estate taxes at the federal level, the FairTax would raise lifetime utility; the introduction of a federal sales tax would work in the other direction.
The other major actor is the government, which imposes taxes and uses the revenue to spend on goods and services, as well as to make transfer payments to households. We have calibrated the model so that the effects of the FairTax will be revenue-neutral.
Implicitly, there is also a production sector where producers/firms buy inputs (labor, capital, and intermediate goods that are produced by other firms), and transform them into outputs. Producers are assumed to maximize profits and are likely to change their decisions about how much to buy or produce depending on the (after-tax) prices they face for inputs and outputs. The endowment of capital depreciates over time, and is reconstituted through investment, which is undertaken in anticipation of future profits. The implementation of the FairTax raises the levels of investment and capital stock by To complete the model there is a rest-of-the world sector that provides goods (U.S. imports) and purchases U.S. exports. Trade is represented by the standard Armington assumption, which uses a constant-elasticity-of-transformation function to determine the allocation between domestic sales and exports. The benchmark reference part of the economy is represented by a steady-state growth rate for quantities of all goods and services.
Complex as it may seem, Fig. 1 is still relatively simple, because it lumps all households into one group, and all firms into another. To provide further detail it is necessary to create sectors; our model has 68 economic sectors. Each sector is an aggregate that groups together segments of the economy. We separate households into seven income classes and firms into 27 industrial sectors. In addition, we distinguish between 19 types of taxes and funds (nine at the federal level and 10 at the state and local level) and 11 categories of government spending. To complete the model, there are two factor sectors (labor, capital), an investment sector, and a sector that represents the rest of the world. The choice of sectors was dictated by the availability of suitably disaggregated data (for households and firms), and the purposes of the model. The underlying data are gathered into a 68 by 68 social accounting matrix (SAM), which includes an input-output table as one of its components.

The formal specification of the model
Space does not permit an exhaustive presentation of our model, so here we set out just the key components.
Infinitely-lived households allocate lifetime income to maximize the present value of lifetime utility LU h À Á ; which itself is a time-discounted CES aggregation of a composite consumption good (C t h ) and leisure (L t h ), with an elasticity of substitution between consumption and leisure given by σ u h (as in Bhattarai 2001Bhattarai , 2007. Note that the composite consumption good is in turn a Cobb-Douglas aggregation of 27 domestically-produced, and 27 imported, goods and services. The representative household faces a wealth constraint where the present value of consumption and leisure cannot exceed the present value of its full disposable income (J t h ), which gives lifetime wealth (W h ). Under current tax rules, this implies where μ t ð Þ is a discount factor, P t is the price of consumption, C t h is composite consumption, t vc is the sales tax on consumption, t l represents taxes on labor income, and w h t is the wage rate. With the FairTax, this constraint becomes where t F represents the FairTax rate, and D t is the demogrant that represents a cash payment to every person.
The structure of production is summarized in Fig. 2. Starting at the bottom, and for each of the 27 production sectors, producers combine labor (which comes from seven different categories of households) and capital (using a CES production function, with elasticity of substitution σ v ) to create value-added, which is in turn combined with intermediate inputsassumed to be used in fixed (BLeontief^) proportionsto generate gross output. This output may be exported or sold domestically, modelled with a constant elasticity of transformation (CET) export function between the U.S. markets and all other economies. The domestic supply is augmented by imports, where we use a constant elasticity of substitution (CES) function between domestically supplied goods and imports. The underlying growth rate in the BHI CGE model is determined by the growth rate of labor and capital. Labor supply, which is equivalent to the household labor endowment less the demand for leisure, rises in line with population. The capital stock (K) for any sector in any period is given by the capital stock in the previous period (after depreciation) plus net investment (I). On a balanced-growth path, where all prices are constant and all real economic variables grow at a constant rate, the capital stock must grow at a rate fast enough to sustain growth. This condition can be expressed as: where the subscript T denotes the terminal period of the model, δ i is the depreciation rate, and g i is the growth rate for sector i and is assumed uniform across sectors for the benchmark economy.
Although the time horizon of households and firms is infinite, in practice the model must be computed for a finite number of years. Our model is calibrated using data for 2004 and stretches out for 27 years (i.e. through 2031). To ensure that households do not eat into the capital stock prior to the (necessarily arbitrary) end point, a Btransversalityĉ ondition is needed, characterizing the steady state that is assumed to reign after the end of the time period under consideration. We assume, following Ramsey (1928), that the economy returns to the steady state growth rate of 3 % at the end of the period.
The model also requires a number of identities. After-tax income is either consumed or spent on savings. Net consumption is defined as gross consumption spending less any consumption tax. The flow of savings is defined as the difference between after-tax income and gross spending on consumption, and gross investment equals national saving plus foreign direct investment.
A zero trade balance is a property of a Walrasian general equilibrium model; export or import prices adjust until the demand equals supply in international markets. However, foreign direct investment (FDI) plays an important role in the U.S. economy, as exports and imports are not automatically balanced by price adjustments. Therefore our Walrasian model is modified here to incorporate capital inflows so that the FDI flows in whenever imports exceed exports. Thus where for period t, FDI t is the amount of net capital inflows into the U.S. economy, ∑ i PM i;t M i;t is the volume of imports and ∑ i PE i;t E i;t is the volume of exports.

Calibration to steady state
The model is truly Bdynamic^in that it is optimized over time, and is calibrated using data for 2004. The model is programmed in GAMS (General Algebraic Modeling System), a specialized program that is widely used for solving CGE models (Brooke et al. 1998). The core of the model is programmed in the mathematical programming for system of general equilibrium (MPSGE) code, which was written by Thomas Rutherford (1995) to facilitate the development of market-clearing dynamic CGE models; see also Lau et al. (2002).
The model is calibrated to ensure that the baseline grows along a balanced growth path. In the benchmark equilibrium, all reference quantities grow at the rate of labor force growth, and reference prices are discounted on the basis of the benchmark rate of return. The balance between investment and earnings from capital is restored here by adjustment in the growth rate g i that responds to changes in the marginal productivity of capital associated with changes in investment. Readjustments of the capital stock and investment continue until this growth rate and the benchmark interest rates become equal.
If the growth rate in sector i is larger than the benchmark interest rate, then more investment will be drawn to that sector. The capital stock in that sector rises as more investment takes place, leading to diminishing returns on capital. Eventually the declining marginal productivity of capital retards growth in that sector.
To solve the model, we allow for a time horizon sufficient to approximate the balanced-growth path for the economy. Currently the model uses a 26 years horizon, which can be increased if the model economy does not converge to the steady state.

Behavioural elasticities of substitution in consumption and production
Our CGE model simulates the effects of tax changes. The structure of the model depends not only on the magnitudes in the social accounting matrix, but also on the behavioural parameters, which reflect how consumers and producers react to changes in prices. These parameters are mainly in the form of elasticities of substitution, but also include depreciation and discount rates, and an assumed steady state growth rate. The parameters we use are set out in Table 1, and are comparable to those found in the existing literature; including Tuerck et al. (2006), Bhattarai and Whalley (1999), Killingsworth (1983), Kotlikoff (1993Kotlikoff ( , 1998, Kydland and Prescott (1982), Ogaki and Reinhart (1998a, b), Piggott and Whalley (1985), and Reinert and Roland-Holst (1992). Inter-temporal elasticity of substitution, σ Lu 1.0 Intra-temporal elasticity of substitution between leisure and composite goods, σ u 0.2 Elasticity of substitution in consumption goods across sectors, σ C 1.0 Elasticity of substitution between capital and labor, σ v 2.0 Reference quantity index of output, capital and labor for each sector, Q rf (1 + g) t − 1 Reference index of price of output, capital and labor for each sector, P rf 1/(1 + r) t − 1 A few further comments are in order. The intertemporal elasticity of substitution (σ Lu ) measures the responsiveness of the composition of a household's current and future demand for the composite consumption good to relative changes in the rate of interest, and is a crucial determinant of household savings. There is little consensus in the literature about a reasonable value for this elasticity: Ogaki and Reinhart (1998a, b) estimate it to be between zero and 0.1 in the case of durable goods; Hall and Rabushka (1983) finds it to be very small, even negative, while Hansen and Singleton (1983) note the lack of precision in the estimates of σ Lu . Auerbach and Kotlikoff (1987) assume it to be about 0.25; Kydland and Prescott (1982) assume it to be 1.0, which is also the value we use.
The intratemporal elasticity of substitution between consumption and leisure (σ u ) determines how consumers' labor supply responds to changes in real wages. Indirect evidence on this elasticity is derived from various estimates of labor supply elasticities that are available in the literature (Killingsworth 1983). Here we adopt a value of 0.2 for this substitution elasticity. Further discussion on how to derive numerical values of substitution elasticities from labor supply elasticities is provided in earlier studies on tax incidence analysis (Bhattarai and Whalley 1999).
The intratemporal elasticity of substitution among consumption goods (σ C ) captures the degree of substitutability among goods and services in private final consumption. A higher value implies more variation in consumption choices when the relative prices of goods and services change. Consistent with Piggott and Whalley (1985), we specify a value of 1.0 for this parameter.
The Armington elasticity of transformation (σ e ) determines the sale of domesticallyproduced goods between the home and foreign markets in response to relative prices between these two markets. The Armington substitution elasticity (σ m ) determines how the domestic and import prices affect the composition of demand for home and foreign goods. Higher values of these elasticities mean a greater impact of the foreign exchange rate in domestic markets. Reinert and Roland-Holst (1992) report estimates of substitution elasticities for 163 U.S. manufacturing industries and find these elasticities to be between 0.14 and 3.49. Piggott and Whalley (1985) suggest central tendency values of these elasticities to be around 1.25.
Early estimates of the elasticity of substitution between capital and labor (σ v ) may be found in Arrow et al. (1961). They estimated constant elasticities of substitution for U.S. manufacturing industries using a pooled cross country data set of observations on output per man hour and wage rates for a number of countries; we use a value of 2.0.

Results
We formulate and solve the model using the GAMS/MPSGE software (Rutherford 1995), with the PATH solver in GAMS (Brooke et al. (1998)). The model is first calibrated. The data from the SAM, and the assumed elasticities, are used to identify the parameters of the model's equations. These equations are then solved. If they generate the same numbers as the SAM, then the model has been calibrated successfully. The benchmark model is first solved on the assumption that the current Federal tax system persists into the foreseeable future. This provides a benchmark against which to judge the effects of major tax changes.
We then assume that in 2007, the major Federal direct taxes (personal and corporate income taxes, payroll taxes, and gift and estate duties) are replaced by the FairTax, at a rate that is revenue-neutral in 2007, and turns out to be 23 % on a tax-inclusive basis. The same FairTax rate is applied every year thereafter.  The essential results from the solutions of the benchmark and FairTax economies are summarized in Table 2, and in Fig. 3, where the graphs are designed so as to begin in the first year of implementation of the FairTax.
The key result is striking: by implementing the FairTax, real output would be 3.9 % higher within a year, 6.8 % greater in year five, and 10.1 % above the benchmark by the end of year 25. These results slightly higher than those found by Kotlikoff and Jokisch (who use a very different model), and in line with those found by Arduin et al. (2005). The growth would be driven by a surge in savings and investment (Fig. 3, bottom left), which would eventually raise the capital stock by a fifth (Fig. 3, bottom right); there would be a modest rise in employment, and consumption, after falling initially (to allow for higher savings) would eventually rise by about 4 % (Fig. 3, middle panels). Increase in revenue due to higher growth makes the tax system less distortionary in the future as argued in Burger and Zagler (2008). The disaggregated model also allows one to break down the increase in output by sector when the FairTax is put in place, as shown in Table 3. The investment boom will favor sectors that provide capital goods, including industrial machinery and equipment (where output eventually rises by 46 %), business machines and equipment (+20 %), electronics (+36 %), construction (+13 %), and metals (+13 %). Over time, as consumption spending rises, there is also increasing demand for most other sectors, including motor vehicles (+13 %), food and tobacco (+5 %), textiles and garments (+5 %), and entertainment and hotels (+3 %).
The rise in sectoral output is enabled by increases in the capital stock, and in labor inputs. The details of these increases are shown in Appendix Tables 5 and 6. In every sector the capital stock will rise faster than employmentan understandable result given that the FairTax proposal would make capital less expensive relative to labor.
As noted above, household real consumption, and wellbeing (Butility^) would fall in the first few years after the introduction of the FairTax, but would then rise above the benchmark, so that ultimately the tax change would leave people better off. An interesting question is whether the FairTax would benefit all income groups equally. This is addressed in the numbers presented in Table 4, and the associated graphs in Fig. 4, where the effect of the FairTax on utility, employment, and real consumption is shown, over time, for seven different income groups. Two groups would benefit unambiguously from the introduction of a FairTaxthe poor and the affluentas the top panel in Table 4 (and the top panel in Fig. 4) makes clear. Very poor households would benefit because the FairTax proposal includes a demogrant, which would provide a cash payment to every household that is set at a level that ensures that anyone spending up to the poverty line would not pay any tax. Currently, poor households do pay some taxes, and by detaxing them, the FairTax would leave them better off. In addition, the growth associated with the FairTax would raise their incomes over time.
At the other end of the spectrum, well-off households would benefit because the FairTax would replace their current relatively high marginal tax rates with a flat tax. Flush with additional purchasing power, this group would take part of its gain in the form of more leisure, thereby reducing its labor supply. In between the two extremes, people the other income groups would be less well-off initially, but would see their utility (and real consumption) rise eventually, lifted by rising incomes. The one exception are the households with per capita incomes in the $50,000-75,000 range, who would unambiguously lose. In effect the FairTax would, to some extent, redistribute income from the middle class to the two extremes of the income distribution.
Issues on growth, income inequality and poverty as outlined in Haughthon and Khandker (2009) and particularly in the context of overlapping generation models will be taken up in our forthcoming studies.

Conclusion
This paper develops a dynamic computable general equilibrium model of the U.S. economy to simulate the principal economic effects of the FairTax on the US economy. The model shows that, by replacing the current income tax with a national sales tax with a demogrant, the proposal would end the double taxation of saving inherent in the existing tax code and, by doing so, raise output, employment, investment and capital stock relative to the benchmark economy.
While these positive effects would be felt almost immediately, the FairTax is very much an investment in the future. Its full benefits would be realized only after the economy achieved a new Bsteady state,^some 20-25 years into implementation. Only by that point will the effects on growth have been fully absorbed into the economy and the wellbeing of most households across most income groups improved. The policy choice, then, is between the status quo, on the one hand, and a new policy that would inflict some short-run pain as the price of a permanently expanded economy.