dR / dτ (gen) dR / dτ ( par)
where the numerator of (25) is the response of total revenue collection to tax rate changes in a general equilibrium sense (in which all endogenous variables react to the rate change) while the denominator is the response of total revenue collection to tax rate changes in a partial equilibrium sense (in which the response of endogenous variables is shut off). The intuition behind this definition is that if x=1 then the general equilibrium effect of tax changes on revenue collection is equal to the partial equilibrium effect. In this case there is no self- financing (the degree of self-financing is zero) and the partial equilibrium methodology used by the JCT to evaluate the impact of proposed tax legislation is appropriate. In most cases, however, the degree of self-financing is likely to be positive.
Mankiw and Weinzierl (2006), for example, calculate it to be 50 percent for capital income taxes and 17 percent for labor income taxes for the US. While Trabandt and Uhlig (2006) find values of 47 percent (capital income) and 19 percent (labor income) for the US and 85 percent (capital income) and 54 percent (labor income) for EU-15. Leeper and Yang (2008) mostly focus on revenue-neutral exercises in which equation (25) is not applicable. They do look, however, at a case in which income tax cuts are financed by lower transfers, finding a degree of self-financing of 47 percent.
Since we have introduced money and nominal rigidities in our model, we can calculate the degrees of self-financing in terms of both nominal and real revenues. Using (21) and (22), we can easily calculate the ratio defined in (25) for our model. This ratio is given at any time horizon by
ˆ ˆ ˆ ˆ ˆ ˆ ( ) ( 1 ) ( ) ˆ ˆ ( 1 ) ( ) I C t t t t t I C t t u w l u C P u u τ τ τ τ + + + − + + + −
for the case of nominal revenue collection and by
ˆ ˆ ˆ ˆ ˆ ˆ ( ) ( 1 ) ( ) ˆ ˆ ( 1 ) ( ) I C t t t t t I C t t u w l P u C u u τ τ τ τ + + − + − + + −
for the case of real revenue collection. The numerators of equations (26) and (27) are the general equilibrium responses of tax collection to tax rates changes, while the denominators are the partial equilibrium responses in which endogenous variables do not react to tax
c h a n g e s ( ) 0 ˆ = = = = t t t t P C l w .