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Wednesday, May 04, 2005

The optimal cigarette tax in Texas?

The state legislature is proposing raising the state cigarette tax from $0.41 per pack to $1.01 per pack. This is to raise funds for educating the sons and daughters of Texas.

I went out and grabbed state tax revenue and taxes and packs sold and estimated a couple of simple Laffer curves. These are reduced form and naive models, but the upshot seems to be that $1.01 is considerably higher than the revenue maximizing level of the tax.

Here are the fitted Laffer curves where taxes in pennies from 0 to 200 are on the horizontal axis, tax revenue in thousands is on the horizontal axis. The naive models would put the optimal taxes somewhere near $0.60, considerably less than the $1.01 that has been proposed. Is the proposed level set "too high" in order to reach a compromise position closer to the optimum, or are the good folks in Austin not believe in the Laffer curve?

I updated the econometrics overnight. Estimating a reduced form model, restricting the interecept to zero (as it theoretically should be), we get the following estimation results (dependent variable is total tax revenues in thousands):

Number of obs = 32
F( 2, 30) = 1338.85
Prob > F = 0.0000
R-squared = 0.9895
Root MSE = 44339
| Robust
total | Coef. Std. Err. t P>|t|
taxes | 17505.17 938.3976 18.65 0.000
taxes2 | -113.1546 27.03488 -4.19 0.000

What does it all mean? The estimation indicates that a one penny increase in the cigarette tax will have a marginal impact on tax revenues of 17505.17 -2x113.1546xTax Rate. In other words, there is a tradeoff in raising cigarette taxes. The state will get more tax revenue on the packs of cigarettes that are sold, but there are likely to be fewer packs sold (eventually) and therefore revenues can eventually fall.

I generated a better picture than I had last night:

From this graph it is pretty apparent that the optimal cigarette tax is no where near the $1.01 level. Currently the total tax on cigarettes is comprised of both state and federal taxes. I am assuming federal taxes have stayed the same, but I will check this out and get the federal tax levels.

From simple calculations here, the state tax revenue maximizing tax rate is approximately $0.77 per pack, with a standard deviation of 14.53. Hence, a 95% confidence interval is [47.63085, 107.0705]. While it is true that the $1.01 tax falls in the 95% confidence interval, testing the null hypothesis that the optimal tax is statistically equal to $1.00 yields an F-test of 27.53 (p=0.000). In other words we can strongly reject the hypothesis that the optimal tax is equal to $1.00 (or $1.01).

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