Draft: Please do not quote without the author's permission


The Dead Hand:

The Influence of Past Elasticity on Present Revenue*

by David Friedman

Olin Fellow

University of Chicago Law School

January 31, 1991

Draft: Not for Quotation


Part I: Introduction

To what degree can the behavior of governments be explained as a response to the circumstances they face and to what degree must it be explained as the result of past decisions? If two governments with different histories face the same current circumstances, will they behave in the same way?

If a government behaves like an individual save that it seeks to maximize social welfare, the utility of the median voter, or some similar variable, rather than individual utility, the immediate answer is that, for governments as for individuals, sunk costs are sunk costs. All decisions should be made in terms of present circumstances. On further consideration that conclusion should be qualified to take account of the costs of acquiring information, rapidly altering the productive plant, and the like, but we would still expect the decisions of governments to depend primarily on circumstances in the present and the recent past.

There are, however, other models of government behavior which do not have that implication. Imagine, for example, a constitution under which new taxes can be imposed or old taxes repealed only by something more than a simple majority--perhaps the separate assent of both houses of a bicameral legislature or the assent of both the legislature and the voters. Under such arrangements less support is require to keep a tax than to pass one, hence general support for a high level of government expenditure in the past may result in high taxes in the future even if the conditions that generated that support disappear.[1 ]The same result could also be derived from an interest group model in which government expenditures tend to create organized interest groups, such as the employees or beneficiaries of particular programs, which then provide continuing political support for maintaining the expenditures.

The question of whether governments behave, in this regard, like rational maximizing individuals is important both for theory and for practice: for theory because some theories of governmental behavior imply that they do and some that they do not; evidence one way or the other is thus evidence against one or the other family of theories. For practice because if fiscal decisions are only for the present and the fiscal structure can be continually readjusted to meet changing circumstances, the case for supporting the introduction (or repeal) of a particular tax may be very different than if current decisions impose a tax upon (or remove a tax from) our children and our grandchildren as well as ourselves.

While the ultimate question I am interested in is whether governments behave like maximizing individuals, what I am actually testing is a particular implication of such behavior--that current government behavior is overwhelming determined by conditions in the present or recent past. Hence in the next four sections I will refer to the alternative models as "present-oriented" and "inertial."

II. The Test

For statistical tests of the implications of theories about government behavior, it is convenient to have uniform data on a large number of similar governments over a substantial period of time. Roughly comparable data are available across forty-eight states of the U.S. for a period of about ninety years. Given such data, as well as data over the same period on various characteristics of the states, one possible approach is to fit regressions that express some measure of the behavior of state governments at a given date as functions of characteristics of the states at that same date, and try to find a relation that is stable across both time and states. The results of such an effert are reported in an earlier paper of mine (Friedman 1983). The conclusion reached was that, with the characteristics and functional forms used, no stable relation existed for either state or state plus local real expenditure per capita.

Although a positive result obtained in this way would be good evidence that government behavior, or at least some government behavior, is determined by current circumstances, a negative result is only weak evidence that it is not. It is always possible that a different functional form or a different choice of characteristics, possibly including some for which data is not available, would give a stable relation.

This paper reports a different approach, designed to give a positive result if government behavior is inertial rather than present oriented. The approach is to find a past characteristic that would affect government behavior in a particular way if there is a tendency for tax laws to remain unchanged even if circumstances change. The ideal such characteristic would have little or no connection with unobserved current characteristics that are themselves likely determinants of current governmental behavior. Given such a characteristic, the next step is to regress the current behavior of state governments on whatever current characteristics are regarded as important plus the past characteristic. If the latter has a significant effect in the direction to be expected from the inertial theory, the result is evidence for that theory and against the alternative.

The distinction between variables that should and should not affect the behavior of a present-oriented government is not a sharp one; as I suggested above, even a government (or individual) maximizing current objectives will be affected by the past to some degree since it may be expensive to alter rapidly the scale of provision of public goods or to acquire the information necessary for some new government activity. One way to deal with this problem is to push the past characteristic further and further into the past in order to see how recent it must be to affect current behavior significantly. We may then decide whether the result is consistent with the time lags we would expect to observe in present-oriented government behavior. The results are reported in part V.

III. Choosing a Variable--Average Elasticity[2]

The revenue generated by a system of taxes depends on the tax rates and the size of the tax base. If tax rates do not change, revenue changes depend on the elasticity of the existing taxes with respect to their base and changes in the size of that base. If state tax revenues today are largely determined by the imposition of taxes in the past, then information about the elasticity of past taxes should help explain present levels of expenditure.

Suppose we knew the income elasticity of the tax system of every state in every year over an extended period of time; further suppose we knew income had been growing. We could calculate an average elasticity for each state over the period and predict that states with higher average elasticities would have higher levels of current revenue.

We could do better than that. Consider two states, each with an average elasticity (of per capita tax revenue with respect to per capita income) of 1.2 . Suppose that the system of taxes in one state had an elasticity of 1 in period one and 1.4 in period 2; in the other state the other way around. In period 1 per capita income rose sharply in both states; in period two it stayed constant. We would expect the second state to end up with higher revenues than the first.

At this point it may appear that the inertial model is internally inconsistent. I base the model on the tendency of taxes to stay the same, yet I talk about changes in the income elasticity of state tax systems which presumably result from changes in their taxes. How can changes in elasticity be made consistent with strong inertial effects?

The answer is that while tax rates may tend to remain the same I do not assume that they never change--obviously they do. If, every time tax rates change, the new rates are designed to generate some "optimal" level of revenue determined by characteristics of the state at the time of the change, then inertial effects will be observed only in the short run. I assume instead, for reasons I have discussed elsewhere (Friedman (1982)), that there is inertia in expenditure as well as in tax rates. As long as tax rates remain fixed additional revenues generated by increases in the base are absorbed by additional expenditure; when tax rates are changed, the new rates generate about the same revenue as the old rates generated immediately before the change. In the example suggested earlier, where the passage or repeal of taxes requires something more than a simple majority, one can easily imagine situations where the "high tax" and "low tax" coalitions each had enough support to veto a "vertical" change (higher or lower taxes) but could agree on a "horizontal" change (different taxes with about the same revenue).

If this were a complete description of what actualy happens in the states, then changes in base and elasticity would completely determine current levels of expenditure. My conjecture is only that they are important determinants. Other factors, which result in changes in tax rates designed to increase (or decrease) revenue, are beyond the scope of this paper although not of the study of which it is a part.

The example I have given of two states with the same average tax elasticity suggests that what we really want is a weighted average of the elasticity, with the weights depending on the change in the tax base. Consider a state whose tax system has an income elasticity of e1 in time period 1 (from t=0 to t=1) and e2 in time period 2 (from t=1 to t=2), and whose per capita income goes from Incpc(0) to Incpc(1) to Incpc(2). Assuming, by continuity, that the rate of revenue R(t) is the same at the end of period 1 and the beginning of period 2, we have:

(Eqn. 1)

Taking logarithms of both sides we get the logarithm of revenue at time t=2 equal to the logarithm of revenue at time t=0 plus a weighted sum of the elasticities during the two subperiods, with the weights being the differences of the logarithms of the tax base at the beginning and end of each of the subperiods. This suggests that the way to test the influence of past elasticities on present expenditure is to construct for each state a weighted average elasticity, using changes in the logarithms of the tax base as the weights, and then use it as one of the variables in a fit of the logarithm of tax revenues. In order to make the variable a measure of average elasticity rather than of both elasticity and current income (which in any case will be in the regression separately) we can divide the weighted sum by the sum of the weights. Thus the formula for the average elasticity of per capita income as a function of per capita income for a particular state is:

(Eqn. 2)

The formula generates a set of average state elasticities es(t); in Equation 2 the subscript s has been suppressed for purposes of clarity. t is the end of the period over which the average is taken; it need not be the same as the date for which tax revenue is being estimated. Taking the average all the way up to that date should give the best fit, assuming elasticity really is determining revenue, but it also introduces the possibility of confounding short run adjustments with long run inertial effects. I therefore first calculated the average elasticity over a period that ended five years before the date at which I measured revenue and then calculated three more average elasticities, each time moving the end point back a decade. Thus the most recent information contained in the average for the shortest period is the level of per capita income thirty-five years before the date of the revenue being estimated.

IV. Estimating Past Elasticities

Unfortunately the very useful tables published in Historical Statistics of the U.S. do not include a table showing the income elasticity of the tax base of state governments by state and year. To estimate elasticities I use an idea borrowed from the Advisory Commission on Intergovernmental Relations, which in ACIR (1977) estimated the income elasticity of various taxes from figures reported in the literature and estimated the income elasticity in 1970 of the fiscal system of each state as an average of the elasticities of the individual taxes weighted by the share of each tax in the total for that state. I used the ACIR figures for the average income elasticities of six taxes (General sales, Motor Fuels, Tobacco, Personal Income, Corporate Income, and General Property) to calculate for each state at each of eight different dates from 1903 to 1970 the average income elasticity of that part of its tax revenue coming from those taxes. I define my variables as:

Ej : the elasticity of each of the designated taxes (j=1 to 6)

Ti,j,s : the receipts for each designated tax in year i for state s

E : average elasticity of all other taxes (assumed the same for all states)

Ti,s : total receipts in year i for state s

fi,s =

Then the average elasticity of the designated taxes in a particular state at a particular time is

(Eqn. 3A)

And of all taxes,

ei,s = ei,s' x fi,s + E(1-fi,s) (Eqn. 3B)

I dealt with the problem of the non-designated taxes in two alternative ways: first by setting E=1, second by letting E be an additional parameter in the regression. The two methods gave virtually identical adjusted R2's in my regressions. I report results below only for the second method.

I estimated the income elasticity of state taxes each decade from 1970 back to 1930 and for 1923, 1913 and 1903; the last three dates were determined by data availability. To calculate the weighted averages I used personal income per capita from 1975 to 1900, dividing my periods at the midpoints between the years for which I had elasticity estimates. Hence the first period was from 1900 to 1908, the second from 1908 to 1918, and so on, with the final period from 1965 to 1975. The weighting factor for the first period was the difference between the logarithm of income per capita in 1908 and the logarithm of income per capita in 1900 divided by the difference between the logarithm of income per capita in 1975 and the logarithm of income per capita in 1900; it was used to multiply the estimated elasticity in 1903. In the same way the weighting factor for the second period multiplied the estimated elasticity in 1913, etc. I also calculated weighted average elasticities from 1965 to 1900, from 1955 to 1900, and from 1945 to 1900 in the same way, changing the denominators of the weights and dropping the later terms in the sum. Thus my "earliest" weighted average elasticity used the difference between the logarithm of income per capita in 1945 and in 1900 as the denominator, and included estimated elasticities from 1903 to 1940. The general formula for weighted elasticity is then


= (Eqn. 4)

and is calculated for values of t corresponding to 1975, 1965, 1955, and 1945.

V: Regressions and Results

To find out whether the weighted average of elasticity was significant, I used it in regressions for which the dependent variable was the logarithm of state tax collections per capita in 1980 and the other independent variables were current state characteristics (Ck,s(1980)). The equation took the form

ln(Tax/capitas) = A + + D x es + [[epsilon]]

= A + + D x es' + D x E x + [[epsilon]]s (Eqn. 5)

The second line of the equation makes explicit the presence of two elasticity parameters, D and DxE, where E is the average elasticity of all undesignated taxes. es' is just like es in equation 4 except that ei,s is replaced by ei,s'. [[epsilon]]s is a random error term.

The one step remaining before fitting the regression is to choose the variables Ck,s(1980). The characteristics that have been used most commonly since Fabricant (1952) are the ones he chose--income per capita, urbanization (urban population per capita), and population density. In addition, a large number of studies,[3] including my previous paper show that including federal aid per capita improves the fit considerably for recent decades.

It is not clear whether the reason for this result is that federal aid determines tax levels or that tax levels determine federal aid.[4] Many federal programs take the form of matching funds and therefore give more revenue when state expenditures are higher. Also it is sometimes argued that the states most deserving of federal aid are those with high "tax effort"--those presently collecting a particularly large fraction of their citizens' income. If aid is actually given on that basis then the amount of aid is an effect of levels of taxation instead of (or in addition to) a cause. Finally, high levels of taxation and expenditure by state (and local) governments may be both cause and effect of the political strength of those governments, and politically powerful governments may be in a particularly good position to obtain federal aid. This again suggests that federal aid may be an effect rather than a cause. Accordingly, I computed regressions both including and excluding federal aid as an independent variable. Table I shows the results.[5]


Table I

Past Elasticity Variable


Current Variables






Adjusted R2









" " ", Federal Aid/c












t values (D/DxE)








" " ", Federal Aid/c





Elasticity of "all other taxes"[6]


Income/c, Density, Urbanization






" " ", Federal Aid/c





Line 1 of the table gives the adjusted R2's for five regressions. The first regression has income per capita, urbanization, and density as independent variables; the other four add a weighted average of elasticity. In the second the average is for 1975 to 1900, in the third, from 1965 to 1900, in the fourth, from 1955 to 1900; in the fifth from 1945 to 1900.

The second line of the table is like the first, except that federal aid per capita is also included in all regressions. The third line has only weighted average elasticity as an independent variable. The fourth line shows, for the regression of line 1, the t values for the two parameters associated with elasticity (D and DxE). Line 5 is the equivalent for the regression of line 2 (with federal aid included).

The results shown on line 1 are striking; average elasticity improves the fit substantially. It continues to do so when the near end of the weighting period is fifteen, twenty-five, and even thirty-five years before the date for which tax revenue is being estimated. The second line is similar but not as striking; one possible explanation is that federal aid is in part a consequence of tax levels that are in turn partly a consequence of average elasticity, hence it absorbs part of the variance due to average elasticity. Line 3 shows that weighted elasticity by itself explains a substantial amount of the variance of tax revenue. The result is particularly impressive given that our elasticity estimates are very approximate ones. Lines 4 and 5, as one would expect from lines 1 and 2, show significant t values; the signs are positive as we would expect. Lines 6 and 7 show the estimated value of E, the average elasticity of "all other taxes;" the results do not seem unreasonable.

It may be objected that my explanation of why line 2 shows a smaller effect for average elasticity than line 1 assumes its conclusion; perhaps (current) federal aid is really determining state tax levels and is itself in part determined by some of the past state characteristics that go into the elasticity measure. If so we still have evidence for an "inertial" government, although it is federal rather than state.

Table II: Correlation Coefficients

State Tax/c 1980

Federal Aid/c 1980

State Tax/c 1915

State Tax/c 1980




Federal Aid/c 1980




State Tax/c 1915




One can get evidence on whether federal aid is in part an effect rather than a cause of tax revenue by correlating federal aid with a third variable that itself correlates with tax revenues and cannot possibly be affected by federal aid. The variable I choose is tax revenue per capita in 1915. Since we know there is considerable persistence in revenue differences, we can expect it to correlate with 1980 tax revenue. It obviously cannot be affected by 1980 federal aid. It is hardly likely that a correlation between taxes in 1915 and aid in 1980 reflects a correlation between aid at the two dates, with aid in 1915 determining taxation in 1915, since federal aid in 1915, and presumably its effects on taxation, were negligable by modern standards. The correlation coefficients are shown in Table II; they suggest that federal Aid is at least in part a consequence of tax revenues.

VI. Conclusions and Counter Arguments

These results suggest that past characteristics of states substantially affect present levels of taxation in the way that would be expected if expenditure was determined in part by revenue rather than revenue by expenditure "needs," with revenue in turn determined in part by the effect of changes in the tax base on a relatively stable set of tax rates. The effect continues to be observed even when we limit ourselves to characteristics so far in the past as to make any explanation involving rational maximizing governments whose behavior is constrained by adjustment costs either implausible or empty.

At least two objections might be made to this conclusion. The first is that since the mix of taxes that a state employs is relatively stable over time, my measures of elasticity in, say, 1930 are really serving as proxies for elasticity between 1975 and 1980. States that had high elasticity during that period received as a result substantial increases in their tax revenue and have not yet adjusted to them. While this argument concedes that adjustment of revenues to "needs" is not instantaneous, it assumes only short run adjustment effects.

The weakness of this objection is that adjustment effects ought to apply only to unexpected changes in revenue. Insofar as revenue changes are the result of stable factors such as a tax system that is and always has been highly elastic, a state government that behaves like a rational maximizer should compensate for them by routinely lowering tax rates as incomes rise. But the figures in Table I show that the "errors" (from the standpoint of a rational maximizer) of the states can be, to a considerable extent, predicted with information from thirty-five years earlier.

A second objection that can be made to my conclusion is that states are not only rational maximizers, they are so rational that they design their fiscal systems to match future demand for state services. A state that has an income elastic demand for its services constructs an income elastic set of taxes, thus reducing the cost of changing tax rates to deal with future changes in income. This hypothesis does indeed explain my results; how plausible it is I will leave to the reader.


Appendix: Buried Results

In addition to the results I report, I also fitted similar regressions on state plus local data. The advantage of state plus local data is that they yield better fits, presumably because one source of variation in state data is variation in the division of responsibilities between state and local governments. One disadvantage is that the data are poorer. In compiling elasticity estimates the only category of local taxation for which I could find separate data was property taxes.

This problem interacts with a second, which is that local governments have a less diverse tax base than state governments--on average about eighty to ninety percent of their tax revenue comes from property taxes. The combined result of the two problems is that the variation across states of my estimate of weighted average elasticity for state plus local governments was much less than for state governments; the ratio of standard deviation to mean for the elasticity measure that multiplies D in equation 4 for state data was about three times as high as for state plus local; the corresponding ratio for the measure that multiplies DxE was about 1.4. The results of the fits to state plus local data were qualitatively similar to those I report for state data, but the size of the effect of the elasticity variable on adjusted R2 was considerably less. With federal aid omitted it raised adjusted R2 from .58 to .64; with federal aid included from .79 to .81.



Bahl, R. W. and Saunders, R. J., "Determinants of Changes in State and Local Government Expenditures," National Tax Journal, March 1965.

Bahl, R. W. and Saunders, R. J., "Variations in State and Local Government Spending," Journal of Finance, September 1966.

Bahl, R. W. and Saunders, R. J., "Fabricant's Determinants After Twenty Years: A Critical Reappraisal," American Economist 10, 1966

Bolton, R. E., "Predictive Models for State and Local Government Purchases" in James S. Duesenberry, G. Fromm, L. R. Klein, E. Kuh (eds.) The Brookings Model: Some Further Results, Chicago: Rand McNally 1969, pp. 229-273.

Buchanan, James M. and Tollison, R. S., (eds.), The Theory of Public Choice: Essays in Application, Ann Arbor: University of Michigan Press 1972.

Buchanan, James M. and Tullock, Gordon, The Calculus of Consent, Ann Arbor, Mich.: University of Michigan Press, 1962.

Craig, Eleanor D. and Heins, A. James, "The Effect of Tax Elasticity on Government Spending," Public Choice 35, 1980 pp. 267-275.

Friedman, David D., "A New Approach to Explaining Government Expenditures", Draft available from author, 1982.

Friedman, David D., "Fabricant Reconsidered: Fitting Government Expenditure Through Space and Time," Preprint available from the author, January 1983.

Gramlich, E. M., "The Effect of Federal Grants on State-Local Expenditures. A Review of the Econometric Literature," National Tax Association Papers and Proceedings, 1969.

Gramlich, E. M., "A Clarification and a Correction," National Tax Journal June 1969, 22(2), pp. 286-290.

Gramlich, E. M., "State and Local Governments and Their Budget Constraint," International Economic Review, June 1969, 10(2), pp. 163-182.

Gramlich, E. M., "A Comment on O'Brien's 'Grants-in-Aid'," National Tax Journal, March 1972.

Gramlich, E. M., and Galper, H., "State and Local Fiscal Behaviour and Federal Grant Policy," Brookings Papers on Economic Activity, 1973:1.

Harlow, R. L., "Factors Affecting American State Expenditures," Yale Economic Essays, Fall 1967.

Harlow, R. L., "Sharkansky on state Expenditures: A Comment," National Tax Journal, June 1968, 21(2), pp. 215-216.

Kurnow, E., "Determinants of State and Local Expenditures Re-examined," National Tax Journal, Sept. 1963.

Oates, W. E., "The Dual Impact of Federal Aid on State and Local Expenditures: A Comment," National Tax Journal, June 1968.

Oates, W. E., "Automatic Increases in Tax Revenues -- the Effect on the Size of Public Budget." in W. E. Oates, (Ed.), Financing the New Federalism. Johns Hopkins Press. 139-160.

O'Brien, T. ,"Grants-in-Aid: Some Further Answers," National Tax Journal, March 1971.

Ohls, J. C. and Wales, T. J., "Supply and Demand for State and Local Services," Review of Economics and Statistics, November 1972.

Olson, Mancur, The Logic of Collective Action. Cambridge,Mass.: Harvard University Press, 1965.

Osman, J. W., "The Dual Impact of Federal Aid on State and Local Government Expenditures," National Tax Journal, December 1966.

Osman, J. W., "On the Use of Intergovernmental Aid as an Expenditure Determinant," National Tax Journal, December 1968, 21(4), pp. 437- 447.

Pogue, T. F., and Sgontz, L. G., "The Effects of Grants-in-Aid on State and Local Spending," National Tax Journal, June 1968, 21(2), pp. 190- 199.

Sacks, S. and Harris, R., "The Determinants of State and Local Government Expenditures and Intergovernmental Flows of Funds," National Tax Journal, March 1964.

Sharkansky, I., "Some More Thoughts About the Determinants of Government Expenditures," National Tax Journal, June 1967, 20(2), pp. 171- 179.

Sharkansky, I., "A Reply to Professor Harlow," National Tax Journal, June 1968, 21(2), pp. 217-219.

Smith, D. L., "The Response of State and Local Governments to Federal Grants," National Tax Journal, September 1968.

Wildavsky, Aaron, The Politics of the Budgetary Process, Boston: Little, Brown, 1964.

Wilde, J. A., "The Expenditure Effects of Grants-in-Aid Programs," National Tax Journal, September 1968, 21(3), pp. 340-348.


Data Sources

Advisory Commission on Intergovernmental Relations, Significant Features of Fiscal Federalism, 1976-77 Edition, Vol. 2.

The Council of State Governments, Federal Grants-in-Aid, 1949.

Easterlin, Richard A., "Interregional Differences in Per Capita Income, Population, and Total Income, 1840-1950," in Trends in The American Economy in the Nineteenth Century, Princeton University Press, Princeton: 1960 (pp.73-140).

Maurice Leven, Income in the Various States, National Bureau of Economic Research, New York:1925.

U.S. Bureau of the Census, Historical Statistics of the United States, Washington: 1975.

, Statistical Abstract of the United States, various years.

, Governmental Finances in the United States, various years.

, Financial Statistics of States, various years.

U.S. Department of Commerce, Office of Business Economics, Personal Income by States Since 1929, Washington: 1956.

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