# Appendix: The Savings Elasticity Controversy

## A1 Boskin (1978)

It is useful to overview the savings elasticity controversy after Boskin’s (1978) paper. Early work tended to produce rather low estimates for the interest elasticity of saving, typically in the neighborhood of 0.10-0.20, meaning that a decrease in the interest rate from 10 to 5 % would reduce savings by approximately 13 % if the elasticity were 0.20. However, there were some estimates of the elasticity of saving that were insignificantly different from zero. It follows that the income effect and the substitution effect are almost the same in terms of magnitude.

Boskin, however, estimated an elasticity nearly twice the magnitude of earlier estimates. His estimated range for the elasticity of saving was between 0.30 and

0.60, with the preferred estimate being 0.40, which was twice the magnitude anyone else had found using similar data. Further, his preferred estimate of the elasticity of saving implied that the taxation of capital income causes an annual excess burden of approximately US $60 billion, which was an astonishing result, to say the least. As explained in the main text, if the substitution effect is large, the size of the excess burden is also large.

Boskin’s result was quite controversial and started a debate over the magnitude of the elasticity of saving. He estimated an ad hoc consumption function and used an instrumental variables technique to control for the possible endogeneity of some of the regressors; for example, income. The data used were annual time series observations for the United States for the period 1929-1969, omitting the war years.

The key to Boskin’s large estimate is the interest rate variable used in the estimated regression equation. The theoretically preferred variable is the expected, real interest rate, net of tax. Unfortunately, this variable is not directly observed; it must be constructed, which means that a number of thorny measurement issues arise.

First, which interest rate should be used? Second, the interest rate must be adjusted for taxes. Again, it is not immediately obvious how to deal with this when there is more than one tax rate and more than one government, for example, central government and local governments, imposing taxes on capital income. Third, the interest rate must be adjusted for inflation because it is the real rate that is important for intertemporal decision-making. Thus, which price index should be used to calculate the inflation rate? Fourth, it should be the expected, real interest rate net of tax that belongs in the consumption or savings function equation. Calculating the expectations of the taxpayer and aggregating to the economy level is a difficult task. Clearly, any technique used will be somewhat arbitrary and difficult to defend.

Finally, the consumption function estimated is somewhat ad hoc; it was not derived from the optimizing behavior of consumers. This makes it difficult to interpret the specific results because it is unclear what the parameters mean. This is an application of the so-called Lucas critique.