If underdeclaration does not respond at all to changes in tax rates, then revenues would rise or fall based entirely on the change in the tax rate; that is, a given percent change in the tax rate would give rise to a proportional change in stamp duty revenues. We examined historical data to test whether this hypothesis holds. Annex II provides a time series of historical stamp tax rates covering FY1980-1981 to FY2003-2004, collated for the purpose of this paper. Ideally, regression analysis could be used to test such a hypothesis. However, as perusal of Annex II shows, stamp duty rates, with the exception of West Bengal, have not changed often enough to get reliable estimates of regression coefficients for individual States.<sup>44</sup> Our analysis compared changes in stamp duty rates to revenue changes over the period in eleven major Indian States where duty rates have changed, as shown in Figures 1 to 11. Recall that Figures 1 to 11 show the trend analysis on a State by State basis. The pattern that emerges is quite clear: reductions in rates rarely result in a proportional decline in revenues. Indeed in several cases, revenues actually increase in response to a rate change. Likewise, rate increases (except in Kerala) tend to result in less than proportional revenue improvement, again indicating that underdeclaration tends to rise with rate increases. Figure 12 assembles all the instances of rate changes and associated revenue changes. All other factors held equal, if underdeclaration does not respond to tax rate changes, then we would expect these observations to be close to a 45-degree line, as a given percentage change in the tax rate feeds into a similar increase in taxes. However, the fitted line shows a slightly negative relationship between rate changes and revenue changes, although clearly there is a good deal of variability that is not explained by the rate changes alone. In statistical terms, the slope of the line is not significantly different from zero (the confidence level is about 65 percent). (See Annex III for the regression results and Annex IV for the analysis of a single state, West Bengal.) This result suggests strongly that other factors such as shifts in underdeclaration of property values are at play.<sup>45</sup> In Figures 13 to 16, we examine the impact of tax rates changes for a few States for which we have more data. Stamp tax revenues are a function of rates, property values transacted, and the number of transactions, or R = t * PRE * N, where R is stamp duty revenues, t is the stamp duty rate, PRE is the average price of real estate transacted in the period, and N is the number of transactions in a given period. Differentiating this expression gives: where ^ indicates a proportional change. Using this relationship, we can create a predicted value of revenue changes in a given period based on changes in the determinants of revenues. Note that this is not a behavioral equation against which hypotheses would be tested, but rather it is an identity.

Now if we were could observe all of these variables directly, then we could simply ∧ substitute the right hand side variables to get a predicted _R_ . We do have information on some,

> 44 For West Bengal, a time series analysis from 1992-93-2000-2001 provides a significant and negative coefficient for the quadratic term on the tax rate, demonstrating a Laffer curve effect, in spite of very low degrees of freedom due to data limitations. Annex III shows the results of this analysis.

> 45  These findings are consistent with those of Das Gupta (2002) on Karnataka. He found that a 1 percent increase in the effective tax rate led to a 0.6 percent decrease in revenues for the period 1980-1981 to 1997-1998.

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