Elasticity of Sales to the Tax Rate

Average firm size in a sector is a proxy for informality and for evasion opportunities that is often used in the literature (Kumler, Verhoogen, and Frías 2020). There are good theoretical reasons for using this proxy. Thus, Kleven, Kreiner, and Saez (2016) argue that taxes become more difficult to enforce as the number of employees in a firm grows because the probability that any employee acts as a whistle-blower increases. In addition, ample evidence suggests that tax administrations devote more resources to monitoring larger firms and that larger firms are more likely to use accounting records and electronic forms of payment, generating the kind of information trails that help tax officials assess tax liabilities (Bachas, Fattal Jaef, and Jensen 2019; Basri et al. 2019).

It is assumed that all firms in the UME are informal, while firms in the ASI are formal only if they report that they paid the VAT. The two datasets are combined using the sampling weights of firms to obtain a representative sample of firms in India. Firms are also weighted using total sales to obtain the formal market share by sectors of activity. Figure 4.3, panel b plots the resulting formal market share by sector. Capital-intensive sectors (transport, metals) exhibit the highest formality share, while textiles and agricultural industries (notoriously more difficult to tax) show the lowest formality share.

EMPIRICAL STRATEGY

The objective of the analysis is to measure the ETI to the tax rate. The ETI is the percentage change in taxable income after a 1 percent increase in the tax rate. In the context here, the taxable income corresponds to the sales reported by GST-registered firms. Two types of tax rates may be observed in the data: the statutory tax rate that is based on the tax code and that should apply to a product sold by a firm, τStat, and the ETR selfreported by the firm in the firm’s tax return, τEff. If these two rates were exactly the same and if effective rates only changed together with changes in statutory tax rates, a simple panel regression could be implemented to measure the ETI, as follows:

α γ β τ= + + + +∈ln ln() .(1 )y ipt i t pt ipt,

(4.1)

where ln(y)ipt is the log of sales of firm i selling product p in month t; ln(1+ τpt) is the log of 1, plus the tax rate; and αi and γt are, respectively, firm and time-fixed effects.

Although statutory tax rates and ETRs are positively correlated, they differ in practice for several reasons. First, ETRs are filed directly by the firms and can thus be manipulated. Second, the law might not systematically be known or enforced, and reported ETRs might not react to statutory rate changes. Third, the statutory rates collected for the analysis may be subject to measurement error, given the difficulty in assigning product descriptions to specific product codes.

Thus, if the ETI is measured using the observed ETRs, the panel regression estimate will likely be biased because the changes in ETRs are partly driven by the choices of firms. To address this issue, an instrumental variable strategy was run in the analysis

whereby the reform-induced changes in ETRs were used to measure the elasticity of the reported sales of firms. The identification assumption is now that (1) the changes in statutory tax rates are not decided on the basis of the economic situations of firms and that (2) the sales of firms the products of which face a rate change would have trended parallel to the sales of firms on which the tax rate is constant, absent the rate change. This is the standard parallel trends assumption for which support may be provided by looking at pretrends.

The first stage regresses the log of the ETR on the log of the statutory tax rate, which only changes after a reform. A similar, alternative instrument is a dummy taking the value of 1 in the months after the rate change among firms selling a treated product.

ln(1 ln) . (1 ) .τ α γ β τ+ = + + + + ∈ pt Eff ipt i t pt Stat i (4.2)

The second stage then regresses the predicted change in the ETR on sales, as follows:

ln() α γ= +y ipt i t ln(1 φ τ+ + ) . +∈

Eff pred ipt ipt (4.3)

The reduced form regression is a regression of the log sales on the log of the statutory tax rate. It is equivalent to a generalized difference in differences or generalized event study with a pure control group that compares changes in sales before a tax rate cut versus after the cut among firms that faced a cut versus firms that did not face a change in the tax rate. Formally, this gives the following:

b ln ln() (1∑α γ ψ τ= + + +y ipt i t pt Stat ) . +∈ipt

k α= (4.4)

To show the dynamic effects, the analysis also ran a period by period event study of the changes in sales relative to the month after the reform, as follows:

b α γ= +ln() y ipt i t ∑ψ D + + ∈

k k pt ipt, (4.5)

where ln(y)ipt are log sales of firm i selling product p at time t; αi and γt are, respectively, firm and month fixed effects; Dpt k is a dummy indicating that product p faced a rate change exactly k periods ago at time t; and a < 0 < b are periods relative to the tax rate cut for product p. The analysis included measurement of the effects relative to a period previous to the tax rate change and omitted k = −3 as the base period. Firms selling products that never face a rate change thus show a value for the dummy Dpt equal to zero for all k.

The identifying assumption in interpreting ψk as the causal impact of the tax rate cut on reported sales is the classic parallel trends assumption invoked in difference in differences. It implies that, in the absence of a tax rate cut, the sales of firms that faced a rate cut and of firms that did not face a rate cut would have trended similarly. While this is not testable, an analysis may compare the behavior of firms in the periods before a tax change by looking at the coefficients on k < 0. This specification also allows an

k α=

observation of dynamic trends in the impact of tax cuts on sales over time by comparing the effects at impact (k = 0) with the effects several months after the reform.

The equivalent dynamic effects regressions may also be run from equation 4.5 by instrumenting the change in the ETR with the reform dummy. The interpretation of the coefficient of this regression then becomes the interpretation of an elasticity of taxable sales: after a 1 percent drop in the ETR because of a reform-induced cut in the statutory tax rate, by how much do firms increase their reported sales?

To interpret the coefficients as the structural elasticity of income, this empirical design also implicitly assumes limited (or diffuse) substitution among goods that face a rate change and goods that do not face a rate change. This is likely to be erroneous if one compares products within narrow groups. To account for this issue in estimating sector-level elasticities, the analysis keeps all untreated firms in the control group, not only the firms in the sector in which the elasticity is being measured.

RESULTS

Figure 4.4 displays the main results of the analysis. Figure 4.4, panel a, shows the first stage of the regression: the impact of a tax cut on the ETR reported by treated versus control firms relative to the period of the tax cut. The dashed vertical line in each panel corresponds to the month of the announcement of the reform, and the solid vertical line in each panel represents the application of the reform one month later. The month of application of the rate change is normalized to zero to count all other months relative to the reform month.

A slight anticipation effect may be observed in the lines. This is likely because firms (erroneously) applied the lower statutory tax rate at the time of the announcement of the tax cut, one month prior to its application. Upon application of the reform, the average reported ETR dropped by 1.7 percentage points and continued to drop slightly in subsequent months, thereby approaching a 2 percentage point drop. The pretrends in ETRs were small. They suggest that the drop in ETRs was slightly overestimated, which implies that elasticities were underestimated in absolute value.

Figure 4.4, panel b shows the main result, which is estimated from equation 4.5, that is, following a tax cut, sales increased by an average of 4 percent. There are no pretrends. In the periods before the rate change, the period dummies are close to zero. Firms selling products that faced a tax cut thus reported substantially more sales postreform than firms that did not face a rate change. Combining both panels allows an approximation of the ETI. The tax cuts led to a decline in the ETR by slightly less than 2 percent, which was associated with a 4 percent rise in sales. Dividing the reduced form by the first stage produces an elasticity slightly above 2.

The analysis formally ran the regression of log sales on the ETR (table 4.4). The coefficient is the elasticity of sales with respect to a firm’s tax rate. Column (1) shows the results from the panel ordinary least squares (OLS) regression. It reveals a large elasticity of –6.1: as the reported ETR drops by 1 percent, reported sales increase by 6.1 percent.