IN CONSIDERING CRITERIA for a tax system in a developing country the response of tax revenue to changes in income has often been singled out as a vital ingredient.¹ This response is measured by the concepts of tax elasticity and tax buoyancy, the former measuring in some sense the automatic response of revenue to income changes (i.e., revenue increase, excluding the effects of discretionary changes), and the latter measuring the total response of tax revenue to changes in income. A high tax elasticity is said to be a particularly desirable attribute, as it allows growth in expenditure, preferably related to development, to be financed by rising tax revenue without the need for politically difficult decisions to raise taxes. However, in fact, major sources of government revenue may have a low elasticity, in which case the authorities must seek additional revenue by introducing discretionary changes. Then, growth in tax revenue may come about through a high buoyancy ²—including growth through discretionary changes—as opposed to the natural growth through elasticity. Using Paraguay as an example, this paper analyzes the growth of tax revenues over the 1962-70 period—an era of conscious tax reform—by examining two major questions: (1) what was the elasticity of the system and its components, and how is the size of the elasticity coefficient explained? and (2) what was the buoyancy of the system relative to its elasticity? With respect to individual taxes, where were the major differences between buoyancy and elasticity found? These latter questions point to the effect of discretionary changes.

Definition of elasticity

Although the elasticity of tax revenue to income is often presented in aggregate models as a single number, it is more realistically visualized as the weighted average of the sum of the elasticities of separate taxes that often have widely divergent responses to changes in income. Thus overall tax elasticity must be examined by studying the separate elasticities of individual taxes. In turn, the income elasticity of each separate tax may be decomposed into two elements: the elasticity of the tax to the base and the elasticity of the base to income. These ideas may be summarized symbolically as follows, where:

T_t ≡ total tax revenue

T_k ≡ revenue from kth tax

Y ≡ income (GNP)

B_k ≡ base of kth tax

Elasticity of total tax revenue to income $E_{T_{t^y}}\equiv \frac{{\mathrm{\Delta }T}_t}{\mathrm{\Delta }Y}\times \frac{Y}{T_t}$

Elasticity of kth individual tax to income $E_{T_{k^y}}\equiv \frac{{\mathrm{\Delta }T}_k}{\mathrm{\Delta }Y}\times \frac{Y}{T_k}$

Elasticity of kth individual tax to base $E_{T_k{B}_k}\equiv \frac{{\mathrm{\Delta }T}_k}{{\mathrm{\Delta }B}_k}\times \frac{B_k}{T_k}$

Elasticity of kth individual base to income $E_{B_{k^y}}\equiv \frac{\mathrm{\Delta }{B}_k}{\mathrm{\Delta }Y}\times \frac{Y}{B_k}$

Given these definitions it follows that in a system of n taxes:

Identity (1) states that the elasticity of total tax revenue to income is equal to the weighted sum of individual tax elasticities. In addition, as stated in identity (2), the elasticity of any separate tax may be decomposed into the product of the elasticity of the tax to its base and the elasticity of the base to income.

Finally, as stated in identity (3), the elasticity of total revenue to income in a system of n taxes depends on the product of the elasticity of tax to base and base to income for each separate tax, weighted by the importance of that tax in the total system.

Analysis of the income elasticity of a tax system in such a manner permits identification of the sources of fast revenue growth or, conversely, the causes of lagging revenue growth. It also permits identification of that part of revenue growth within the control of the authorities. On the one hand, the tax-to-base constituent of elasticity may be raised by an improvement in administration. (This effect will also take place if the tax structure is progressive.) In this sense the tax-to-base constituent of elasticity is partly within the control of the authorities. On the other hand, the growth of the tax base lies outside the control of the authorities (apart from the influence of tax policy itself) and is largely determined by the way in which the structure of the economy changes with economic growth. In designing taxes that would prove income elastic, both the predicted response of the tax base to income and the potential for an effective and/or improving level of administration should be taken into account.

Measurement of elasticity

The measurement of tax-to-income elasticity has been the subject of considerable study. Two general problems have been encountered: (1) what should be the form of the equation used to estimate the tax-income relationship? and (2) how should the effect of discretionary changes be separated from other tax revenue growth?

Turning to the first problem, it is found that in the least squares regression

logT = logα + β logY,

the regression coefficient (β) gives the percentage change in tax receipts (T) that accompanies a 1 per cent change in income, i.e., it is the coefficient of income elasticity. This form of the equation relating taxes and income is used here to obtain a measurement of elasticity. Such a form implies that the relation between revenue receipts and income is approximated by the function:

T = αY^β

from which the double log function is derived. It contains an important assumption that the income elasticity is constant over the range of income considered. This constancy requires that the proportionate response of the tax to an income change of 1 per cent will be the same, regardless of the level of income. Since no attempt is made to measure changes over long historical periods or great changes in per capita income, the assumption should be reasonably valid. (One indication whether the function is well specified is the level of the statistic ${\overline{R}}^2$, which measures the goodness of fit of the functional relationship being measured.) No attempt has been made here to formulate more accurately the relationship between tax receipts and income by adding other independent variables to the estimating equation, such as lagged income or population.

Given the form of the equation for measuring elasticity, that part of the growth of tax receipts accounted for by discretionary changes must be eliminated from the tax receipt series. Discretionary changes are defined for purposes of this paper as legal changes in tax rates or in the tax base, the introduction of new taxes, and certain administrative efforts. The yield effects of normal (trend) improvements in administration unaccompanied by legal changes are thus included in this measurement of elasticity.

Two general methods have been used to separate automatic and discretionary tax revenue changes. By one method, figures of actual tax receipts, as well as data on the monetary value of the legal tax bases and their corresponding tax rates, are collected for a series of years. Figures for actual tax receipts are then divided by indices of base and rate changes, yielding a series net of discretionary changes. This method assumes a zero elasticity of demand,³ since changes in tax rates or in the tax base are held to yield a proportionate change in tax revenue. The method is particularly suitable where data on the legal tax bases are available and the rate structure is not complex. In developing countries, data on the legal tax bases are often not available and/or the rate structure (of import and export duties, for example) may be highly complex.

An alternative method of separating discretionary effects, used by A. R. Prest in studying the personal income tax in the United Kingdom, is used here.⁴ This method begins with estimates of the effects of discretionary tax changes on the year’s receipts, often prepared by treasury officials. The separation of discretionary effects is then accomplished in two steps. First, a preliminary series of adjusted tax yields is prepared by subtracting from the actual yield for each year the estimated amount attributed to the discretionary change in that year. This “adjusted” series is then further refined by the application of the formula shown below to form a “final” series that excludes the continuing impact of each discretionary change on future years, so that the elasticity of a given tax structure in the base year may be estimated.

The Prest formula may be developed symbolically as follows:

(a) T_1, T₂ … T_t … T_n are actual tax yields for a series of years.

(b) D₁, D₂ … D_t … D_n measures the effect of a discretionary change in the rth year on the tth year’s revenue outturn.

(c) T_ij indicates the jth year’s actual tax yield adjusted to the tax structure that existed in year i.

If i = 1 is the reference year, the series T₁₁, T₁₂, T₁₃ … T_1t … T_1n represents what the tax receipts would have been if the tax structure had remained as in year 1 with all discretionary changes removed from the years following year 1. It is this series that forms the basis used here for measuring the elasticity of a tax. The series is developed as follows:

An interpretation of the formula is as follows: To adjust the tax yield of any year to the hypothetical yield for that year, if a base-year tax structure had prevailed, the actual tax yield is multiplied by a sequence of multiplicative factors. The effect of any one of these factors is to adjust tax yields to the tax structure that prevailed in the year to which the factor referred. Each such factor reveals what proportion of the total yield for that year would have accrued automatically in the absence of any discretionary changes for that year; the factor is found by dividing the actual tax yield (net of the discretionary effects of that year) by the total tax yield. An important assumption, reasonably well satisfied in the case of Paraguay, is that the discretionary changes are no more or less progressive than the tax structure they modify. In the discussion that follows, tax elasticity for individual taxes and for the system as a whole is calculated, using the years 1962-70, with 1962 as the base year.

Application of analysis to Paraguay

The years 1962-70 were a period of marked increase in the ratio of taxes to income in Paraguay. On the basis of a recent survey of tax trends in developing countries, the ratio in Paraguay increased from 5.0 per cent for 1953-55 to 9.5 per cent for 1966-68. This increase placed Paraguay among the leaders in this respect in a sample of 27 countries.⁵ A continuous time series available for the period 1962-70 also shows an improving trend, rising from an average of 7.9 per cent for 1962-64 to 10.6 per cent for 1970 (Table 1). The analyses that follow focus on the increase in the ratio for the years 1962-70, a period of conscious tax reform.

Table 1.

Paraguay: Tax Revenue and Gross Domestic Product, 1953-55 and 1962-70

(In millions of guaraníes)

Source: Data provided by the Paraguayan authorities.

¹Estimated.

Table 1.

Paraguay: Tax Revenue and Gross Domestic Product, 1953-55 and 1962-70

(In millions of guaraníes)

	1953-55	1962	1963	1964	1965	1966	1967	1968	1969	19701
Tax revenue	549.0	3,915.8	3,658.8	3,832.1	5,241.2	5,493.2	5,832.9	6,295.1	7,775.5	8,002.5
Gross domestic product	10,098.7	45,394.0	48,280.0	51,334.0	55,812.0	58,575.0	62,027.0	65,220.0	69,904.0	75,148.0
Ratio of tax revenue to GDP (per cent)	5.0	8.6	7.6	7.5	9.4	9.4	9.4	9.7	11.1	10.7

Source: Data provided by the Paraguayan authorities.

¹Estimated.

View Table

Table 1.

Paraguay: Tax Revenue and Gross Domestic Product, 1953-55 and 1962-70

(In millions of guaraníes)

	1953-55	1962	1963	1964	1965	1966	1967	1968	1969	19701
Tax revenue	549.0	3,915.8	3,658.8	3,832.1	5,241.2	5,493.2	5,832.9	6,295.1	7,775.5	8,002.5
Gross domestic product	10,098.7	45,394.0	48,280.0	51,334.0	55,812.0	58,575.0	62,027.0	65,220.0	69,904.0	75,148.0
Ratio of tax revenue to GDP (per cent)	5.0	8.6	7.6	7.5	9.4	9.4	9.4	9.7	11.1	10.7

Source: Data provided by the Paraguayan authorities.

¹Estimated.

The elasticity of the tax system

What was the built-in elasticity of the tax system and its individual components during the years 1962-70? As noted above, in order to answer this question an examination must first be made of the direct impact of discretionary changes in the year each change took effect. A summary of discretionary measures appears in Table 2. The most significant measures were the extensive revision of import taxes at the end of 1963, the adjustment of stamp tax rates in 1965 and 1969, the lowering of rates on imported cigarettes for domestic consumption and transit (re-export) in 1968 and further lowering for re-export in 1969, and increases in import surcharges having effect in 1965 and 1967. Other measures of revenue significance were the enactment of “substitute” income taxes on exports and on meat, an increase in income tax rates, the taxing of income in the form of interest and rent, the creation of a tax on corporate net worth, revaluation of property assessments, changes in the estate tax rates, changes in exemptions under import surcharges, changes in the tax rates on transfers of cattle, lowering of export rates, and increasing exemptions from export taxes. Discretionary changes of little revenue significance are not included in this analysis.

Table 2.

Paraguay: Revenue Effects of Discretionary Tax Changes, 1962-70

(In millions of guaraníes)

Source: Estimates by the author, based on data provided by the Paraguayan authorities.

¹Increased administrative effort to suppress smuggling, associated with fixing of lower rates, led to higher revenue.

Table 2.

Paraguay: Revenue Effects of Discretionary Tax Changes, 1962-70

(In millions of guaraníes)

		1962	1963	1964	1965	1966	1967	1968	1969	1970
Income tax
	Increase in rate	50
	Substitute tax on exports					50
	Tax on interest and rent						25
Wealth taxes
	New tax on corporate capital				32
	Revaluation of property					17				20
	Estate tax (rate change)				16
Import taxes
	Increases in import surcharges				100		77
	Specific tax on cigarettes (lower rates)1							150	222
	Specific tax on beverages (rate change)								25
	Change in exemptions under import surcharge					40
	New sales tax (predominantly on imports)								323
	Extensive revision in import taxes at end of 1963			100
Cattle taxes
	Tax on transfers of cattle (rate change)				60
	Net gain from introduction of cattle head tax		15
Export taxes (reduced rates and increased
	exemptions)		−50	−50				−50
Stamp taxes					135				293

Source: Estimates by the author, based on data provided by the Paraguayan authorities.

¹Increased administrative effort to suppress smuggling, associated with fixing of lower rates, led to higher revenue.

View Table

Table 2.

Paraguay: Revenue Effects of Discretionary Tax Changes, 1962-70

(In millions of guaraníes)

		1962	1963	1964	1965	1966	1967	1968	1969	1970
Income tax
	Increase in rate	50
	Substitute tax on exports					50
	Tax on interest and rent						25
Wealth taxes
	New tax on corporate capital				32
	Revaluation of property					17				20
	Estate tax (rate change)				16
Import taxes
	Increases in import surcharges				100		77
	Specific tax on cigarettes (lower rates)1							150	222
	Specific tax on beverages (rate change)								25
	Change in exemptions under import surcharge					40
	New sales tax (predominantly on imports)								323
	Extensive revision in import taxes at end of 1963			100
Cattle taxes
	Tax on transfers of cattle (rate change)				60
	Net gain from introduction of cattle head tax		15
Export taxes (reduced rates and increased
	exemptions)		−50	−50				−50
Stamp taxes					135				293

Source: Estimates by the author, based on data provided by the Paraguayan authorities.

¹Increased administrative effort to suppress smuggling, associated with fixing of lower rates, led to higher revenue.

Elasticities of the total tax system and of the major taxes are presented in Table 3. The elasticity of the total system was 1.14 over the 1962-70 period. Elasticities of individual taxes were rather divergent. The elasticity of import duties—the bulwark of the system—was 1.21.⁶ The stamp tax, another important tax, had an elasticity of 1.34; income tax, 1.08; wealth taxes, 1.52; and cattle taxes, 2.05. Export taxes had a low elasticity of 0.06.

Table 3.

Paraguay: Elasticity of Major Taxes and of the Total Tax System, 1962-70

¹Components of the major taxes do not necessarily add to total, because certain minor taxes are excluded.

²Includes fuel tax after 1966 as an import tax.

³Excludes fuel tax from excise taxes.

Table 3.

Paraguay: Elasticity of Major Taxes and of the Total Tax System, 1962-70

			Weight of
			Tax in 1970
		Elasticity	(In per cent
		Coefficient	of total) 1	${\overline{R}}^2$	T-Test
Income tax		1.08	10.5	0.92	9.55
Wealth taxes		1.52	7.5	0.95	12.15
	Property	1.53	5.5	0.97	16.08
	Estate	−0.08	0.6	0.00	0.10
	Vehicle transfer	2.26	0.3	0.74	4.84
Cattle taxes		2.05	5.3	0.88	7.72
	Slaughter	2.63	2.1	0.67	4.14
	Cattle transfer	1.22	2.1	0.75	4.95
Import taxes2		1.21	55.7	0.83	6.27
Export taxes		0.06	3.4	0.00	0.23
Excise taxes 3		0.39	4.4	0.30	2.10
	Cigarettes	−0.01	2.2	0.00	0.07
	Beverages	0.68	2.2	0.01	0.02
Former sales tax		−0.01	…	0.07	1.02
Stamp taxes		1.34	12.3	0.93	10.63
Other taxes		1.50	0.7	0.38	2.44
Total tax system		1.14	100.0	0.92	9.55

¹Components of the major taxes do not necessarily add to total, because certain minor taxes are excluded.

²Includes fuel tax after 1966 as an import tax.

³Excludes fuel tax from excise taxes.

View Table

Table 3.

Paraguay: Elasticity of Major Taxes and of the Total Tax System, 1962-70

			Weight of
			Tax in 1970
		Elasticity	(In per cent
		Coefficient	of total) 1	${\overline{R}}^2$	T-Test
Income tax		1.08	10.5	0.92	9.55
Wealth taxes		1.52	7.5	0.95	12.15
	Property	1.53	5.5	0.97	16.08
	Estate	−0.08	0.6	0.00	0.10
	Vehicle transfer	2.26	0.3	0.74	4.84
Cattle taxes		2.05	5.3	0.88	7.72
	Slaughter	2.63	2.1	0.67	4.14
	Cattle transfer	1.22	2.1	0.75	4.95
Import taxes2		1.21	55.7	0.83	6.27
Export taxes		0.06	3.4	0.00	0.23
Excise taxes 3		0.39	4.4	0.30	2.10
	Cigarettes	−0.01	2.2	0.00	0.07
	Beverages	0.68	2.2	0.01	0.02
Former sales tax		−0.01	…	0.07	1.02
Stamp taxes		1.34	12.3	0.93	10.63
Other taxes		1.50	0.7	0.38	2.44
Total tax system		1.14	100.0	0.92	9.55

¹Components of the major taxes do not necessarily add to total, because certain minor taxes are excluded.

²Includes fuel tax after 1966 as an import tax.

³Excludes fuel tax from excise taxes.

Before analyzing individual elasticities in greater detail, certain points should be noted:

1. The overall elasticity of the tax system of only 1.14 shows that discretionary changes were needed to raise the ratio of taxes to gross domestic product (GDP). Without such changes the tax ratio would have risen only marginally.

2. Although no suitable time series for the fuel tax exists (as it was grouped with import taxes before 1966), the evidence suggests that the yield from this tax grew very rapidly. A related tax, the motor vehicle transfer tax, also had a high elasticity. Thus, taxes related to motor vehicles had high elasticity, which might be expected as the road system and the number of cars have been rapidly expanding. A high elasticity for taxes related to motor vehicles may be typical for a number of developing countries.

3. Import duties, Paraguay’s main source of revenue, had an elasticity above unity, considering the fuel tax as an import tax. As shown below, this relatively high elasticity stems from the fact that imports of consumer goods rose more rapidly than GDP over the period. While a heavy dependence on international trade taxes is often considered an undesirable attribute because it may lead to instability of receipts, Paraguay’s dependence on import duties actually had distinct advantages for revenue growth.

4. The elasticity of stamp taxes was surprisingly high. These taxes are very comprehensive and reflect a turnover of goods, as well as financial transactions. Their high elasticity may be related to the more rapid rise of consumer imports, financial transactions, and bank credit and deposits than of GDP.

5. Elasticities of taxes on wealth, including the property tax, are quite high, in view of the fact that in theory such taxes are often considered inelastic. Although no firm statistical evidence is available on the base and administration of the tax, it appears that property tax assessments have been very low relative to the true market price. The high elasticity of the tax may reflect the greater scope for improvement in terms of raising the valuation and collecting existing taxes. If similar opportunities exist in other developing countries, the potential of the tax for a high elasticity (including the effects of “administrative improvements”) may be great, at least in the short-to-medium run.

6. Excise taxes, excluding fuel, have low elasticities, owing in part to the effect on the domestic tobacco industry of the smuggling of imported cigarettes, and in part to the use of some specific duties on beverages. Weak administration may also have been a factor in the low elasticity coefficients for excise taxes.

7. Interpretation of the statistic ${\overline{R}}^2$ for the total tax system and for the various taxes is important, since this statistic measures the extent to which changes in tax revenue are systematically correlated with changes in GDP. For total taxes the level of ${\overline{R}}^2$ is 0.92, indicating that the correlation is rather high. This finding is of some interest, as many aggregate economic models assume that tax revenues are functionally related to GDP. The high level of ${\overline{R}}^2$ for total taxes in Paraguay would tend to bear out such an assumption on purely statistical, as opposed to causative, grounds. The range of ${\overline{R}}^2$ is rather wide for particular taxes, varying from high levels for the stamp tax, import taxes, wealth taxes, and income tax to low levels for export taxes and certain excise taxes.

A decomposition of elasticities

It has been shown above that the elasticity of a given tax $\frac{{\mathrm{\Delta }T}_k}{\mathrm{\Delta }Y}\times \frac{Y}{T_k}$ is composed of two elements: the elasticity of the tax collected relative to the base $\frac{{\mathrm{\Delta }T}_k}{{\mathrm{\Delta }B}_k}\times \frac{B_k}{T_k}$ (tax-to-base elasticity) and the elasticity of the base to income $\frac{{\mathrm{\Delta }B}_k}{\mathrm{\Delta }Y}\times \frac{Y}{B_k}$ (base-to-income elasticity). This relationship is expressed in the identity: ⁷

Since the legal base of each tax is not available, the yields of four major types of taxes in Paraguay—accounting for about 75 per cent of total tax revenue—have been related to approximate or proxy bases and then the proxy bases have been related to GDP. These relationships are summarized in Table 4 and are discussed below.

Table 4.

Paraguay: Decomposition of Tax Elasticities, 1962-70

Sources: Banco Central del Paraguay, Boletín Estadístico Mensual; and national accounts data.

¹The fuel tax is included as an import tax.

Table 4.

Paraguay: Decomposition of Tax Elasticities, 1962-70

						Proxy Base-		Tax-to-
				Tax-to-Income		to-Income		Proxy Base
				Elasticity		Elasticity		Elasticity
		Tax and Related Proxy Base		Coefficient	${\overline{R}}^2$	Coefficient	${\overline{R}}^2$	Coefficient	${\overline{R}}^2$
Import taxes and consumer imports 1				1.21	(.83)	1.56	(.87)	0.70	(.77)
Export taxes and exports				0.06	(.00)	1.05	(.67)	0.17	(.00)
Excise taxes
	Cigarette tax and production			−0.01	(.00)	0.54	(.12)	0.44	(.31)
	Beverage tax and gross sales			0.68	(.01)	1.54	(.96)	0.58	(.14)
Cattle taxes and cattle slaughtered				2.05	(.88)	0.23	(.35)	4.81	(.52)

Sources: Banco Central del Paraguay, Boletín Estadístico Mensual; and national accounts data.

¹The fuel tax is included as an import tax.

View Table

Table 4.

Paraguay: Decomposition of Tax Elasticities, 1962-70

						Proxy Base-		Tax-to-
				Tax-to-Income		to-Income		Proxy Base
				Elasticity		Elasticity		Elasticity
		Tax and Related Proxy Base		Coefficient	${\overline{R}}^2$	Coefficient	${\overline{R}}^2$	Coefficient	${\overline{R}}^2$
Import taxes and consumer imports 1				1.21	(.83)	1.56	(.87)	0.70	(.77)
Export taxes and exports				0.06	(.00)	1.05	(.67)	0.17	(.00)
Excise taxes
	Cigarette tax and production			−0.01	(.00)	0.54	(.12)	0.44	(.31)
	Beverage tax and gross sales			0.68	(.01)	1.54	(.96)	0.58	(.14)
Cattle taxes and cattle slaughtered				2.05	(.88)	0.23	(.35)	4.81	(.52)

Sources: Banco Central del Paraguay, Boletín Estadístico Mensual; and national accounts data.

¹The fuel tax is included as an import tax.

Import taxes

Although in theory import surcharges, which bring in the bulk of import duty revenue, apply to all imports, exemptions for capital goods and raw materials are generally granted under Paraguay’s development incentives legislation. Therefore, a selected series of consumer imports has been chosen as best approximating the import duty base. It is interesting to note that the relatively high overall elasticity of 1.21 for import duties, including the fuel tax, is the product of a high base-to-GDP elasticity (1.56) and a low tax-to-base elasticity (0.70). The ${\overline{R}}^2$ statistic is relatively high for all three coefficients, indicating that the function assumed is a good fit of the data. Thus, over the 1962-70 period, demand for imports of consumer goods—enhanced by the lack of growth of import substitution industry and a relatively stable exchange rate—has apparently been strong, leading to a high rate of growth for this very important component of Paraguay’s total tax base. At the same time, tax collections have lagged proportionately to the growth of imports of consumer goods, as indicated by the tax-to-base elasticity of 0.70. This latter coefficient probably reflects the combined effect of the use of some specific rather than ad valorem duties, granting of exemptions, and lax administration, although the relative importance of these elements would be difficult to ascertain.

Export taxes

Export taxes show an interesting pattern in that the base—exports—rose more or less proportionately to GDP (1.05 base-to-income elasticity), but the tax-to-base elasticity was very low (0.17), and the ${\overline{R}}^2$ statistic for the tax to base elasticity was 0.00, indicating no systematic correlation. Exemptions from export duties, given deliberately to help exporters when market conditions warranted, account for the low and random nature of the tax-to-base coefficient.⁸

Excise taxes

The two major excise taxes are an ad valorem tax on domestically produced cigarettes, and taxes on beer, wine, and soft drinks (grouped together as beverages). The elasticity of each of these excise taxes was less than unity, with 0.68 tax elasticity to GDP for beverages and—0.01 tax elasticity to GDP for cigarettes. For beverages, the base (measured in value terms) grew rapidly, showing an elasticity of 1.54 with respect to income. However, tax collections relative to the base had an elasticity of only 0.58, in part because some excise taxes are specific and the volume of production apparently lagged relative to value. It is interesting to note that the ${\overline{R}}^2$ statistic was very high for the beverage base-to-income elasticity, reflecting a consistent growth of the base with income. The ${\overline{R}}^2$ statistic for the beverage tax-to-base elasticity was very low, however, indicating that the growth of collections relative to the base has been very erratic.

For cigarettes, the elasticity of the tax to income was virtually zero (-0.01), and the ${\overline{R}}^2$ statistic indicated no relationship between tax collections and income. Both the tax-to-base and base-to-income elasticities were low (0.44 and 0.54, respectively) and the ${\overline{R}}^2$ was low for each (0.31 and 0.12, respectively). The seeming lack of consistency between the three elasticity coefficients is due to the low values of the ${\overline{R}}^2$ statistic. The lack of consistent relationships, as well as the low value of the elasticity coefficients, probably reflects the fact that smuggling of imported cigarettes has occasionally tended to hold down both the growth of the domestic industry and the tax collections from that industry.

Cattle taxes

Cattle taxes represent a departure from the pattern of the three previous groups, in that the base-to-income elasticity was very low (0.23), whereas the tax-to-base elasticity was very high (4.81), resulting in a high overall elasticity coefficient (2.05). The stagnation of cattle herds was a well-known phenomenon in this period, and therefore there is little reason to doubt the trend of the base figures. The high tax-to-base elasticity apparently reflects much improved administration.

Summary of decomposition analysis

Analysis of the components of the overall tax elasticities brings out the importance of the generally low value of tax-to-base elasticities as the key factor in explaining the fairly low elasticity of the system. This conclusion follows from the fact that the bases of import duties, export duties, and excise taxes (accounting for the bulk of tax revenue) grew more rapidly than GDP. If tax collections had grown at least proportionately with these expanding bases, overall elasticity would have been much higher. Improvement in tax-to-base elasticity arises from a variety of elements, including better tax administration (in the narrow sense of more efficient procedures) and prevention of evasion, as well as elements of tax policy, such as using ad valorem rates to increase revenues as the value of the base rises.

Tax buoyancy versus tax elasticity

Tax buoyancy measures the total percentage change in tax revenues, including discretionary changes, associated with a given percentage change in income. For the system as a whole buoyancy is represented by $\frac{{\mathrm{\Delta }T}_t}{\mathrm{\Delta }Y}\times \frac{Y}{T_t}$ and for any given tax by$\frac{{\mathrm{\Delta }T}_k}{\mathrm{\Delta }Y}\times \frac{Y}{T_k}$. As in the case of elasticity, the buoyancy coefficient has been estimated from a double log function implying the original form:

T = αY^β

The difference between tax-to-income elasticity and tax buoyancy shows the importance of discretionary changes, while a tax-by-tax comparison of the two measures points to the taxes for which discretionary changes were most important.

As shown in Table 5, the tax system as a whole had a buoyancy of 1.69, compared with an elasticity of 1.14. This large difference indicates that discretionary changes considerably improved the performance of the tax system.

Table 5.

Paraguay: Difference Between Tax Buoyancy and Tax Elasticity for Total Taxes and Selected Major Taxes, 1962-70

Sources: Appendix Tables 6 and 7.

¹Including fuel.

²Excluding fuel.

Table 5.

Paraguay: Difference Between Tax Buoyancy and Tax Elasticity for Total Taxes and Selected Major Taxes, 1962-70

			Difference
			(In percent-
	Buoyancy	Elasticity	age points)
Total taxes	1.69	1.14	+0.55
Income tax	1.42	1.08	+0.34
Wealth taxes	2.04	1.52	+0.52
Cattle taxes	2.77	2.05	+0.72
Import taxes 1	1.82	1.21	+0.61
Export taxes	−0.89	0.06	−0.95
Excise taxes2	0.39	0.39	—
Stamp taxes	3.02	1.34	+1.68
Other taxes	1.50	1.50	—

Sources: Appendix Tables 6 and 7.

¹Including fuel.

²Excluding fuel.

View Table

Table 5.

Paraguay: Difference Between Tax Buoyancy and Tax Elasticity for Total Taxes and Selected Major Taxes, 1962-70

			Difference
			(In percent-
	Buoyancy	Elasticity	age points)
Total taxes	1.69	1.14	+0.55
Income tax	1.42	1.08	+0.34
Wealth taxes	2.04	1.52	+0.52
Cattle taxes	2.77	2.05	+0.72
Import taxes 1	1.82	1.21	+0.61
Export taxes	−0.89	0.06	−0.95
Excise taxes2	0.39	0.39	—
Stamp taxes	3.02	1.34	+1.68
Other taxes	1.50	1.50	—

Sources: Appendix Tables 6 and 7.

¹Including fuel.

²Excluding fuel.

Among selected major taxes the greatest difference between buoyancy and elasticity was for stamp taxes, where substantial rate adjustments occurred in 1965 and 1969. Import taxes also showed a large difference between buoyancy and elasticity, as did taxes on the slaughter and transfer of cattle. It is interesting to note that these taxes are indirect by conventional usage. Apparently changes in rates of indirect taxes could be counted upon to produce more revenue with relative certainty in these areas. For direct taxes on income and wealth, the differences between buoyancy and elasticity were smaller. (The difference between the two measures for wealth taxes reflects mainly the introduction of a tax on corporate equity in 1965, rather than any legal adjustments in existing property and vehicle transfer taxes.) The concentration on indirect taxes indicates that rate and base changes in direct taxes were not tried, probably because they were less likely to produce certain revenue gains without the prospect of significant accompanying administrative effort. It has been noted in this connection that the necessity of raising tax revenue in developing countries may lead to a lopsided development of the tax system through the frequent raising of rates on easily administered taxes while taxes that are difficult to administer are neglected.⁹

Conclusion

These results show that in the period 1962-70, Paraguay’s tax ratio rose significantly, even though the built-in elasticity of the tax system was only slightly more than unity and tax-to-base elasticities of major taxes were substantially less than unity. Balanced against these unfavorable factors were important discretionary changes—mainly rising rates of indirect taxes, such as import and stamp taxes—and the adoption of a new sales tax falling mainly on imported goods. These discretionary changes resulted in a buoyancy of 1.69 for total taxes, a much higher figure than the built-in elasticity of tax revenue to income. Another important favorable influence on both elasticity and buoyancy was the relatively high base-to-income elasticity of most major taxes.

In summary, these quantitative results point to a picture of expanding tax bases and significant discretionary changes, in part offset by evasion, exemptions, the specific nature of a number of duties, and probably weak administrative effort in collecting taxes at existing rates. The rather modest overall income elasticity of the major taxes cannot be ascribed to stagnant or slowly growing bases; hence, the key factor in improving the income elasticity of the tax system is an increase in the tax-to-base elasticities.