Updated: 04 Oct 2007 ECON 635: PUBLIC FINANCE Lecture 2 Topics to be covered: . Mobilizing Resources for Development a b. c. d. e. f. g. h. Impact of Savings on Growth Please Effect Private Savings and Growth Tax Capacity and Tax Effort Tax Elasticity and Buoyancy Income Tax, Indirect Tax GDP Based Estimating Models
Mobilizing Resources for Development • We will study the relationship between the annual growth rate of the economy, the available savings, the amount of investment and the incremental capital output ratio (ICOR) for the economy. • The incremental capital output ratio (ICOR) is the number of units of investment needed to generate one unit of additional income each year in the future. 1
Mobilizing Resources for Development (Cont’d) • K: change in capital stock equals new net investment • Y: change in GNP • ICOR = by definition. • Or (Dividing both sides by Y) • But Y/Y is growth rate of income. Let it be denoted by GY. • Also K=I (Investment) • or Harrod Domar Growth Equation 2
Mobilizing Resources for Development (Cont’d) • If I/Y and ICOR for a country are known, GY can be calculated. • For Example: • If I/Y is 15% and ICOR=3, then • In Singapore, I/Y is about 40% and even for an ICOR of 5, the potential growth rate for the country works out to 8%. • India too has a high savings rate, I/Y is about 25%. But its ICOR is 6, hence, the potential growth rate for India comes down to 4. 24%. • ICOR is an indicator of efficiency of the productive process in the economy. • Countries that have policies that promote capital intensive import substitution industries tend to have a high ICOR. 3
Impact of Savings on Growth If, for a country: • C: Consumption • S: Total Savings • T: Tax Revenue • Y: GNP (National Income) Therefore: Y = C + S + T Also, If: • G: Government Expenditure • X: Exports • M: Imports • I: Investment • Y: GNP (National Income) Therefore: Y = C + I + G + X - M (Definition 1) (Definition 2) 4
Impact of Savings on Growth (Cont’d) • • Set, Definition 1 = Definition 2 C + S + T = C + I + G + X – M I = S + T – G + M – X (1) Investment = Savings (private) + (T - G) Government Savings + (M - X) Foreign Savings • I = Spvt + Sgovt + Sforeign (2) Sforeign = 0 (That is M-X=0) denote, t = Average tax rate denote, a= G/Y = ratio of government expenditure to GNP denote, s = marginal propensity to save or the personal savings rate • then, Sprivate = s (Y-T) • and Sgovernment = t. Y - a. Y 5
• Substituting values of Sprivate and Sgovernment to the (2), I = s (Y – T) + t. Y – a. Y + 0 or I = s (Y – t. Y) + t. Y – a. Y or I/Y = s (1 – t) + t – a But I/Y=GY *(ICOR) Harrod Domar Equation g. Y ICOR = s (1 – t) + t – a or, 6
Impact of Savings on Growth (Cont’d) • For Example: If for a country s=0. 2, a=0. 15, t=0. 15, ICOR=4 then g. Y = 4. 25% • But if tax rate increases to 20%, keeping other factors fixed, then g. Y = 5. 25% • For the growth rate to go up by 1 percentage point, tax rate has to go up by 5 percentage points or 33 percent. 7
Please Effect • It is also possible that as tax revenue goes up, government spending may increase. • In that case, the economic growth rate may actually decrease as taxes increase. • From equation (1) we have, I = S + T – G + M – X, suppose S=s(Y-T) or I = s (Y – T) + (T – G) + (M – X) if (M – X)=0, and T=t. Y, S=s (Y- t. Y), and G=v. T=vt. Y I = s (Y – t. Y) + (t. Y – vt. Y) or I = s. Y (1 – t) + Y (t – vt) or I/Y = s (1 – t) + t (1 – v) 8
Please Effect (Cont’d) • Substituting for I/Y in growth equation gives us, • If v = 1, then government spends all the tax revenue even when tax rates are increased. In that case: • When the tax rate goes up, Gy goes down. 9
Please Effect (Cont’d) • When v = 1 all the extra collection of tax revenue will be spent by the government. • As a result, private savings, government savings, and investment go down. This lowers the growth rate. t Sprivate , G , Stotal , I , GY • This phenomenon of rising government expenditure in correspondence with the increase in the collection of tax revenues is called the "Please Effect". 10
Please Effect (Cont’d) Empirical relation • Based on the government expenditure and tax revenue of different countries, the following regression has been estimated. v = 0. 888 - 0. 0054 * TR GNP [t value = 2. 3] where v=G/T and TR = Tax Revenue • This implies that governments will spend about 89% of the any increase tax revenue. • As tax revenue increases, the ratio of government expenditure to the tax revenue will be slightly lower than 89%. 11
Please Effect (Cont’d) • The government savings will show an increasing trend with an increase in tax revenue. • Based on data from different countries, the regression of (G/T) on TR has a slightly negative slope as shown below. V=G/T 0. 89 TR GNP • This regression represents the general trend. There are large variations among countries. 12
Private Savings and Growth • When the private savings rate or the propensity to save increases, the growth rate can be increased. • When s increases, keeping "t" and "a" fixed, the numerator will increase, thereby increasing "g. Y". Example, Singapore, Malaysia and Japan. • The effect of reducing ICOR can increase g. Y dramatically. Eg. , Korea, ICOR 1960 = 12, ICOR 1970 = 4, Indonesia ICOR 1984 = 9, ICOR 1987 = 4. • It is better to change only one of the variables at a time to see its impact on gy. 13
TAX CAPACITY AND TAX EFFORT The taxable capacity • Represents the average or normal share of income that can be collected in the country. • Tax capacity will depend upon the nature of the economy and the sources of government revenue. 14
TAX CAPACITY AND TAX EFFORT (Cont’d) Tax Collection over time: T = Tax Revenue Y = Net National Income • Then (T/Y) measures the actual ratio of tax revenue to total income. • Actual tax collections may be greater or less than a country’s estimated tax capacity. • Tax capacity depends on the characteristics of the economy that affect the ability of the government to collect revenue, factors such as per capita income, export volume, mineral resources, manufacturing and agricultural output. 15
TAX CAPACITY AND TAX EFFORT (Cont’d) • Chelliah, Baas and Kelly studied the tax ratio of 47 developing countries (1966 to 1971) • The average T/Y ratio was 13. 6 percent in 1966 -67 • Increased to 15. 1 percent by 1971 • For sixteen developed countries in Europe and North America, the ratio T/Y for the period was 26. 2 percent • For fifteen OECD developed countries, the average T/Y ratio, including social security taxes, was as high as 36 percent in 1974. • Conclusions: a) The ratio T/Y and expenditures /Y in developing countries has increased over time as the income of these countries has gone up. b) T/Y ratio and expenditures /Y in developed countries is higher than in developing countries. 16
TAX CAPACITY AND TAX EFFORT (Cont’d) Public Expenditures in Developing Countries over Time Ratio of Government Expenditure to GDP Years 1960 1985 France Japan Sweden 35% 18% 32% 52% 33% 65% U. S. A. 28% 37% • The average ratio of government expenditure to GDP for developing countries increased from 16% in 1960 to 23% in 1985 • The growth of public expenditure in developed countries has been even faster 17
TAX CAPACITY AND TAX EFFORT (Cont’d) Estimation of Tax Capacity T/Y = a + b × (Y/N) + c× (X/Y) + d× (R/Y) + e×(A/Y) Expected sign of a, b, c, d and e coefficients: a ? b ? c ? d ? e ? • Where: Y = GNP T = Tax revenue N = Population X = Exports (excluding mining and petroleum) Is c bigger or smaller than d? R = Mining and Petroleum Exports A = Agriculture output 18
TAX CAPACITY AND TAX EFFORT (Cont’d) Actual Estimation T/Y = 0. 1134 + 0. 0024×(Y/N) + 0. 2218×(X/Y) + 0. 570×(R/Y) ^ • is estimated for the level of income Y (GNP) for a given country and values of other variables for a given country. ^ • This estimated ratio is denoted by • In this regression the value for e was not significant, hence, the variable A/Y was dropped 19
TAX CAPACITY AND TAX EFFORT (Cont’d) ^ • If the tax effort of a given country is less than one, the country is able to make changes in its tax base or tax rates or both and increase revenues without excessive difficulty • Currently exploiting its tax potential to a lesser extent than other countries with similar economic characteristics. • If the tax effort is more than one, then its tax system is raising more tax revenues than is indicated as country's potential for tax collections 20
TAX CAPACITY AND TAX EFFORT (Cont’d) Tax Effort (1972 -1976) COUNTRY TAX EFFORT India 1. 25 Pakistan 0. 915 Nepal Tanzania 0. 489 1. 34 Mexico 0. 733 21
TAX CAPACITY AND TAX EFFORT (Cont’d) • Higher tax effort does not necessarily mean that the country has a government budget surplus or is following a sound set of economic policies • Some countries, have a high tax effort (greater than one), and yet suffer from high budget deficits because of a poor use of public sector resources • The misallocation of government expenditures is a major problem in many countries 22
Tax Elasticity and Buoyancy • The response of tax revenues to changes in the GDP is measured by tax elasticity and tax buoyancy. • These concepts, a) help to explain the overall structure of a tax system. b) serve as valuable analytical tools for designing tax policy.
Tax buoyancy • Tax buoyancy measures the total response of tax revenues to changes in national income. Takes into account both the effect of increases in income and discretionary changes (i. e. , tax rates and bases) on the revenues from a tax. • Tax buoyancy is a measure of both the soundness of the tax bases and the effectiveness of past tax changes in terms of revenue collection. 24
Tax elasticity : a) measures the pure response of tax revenues to changes in the national income. b) reflects only the built-in responsiveness of tax revenue to movement in national income. • The tax elasticity calculation excludes the impact of changes in tax rates and tax bases. It considers only the effects due to changes in income levels, whether or not changes were made in the tax structure during that time period. 25
Measurement of Tax Buoyancy • Tax buoyancy can be expressed as follows: Eb. TY = Buoyancy of tax revenue to income Tb = Total tax revenue ΔTb = Change in total tax revenue Y = Income ΔY = Change in income • Buoyancy may be better expressed by breaking down the total tax system into individual taxes. • Suppose there are sales tax, trade tax, and income taxes in the tax system. Following relations should hold: Tb= Tb 1 + Tb 2 + Tb 3 ΔTb = ΔT 1 b + ΔTb 2 + ΔT 3 b 26
where: T 1 b = Revenue from tax 1 (sales tax), Tb 2 = Revenue from tax 2 (trade tax), T 3 b = Revenue from tax 3 (income taxes). ΔTb 1 + ΔTb 2 + ΔTb 3 Y Eb. TY = ΔY Tb stand for buoyancy of the tax revenues 1, 2, and 3 with respect to income, then 27
• Buoyancy for a specific tax, say T 1 (sales tax), where B 1 stands for the base of tax 1. The first term, a) represents the elasticity of the tax with respect to the tax base. b) Is a function of the legal structure and tax compliance and a measure of the effectiveness of the tax policy. • The second term, , represents the elasticity of the tax base with respect to income. 28
Tax Buoyancy Cont’d, Total tax buoyancy : • This expression shows how each tax base responds to changes in income over time. • Some tax bases may get reduced with changes in economic activity. • Buoyancy is reduced if tax exemptions or tax rates are lowered over time • Buoyancy may also be low if the fundamental tax elasticity of tax system is low 29
Tax Elasticity • Is the relevant parameter for revenue forecasting purposes. • The value of the tax elasticity gives an indication to policy-makers of whether tax revenues will rise at the same pace as the national income. • Tax elasticity is the ratio of the percentage change in tax revenue to the percentage change in income or GDP, assuming that no discretionary changes have been made in the tax rate or tax base. Elasticity of tax revenue to income or GDP, T = Change in tax revenue holding tax rate and the definition of tax base constant, and Y = Change in income GDP 30
Tax Elasticity Cont’d • Since tax elasticity is a measure of the responsiveness of a given tax structure to changes in income, it is necessary to segregate the revenue effects of changes in the tax rates and tax bases from the calculation. • An elastic tax system is a highly desirable system, as it provides the government with a sustained fiscal resource base for financing its outlays. • Inelastic tax system forces governments to continuously make discretionary changes, either in the tax bases or in the tax rates or both. • A tax system that is subject to constant adjustments by policy-makers generates greater uncertainties and has adverse effects on long-term investments, due to uncertainties in the tax system. • A comparison of buoyancy and elasticity coefficients gives the analyst a useful insight into the tax system. 31
Comparisons of Tax Elasticity and Buoyancy Country Buoyancy Elasticity 1 Bangladesh (1979 -84) 0. 99 0. 71 2 Malaysia (1976 -82) 1. 23 0. 50 3 Philippines (1980 -85) 0. 80 0. 50 (1978 -85) 4 Sri Lanka (1978 -84) 0. 75 0. 73 5 Thailand (1977 -85) 1. 13 0. 92 32
Tax Elasticity Cont’d • Although tax buoyancy is a useful tool for the purposes of policy design, the income or GDP based revenue-forecasting models rely on tax elasticity for estimating future tax revenue collections based on the current tax system. • The forecast of aggregate revenues in the future are done within a given tax structure. 33
Case 4: Sri Lanka 1977 -1985 Buoyancy Elasticity Import Duties 1. 456 0. 901 Excises 0. 657 0. 168 Turnover Taxes 1. 641 0. 897 Personal Income Tax 1. 115 1. 194 Corporate Income Tax 1. 046 0. 909 Overall Tax Structure 0. 915 0. 740 34
Tax Elasticity by Tax Income Tax • Personal income tax can be quite elastic if the exemptions and deductions are limited. As more income grows, more tax payers become subject to income tax and also people already in the system pay higher average taxes. • If personal income tax is not inflation adjusted then amount of taxes paid in real terms may grow as the nominal GDP increases due to inflation. • Elasticity of the Income Tax system again depends on whether growing sectors of the economy are taxed or not. 35
Indirect Tax (Sales, Excise, Trade Taxes) • Elasticity of indirect taxes depends mainly on two factors. • The type of tax , i. e. , whether it is a unit tax or an ad valorem (percentage) tax. • As nominal GNP increases due to the general rate of inflation the revenue from a unit tax remains constant in nominal value. This means that real tax revenue will fall. • This causes a decrease in the ratio of tax revenue to GNP. • The tax revenue from a percentage (ad valorem) tax would increase in the same proportion as the price level. 36
Indirect Tax (Cont’d) • The growth in demand of certain goods and services may not increase at as fast a rate as the national income. • As the per capita income of a country increases the income elasticity of each of the goods and services will change. • For the indirect tax system to have a tax elasticity of greater than one its base will have to include a large proportion of goods and services that have income elasticities of demand greater than 1. 37
Computation of Buoyancy • Example: All the values of GDP and income taxes are expressed in current dollars. Calculate the tax buoyancy. YEAR 1982 GDP 7, 426 8, 634 Income tax 599 710 GDP deflator • 1981 1. 83 2. 04 Steps: 1. Estimate income and tax in real terms; 2. Estimate % change of income and tax in real terms; 3. Apply the above formula. 38
Step One: Computation of Buoyancy Cont’d • Estimate GDP and income tax in real term. Year 1981 1982 GDP 7, 426 8, 634 Income tax 599 710 GDP deflator 1. 83 2. 04 Real GDP 4, 057. 92 4, 232. 35 Real Income Tax 327. 32 348. 04 Step Two: • Estimate % change of income and tax in real terms: %Y = ( Y)/Y = (Y 1 – Y 0)/Y 0 %T = ( T)/T = (T 1 – T 0)/T 0 where 0 refers to the base year, 1981 and 1 refers to 1982. 39
Computation of Buoyancy Cont’d Step Three: • To estimate elasticity, one needs to segregate the effects of changes made in the base and tax rates. This method is more complex than the calculation of buoyancy. 40
GDP Based Estimating Models • Aggregate tax revenue forecasting plays a crucial role in the process of annual budget formulation. • It provides policy makers and fiscal planners with first-hand insight and allows them to formulate policy options to balance the budget in the short run as fiscal policy interventions to rectify financial anomalies over the medium term. • First estimate the elasticity with respect to the aggregate tax base and then forecast revenues for the future. 41
Dynamic versus Static Models • Expect to find a close relationship between taxes and their bases in a revenue forecast. • For example, the amount of income tax should depend on the amount of taxable income and the tax rate. • The magnitude of income tax liability will affect the incentive to work and the resulting wages and salaries received. • Sophisticated econometric models can be developed in order to illustrate the linkages (both direct and indirect) between a change in the tax structure and its effects on revenue. • The indirect effect of income is harder to measure than the direct effect. • Once the effects are known, the revenue implications can thus be calculated. Such models as known as dynamic models. 42
• Dynamic models take into account the responses of tax bases when discretionary changes are introduced into the tax system. • Dynamic models consider the expected behavioral responses of economic sectors to the introduction of new taxes or to changes in the existing tax laws. • To capture such linkages require a relatively large amount of solid information, which may not be possible in most countries. • Considering their information-intensive nature, these dynamic models are often not suitable for most countries that are trying to put a working model into place. • Static forecasting models are used because of information constraints and lack of sophisticated computer and economic modeling skills. • Forecasting models are based upon predetermined relationships for different types of taxes. • Static models do not provide feedback between taxes and bases, as the bases are considered to be predetermined. 43
• The GDP-based tax forecasting models, as a first step, require the construction of data series for tax revenues and their bases for each tax. • All major revenue generating taxes should be desegregated as well as their bases. • The next step is to collect information on the tax bases from which these taxes were collected. • It may not be possible to directly quantify the legal tax bases of all tax receipts but one can use proxies for such bases. • All these tax bases are obtained from macroeconomic variables derived from national accounts and balance of payments aggregates. 44
Estimating of Tax Elasticities • Segregation of the pure response of tax revenues to increases in income or expenditure (i. e. , tax base growth) from changes in revenue brought about by discretionary changes (e. g. , legal or administrative). • This can be done in two alternative ways : 1. Constant rate structure method 2. Proportional adjustment method 45
1. The Constant Rate Structure Method • • The method is to apply the current year’s tax rates and lower governing the tax base to the previous year’s income and to construct the adjusted tax revenue series that would have been obtained, had the same tax structure been applied consistently over time. Necessary to have a detailed tax-base data for all the individual taxes, which can be dıffıcult to obtain in most developing countries. • This method can be used if the number of items is small, the range of tax rates is narrow, and the data can be compiled relatively easily (as in some excise tax cases). • For some countries, the tax data bases are so comprehensive that this kind of analysis now can be done (e. g. Canada, Australia, UK, USA) 46
2. Proportional Adjustment Method (Practical Method) • Based on the construction of revenue series by adjusting for the effects of discretionary changes introduced in tax systems over time. • Requires only basic information about revenue collections for constructing the adjusted tax base series. Details of the Proportional Adjustment Approach • Three steps are involved : 1) Compile actual revenue collections throughout the period. Tax revenues over n periods: T 1, T 2, . . . , Tn-1, Tn 2) Compile data series for discretionary changes. Revenues collected from discretionary changes: D 1, D 2, . . . , Dn-1, Dn 3) Adjust actual tax revenue series using discretionary change coefficient. 47
Proportional Adjustment Method Cont’d • Starting out from the current year’s tax structure (Tn), the adjustment process removes the effects on revenue collection produced by discretionary changes introduced over time. • For the nth period, no adjustment is needed, since the tax revenue in the nth period reflects the current tax structure. n refers to now, the present period from which the forecast is to be made. • The Tax revenue impacts of the discretionary changes in tax system, Dn-1, Dn-2, Dn-t, can usually be found in the annual proposed budget documents of Ministry of Finance. 48
Proportional Adjustment Method Cont’d • The adjustment for the year n-1 is as follows: ATn-1 = Tn-1 * [Tn / (Tn - Dn)] where ATn-1 denotes adjusted series for Tn-1. • ATn-1 reflects the tax revenues for the year n-1, if the tax system were the same as the one in the year n. • Adjusted series for the year n-2 equals the actual tax revenue for year 2 times the cumulative adjusted coefficient: ATn-2 = Tn-2 * [Tn / (Tn - Dn )] * [Tn-1 / (Tn-1 - Dn-1)] Tax changes introduced current year in previous year = ATn-1 * [Tn / (Tn - Dn)] • The expression may be expanded for subsequent years. 49
• Factoring out discretionary changes, we may calculate the value of elasticities (ETY) for the particular tax, say, income Y in year 2: AT 2 - AT 1 Y 1 ETY = -------- * ----- Y 2 - Y 1 AT 1 • The buoyancy (Eb) of the same tax in year 2 can be expressed as follows: T 2 - T 1 Y 1 Eb = -------- * ----- Y 2 - Y 1 T 1 50
• If unadjusted tax revenue is used to regress on the respective GDP, the result is buoyant. • When an adjusted tax revenue stream is employed, the result is tax elasticity. • An Example: following data series for tax revenues and discretionary changes for a given country during period 1 to 5: T 1=100 T 2 = 140 T 3 = 170 T 4 = 250 T 5 = 320 D 1 = 0 D 2 = 20 D 3 = 0 D 4 = 30 D 5 = 0 51
• Adjustments to the revenue series to account for discretionary changes T 5 320 a 5 = ------ = 1 T 5 – D 5 320 – 0 T 3 170 a 3 = ------ = 1 T 3 - D 3 170 – 0 T 4 250 a 4 = ----------- = 1. 1364 T 4 – D 4 250 – 30 T 2 140 a 2 = ------ = 1. 1667 T 2 - D 2 140 – 20 • Discretionary changes made in the tax structure in these periods increased revenues by 16. 67% and 13. 64%, respectively. 52
• In year n-2, AT 5 = 320. AT 4 = 250 * 1= 250, where [a 5 = 1]. AT 3 = 170 (1) (1. 1364) = 193. 2, where [a 5 =1], [a 4 = 1. 1364]. AT 2 = 140 (1) (1. 1364) (1) = 159. 5, where [a 5 =1], [a 4 = 1. 1364], [a 3 = 1]. AT 1 = 100 (1) (1. 1364) (1. 1667) = 132. 60, where [a 5 =1], [a 4 = 1. 1364], [a 3 = 1], [a 2 = 1. 1667]. • Based on the assumption that both discretionary changes, D 2 and D 4, were made at the beginning of periods 2 and 4, so that values of T 2 and T 4 already includes the impacts of the respective discretionary changes. 53
Relationship between Tax Revenue and Tax Base • Establish an exact relationship between the adjusted tax data (AT) and the economic variables (i. e. , proxy base). • Task is to find out which component of the national account that corresponds most closely to the base for a particular tax. • In the case of excise taxes, the tax levied on the sale of tobacco products: AT TOBACCO = f (tobacco sales) • Case of personal income tax (PIT), AT PIT = f (wages and salaries, bonuses, interest, dividend, rents, profits from incorporated businesses) • Value-added tax, adjusted tax revenues are linked with total consumption expenditure on goods and services. ATVAT = f (Consumption expenditures) 54
Functional Form • Regression analysis is carried out to forecast future revenue collections. • The general form of the forecasting model is expressed as: ATj = + * Yj where ATj is the adjusted tax revenues in year j, Yj is the tax base in year j, and are coefficients to be estimated. • Alternatively, the same relationship may be expressed in log terms. Ln ATj = + * Ln Yj • = [ ATj / ATj ]/ [ Yj / Yj ] = [%ATj]/[ %Yj ]. The advantage of using log form is that the coefficient of Yj, , becomes the tax elasticity. • ATj takes the form of the adjusted series and the national account component which is used as the tax base proxy becomes the independent variable. 55
• Dummy variables are often introduced into the model to account for the other relevant explanatory variables in the model. AT VAT = a + b * Consumption + g * D Consumption AT VAT = a + (b+g. D) Consumption D: stands for other relevant variables affecting tax collections (e. g. , D=1 for the Iran-Iraq war affecting tourism in Cyprus in 1991 otherwise D=0). • The following equation is obtained from the model ATVAT, 91 = 2. 0 + (0. 1) * (Consumption) 91 = 10. 0 million, if (Consumption) 91 is 80 million. • Supposing that the actual revenue collection from the VAT in 1991 is 9 million. The difference between the estimated revenues (10 million) and the actual collections (9 million) is regarded as the tax compliance gap. 56
Summary Steps to Forecast Future Tax Revenues The following steps are necessary to forecast future tax revenues: (1) Convert all categories of taxes from nominal to real terms; (2) Obtain and convert all corresponding nominal discretionary changes to real; (3) Calculate the adjusted coefficient and cumulative coefficient to reflect discretionary changes; (4) Multiply real tax revenues with the cumulative coefficient of discretionary changes to get an adjusted tax series; (5) Regress the respective adjusted tax revenues with the corresponding tax base to find the tax elasticity. (6) Use the estimated elasticity to forecast the future revenue stream. 57
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