Policy, Research, and External Affairs WORKING PAPERS j [ Public Economics Country Economics Department The World Bank February 1990 WPS 334 An Econometric Method for Estimating the Tax Elasticity and the Impact on Revenues of Discretionary Tax Measures (Applied to Malawi and Mauritius) Jaber Ehdaie The author develops an econometric technique that deals with shortcomings of existing methods for estimating the tax elastic- ity and the impact on revenues of discretionary tax measures. He applies this model to Malawi and Mauritius to highlight the roles that discretionary tax measures and economic growth play in effecting the shift from the taxation of international trade to the , taxation of domestic transactions. - . V 5 The Policy, Research, and Extemal Affairs Cornplex distnbutes PRE Working Papers to dissemr,uate the findings of work in progress and to encourage the exchange of ideas among Bank staff and all others inte.:sted 'n development issues. These papers carry the names of the authors, reflect only thetr views, and should be used and cited accordingly The findings, interpretations, and conclusions are the authors' own They should not be attrbuted tothe World Bank. its Board of Directors ts management, or any of its member countnes. Policy, Research, and External Affairs Public Economics This paper -a product of thc Public Economics Division, Country Economics Dcpartnment -is part of a larger effort in PPR to study the fiscal aspects of structural adjustment. It proposes a mcthod for estimating the additional revenues that might be mobilized within the existing tax system as GDP grows. Copies are available free from the World Bank, 1818 H Street NW, Washington DC 20433. Please contact Ann Bhalla, room Nl()-059, cxtension 37699 (90 pages with figures and tables). In reducing the fiscal deficit as part of structural the taxation of domestic transactions. His adjustment programs, it is important to be able overall conclusions arc: to project what additional revenues can be mobilized within ihe existing tax system as GDP * Discrctionary tax mcasures havc becn grows. effective in mobilizing resources from the privatc sector in both countries. To know if it is necessary to generate more revenues - particularly through politically * Individual and overall tax revenues have difficult discretionary tax measures - it is becn inelastic in connection with GDP - except important to be able to estimate the built-in tax for corporate income tax in Malawi and import elasticity as percentage increascs in tax revenue tax in Mauritius, whosc long-term elasticities ex- that result from endogenous incrcases in the base cecd one. Thcsc two taxes are inclastic in when GDP rises I pcrcent. tcrms of their own tax bascs. Imports in Mauri- tius and value added in the nonagriculture sector Existing methods for estimating this elastic- in Malawi havc grown faster than GDP. ity are inadequate, so Ehdaic develops an econ- omctric method for estimating built-in tax * The domestic consumption tax had more elasticity and the impact on revenues of discre- built-in elasticity than import tax in Malawi; in tionary tax measures. Mauritius, the domestic consumption tax fell short of the import tax. Because of thesc His dynamic simultaneous-equation macro- structural differences, economic growth has fed econometric model of taxation captures the the shift from taxing imports to taxing domestic interaction between GDP, individual tax sys- transactions in Malawi: it has reversed the shift tems, and individual Lax revenues and bases. It in Mauritius. Without cconomic growth, both requires only timc series data on tax revenues, countries would shift from taxing imports to tax bascs, and GDP. taxing domestic transactions. Ehdaic's model can also bc used to (1) * In both countries, discretionary tax mcas- evaluatc thc macrocconomic impact of a tax ures have contributed more to the trcnd toward rcfomi program and (2) examine various tax-re- domestic consumption tax than to the trend lated economic issues. toward import taxes. In this paper, Ehdaic applies this model to * In Malawi, economic growth and discre- the time series data for Malawi and Mauritius to tionary tax measures have played almost equal highlight the roles that economic growth and roles in the shift from taxing intemational trade discretionary tax measures play in cffecting the to taxing domestic transactions. In Mauritius, shift from the taxation of international trade to economic growth has been the principal factor in revcrsing this shift. The PRE Working Paper Series disseminates thc Findings of wo-k under wa, ni the Bank's Policy, Research, and External Affairs CorTiplex. An objectivc Of the scrics is to gc; thcsc findings out quickly, even if presenitations arc lcss than f aily polished. The findings, interpretations, and conclusions in these papers do not neccessarily represent official policy if thc Bank. Produced at the PRE Dissemination Center TABLE OF CONTENTS LIST OF TABLES LIST OF FIGURES hapters I. INTRODUCTION ................................................. 1 II. THEORETICAL DEVELOPMENT OF THE MODEL .......................... 16 Individual Tax Yield Equations Block .......... . ........... 17 Individual Tax Base Functions Block ........................ 25 Identities Block ........................................... 32 Entire Model and Its Dynamic Multipliers ................... 34 III. APPLICATION OF THE MODEL ...................................... 47 Estimation Method and Empirical Results .................... 47 Trends of Tax Effort and Tax Shares ........................ 58 IV. CONCLUSION ................................................... 65 APPENDIX A: Historical Time Series Data .............................. 71 APPENDIX B: Generalized Version of the Model ......................... 79 APPENDIX C: An Operational Guidlin3 on the Application of the Model..82 BIBLIOGRAPHY ...................................................... 88 I am grateful to Javad Khalilzadeh-Shirazi, JesuLs Seade, Pradeep Mitra, Wayne Thirsk, and William McCleary, who inspired me to undertake this study and provided useful comments. I am also thankful to Bela Balassa, Emmanuel Jimenez, Martha de Melo, P. Shome, Zmarak Shalizi and Anwar Shah for helpful comments. LIST OF TABLES 1. Structural Form of the Model ........................................ 35 2. Entire Model with Estimable Parameters .............................. 36 3. Short Run and Long Run Individual and Overall Tax Elasticities in Terms of the Parameters Included in the Model ................ 40 4. Direct and Indirect Responses of Individual and Overall Tax Revenues to the Changes in the Import Tax System ........................ 41 5. Direct and Indirect Responses of Individual and Overall Tax Revenues to the Changes in the Domestic Consumption Tax System ........... 42 6. Direct and Indirect Responses of Individual and Overall Tax Revenues to the Changes in the Corporate Income Tax System .............. 43 7. Direct and Indirect Responses of Individual and Overall Tax Revenues to the Changes in the other direct Taxes System ................ 44 8. Test Results For Serial Correlation ................................. 49 9. Econometric Model of Taxation of Malawi (N3SLS Estimation Results) ....................................... 51 10. Econometric Model of Taxation of Mauritius (N3SLS Estimation Results) ....................................... 52 11. Short Run and Long Run Impacts of Changes in Individual Tax Systems and GDP on Tax Revenues and Bases in Malawi ...................... 56 12. Short Run and Long Run Impacts of Changes in Individual Tax Systems and GDP on Tax Revenues and Bases in Mauritius .................. 57 13. Individual and Overall Tax Buoyancies and Elasticities in Malawi and Mauritius .................................................... 61 14. Contribution of Economic Growth and Discretionary Tax Measures to Trends of Tax Shares and Effort in Malawi and Mauritius .......... 63 LIST OF FIGURES 1. Decomposition of response of An Individual Tax Yield to Discretionary Tax Measures ................................................... 6 2. Actual and Predicted Values of Individual Tax Yields in Malawi ..... 53 a. Import Tax ..................................................... 53 b. Domestic Consumption Tax ....................................... 53 c. Corporate Income Tax ........................................... 53 d. Other Direct Taxes ............................................. 53 3. Actual and Predicted Values of Individual Tax Yields in Mauritius..54 a. Import Tax ..................................................... 54 b. Domestic Consumption Tax ....................................... 54 c. Corporate Income Tax ........................................... 54 d. Other Direct Ta-tes ............................................. 54 CHAPTER I INTRODUCTION The objective of this study is twofold: first, to develop an econometric method of estimating built-in tax elasticity and, hence, isolating the revenue impact of discretionary tax measures from that of economic growth; and second, to apply this model to selected Sub-Saharan Africa countries in order to highlight the contribution of discretionary actions taken by fiscal authorities to trends of tax effort and individual tax shares during the past two decades.1 The structural adjustment programs of sloping countries use fiscal deficit reduction as one of the policy tools for achieving real economic growth with price stability and balance of payments viability. In dealing with this deficit within such a framework, projections need to be made of the additional revenues which can be mobilized within the existing tax system as GDP grows. These projections indicate the need to activate additional means of revenue generation, particularly politically difficult discretionary tax measures. Thus, it becomes essential to be able to estimate built-in tax elasticity (hereafter, tax elasticity) which measures 1/ There are a variety of taxes, such as import tax, export tax, excise tax, sales/value added/turnover tax, corpora-e income tax and so on; throughout this study, the term "individual tax" will be used to refer to each of these taxes. Each tax has its own tax system--a set of laws and regulations governing the process of estimation, assessment and collection of its corresponding tax revenue--which will be called the "individual tax system". The term "discretionary tax measures (DTMs)" will be used to describe changes in these systems which include changes in statutory tax rates, tax bases, tax allowances and credits, and of tax administrative efficiency. -2- percentage increases in tax revenue resulting from the endogenous changes in the base caused by a one percent rise in GDP. However, its estimation by means of any of the existing methods suffers from a specification bias due to the lack of an observable quantitative variable capable of reflecting all changes in an individual (or overall) tax system in public finance. There have been two major approaches employed by priori studies on this subject to deal with this gap. One approach has been, first, to eliminate discretionary tax changes from the historical time series tax data (HTSTD), and then to estimate tax elasticity using the adjusted HTSTD by means of the following single-equation econometric model. ln(T' )t - "o + plln(Y)t + Et (1) where T'- adjusted HTSTD to discretionary tax changes, Y - tax base (or GDP in aggregate level), E = disturbance term, and p1l tax elasticity, defined as percentage increases in tax revenue net of discretionary tax changes due to one percent rise in the base (or GDP in aggregate level). However, a complete adjustment of HTSTD to discretionary tax changes is impossIh'e by means of any of the existing two major adjustment methods --proportional adjustment (PA) and constant rate structure (CRS) techniques. In accordance with the proportional adjustment technique, the historical time series tax data are first adjusted to a preceding-year -3- base.2 This is done by subtracting the budget estimate of the revenue impact o1 DTMs implemented in a given year from the actual tax revenue collected in that year, that is, Tt,t = Tt - Dt where Tt - the actual tax revenue collected in the tth year, Dt - the budget estimate of the revenue impact (negative or positive) of the DTMs implemented in the tth year, and Tt,t- the actual revenue in the tth year adjusted to the structure of that year. Then, to convert the Tt,ts to the first-year base, the adjusted tax revenue for the tth year (Tt,t) is multiplied by the previous year's ratio of the adjusted tax revenue according to tha first year's structure (Tl,t-l) over the actual tax yield (Tt.l), that is, (T) )1 Tl,l - [ (T')1t| (T')t = T tl3Tt,t Tt -1 After making successive substitutions, the following formula is derived for (T )t, which is in terms of Tts and Dts. 2/ This technique was first developed by Prest (1962). Later, Sahota (1961) employed a PA technique that, on the face of it, seemed different from Prest's method but yielded an identical result. - 4 - t- Ti -D; (T )t -(Tt-DtJ) I (2) jl1 Ti According to this method, changes in an individual tax system directly result in an exogenous change in its tax revenue, in other words, a shift in equation (1). These changes are, however, assLmed not to affect its own and other individual tax bases endogenously, and thus, its consequences are not applied to the tax revenue. This is a strong assumption which is not supported theoretically3 and its validity has not been tested empirically by any of the studies using this method.4 For example, an increase in the tariff on imports of consumption goods raises the price of these products (Pm) compared with that of competitive goods produced in the home economy (Rd), in other words, Pm/Pd* In an attempt to maximize their utilities, consumers will decrease and increase their demand respectively for the imported goods and domestic products. As a result, the import tax yield will decline due to the decrease in its base inducer. by an increase in its rate through the price mechanism. Domestic production of these products and/or their price will rise because of the increased demand, causing an increase in the companies' profit (corporate income tax base) and a rise in the potential base for taxes on domestic transactions, such as value added, turnover or sales tax. Consequently, the revenues stemming from the taxation of these sources will 3/ This assumption is strongly rejected, at least by the studies which deal with the use of tariffs as a policy instrument to protect domestic industries, for example, see Balassa (1989). 4/ For examples, see Prest (1962), Mansfield (1972), Jeetun (1978), Sury (1985), Gillani (1986), Lambert and Suckling (1986) and Sahota (1961). -5- rise due to the increased tariff on imports of consumption goods (a change in other individual tax yip-ds). Similarly, the impcrt tax revenue endogenously responds to changes in other individual tax systems. For instance, an ir.crease in the income tax rate will reduce disposable income; private consumption will decline, including the consumption of goods imported from abroad. As a consequence, the import tax yield will fail because of the decrease in its base induced by a rise in the income tax rate through the income channel. Figure 1 represents the decomposition of response of an individual tax yield to DTMs within this framework. It is apparent from this Figure that an individual tax revenue directly responds to changes in its own tax system ("own-DTM direct response") and to endogenous changes in its base. The base is endogenouslv influenced (i) by changes in its own and other individual tax systems throu6h price mechanism, investment, savings and/or income channels, and (ii) by factors other than DTMs, particularly variations in GDP. Therefore, the tax revenue indirectly responds to changes in its own ("own-DTM indirect response") and other i.dividual tax systems ("cross-DTM indirect response") through their impacts on its base. More specifically, in the PA method, the own- and cross-DTM indirect responses of tax revenues are not incorporated in the procpss of the adjustment of HTSTD to discretionary tax changes. Furthermore, this method ignores the impact of changes in the degree of evasion or of administrative efficiency on tax revenues. Finally, the PA method uses the budget estimates of discretionary tax changes (Dts). Such data are difficult to obtain in many countries and, - 6 - FIGURE 1: Decomposition of Response of an Individual Tax Yield to Discretionary Tax Measures 'Own-DTMs Direct Response" .0 > @or flvr"Direct Resporse to DTMs" An Ir.dividual Tax Yield 0v s A "Own-DTMs Indirect Response" "Cross-DTMs Indirect Response" Endogenous Changes in its Base Changes in Changes in Other Its Own Tax Individual Tax System Systems Factors Other than DTMs, particularly CDP "Indirect Response to DTMs"-sum of own- and cross-DTMs indirect responses. 7. if available, they are of qt1zstionable reliability as they differ substantially from actual discretionary outturns. The CRS method requires data on income bracket (or commodity) rates and sufficAently disaggregated information on the growth and distribution of the reported tax bases.5 If such disaggregated information is available, it would be possible to construct a constant rate-base series that would represent hypothetical yields under a system assumed to remain unchanged during the period under review as follows:6 n (T )t _ z (Ti)O(Xi)t (3) i=O where (ri)o - the base-year statutory tax rate on the ith income bracket (or commodity), (Xi)t - the reported tax base in the ith income bracket (or commodity) in the tth year, and n - number of income brackets (or commodities). It is revealed from equation (3) that the CRS method incorporates only the discretionary tax changes resulting from changes in statutory tax rates; thus, it ignores those discretionary tax changes which emerge from changes in administrative efficiency and in tax base, tax credit and tax allowances. Also, in this method, as in the PA technique, the own- and cross-DTM indirect responses of tax revenues are not taken into account in the process of the adjustment. 5/ See Bahl (1972), Andersen (1973), Chelliah and Sheetal (1974) and Choudhry (1975). 6/ Chelliah and Sheetal (1974), PP. 12-13. -8- Furthermore, the needed information, particularly on the distribution of tax bases by rate categories, is not readily available; hence, the effective tax rates --defined as assessed tax revenue over the base-- of broad income classes (or commodity groupings) that are empirically used assume that interaclass (or irteragrouping) distribution of the base will remain unchanged during the period under review. Naturally, the validity of this assumption will decline as the number of the income classes or commodity groupings in the breakdown falls due to aggregation. Finally, Choudhry (1979) argues that the constant rate structure method becomes inefficient (P. 110), first, where a tax system has many progressive elements and, second, where tax bases grow at the same rates. Under the first circumstance, this method does not guarantee that the estimate of tax elasticity will be larger (or smaller) than that of tax buoyancy even when discretionary changes produce overall negative (or positive) revenue effects.7 Under the second circumstance, there is the possibility that the elasticity estimate fails to detect the effects of discretionary changes. Consequently, the adjusted HTSTD to discretionary tax changes by means of any of the existing methods (PA and CRS) involve measurement 7/ Tax buoyancy measures percentage changes in tax revenue, including discretionary tax changes, due to a one percent increase in the base (CDP, in aggregate level). It is simply estimated by means of the following single-equation econometric model: log(T) - ao + allog(Y) +c where T = total tax revenue, Y - tax base, and al- tax buoyancy. - 9 - errors which, in turn, create a specification bias in the estimate of tax elasticity. The other approach has been to estimate tax elasticity directly from HTSTD using time trends or dummy variables as proxy for DTMs. Choudhry (1979) employs a divisia index (DI) method in which time trends are introduced as proxy for DTMs in the tax and base functions.8 Briefly, this method involves three steps. First, a formula is derived which generates an index representing the revenue impact of DTMs. Second, the growth rate of this index is divided by that of the tax base; this ratio measures the growth rate of tax revenue resulting from DTMs in terms of a one percent increase in the base. Finally, tax elasticity is calculated by subtracting this ratio from the tax buoyancy. Apart from the questionability of using time trends as representative of DTMs, the major empirical implication of this technique is that the formula derived in the first step is a line integral and, in practical application, its discrete version is used, causing bias in the estimate of the revenue impact of discretionary measures. The bias is downward (or upward) when the discretionary changes produce positive (or negative) revenue effects, resulting in an overestimate (or underestimate) of tax elasticity.9 Singer (1968), Chand and Wolf (1973), Khan (1973) and Artus (1974) use one dummy variable (simple or mixed) as proxy for each of the DTMs 8/ This method is widely used in measuring the impact of changes in technology on the productivity of labor. 9/ For proof of this implication see Choudhry (1979), pp. 87-121. - 10 - taken during the period under review and they estimate tax elasticity by means of the following single-equation econometric model. n ln(T)t -= + Olln(Y)t + Zfi2iDi + Ut (4) i-i where T - tax revenue, Y - tax base or GDP in aggregate level, Di- dummy variable (simple or mixed) as proxy for the ith DTM taken during the period under review, and 01 tax elasticity; in aggregate level, it measures percentage increases in the tax revenue resulting from the endogenous changes in the base caused by a one percent rise in GDP. However, the estimate of tax elasticity obtained by this technique is not precise and reliable because of the serious multicolinearity problem created as a result of entering more than one dummy variable into the tax function.10 The degree of preciseness of and reliability on the elasticity estimate are inversely related to the degree of multicolinearity which, in turn, greatly depends on the time-intervel that existed between two successive discretiornary actions taken by fiscal authorities. For instance, the partial correlation coefficient of two dummy variables is 99 percent and 84 percent when the time-intervals are one year and five years respectively. This indicates that the degree of multicolinearity rises as the time interval between two successive DTMs falls, and it is still too 10/ For more details on the impact of multicolinearity on the preciseness of the parameters estimates see G.S. Maddala (1977), pp. 183-190. - 11 - high even when the time interval is five years. This simply means that getting a precise and reliable estimate of tax elasticity by means of this technique is empirically impossible, particularly when thera are frequent discretionary tax changes during the period under review. Therefore, all the existing estimation methods of tax elasticity suffer from a specification bias which is mainly due to the lack of an observable quantitative variable capable of reflecting all changes in an individual (o; overall) tax system in public finance. The primary objective of this study is to develop an econometric method of estimating tax elasticity and the revenue impact of DTMs which deals with this lack and, thus, with its consequences on the estimate of tax elasticity. Briefly, this method is a dynamic simultaneous-equation econometric model of taxation which captures the interaction of individual tax systems, individual tax revenues and bases and GDP. As representative of each individual tax system, its "average effective tax rate net of endogenous (built-in) changes in the tax yield and base" (AETRN) is introduced into the model. Time series data on AETRNs are automatically generated in the process of estimating the model parameters. The model explicitly incorporates both the direct and indirect responses of each individual tax revenue to changes in its own and other individual tax systems, i.e., own- DTM direct, own-DTM indirect and cross-DTM indirect responses. Its application requires only historical time series data on tax revenues, tax bases and CDP, all of which are already available for most countries. In addition to its application as a method for estimating tax elasticity and the revenue impact of DTMs, this model can be used as an empirical framework: - 12 - (a) to forecast a government's revenue stemming from various sources of taxation; (b) to evaluate the macroeconomic impact of a tax reform program which is aimed at either generating additional revenue and/or dealing with specific economic problems; and (c) to deal with various tax related economic issues-- for example, to investigate the welfare impact of moving from differential tariffs towards uniform ones, which is often recommended by the Bank, or to examine the controversial view that uniform tariffs results in uniform rates of effective protection in industrial and non- industrial activities. In this study, this model is used as an empirical tool to highlight the contribution of discretionary tax measures to trends of tax shares and tax effort in selected Sub-Saharan Africa countries during the 1965-85 period. A shift from the taxation of international trade to the taxation of domestic transactions is recommended as one of the main objectives of an administratively feasible tax reform program in SSA countries, where such reform is often included in structural adjustment programs. The presumption, however, is that discretionary tax measures play a crucial role in effecting this shift. This description emerges from the experience of a number of Sub-Saharan Africa countries where tax effort has grown, the share of tax on domestic transactions in total tax revenue has risen and the import tax share has declined at least since the mid-1960s, though all three trends have halted or reversed since the late 1970s.11 11/ Shalizi and Squire (1988), P. 2. - 13 - However, discretionary tax measures have not been the only source of variation of tax shares; they have also been affected by endogenous changes in tax bases causcd by factors other than these measures, particularly econo:ic growth. In SSA countries, fiscal authorities have taken a variety of discretionary actions in order to generate revenue and to deal with specific economic issues during the past two decades. In addition to their revenue generating objective, corporate income tax has been used to improve investment incentives and stimulate private sector investment in specific economic activities/regions; import tax has been applied as one of the policy instruments to protect infant domestic industries against competition of foreign ones; and domestic consumption tax has been utilized to deal with equity issues and cascading problems in the production chain. During the same period, nominal and real gross domestic product have also grown, recording annual average rates of 13.4 percent and 2.6 percent respectively.12 Among the major economic sectors, non-agriculture (industry and service) has been the principal contributor to the overall economic growth; the share of its value added in GDP has increased from 61 percent in 1965 to 67.8 percent in 1985. This has been associated with the vertical and horizontal expansion of companies in this sector, resulting in endogenous changes in companies' net operating profit which is the potential corporate income tax base.13 12/ The World Bank, World Development Report, (Oxford: Oxford University Press, 1987), PP. 16 & 173. 13/ Table 1 in Appendix A. - 14 - Expansion of the non-agriculture sector has been mainly due to sharp increases in domestic demand for consumption goods produced in this sector. This inLcrease in demand has been influenced by a consumption goods import-substitution policy implemented by governments in order to industrialize the economy. So the share of consumption goods produced and consumed in the home economy (consumption tax base) in GDP has risen from 66 percent in 1965 to 78 percent in 1985; in the same period, the share of consumption goods imported from abroad in GDP has declined from 15 percent to 10 percent and that of other imports has grown slightly from 10 percent to 11 percent resulting in an annual average decrease of 0.20 percentage point in the share of total imports (import tax base) in GDP. These historical observations indicate the interaction of economic growth with the trends of tax shares and efforts in SSA countries. This study highlights the contribution that discretionary tax measures have made to the shift from the taxation of international trade to the taxation of domestic transactions in countries, such as Malawi, where such a shift has taken place. It also questions the effectiveness of these measures as a policy instrument for bringing about such a shift in other countries, like Mauritius, where the country's reliance on the foreign trade tax has risen during the past two decades. These are the tasks which have been neglected by previous studies and are addressed by this research. The theoretical development of the model is discussed in Chapter II. To simplify its discussion, the model is disaggregat3d into three blocks--individual tax yield functions, individual tax base equations and identities. After discussing each block separately, the entire model as a method for estimating tax elasticity and the revenue impact of DTMs is - 15 - represented, and its dynamic multipliers are derived. These multipliers measure the short run and long run impacts of economic growth and changes in each individual tax system on tax revenues and bases. The application of the model to Malawi and Mauritius is discussed in Chapter III which consists of two sections. In the first section, the estimation method and results are discussed and the dynamic multipliers of the model are derived. Using these results, the contribution of discretionary tax measures to trends of tax effort and shares is analyzed in the second section. Briefly, the econometric application of the model to these countries yields a number of interesting results. For instance, it shows that: (i) discretionary tax measures have been an effective policy instrument in mobilizing resources from the private sector to the public sector, to the extent that tax effort would fall in the absence of DTMs; (ii) individual and overall tax revenues have been inelastic with respect to GDP, except corporate income tax in Malawi and import tax in Mauritius; (iii) economic growth and discretionary tax measures have had almost equal roles in shifting from the taxation of international trade to the taxation of domestic transactions in Malawi, contributing respectively 51 percent and 49 percent to the overall growth rate of domestic consumption tax- import tax; and (iv) in Mauritius, economic growth has been the principal factor in reversing this shift, to the extent that the country would sh::ft from the taxation of international trade to the taxation of domestic transactions in the absence of nominal economic growth. Finally, a summary of findings and suggestions for further research is presented in Chapter IV. CHAPTER II THEORETICAL DEVELOPMENT OF THE MODEL It is revealed from Figure 1 that changes in an individual tax revenue directly result from changes in its own tax system and/or "endogenous changes" in its base. Its base is endogenously affected (i) by changes in its own and other individual tax systems through price mechanism, investment, savings or income channels, and (ii) by factors other than DTMs, particularly variations in GDP. In other words, individual tax systems, individual tax bases and yields and GDP are all interrelated. Tt.eir interaction is modelled in this chapter in order to estimate (a) the direct and indirect responses of each individual tax yield to changes in its own and other individual tax systems, and (b) elasticities of indiriidual tax yields, individual tax bases and overall tax revenue with respect to GDP. The concept of "tax elasticity" is defined to measure percentage increases in *hte tax revenue resulting from the endogenous changes in its base caused by a one percent rise in GDP. It is the product of elasticities of the tax yield to its base and the base to GDP. Regarding the second objective of this research, all individual taxes are classified into five major categories. These are: (1) corporate income tax, (2) other direct taxes (individual income tax, social security, payroll tax, tax on property and other taxes on net income and profits), (3) import tax ( tariff/customs duties and other charges), (4) tax on exports, and (5) tax on domestic consumption (general sales, turnover or value added taxes, selective excises on goods and services, taxes on use of - 17 - goods or property and permission to perform activities, stamp tax and other domestic indirect taxes). To simplify this discussion, the model is disaggregated into three blocks--individual tax revenue equations, individual tax base functions, and identities. First, each of these blocks is separately discussed; then, the entire model as an empirical framework for estimating tax elasticity and the revenue impact of DTMs is discussed. Individual Tax Revenue Equations Block As explained above, an individual tax revenue is directly affected by changes in its own tax system and its base. To separate out the direct revenue impacts of these two factors, each individual tax revenue assessed by tax inspectors (Ti*) is considered to be a function of two proxy variables, one for its potential tax base (Xi) and another as representative of its own tax system (ri), that is, log(Ti*)t- QiO+ aillog(Xi)t+ ai2(7i)t+ Lit (1) where Ei - disturbance terms as representative of other explanatory, variables excluded from the model, i - d, tax on domestic transactions, - m, tax on imports, - x, tax on exports, - c, corporate income tax, and - 18 - o, other direct taxes. This function was specified in semi-log-linear form essentially for a reason of convenience, that is, it allows a direct estimate of tax elasticity which is the primary objective of this research; furthermore, this is also a preferred functional form used in the previous studies.1 Its generalized version is, however, discussed in appendix B. Given a discrepancy between the assessed and actual tax revenue, tax inspectors will adjust the actual tax yields toward their assessed level. This adjustment process is not, however, completed instantaneously. Using a partial adjustment method, let us assume that they adjust actual individual tax revenues, (Ti)t, toward their assessed level, (Ti*)t, by adding a fraction of the difference between the assessed tax yield, (Ti*)t, and the actual tax revenue of previous period, (Ti)t.l, to the actual tax revenue collected in the previous period, (Ti)t.l. This adjustment mechanism is written in its log-linear form as follows: Alog(Ti)t- Ai[log(Ti*)t-olg(Ti)t_l] (2) where Ai denotes the coefficient of adjustment of the ith individual tax yield, and 1> Ai >0. The average time lag of the adjustment of the ith indi-idual tax revenue is (l-Ai)/Ai, measuring the average period of time needed vy tax inspectors to complete inspection of the tax files related to the it!, individual tax. 1/ For examples, see Mansfield (1972), Khan (1973), Artus (1974) and Chelliah and Sheetal (1974). - 19 - By substituting (2) in (1), actual individual tax revenue function is derived, that is, log(Ti)t- AiaiO+ Ajcillog(Xi)t + (l-Ai)log(Tj)t_.+ Aiai2(Ti)t+ Uit (3) where Uit = XiEit, stochastic term. Estimating parameters of this equation, Dwever, requires the specification of proxy variables for the potential tax bases--time series data on these bases are not available in most developing countries--and the definition of ri, an observable quantitative variable as representative of the ith individual tax system. Specifying proxy variables for potential tax bases is straight- forward. For instance, regarding the data availability and tax structure in SSA countries, Skinner (1988) considers respectively private consumption (Xd), imports (Xm), exports (Xx), value added in the non-agriculture sector (Xc) and gross domestic product (XO) as proxy for the potential bases of domestic consumption tax (Td), import tax (Tm), export tax (Tx), corporate income tax (Tc) and other direct taxes (TO). However, it has been the lack of an observable quantitative variable as representative of an individual (or overall) tax system in public finance which has complicated the issue of estimating individual and overall tax elasticities discussed in the previous chapter. To deal with this gap, this study defines ri as follows: (ri)t= [Ri/Xi*]t (4) 20 - where (Ri)t - the ith individual tax yield at time 'It" net of the changes caused by endogenous changes in its base during the first year through the tth year of the period under review, and (Xi*)t- the ith individual tax base at time "t" net of endogenous changes during the first year through the tth year of the period under review. It is revealed from this definition that value of ri in a given year, say 'tt", represents the average effective tax rate of the ith individual tax in that year in the absence of endogenous changes in its base and in its tax yield during the first year through the tth year of the period under review. Therefore, ri directly reflects all changes in the ith individual tax system which are the only source of its variations. However, ri is not an observable variable because time series data on Xi* and Ri are not available. This study derives a formula for each of these variables and, hence, for ri in terms of the observable variables ana parameters included in the model, whose substitution in equation (3) generates an individual tax equation with estimable parameters. Let git denote percentage endogenous changes in the ith individual tax base during the first year through the tth y.-ar of the period under review--on which time series data are endogenously generated within the model proposed to be developed in this chapter (see tax base functions block). Using gits, the ith individual tax base (Xi) is decomposed into two separable parts in terms of its two major sources of variation mentioned above, that is, - 21 - (Xi)t- (Xi*)t(l + git) (5) (Xi*)t is that part of (Xi)t which is exogenously affected by changes ii its potential tax base made by fiscal authorities and (l+git) is that part of (Xi)t which is influenced by the factors resulting in endogenous changes ih (Xi) t. By solving equation (5), the following formnula is obtained for Xi* (Xi*)t= [(Xi)t/ (l+git)] (6) According to the definition of ri, its coefficient in equation (3), Aia2i, measures the direct response of the ith individual tax to DTMs (own-DTM direct response), and the coefficient of Xi, Aiali, measures its response to the endogenous changes in its base--percentage changes in Ti due to a one percent endogenous increase in Xi (elasticity of Ti with respect to Xi). Using Aialis, each individual tax yield can be decomposed into two separable parts in terms of its two major sources of variation- -these are changes in its own tax system and endogenous changes in its tax base--as follows: (Ti)t= (Ri)t(l + Aiacilgit) (7) where Aiailgitthe percentage changes in the ith individual tax yield during the first year through the tth year of the period under review - 22 - which result from git percent endogenous change in its base taken place throughout the same period. Ri is that part of Ti which is directly affected by changes in the ith individual tax system, which is the only source of its variation; its value at any point of time, say "t", represents the amount of the tax yield collected from the ith individual tax source at that time in the absence of endogenous changes in its tax base during the first year through the tth year of the period under review. Changes in Ti resulting from endogenous changes in its base are realized through (1+Aiailgit). By solving equation (7), the following formula is derived for Ri. (Ri)t= [(Ti)t/ (1 + Ajiilgit)] (8) Now, by sub_tituting (6) and (8) in (4), the following formula is obtained for ri, which is in terms of the parameters and observable variables included in the model proposed to be developed in this study. (Ti)t (1 + Aiailgi)t [ (1 + gi)t (ri)t -ri_ | )t (9) (Xi)t (1 + Aiailgi)t (1 + gi)t where (ri)t= (Ti/ Xi)t= average effactive indi-idual tax rate. In accordance to equation (9), in fact, ri is the ratio of the ith individual tax yield (Ti) deflated by the index of that part of the tax - 23 - revenue gained from endogenous changes in its base, (l+Aiailgi), over its base (Xi) deflated by ihe index of that part of the base which is not directly affected by changes in its potential base made by fiscal authorities, (l+gi). Substituting (9) in (3) produces the following equation with estimable parameters for individual tax yields. log(Ti)t= AiaiO+ Aiaillog(Xi)t + (l-Ai)log(Ti)t_l + Aiai2(ri[(l+gi)/(l+Aicilgi)]}t+ Acit (3) where Ai = coefficient of adjustment, ail =long-run elasticity of Ti with respect to Xi Aiail=short-run elasticity of Ti with respect to Xi, Aiai2=percentage changes in Ti due to one percentage point increase in ri 'own-DTM direct response) in the short-run ai2 =percentage changes in Ti due to one percentage point increase in ri (own-DTM direct response) in the long-run. Equation (3)' is non-linear in both parameters and variables. It is exact identified. Its parameters can be estimated by means of a non- linear econometric estimation method. After estimating its parameters, time series data on ris are generated by means of equation (9) using a simulation technique~. These data can be used independently to deal with various tax related economic issues. - 24 - Equation (3), for i-d, m, c, x, and o, stands for the individual tax yield functions 'lock of the model. Estimates of its parameters are obtained by estimating parameters of equation (3)'. If the specified proxy variables for potential tax bases are not exogenously affected by discretionary changes in potential tax bases (or there have not been any discretionary changes in these tax bases during the period under review), historical time series data on Xis can be used to generate time series data on gis. However, in the theoretical framework, each individual tax base (Xi) is linked to its own as well as other individual tax systems (ris) through various economic channels--that is, the impact of changes in rc and ro on individual tax bases are realized through investment, savings and/or income channels, and that of changes in rm, Td, and rx are recognized through the price mechanism. This linok, may empirically result in a high degree of linear correlation between Xi and ri in equation (3) as a single-eguation econometric model, thereby reducing the degree of preciseness and reliability of the estimate of its parameters and, hence, of the generated time series data on ris. Fortunately, this econometric issue is not a multicolinearity problem which is a feature of the sample; it is a simultaneity issue which can be easily overcome by expanding the single-equation econometric model, in other words, equation (3), to a simultaneous-equation model in which individual tax base functions become an integral part of it. Having defined ris as observable proxy variables representing individual tax systems, the development of individual tax base equations is straight-forward. - 25 - Individual Tax Base Eguations Block Unlike in the case of individual tax revenue equations, developing a single-functional form as representative of all individual tax base equations is impossible. Because, as explained above, there is not a single-economic channel through which changes in individual tax systems affect individual tax bases. For this, the development of each individual tax base equation is discussed separately, using as an example a country whose economic structure and tax system is similar to those of Sub-Saharan Africa countries. In particular, this means a country in which private consumption, imports, exports, value added in non-agriculture sector and GDP can respectively be used as proxy variables for potential tax bases of domestic consumption tax, import tax, export tax, corporate income tax and other direct taxes. Domestic Consumption Tax Base Function Using a Keynsian approach, private consumption (Xd)--as a proxy variable for the potential base of tax on domestic transactions--is considered to be a function of disposable income (yd) defined as gross domestic product (GDP) minus total direct taxes (Tc+To). By entering Yd as an explanatory variable in this function, the impact of the DTMs related to direct taxes (changes in rc and ro) on Xd is explicitly taken into account. That is, any change in rc and/or ro directly affects Tc and/or To through - 26 - equation (3), resulting in changes in disposable income and, hence, private consumption. Consumers also react to the discretionary tax measures related to indirect taxes (changes in rm and Td) through the price mechanism channel. For example, an increase in the tariff on imported consumption goods will raise the price of these products (Pm) compared with that of competitive products (Pd) produced in the home economy, in other words, Pm/Pd. In an attempt to maximize their utilities, consumers will increase their demand for the competitive products produced in the home country and decrease their demand tor those imported from abroad. As a result, the potential base for the cax on domestic transactions will go up while the import tax base will fall. Another explanatory variable, (rm/Td), is entered into the consumption function in order to take into account the impact of .he DTMs related to indirect taxes on Xd explicitly. Obviously, the impact of that part of the changes in Pm/Pd caused by the factors other than DTMs on Xd is implicitly incorporated in the model by entering the nominal values of Xd (private consumption net of Td) and Yd in it. The equation for this tax base is assumed to have the following functional form. ln(Xd)t- fdO 6dlln(Yd)t+ Pd2(7m/rd)t+ Vdt (10) where Xd = nominal private consumption at factor cost, Yd = GDP - Tc- T., nominal disposable, Odl >O, elasticity of Xd with respect to Yd' - 27 - Pd2 >0, percentage changes in Xd due to one unit increase in (Tm/rd), Vd- disturbance terms as representative of the explanatory variables excluded from the model with standard classical assumptions. By substituting equation (9) in (10), the domestic consumption tax base function with estimable parameters is derived, that is, rrm[ (l+gm)/(l+amlgm ), ln(Xd)t -dO+ Pdlln(Yd)t+ 8d2 ---- --r------------ + vdt (10)' rd[(l+gd)/(l+adlgd)] t Import Tax Base Function Similarly, using the traditional approach to import function, the nominal value of imports net of import taxes--as a proxy for the import tax base--is considered to be a function of nominal GDP at factor cost, (rm/rd) and rc' that is, ln(Xm)t- PmO+ Pmlln(ODP)t+ fm2(Tm/Td)t+ Pm3(Tc)t + Vmt (11) where Xm =nominal value of imports net of Tm, GDP-nominal gross domestic products at factor cost, Pml>,1 elasticity of Xm with respect to GDP, fim2<0, percentage changes in Xm due to a one percentage point increase in (rm/rd), ,m3>0, percentage changes in Xm due to a one percentage point increase - 28 - in rc, Pm3>O, percentage changes in Xm due to a one percentage point increase in rc' and vmt-disturbance terms as representative of other sources of variation in Xm resulting from the factors excluded from the model. The import tax base function with estimable parameters is derived by substituting (9) in (11), that is, rm[ (l+gm)/(l+amlgm) Ii rc(l+gc) ln(Xm)t=OmO+f6mlln(GDP)t+6m2 - -| +fm3 +vmt (11) rd[(l+gd)/(l+adlgd)] t (l+aclgc) Corporate Income Tax Base Function The impacts of changes in the corporate income tax system (rc) and the variations in GDP on value added in the non-agriculture sector (X,)--as representative of the potential base of corporate income tax--are realized through investment channels.2 Any change in the corporate income tax system (say, a decrease in rc) will affect (raise) the after-tax marginal rate of return to capital in this sector which will influence (enhance) the level of investment in the non-agriculture sector resulting in a change (an increase) in Xc. Variations in GDP can also affect investment through the acceleration principle which, in turn, influences value added in the non- agriculture sector; that is, an increase (or a decrease) in GDP raises (or 2/ Value added in the non-agriculture sector (Xc) is considered as a proxy for the potential base of corporate income tax due to the lack of time series data on the wage bill in this sector in most LDCs. However, in the countries where such time series data are available, the wage bill should be deducted from Xc. - 29 - reduces) aggregate demand, including demand for goods and services produced in the non-agriculture sector. As a result, investment in this sector rises (or falls), resulting in an increase (or a decrease) in Xc. Consequently, Xc is negatively related to rc and positively linked to gross domestic product. Its equation is assumed o have the following functional form.3 ln(Xc)t- PcO+ Pclln(GDP)t+ fc2(rc)t + Pc3(Tm/Td)t+ vct (12) where XC -nominal value of value added in non-agriculture sector net of corporate income tax at factor cost, vct'disturbance terms as representative of other sources of variation of Xc resulting from the factors excluded from the model, Pcl>0, elasticity of Xc with respect to GDP, and 6c2 Pml(Xm/GDP) However, the ambiguity on the sign of Pc3 can be easily overcome by disaggregating import taxes into two major categories of imports, in other words, imports of consumption goods and other imports. By substituting equation (9) in (12), the corporate income tax base function with estimable parameters is obtained, that is, ln(Xc)t- Pco+ 6clln(GDP)t+ Oc2(rd[(l+gd)/(l+cdlgd)])t + rm[ (l+gm)/(l'+mlgm) ] 1 t + Pc3 + vct (12)' rd[(l+gd)/(l+adlgd) it Export Tax Base Function The nominal value of exports net of export taxes as a proxy for an export tax base is simply considered to be a function of the weighted - 31 - average of GDP of importer countries (GDPw)--the weight for each importer country being the ratio of exports to this country over total exports--and ris. Its equation is assumed to have the following functional form. ln(Xx)t.pxo+,8xlln(GDPw)t+ E[Pxj(rj)t]+ vXt (13) where Xx -nominal export net of export taxes in terms of the exporter national currency, GDPW-weighted average of nominal GDP of the importer countries in terms of national currency of the exporter country, Px1>O, elasticity of Xx with respect to GDPW, and Pxj0, 72-(Tc/Yd)* <0, 73-(To/Yd)* <0, and "*" denotes geometric mean value. The total tax revenue net of export taxes is simply the sum of the other individual tax yields, that is, (T)t= (Tc)t + (To)t + (Td)t +(Tm)t (17) Using the method mentioned above and expanding equation (17) around the geometric mean value of the variables included in it and then making a simple manipulation, this equation is converted to the following log-linear form which allows a direct estimate to be made of the automatic response of the overall tax system to variation in GDP: - 34 - ln(T)t- 60+ 6eln(Tc)t+ Soln(TO)t+6dln(Td)t+6mln(Tm)t (18) where 60- log(T)*- E[(Ti/T)*log(Ti)*, 6i- (Ti/T)* >0, and i-c, o, d, m. Equations (16), (17) and (19) are deterministic functions whose parameters can be estimated either by using the mean value of time series data on the variables included in them or by the OLS estimation method. Entire Model And Its Dynamic Multipliers Equations (3)--for isc, d, m, o--, (10), (11), (12), (16) and (18) provide the structural form of the model developed in this s,udy (Table 1). Efficient and consistent estimates of its parameters are obtained by estimating the parameters of equations (3)', (10)', (11)', (12)', (16) and (18) by means of a simultaneous-equation non-linear econometric estimation technique (Table 2).4 Using the estimated parameters, the time series data on ris are generated by means of equation (9). These data can be used independently to investigate the impact of changes in individual tax systems on various key macroeconomic variables, such as savings, inflation, investment, economic growth, international balance of payments, and so on. To simplify the derivation of the revenue impact of changes in each individual tax system 4/ There are four simultaneous-equation non-linear estimation methods. These are: three-stage non-linear least squares, iteration, search and maximum likelihood estimation techniques. For more details, see Maddala(1977), pp. 144-146; also Fair(1984) pp. 120-138. - 35 - Table 1: Structural Form of the Model log(Td)t A.dadO+ Adadll0g(Xd)t + (l-Ad)log(Td)t-l+ Adad2(Td)t+ Udt log(Tm)t- AlnamO+ Am*mllg(Xm)t + (l-Am)log(Tm)t-l+ A%im2(7m)t+ Umt log(Tc)t- caco+ Acacllog(Xc)t + (l-Xc)log(Tc)t-l-. Acac2(rc)t+ Uct log(To)t-= AoaoO+ Xoaollog(Xo)t + (l-Ao)logkTO)t_.+ XoQo2(ro)t+ Uot ln(Xd)t- OdO Pdlln(Yd)t+ Pd2(7m/fd)t+ vdt ln(Xm)t- PmO+ 8mlln(GDP)t+ Pm2(rm/rd)t+ Pm3(rc)t + umc ln(XC)t- Pco+ 6clln(GDP)t+ Pc2(Tc)t + Pc3(?m/Td)t+ Vct ln(T)t - 60+ Sdln(Td)t+ 6mln(Tm)t+ Scln(Tc)t+ Soln(TO)- ln(Yd)t °O +-tlln(GDP)t+ 721n(TC)t+ 131n(TO)t (Tm/Td)t= 90 + l(rm)t + 02(fd)t where Td= Tax on domestic transactions (endogenous variable), Tm- Import tax (endogenous variable), Tc= Corporate income tax (endogenous variable), To= Other direct taxes (endogenous variable), Xd- Private consumption (endogenous variable), Xm= Imports (endogenous variables), Xc= Value added in non-agriculture sector (endogenous variable), XO= GDP- gross domestic products (exogenous variable), ri= The ith individual realized tax rate (exogenous variable), for i- d, m, c, o, Yd- Disposable income (endogenous varI'able), r- Total tax revenue net of export taxes (endogenous variable). - 36 - Table 2: Entire Model with Estimable Parameters l+9d1 ln(Td)t- AdcadO+ Adadlln(Xd)t + (l-Ad)ln(Td)t-l +Adc1d2 rd -+g 1 - I-+dt 1+Adcldlgd J t ln(Tm)t° Amamo+ Amamlln(Xm)t + (l-Xm)ln(Tm)t-l +Amsm2 jrm ]+mt l+Amamlgm t [ 1+g 1 ln(Tc)t Acaco+ Acaclln(Xc)t + (l-Ac)ln(Tc)t-l +Ac%2 rc g J 1+A\CIc lgC- t r l+g0 1 ln(TO)t- Aoaoo+ Aoaolii-.Xo)t + (l-Ao)ln(To)t-l +Aoao2 r0 - g + 1 +A\oaolgo .t r rm[ (l+gm)/(l+amlgm)] 1 ln(Xd)t P-dO+ Pdlln(Yd)t+ Pd2 g + vdt rd[(l+gd)/(l+adlgd)] t frm[ (l+gm)/(l+amlgm)] 1 rC(l+gc) ln(Xm)tsPmo+PmllnC(GDP)t+Pm2 +Pm3 +vmt rd[(l+gd)/(l+adlgd)] t (l+aclgc) l+gd 1 rrm(l+gm)/(l+amlgm) ln(X0)t- PcO+ Pclln(GDP)t+ 1+c2 rd + Pc3 - +Uct 1+atdlgd Jt rd(l+gd)/(I+cgdlgd) t ln(T)t - 60+ 6dln(Td)t+ 6mln(Tm)t+ 6cln(Tc)t+ 601n(To)t ln(Yd)t = YO +ylln(GDP)t+ y2ln(Tc)t+ y31n(TO)t g(i)t- ln(Xi)t- ln(Xi)O for i-d, m, c, o Est-mating the parameters of the model requires time series data on Tis, T, Xis, ria, and GDP which are readily available for most LDCs in GFS(an IMF publication) and World Tables (a World Bank publication). -37 - from the estimated parameters of the model, this study uses the generated time series data on ris to linearize ('m/'d) in order to keep the entire model in semi-log linear form. Its linear form is obtained by expanding it around the mean value of ris using Taylor's series, which is, (Tm/rd)t -0 + 1l(rm)t + 62(id)t (19) where 00(Tm/rd)* >0, 0l1(l/rm)* >0, and 2- [rm/(Td)2]* <0. Equation (19) is a deterministic equation whose parameters can be estimated using either the mean value of the generated time series data on ris or the OLS estimation technique. Consequently, the structural form of the model with estimated parameters will include ten equations--equations (3), for i-d, c, o, m, and (10), (11), (12), (16), (18) and (19)-- and ten endogenous, five exogenous, and four predetermined endogenous variables. It is a simultaneous equations system which can be written in the following form using matrix notation. A + B(Y)t + C(Y)t-l + D(X)t 0. (21) where A- lOxlO matrix of constant terms, B- lOxlO matrix of coefficients of dependent variables, C- lOxlO matrix of coefficients of lagged dependent variables, - 38 - D- lOx5 matrix of coefficients of exogenous variables, Yt- lOxI column vector of endogenous variables, and Xt- 5xl column vector of exogenous variables. By treating predetermined lagged dependent variables as exogenous ones, the model is an ordinary equations system; by solving it, the reduced form of the model is obtained, that is, Yt= -B-1A - B-lC(Y)t-l B-lD(X)t (22) In this equation, each of the endogenous variables is a function of all the exogenous variables included in the model--these are ln(GDP)t, ln(Ti)t-l and ris. The ijth element of [-B-1D] measures the instantaneous impact of a unit change in the jth exogenous variable on the ith endogenous variable (impact multipliers). For instance, the ith individual tax yield equation in its reduced form will be: ln(Ti)t=4iO + 4illn(GDP)t + ZOij2ln(Tj)t-l + ZOij3(rj)t (20) where j cm, d, c, o, Oil -short-run elasticity of the Ti with respect to GDP, 4ij3=percentage changes in Ti due to a one percentage point change in rj; for i#j, it measures the short-run impact of changes in the jth individual tax system on the ith individual tax revenue (cross-DTM indirect response), - 39 - and, for i-J, it measures the short run overall impact of a one percentage point increase in ri on its corresponding tax yield (sum of the own-DTM direct and indirect responses). Its short run own-DTM direct response is measured by the coefficient of ri in equation (3), in other words, ai3; therefore, its short run own-DTM indirect response is simply measured by 'ii3-ji3- The elements of [-B-1D] related to the coefficients of ln(GDP), measuring the short-run tax elasticities, and rjs, measuring the short-run revenue impacts of DTMs, are presented in Tables 3-7. By treating lagged dependent variables as endogenous ones, the structural form of the model is a system of difference eguations; by solving it, the final form of the model is obtained which is, Yt [I + B1lC]Pl B-1A] + [I + B-lC]-G[-B-lD](X)t (23) where I= lOxlO unit matrix. In this equation, each of the endogenous variables is a function of all the exogenous variables included in the model--these are ln(GDP) and rjs. The ijth element of ([I+B-lC]-l[-B-lD]) measures the total impact of a unit change in the jth exogenous variable on the ith endogenous variable (total multipliers). For instance, the ith individual tax yield equation in its final form will be: ln(Ti)t= 'iO + Oilln(GDP)t + ZOij2(rj)t for j=m,d,c,o (21) - 40 - Table 3: Short Run and Long Run Individual and Overall Tax Elasticities in Terms of the Parameters Included in the Model Tax Yields Tax Elasticities A. Short Run: Total Tax $mamlPml+6dadlpdl(Yl+aclOcl72+Y3aol)+6c%clpcl+&oaol (T) -Import Tax %mlpml (Tm) -Consumption Tax adlpdl(l+aclPcl72+Y73aol) (Td) -Corporate Income Tax aclocl (Ta) -Other Direct Taxes a (To) B. Lon, Run: Total Tax (T) 6mamlfml 6d'tdlpdl [ alcl72+ 73aol 1 6caclcl boaol + - x Xy + + 1+ + 1- am2 1-Qd2 1 - ac2 1-o2 J 1 -ac2 l-ao2 -Import Tax amlpml (Tm) 1- am2 -Consumption Tax adlpdl aclPcl72+ 73l1ol (Td) x al + - + l-ad2 1 - %c2 1-ao2 -Corporate Income Tax aclocl (TC) 1 -ac2 -Other Direct Taxes aol (To) 1-ao2 - 41 - Table 4: Direct and Indirect Responses of Individual and Overall Tax Revenues to the Changes in the Domestic Consumption Tax System Type of Tax Percentage Changes in Tax Yields due to A7d=l% A. Short Run Response: Total Tax Direct Response Sdad3 Indirect Response 6mamlfm262+&dadlO2(Pd2+72PdlaclPc3)+6cac1Pc382 -Import Tax Indirect Response Qmlflm202 -Consumption Tax Direct Response cad3 Indirect Response adl62(pd2+ 72#dlaclfc3) -Corporate Income Tax Indirect Response aclPc362 B. Long Run Response: Total Tax Direct Response 6d(ad3)/(l - ad2) Indirect Response 6d'dl62 [ 72Pdl%clfc3 6mamlfm262 6cac%1c302 x d2 + + + 1-cad2 L - 'c2 1 - am2 1 - ac2 -Import Tax Indirect Response (`mlfm202)/(l - dm2) -Consumption Tax Direct Response (ad3)/(l - td2) Indirect Response adlO2 72 `dl%clfc3 1 x fd2+ 1~~ -lad2 1 2 JC -Corporate Income Tax Indirect Response (aclPc362)/(1 - %c2) - 42 - Table 5: Direct and Indirect Responses of Individual and Overall Tax Revenues to Changes in the Import Tax System Type of Tax Percentage Changes in Tax Yields due to Arm=l% A. Short Run Response: Total Tax Direct Response 6mQm3 Indirect Response 6mamlPm2Gl+ Sdadl0l(Pd2+ Pdl2Y2acl/3c3)+ ScaclPc3Ol -Import Tax Direct Response am3 Indirect Response amlPn281 -Consumption Tax Indirect Response adl0l(Pd2+ PdlM2aclPc3) -Corporate Income Tax Indirect Response aclfic3O1 B. Long Run ResRonse: Total Tax Direct Response 6m(am3)/(l - am2) Indirect Response 6dodl9l r %clc3fidl121] 6mmlfin2 Sc'clPc301 x /d2+ --- ----+ + 1-id2 1 -ac22 1am2 1-c2 -Import Tax Direct Response (am3)/(l - `m2) Indirect Response (am1Pm2Ol)/(l - am2) -Consumption Tax Indirect Response crdlOl aclOc3fidl2 fx d2+ - 1-'d2 1 - ac2 -Corporate Income Tax Indirect Response (QclPc30l)/(l - ac2) - 43 - Table 6: Direct and Indirect Responses of Individual and Overall Tax Revenues to the Changes in the Corporate Income Tax System Type of Tax Pe.centage Changes in Tax Yields due to Arc=l% A. Short Run Response: Total Tax Direct Response 6ccc3 Indirect Response 6cQcl6c2 + 6dadlPdlY2(cclPc2 + ac3) +6mamlOm3 -Import Tax Indirect Response amlPm3 -Consumption Tax Indirect Response adlPdly2(%clPc2 + ac3) -Corporate Income Tax Direct Response ac3 Indirect Response %clPc2 B. Long Run Response: Total Tax Direct Response (6c%c3)/(1 - ac2) Indirect Response 6caclfc2 6dcdlPdl72(acl#c2 + ac3) amlfm3 = ==_+ + (1 - ac2) (1 - ac2)(1 -ad2) I-am2 -Import tax Indirect Response aml6m3/(l-m2) -Consumption Tax Indirect Response cdlPdl72(aclPc2 + ac3) (1 - ad2)(1 - ac2) -Corporate Income Tax Direct Response (ac3)/(l - ac2) Indirect Resnonse (aclPc2)/(l - 'c2) - 44 - Table 7: Direct and Indirect Responses of Individual and Overall Tax Revenues to the Changes in Other Direct Tax Systems Type of Tax PErcentage Changes in Tax Yields due to Arol% A. Short Run Response: Total Tax Direct Response Soao3 Indirect Response Soadlfdld3ao3 -Consumption Tax Indirect Response adl6dl73ao3 -Other Direct taxes Direct Response ao3 B. Long Run Response: Total Tax Direct Response (60ao3)/(l - a02) Indirect Response 6oadlPdl73ao3 (1 - a02) (1 - ckd2) -Consumption Tax Indirect Response adlPdl3czO3 (1 - ad2)(1 - ao2) -Other Direct Taxes Direct Response (ao3)/(l - ao2) - 45 - where i'il -long-run elasticity of Ti with respect to GDP, and Oij2-the long-run Response of Ti to one percentage point change in rj The elements of ([I+B-lC]-l[-B-lD]) which are related to the coefficients of ln(GDP)--the long run individual and overall tax elasticities--and r;s--the long run direct and indirect responses of tax revenues to DTMs-- are presented in Tables 3-7. To summarize, all the existing estimation methods of tax elasticity suffer from a specification bias which is created in the process of dealing with the lack of an observable quantitative variable capable of reflecting all changes in an individual (or overall) tax system in public finance. The estimation technique developed in this chapter is a dynamic simultaneous- equation econometric model of taxation which deals with this lack and thus, with its consequences on the estimate of tax elasticity. That is: (i) as representative of each individual tax system, its "average effective tax rate net of endogenous changes in its tax yield and base" (AETRN) is introduced in the model on which time series data are automatically generated in the process of estimating the model parameters; (ii) this model incorporates both the direct and indirect responses of each individual tax yield to the changes in its own as well as other individual tax systems, i.e., own-DTM direct, own-DTM indirect and cross-DTM indirect responses; and (iii) its application requires only historical time series data on individual tax revenues and bases and gross domestic products, all of which are already available for most countries. The parapeters of the model are estimated by means of a simultaneous-equation econometric technique. Its impact and total - 46 - multipliers (dynamic multipliers) are then derived by solving it respectively as an ordinary and a difference equations system. These multipliers measure the short run and long run (i) elasticities of individual tax yields, individual tax bases and overall tax revenue with respect to CDP, and (ii) responses of each individual tax yield and tax base to the changes in its own and other individual tax systems. In addition to its application as a method for estimating tax elasticity and the revenue impact of DTMs, this model can be used as an empirical fiamework: (1) to forecast a government's revenue from various sources of taxation; (2) to evaluate the macroeconomic impact of a cax reform program which is aimed at either generating additional revenue and/or dealing with specific economic problems--this simply requires converting the DTMs included in that reform into AETRNis (for more details see Appendix C); and (3) to deal with various tax related economic issues which may require further disaggregation of individual tax yields and bases--for example, to investigate the welfare impact of moving from differer.tial tariffs towards uniform ones, which is often recommended by the Bank, or to examine the controversial view that uniform tariffs result in uniform rates of effective protection in industrial and non-industrial activities. CHAPTER III APPLICATION OF THE MODEL The objective of this chapter is to highlight the contribution of discretionary tax measures to trends of tax shares and tax effort in two SSA countries during the past two decades. These are Malawi and Mautitius which have exhibited different trends in an important aspect of public finance, that is, a shift from the taxation of international trade to the taxation of domestic transactions which has taken place in Malawi while, in Mauritius, government's reliance on foreign trade taxes has risen. The model developed in the previous chapter is econometrically applied to the time series data of these countries in order to accomplish this aim. In the first section, the estimation method and results are discussed, and the dynamic multipliers of the model are derived. Using the obtained results, the trends of tax shares and effort are analyzed in the second section. Estimation Method and Empirical Results Time series data are used to estimate the parameters of the model. These data and their corresponding sources are supplied in the Appendix A. Because of using time series data, there is the possibility of the presence of serial correlation. If this is ignored, the estimate of the parameters will be (a) inconsistent, which means that conducting any kind of test related to these parameters will be unreliable, and (b) biased, - 48 - that is, parameters of such an equation will be overestimated (or underestimated) if the coefficient of the serial correlation is positive (or negative).1 To test the hypothesis of zero autocorreiation in the tax base and tax yield equations, "DW" and "h" statistics are respectively used in this study.2 To estimate these two statistics, the parameters of the model were estimated by means of a non-linear two-stage least squares (N2SLS) method. All of the estimated parameters had the expected signs and plausible sizes except those of the lagged depender.c variable in Malawi's domestic consumption tax yield function and those of other direct tax and domestic consumption tax equations of Mauritius, which had contrary signs and were insignificant. These variables were dropped from those equations and the model parameters re-estimated by means of N2SLS. Then, the estimation results were used to calculate the "h" and "DW" statistics which are presented in Table 8. It is apparent from the information supplied in this Table that the hypothesis of zero serial correlation is not rejected at the 5 percent level in the domestic consumption tax yield and import tax base equations 1/ See Maddala (1987), pp. 371-73. 2/ DW statistics are derived under the assumption that regressors are fixed (non-stochastic); hence, they are not applicable in cases where some of the regressors are lagged dependent variables, such as the tax revenue equations in the model developed in this study. In such cases, "h" statistics are applied whose estimate is derived as follows: h-p[n/ (l-na2)]0.5 where p-coefficient of serial correlation, n-number of observation and a-sample standard deviation of coefficient of the lagged dependent variables. This statistic has standard normal distribution and the null hypothesis of zero autocorrelation is rejected at the 5 percent significance level if h > 1.64; for more details see Durbin (1970). of Malawi. The test is inconclusive in the import and corporate income tax base functions of Mauritius. The following procedure was used to deal with this econometric problem in these equations. Using the first-order autocorrelation scheme, Table 8: Test Results for Serial Correlation Equations Malawi Mauritius DW h DW h Tax Revenue Block: Import Tax -- 2.54 -- 2.07 Consumption Tax 0.512* - 1.86 - Corporate Income Tax - 1.70 - 2.72 Other Direct Tax - 1.84 1.77 Tax Base Block: Import Tax 0.940* - 1.16** Consumption Tax 1.65 1.98 Corporate Income Tax 1.54 3.04** * Hypothesis of no serial correlation is not rejected. **The test is inconclusive. the original equation was lagged one period. Both sides of thie equation were then multiplied by the coefficient of serial correlation (p) whose estimate is unknown; its subtraction from the original equatior produced a new equation in which disturbance terms were not correlated pairwisely. Finally, this new equation was replaced by the original one in the process of estimation. After correcting for serial correlation, the efticient and consistent estimates of r,arameters of the model as a difference equations - 50 - system were obtained by means of a non-linear 3SLS technique. The N3SLS estimation results--the stzuctural form of the models with estimated parameters--for Malawi and Mauritius respectively are presented in lables 9 and 10. In order to test the goodness-of-fit of the entire estimated model a within-sample dynamic simul&tion was performed for all of the endogenous variables. A comparison of the actual and simulated values gives an indication of whether the model is able to capture the historical behavior of the endogcnous variables. The simulated and actual values of the individual tax yields (logs) for Malawi and Mauritius respectively are shown in figures 2a-2d and 3a-3d. These charts indicate that these models are fairly accurate in capturing the historical movements of those variables. The coefficients of determination and mean-sum of squares of errors presented in Tables 9 and 10 support the goodness-of-fits observed in Figures 2a-2d and 3a-3d. The estimated coefficients of all of the explanatory variables in these models have the expected signs and plausible sizes. All are significantly different from zero at more than 95 percent probability level except (a) those of ris in the corporate income tax base equation of Malawi--these being significantly different from zero at the 85 percent probability level--and (b) the adjustment coefficients of the Tm and To in this country--these being significantly equal to one. Consequently, in both countries, discretionary tax measures have had a significant impact on both individual tax revenues and bases during the past two decades. This means that the market mechanism works fairly well in these countries and that tax policy has been an effective policy instrument - 51 - Table 9: Econometric Model of Taxation in Malawi (N3SLS Estimation Results) Equations included in the model* Stochastic Equations: ln(Tm)t- -2.726 + 0.8981n(Xm)t+ 0.0191n(Tm)t.l+ 0.081(rm)t R2-0.987 (-10.81) (14.41) (0.43) (12.23) MSE=0.0025 ln(Td)t- -3.623 + 0.9051n(Xd)t+ 0.194(7d)t R2-0.961 (-2.2) (3.11) (15.77) MSE=0.0173 ln(Tc)t- -3.261 + 0.8521n(Xc)t+ 0.1291n(Tc)t-l+ 0.141(rc)t R2-0.992 (-9.51) (10.96) (2.26) (8.44) MSE=0.0022 ln(TO)t= -4.485 + 0.9601n(GDP)t+ 0.0271n(TO)t-l+ 0.380(rot)t R2=0.998 (-32.1) (34.3) (1.35) (32.5) MSE=0.0001 ln(Xm)t- +0.394 + 0.6311n(GDP)t- 0.030(rm/rd)t+ 0.073(rc)t R2-0.966 (1.23) (5.41) (-1.88) (2.45) MSE-0.0111 ln(Xd)t= -0.033 + 1.0211n(Yd)t+ 0.024(7m/rd)t R2=0.982 (-2.10) (42.7) (4.02) MSE=0.0038 ln(Xc)t= -1.09 + 1.lllln(GDP)t- 0.014(rc)t+ 0.0047(Tr/rd)t R2=0.990 (-11.4) (65.4) (-1.67) (1.34) MSE=0.0014 Identities: ln(T)t= 1.41 + 0.286n(Tm)t+ 0.2921n(Td)t + 0.2421n(Tc)t+ 0.1801n(TO)t ln(Yd)t= -0.29 + 1.0661n(GDP)t- 0.0381n(Tco)t- 0.0271n(TO)t (rm/rd)t- 1.845 +0.08(rm)t - 0.271(Td)t * Within parentheses are "t" statistics; MSE-mean squares errors; ris are in percentage form. - 52 - Table 10: Econometric Model of Taxation in Mauritius (N3SLS Estimation Results) Equations included in the model* Stochastic Equations: ln(Tm)t- -1.643 + 0.6831n(Xm)t+ 0.2311n(Tm)t-l+ 0.048(rm)t R2-0.998 (-6.30) (10.41) (4.22) (8.53) MSE-0.0001 ln(Td)t- -3.817 + 0.9981n(Xd)t + 0.169(rd)t R2C0.999 (-236.4) (429.5) (83.7) MSE-0.00004 ln(TC)t -3.68b + 0.8281n(Xc)t+ 0.0951n(Tc)t-l+ 0.330(rc)t R2-0.992 (-7.91) (10.1) (1.44) (8.31) MSE=0.0089 ln(TO)t- -3.965 + 0.9721nkGDP)t+ 0.223(rot)t R2=0.997 (-31.6) (69.7) (23.9) MSE=0.0022 ln(Xm)t- -1.844 + 1.1571n(GDP)t- 0091(rm/rd)t+ 0.047(rc)t R2-0.994 (-1.12) (50.9) (-2.30) (3.44) MSE=0.0066 ln(Xd)t- 2.296 + 0.763Ln(Yd)t+ 0.088(7m/Td)t R20.996 (1.19) (8.62) (2.51) MSE-0.0041 ln(Xc)t- -0.258 + 0.9931n(GDP)t- 0.020(rc)t+ 0.095(rm/rd)t R20.999 (-2.85) (83.2) (-3.41) (6.43) MSE=0.0009 Identities: ln(T)t- 1.25 + 0.5041n(Tm)t+ 0.1551n(Td)t + 0.0991n(Tc)t+ 0.2451n(TO)t ln(Yd)t- -0.258 + 1.0561n(GDP)t- 0.0201n(Tc)t- 0.0361n(TO)t (Tm/fd)t 2.99 + 0.06(rm)t - 0.54(7d)t * Within parentheses are "t" statistics; MSE=mean squares errors; ris are in percentage form. - 53 - Figures 2a-2d: Actual and Predicted Values of Individual Tax Yields in Malawi (1965-85) a: Import Tax b: Dan. Commptiou tax :Corporate Income Ta d: Other direct Taxes a Actual tax yield Predicted tax yield - 54 - Figures 3a-3d: Actual and Predicted Values of Individual Tax Yields in Mauritius (1965-85) I: mport Tax b: Don. Cousimption Tax 66. ~ ~ ~ ~ ~ ~ ~ . - ~~~~~~~~~~~~~~~~~* * e - u a.a X a a- c: Corporate Income Tax d: Other Direct Taxes ~~~~~~~~~~~'m 40.~~~~~~~e a*Actua t yield * ee * e *ld * Actual tax yield __ Predicted Ta x ield - 55 in mobilizing resources from the private sector to the public sector. This result strongly rejects the view that mobilizing resources through the tax system has been difficult in SSA countries (see Shalizi and Squire). Tables 9 and 10 respectively presented the structural form of the models with estimated parameters for Malawi and Mauritius. Using the method explained in Chapter II, each of these models was solved as ordinary and difference equations systems in order to estimate the short run and long run impacts of changes in exogenous variables, ln(GDP) and ris, on endogenous ones, individual tax yields and bases and total tax revenue. The obtained results for Malawi and Mauritius are respectively presented in Tables 11 and 12 --where built-in elasticity of tax yields and bases with respect to GDP are supplied in column (a) and columns (b)-(e) represent the responses of each of the tax yields and bases to the changes in each of the individual tax systems (Ari-l) included in the model. It is revealed from column (a) that the total and individual tax revenues are inelastic with respect to GDP except for import tax yield in Mauritius and corporate income tax revenue in Malawi whose long run elasticities exceed one. These exceptions emerge from the fact that imports in Mauritius and value added in the non-agriculture sector in Malawi grow faster than GDP. In other words, these two individual taxes are still inelastic with respect to their corresponding economic tax bases (0.78 and 0.91 respectively). The data presented in columns (b) and (c) indicate that the overall response of the total tax revenue to a one percentage point increase in Tm is larger than its direct response in both countries. This is due to the fact that a rise in rm reduces imports but raises private consumption and - 56 - Table 11: Short Run and Long Run Impact of Changes in Individual Tax Systems and GDP on Tax Revenues and Bases in Malawi* Tax Revenues and Aln(GDP)-l% ATm-l Ard-1 A 1ro- Bases (a) (b) (c) (d) (e) A.Short Run Impacts: Aln(T) 0.8336 0.0229 0.0567 0.0486 0.0657 (0.0232) (0.0566) (0.0341) (0.0684) Aln(Tm) 0.5666 0.0788 0.0073 0.0656 0.0000 (0.0810) Aln(Td) 0.9295 0.0017 0.1881 -0.0042 -0.0091 (0.1940) Aln(T.) 0.9466 0.0003 -0.0011 0.1291 0.0000 (0.1410) tln(TO) 0.9600 0.0000 0.0000 0.0000 0.3800 (0.3800) Aln(Xm) 0.6310 -0.0024 0.0081 0.0730 0.0000 Aln(Xd) 1.0270 0.0019 -0.0065 -0.0046 -0.0101 Aln(XC) 1.1110 0.0004 -0.0013 -0.0140 0.0000 B.Long Run Impacts: Aln(T) 0.8740 0.0233 0.0567 0.0534 0.0676 (0.0236) (0.0567) (0.0392) (0.0703) Aln(Tm) 0.5776 0.0804 0.0074 0.0668 0.0000 (0.0826) Aln(Td) 0.9243 0.0017 0.1882 -0.0048 -0.0094 (0.1940) Aln(TC) 1.0868 0.0004 -0.0012 0.1482 0.0000 (0.1619) Aln(TO) 0.9866 0.0000 0.0000 0.0000 0.3905 (0.3905) Aln(Xm) 0.6310 -0.0024 0.0081 0.0730 0.0000 Aln(Xd) 1.0213 0.0019 -0.0065 -0.0053 -0.0104 Aln(Xc) 1.1110 0.0004 -0.0013 -0.0140 0.0000 F Within the parentheses is the direct response of tax revenue to the DTMs. 57 - Table 12: Short Run and Long Run Impacts of Changes in Individual Tax Systems and GDP on Tax Yields and Bases in Mauritius* Tax Revenues and Aln(GDP)-1% Arm-1 A?dl Arc-l ArO- Bases (a) (b) (c) (d) (e) A.Short Run Impacts: Aln(T) 0.8364 0.0237 0.0317 0.0465 0.0537 (0.0328) (0.0262) (0.0327) (0.0546) Aln(Tm) 0.7902 0.0445 0.0336 0.0321 0.0000 (0.0650) Aln(Td) 0.7649 0.0052 0.1221 -0.0048 -0.0061 (0.169) Aln(TC) 0.8222 0.0047 -0.0426 0.3134 0.0000 (0.3300) Aln(TO) 0.9720 0.0000 0.0000 0.0000 0.2230 (0.2230) Aln(Xm) 1.1570 -0.0055 0.0492 0.0470 0.0000 Aln(Xd) 0.7665 0.0052 -0.0470 -0.0048 -0.0061 Aln(Xc) 0.9930 0.0057 -0.0514 -0.2000 0.0000 B.Long Run Impacts: Aln(T) 0.9644 0.0305 0.0363 0.0545 0.0537 (0.0426) (0.0262) (0.0361) (0.0546) Aln(Tm) 1.0276 0.0578 0.0437 0.0417 0.0000 (0.0845) Aln(Td) 0.7636 0.0052 0.1222 -0.0053 -0.0061 (0.1690) Aln(TC) 0.9085 0.0052 -0.0470 0.3463 0.0000 (0.3650) Aln(TO) 0.9720 0.0000 0.0000 0.0000 0.2230 (0.2230) Aln(Xm) 1.1570 -0.0055 0.0492 0.0470 0.0000 Aln(Xd) 0.7652 0.0052 -0.0469 -0.0053 -0.0061 Aln(Xc) 0.9930 0.0057 -0.0514 -0.0200 0.0000 § Within the parentheses is the direct response of tax revenue to the DTMs. - 58 - hence, value-added in the non-agriculture sector. As a result, import tax declines and domestic consumption and corporate income taxes rise, causing a net indirect increase in total tax revenue. This process is reversed when rd rises, that is, the overall response of the total tax revenue to a one percentage point rise in rd falls short of its direct response in both countries. As far as changes in corporate income and other direct taxes are concerned, an increase in rc indirectly raises import tax and reduces domestic consumption and corporate income tax yields, resulting in a decline in the direct response of the total tax yield to rTc This process is reversed when ro rises. It is worth mentioning that, in Malawi, the elasticity of the domestic consumption tax revenue with respect to GDP is higher than that of the import tax yield while, in Mauritius, the former falls short of the latter. Furthermore, in Malawi, the direct revenue impact of changes in the domestic consumption tax system is much higher than that of the same changes in the import tax system while, in Mauritius, the former is smaller than the latter. These differences will obviously require a different reform combination of discretionary tax measures if such a reform is aimed at shifting from the taxation of international trade to the taxation of domestic transactions in these countries. Trends of Tax shares and Tax Effort During the 1965-1985 period, the tax effort (total tax revenue over GDP) has grown by an annual average rate of 4.6 percent in Malawi and 1.4 - 59 - percent in Mauritius. The share of domestic consumption in total tax revenue 4n Malawi has increased by an average annual rate of 2.56 percent and that of import tax yield has declined by 1.72 percent. In Mauritius, the trends of these shares have been reversed, recording average annual percentage changes of -0.62 and +1.83 respectively. As a result, the ratio of domestic consumption tax over import tax, measuring the size and direction of shift from the taxation of imports to the taxation of domestic transactions has changed by +4.3 and -2.4 percent per annum in these countries respectively.3 The time series data generated on ris reveal that fiscal authorities have taken a variety of discretionary tax measures in both countries during the same period, to the extent that rm' Td, rc and ro have increased respectively by average annual percentage points of 0.49, 0.44, 0.91 and 0.03 in Malawi and 0.45, 0.10, -0.02 and zero in Mauritius. Furthermore, nominal GDP has grown by an average annual rate of 12 percent in Malawi and 14 percent in Mauritius.4 It is important to isolate the contribution of DTMs from that of economic growth to the trends of tax effort and tax shares in these ccuntries, as it makes it possible to explore the role that DTMs have played in effecting the shift from the taxation of imports to the taxation of domestic transactions in Malawi, and to question the effectiveness of DTMs as a policy instrument for bringing about such a shift in Mauritius. To accomplish this aim, first, the built-in elasticity of each of these trends with respect to GDP is derived using the individual and overall tax 3/ Tables 2-7 in Appendix A. 4/ Tables 2-7 in Appendix A. - 60 - elasticities estimated in the previous section. Then, their buoyancies are estimated using the estimate of the individual and overall tax buoyancies presented in Table 13, and finally, the contribution of DTMs to each of these trends is calculated by subtracting the elasticity of that trend from its buoyancy. The built-in elasticity of each of these trends is the difference between the built-in elasticities of the variables appearing in its numerator and denominator, that is, [Aln(Ti/T)I/[Aln(GDP)] - pi - (i) [Aln(T/GDP)I/[Aln(GDP)] - p - 1 (ii) [Aln(Td/Tm)]/[Aln(GDP)] - Ad - Pm (iii) where i= d, domestic consumption tax, - m, import tax, - c, corporate income tax, -o, other direct taxes, pj= built-in elasticity of the ith individual tax yield, and p -built-in elasticity of overall tax revenue. Using the estimates of p and pis presented in Table 13, the built-in elasticities of these tren.ds--measuring their automatic response to variations in GDP--were estimated by means of equations (i), (ii) and (iii). The results are presented in Table 14. Similarly, the buoyancy of each of them is the difference between the buoyancies of the variables appearing in its numerator and denominator, that is, . 61 - tAln(Ti/T)*]/[Aln(GDP)] - ( ' (i) [Aln(T/GDP)*]/[Aln(GDP)]- - 1 (ii) [Aln(Td/T.)*]/[Aln(GDP)]- Cd -m (iii) where buoyancy of overall tax revenue, and (i buoyancy of the ith individual tax yield. Using estimates of 4 and eis presented in Table 13, the buoyancy of these trends--measuring their total response, including the impact of DTMs, to variations in GDP--were estimated by means of equations (i)', (ii)' and (iii)'. The results are presented in 'fable 14. Table 13: Individual and Overall Tax Elasticities and Buoyancies in Malawi and Mauri.tius Malawi Mauritius Buoyancyl Elasticity2 Buoyancyl Elasticity2 Total Tax 1.31 0.88 1.09 0.97 Import Tax 1.06 0.58 1.19 1.03 Consumption Tax 1.72 0.92 1.05 0.76 Corporate Income Tax 1.43 1.09 0.97 0.91 Other Direct Taxes 1.09 0.99 0.95 O.27 I/ Tax Buoyancies were obtained by estimating the parameters of the following econometric model. ln(Ti)t-wo + wiln(GDP)t + ut where wi is buoyancy. 2/ From Tables 11 and 12. - 62 - Finally, by subtracting the elasticity of each of these trends from its buoyancy, the contribution of DTMs to that trend was estimated in terms of variations in GDP. The results are presented in Table 14. It is revealed from this Table that the growth of tax effort has been mainly due to discretionary tax measures, to the extent that tax effort would fall in the absence of these measures during the period under review. This result is in strong opposition to the view that mooilizing resources from the private sector to the public sector through the tax system has been difficult in SSA countries. In Malawi, 88 percent of the overall growth rate of domestic consumption tax share has emerged from discretionary tax measures while, in Mauritius, economic growth has dominated the trend of this tax share, contributing 500 percent to its overall negative growth rate. Economic growth has been the principal contribuLor to the downward trend of import tax share in Malawi. Its contribution accounts for 116 percent of the overall average annual percentage decline in this tax share. In Mauritius, both discretionary tax measures and economic growth have significantly contributed to the overall growth rate of import tax share, out of which 40 percent has emerged from the former factor and 60 percent has come from the latter one. It is apparent from the information presenced in Table 14 that the contribution of discretionary tax measures to the trend of domestic tax share has been higher than its contribution to the trend of import tax share in both countries. This simply means that both countries would shift from the taxation of international trade to the taxation of domestic transactions in the absence of any change in GDP. However, due to - 63 - Table 14: Contribution of Discretionary Tax Measures and Economic Growvh to Trends of Tax Shares and Effort in Malawi & Mauritius (percentage changes) Contribition of Buoyancy Built-in Discretionary Elasticity Tax Measures Malawi: Tax Effort +0.31 -0.12 +0.43 Import Tax Share -0.25 -0.29 +0.04 Domestic Consumption Tax Share +0.41 +0.05 +0.36 Corporate Income Tax Share +0.10 +0.21 -0.11 Other Direct Tax Share -0.21 +0.11 -0.33 Domestic Consumption Tax over +0.66 +0.34 +0.32 Import Tax Mauritius: Tax Effort +0.09 -0.03 +0.11 Import Tax Share +0.10 +0.06 +0.04 Domestic Consumption Tax Share -0.04 -0.20 +0.16 Corporate Income Tax Share -0.12 -0.06 -0.06 Other Direct Taxes Share -0.14 +0.01 -0.15 Domestic Consumption Tax over -0.14 -0.26 +0.12 Import Tax - 64 structural differences mentioned in the previous section, this shift has been accelerated in Malawi and has been reversed in Mauritius. In Malawi, economic growth and discretionary tax measures have played almost equal roles in shifting from the taxation of international trade to the taxation of domestic transactions; they have contributed 51 and 49 percent respectively to the overall growth in domestic consumption tax-import tax ratio. In Mauritius, ecoromic growth has dominated the downward trend of this ratio, indicating that this trend can be reversed only by means of an appropriate combination of discretionary tax measures. - 65 - CHAPTER IV CONCLUSION The structural adjustment programs of developing countries use fiscal deficit reduction as one of the policy tools for achieving real economic growth with price stability and balance of payments viability. In dealing with this deficit within such a framework, projections need to be made of the additional revenues which can be mobilized within the existing tax system as GDP grows. These projections indicate the need to activate additional means of revenue generation, particularly politically difficult discretionary tax measures. Thus, it becomes essential to be able to estimate built-in tax elasticity which measures percentage increases in tax revenue resulting from the endogenous changes in the base caused by a one percent rise in CDP. However, its estimation by means of any of the existing methods suffers from a specification bias due to lack of an obervable quantitative variable capable of reflecting all changes in an individual (or overall) tax system in public finance. The central theme of this study has been twofold: first, to develop an econometric method of estimating tax elasticity and the revenue impact of DTMs which deals with this lack and, thus, with its consequences on the estimate of tax elasticity; and second, to use this model as an empirical framework to highlight the contribution of DTMs to trends of tax effort and tax shares in selected SSA countries during the past two decades. The method to be developed in this research is a dynamic simultaneous-equation macroeconometric model of taxation which captures the - 66 - interaction of individual tax systems, individual tax revenues and bases and GDP. As representative of each individual tax system, its "average effective tax rate net of endogenous (built-in) changes in the tax yield and base" (AETRN) is introduced into the model. Time series data on AETRNs are automatically generated in the process of estimating the model parameters. This model explicitly incorporates both the direct and indirect responses of each individual tax revenue to changes in its own and other individual tax systems, i.e., own-DTM direct, own-DTM indirect and cross- DTM indirect responses. Its application requires only historical time series data on tax revenues, tax bases and GDP, all of which are already available for most countries. In addition to its application as a method for estimating tax elasticity and the revenue impact of DTMs, this model can be used as an empirical framework: (a) to forecast a government's revenue from various sources of taxation; (b) to evaluate the macroeconomic impact of a tax reform program which is aimed at either generating additional revenue and/or dealing with specific economic problems; and (c) to deal with various tax related economic issues--for example, to investigate the welfare impact of moving from differential tariffs towards uniform ones, which is often recommended by the Bank, or to examine the controversial view that uniform tariffs result in uniform rates of effective protection in industrial and non- industrial activities. A shift from the taxation of international trade to the taxation of domestic transactions is recommended, by both the Bank and the Fund, as one - 67 - of the main objectives oL a tax reform program in most developing countries. Such a reform is often included in structural adjustment programs. The presumption is that discretionary tax measures play a crucial role in effecting this shift. However, there is evidence indicating that this shift is also affected by endogenous changes in tax bases caused by factors other than these measures, particularly economic growth. The model developed in this study has been used as an empirical tool 'n order (i) to highlight the contribution that discretionary tax measures have made to the shift from the taxation of international trade to the taxation o, domestic transactions in the countries, such as Malawi, where such a shift has taken place, and (ii) to question the effectiveness of these measures as a policy instrument for bringing about such a shift in other countries, such as Mauritius, where the country's reliance orL the foreign trade tax has risen during the past two decades. The econometric application of the model to the time series data of these countries yields a number of interesting results, for example: (a) Discretionary tax measures have been an effective policy instrument for mobilizing resources from the private sector to the public sector in both countries, to the extent that tax effort would decline in the absence of DTMs. This result is strongly opposed to the view that mobilizing resources through the tax system has been difficult in SSA countries. (b) Individual and overall tax revenues have been inelastic with respect to GDP in both countries except corporate income tax in Malawi and import tax in Mauritius whose long run built-in elasticities exceed one. These exceptions emerge from the fact that imports in Mauritius - 68 - and value added in non-agriculture sector in Malawi have grown faster than GDP; in other words, these two individual taxes are still inelastic with respect to their corresponding tax base. (c) The built-in elasticity of domestic consumption tax has exceeded that of import tax in Malawi while, in Mauritius, the former has fallen short of the latter. Therefore, economic growth has contributed to the shift from the taxation of imports to the taxation of domestic transactions in Malawi and has had a negative impact on this shift in Mauritius. (d) The contribution of discretionary tax measures to the trend of domestic consumption tax share has been higher than its contribution to the trend of import tax share in both countries. This simply means that both countries would shift from the taxation of imports to the taxation of domestic transactions in the absence of economic growth. However, due to the structural differences mentioned above, economic growth accelerated such a shift in Malawi and reversed it in Mauritius. (e) Finally, economic growth and discretionary tax measures have had almost equal roles in the shift from the taxation of international trade to the taxation of domestic transactions in Malawi,contributing 51 and 49 percent to the overall growth rate of domestic consumption tax-import tax ratio respectively. In Mauritius, economic growth has been the principal factor 'n reversing this shift, to the extent that this country would shift from the taxation of international trade to the taxation of domestic transactions in the absence of nominal economic growth. - 69 - The low degree of automatic responsiveness of tax yields to variations in GDP (tax elasticity) in these countries raises the following interesting question, which demands further research: "Is there any way to improve the elasticity of these inelastic tax systems and, hence, gradually to reduce the need to take politically difficult discretionary tax measures?" This is a major gap remaining in the design of a tax reform.5 It is an empirical matter which demands country-specific and/or cross-country analysis of trends of individual and overall tax elasticities. The model developed in this study can be used as an empirical tool to conduct such research. Furthermore, it has been recognized, both by the Bank and the Fund, that most LDCs are in need of tax reform. A proper design of such reform, however, requires quantitative information on the impact of changes in each individual tax system not only on its correspondirg tax revenue and base but also on the other individual tax yields and bases. Providing such information has been a complicated issue due to the lack of a satisfactory empirical framework. The model developed in this research is capable of producing this information. However, the generated information is at a highly aggregated level. That is, it provides estimates of impact of overall changes in each individual tax system on its corresponding and other individual tax bases and revenues, but it is not directly capable of disaggregating these impacts in terms of the various sources of changes in that individual tax system, such as changes in the statutory tax rate, tax 5/ See Shome (1987). - 70 - base, tax credits, tax allowances and tax administrative efficiency. Providing such disaggregated information demands further effort. APPENDiX A: HISTORICAL TIME SERIES DATA Table 1: Trends of Tax Shares, Tax Bases and Tax Effort in Sub-Saharan Africa Countries Table 2: Individual and Overall Tax Revenues in Malawi Table 3: Individual and Total Tax Bases in Malawi Table 4: Individual and Total Tax Revenues in Mauritius Table 5:Individual and Total Tax Bases in Mauritius Table 6: Generated Time Series on ris in Malawi Table 7: Generated Time Series on ris in Mauritius - 72 - Table 1: Trends of Tax Shares, Tax Bases and Tax Effort in Sub-Saharan Africa Countries (annual average percentage point changes) Trends A. Tax Effort +0.40 B. Tax Shares -Corporate Income Tax +0.32 -Domestic Consumption Tax +0.15 -Import Tax -0.62 C. Tax Bases -Corporate Income Tax Vn/GDP +0.31 (Vi/GDP) (+0.40) -Domestic Consumption Tax Cp/CDP +0.30 L (Cp+G)/GDP] [+0.31] [(Cp+G-Mc)/GDP] [+0.09] -Import Tax M/GDP -0.20 (Mc/GDP) (-0.24) W Vi-value added in industry sector, Vn-value added in non-agriculture sector, Cp=private consumption, C-government consumption, Mc-consumption goods import,M-total imports, and GDP-gross domestic products. Sources: For A Ehdaie, Gandhi and Shalizi and for B World Development Report 1987, pp. 16, 172, 212. - 73 - Table 2 : Individual and Overall Tax Revenues in Malawi (000 000) Tax on Corporate Other Total Import Export Domestic Income Direct Year Tax Tax Tax transactions Tax Taxes 1965 11.8 4.2 0.0 2.4 1.8 3.4 1966 16.2 7.1 0.0 2.8 2.6 3.7 1967 19.1 8.9 0.0 1.9 4.2 4.1 1968 20.9 8.9 0.0 2.2 5.2 4.6 1969 27.5 11.1 0.0 3.9 6.1 6.4 1970 28.2 9.3 0.0 7.0 6.1 5.8 1971 36.1 10.6 0.0 11.4 7.7 6.5 1972 39.3 10.3 0.0 12.7 9.1 7.1 1973 43.6 10.6 0.0 14.3 10.5 8.1 1974 53.8 13.6 0.0 18.5 12.8 9.0 1975 66.6 14.9 0.0 21.1 20.3 10.3 1976 73.2 13.3 0.0 24.6 24.2 11.1 1977 89.9 16.3 0.0 30.4 29.5 13.7 1978 121.9 25.8 0.0 38.8 38.9 18.4 1979 143.9 32.7 0.0 51.8 38.1 21.3 1980 166.9 42.1 0.0 59.8 39.5 25.6 1981 178.9 50.2 0.0 66.7 34.1 27.9 1982 207.7 52.5 0.0 75.6 45.2 34.4 1983 240.0 58.5 0.0 87.5 53.3 40.7 1984 296.3 66.6 0.0 112.3 72.2 45.2 1985 367.1 92.6 0.0 124.7 102.3 47.5 Sources: NA data file of Bank Economic and Social Data Base; GFS data file of IMF; Country Economic Memorandums, World Bank; and Recent Economic Development Report, IMF. - 74 - Table 3 : Individual and Total Tax Bases in Malawi (000'000) Value Private Added in Year GDPMP Import Consumption Export Non-Ag. 1965 157.3 54.5 137.7 85.3 31.9 1966 176.1 69.4 152.5 100.6 40.0 1967 184.6 68.2 156.9 109.4 47.0 1968 193.2 80.0 167.2 117.7 48.7 1969 206.5 87.7 179.9 129.1 52.0 1970 225.8 94.8 176.3 142.9 58.7 1971 281.7 107.7 236.9 178.5 71.2 1972 302.5 123.5 248.6 187.1 75.8 1973 339.1 136.8 270.0 222.3 100.6 1974 429.5 179.8 320.2 283.1 129.3 1975 493.7 243.1 365.2 336.0 154.3 1976 574.1 237.9 416.6 378.9 186.3 1977 681.3 252.1 483.4 430.0 218.4 1978 736.1 329.2 502.2 505.8 185.7 1979 747.4 380.4 577.0 532.3 209.7 1980 913.0 410.5 714.3 696.1 269.7 1981 986.9 348.6 773.4 758.6 284.4 1982 1114.3 359.3 835.7 837.4 280.2 1983 1288.9 407.1 979.8 965.3 298.2 1984 1509.4 433.6 1150.4 1115.5 478.6 1985 1807.0 568.2 1409.5 1360.8 475.0 Source: NA data file of Bank Economic and Social Data Base. - 75 - Table 4 : Individual and Total Tax Revenues in Mauritius (000'000) Tax on Corporate Other Total Import Export Domestic Income Direct Year Tax Tax Tax transaction Tax Taxes 1965 200.4 56.2 12.9 35.4 na na 1966 146.9 52.3 15.2 38.6 12.0 28.8 1967 161.5 56.6 13.4 41.8 13.8 35.9 1968 174.8 62.2 15.3 43.7 18.0 35.6 1969 182.6 64.1 14.6 47.8 17.6 38.5 1970 179.0 63.8 16.8 48.2 14.3 35.9 1971 204.2 73.8 18.7 50.1 23.2 38.4 1972 234.2 86.6 19.6 55.7 24.7 47.6 1973 313.0 107.1 29.9 82.9 36.2 56.9 1974 439.8 141.6 48.2 108.1 59.1 82.8 1975 660.0 187.8 129.8 123.0 92.5 126.9 1976 946.5 260.5 126.1 136.3 138.8 284.8 1977 1072.9 349.1 124.9 173.3 224.0 201.6 1978 1109.5 412.7 139.8 220.2 132.2 204.6 1979 1260.7 469.9 145.2 271.1 128.4 246.1 1980 1601.5 647.4 287.3 319.8 118.5 228.5 1981 1801.1 713.4 268.2 373.4 180.9 260.2 1982 1953.4 701.0 377.8 420.7 162.7 291.2 1983 2436.5 1001.1 416.4 538.9 146.9 333.2 1984 2802.7 1174.4 442.0 667.4 154.3 364.6 1985 2993.0 1375.7 369.9 716.2 134.9 396.3 1986 3502.3 1740.6 459.3 788.1 169.0 345.3 Sources: NA data file of Bank Economic and Social Data Base; GFS data file of IMF; Country Economic Memoranda, World Bank; and Recent Economic Development Report, IMF. 76 - Table 5 :Individual and Total Tax Bases in Mauritius (000'000) Value Private Added in Year GDPmp Import consumption Export Non-Ag. 1965 976.3 435.0 799.8 933.3 393.0 1966 963.0 402.0 814.1 927.6 392.0 1967 1024.1 435.0 842.9 984.7 378.0 1968 1011.2 479.0 870.4 988.6 452.0 1969 1088.0 449.0 863.5 1047.7 475.0 1970 1099.8 515.0 924.6 1063.2 531.0 1971 1218.4 583.0 1042.0 1165.8 523.0 1972 1516.7 722.0 1165.6 1415.7 759.0 1973 1951.1 1037.0 1441.0 1803.0 991.0 1974 3471.8 1902.0 2237.7 2784.3 2124.0 1975 3563.4 2227.0 2466.0 3233.8 2269.0 1976 4181.1 2712.0 2956.0 3766.0 2388.0 1977 4794.7 3235.0 3658.0 4503.0 2656.0 1978 5485.3 3477.0 4249.0 5281.0 2705.0 1979 6753.8 4158.0 5144.0 6416.0 3260.0 1980 7442.5 5342.0 6562.0 7783.0 4450.0 1981 8849.0 5634.0 7277.0 8952.0 4566.0 1982 10225.5 5859.0 8301.0 10195.0 5529.0 1983 10806.6 5999.0 8874.0 11298.0 5953.0 1984 12076.2 7470.0 9841.0 12624.0 6989.0 1985 14155.2 9210.0 11127.0 14494.0 8885.0 1986 15812.0 10515.0 12090.0 16405.0 11880.0 Source: The same as Table 4. 77 - Table 6 Generated Time Series on ris in Malawi (percentage) Import Consumption Corporate Other Year Tax Tax Income Tax Direct Taxes 1965 8.35 1.77 5.64 2.07 1966 11.65 1.91 6.75 2.00 19G7 15.28 1.26 9.47 2.12 1968 12.93 1.38 11.36 2.28 1969 15.05 2.32 12.56 2.93 1970 11.37 4.30 11.25 2.44 1971 11.44 5.43 11.85 2.18 1972 9.67 5.83 13.23 2.25 1973 8.97 6.10 11.70 2.29 1974 8.76 6.76 11.18 2.01 1975 7.07 6.82 14.98 2.02 1976 6.40 7.05 14.91 1.89 1977 7.46 7.60 15 58 1.96 1978 9.26 9.49 24.03 2.39 1979 10.24 11.24 20.94 2.67 1980 12.46 10.50 16.95 2.63 1981 18.30 10.88 13.90 2.64 1982 18.61 11.49 18.69 2.90 1983 18.27 11.39 20.76 2.97 1984 19.79 12.62 17.69 2.60 1985 21.31 11.38 25.24 2.46 - 78 - Table 7 Generated Time Series on Tis in Mauritius Import Consumption Corporate Other Year Tax Tax Income Tax Direct Taxes 1965 14.84 4.63 - 1966 14.69 4.98 3.39 2.69 1967 14.95 5.22 4.05 3.16 1968 15.20 5.29 4.53 3.15 1969 16.71 5.86 4.26 3.18 1970 14.59 5.50 3.12 2.93 1971 15.21 5.05 5.16 2.84 1972 14.66 5.02 3.86 2.86 1973 12.77 6.11 4.47 2.65 1974 9.20 5.08 3.42 2.23 1975 10.58 5.26 5.03 3.22 1976 12.28 4.84 7.21 6.15 1977 14.04 4.98 10.59 3.77 1978 15.66 5.47 6.24 3.33 1979 14.88 5.57 5.07 3.28 1980 16.19 5.13 3.41 2.68 1981 17.17 5.42 5.13 2.60 1982 15.98 5.35 3.80 2.53 1983 23.54 6.47 3.24 2.66 1984 22.02 7.29 2.93 2.59 1985 20.80 6.89 1.99 2.43 1986 23.53 6.98 1.84 1.87 - 79 - APPENDIX B: GENERALIZED VERSION OF THE MODEL In Chapter II, all of the equatior.s included in the model are assumed to have a specific functional form, i.e., semi-log linear. This assumption is relaxed in this annex and, hence, the generalized version of the model is discussed. An individual tax yield assessed by tax inspectors is considered to be a function of Xi and ri, that is, (Ti*)t- Fi[(Xi)t, (ri)t] (1) Let us assume that tax inspectors adjust actual tax revenues towards their assessed level according to a partial adjustment mechanism, that is, A(Ti)t- Ai[(Ti*)t - (Ti)t.l] (2) Then, the actual tax y.eld function is obtained by substituting (2) in (1), that is, (Ti)t= (l-Ai)(Ti)t-l + AiFi[(Xi)t,(ri)t] for i-l to n (3) where (aTi/aXi)=coefficient of built-in flexibility of Ti with respect to Xi (CBFXi), (8ri/8ri)-own-DUMs direct response ; ' - - !~~~~~~~~~~~~~~~~~~~~ - 80 - Using the concept of the "realized individual tax rate" defined in Chapter II, its formula will have the following form after making a simple manipulation. 1 + Git rit= rit (4) Git(l+Git) 1+ ( CBFXi ) - rio+ Git(CBFXi) where rit is average effective tax rate of Ti at time "t" and (Gi)t=ln(X,)t-ln(Xi)o (5) In its final form, each individual tax base is related to all ris and GDP, that is, (Xi)t - Di[(GDP)t, (rI)t .................. 9(rn)t] (6) where [(CBFXi)(pXi/3GDP)]- coefficient of built-in flexibility of Ti with respect to GDP (CBFYi), (CBFXi)(8Xi/8ri)- own-DTMs indirect response, and (CBFXi) (83Xi/.-,j)= cross DTMs indirect response. Finally, the model is closed by adding the overall tax revenue identity, that is, (T)t(Ti)t+ .............. +(Tn)t (7) - 81 - Equations (3), (5), (6) and (7) perform the structural form of the model. Parameters of the model are estimated after substituting equation (4) in it. After estimating CBFYis, the built-in tax elasticity of each individual tax with respect to GDP will be: Eit- (CBFYi) (GDP/ATi)t where ATi is the adjusted tax revenue to discretionary tax changes obtained by simulating, the model for rit-riO. - 82 - APPENDIX C: AN OPERATIONAL GUIDELINE ON THE APPLICATION OF THE MODEL This appendix provides a brief guideline on the application of the model as an empirical framework for: (i) estimating tax elasticity and the revenue impact of DTMs, and (ii) evaluating the macroeconomic impact of a tax reform program aimed at generating additional revenue and/or dealing with various tax related economic issues which require converting the DTMs included in the reform to AETRNs and vice versa. i. Estimating Tax Elasticity and the Revenue Impact of DTMs The structural form of the model is presented in Table 1. Estimates of its parameters are obtained by estimating the parameters of the model presented in Table 2. Estimating its parameters requires time series data on the following variables, which are readily available for most countries in GFS (an IMF publication) and the World Tables (a World Bank publication): Td =Tax on domestic transactions Tm -Tax on imports Tc -Corporate income tax To -Other direc. r-xes T =Overall ta-' re'4?nte ret of export taxes Xd -Private consumption Xc -Value added in non-agriculture sector net out of wage bill Xm -Imports XO =GDP - 83 - Table 1: Structural Form of the Model log(Td)t- AdadO+ Xdadll0g(Xd)t + (I-Ad)lvg(Td)t-l+ Adad2(7d)t+ Udt log(Tm)t- Amamo+ Amamllog(Xm)t + (l-Xm)log(Tm)t-l+ Aemm2(Tm)t+ Umt log(Tc)t= Ac%cO+ AXccllog(Xc)t + (l-Ac)log(Tc)t-l+ Acac2(Tc)t+ Uct log(To)t= Aoaoo+ Aoaollog(Xo)t + (l-Ao)log(To)t-l+ Aoao2(ro)t+ Uot l(Xd)t= fidO Odlln(yd)t+ fd2(rm/rd)t+ udt ln(Xm)t= PmO+ Pmlln(GDP)t+ flm2(rm/Td)t+ Pm3(rc)t + Vmt ln(Xc)t- PcO+ Pclln(GDP)t+ Pc2(7c)t + fc3(rm/fd)t+ vct ln(T)t = 0+ dln(Td)t+ Smln(Tm)t+ 6cln(Tc)t+ 6oln(To)t ln(Yd)t = 70 +7yln(GDP)t+ 721n(TC)t+ -y31n(To)t (rm/rd)t= 00 + l(rm)t + 02(td)t where, Td- Tax on domestic transactions (endogenous variable), t Tc=1 - w ! r r r e5- , .fe r>-, To- Other direct taxes &cndogenous variable), Xd= Private consumption (endogenoun variAble), ….lt-- - - _s~ :_ ; ;__;_ . g.l;t Xc- Value adodei. I!- AsgenCsa;bZ Xv- CD°- grcss domestic r,oducts (exoRenuus va&1d1,1>) r1- The it" 'Lndividual realized tax rate (exogenous variable), tor i= d, m, c, o, Yd- Disposable income (endogenous variable), T= Total tax revenue net of export taxes (endogenous variable). - 84 - Table 2: Entire Model with Estimable Parameters* I- l+gd ln(Td)t- Xd*dO+ AdQdlln(Xd)t + (l-Xd)ln(Td)t-l +IXdad2 rd +dt 1+,\dadlgd -t ln(Tm)t AmamO+ Amamlln(Xm)t + (l-Am)ln(Tm)t l +Amam4rm l+g +mt 1+,\mamlgm t ln(Tc)t= XcacO+ Acaclln(Xc)t + (l-Xc)ln(Tc)tl +Xcac2Irc -+g- 1 + l+,\caclgc Jt [ l+Aago 1t ln(To)t XoaOo+ Aoaolln(Xo)t + (l-Xo)ln(To)tl r +o | +ot l+Aotolgo it r rm,[ (l+gm)/(l+amlgm)] 1 ln(Xd)t - fdO+ Pdlln(yd)t+ fld2 [rdl egm/l+amg )] + vdt rdl(l+gd)/(]+adlgd)] tld ln(X -Oo+Omll(GDP)tpm rm [( l+gm) / ( +amlgm) ] rc (l+gc ) ln(Xm)tfmO+ mll (GDP)t+m2 +lm3 +vmt rdf(l+gd)/(I+adlgd)]- t (I+Oclgc) +d 1 rm(l+gm)/(l+emlgm) ln(Xc)t= RcO+ 3clln(GDP)t+ BC9 rd ,. 1+ . 14..-. 1, I .(t1 4.og\Jf!- 4 L-dlgd t L-U'-' \C' '-' uF .ol/J -l_ nfT j , , U- 3.an(Th:?; + 2 l T.)+ 6Cln(Tc)t+ 601n(To)t -;d; ti il;- 2 f 1cSt: 731n(TO)t 9(i)t l'(Xi)t- ln(Xi)O for i=d, in, C, O * Estimating the parameters of the model requires time series data on Tis, T, Xis, ris and GDP which are readily available for most LDCs in GFS(an IMF publication) and World Tables (a World Bank publication). - 85 - Yd=Disposable income ri-The ith individual average effective tax rate (T/X), for i-d, m, c, o, and GDP- Gross domestic product. Using these time series data, the efficient and consistent estimates of the parameters of the model presented in Table 2 are obtained by means of a simultaneous-equation econometric technique. A within-sample dynamic simulation is performed for all the endogenous variables included in the model in order to generate time series data on gis. Using this data and estimates of Ais and ais, time series data on ris are generated by means of the following equation. - ~(1 + gi)t (ri)t [ (ri)t (-] (1 + Xiailgi) t The generated time series data on ris can be used independently to explore the impact of changes in each individual tax system on key macroeconomic variables such as inflation, economic growth, budget deficit, real exchange rate and internathonal balance of paymentR. To linearize the structural form of the msodel presented in Table 1, tl-hese data are used to estimate thz pArAn1terE of- the follc;ir'- rN-mi; d' -r -crds, t_ linearize (r,jr. !) lcinci one '-f tcchnfccLn.J .q ...- ' ii the Le;Xt (Tm/rd)t= 00 + 01(7m)t + 82(7d)t - 86 - Now, by substituting the estimated value of the parameters in the original equations of the model presented in Table 1, the structural form of the model with estimated parameters (SFM) is obtained. The short run and the long run elasticities of individual tax yields and base and overall tax revenue wich respect to GDP, and the direct and indirect responses of each individual tax yield to the changes in its own and other individual tax systems are simply obtained either by substituting the estimated parameters into the formulas presented in Tables 3 to 7 of the text or by directly solving the SFM as an ordinary and a difference equations systems and, hence, deriving the reduced (RFM) and final (FFM) forms of the model.1 ii. Evaluatine/Designing A Ouantitative Tax Reform Program The reduced/final form of the model can be used as an empirical framework to evaluate the sport run/long run macroeconomic impact of a tax reform program and to forecast a government's revenues from various sources of taxation. However this requires converting the proposed DTMs to ris or vice versa. An example from Malawi is considered to illustrate how to convert the proposed DTMs to ris and vice versa. Let us assume that the Malawian government wants to raise total tax revenue by 5.67 percent using statutory surtax rate (SSR) as a policy instrument- Then, the eue!Etions are: How much of an increase in the surtax rate will result in a 5 67 percent increase in total tax revenlie? And what 'zS -cvz. t. ^ impct n4^f^rtli,7 1 ° )o these quesLions requires quantitative knowledge ua LLie iimpact of a orne percentage point increase in SSR on both its corresponding and other 1/ For more details on solution of a dynamic macroeconometric model see Ehdaie (1987). - 87 - individual tax yields and bases. Providing such information, first of all, requires converting a one percentage point increase in SSR to rd. In this country, surtax was introduced in 1970/71 at a statutory tax rate of 18 percent. Then, this rate was increased to 25 percent in 1983/84. Given one of these DTMs, say the former, and time series data on rd, the amount of increase in Td due to a one percentage point increase in SSR is calculated as follows. As a result of introducing surtax in 1970 (fiscal year 1970/71), Td rose from 2.32 percent in 1969 to 4.30 percent in 1970 (see Table 6 in Appendix A). Given 18 percent SSR, rd went up by 0.111 percentage points due to a one percent point increase in SSR (the same result is obtained using the DTMs of 1983/84). It is apparent from the coefficient of Td in the overall tax e(quation presented in Table 11 of the text that total tax revenue will rise by 5.67 percent as result of a one percentage point increase in 7d, whose equivalent is a 9 percentage point increase in the statutory surtax rate. In other words, the new SSR will be 34 percent (25 percent plus 9 percent) which will result in a 5.67 percent increase in overall tax yield. Using the coefficients of rd in the other equations included in the model presented in Table 11 of the text, the macroeconomic impact of this di8cretionary tax measure will us as follows. First, tax on imports >-. wi i--creasc by 0.73 and 18.81 percLZt- re.spcc4-Je&y. S-conc, corporate income tax will decline by 0.11 Percent. iiiild, pri-vave cousw-nption ana vaiue aaded in the non-agriculture sector of the economv will fall by 0.65 and 0.13 percent respectively, and finally, imports will rise by 0.81 percent. - 88 - BIBLIOGRAPHY Andersen, S.P. (1973) "Built-in Flexibility of Sensitivity of the Personal Income Tax in Denmark" Swedish Journal of Economics, vol. 75. Artus, K.K. (1974) "Tax Revenue Forecasting: A Methodological Study with Application to Turkey", Studies in Domestic Finance, no. 5 Washington, D.C.: IBRD. Bahl, R.W. (1972) "Alternative Methods for Tax Revenue Forecasting in Developing Countries: A Conceptual Analysis", IMF, unpublished paper, October. 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Jonnakuty of Public Sector Deficits Klaus Schmidt-Hebbel 37453 WPS322 Earmarking Government William McCieary December 1989 A. Bhalla Revenues: Does it Work? 37699 WPS323 The Old and the New in Heterodox Miguel A. Kiguel December 1989 R. Luz Stabilization Programs: Lessons Nissan Liviatan 61588 trom the 1960s and the 1980s WPS 324 Ethical Approaches to Family F. T. Sai December 1989 S. Ainsworth Planning in Africa K. Newman 31091 WPS325 Manufacturers' Responses to Infra- Kyu Sik Lee December 1989 L. Victorio structure Deficiencies in Nigeria Alex Anas 31009 WPS326 Do Exporters Gain from Voluntary Jaime de Melo January 1990 M. Ameal Export Restraints? L. Alan Winters 61466 WPS327 Making Noisy Data Sing: A Micro James R. Tybout January 1990 M. Ameal Approach to Measuring Industrial 61465 Efficiency WPS328 Europe, Middle East, and North Rodolfo A. Bulatao November 1989 S. Ainsworth Africa (EMN) Region Population Eduard Bos 31091 Projections, 1989-90 Edition Patience W. Stephens My T. Vu WPS329 Latin America and the Caribbean Rodolfo A. Bulatan November 1QR9 S Ainsworth ki_n0) i FU9iVII PU8u;cA1;Qil itLUUaliU OUb Projections, 1989-90 Edition Patience W. Stephcns M%-, T Vul WPS330 Africa Region Popu!ation Rodolfo A. Bulatao Novembe' '989 S. A'nsworth Projections, 19ld-90 Edition Eduard Bos 31U91 Paiience YW. Stepnens My T. Vu WPS331 Asia Regior. Population Projections, Rodolfo A. Bulatao November 1989 S. Ainsworth 1989-90 Edition Eduard Bos 31091 Patience W. Stephens My T. Vu WPS332 Effective Incentives in India's Ashok Gulati January 1990 G. Bayard Agriculture: Cotton. G3rouindnuts, with James Hanson 38004 Wheat, and Rice and Garry Pursell PPR Work;ng Paper Series Contact ITlt Author Dae for 12ager WPS333 An Option-Pricing Approach to Stijn Claessens January 1990 S. King-Watson Secondary Market Debt (Applied Sweder van '.Vijnbergen 31047 to Mexico) WPS334 An Econometric Method for Jaber Ehdaie February 1990 A. Bhalla Estimating the Tax Elasticity and the 37699 Impact on Revenues of Discretionary Tax Measures (Applied to Malawi and Mauritius) WPS335 Macroeconomic Adjustment and Ramon E. Lopez December 1989 L. Riveros the Labor Market in Four Latin Luis A. Riveros 37465 American Countries WPS336 Complementary Approaches to Germano Mwabu Financing Health Services in Africa WPS337 Projecting Mortality for All Rodolfo A. Bulatao December 1989 S. Ainsworth Countries Eduard Bos 31091 Patience W. Stephens My T. Vu WPS338 Supply and Use of Essential Drugs S. D. Foster in Sub-Saharan Africa: Issues and Possible Solutions WP-,339 Private Investment and Macro- Liis Serven December 1989 E. Khine economic Adjustment: An Andres Solimano 37469 Overview WPS340 Prudential Regulation and Banking V/incent P. Polizatto January 1990 WDR Office Supervision: Building an Institutional 31393 Franework for Banks WPS341 Cost-of-Living Differences between Martin Ravallion December 1989 C. Spooner Urban and Rufs' Areas of Indonesia Dominique van de Walle 30464 WPS342 Human Capital and Endogenous Patricio Arrau December 1989 S. King-Watson Growth in a Large Scale Life-Cycle 31047 Model WPS343 Po;icy Determinants of Growth: William R. Easterly December 1989 R. Luz Survey of Theory and Evidence Deborah L. Wetzel 61588 WPS344 Policy Distortions, Size of William Itisterly December 1989 R. Luz Government, and Growth 61588 WPS345 Private Transfers and Public Poiicy Donald Cox December 1989 A. Bhalla in Developing Countries: Emmanuel Jimenez 37699 A Case Study for Peru