MASTER FILES ROOM C-5E5 0440
This is a Working Paper and the author would welcome any IMF WORKING PAPER comments on the present text. Citations should refer to a Working Paper of the International Monetary Fund, men- tioning the author, and the date of issuance. The views © 1992 International Monetary Fund expressed are those of the author and do not necessarily represent those of the Fund.
WP/92/11 INTERNATIONAL MONETARY FUND
European Department
A Cross-Country Analysis of the Tax-Push Hypothesis
Prepared by Fiorella Padoa Schioppa Kostoris *
Authorized for distribution by Massimo Russo
February 1992
Abstract
This paper presents a microeconomic theoretical model of union optimi- zing behavior which is then used to test the relevance of the tax-push hypo- thesis for wage formation in nine Western European countries. Two factors-- the compensation and the progressivity effects--are shown by the model to account for the effect (if any) of tax rates on wage formation. A wage equation tested for the period 1960-1988 shows that in general small open economies have negligible compensation and progressivity effects, while in larger economies direct, indirect and social security tax rates are trans- ferred onto the real labor cost. All countries show a weakening of the tax shifting starting at the end of the 1970s or the beginning of the 1980s.
JEL Classification Numbers: E24, E62, J51, P52
* The author is Full Professor in Economics at the University of Rome "La Sapienza". This paper was prepared while she was a visiting scholar in the European Department of the International Monetary Fund. The author is very grateful to three brilliant research assistants, Leonardo Felli, Chiara Rossi and Elena Schioppa. She also wishes to thank the country desk economists of the European Department at the IMF and the participants at various seminars where a previous version of this paper was presented for their useful comments. All remaining errors are hers.
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Contents Page
I. Introduction 1
II. A Testable Model of the Average Direct Tax Rate for Nine European Countries 5
III. A Microeconomic Model of Tax Shifting on Optimum Wage Setting 21
1. The compensation effect (of S, T, and flat A) 27 2. The progressivity effect (of a progressive A) 28 3. The effects of a change in A when the average and the marginal direct tax rates vary together 28
IV. A Testable Model of the Wage Setting for Nine European Countries 30
V. The Tax-Push Hypothesis Revisited for Nine European Countries 37
Text Tables
1. Personal Income Taxes in Europe: An Institutional Perspective in 1988 10 2a. Estimates of the Average Direct Tax Rate Equation in Nine European Countries, 1960-88 15 2b. Estimates of the Average Direct Tax Rate Equation in Nine European Countries, 1960-88 17 3a. Estimates of the Wage Equation in Nine European Countries, 1960-88 34 3b. Estimates of the Wage Equation in Nine European Countries, 1960-88 35 4. Long-Run Estimated Semi-Elasticities of the Wage Rate to the Direct Tax Rate in Some Large European Countries 39
Charts
1. Temporal Dynamics of the Average Direct Tax Rate, of the Nominal and Real Wage Rate 8a 2. Estimate of the Wage Equation: Observed and Fitted Values 38a
Appendix I. Variables, Definitions and Data Sources 40
References 42
©International Monetary Fund. Not for Redistribution I. Introduction
The main purpose of this paper is to test for nine (Western) European countries the relevance of the tax-push hypothesis for wage formation. To this end, we adopt a microeconomic theoretical model of union optimizing behavior (which generalizes the analysis of Padoa Schioppa, 1990) to derive a macroeconomic, testable model of union wage setting.
According to our microeconomic model (see Chapter III), the union optimally chooses the nominal wage so as to maximize an objective function which depends positively on the net real wage and on employment (and on various parameters, the most important of which is the net real reservation wage), under the constraint of the firm's perceived labor demand. Of course, optimality implies that the trade-off between the nominal wage and employment along the firm's labor demand must be the same as the one along the union indifference curve. The latter is a function both of the weight the union assigns to employment relative to the net real wage, and of the progressivity of direct taxation. The relevant progressivity index turns out to be the ratio between the marginal minus the average direct tax rate (the numerator) and 1 minus the average direct tax rate (the denominator); it ranges between 0 and 1.
Let us first discuss the importance of the weight assigned by the union to employment relative to the net real wage (i.e., the nominal wage, deflat- ed by the consumer price, net of the average direct tax rate). If given the union's objective function this weight is fixed and independent of fiscal policy, the real labor cost (i.e., the nominal wage, deflated by the product price at factor cost, augmented by social security contributions paid by employers) is necessarily unaffected by the tax wedge (the latter is approx- imated by the sum of the social security, the indirect and the direct tax rates). In this event, assuming that all tax rates are flat--an assumption which will be relaxed later--workers bear the consequences of any increase in the social security tax rate paid by employers, through a decrease in nominal wages. They also lose as consumers as a result of a cut in purchas- ing power when, the nominal wage being unchanged, the direct tax rate rises and therefore the net wage decreases or when the indirect tax rate rises and therefore the consumer price increases. In these circumstances, the compen- sation effect is said to be zero.
If, on the contrary, the weight mentioned above depends on the net real wage, any increase in the tax wedge is fully transferred into a higher real labor cost at the employers' expense, while the workers' net real wage remains unaffected: in this instance, the compensation effect is said to be positive.
The most interesting case, however, arises when the weight assigned by the union to employment relative to the net real wage not only depends positively on the net real wage but also negatively on the net real reserva- tion wage. This may well be so because, caring about "relativities," workers are interested, for a given net real wage, in having the lowest net real reservation wage, as the latter is what they would get at full employ- ment in the union's absence. Therefore, downward pressures on the net real wage target arise, ceteris paribus, the lower is the net real reservation
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wage. Most union utility functions used in the economic literature appear to bear this characteristic, for example the Stone-Geary and the utilitarian union utility function (but not the Dunlop one, where the weight assigned to employment relative to the net real wage is constant).
When the union cares about "relativities," three important consequences are observed in the optimal union behavior and therefore in the macroeconom- ic wage equation. First, wage setting is negatively affected by the unem- ployment rate, because, ceteris paribus, a higher unemployment rate implies a lower net real reservation wage, hence a lower net real wage target. Second, for a given labor supply, any increase in the tax wedge, lowering the net real reservation wage, reduces the compensation effect. While in the two cases discussed above, the compensation effect could only be either zero or positive, now the compensation effect becomes weaker and may even be negative.
Third, the tax wedge is proved to be (in Chapter III) the only relevant fiscal parameter in the wage equation only if all tax rates are flat. While this hypothesis is acceptable for the employers' social security tax rate and for the indirect tax rate, it is unrealistic for the direct tax rate due to income tax progressivity. Therefore, when the weight assigned by the union to employment relative to the net real wage is either constant or only dependent on the net real wage, a higher income tax progressivity leads to reductions, ceteris paribus, of the gross wage target because it makes wage benefits relatively less desirable than employment benefits: the progressivity effect is then said to be negative. I/
By contrast, when the union cares about "relativities" and the weight it assigns to employment relative to the net real wage depends positively on the latter but negatively on the net real reservation wage, the progressivity effect becomes stronger and may even be zero or positive. This is because a counterbalancing factor is (at least partially) at work, as a higher direct tax progressivity affects the net real reservation wage less than the net real wage; this would reduce, ceteris paribus, the distance between the net real wage and the net real reservation wage, thus inducing the union to increase the gross wage target.
In sum, two factors determine the (backward or forward) shifting, if any, of tax rates on wages: the compensation effect and the progressivity effect. The former explains wage movements caused by changes in the indirect tax rate, in social security contributions, and also in the direct tax rate to the extent that this may vary in the average at given marginal rate; the latter effect explains wage movements caused by changes in the direct tax progressivity at constant average. The most general theoretical model presented here shows that the compensation and the progressivity
I/ It should be noted here that in Padoa Schioppa (1990) a similar case was described as an instance of positive progressivity effect.
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effects can be positive, zero or negative and of equal or different sign, but their signs must be internally consistent.
Empirical analysis becomes therefore essential. Under the hypothesis that the firms' labor demand is derived from a CES production function, we obtain from our microfounded model (in Chapter IV) a steady state wage equation. Our testable, nested macroeconomic wage equation is used in the estimation for all the EC countries (except Luxembourg, Ireland, Greece, Spain and Portugal due to lack of data) plus Austria and Sweden over the 1960-88 period.
The econometric results reported by Tables 3 and 4 for the nine selected European countries seem to show three robust regularities (see Chapter V):
In general, small and open economies, such as Austria, Den- mark, the Netherlands, show zero compensation and progressivity effects, fixing their steady state target in terms of a real labor cost per unit of value added, probably to maintain their external competitiveness; the only exception is Belgium, particularly up to its entry in the EMS.
Larger and less-open economies, in contrast, transfer in the long-run indirect and social security tax rate increases to the real labor cost (except the United Kingdom and Italy). In these greater economies, a rise in the direct tax rate raises the steady state gross real wage, both where the compensation and the progressivity effects move in opposite direction (as in Germany, France and Sweden), and a fortiori where, like in very open economies, the compensation effect is approximately zero, but the progressivity effect is posi- tive (Italy and the United Kingdom).
All European countries show a weakening of the tax shifting to the real labor cost between the end of the 1970s and the beginning of the 1980s. This changing union attitude usually coincides with the introduction of de facto fiscal indexation and the decrease of tax progressivity, and leads to fix the steady state wage rate so as to safeguard the country's external competitiveness: that is the case not only of small open economies, but also of Germany after 1976, of the United Kingdom after 1978, of France after 1982, of Italy after 1982 and, to a limited extent, Sweden after 1978.
The answer to the question of whether the tax-push hypothesis is confirmed or not by our analysis is complex; the tax-push is different in different countries, in different times, and for different fiscal policies. One may, then, wonder why, unlike in single-country studies, previous cross-
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country econometric I/ studies showed no significant effect of taxes on wage formation (e.g., Grubb, 1985, Bean et al., 1986, Coe and Gagliardi, 1985, Dreze and Bean, 1991, the exception being Knoester and van der Windt, 1987) .
In our opinion the reason is twofold. First, the microeconomic founda- tion of the presence of fiscal parameters in the macroeconomic wage equation had not been fully clarified. This led many authors to introduce only the tax wedge as a fiscal regressor in the estimated wage equation, a misspecification except when all tax rates are flat. The essential distinc- tion between the compensation and the progressivity effect, captured in the best theoretical models (for example Nickell and Andrews, 1983), has never been applied, to our knowledge, to cross-country econometric analyses, not even in the most robust estimations (Knoester and van der Windt, 1987).
A second reason for the partial failure in finding support for the tax- push hypothesis in previous cross-country econometric studies is the insuf- ficient attention they have devoted to the specific institutional and analytical characteristics of the various countries' tax systems (in terms of progressivity, de jure or de facto fiscal indexation, etc.) and to their main structural changes in the almost 30 years under observation. Such an effort has been made in a parallel paper (Padoa Schioppa, 1992) and is briefly documented here by Table 1 and Chart 1 in Chapter II.
We have carefully examined the fiscal settings of the nine European countries and their tax reforms aiming at increasing progressivity (in the mid-1970s in Italy), or decreasing it (mainly in the 1980s, starting with the Thatcher reform in the United Kingdom), we have also analyzed their fiscal adjustments for inflation--through legal indexation like in Denmark between 1970 and 1983, or de facto indexation obtained (as in Sweden) after the splitting of the family income as a base for personal income taxation, or obtained (like in Germany) through fine-tuning variations in tax allow- ances and in the number or the nominal value of income brackets. Identifi- cation of the years where the fiscal structural changes have occurred in each country proves to be essential both for the estimation of each tax system's degree of progressivity or its de facto fiscal indexation (Chapter II) and for testing the tax-push hypothesis (Chapters IV and V).
To be sure, a better job would have been performed if cross-section data were available to correlate for each year and each country, the direct tax rate and the nominal and the real wage rate of different individual taxpayers. In the absence of such data for most countries, we think that, as a first step, the issue can be examined on the basis of time series data by assuming that fiscal systems are stable over time, except for those specific years when a structural break in the tax structure is recorded, due to some reform or some similar policy change.
_!/ However, the tax-push hypothesis has been confirmed in previous cross- country economic studies such as Tanzi (1980).
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On the basis of this approach, we estimate in Table 2 (of Chapter II) the average and the marginal tax rate of the average taxpayer, the degree of progressivity and de facto indexation of direct taxation in the nine European countries under observation. Although the average direct tax rate estimation is only a means to better estimate the wage equation, the problem of collinearity of its two main regressors--wages and consumer prices--is carefully analyzed, and the implications for the wage equations are taken into full consideration. Moreover, the endogeneity bias introduced in the direct tax and the wage equations by the simultaneous presence of prices, wages, income taxes, labor productivity and unemployment, is corrected through appropriate use of instrumental variables.
Cross-country comparability of the estimation results is allowed for by the use of an identical theoretical and econometric model for all European countries and by homogeneous and rich cross-country data set provided in the OECD time series. I/
II. A Testable Model of the Average Direct Tax Rate for Nine European Countries
Let us start by recalling some results reached in Padoa Schioppa (1992). We show there that, if direct taxation 2_/ is progressive and progressivity obtains by charging different marginal tax rates on different wage brackets, the observed average direct tax rate, A, in the absence of fiscal indexation, is a log-linear function of the nominal wage, W (log W is
I/ In fact, the OECD sources are three: the Economic Outlook, the Analytical Data Base, and the National Accounts (Households Accounts in Vol. 2). Further technical details on this empirical evidence are supplied in Appendix A. 2_/It seems convenient to look at all taxes levied on employees, based on their wages, rather than distinguishing personal income taxes (usually progressive) from employees' social security contributions (usually with a flat rate). The direct tax rate, being the sum of the personal income and the social security tax rate of employees, is progressive because it is the sum of a progressive and a flat rate. Due to lack of data, the employees' income tax rate is proxied by the households' personal income tax rate (see Appendix A for further explanations).
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labeled as w). \J If direct taxation is progressive and fully indexed to the price dynamics (the usual case of fiscal indexation), the corresponding observed average tax rate, A, is a log-linear function of the real wage, WR (log WR, labeled wr): this implies that A increases only if the nominal wage rate grows proportionally more than the consumer price index, P (log P = p). Moreover, if direct taxation is progressive and only partially indexed, A is a linear function both of the logarithm of the nominal wage, and (with opposite sign) of the logarithm of the consumer price: the semi- elasticity of A relative to W (labeled as ft) should be in absolute value higher than the semi-elasticity relative to P (labeled as 7). Finally, if direct taxation is progressive and fully indexed to the wage rather than to the price dynamics (as used to be the case in Denmark for example), the observed average tax rate, A, is constant: thus, there exist two possible indexes--the wage rate and the consumer price--relative to which nominal taxes are adjusted to account for undesirable changes in tax rates induced
.I/The model synthetically reported here illustrates how the direct tax rate is related to the wage rate as if all individuals were alike. If there does not exist a representative individual, one can show that under the same conditions of tax progressivity, due to convexities, the aggregate direct tax rate is log-linearly dependent not only on the average nominal wage rate and the price level, but is also positively related to the wage dispersion around the average wage. In our econometric analysis we will not introduce in the A estimation any dispersion index around the average wage for two reasons: cross-country comparable sectoral data on wages exist only in a much smaller time interval than other data on average wages used in the regres- sions (typically, only since 1970)--the time interval since 1970 being too short for testing any sensible wage equation. Moreover, sectoral wages are only proxies of what would really be needed to measure the wage dispersion, namely within-sectors wage rates for different skills; the introduction of the wage dispersion in the A estimation would increase the simultaneous determination of A and W because of the following reason: if on average there exists a tax-push of A on W, that means that, due to progressivity, the top gross wages should grow more than the bottom gross wages when the average direct tax rate rises, determining an increase in wage dispersion, which in turn should raise A for the reasons specified above. Counterbalancing forces, however, exist in many countries, typically unions, which try to set independently the wage level and the wage disper- sion: for example, in Italy it seems that, starting in the mid-1970s for approximately a decade, the unions were able both to raise the average wage rate and to reduce the wage dispersion.
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by inflation; I/ from now on, unless explicitly mentioned, we will analyze fiscal indexation only with reference to this second kind of adjustment rule.
Accordingly, it is shown (Padoa Schioppa, 1992) that the observed average direct tax rate can be described as follows:
with /? > 7; 7 > 0; a of any possible sign but certainly positive if both ft and 7 equal zero. Recalling that the consumer price, p, is a weighted average of the product price, p, and the imported commodity price, pirn (both in logarithm), with weights respectively equal to 7^ and 1 - 7-^, equation (1) can be rewritten 2/ as
These equations represent a nested form, which includes four fiscal subcases:
(1) proportional direct taxation or progressive indexed direct taxa- tion with fiscal indexation obtained by adjusting the nominal tax bill to the wage rate rather than to the consumer price dynamics, with ,9=7=0 : dA/dw = dA/dwr = 0 and A is constant;
(2) progressive direct taxation without indexation in the fiscal system: ft > 0, 7=0; dA/dw = /3 > 0 and A is positively and uniquely dependent on the nominal wage rate;
(3) progressive, fully indexed direct taxation: ft = 7 > 0 and A is a positive function of the real wage rate; this implies dA/dwr = ft and dA/dw = /3[1 - (dp/dw)], with A increasing with the nominal wage rate if the latter
I/ According to the first rule of indexation (to the wage rate), there is fiscal indexation if the direct tax rate remains constant over time, both when the nominal wage varies because of inflation (with constant wr) and when productivity gains arise (with rising wr). According to the second rule (to the consumer price), there is fiscal indexation if direct taxation in real terms remains constant, in the absence of any change in the fiscal setting and in the real wage. Of course, both conditions just mentioned are satisfied when direct taxation is proportional. 2/ In small and very open economies, resident producers may become price takers, with 7^ = 1, p = pirn = p. Otherwise, 0 < 7^ < 1.
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is not fully indexed, but with constant I/ A if there is wage indexation (and dp/dw =1); in general dp/dw and dp/dw range between zero and one, being assumed to be non-negative constants, hereafter labeled 2/ as
(4) progressive, partially indexed direct taxation: ft > 7 > 0 and A is not a function of the real but of the nominal wage rate, besides being a function of the price level; dA/dw - /3 - 7(dp/dw) > 0 because ft > 7 and q < 1. Note that partial indexation in direct taxation should be expected when income brackets are indexed but tax credits or tax allowances identical for every wage earner are not, or when the latter are indexed but the former are not. On the contrary, a full fiscal indexation would arise in a progressive tax system (with ft = 7 > 0) , when both income brackets and tax deductions are indexed or when the former are indexed and tax allowances are set in proportion to the nominal wage of each taxpayer.
Two important analytical properties of the A equation are worth notic- ing. First, when the average direct tax rate is a log- linear function of the nominal wage and the price level, the marginal direct tax rate of the average taxpayer (labeled as N) is simply equal to the average plus a constant. Indeed, given (1) and (3),
Second, when A is a log-linear function of W and P, the well-known progressivity index (see Jackobsson, 1976)
IT _ -i _ 1 ~ marginal direct tax rate _ marginal - average direct tax rate (5) 1 - average direct tax rate I"-"average direct tax rate
I/ Therefore, a flat A would include a case of proportional direct taxation (no relation between A and w or p); a case of fiscal indexation obtained through readjustments of nominal income brackets and tax deductions to the wage rather than to the consumer price dynamics; finally a case of perfect indexation (to prices) both of nominal wages and of income brackets and tax deductions (/3 - 7 > 0 and wr constant) . Notice that in the latter case, unlike in the two previous ones, the constancy of A is not combined with p = 7 = 0. 2/ Remark that q can only be zero if q equals zero.
©International Monetary Fund. Not for Redistribution - 8a - Chart 1 Temporal Dynamics of the Average Direct Tax Rate, of the Nominal and Real Wage Rate1
Source: OECD data described in Appendix A.
1/ The dynamics is relevant while the levels of the direct tax rate, the nominal and the real wage rate shown in this chart are conventional. ©International Monetary Fund. Not for Redistribution - 8b -
Chart 1 Temporal Dynamics of the Average Direct Tax Rate, of the Nominal and Real Wage Rate1
Source: OECD data described in Appendix A.
I/ The dynamics is relevant while the levels of the direct tax rate, the nominal and the real wage rate shown in this chart are conventional. ©International Monetary Fund. Not for Redistribution - 8c - Chart 1 Temporal Dynamics of the Average Direct Tax Rate, of the Nominal and Real Wage Rate1
Source: CECD data described in Appendix A.
I/ The dynamics is relevant while *he levels of the direct tax rate, the nominal and the real wage rate 5h^*n in thK chert are conventional. ©International Monetary Fund. Not for Redistribution This page intentionally left blank
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which ranges between 0 (when the marginal tax rate equals the average, at constant A) and 1 (when the marginal tax rate approaches 100 percent), takes the simple form of
As it will be seen below, we will extensively use the index H in the analy- sis of the wage formation.
Equation (1) can in principle be estimated and, given (4) and (5), both the marginal tax rate and the degree of progressivity of direct taxation can be evaluated for the nine European countries under observation. But three major econometric problems emerge in the estimation of the A equation: a data problem due to the absence of appropriate cross-section, implying that time series data on A, w, p have to be utilized and that dummies have to be used to account for structural changes concerning direct taxation; a simultaneity bias introduced in (1) by the presence of two endogenous variables such as w and p; a multicollinearity bias between the regressors w and p, given the existence in many countries of some form of wage indexation. A fourth econometric problem, the non-stationarity of variables appearing in (1) will not be discussed here, as there is no reason to suspect that the average direct tax rate suffers from non-stationarity on two counts: first, because the average direct tax rate is in any case bounded between 0 and 1; second, because, being a policy instrument, the average direct tax rate is not subject to uncontrolled stochastic errors.
On the first econometric problem, we remark that the marginal direct tax rate, progressivity and fiscal indexation should be measured through cross-section comparisons concerning the observed direct tax rate borne by different taxpayers earning different levels of nominal and real wages. The second best choice of estimating the marginal direct tax rate, progressivity and fiscal indexation through time series aggregate data on the observed average direct tax rate, on nominal and real wages, is based on the hypothesis that fiscal systems are stable across time except for specific years, different in different countries, when a tax reform or major policy variations impose a structural change. The rationale for the structural breaks appearing in our estimation of the A equation is given by a detailed historical and institutional analysis of the European personal income tax systems, provided in Padoa Schioppa, 1992: here we limit our presentation to some synthetical information reported by Table 1 and by Chart 1, below. From the institutional viewpoint supplied by Table 1 and furthermore from the empirical evidence on A, w, wr illustrated by Chart 1, it is noticeable that different European countries follow different regimes and different paths in setting the degree of tax progressivity and de jure or de facto fiscal indexation.
On the second econometric problem of the estimation of the A equation, we recall that the procedure used to estimate A--and the following wage equation--is the instrumental variable technique that corrects the coeffici- ents' values for the biases induced by the presence of jointly endogenous
©International Monetary Fund. Not for Redistribution Table 1. Personal Income Taxes in Europe: An Institutional Perspective in 1988
United Tax Systems Belgium Denmark France Germany Itaxy Netherlands Spain Kingdom Austria Sweden
Personal Progressive Progressive Progressive Progressive Progressive Progressive Progressive Progressive Progressive Progressive incooa tax I/ schedule a. Hasher 25 in 1976 3 13 before 4 ranges of 37 in 1962. 9 in 1974; 16 in 1976; 10 in 1977; 11 in 1975- 8 in 1974; of brackets (2nd 1982; 1* marginal tax 9 in 1983; 10 in 1975, 28 from 1977 11 in 1978; 81; 10 in 11 in 1975; bracket afterwards rates: 6 later 1978-79; to 1980; 7 in 1979; 1982-83 12 in 1976; lump sum first two 13 in 1980; 30 in 1981; 6 from 1981 16 in 1977; tax); flat; third. 10 in 34 from 1983 to 1987, with 15 in 1978; 29 in 1979 pro- 1981/83; to 1982 with a reduction 18 in 1980- (2nd gressive; 9 in 1984-85 a reduction since 1988 81; 15 in bracket Xorth. flat since 1988 1982; 16 in lump sum 1983-84; tax); 11 in 1985-88 2* in 1978-82 b. Minimum 01-601 in 14. 401-39. 60S 01-601 in OX-19X-53X 10X-7ZX in 25X-71X in 15X-62X in 33Z-83X in 23Z-62X in 7X-56X in and maximum 1975-83; in 1973 1975-81; in 1977; 1975-82; 1974; 1976; 1977; 1975-81; 1974-75; marginal OZ-72Z +20.21 OX-65X in OX-22X-56X 18X-65X in 20X-71X in 1SX-65X in 25Z-83X in 21X-62X in 2X-S8X in rate 1978-82; average 1982; in 1986-90 1983; 1975; 1977-81; 1978; 1982-83 1977-79; 01-86.71 in local OX-70.2X in ittm^ifimjgn 20X-72X in 16.14X-66X 30X-60X in 1986 1X-58X in 1986 income 1983-85; rate 76X 1976-79; in 1983: 1980-83; 1980-82; tax rate. OX-58X in in 1985; 17X-72X in 16X-65X in 29X-60X in OX-54X in with small 1986; maximum 1980-83; 1984-85; 1986-87; 1983; changes in OX-56.8X rate 62X 16X-72X in 8X-66X in 27X-60X in OX-50X in the local since 1987 in 1986 1984-85 1986-87; 1987-88 198S tax up to 25X-S6X 1982; since 1988 73X maximum global (central * local) rate in 1985; 6BX ma»JB»» global rate in 198* c. Marginal 44. OX 28.81 25. OX 32. OX 19. OX 31. OX n.a. 34. OX 33.01 29. OX tax rate for SOX of employees J/
©International Monetary Fund. Not for Redistribution Table 1 (Continued). Personal Income Taxes in Europe: An Institutional Perspective in 1988
United Tax Systems Belgium Denmark France Germany Italy Netherlands Spain Kingdom Austria Sweden d. Income No, few Yes , non- Discretion- No, some No, few Dlscre- No, yearly Discretionary No, only two Yes, non- brackets changes since discretionary ary since changes to changes tionarily changes since 1981 changes to discretionary indexation 1979 to in 1973-83; 1969; account for after 1983 adjusted since 1981 but usually account for in 1979-82; account for discretionary partial up inflation to account approxi- to increase enforced inflation discre- inflation thereafter to 1982; since 1977 for mately by progress- tionary full but inflation 60X-80X ivity thereafter still since 1971 discretion- ary later
e. Tax TA, TC TA, TC TA TA TA, TC TA TA. TC TA TA, TC TA, TC credits (TC) and/or tax allowances (TA) 3/
f. Tax No No Yes, with No No No Yes, No No, but sharp Partly fixed allowances ceiling regressive increases in and partly proportional up to 1978 tax credits proportional to income since 1978-79
g. Tax No, few Yes. nondis- No, some No, some No Dlscretion- No , yearly Yes, nondis- No Yes, nondis- credits and changes to creticnary in changes in changes in arlly changes cretionary cretionary in tax account for 1970-83; the ceiling 1979 and in adjusted by since 1979 since 1978 1979-82; allowances inflation discretionary to account 1981 approxi- discretion- indexation thereafter for mately 601- ary there- inflation 801 since after 1971
©International Monetary Fund. Not for Redistribution Table 1 (Concluded): Personal Income lazes in Europe: An Institutional Perspective in 1988
United Tax Systems Belgium Denmark France Germany Italy Netherlands Spain Kingdom Austria Sweden
h . Main 1962: tax 19B7: tax 1983: start 1986-90: 1974: tax 196*: tax 1975: tax 1979: tax 1989: tax 198Z: tax structural reform for reform to of a tax reform reform reform for reform reform to reform to reform for changes in tha intro- enlarge the restruc- program to for the the intro- that enlarge the enlarge the the reduc- the Last 30 duction at tax base turing widen the introducr duction of introduced tax base tax base, tion of years progres- and reduce that in- tax base. tion of tha actual the and lower and top rates sivity. top rates creased reduce the progres- actual reduce top flatten the 1985: tax 1988-89: tax the tax marginal actual sive tax progres- rates marginal reform to reform to base and rates and progres- system sive tax income tax reduce the enlarge the reduced introduce sive tax 1986: pro- system. rates and number of tax has* top rates a linear system. posed 1988: fiscal reduce the brackets and reduce progres- 1983: re- reform reform number of and top top rates sive tax duction with the that brackets V rates */ scale. of number intent to enhanced signif- of simplify progras- icantly brackets th« tax sivity affecting and top structure the third rates income bracket »/
Sourcan: Andarsson, K. (1988), "Tax Rarorroa in Scandinavia during tha 1980s"; Bayor. A (1989), "Un« Evaluation da 1« Raforma Fiscal* »n Bslgiqua"; Lipschitz, L. Kramars. J., May»r, T.. and D. McDonald (1989), "Tha Fadaral Republic of Garmany. Adjustment, in a Surplus Country"; L&paz-Claros, A. (1988), "Tha Saarch for Efficiency In tha Adjustment P-oc«s»: Spain in th« 1980s"; OECD (1976), Tha Adjustment of Personal Incoma Tax Systems for Inflation; OECD (1977), Tha Treatment of Family Units; OECD (1981a>. The Impact of Consumption 7a*«s at Dlftacant tncoma Levels; QECO (1981fa), Inconia Tax Schadulas; OECD (19B6a), An Empirical Analysis of Channes in Peraonal Incoma Tax; OECD (1986b), Tha TaK/B»n»Ut Poattion of Production Workers 1979-84; OECD (1986c). P»r»onal tncom« Tax Syatsma Under Chanitinn Economic Conditions: QECO (19B9a), The Tax/B«n«tit Poaition of Froouction Workarj 1985-83,- OECD (1989b), Taxlnx Conaumptlon; Pachman, J. (1987), Compatativa Tax Syatems: Europ» Canada and Japan: Tanzi, V. (1980), Inflation and th» Personal Incoma Tan; An Int«rnationai. Parspective.
i/ Tha Gannan p»raonal incona tax scb»dula piaaanta an upward sloping marginal tai rat* function for on» of tha incoo» brackata, not a atap function for avary brackat. Z/ All information raf«r to 1981 and only to tha tax rataa leviad by tha cantral ftovarntnant. Tha distinction is particularly Important for sona countriaa: for exampla. In Swadan local govarnmant incca>a taxas ara laviad at a flat rata of about 30 parcant. 3/ Data includa incoma and nonincoma ralatad tax sllcmancaa and tax cradita with tha «xc«ption of Danmark whoaa tax allowancaa ara only incoma ralatad. y Significant changaa in tha incoma tax systoma hav* takan placa in tha 1960s and in tha 1970s in Garmany, in Austria, and in Smdtn.
©International Monetary Fund. Not for Redistribution - 13 -
variables. In particular, inasmuch as it concerns the average direct tax rate equation, both regressors w and p are probably jointly endogenous with A. Indeed, the wage rate, w, as will be seen below, is determined by many regressors, including A and p; at the same time, the consumer price, p, may be considered jointly endogenous, too. The natural choice of instruments for the variable w is clearly represented by the exogenous variables of the wage equation and by the additional instruments used there. !_/ The selection of instruments for the variable p is more subtle since no theoretical model for the consumer price equation is formulated in this paper. The choice is then arbitrary, falling on the GDP deflator of the whole set of OECD countries, on the imported commodities price (actual and lagged) and on the lagged product price, all supposed to be exogenous.
Finally, concerning the multicollinearity problem, in the estimation of the A equation (1) , it is possible to evaluate ft and 7 separately only if wages and prices are not correlated and collinear. In practice this is not always the case. Therefore, our econometric analysis is realized in two steps. In step 1. equation (1) is estimated. If the estimation shows ft > 0 and 7 > 0 [case (a)], there is no reason to suspect the presence of colline- arity; therefore, dp/dw = q is assumed to be zero. However, if j9 and 7 are both insignificant or wrongly signed in the first step, the presence of multicollinearity becomes very likely (q > 0) and therefore step 2 is needed, where the two following estimations are performed
A
and
Let us notice that z is exogenous as are the constants a and 3; the constant /3 equals /3 - 7q , while the constant 7 equals (/3/q) - 7- Two possibilities then arise with regard to the estimates of /3 and 7, which lead to four different econometric solutions for the average direct tax rate: either /3 and 7 are both zero, or they are both positive.
A If both /3 and 7 are zero, that means that the progressivity index H is zero, A is flat and may appear only as an exogenous variable in the wage equation. Two subcases are relevant. In case (b) A is constant because p = j = o and q < 1: this happens when direct taxation is proportional or when it is progressive but indexed to the wage, not to the consumer price dynamics. In case (c) /3 = 7 > 0 and q = 1: in this event, A is flat because the real wage is constant and there exists full fiscal indexation,
I/ Of all the additional instruments appearing in the wage equation, we use as an instrument of w in the A equation only the sum of the employers' social security tax rate and of the indirect tax rate, both supposed to be flat rates.
©International Monetary Fund. Not for Redistribution - 14 -
but while in case (b) the wage equation is the very general one (discussed below), here the proper wage equation is constrained by the condition q — 1.
A A AIf ft and 7 are both positive, two subcases arise: (d) either 0 - 7 or (e) ft < y. In the former case (d), the result is only possible for q = 1 which in turn implies ft > 0, 7 > 0 and /3 > 7: thus, direct taxation is progressive and certainly not fully indexed (A is endogenous and dependent both on w and on p), while the real wage rate, given q — 1, is exogenous and independent of the average direct tax rate and gn any other endogenous variable. On the contrary, case (e), with 0 < ft < 7, implies q < 1 within three unidentifiable situations, namely ft > 0, 7-6; /3 > 7 > 0; £ - 7 > 0. As we will see below, this lack of identification is irrelevant in the estimation of the wage equation because only the estimated value of ft is needed there.
Let us now be more specific about the estimation of the A equation. Step 1 is characterized by the instrumental variables estimate of (1). The estimated coefficients ft and 7 for the nine countries under observation are reported in the second and third column of Table 2a; t-statistics are pre- sented in parenthesis under the coefficients. Only for very few countries and time spans, these estimated coefficients are consistent with the theo- retical model underlying equation (1). These are the countries and time periods for which case (a) described above is applicable, namely Germany in 1977-88, Italy except in the interval 1975-82, the Netherlands in 1967-80, the United Kingdom, Austria in 1960-78, Sweden in 1972-87. For the remaining countries, either ft and 7 are both insignificant, or they have signs inconsistent with the theory, a fact that can be interpreted as a sign of the high degree of collinearity that characterizes the behavior of the two regressors w and p.
According to this interpretation, if no collinearity exists, i.e., q = 0, the coefficient (ft - 7q)--whose estimates are presented in the fourth column of Table 2a--coincides with the estimated coefficient ft. However, if some multicollinearity arises and q > 0, step 2 proceeds to the estimation I./ of equation (7)--whose results are shown in the first and fourth column of Table 2a: the usual statistics and tests reported by columns 6-7 of Table 2a and by columns 1-2 of Table 2b refer to this basic
I/ In the estimation of the A equation, some serial correlation was originally emerging in the estimated regression errors; further tests clarified that such a serial correlation was of the first order in the case of France and of the first and fourth order in the case of Germany. In the United Kingdom two corrections were necessary: the first of the first, third and fourth order; the second of the first, second and fourth order. Fair correction for serial correlation depurated the coefficients' esti- mates, presented in Table 2a, of inconsistencies due to serial correlation.
©International Monetary Fund. Not for Redistribution Table 2a. Estimates of the Average Direct Tax Rate Equation in Nine European Countries, 1960-88
Regressors
Constant "T PT WT PT . a f -7 0"tq*/3 0/q-T-T R2 DW Countries
Belgium -0.275 * (D60-78) 0.037 * (D60-78) 0.145 * (D60-78) 0.086 * (D60-78) 0.172 * (D60-78) 0.99 1.58 (1960-88) -18.30) (1.81) (3.00) (30 .20) (32.24) + + + + + -0.043 * (D79-88) -0.185 * (079-88) 0.127 * (D79-88) 0.050 * (D79-88) 0.043 * (D79-88) SER - 0.007 (-0.44) (-0.08) (0.72) (3 .34) (3.17)
-0.812 * (D66-69) -2.69 * (D66-69+ 4.334 * (066-69+ 0.321 * (D66-69* 0.480 * (D66-69+ 0.89 1.66 Denmark (-2.84) (-1.34) +DB4-88) (1.51) +084-88) (3 .73) +D84-88) (3.98) +084-88) (1966-88) + + •f + + 0.300 * (D70-83) -0.149 * (D70-83) 0.175 * (D70-83) 0.012 * (D70-83) 0.014 * (070-83) SER - 0.016 (7.27) (-0.60) (0.65) (1.24) (1.31)
-1.219 * (D84-88) (-2.80)
France 0.209 * (063-68+ 0.220 * (063-68+ -0.225 * (063-68+ 0.055 it (D63-68+ 0.069 * (D63-68+ 0.95 1.56 (1963-88) (37.54) +083-88) (1.12) +D83-88) (-0.87) +083-88) (17 .44) +D83-88) (15.50) •1-084-88) + + + + •t- 0.189 * (D69-82) -0.249 * (D69-82) 0.396 * (D69-82) 0.050 * (D69-82) 0.064 * (D69-92) SER - 0.005 1 (37.57) (-2.36) (2.80) (17 .74) (11.26)
Germany 0.061 * (D60-76) -0.104 * (D60-76) 0.383 * (D60-76) 0.074 * (D60-76) 0.164 * (060-76) 0.92 1.69 (1960-88) (3.80) (-5.31) (8.67) (8.62) (12.90) + + + + 0.065 * (D77-88) 0.071 * (D77-88) -0.062 * (D77-88) 0.071 * (D77-88) not defined SER - 0.006 (3.02) (7.77) (-1.97) (7 .77)
Italy -0.013 * (D60-74) 0.052 * (060-74+ -0.066 * (060-74+ 0.052 * (D60-74+ not defined 0.99 1.46 (1960-85) (-0.29) (3.87) +DB3-85) (-2.34) +083-85) (3.87) +D83-85) + + + + 0.009 * (D75-82) -0.246 * (D75-82) 0.374 * (D75-82) 0.071 * (D75-82) 0.084 * (075-82) SER - 0.004 (1.22) + (-1.77) (2. 28) (19 .34) (20.31) 0.106 * (D83-85) (4.49)
©International Monetary Fund. Not for Redistribution Table 2a (Concluded). Estimates of the Average Direct Tax Rate Equation in Nine European Countries, 1960-88
Regressors
Constant at R2 OH Countries
Netherlands -0.481 * (067-80) 0.237 * (067-80) -0.222 * (D67-80) 0.237 * (067-80) not defined 0.93 1.51 (1967-88) (-1.57) (2.85) (-1.78) (Z.85)
0.385 * (D81-88) -0.682 * (D81-88) 0.785 * (081-88) 0.005 * (081-88) 0.0*0 * (081-88) SER " 0.012 (1.05) (-1.25) (1.29) (0.05) (0.36)
United 0.228 * (060-78) 0.047 * (060-78) 0.016 * (060-78) 0.0*7 * (060-78) not defined 0.9* 1.73 Kingdom (4.07) (2.71) (1.23) (2.71) (1960-88) •f 0.231 * (079-88) 0.028 * (079-88) -0.027 * (079-88) 0.028 * (079-88) not defined SER - 0.005 (4.73) (1.65) (-1.79) (1.65)
Austria 0.121 * (060-78) 0.069 * (060-78) -0.045 » (060-78) 0.069 * (060-78) not defined 0.9* 1.76 (1960-87) (-0.64) (1.77) (-0.61) (1.77) •t- 0.150 * (079-87) -0.035 * (079-87) 0.062 * (079-87) 0.017 * (079-87) 0.021 * (079-87) SER - 0.008 (1.4*) (-0.24) (0.36) (0.85) (0.89)
Sweden -0.138 * (D60-71) 0.153 * (060-71) -0.025 * (060-71) 0.138 * (060-71) 0.230 * (060-71) 0.97 1.98 (1960-87) (-4.38) (0.66) (-0.06) (13.14) (12.15) •h -0.4*3 * (072-87) 0.189 * (072-87) -0.147 * (072-87) 0.189 * (072-87) not defined SER - 0.007 (-1.55) (2.74) (-2.34) (2.74)
©International Monetary Fund. Not for Redistribution Table 2b. Estimates of the Average Direct Tax Rate Equation in Nine European Countries, 1960-88
Estimated Marginal Direct Tax Rate (Ne-Ae+0> \l Estimated Progressivity Index Test on 0—7 or on [He"0/(l-Ae)] 2/ 0-1 when 7 is not defined Test on 0 Stability (with probability Countries (With probability 951) 951) 1965 1970 1975 1980 1985 Consequences for the Wage Equation
J3>0;7-0 U(w). q
Denmark ,8* (066-69+084-88) 0<0<7 3/ (66-69 Ne 4/ 0.509 0.351 0.351 0.351 0.702 1966-69 0>0;7-0 U(w) q France 0*(D69-82)-0*(D63-68+ 0<0<7 (63-68 N" 0.213 0.222 0.235 0.278 0.328 1963-68 |0>0;7-0 U(w), q /J>0;7-0 U(w). q 0>0;7-0 U(»), q e Italy 0*(D60-74+D83-85) 0-7>0 (60-74 N 0.148 0.161 0.177 0.243 0.271 1960-74 (1960-85) -0*(D75-82) 83-85) : 0-7>0, A(wr), 1983-85 0>0;7-0 U(w). q e Netherlands 0*(D67-80)i»0*(D81-88) 0-7>0 (67-80) N I/ 0.481 0.542 0.594 0.613 0.402 1967-80: /3"7>0, A(wr), (1967-88) |0-7>0, q-1 e 0-7-0 (81-88) H 0.313 0.341 0.368 0.379 0 1981-88: j A-const. 10-7-0, q ©International Monetary Fund. Not for Redistribution Table 2b (Concluded). Estimates of the Average Direct Tax Rate Equation in Nine European Countries, 1960-88 Estimated Marginal Direct Tax Rate (Ne=Aa+0) I/ Estimated Progressivity Index Test on £-7 or on [H8-/9/U-Ae)l Z/ 0«7 when 7 is not defined Test on ft Stability (with probability Countries (With probability 95Z) 951) 1965 1970 1975 1980 1985 Consequences for the Wage Equation United 0*(D60-78)-3*(D79-88) 0>0 ; 7-0 (60-78) N8 6/ 0.279 0.281 0.296 0.244 0.241 1960-78: 0>0;7-0; A(w) Kingdom 8 (1960-88) 0-1>0 (79-88) H 0.061 0.061 0.062 0.036 0.036 1979-88: P-1>0; A(wr). e Austria 0* 0X1-.1-0 A(w). q 0-l>0 (72-87) H« 0.187 0.200 0.281 0.287 0.289 1972-87: 0~1>0; A(wr), I/ The estimated marginal direct tax rate, labeled as Ne, equals the estimated average direct tax rate (A8) plus 0. Notice that the estimated marginal direct tax rate concerns the marginal rate paid by the taxpayer, earning the average wage. The value of A8 is obtained through a static simulation of equation (1), where the coefficients a. 0, ^ are illustrated in the first four columns of this table. When 0 and 7 are both estimated to be zero (Denmark in 1970-83, Netherlands in 1981-88, Austria in 1979-87), the estimated value of a is reobtained after imposing on the estimation the constraint on £-7-0. 2/ The estimated progressivity index, labeled as H8, equals the ratio between the coefficient 0 and one minus the estimated average direct tax rate (A8). 3/ In Denmark the hypothesis 0*1 in the period 1966-69 and 1984-88 is accepted with probability 81 percent. V In Denmark the first year for which an estimation exists is 1966, because the data are not available before. V In the Netherlands the first year for which an estimation exists is 1967, because the data are not available before. 6/ In the United Kingdom the first year for which an estimation exists is 1968 due to lags in the estimated equation (1). ©International Monetary Fund. Not for Redistribution - 19 - estimation. Step 2 leads also to the estimation of equation (8), whose results are shown in the fifth column I/ of Table 2a. A The estimation of y3 in column 4 of Table 2a is of particular importance both for the estimation of the marginal direct tax rate (Ne) and the progressivity index (tfe), reported by column 3, and for the estimation of the wage equation, as hinted by column 4 of Table 2b. We also test the stability of /3 over time, as indicated by column 1. De facto fiscal indexation is observed only ,when the estimated values of ft and 7 are identical: while a test on ft = 7 is reported by column 2 of Table 2b, this same column indicates that in most cases a test is only possible on /3 and 7. To understand why, we recall our previous discussion on cases (b), (c) , (d), (e) which hold true when some collinearity exists betweenAw and p (q > 0). In particular, let us assume that HQ is ft = 7, with R^: p < 7. If HQ is rejected, necessarily q is smaller than 1, as in (e) above. It appears from column 2 of Table 2b that this is the situation of Belgium in 1960-78, Denmark except in the period 1970-83, France, Germany in 1960-76, Italy in 1975-82, and Sweden in 1960-71. If the hypothesis HQ is not rejected, the following next test is performed assuming that HQ is {! = 7 = 0 with H^: {) = 7 > 0. Then, either HQ is not rejected and therefore A is constant (which is the case of Denmark in 1970-88, of the Netherlands since 1981 and Austria since 1979, as in (b) and (c) above), or HQ is rejected, as in case (d) above; the latter is the Belgian situation since 1979. All these estimates and tests have important consequences and impose various constraints on the wage equation. In order to appreciate the economic meaning of the econometric results obtained in Table 2, it is useful to refer, for an immediate intuition, to Chart 1. There a plot of A, w and wr for each of the nine European coun- tries under examination enables us to "observe" the degree of progressivity, and de facto indexation of each country's direct tax system, as well as their changes over time. As expected from the short description of the scheduled personal income tax system supplied by Table 1, in Belgium the direct tax rate, A, shows in Chart 1 a structural break around 1979. At that time the strong positive correlation apparent in previous years between A and the nominal wage rate, w, becomes weaker, while the correlation with the real wage rate, wr, seems to become stronger. Interestingly enough, the econometric analysis in Table 2b confirms the opportunity to fix at 1979 a structural break for A, while showing that ft (in column 1) and the progressivity index (in column 3) have declined since then, within a fiscal system partially indexed (with /9 > 0 and 7 > 0 as indicated in column 4). Therefore, in the 1980s, A remains a \/ When q = 0, no estimate is presented for the coefficient (fi/q - 7) which is in fact undetermined. ©International Monetary Fund. Not for Redistribution - 20 - function of the nominal wage rate but q equals 1, meaning that the real wage becomes approximately constant and independent of A. Given the particular form of the legal income tax indexation in Denmark during the interval 1970-83, it is not surprising to see from Chart 1 that Denmark presents a flat direct tax rate in that period, while before 1970 and after 1983 the direct tax rate is increasing presumably with some correlation with w and wr. The estimation results for A, presented in Table 2A precisely point out that the Danish direct tax system had a much higher ft, hence a higher degree of progressivity before 1970 and particular- ly after 1983, being fully indexed to the wage dynamics in the interval 1970-83. The introduction in France of a partial legal indexation in the person- al income tax system, starting in 1969, is indicated by Table 1 and is also observable in Chart 1. This innovation and the "Thatcherian" fiscal changes adopted since 1983 determine the structural breaks appearing in our regres- sion results presented in Table 2: but the French direct tax system seems to have probably benefitted de facto from some form of partial indexation in the whole period under observation, while ft and the degree of progressivity have not remarkably changed within and outside the time interval 1969-82. Germany, as expected from the analysis conducted in Padoa Schioppa (1992) and synthesized in Table 1, is a country where legal indexation is prohibited, but according to our econometric results reported by Table 2, de facto fiscal indexation has obtained since 1977 (possibly even before), through frequent, small changes in the personal income tax system; moreover, /9 and the degree of progressivity of direct taxation have not been essen- tially modified in the last decade: Chart 1 intuitively confirms the validity of these estimates. As shown by Table 1, in 1975, a fiscal reform largely increasing the progressivity of personal income taxation was enforced in Italy. In 1983, however, a kind of "Thatcherian" structural change was introduced, that decreased the number of income brackets, reduced top marginal tax rates and broadened the tax base. AAs a consequence, according to our estimates illustrated by Table 2, ft and progressivity sharply grew between 1975 and 1982, declining later, while de facto fiscal indexation has obtained since 1983 through the adjustments for inflation mentioned above: these econometric results are intuitively confirmed by Chart 1. The Thatcher fiscal reform appears (from Table 1, Chart 1 and from the estimations of Table 2) to have implied in 1979 a structural break of the United Kingdom's direct taxation. According to our econometric results, the direct tax system was highly progressive and de facto not indexed at all before 1979, while becoming less progressive and fully indexed in the later years. Table 1 tells us that in the Netherlands, the personal income tax schedule has been legally but partially and discretionarily indexed since ©International Monetary Fund. Not for Redistribution - 21 - the beginning of the 1970s. Therefore, it is not surprising to observe from our econometric results and from Chart 1 that in this country a correlation between the average direct tax rate and the real wage has de facto existed in the whole period under consideration. The same Chart 1 and Table 2 indicate that the reduction in the number of income brackets and in some of the marginal income tax rates decided in 1981 (see Table 1) have produced around that year a main change in the determination of A which, in fact, became constant after 15 years of almost uninterrupted increase. Our econometric results further illustrate that ft and progressivity have dramat- ically decreased since 1981. The Austrian direct tax system seems from Chart 1 and from the econometric results reported by Table 2 to have been affected by a structur- al break around the end of the 1970s, so that /3 and progressivity sharply declined in the 1980s, as in the Netherlands, while fiscal indexation (nonexistent before) was de facto adopted around that year through fine- tuning fiscal adjustments, though remaining, as in Germany, ex lege prohib- ited. Finally, the splitting of the family income as a base for personal income taxation, decided in Sweden in 1971, explains why Chart 1 and our econometric results of Table 2 show a structural break of the average direct tax rate at the beginning of the 1970s, when fiscal de facto indexation was introduced even if legal indexation was adopted only in 1979 by the Conser- vative government. Unlike in other European countries, in Sweden, however, according to our econometric results, the degree of progressivity of direct taxation kept rising over time, so that it consistently remained among the highest in Europe (today being second only to the Danish degree of progressivity). Ill . A Microeconomic Model of Tax Shifting on Optimum Wage Setting What is the influence, if any, of each country's fiscal system and of its main structural changes on wage formation? In order to answer to this question, we construct a microeconomic model of wage determination to derive a testable macroeconomic wage equation (which generalizes the results obtained by Padoa Schioppa, 1990). We suppose that in each firm a monopoly union chooses the wage rate under the constraint of the perceived firm's labor demand. Thus, the union's optimal program is max U(SR, L; . . .SR*. . . (9) (W) s. t. (1) and s.t. ©International Monetary Fund. Not for Redistribution - 22 - with q defined in (3) and The union's objective function, U, depends positively on the net real wage, SR [SR » W(l - A)/P] , on the employment level, L, and possibly on some parameters described in the U function by a few dots after the semicolon, the most important of which is SR* (SR* is the net real reservation wage related to the full employment net real wage, as specified below). The maximum is constrained by the firm's elasticity of labor demand to wage, as perceived by the union, labeled 77 [in this paper we consistently use small letters to indicate logarithms and capital letters to indicate natural values (for example, t «• logL, sr e logSR) ] ; rj is non-positive under the usual hypothesis on the production function, F, with F^ > 0 and F-^ < 0, provided q, which is the elasticity of product prices relative to the wage rate, as perceived by the union, is a non-negative constant ranging between 0 and 1. This maximization deserves four comments. First, the constraint on \/r\ is directly derived from the marginal productivity condition where, by definition, TW = [ (1+S) (1+T)/(1-A) ] [P/P] and CR ^ W(1+S) (1+T)/P. In (10) the marginal product of labor, F^, equates the real labor cost, CR, multiplied by one plus the mark-up (the mark-up equaling M - 1; P is the product price at market value, comprehensive of the indirect tax rate, T; S is the social security tax rate paid by the firm; S and T are both flat rates). In (9.2) 1/fj is perceived by the union as a function only of L, because the union assumes fixed capital and constant mark-up. From (10) we deduce where the (logarithm of the) tax wedge, tw, is approximated by S + T + A, while in a more comprehensive definition the enlarged tax wedge, tw, also includes the logarithmic difference between the consumer and the product prices, both at market values (hence, tw = tw + p - p) . Second, by definition, the net real reservation wage, being the net real wage holding at full employment, is SR* = W* (1 - A*)/P* (where the stars indicate the full employment level of each variable). In fact, we may calculate the value of the real wage rate that would make the full employ- ment marginal product of labor equal to the real labor cost times one plus the mark-up, under the hypothesis of constant capital and mark-up. Labeling as F* such a full employment marginal product of labor [i.e., ©International Monetary Fund. Not for Redistribution - 23 - st FL = FL(LF) with LF defined as the exogenous labor supply], we derive which determines W*/P* and therefore W*/P*, the difference between P* and P* being known and exogenous [see the discussion about equation (2)]. By analogy with (10.1), we obtain from CIO.2) where tw is the tax wedge expected to hold at full employment, and tw* is the corresponding enlarged full employment tax wedge. Given that S and T are supposed to be flat tax rates, one can prove: \J where H is defined above in equation (6). Notice from (10.4) that, ceteris paribus, the enlarged tax wedge tw at full employment is lower than the observed tw, the higher is the progressivity index of direct taxation, H. The third consideration concerns the way in which (9.1) and (10.2) are formulated, which implicitly contains a very important hypothesis. The price elasticity to wages, which is relevant in the computation of the elasticity to wages of labor demand as perceived by the union, is derived from the information contained in the fiscal system. In particular, we suppose that the union knows the average direct tax rate function (1), hence the parameters a, ft, 7, sets w and observes the realized level of A, thus ]_/ Using a linear approximation for p - p, from one gets which appears in formula (10.4). ©International Monetary Fund. Not for Redistribution - 24 - inferring dp/dw if 7 * 0. We further assume that the union takes dp/dw to be exactly the value emerging from the direct tax system and calculates q = (dp/dw) = (dp/dw)/7i = q/7|. That is to say that the union takes dp/dw to be zero if the fiscal system is not indexed at all, .!/ with 7=0, or if it is indexed but dp/dw in the tax system appears to be zero. If the latter condition does not hold and the tax system is fully or par- tially indexed (7 > 0), the union observes through the fiscal system the impact on prices of its wage setting and therefore exactly forecasts dp/dw > 0. This leads us to our last comment. While the union knows the average direct tax rate equation (1), we do not; therefore, we have to estimate it. Three points are worth stressing. In the estimation, as illustrated above, it turns out that our knowledge of the average direct tax system is (al- most) 2/ as complete as the one of the union if q = q = 0 and the system is progressive. In fact, in this event /3 > 0 and 7 > 0 can be estimated [as in case (a) above]. On the contrary, if q and q are different from zero,A only some inferences on j3 and 7 are possible, based on the estimation of ft and 7 [as in cases (b), (c), (d), (e) above]. However, it is already apparent from (10.4) and will appear even clearer below, that only the estimate of ft and 7 is needed for the full specification of the union behavior and the wage equation. After these four comments, let us go back to the union maximization of (9) subject to (9.1). This requires: which can be reformulated as where I/ It is only natural to suppose that, if the tax system is not indexed at all (7=0), this institutional "myopia" is combined with an individual "myopia", even though the realized consumer price elasticity to wages may be different from 0. 2/ It remains less good because of the presence of estimation errors. ©International Monetary Fund. Not for Redistribution - 25 - By definition, E equals the elasticity of the net real wage to the nominal wage, and is inversely related to our basic progressivity index H, depending on ft , 7, q. By definition, I is the percentage increase in the net real wage necessary to maintain constant the union's utility for a given percentage reduction in employment; it represents the union's rate of substitution between the net real wage and employment, indicating, in absolute value, the weight assigned by the union to employment relative to that assigned to the net real wage. Looking at the taxonomy of the union utility functions usually considered in the literature, it appears that three possibilities (mutually exclusive) on I hold true: (A) I is constant; (B) I is increasing with SR and independent of SR*; (C) I is rising with SR, but decreasing with SR . The functional dependence of I on SR indicates a reduced form because , in general, I is a function of two variables, SR and L, besides being possibly dependent on SR . However, through the connection between SR and L established in (10), I may be treated uniquely as a function of SR, or of L, besides being possibly dependent on SR*. The important hypothesis on I is that it is not on the whole an increasing function of L. Not only does this assumption appear more sensible because the relative weight assigned by the union to employment is unlikely to decline at lower levels of employment but, combined with our technological and fiscal hypotheses, it also ensures the existence and the uniqueness of the union's interior maximum (see Padoa Schioppa, 1990). Condition (11) implies that the optimum nominal wage is set at a level that equates the firm's trade-off between wage and employment, as perceived by the union, with the union's trade-off between those variables: (1/f?) = -(I/E); moreover, in this situation the union perceives a gain from the increase in employment offered by the firm consequent upon a reduction in wage. Any union's optimum selection of the nominal wage rate (call it w) can be transformed into anAoptimum implicit union's choice of the expected employment level (call it J? ) so that the maximum U can be expressed in terms of i or w. Now we wish to examine the impact of fiscal parameters A,AS, T on the selected optimum wage w and on the implicit union's choice of I . To do this exercise in comparative statistics, we rewrite (11) as where U^ and U^ are the first and the second derivatives of the union's objective function relative to t in H = i . Remark that equation (11.3) is relevant only for 0 < q < 1, hence for 0 < q < 1. When q = 1, equation (11.3) is not defined. Fortunately, we do not need a very elaborate analysis on the wage equation when q = 1. This condition itself indicates that the product wage, (i.e., the real wage ©International Monetary Fund. Not for Redistribution - 26 - deflated with the product price at market value) is a constant or only depends on exogenous variables (like pirn, S or T, generally not A). When, on the other hand, q - 1, that means that the real wage deflated by the consumer price is constant or only a function of exogenous variables. If, in this event, A is also constant because direct taxation is progressive and fully indexed, then the wage equation can be formulated in terms of a net real wage target. From now on, unless otherwise mentioned, we will only discuss cases where q < 1 and therefore q < 1. From (11.3) we observe that a change in any fiscal^parameter (call it X) modifies £he optimum £ by dl/dX ~A-(Ugx/U^) , where U^x is the partial r an derivative 3Ug/3X: given U^g < 0, dt/dX. has the sign of Ugx i f° y X, i.e.,X=AorX=SorX=T. On the contrary, using (9.1) and (10), we obtain A where the sign of dw/dX is certainly opposite to Ugx only for X = A, (Ujjg and T] being both negative), while some ambiguity remains in the sign of dw/dS and similarly of dw/dT. A A Looking at (11.3), we understand that dH/dS = dt/dT because neither E nor r] vary with S or T and because S and T have an identical impact on I: both the net real reservation wage and the net real wage depend on the sum (S + T). AA similar argument explains why d£/dA is also equal to d£/dS = dH/dl when A is flat. Consequently, if all tax rates are flat, the only fiscal parameter possibly relevant for I is the tax wedge, tw, while E is constant. It follows from our discussion and from (11.4) that dw/dS = dw/dT and both are equal to -1/(1 - q) + (dw/dA)Awhen A is flat. Indeed if every fiscal parameter has the same impact on i , it necessarily has the same effect not on w but on the real labor cost. Obviously, when direct taxation is progressive, the consequence on i of a variation in A is differentAfrom that caused by a change in S or T: in this case, E depends on A and /9, and 3sr/3A < 3sr /3A because an increase in (the exogenous component of) A reduces E, reinforces progressivity and shortens, ceteris paribus, the difference between sr and sr . The technical details of these results are given by the three following subsections: the uninterested reader is invited to skip 1, 2, and 3, and go directly to Chapter IV, relying for the basic intuition on the explanations supplied in the Intro- duction. ©International Monetary Fund. Not for Redistribution - 27 - 1. The compensation effect (of S. T, and flat A) First, we remark from (10.1), (10.3), (10.4) that Therefore, if (and only if) A .is. a flat tax rate. given that .S and T are always flat tax rates. we deduce from (11.3), (11.4), (11.5), Hence the tax wedge is the only relevant fiscal parameter for the choice of ? when A is flat. In this event, depending on whether In interpreting (12) and (12.1), we remark that if A is flat and the weight, I, assigned by the union to employment relative to the net real wage is constant or remains unchanged following upon a variation in the taxA wedge, [(9i/3sr)= -(di/dsr )], the implicit optimum employment level, £, does not vary with the tax wedge; in this event, wage setting, w, is inde- pendent of direct taxation, while the union reduces the nominal wage when S rises or passively accepts the increase in the product price at market value when T increases, in order not to reduce the employment level, which is negatively correlated to the real labor cost. Then, we say that the compen- sation effect is zero. If I declines as a consequence of an increase in the tax wedge, the compensation effect is positive, the real labor cost rises with the tax wedge. The opposite holds true when I increases. Thus, when A is flat, w is independent of direct taxation and the real labor cost is independent of the tax wedge if I falls under case (A). If / falls under case (B), the real labor cost rises with a higher A, S, or T. ©International Monetary Fund. Not for Redistribution - 28 - If I falls under case (C), the real labor cost may increase, decrease or remain constant, depending on the relative influence of sr and sr* on i: it remains unchanged when I depends only on the ratio of SR to SR*. 2. The progressivity effect (of a progressive A) When direct taxation is progressive, it becomes possible to distinguish the wage effects of a change in the marginal and in the average direct tax rate. We examine first a change in the marginal direct tax rate, for given average, recalling that the former equals the latter plus /3-7q. This amounts to examining movements in (/3-7q) = ft, at constant A (therefore a has to vary as well). By the usual procedure, we get A with dH/dfi — 1/(1-A)>0. According to (13), an increase in the marginal direct tax rate, for given average, tends to increase i if the weight assigned by the union to employment is unaffected by the perceived net real reservation wage (3i/dsr* = 0), being r;<0. In this event, which arises when I falls under cases (A) or (B), the progressivity effect is said to be negative. The latter effect may remain negative even if I falls under case (C) and is negatively influenced by SR , but two counterbalancing factors are then at work. On the one hand, as in the previous cases, the rising marginal tax rate makes the nominal wage benefits less desirable than the employment benefits, providing an incentive to reduce the nominal wage rate; on the other hand, in the absence of movements in the nominal wage rate, the rising marginal tax rate would diminish the gap between the net real wage and the net real reservation wage, supplying an incentive to increase the nominal wage rate, if the union cares about "relativities". In general, when I falls under case (C), the progressivity effect can be positive, zero or negative. Therefore, the sign of the wage elasticity to the marginal direct tax rate, given the average tax rate, is the sign of the progressivity effect, being if I falls under cases (A) or (B) because the progressivity effect is negative; (13.1) if I falls under case (C) because the progressivity effect can be negative, zero or positive. (13.2) 3. The effects of a change in A when the average and the marginal direct tax rates vary together Consider now the consequences of a change in the (exogenous component of the) average direct tax rate when the average, A, and the marginal, ©International Monetary Fund. Not for Redistribution - 29 - A + /3 - -yq, vary together. The analysis of the impact of A on w may be logically divided in two parts: one concerning the effects of the modifica- tion in the average direct tax rate for given marginal (as if A were flat) and one concerning the implications of the change in the marginal direct tax rate for a given average (as if /3--yq varied but A were fixed) . We thus expect the compensation and the progressiyity effects to be the relevant factors in explaining the semi-elasticity of (. and w relative to A, when the average direct tax rate^is progressive. Indeed, from (11.3), (11.4), (11.5), we derive that d£/dA has the sign of the second term on the right hand side of (14) exactly corresponds to the compensation effect; the first is proportional to the progressivity effect. Formula (14) is a very general one, holding true in all three subcases of progressive direct taxation mentioned above (non-indexed; partially indexed; fully indexed) and in the case of a flat direct tax rate [where H = 0 and only the compensation effect is at work, as in (12)]. Therefore, when direct taxation is progressive, a change in A affecting both the average and the marginal direct tax rates implies if I falls under case (A) because the compensation effect is absent and the progressivity effect is negative; in this event the unemployment rate, connected to F£, does not appear in the wage equation; (14.1) if I falls under case (B) because the compensation and the progressivity effects work in definite but opposite directions, the former being certainly positive, the latter being certainly negative; in this event, the unemployment rate does not appear in the wage equation; (14.2) when I falls under case (C) because both the compensation and the progressivity effects have uncertain signs; in this event, the unemployment rate certainly enters as a regressor in the wage equation with a negative sign (as indicated below). (14.3) If the progressivity effect is negative, an increase in the (exogenous component of the) average direct tax rate, automatically raising the margin- ©International Monetary Fund. Not for Redistribution - 30 - al, leads to fixing the wage rate at a lower level than would be set, were the direct tax rate flat or were the marginal tax rate kept constant. The wage elasticity to the progressive direct tax rate can be higher than (or equal to) that to the flat direct tax rate only if I falls under case (C), because only then can the progressivity effect be positive (or zero). IV. A Testable Model of the Wage Setting for Nine European Countries We will now try to obtain from the microeconomic theoretical model discussed so far a nested, macroeconomic testable model of wage setting for the European countries under review, on the assumption that the technology is a CES with elasticity of substitution between capital and labor smaller than one (a < 1). We then rewrite the optimum condition for wage setting, (11), as where 72 i-s perceived by the union as a positive constant, (with -^2 = M-'-'^Q^ and a-^ denoting the multiplying coefficient of labor in the CES production function). By a log-linear approximation, I/ (15) can be transformed into where Supposing that log I = i is a log-linear function of its arguments, then i is constant under case (A), it is a positive multiple of sr under case (B), it is positively correlated to sr and negatively correlated to sr I/ The approximation goes as follows. Taking the logarithm of (15), one obtains where -loga(l - q) is labeled as //" and is certainly positive because a < 1, and 0 < q < 1. If q = 1, the wage equation is not identified through (15) but through a different equation specified elsewhere. Taking again the logarithm of the LHS and the RHS of the equation, one gets (15.1), by the usual logarithmic approximation. ©International Monetary Fund. Not for Redistribution - 31 - under case (C). Then, when these nested hypotheses are embodied in the general model (15.1), recalling (10.1)-(10.4), we use to identify the form of the union's rate of substitution between the net real wage and employment. Remark that in (15.2) (ft = ^/(l - q) is positive while 62 a &l/(\ - thus, <5i is positive both under cases (B) and (C) and is zero in case (A), while 2>2 is positive only under case (C) and zero otherwise. In the CES production function we derive the full employment marginal product of labor as where nrg - -logo^ > 0. To estimate (16), however, we have to evaluate y* and (y - £f), namely the logarithm of the full employment level of output and the full employment average productivity of labor which are not observable. Supposing Y - F[LF, K], Y is obtained by linear approximation from Y = F[L, K] as Y* = Y + (3Y/3L)(LF - L). Thus, the average produc- tivity of labor at full employment, (Y*/LF), is a weighted average of the observed average productivity and the observed marginal productivity of labor with weights equal to the employment rate (L/LF) and to the unemployment rate [1 - (L/LF)] respectively, where the latter is labeled as ur and approximated by (-if - I). From (15.2)-(16), transforming marginal productivities in linear functions of average productivities, the following formulation of the macroeconomic wage equation is obtained, once a simple aggregation of the supposedly identical firms and unions is assumed: ©International Monetary Fund. Not for Redistribution - 32 - where GQ is constant; Notice in (17) that the compensation effect has the sign of the coeffi- cient of the tax wedge, tw = S + T + A, while the progressivity effect has the sign of the coefficient of the progressivity index, H = (/3 - 7q)/(l - A), where H is positive only if A is not flat. Moreover, if <5^ = f>^ - 0, I falls under case (A); if 6^ > 0 and 62 > 0, I falls under case (C); if 5^ > 0 and &2 — 0, I falls under case (B). Finally, provided the union's rate of substitution between the net real wage and employment depends both on sr and sr , i.e., provided 5^ > 0, the wage setting in (17) shows three distinctive features: it is certainly negatively elastic to the unem- ployment rate (ur); it is possibly influenced by a negative compensationA effect (if 6^ - ^2 < 0); and by a non-negative progressivity effect (if 6274 - * > 0). Equation (17) is valid only in the long run. In order to introduce some adjustment lags in the short-run wage equation, an error correction mechanism is adopted in the following form where r refers to time. While equation (17) is micro-founded, the dynamics appearing in the short-run wage equation (18) is chosen ad hoc after some trials and errors. Notice, however, that the steady state solution of (18) exactly corresponds to equation (17): in particular, 63/33 = -$2lQ/a> 04/33 = <5-L - 62, 65/33 = ($274 - The macroeconomic wsge equation (18) is estimated for nine European countries in the period 1960-88, using yearly comparable data supplied by the OECD. I/ The instrumental variable technique is adopted to correct for the endogeneity bias due to the presence in (18) of simultaneously j_/ More information on the data are presented in Appendix A. ©International Monetary Fund. Not for Redistribution - 33 - endogenous variables (p, y - £ and w). I/ We use in each country the labor force and the business sector capital stock (in volume) as instruments for labor productivity, y - I, and the GDP deflator of the whole set of OECD countries, besides the lagged values of the product and the imported commodities prices, as instruments for the product price, p. Some structural breaks appear in the estimations of the wage equation (18) reported by Table 3. They essentially relate to changes in fiscal policy, in union attitude relative to taxes and in union flexibility with respect to unemployment. Special attention is devoted in our estimates to the influence on wage formation of the level and the dynamics of progressivity or de facto indexation of direct taxation. In particular, if the coefficient /3 - 7q has been institutionally modified in some places, over the 1960-88 period, this variation is embodied in the switching coefficient of the progressivity index H appearing in (18). In some cases, progressivity has stopped existing de facto, and therefore that coefficient turns out to be zero; this situation holds true in all those countries (Denmark 1970-83, Netherlands 1981-88, Austria 1979-87) in which A became flat due to a specific form of fiscal indexation or to a fiscal indexation combined with a wage indexation. In other countries (notably France since 1983, Germany since 1977, United Kingdom since 1979) the union attitude relative to fiscal policy has changed in the sense that it fully neutralized in the long term the effects on wages of progressivity although the latter did not disappear (this is also true of Belgium since 1979, with the difference relative to the countries mentioned above that Belgium fully indexed its wage system in the 1980s). 2/ In other countries (notably Sweden since 1979), the long-run semi-elasticity of the wage rate relative to progressivity changed 3J and declined but very mildly. Finally, in Italy, although the progressivity of direct taxation decreased in the latest years (not to the point of becoming zero), the long-run semi-elasticity of the wage rate to the progressivity index remained constant. I/ In (18), unlike (17), w and A are not simultaneously determined because only the lagged value of the direct tax rate appears in the (short- run) wage equation. Notice, however, that if there were simultaneity, the structural breaks introduced in the estimation of the A equation (different for each country) would allow for the identification of the wage equation: the ideal--and the only available-- instrument for the linear effect of A on w would be the dummy variable corresponding to each country's tax structural break. At the same time, the variable showing the non-linear effect of A on w i.e. 1/(1 - A) never needs to be instrumented and can be treated as an exogenous variable in (17), since the instrumental variable estimation and the specification of equation (1) imply that w has no linear effect on 1/U - A). 2./ That is why the real labor cost equation for Belgium excludes after 1978 all endogenous variables like y - t, ur or A as its regressors. I/ The Swedish case is interesting because the change in union attitude relative to progressivity arises some years after the structural break in direct taxation. ©International Monetary Fund. Not for Redistribution Table 3a. Estimates of the Wage Equation in Nine European Countries, 1960-88 I/ Aw = constant Regressors - (w+T+S (pim-p)T (pim-p)T_1 A(y-£)T (y-«)T-! -?),.-!-«:,.-! urr-l CS+TV! Countries Gl Gll G12 G2 a3 G3 G4 Belgium 0.90 0.98 0.71 * (D60-78) 0.71 * (D60-78) 0.79 0.87 * (D60-78) 0.75 (1960-88) (-17.31) (18.89) (3.13) 2/ (3.13) 2/ (5.34) (-2.07) (2.69) 3/ Denmark -0.95 0.95 0.27 0.27 0.27 -0.31 0.008 (1966-88) (-20.69) 4/ (-20.69) 4/ (2.13) 2/ (2.13) 2/ (2.13) 2/ (-2.93) (0.14) France -0.97 0.97 -0.10 0.24 0.19 -0.71 * (D69-82) 0.19 * (D69-82) (1963-88) (-34.22) 4/ (34.22) 4./ (-0.30) (2.08) (1.80) 5/ (-2.43) (1.80) I/ + -0.75 * (D63-68+ (-2.10) D83-88) Germany -0.99 0.99 0.50 0.50 0.54 -0.97 * (D60-76) 1.16 * (D60-76) (1960-88) (-38.84) 4/ (38.84) 4/ (6.92) 2/ (6.92) 2/ (8.12) (-4.47) (5.37) + -0.63 * (D77-88) (-4.75) Italy -1.05 1.05 0.50 0.50 0.47 -0.89 * [(D60-74) -0.053 (1960-85) (-25.98) Netherlands -0.95 0.95 0.49 0.49 0.49 -0.31 * (D67-80) -0.043 (1967-88) (-19.28) 4/ (19.28) 4/ (2.95) 2/ (2.95) 2/ (2.95) 2/ (-0.33) (-0.13) United -1.02 1.02 0.69 0.69 0.50 -2.15 * (D61-78) -0.084 Kingdom (-31.38) 4/ (31.38) 4/ (5.87) 2/ (5.87) 2/ (5.43) (-5.13) (-0.64) . (1961-88) +•f -0.27 * (D79-83) (-1.53) Austria -O.S9 0.99 0.35 0.35 0.35 0.75 * (D60-78) 0.001 (1960-87) (-15.16) 4/ (15.16) 4_/ (2.38) 2/ (2.38) 2/ (2.38) 2/ (0.55) (0.01) Sweden -1.02 0.96 0.29 0.29 0.52 -1.13 0.38 C061-87) (-37.30) (37.76) (4.15) 2/ (4.15) 2/ (7.54) (-2.29) (6.51) I/ The estimated constants are not reported. = 2/ The G12=G2 hypothesis is not refused by the data and therefore the Gj^ G2 constraint is imposed on the estimate; when the a3=Gi9=^2 hvpothesis is not refused by the data, also this constraint is imposed on the estimate. 3/ The hypothesis that the estimated coefficient of (S+T)T_1 is equal to that of AT_^ is refused by the data; everywhere else, it is a- c ert ed and therefore imposed on the estimate. <-/ The Gi=G^} hypothesis is not refused by the data and therefore the G1=G11 constraint is imposed on the estimate, 5 ' The not refused ©Internationalbv the data and therefor Monetarye the aFund.i=Gi constrain Not fort iRedistributions imnosed on the estimate. Table 3b. Estimates of the Wage Equation in Nine European Countries, 1960-88 I/ Aw - constant + ApimT + G1(pim-p)T + G11(pim-g)r.1 + G12A(y-£)T + G2(y-i)r.i + Gjur,.^ + G4(S-H)T.1 + G^A,.^ + G5{3tl/(l-A)] }T.l - a3(w+T+S-f!)T_1 Regressors V-1 Compensation Progressivity Gj0 R^C Durbin-H SER D.F. 2/ A.D.F. 2/ Effect Effect Countries Belgium 2.30 * (D60-78) 3/ -5.06 * [0.086*(D60-78)J 0.97 0.200 0.010 t0— 4.95* tx— 3.26* + - (1960-88) (3.69) (-4.02) (30.20) 0 0 Denmark 0.008 0.004 * [0.321*(D66-69) 0.97 0.176 0.012 t0— 1.93** tx— 1.71*** 0 0 (1966-88) (0.14) (0.29) +(084-88)] 0 0 (3.73) 0 0 France 0.19 * (D69-82) -2.07 * [0.05*(D69-B2)J 0.98 0.990 0.010 t0— 1.67*** tj— 2.08** 0 0 (1963-88) (1.80) 4/ (-1.81) (17.74) •f - 0 0 Germany 1.16 * (D60-76) -6.35 * [0.074*(D60-76)1 0.99 0.699 0.006 t0— 1.73*** tj-- 3.13* + - (1960-88) (5.37) (-5.34) (8.62) 0 0 Italy -0.053 0.48 * [0.071*(D75-82) 0.99 0.251 0.012 t0— 2.43** ti— 3.81* 0 0 (1960-85) (-0.26) (1.86) (19.34) 0 + U) +0.052*(D83-85)] 0 + (3.87) 1 Netherlands -0.043 * (D67-80) 0.16 * [0.237*(D67-80)1 0.96 0.680 0.017 t0— 2.66* tj — 3.72* 0 0 (1967-88) (-0.13) (0.87) (2.85) 0 0 United -0.08« 1.38 * [0.047*(D61-78)I 0.98 0.827 0.010 tfl— 2.43** tj— 2.08** 0 + Kingdom (-0.64) (4.07) (2.71) 0 0 (1961-88) Austria 0.001 -0.06 * [0.069*(D60-78)1 0.91 0.489 0.011 t0— 1.98*** t!— 1.78*** 0 0 (1960-87) (0.01) (-0.22) (1.77) 0 0 Sweden 0.38 -0.22 * [0.138*(D61-71)+ 0.99 0.700 0.006 t0— 2.92* tx— 2.71* + - (1961-87) (6.51) (-2.35) (13.14) +0.189*(D72-78)] + - (2.74) -0.27 * [0.189*(D79-87)1 + - (-2.62) (2.74) \t The estimated constants are not reported. 2/ * means that the null hypothesis of a unitary root is rejected at 0.01; ** means thatthe null hypothesis of a unitary root is rejected at 0.05; *** means that the null hypothesis of a unitary root is rejected at 0.10. 3_/ The hype>thesis that the estimated coefficient of (S+T)T_1 is equal to that of AT.1 is refused by the data; everywhere else, it is accepted and therefore imposed on the estimate. V The «3^54 hypothesis is not refused by the data and therefore the «3^34 constraint is imposed on the estimate. ©International Monetary Fund. Not for Redistribution - 36 - Similar reasoning is valid for the union attitude relative to the tax wedge and its change over time. Furthermore, in our estimations it appears that approximately at the same time in which a structural break occurred in the tax system and in the wage elasticity to fiscal parameters, another structural variation emerged in wage setting: in every country except Sweden and Denmark, a switching fiscal policy was generally accompanied by a behavioral change concerning the steady state wage elasticity relative to unemployment, a proxy of what may be judged a union flexibility index. Apart from these structural breaks, we did not try to introduce and test any other break or lag, due to the short estimation interval, because a parsimonious estimate is preferable when the degrees of freedom are limited. This is the reason, we believe, why some serial correlation in the residuals may still be present in (18) although not much, judging from the Durbin-H statistics reported by Table 3b. Altogether, the estimates of the wage equation (18) look robust: the coefficients which, according to the theory, have a definite sign, namely a^ > 0, 62 > 0, 63 < 0, are all correctly signed and significant (t-statistics are presented in parenthesis under the parameter estimates); the coefficients G^, G^ which, according to the theory, may be of any sign but must be internally consistent, are indeed internally coherent, as later specified. The connection established between the coefficients of the long- run equation (17) and those determining the steady state solution of the short-run equation (18) , is based on the hypothesis that the latter represent the equilibrium outcome for wage setting. This presumption, which is accepted in the traditional econometric approach (see Banca d'ltalia, 1990), is here tested in the following way: if these variables determine the equilibrium solution for wage setting, it means that they have to be cointegrated; therefore the residuals (labeled as res) obtained taking the difference between the observed real labor cost (in log) and the simulated steady state solution of real labor cost (in log) derived from our estimates in (18), should be stationary. Thus the two following tests are performed on these residuals: A Dickey Fuller test (D.F.), based on the t-statistics, tQ, of the coefficient x °f tne regression Augmented Dickey Fuller test (A.D.F.), based on the t-statistics t^, of the coefficient x °f tne regression where e.r is the error term and £ is a parameter to be estimated. The results of these tests are reported in Table 3b and, compared with Fuller, ©International Monetary Fund. Not for Redistribution - 37 - 1976, I/ indicate that the null hypothesis of a unitary root in the residuals is for all countries 2/ rejected at least at a 10 percent level and for most countries at a 1 percent level. Thus we accept the assumption that the steady state solution of (18) indicates indeed the equilibrium solution for wage setting. Our tests (high R^C and low SER) also reveal that our model is able to reasonably explain the short-run wage movements of the nine European countries: the fit is good, as confirmed by Chart 2, which shows for each country the observed and the simulated value of the growth rate of the real labor cost, according to (18). This is even more satisfactory taking into consideration that the same wage equation is being utilized for so different countries, without searching for the best equation for each country and without proceeding to any data adjustment or data mining so common in single-country studies. I/ The cross-country comparability of the results is therefore fully granted. V. The Tax-Push Hypothesis Revisited for Nine European Countries Of special interest are in Table 3 not only some cross-country empirical regularities, together with some relevant cross-country differences, but also the internal consistency of each country's estimation results. Starting with the former, we observe, for example, that very often the labor productivity coefficient, G^, appears from Table 3a to be very similar to the error correction coefficient of the real labor cost, a^, indicating that the long-run union realized target could be expressed in terms of a value-added share. The possible exceptions to this cross-country regularity are France, the United Kingdom and Sweden. Another robust cross-country regularity illustrated by Table 3a concerns the signs and the values of G-^ and G^Q which are everywhere very similar, G^ being always negative, G^ being always positive and both very significant. Moreover, the sum G-^ + G-Q is in many countries equal to zero, indicating that the long-run wage rate is set in proportion to the product I/ See also Dickey-Fuller, 1979, and Dickey-Fuller, 1981. 2/ Given that everywhere (except in Denmark and Sweden) a structural break in the wage elasticity to the unemployment rate implies that, accord- ing to (18), there are two long run solutions in wage setting, we only report in Table 3b the D.F. and the A.D.F. tests for the time interval starting after the structural break: this is more relevant for forecasting purposes. For Sweden and Denmark we present the D.F. and the A.D.F. tests for the whole period under consideration. I/ Notice, however, that our estimation results are remarkably similar to those recently obtained in single-country econometric studies, as reported by Dreze-Bean, 1991. 4/ All the constraints imposed on the estimations are imposed after testing, including the constraint G^ = -G^ when it appears in Table 3a. ©International Monetary Fund. Not for Redistribution - 38 - price. The major exceptions from this viewpoint are Belgium and Sweden, showing that the steady state wage rate is set in proportion to a weighted average of the product price and the imported commodity price. As expected from our theoretical model [see equation (15.2)], the condition G-^ + G-Q = 0 is usually combined with a zero effect of the tax wedge on the real labor cost (G^ = 0): this implies (in Denmark, Italy, the Netherlands, the United Kingdom, Austria, France since 1983, Germany since 1977) that the long term real labor cost, deflated by the product price at factor cost net of indirect taxes, is independent of S and T. Indeed, in all these cases, the indirect tax rate, T, does not play any permanent role on wages in the sense that any growth in T is borne by employees in terms of a reduction of their purchasing power; and any increase in the social security tax rate, S, paid by employers is backward shifted on employees who proportionally reduce their long-run wages so as to maintain a constant real labor cost; finally, the implications of a rise in the direct tax rate, A, is equally borne by employees in the sense that they do not change their steady gross wage when A varies, only if the marginal tax rate is kept constant or if it varies, being uninfluential (G^ is also zero as is G^): the latter appears to hold true only for a subset of these countries, precisely for all small open economies (Denmark, the Netherlands, Austria, Belgium since 1979) \J and for most large countries in the 1980s (Germany since 1977, France since 1983, the United Kingdom since 1979), the exceptions being in the latest years Italy and Sweden. Moreover, Table 3a shows that everywhere in Europe (except in Austria, the Netherlands and Belgium since 1979) wage setting is negatively affected by the unemployment rate (63 < 0). Thus, for most European countries the weight assigned by the union to employment relative to the net real wage positively depends on the latter, but negatively depends on the net real recervation wage, so that we can state that unions care about "relativities" as in case (C) above, with 6^ > 0- 2.7 In most of these countries (i.e., in Belgium up to 1978, in France up to 1982, in Germany up to 1976, in Sweden) the weight assigned by the union to employment is influenced more by I/ In Belgium both G^ and Gj become zero after 1978; before that year the compensation effect is certainly positive but the constraint on the equality of the AT.^ and (S + T)r.^ coefficients is not accepted by the data. 2/ Case (C) is applicable to every European country under observation, except Belgium since 1979, Austria and the Netherlands. In Belgium, after 1978 equation (18) is not appropriate because, as suggested by the last column of Table 2b, q = 1; indeed, the estimation results of Table 3 confirm for Belgium a wage indexation mechanism since 1979. In Austria and the Netherlands presumably case (A) is applicable (with 6-^ - b^ = 0) , although this is not fully coherent with our theory for Austria up to 1978 and the Netherlands up to 1980, because 65 should be significantly negative (but it is not negative according to our econometric results); after 1978 (in Austria) and 1980 (in the Netherlands) H equals 0 and therefore it is no more a regressor in the wage equation (18). ©International Monetary Fund. Not for Redistribution - 38a - Chart 2 Estimate of the Wage Equation: Observed and Fitted Values Sojrce: OECD data described in Appendix A. ©International Monetary Fund. Not for Redistribution - 38b - Chart 2 Estimate of the Wage Equation: Observed and Fitted Values Source: OECD data described in Appendix A. ©International Monetary Fund. Not for Redistribution - 38c - Chart 2 Estimate of the Wage Equation: Observed and Fitted Values Source: OECD data described in Appendix A. ©International Monetary Fund. Not for Redistribution This page intentionally left blank ©International Monetary Fund. Not for Redistribution - 39 - the net real wage than by the net real reservation wage (0 < b^ < &]) , given that the compensation effect is positive (G^ > 0). In these periods and in these countries, the concern with "relativities" is confirmed to be weak by the fact that the progressivity effect is negative (0 < ^74 < Given the opposite sign of the compensation and the progressivity effects in most large European countries in the 1960s and in the 1970s and the change of these signs across time, particularly since the 1980s, it may be interesting to conclude by showing what would be the long-run implications on wages of an increase of the average direct tax rate when the marginal and the average rates move together. In practice in Table 4 we present for large European countries and for some selected years the estimated semi-elasticity dw/dA obtained from the steady state solutions of Table 3, recalling that in general these semi-elasticities are zero for small open European economies. Table 4. Long-run Estimated Semi-Elasticities of the Wage Rate to the Direct Tax Rate in Some Large European Countries. United France Germany Italy Kingdom Sweden 1965 0 0.611 0 0.181 0.623 1975 0.185 0.271 0.091 0.216 0.657 1985 0 0 0.087 0 0.504 While more general remarks on all this chapter are summarized in Chap- ter I, we believe that Table 4 deserves at least one comment here: it indi- cates that unions in Europe became more and more willing to neutralize in their wage setting any change in direct taxation, in order to fix their long- run real labor cost, precisely like small open economies usually do to maintain their external competitiveness. Italy is the only country among the EEC partners examined here, which still has (to a limited extent) to complete this adjustment probably because it was a latecomer in adopting (in 1975) a substantially progressive personal income taxation. From this viewpoint, in the 1980s the only real outlier among the European countries under observation is Sweden: presumably it is not an accident that Sweden does not belong to the EEC and is not as small as Austria. ©International Monetary Fund. Not for Redistribution - 40 - APPENDIX A Variables. Definitions and Data Sources The non-standard variables used in the econometric analysis of this paper are defined as follows. The personal income tax rate is constructed as the ratio of the total income taxes paid by households to the sum of the employees' total compensation net of employers' contributions to public and private security programs and the self-employed plus the property (unincorporated) incomes. The source of the data on income taxes paid by households and on property (unincorporated) incomes is the OECD Economic Outlook historical data file, while the source of the employees' compensations net of employers' social security contributions to public and private plans is the OECD Analytical Data Base, integrated (through a dynamic interpolation) by the data published in the OECD National Accounts (various issues). The integration occurred for Germany in the period 1960-70, the Netherlands in the period 1967-69, the United Kingdom in the period 1960-61, Austria in the period 1960-70, and Sweden in the period 1960-62. The employees' social security tax rate is constructed as the ratio of the self-employed and the employees' social security contributions to the sum of the employees' total compensation net of employers' contributions to public and private security programs plus the property (unincorporated) incomes plus the self-employed incomes. The numerator of this ratio is obtained as the difference between total social security contributions and employers' social security contributions. The source of the data on total social security contributions is mainly the OECD Analytical Data Base, integrated by the OECD National Accounts (various issues), as indicated above. The integration occurred for Belgium in the period 1960-69, France in the period 1963-70, the Netherlands in the period 1960-70 and the United Kingdom in the period 1967-70. The data source of the employers' social security contributions for countries such as Italy and Austria is the OECD National Accounts (various issues). The direct tax rate, A, is obtained as the sum of the personal income tax rate and the employees' social security tax rate, obtained as previously described. The employers' social security tax rate, S, is constructed as the ratio of the employers' social security contributions to the employees' compensation net of employers' social security contributions. The source of the employers' social security contributions is mainly the OECD Analytical Data Base, inte- grated by the data published in the OECD National Accounts (various issues). The integration occurred for Belgium in the period 1960-69, France in the period 1963-70, the Netherlands in the period 1967-69 and the United Kingdom in the period 1960-70. The data source for the employers' social security contributions for countries such as Austria is the OECD National Accounts (various issues). The wage rate, w, is constructed as the logarithm of the ratio of the employees' compensation net of employers' social security contributions to the total number of employees. The source of the total number of employees is the ©International Monetary Fund. Not for Redistribution - 41 - APPENDIX A OECD Economic Outlook historical data file, integrated with the data published in the OECD National Accounts (various issues) for the Netherlands in the period 1967-69. The consumer price, p, is constructed as the logarithm of the deflator of the consumption expenditure, whose source is the OECD Economic Outlook historical data file. The producer price, p, is constructed as the logarithm of the GDP deflator and the source is the OECD Economic Outlook historical data file. The GDP deflator for the total set of OECD countries is constructed as the ratio of total OECD countries GDP at market value and current prices to the total OECD countries GDP at market value and constant prices. The source is the OECD National Accounts (various issues). The source of the remaining variables utilized in this paper is mainly the OECD Economic Outlook historical data file. ©International Monetary Fund. 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