A Cross-Country Analysis of the Tax-Push Hypothesis
  • 1 0000000404811396https://isni.org/isni/0000000404811396International Monetary Fund

This paper presents a microeconomic theoretical model of union optimizing behavior which is then used to test the relevance of the tax-push hypothesis 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 transferred 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.

Abstract

This paper presents a microeconomic theoretical model of union optimizing behavior which is then used to test the relevance of the tax-push hypothesis 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 transferred 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.

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, deflated 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 approximated 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 purchasing 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 compensation 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 reservation 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 employment in the union’s absence. Therefore, downward pressures on the net real wage target arise, ceteris paribus, the lower is the net real reservation 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 macroeconomic wage equation. First, wage setting is negatively affected by the unemployment 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. 1/

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 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, Denmark, 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 positive (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 country econometric 2/ 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 foundation 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 distinction 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 insufficient 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.

Table 1.

Personal Income Taxes in Europe: An Institutional perspective in 1988

article image
article image
article image
Sources: Andersson, K. (1988), “Tax Reforms in Scandinavia during the 1980s”; Bayar, A (1989), “Une Evaluation de la Reforme Fiscals on Belgique”; Lipschitz, L, Kremers, J., Mayer, T.. and D. McDonald (1989), “The Federal Republic of Germany, Adjustment in a Surplus Country”; Lopez-Claros, A. (1988), “The Search far Efficiency in the Adjustment Process: Spain in the 1980a”; OECD (1976), The Adjustment of Personal Income Tax Systems for Inflation: OECD (1977), The Treatment of Family Units; OECD (1981a), The Impact of Consumption Taxes at Different Income Levels; OECD (1981b), Income Tax Schedules; OECD (1986a), An Empirical Analysis of Changes in Personal, Income Tax; OECD (1986b), The Tax/Benefit Position of Production Workers 1979-84; OECD (1986c), Personal Income Tax Systems Under Changing Economic Conditions; OECD (1989a), The Tax/Benefit Position of Production Workers 1985-88; OECD (1989b), Taxing Consumption; Pechman, J. (1987), Comparative Tax Systems: Europe Canada and Japan; Tanzi, V, (1980), Inflation and the Personal Income Tax; An International Perspective.

The German personal income tax schedule presents an upward sloping marginal tax rate function for one of the income brackets, not a step function for every bracket.

All information refer to 1981 and only to the tax rates levied by the central government. The distinction is particularly important for some countries: for example, in Sweden local government income taxes are levied at a flat rate of about 30 percent.

Data include income and non income related tax allowances and tax credits with the exception of Denmark whose tax allowances are only income related.

Significant changes in the income tax systems have taken place in the 1960s and in the 1970s in Germany, in Austria, and in Sweden.

Chart 1
Chart 1
Chart 1
Chart 1

Temporal Dynamics of the Average Direct Tax Rate, of the Nominal and Real Wage Rate1

Citation: IMF Working Papers 1992, 011; 10.5089/9781451925944.001.A001

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.

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 allowances and in the number or the nominal value of income brackets. Identification 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.

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. 3/

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 4/ is progressive and progressivity obtains by charging different marginal tax rates on different wage brackets, the observed average direct tax rate, ʌ in the absence of fiscal indexation, is a log-linear function of the nominal wage, W (log W is labeled as w). 5/ If direct taxation is progressive and fully indexed to the price dynamics (the usual case of fiscal indexation), the corresponding observed average tax rate, ʌ, is a log-linear function of the real wage, WR (log WR, labeled wr): this implies that ʌ 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, ʌ 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 ʌ relative to W (labeled as /β) should be in absolute value higher than the semi-elasticity relative to P (labeled as γ). 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, ˄ 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 by inflation; 6/ 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:

ʌ=α+βwγp,(1)

with β ≥ γ; γ ≥ 0; α of any possible sign but certainly positive if both β and γ equal zero. Recalling that the consumer price, p, is a weighted average of the product price, p˜, and the imported commodity price, pim (both in logarithm), with weights respectively equal to γ1 and 1 - γ1, equation (1) can be rewritten 7/ as

ʌ=α+βwγγ1p˜γ(1γ1)pim.(2)

These equations represent a nested form, which includes four fiscal subcases:

  • (1) proportional direct taxation or progressive indexed direct taxation with fiscal indexation obtained by adjusting the nominal tax bill to the wage rate rather than to the consumer price dynamics, with β = γ = 0: dʌ/dw = dʌ/dwr = 0 and ʌ is constant;

  • (2) progressive direct taxation without indexation in the fiscal system: β > 0, γ = 0; dʌ/dw = β > 0 and ʌ is positively and uniquely dependent on the nominal wage rate;

  • (3) progressive, fully indexed direct taxation: β = γ > 0 and ʌ is a positive function of the real wage rate; this implies dʌ/dwr = β and dʌ/dw = β[1 - (dp/dw)], with ʌ increasing with the nominal wage rate if the latter is not fully indexed, but with constant 8/ ʌ 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 9/ as

    dp/dwq;dp˜/dwq˜=q/γ1;(3)
  • (4) progressive, partially indexed direct taxation: β > γ > 0 and ʌ is not a function of the real but of the nominal wage rate, besides being a function of the price level; dʌ/dw = β - γ(dp/dw) > 0 because β > γ 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 β = γ > 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 ʌ equation are worth noticing. 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),

N=d(ʌW)dW=ʌ+W(βγq)W=ʌ+(βγq)(4)

Second, when ʌ is a log-linear function of W and P, the well-known progressivity index (see Jackobsson, 1976)

H=11marginaldirecttaxrate1averagedirecttaxrate=marginalaveragedirecttaxrate1averagedirecttaxrate(5)

which ranges between 0 (when the marginal tax rate equals the average, at constant ʌ) and 1 (when the marginal tax rate approaches 100 percent), takes the simple form of

H=βγq1ʌ(6)

As it will be seen below, we will extensively use the index H in the analysis 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 ʌ equation: a data problem due to the absence of appropriate cross-section, implying that time series data on ʌ, 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 ʌ 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 ʌ, 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 ʌ—and the following wage equation—is the instrumental variable technique that corrects the coefficients’ values for the biases induced by the presence of jointly endogenous variables. In particular, inasmuch as it concerns the average direct tax rate equation, both regressors w and p are probably jointly endogenous with ʌ. Indeed, the wage rate, w, as will be seen below, is determined by many regressors, including ʌ 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. 10/ 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 ʌ equation (1), it is possible to evaluate β and γ 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 β > γ and γ ≥ 0 [case (a)], there is no reason to suspect the presence of collinearity; therefore, dp/dw = q is assumed to be zero. However, if β and γ 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

ʌ=α+βwγ(qw)γz=α+(βγq)wγz=α^+β^w(7)

and

ʌ=α+β(pzq)γp=α+(βqγ)pβqz=α˜+γ^p(8)

Let us notice that z is exogenous as are the constants α^ and ã; the constant β^ equals β - γq, while the constant γ^ equals (β/q) - γ. two possibilities then arise with regard to the estimates of β^ and γ^, which lead to four different econometric solutions for the average direct tax rate: either β^ and γ^ are both zero, or they are both positive.

If both β^ and γ^ are zero, that means that the progressivity index H is zero, , is flat and may appear only as an exogenous variable in the wage equation. Two subcases are relevant. In case (b) , is constant because β = γ = 0 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) β = γ > 0 and q = 1: in this event, , is flat because the real wage is constant and there exists full fiscal indexation, 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.

If β^ and γ^ are both positive, two subcases arise: (d) either β^=γ^ or (e) β^<γ^. In the former case (d), the result is only possible for q = 1 which in turn implies β > 0, γ > 0 and β > γ: thus, direct taxation is progressive and certainly not fully indexed (, 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 on any other endogenous variable. On the contrary, case (e), with 0<β^<γ^, implies q < 1 within three unidentifiable situations, namely β > 0, γ = 0; β > γ > 0; β = γ > 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 β^ is needed there.

Let us now be more specific about the estimation of the ʌ equation. Step 1 is characterized by the instrumental variables estimate of (1). The estimated coefficients β and γ for the nine countries under observation are reported in the second and third column of Table 2a; t-statistics are presented in parenthesis under the coefficients. Only for very few countries and time spans, these estimated coefficients are consistent with the theoretical 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 β and γ 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.

Table 2a.

Estimates of the Average Direct Tax Rate Equation in Nine European Countries, 1960-88

ʌτ=α+βwτγpτα^+β^wτ=α˜+γ^pτ

article image
article image

According to this interpretation, if no collinearity exists, i.e., q = 0, the coefficient (β - γq)—whose estimates are presented in the fourth column of Table 2a—coincides with the estimated coefficient β. However, if some multicollinearity arises and q > 0, step 2 proceeds to the estimation 11/ 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 estimation. Step 2 leads also to the estimation of equation (8), whose results are shown in the fifth column 12/ of Table 2a.

Table 2b.

Estimates of the Average Direct Tax Rate Equation in Nine European Countries, 1960-88

ʌτ=α+βwτγpτα^+β^wτ=α˜+γ^pτ

article image
article image

The estimated marginal direct tax rate, labeled as Ne, equals the estimated average direct tax rate (ʌe) plus β^. Notice that the estimated marginal direct tax rate concerns the marginal rate paid by the taxpayer, earning the average wage. The value of ʌe is obtained through a static simulation of equation (1), where the coefficients α β γ are illustrated in the first four columns of this table. When β and γ 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 β=γ=0.

The estimated progressivity index, labeled as He, equals the ratio between the coefficient β^ and one minus the estimated average direct tax rate (ʌe).

In Denmark the hypothesis β^γ^ in the period 1966-69 and 1984-88 is accepted with probability 81 percent.

In Denmark the first year for which an estimation exists is 1966, because the data are not available before.

In the Netherlands the first year for which an estimation exists is 1967, because the data are not available before.

In the United Kingdom the first year for which an estimation exists is 1968 due to lags in the estimated equation (1).

The estimation of β^ 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 (He), 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 β^ over time, as indicated by column 1. De facto fiscal indexation is observed only, when the estimated values of β and γ are identical: while a test on β = γ is reported by column 2 of Table 2b, this same column indicates that in most cases a test is only possible on β^ and γ^.

To understand why, we recall our previous discussion on cases (b), (c), (d), (e) which hold true when some collinearity exists between w and p (q > 0). In particular, let us assume that H0 is β^=γ^ with H1: β^<γ^. If H0 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 H0 is not rejected, the following next test is performed assuming that H0 is β^=γ^=0 with H1: β^=γ^>0. Then, either Hq is not rejected and therefore ʌ 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 ʌ, w and wr for each of the nine European countries 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, ʌ, shows in Chart 1 a structural break around 1979. At that time the strong positive correlation apparent in previous years between ʌ 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 ʌ, while showing that β^ (in column 1) and the progressivity index (in column 3) have declined since then, within a fiscal system partially indexed (with β > 0 and γ ≥ 0 as indicated in column 4). Therefore, in the 1980s, ʌ remains a function of the nominal wage rate but q equals 1, meaning that the real wage becomes approximately constant and independent of ʌ.

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 ʌ, presented in Table 2 precisely point out that the Danish direct tax system had a much higher β^, hence a higher degree of progressivity before 1970 and particularly 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 personal 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 regression 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 β^ 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, β^ and the degree of progressivity of direct taxation have not been essentially 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. As a consequence, according to our estimates illustrated by Table 2, β^ 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 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 ʌ which, in fact, became constant after 15 years of almost uninterrupted increase. Our econometric results further illustrate that β^ and progressivity have dramatically 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 structural break around the end of the 1970s, so that β^ 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 prohibited.

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 Conservative 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).

III. 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(W)U(SR,L;SR*)(9)s.t.(1)ands.t.
1η=dwd=FLLLFL[1(dp˜/dw)]=1η˜(1q˜),(9.1)

with q˜ defined in (3) and

1/η˜=FLLL/FL<0.(9.2)

The union’s objective function, U, depends positively on the net real wage, SR [SR ≡ W(l - ʌ)/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 η [in this paper we consistently use small letters to indicate logarithms and capital letters to indicate natural values (for example, ℓ ≡ log L, sr ≡ log SR)]; η is non-positive under the usual hypothesis on the production function, F, with FL > 0 and FLL < 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 1/η is directly derived from the marginal productivity condition

FL=MW(1+S)(1+T)P˜=MCR=MSRTW˜,(10)

where, by definition, TW¯[(l+S)(l+T)/(lʌ)][P/P˜] and CRW(l+S)(l+T)/P˜. In (10) the marginal product of labor, FL, equates the real labor cost, CR, multiplied by one plus the mark-up (the mark-up equaling M - 1; q˜ 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) l/η˜ 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

sr=logFLmtw˜=logFLmtw(pp˜)=crtw(pp˜),(10.1)

where the (logarithm of the) tax wedge, tw, is approximated by S + T + ʌ, 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+pp˜.

Second, by definition, the net real reservation wage, being the net real wage holding at full employment, is SR* = W* (1 - ʌ*)/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 employment 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 FL* such a full employment marginal product of labor [i.e.,

FL*=FL(LF) with LF defined as the exogenous labor supply], we derive

FL*=MW*(1+S)(1+T)P˜*(10.2)

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 (10.2)

sr*=logFL*mtw˜*=logFL*mtw*(p*p˜*),(10.3)

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: 13/

tw˜*=tw˜log1ʌ*1ʌ+(p˜p˜*)(1γ1)=tw˜{βγ(dp/dw)1ʌ[(1γ1)(dp˜/dw)]}log(FL/FL*)1(dp˜/dw)=tw˜{H=[(1=γ1)q˜]}log(FL/FL*)1q˜,(10.4)

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 α, β, γ, sets w and observes the realized level of ʌ, thus inferring dp/dw if γ ≢ 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)/γ1q/γ1. That is to say that the union takes dp/dw to be zero if the fiscal system is not indexed at all, 14/ with γ = 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 partially indexed (γ > 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 (almost) 15/ as complete as the one of the union if q˜=q=0 and the system is progressive. In fact, in this event β >0 and γ ≥ 0 can be estimated [as in case (a) above]. On the contrary, if q˜ and q are different from zero, only some inferences on β and γ are possible, based on the estimation of β^ and γ^ [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 β^ and γ^ 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:

du=usrdsr+ud=0,withd2u<0,

which can be reformulated as

1η=u/(u/sr)(dsr/dw)=IE,(11)

where

Edsrdw=1+dlog(1ʌ)dwdpdw=1βγq1ʌq=1Hq,(11.1)
Iu/u/sr=(dsrd)u(11.2)

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 β, γ, 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/η) = -(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 an optimum implicit union’s choice of the expected employment level (call it ^) so that the maximum U can be expressed in terms of ^ or w^.

Now we wish to examine the impact of fiscal parameters ʌ, S, T on the selected optimum wage w^ and on the implicit union’s choice of ^. To do this exercise in comparative statistics, we rewrite (11) as

E/η+I=1Hqη˜(1q˜)+I=U^=0withU^<0,(11.3)

where U^ and U^ are the first and the second derivatives of the union’s objective function relative to ℓ in =^.

Remark that equation (11.3) is relevant only for 0q¯<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 deflated with the product price at market value) is a constant or only depends on exogenous variables (like pim, S or T, generally not ʌ). 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, ʌ 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 the optimum ^ by d^/dX=(U^X/U^), where U^X is the partial derivative U^/X given U^<0,d^/dX has the sign of UX for any X, i.e., X = ʌ or X = S or X = T.

On the contrary, using (9.1) and (10), we obtain

dw^dX=dsdX(1q˜)dtdX(1q˜)+d^dX1η=d(S+T)dX(1q˜)U^X/U^η,(11.4)

where the sign of dw^/dX is certainly opposite to U^X only for X = ʌ, (U^ and η being both negative), while some ambiguity remains in the sign of dw^/dS and similarly of dw^/dT.

Looking at (11.3), we understand that d^/ds=d^/dT because neither E nor η 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). A similar argument explains why d^/ is also equal to d^/ds=d^/dT when ʌ 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/(1q˜)+(dw^/) when ʌ is flat. Indeed if every fiscal parameter has the same impact on ^ it necessarily has the same effect not on w^ but on the real labor cost. Obviously, when direct taxation is progressive, the consequence on ^ of a variation in ʌ is different from that caused by a change in S or T: in this case, E depends on ʌ and β^ and ∂sr/∂ʌ < ∂sr*/∂ʌ because an increase in (the exogenous component of) ʌ 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 Introduction.

1. The compensation effect (of S, T, and flat ʌ)

First, we remark from (10.1), (10.3), (10.4) that

srʌ=srtw=1;sr*ʌ=1ifH=0(i.e.,β=γ=0orβ=γ>0andq=1);sr*ʌ=1+Hʌ{[log(FL/FL*)]/(1q˜)}ifH0.(11.5)

Therefore, if (and only if) ʌ is a flat tax rate, given that S and T are always flat tax rates, we deduce from (11.3), (11.4), (11.5),

U^ʌ=I{isr+isr*}=U^S=U^T=U^tw(12)

Hence the tax wedge is the only relevant fiscal parameter for the choice of ℓ when ʌ is flat. In this event,

dw^0,dw^dS=dw^dT=11q˜+dw^11q˜,

depending on whether

isrisr*.(12.1)

In interpreting (12) and (12.1), we remark that if ʌ 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 tax wedge, [(∂i/∂sr) = (∂i/∂sr*)], the implicit optimum employment level, ^, does not vary with the tax wedge; in this event, wage setting, w^, is independent 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 compensation 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 ʌ 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 I falls under case (B), the real labor cost rises with a higher ʌ, S, or T.

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 ʌ)

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 β-γq. This amounts to examining movements in (βγq)β^ at constant ʌ (therefore α has to vary as well). By the usual procedure, we get

U^β^=Hβ^{1ηIisr*[log(FL/FL*)1q˜]},(13)

with H/β^=1/(1ʌ)>0 According to (13), an increase in the marginal direct tax rate, for given average, tends to increase ^ if the weight assigned by the union to employment is unaffected by the perceived net real reservation wage (∂i/∂sr* = 0), being η < 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

(dw^/dβ^)<0ifIfallsundercases(A)or(B)becausetheprogressivityeffectisnegative;(13.1)
(dw^/dβ^)0ifIfallsundercases(C)orbecausetheprogressivityeffectcanbenegative,zeroorpositive.(13.2)

3. The effects of a change in ʌ 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, ʌ, and the marginal, ʌ + β -γq, vary together. The analysis of the impact of ʌ on w may be logically divided in two parts: one concerning the effects of the modification in the average direct tax rate for given marginal (as if ʌ were flat) and one concerning the implications of the change in the marginal direct tax rate for a given average (as β -γq varied but ʌ were fixed).

We thus expect the compensation and the progressivity effects to be the relevant factors in explaining the semi-elasticity of ^ and w^ relative to ʌ, when the average direct tax rate is progressive. Indeed, from (11.3), (11.4), (11.5), we derive that d^/ has the sign of

U^ʌ=I[isrdsr+isr*dsr*]H/ʌη=H/ʌ{1ηIisr*[log(FL/FL*)1q˜]}I[isr+isr*];(14)

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 ʌ affecting both the average and the marginal direct tax rates implies

dw^<0ifIfallsundercase(A)becausethecompensationeffectisabsentandtheprogressivityeffectisnegative;inthiseventtheunemploymentrate;connectedtoFL*,doesnotappearinthewageequation;(14.1)
dw^0ifIfallsundercase(B)becausethecompensationandtheprogressivityeffectsworkindefinitebutoppositedirections.theformerbeingcertainlypositive,thelatterbeingcertainlynegative;inthisevent,theunemploymentratedoesnotappearinthewageequation;(14.2)
dw^0whenIfallsundercase(C)becauseboththecompensationandtheprogressivityeffectshaveuncertainsigns;inthisevent,theunemploymentratecertainlyentersasaregressorinthewageequationwithanegativesign(asindicatedbelow).(14.3)

If the progressivity effect is negative, an increase in the (exogenous component of the) average direct tax rate, automatically raising the marginal, 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 (σ < 1). We then rewrite the optimum condition for wage setting, (11), as

EI=η˜(1q˜)=σ{1γ2[W(1+T)(1+S)p˜]1σ}1(1q˜),(15)

where γ2 is perceived by the union as a positive constant, (with γ2M1σαLσ and αL denoting the multiplying coefficient of labor in the CES production function). By a log-linear approximation, 16/ (15) can be transformed into

w+S+Tp˜=φ^H/(1q)φ^i+constant,(15.1)

where φ^μ/(1σ) is a positive parameter and e ≡ log E = -q - [H/(l -q)] Remark that equation (15.1) is meaningful provided 0q˜<1 and 0 ≤ q < 1.

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* under case (C). Then, when these nested hypotheses are embodied in the general model (15.1), recalling (10.1)-(10.4), we use

w+S+Tp˜=φHδ1sr+δ2sr*+constant=δ˜1logFL+δ^2logFL*+(δ1δ2)tw˜+[φ+δ^2logFL/FL*]H+constant=δ˜1logFL+δ^2logFL*+(δ1δ2)tw+(δ1δ2)(1γ1)(pimp˜)+[δ^2log(FL/FL*)φ]H+constant,(15.2)

to identify the form of the union’s rate of substitution between the net real wage and employment. Remark that in (15.2) φφ^/(1q) is positive while δ^2=δ2/(1q˜) is non-negative. Moreover,

δ˜1δ1(1q˜)+δ2(1γ1)q˜1q˜,δ˜2δ2(1γ1q˜)1q˜:

thus, δ˜1 is positive both under cases (B) and (C) and is zero in case (A), while δ˜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

logFL*=1σ(y*f)γ0,(16)

where γ0 = -logαL > 0. To estimate (16), however, we have to evaluate y* and (y* - ℓf), 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 + (∂Y/∂L)(LF - L). Thus, the average productivity 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 (ℓf - ℓ).

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:

w+S+Tp˜=G0+G10(pimp˜)+G20(y)(δ˜2γ0/σ)ur+(δ1δ2)(S+T+ʌ)+(δ^2γ4φ)[βγq(1ʌ)],(17)

where G0 is constant;G10(δ1δ2)(1γ1);G20[δ˜2δ˜1σ+γ3δ˜2]; γ3 ≡ (ur/σ)(1 - σ)/σ > 0; γ4 ≡ (ur/σ) - [γ0(y - ℓ) (1 - σ)/σ] > 0.

Notice in (17) that the compensation effect has the sign of the coefficient of the tax wedge, tw = S + T + ʌ, while the progressivity effect has the sign of the coefficient of the progressivity index, H = (β - γq)/(l -ʌ), where H is positive only if ʌ is not flat. Moreover, if δ1 = δ2 = 0, I falls under case (A); if δ1 > 0 and δ2 > 0, I falls under case (C); if δ1 > 0 and δ2 = 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 δ2 = 0, the wage setting in (17) shows three distinctive features: it is certainly negatively elastic to the unemployment rate (ur); it is possibly influenced by a negative compensation effect (if δ1 - δ2 < 0); and by a non-negative progressivity effect (if δ^2γ4φ0).

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

Δwt=G0+ΔpimT+G1(pimp˜)τ+G11(pimp˜)τ1+G12Δ(y)τ+{G2(y)τ1+G3urτ1+G4(S+T+ʌ)τ1+G5[(βγq)/(1ʌ)]τ1a3(w+S+T+p˜)τ1},(18)

where τ 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, G3/a3=δ^2γ0/σ,G4/a3=δ1δ2,G5/a3=δ^2γ4φ, so that one expects a3 > 0, G2 > 0, G3 ≤ 0, G4 and G5 of any possible sign but internally consistent with G3, G1, G11

The macroeconomic wage equation (18) is estimated for nine European countries in the period 1960-88, using yearly comparable data supplied by the OECD. 17/ The instrumental variable technique is adopted to correct for the endogeneity bias due to the presence in (18) of simultaneously endogenous variables (p˜,yandw). 18/ We use in each country the labor force and the business sector capital stock (in volume) as instruments for labor productivity, y - ℓ, 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 β - γq 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 ʌ 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). 19/ In other countries (notably Sweden since 1979), the long-run semi-elasticity of the wage rate relative to progressivity changed 20/ 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.

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.

Table 3a.

Estimates of the Wage Equation in Nine European Countries, 1960-88 1/

Δw=constant+Δpimτ+G1(pimp˜)τ+G11(pimp˜)τ1)+G12Δ(y)τ)+G2(y)τ1)G3urτ1+G4(S+T)τ1+G4ʌτ1+G5{β^[1/(1ʌ)]}τ1a3(w+T+Sp˜)τ1

article image

The estimated constants are not reported.

The G12=G2 hypothesis is not refused by the data and therefore the G12=G2 constraint is imposed on the estimate; when the a3=G12=G2 hypothesis is not refused by the data, also this constraint is imposed on the estimate.

The hypothesis that the estimated coefficient of (S+T)τ-1 is equal to that of ʌτ-1 is refused by the data; everywhere else, it is accepted and therefore imposed on the estimate.

The G1=G11 hypothesis is not refused by the data and therefore the G1=G11 constraint is imposed on the estimate.

The a3=G4 hypothesis is not refused by the data and therefore the a3=G4 constraint is imposed on the estimate.