Personal Income Tax: Incentive or Disincentive to

Personal Income Tax: Incentive or Disincentive to Work Effort? Basil Dalamagas and Stelios Kotsios University of Athens, Department of Economics P.O.Box 8444, 10010 Athens, GREECE Abstract This paper investigates the implications of an exogenous increase (decrease) in the income tax schedule for hours worked per employee and per self-employed in a general equilibrium model. The model is estimated for France, Italy, Spain and Portugal using the GMM estimation technique. Steady-state analysis and econometric estimates show that tax withholding provisions diversify the response of employees and the self-employed to adjustments in the direct tax system. Among the results is that, in the presence (absence) of tax withholding provisions, the labor supply curve may become downward (upward) sloping. Thus, the argument advanced by those who advocate the implementation of a strategy aiming at reducing taxes on labor in order to increase incentives to work need to be carefully reconsidered.

Key Words: Hours worked per employee and per self-employed, tax withholding, incentive to work, labor supply curve, marginal income tax rate, income and substitution effects.

JEL: E1, E6

Personal Income Tax: Incentive or Disincentive to Work Effort?

1. Introduction In the last two decades, several countries have implemented tax reforms to increase incentives to work. The conventional wisdom among politicians seems to support the view that tax-induced increases in wages tend to stimulate extra working hours and/or to encourage greater participation rates. On theoretical grounds, the analysis proves to be more complicate and the conclusions tend to vary significantly across researchers. Tax-induced increases in wages may lead to shorter or longer working time schedules, depending on whether the income effect (adverse to work effort) dominates (or is offset by) the substitution effect (favorable to work effort), respectively. In standard static textbook models of the labor-leisure choice, the labor supply curve is upward sloping in the absence of an income effect. Similarly, supply-side economists advocate the implementation of a strategy leading to lower taxes on labor in order to have the private agents’ incentive to work increased. Thus, it appears that income tax-rate cuts are effective only in the context of an upward sloping labor supply curve, where the substitution effect dominates the income effect. However, a number of empirical studies cast serious doubts on this premise by pointing to a downward sloping or backward bending labor supply curve (see Dickinson, 1999, and Chung-Lin, 2003). If this is really the case, the effect of the EU Commission’s proposal for lower taxes on labor and less progressive income tax schedules may turn out to invalidate the initial planning for greater participation rates. Some additional factors that bear on the income tax-working time relationship are also mentioned in the literature:

• The secular rise in leisure may not have been a simple expression of individual choices. Instead, it may have been the product of a complex set of social forces, such as the rise of mass education and the strength of unionism. • Unexpected or sudden tax increases may be felt more keenly and may have a sharper substitution effect than anticipated increases or gradual adjustments. • In examining the response of private agents to changes in the tax regime, a distinction is often made between the male and female working population (see, for example, Klevmarken, 2000), where it is frequently observed that women adjust their hours of work more easily than men. Similarly, distinctions are mentioned in the literature between various races or professions or working-age categories, within the same country –especially in USA – as well as between unionised and non-unionised workers, especially in the UK (see, for example, Belfield and Heywood, 2001). For a description of the contemporaneous trends in the area of labor force decomposition, see Bender et al. (2005). • Tax withholding provisions may be of crucial importance in formulating individual choices. In general, income taxes withheld are noticed less and thus they are less damaging to work effort than direct taxes paid by direct assessment. • The proportion of workers, who are not free to adjust their supply of effort, in the total working population may be a key factor in determining the response of work effort to changes in personal income tax rates. Recipients of lower wages are typically subject to contracts and may have to choose between working a given number of hours or not at all. In this case, income tax leaves work effort more or less unaffected. On the other hand, households commanding high salaries tend to be self-employed, employers or in supervisory positions and, hence, less subject to work discipline. In addition, they may be motivated by non-pecuniary factors, so that their supply of effort is relatively inelastic to income tax changes. Farmers form a specific category of self-employed with a working time schedule being determined largely irrespective of the income tax structure. Lastly, some income recipients (e.g. the executive, who sets his own wage rate) may be able to recover income tax by demanding an increased wage rate. In this case, the response of hours worked to income tax changes is negligible. 2

The present study will explore the validity of the last two propositions; that is, it will attempt to substantiate the argument that both tax withholding and the proportion of employees in the total labor force play an important (and thus far largely neglected) role in determining the shape of the supply curve of labor. To this end, we will distinguish between two groups of labor. The first group encompasses all employees. The term ”employees” covers a wide range of working people (in manufacturing, retail and wholesale establishments, financial institutions, the public sector and so on) who bear two common features. First, they are subject to the provisions of labor legislation and to contracts which do not allow deviations from the prevailing working time pattern. Second, a portion of their wage, corresponding to their personal income tax liability, is retained by their employers who refund it to the tax collection agency on a monthly basis (tax withholding). The second group of the labor force contains the self-employed. In the present context, the term ”self-employed” denotes a large number of income recipients (e.g. employers, managers, farmers, free-lancers, lawyers, physicians, property owners) who are free to adjust their hours of work. They are also not subject to the tax withholding provisions, as their tax liability is assessed each year on income accrued in the previous year. Our analysis has two novel features. First, the labor force is not treated as a homogeneous group of workers subject to the same tax rules, as is the underlying assumption in all previous studies. Tax collection regulations differ between employees and the self-employed and the ratio of employees to the self-employed varies widely across countries and over time; as a result, the response of employees to changes in income tax rates may not be in the same direction or of the same magnitude as the response of the self-employed. Therefore, policy prescriptions for tax reform, in order to encourage incentives to work, may prove to be inefficient if they are based on the average response of the total labor force. Analogous reasoning applies to all of the previous studies which divide the labor force into groups of workers (unionised or not, male or female, high- or low-skilled, white or other races and so on), as no account is taken of whether each group contains employees and/or self-employed. Second, we extend our analysis beyond the limits set out by the general equilibrium model by incorporating the most significant country-specific variables. The inclusion of country-specific variables ensures that the relevant information set, which is used by agents, is superior to the information set assumed by the general equilibrium model. Omitting this superior information is akin to omitting 3

statistically significant variables and may lead to serious mismeasurements of the relative statistics. The paper is organised as follows. Section 2 describes the theoretical foundation of the model and specifies the propositions and hypotheses to be tested. In Section 3, the general equilibrium model is constructed and analysed. Section 4 estimates the model and uses the benchmark economy to illustrate the difficulties of explaining employment behavior when superior information is omitted. Section 5 explores the steady-state dynamic properties of the model. Section 6 introduces superior information, in the form of country-specific variables, and assesses the effect of marginal income tax rate changes on working hours, by utilising standard simulation techniques. The income and substitution effects of taxation are examined in Section 7. Section 8 is the conclusion.

2. Theoretical framework In tracing out the determining factors of the labor supply response to changes in the income tax rate, a general equilibrium model is built and analysed for each of the sample countries (France, Italy, Spain, Portugal) over the period 19652005, using annual data. The reason for choosing these countries is that they are Mediterranean or Southern EU countries whose citizens have approximately the same idiosyncrasy and exhibit closely related attitudes toward the tax collecting agents (medium-to-large informal economic sectors and tax evasion problems). In addition, they have a quite high standard of living and share the same economic principles, growth culture and institutional frameworks. However, a marked crosscountry variation in labor market performance and tax collection provisions is observed. For instance, Italy and Portugal stand out for their excessively tight regulations, as shown by the summary indicator of employment protection legislation — governing the process of hiring and firing workers — for selected OECD countries (OECD Economic Surveys: Italy, 2000, p. 154). Despite some easing in 1999, employment protection legislation in Portugal remains relatively strict, with costly severance payments, reducing the ability of firms to react quickly to shocks. Spain not only suffered from one of the highest unemployment rates for many years but also had one of the highest effective levels of severance payments for permanent workers, whose employment protection continues to be one of the highest in OECD. Moreover, the ratio of employees to total labor force varies across the four countries and over time, as shown in Fig.1. The time path of this ratio is in 4

accordance with the findings of OECD ( OECD Economic Surveys: Portugal, 2003, p.116) showing that the level of self-employment accounts for almost 17 per cent of total non-agricultural civil employment in Portugal (23% in Italy, 16% in Spain), the third highest in the EU (second highest in Italy, fourth highest in Spain), whereas the average share in the EU is 12.5 per cent (France: 7.5%).

Finally, tax withholding takes place in Italy, Spain and Portugal, but not in France. A summary of the last two features for the economies studied is presented in Table 1. On conceptual grounds, two extreme boundaries seem to exist within which the labor supply response to a tax reform would fluctuate. In the first extreme case, personal income tax is withheld for employees who account for the total labor force (there are only a few employers). Under these conditions, there are three reasons to support the argument that the response of the working time schedule to a tax reform will turn out to be negligible: • The amount of tax owed by the employees to the government is retained by the employers in the form of wage-reducing monthly installments. As a consequence, there are no further transactions of employees with the tax authorities and the take-home pay carries no information regarding possible changes in tax liability. • The annual wage bill is less volatile than the annual earnings of the selfemployed as wage rate adjustments are subject to the discipline of the incomes policy rules. Thus, changes in the taxpayers’ status, via shifting from low income brackets (with low marginal tax rates) to high income brackets (with high marginal tax rates) – or vice versa – in a progressive income tax system are not frequently observed in practice (except for periods of a large-scale fiscal drag). • Full-time employees are subject to contracts which predetermine the number of daily (weekly, monthly etc.) hours of work. In this case, changes in marginal tax rates may influence solely overwork and the working time of part-time employees, of (married) women, of new-comers to the labor force and so on. 5

In the second extreme case, the labor force consists solely of the self-employed, with no employees at all, so that personal income tax cannot be withheld. The wedge that is drawn by the income tax between gross income and take-home pay is now clearly expected to be born by taxpayers. The current-year income tax, which will be paid in the course of the next year, is assumed to be fully perceived and discounted by taxpayers and the current-period tax windfalls will be saved in order to pay off the future tax obligation. Under such a scenario, an income tax increase will probably give rise to both an income effect, favorable to work effort, due to the lower level of income, and a substitution effect, adverse to work effort, as relative prices change, following the lower net of tax price of labor. The net result will depend on the relative strength of the two effects, so that a definite conclusion can be reached only in the context of an empirical investigation. The greater sensitivity of hours worked by the self-employed to changes in income tax rates can be attributed to the fact that the self-employed face a cost in the process of obtaining information on their tax burden, the size of the cost being a function of the structure of the tax system. Three kinds of information cost can be monitored. These are the costs attributable to the complexity of the tax system, the visibility of taxes and the timing of tax payments. A complex tax system is one that is dominated by direct taxes, and especially by a personal income tax with different coverage and a variety of marginal tax rates and collection practices. The degree of visibility of the tax system depends on the extent to which the taxpayer is aware of his tax burden. The taxes which directly reduce personal income or wealth and are not withheld are more visible, whereas visibility is reduced when taxes are levied in the course of market transactions. As to the timing of tax payments, it seems reasonable to assume that taxes paid at large intervals and in large amounts are perceived more heavily than taxes of the same total amount which are paid in frequent small installments (e.g. via withholding). As shown in Table 1, none of the sample countries can be assigned to any of the above extreme cases. France with no tax withholding has a low average proportion of self-employed to total labor force. The corresponding proportion for Italy, Spain and Portugal, with tax withholding provisions, is high, but less than 100 per cent. Thus, in exploring the sensitivity of hours worked to tax changes, a determining factor will also be the relative weight of tax withholding vis-a-vis the proportion of employees (or the self-employed) in the total labor force. Different kinds of models have come under the heading of the income tax-work effort relationship. All of them have a common feature, namely that both em6

ployees and the self-employed form a common variable that enters the production function. To study the effects of taxation on labor in the context of such models seems a natural exercise, but existing literature leads to surprisingly different, or even opposing, conclusions. To mention just a few of these studies, Yellen’s (1984) ’rudimentary’ efficiency wage model finds that a wage tax has no effect on the after-tax wage and a negative effect on employment. In contrast, Johnson and Layard’s (1986) moral hazard or shirking model concludes that a labor tax reduces the after-tax wage and leaves employment unaffected. In the adverse selection model of Weiss (1980), a wage tax does not affect the after-tax wage but causes a decrease in employment. Pisauro’s (1991) moral hazard-efficiency wage model predicts that a wage tax has a negative effect on employment. Fiorito and Padrini’s (2001) model separates labor supply into female and male components and their results show that increasing taxation on labor leads employment negatively. In the Aronsson, Lofgren and Sjogren (2002) unionised economy model, where hours of work are determined endogenously, permanently increased tax progressivity raises the real wage rate and reduces employment. For a plethora of relative studies, see the literature in the aforementioned articles. This paper extends the analysis of income taxation and working time to a dynamic general equilibrium framework. The parameters of the derived model are estimated econometrically and the relative coefficient values are used to carry out policy simulations and to evaluate both the elasticity of hours worked with respect to changes in the marginal income tax-rate and the income-substitution effects. This approach enables us to study how the actual working time path, and not just its steady-state counterpart, is affected by changes in the income tax system. We find that a higher marginal (personal income) tax rate leaves employee’s hours of work unaltered in the sample countries that have tax withholding provisions but increases them in France which has no tax withholding. In addition, tax rate increases negatively affect hours worked per self-employed in all of the sample countries.

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3. The model 3.1. Households Consider a two-group economy, in which the first group consists of employees and the second group is made of the self-employed. Households in both groups derive income from providing capital and labor services to firms. The only fundamental uncertainty present in the economy is an exogenous shock to marginal income tax rates. The aim of the present study is to quantify the response of working time of both the average employee and the average self-employed to changes in the marginal rate of the personal income tax. The analysis to follow is crucially dependent upon the way the aggregation problem is dealt with. This problem revolves around the question of which is the most suitable method for incorporating the behavior of the two groups into a single social utility function. General equilibrium models with unemployment usually employ two alternative approaches to address the aggregation problem. The first approach postulates that private agents choose an unemployment-insurance level which allows them to accumulate the same level of asset and, hence, to maintain the same level of consumption, at each state (of employment or unemployment) and at each date (see, for example, Langot, 1996). The second approach assumes that there exists a family whose members pool their income and, hence, insure themselves against income fluctuations, thus being able to keep the same family consumption level over time (see, for example, Merz, 1995). 1 The second approach yields some ground on which to argue that, to a first approximation, group-income pooling provides a plausible description of reality, after allowing for a slight modification of the assumption concerning the working status of the two groups. Instead of referring to employed and unemployed workers, the present study defines the first group as consisting of employees and the second group as consisting of the self-employed. Within this framework, the economy is assumed to be populated by a continuum of identical infinitely lived households. Each household is thought of as a very large extended family which contains a continuum of members. Members in each family perfectly insure each other against income variations which are due to the employment status (employees or self-employed) of the members or 1

I am deeply indebted to an anonymous referee for his guidance on the complicate issue of aggregating the utility levels of employees and the self-employed.

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to changes in their employment status. The social planner evaluates streams of consumption services (ct ) and employment (hours of work, ht ), according to the objective function E0

∞ X

β t U (ct , ht )

t=0

0≺β≺1

with preferences of the representative household specified as ¶ µ h1+σ t U (ct , ht ) = U (ct ) − G (ht ) = log ct − n , σ ≥ 0, n  0 1+σ

(1a)

(1b)

where β is the discount factor, σ denotes the inverse of the intertemporal elasticity of substitution for labor supply, and both U and G represent increasing and concave functions in their respective argument. The representative household can be thought of as consisting of a very large number of members who pool their income and, thus, provide each other with complete insurance against income losses or against changes in occupational status. To enhance both understanding of the workings of an economy composed of employees and self-employed and the ability to model their behaviour, it would be advisable to consider a third approach, which could supplement the approach of Merz (1995), in dealing with the aggregation problem. Since, there are two types of households who differ in their working status, the representative household’s consumption may also be derived by invoking the identity for aggregate consumption in the economy, at a given point in time, C = CE + CF which states that aggregate consumption , C, is equal to the sum of the total consumption of employees , CE , and the total consumption of the self-employed, CF . Dividing the last relationship by the total population of both employees, E, and the self-employed, F, gives the definition of the average or per capita consumption, c, in the economy C CE E CF F = + E+F E+F E E+F F or

9

c = pce + (1 − p)cf

0≤p≤1

(2a)

where ce = CEE is the average consumption per employee, cf = CFF is the average E is the probability of being an emconsumption per self-employed and p = E+F ployee. When p = 1, there are only employees in the economy, whereas, for p = 0, there are only self-employed. A similar procedure to the above leads to the definition of the average or per capita working time, h, in the economy at a given point in time h = phe + (1 − p) hf

(2b)

Substituting (2a) and (2b) into the utility function (1a,b) permits the transformation of the so far exogenously treated occupational status, as indicated by p , into a choice variable for the household. However, the aggregation aspects of this transformation may give rise to several issues which are reviewed in Appendix A. The joint budget constraint faced by both types of households is ct +it = pt we,t he,t (1 − τ t )+(1 − pt ) [wf,t hf,t − (1 − rt ) (τ t−1 wf,t−1 hf,t−1 )]+rt kt +(nw)t (3) where it is investment, we,t (wf,t ) is the hourly wage rate (earnings) for employees (self-employed), τ t is the average (personal) income tax rate, rt is the interest rate, (nw)t is the non-wage income and kt is capital. The law of motion for the capital stock is given by kt+1 = (1 − δ) kt + it , k0 given

(4)

where δ ∈ (0, 1) is the capital depreciation rate. The first term on the right-hand side of Eq.(3) is associated with the tax withholding provisions for employees. When there are only employees in the economy, pt = 1, the budget constraint collapses to the standard form used in previous studies, ct + it = wt ht (1 − τ t ) + rt kt + (nw)t On the contrary, if there are only self-employed in the economy, pt = 0, the first term on the RHS of Eq.(3) is dropped and tax withholding is absent. Each taxpayer, in estimating his take-home pay, will subtract the tax paid on his previousyear income from his current income while augmenting the current income by the interest receipts from the postponement of his tax liability. 10

3.2. Firms There is a continuum of identical competitive firms in the economy, with the total number normalised to one. Each firm produces output yt according to a constant elasticity of substitution (CES) technology ¡ £ ¡ ¢ρ ¢ρ ¤ 1−a ρ yt = Akta pt ebe t he,t + (1 − pt ) ebf t hf,t

(5)

of being an employee), A where ρ ≤ 1, pt is the share parameter ¡ b(probability ¢ be t t f is a neutral productivity term, and e e are factor augmenting productivity terms. More specifically, be is an index of the employee’s productivity which may reflect observed or unobserved components of the employee’s human capital, as well as technical change favoring employees relative to self-employed. This specification implies that the elasticity of substitution between the labor aggregate and capital inputs is equal to one and the elasticity of substitution between employees 1 and the self-employed is σ = 1−ρ . Given the prices of output and factor rewards, the firm’s problem is to choose the amount of both capital and labor services that maximise the present value of profits. Thus, the decision problem is max E0

t ∞ Y X t=0 j=0

Rj−1 (yt − rt kt − we,t he,t − wf,t hf,t )

subject to constraint (5). Note that Rj = 1 + rt − δ . Since in competitive markets all factors are paid their marginal product, we have that wages of employees, earnings of self-employed and the return on capital are given by T we,t (1 − a) yt pt ebe tρ hρ−1 e,t we,t = = (6) ρ ρ b t e he,t pt (e he,t ) + (1 − pt ) (ebf t hf,t )

T (1 − a) yt (1 − pt ) ebf tρ hρ−1 wf,t f,t wf,t = = (7) ρ ρ b t b t e f hf,t pt (e he,t ) + (1 − pt ) (e hf,t ) ayt (8) rt = kt ¡ T ¢ T where we,t = we,t he,t wf,t = wf,t hf,t represent the total annual wage bill (earnings) of employees (self-employed).

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3.3. Government The role of the public sector in our model is to collect taxes and spend the revenues on government purchases. Government spending, gt , is given by gt = j0 + j1 gt−1 + j2 yt

(9)

In Eq.(9), current government spending is a function of both the previous-year government spending – as fiscal authorities do not apply the principle of zerobase budget – and current income (Wagner’s law). A dynamic specification of government spending is frequently employed in Public Economics to capture longterm trends. For example, in Devereux et al. (1996), government expenditure follow a first-order autoregressive process; in J. Guo (2004), the coefficient of lagged public spending governs the persistence of a fiscal shock; in Barro (1987), the first difference of government spending is adequately modeled with second order and moving average terms. The government finances its expenditure by personal income taxes, Ty,t , and other direct and indirect taxes, Tt . The excess of government spending over tax •

revenue is financed by issuing government bonds, B t (= Bt −Bt−1 , with Bt standing for the public debt). Thus, the government budget constraint in period t is •

gt = Ty,t + Tt + B t The progressive element of the personal income tax is captured by the following tax revenue function: Ty,t = θ(T B)γt (10) where (T B)t is the tax base which is given by (T B)t = pt we,t he,t + (1 − pt ) wf,t−1 hf,t−1 In Eq.(10), the parameter γ measures the elasticity of the income tax revenue with respect to the tax base, i.e. the degree of personal income-tax progressivity. The tax is progressive, regressive or proportional, depending on whether γ Â 1, γ ≺ 1, or γ = 1, respectively. It should be noted that the parameter γ measures the time-series progressivity, i.e. the response of tax revenue to changes in household income from one year to the next, as a result of both inflation (fiscal drag) and adjustments in tax rates and tax-base definitions. The time-series progressivity should not be confused with the cross-section progressivity, as the 12

latter measures the extent to which tax revenue rises as we move from low to high income groups within a particular year. The average tax rate, τ t , is given by Ty,t θ(T B)γt τt = = = θ(T B)γ−1 t (T B)t (T B)t whereas the marginal tax rate, τ t , is estimated as follows: τt =

∂Ty,t = γθ(T B)γ−1 = γτ t t ∂(T B)t

(10a)

or

τt (11) γ Since the marginal tax rates are widely used in literature for tracing the sensitivity of work effort to a tax reform (see, however, Fiorito et al., 2001, for a different view), the average tax rate in the household budget constraint (3) will be replaced, in what follows, by its equivalent in Eq.(11). We close our model with the National Accounts identity τt =

yt = ct + it + gt

(12)

3.4. Solving the household’s optimisation problem The household faces the problem of maximising the expected discounted utility (1a,b) subject to the budget constraint (3). Substituting the capital-stock equation (4) into the budget constraint (3) and using Eq. (1a,b) gives the Lagrangian ¸ n 1+σ L = (pt he,t + (1 − pt ) hf,t ) 1 + σ t=0 µ ¶ τt he,t − −λt {pt ce,t + (1 − pt ) cf,t + Kt+1 − pt we,t 1 − γ ¸ ∙ τ t wf,t hf,t − (1 − pt ) wf,t hf,t − (1 − rt ) − (nw)t − (1 − δ + rt ) Kt } π t γ μt ν t m X

∙ β log (pt ce,t + (1 − pt ) cf,t ) − t

13

where πt =

τt τ t−1

, μt =

wf,t hf,t , νt = wf,t−1 hf,t−1

(13a)

The first-order conditions for the choice of consumption and hours worked are βt ∂L = pt − λt pt = 0 ∂ce,t ct or

βt λt = , ct

and

λt+1

β t+1 = ct+1

(13b)

∂L βt = (1 − pt ) − λt (1 − pt ) = 0 ∂cf,t ct or λt =

βt , ct

and

λt+1 =

β t+1 ct+1

(13c)

Note that the derivatives with respect to consumption per employee (13b) and consumption per self-employed (13c) give Lagrange multipliers of the same value. µ ¶ ∂L τt σ t = −β n (pt he,t + (1 − pt ) hf,t ) pt + λt pt we,t 1 − =0 ∂he,t γ Rearranging (13b) and substituting it into the last expression gives ¶ µ τt σ we,t ct n [pt he,t + (1 − pt ) hf,t ] = 1 − γ

(14a)

¶ µ ∂L τ t wf,t σ t =0 = −β n (pt he,t + (1 − pt ) hf,t ) (1 − pt )+λt (1 − pt ) wf,t − (1 − rt ) ∂hf,t π t γ μt ν t Rearranging (13c) and substituting it into the last expression gives ¸ ∙ (1 − rt ) τ t σ ct n [pt he,t + (1 − pt ) hf,t ] = 1 − wf,t γπt μt ν t ∂L = λt (1 − δ + rt ) ∂Kt 14

(14b)

and

∂L = λt+1 (1 − δ + rt+1 ) ∂Kt+1

Combining the budget constraint (3) and the capital-stock equation (4) and differentiating with respect to Kt gives ∂Kt+1 = 1 − δ + rt ∂Kt The last three expressions are combined to give ∂L ∂L ∂Kt+1 = ∂Kt ∂Kt+1 ∂Kt or λt = λt+1 (1 − δ + rt+1 )

(15a)

By properly manipulating the expressions (13b) and (15a), we obtain βt β t+1 = λt = λt+1 (1 − δ + rt+1 ) = (1 − δ + rt+1 ) ct ct+1 or ct+1 = βct (1 − δ + rt+1 )

(15b)

with lim β t

t→∞

kt+1 =0 ct

(16)

being the transversality condition. Eq.(14a) –Eq.(14b) – is an intra-temporal condition that equates the employee’s – the self-employed individual’s – marginal rate of substitution between consumption and leisure to the real hourly wage rate (earnings). Eq.(15b) is the standard Euler equation for intertemporal consumption choices. Note that following a similar procedure for the consumption path of the self-employed, we end up with the same relationship (15b).

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4. Estimating the general equilibrium model 4.1. Determining working hours of the self-employed The general equilibrium model, as described in the previous section, cannot be estimated econometrically as it stands, because the production function (5) contains the unobservable variable hf,t , namely the annual hours of work of the selfemployed. We follow three steps to overcome this problem. As a first step, we recast the production function in two new equivalent forms: yt =

yt =

1−a ρ

Akta pt

Akta

(1 − pt )

ebe (1−a)t h1−a e,t 1−a ρ

∙ µ ¶ρ ¸ 1−a ρ 1 − pt ebf t hf,t 1+ pt ebe t he,t

ebf (1−a)t h1−a f,t

∙ 1+

pt 1 − pt

µ

ebe t he,t ebf t hf,t

¶ρ ¸ 1−a ρ

Our second step is to divide Eq.(6) by Eq.(7), and vice-versa: µ be t ¶ρ T we,t e he,t pt = T 1 − pt ebf t hf,t wf,t µ ¶ρ T wf,t 1 − pt ebf t hf,t = T pt ebe t he,t we,t

(17)

(18)

(19)

(20)

The third step is to substitute Eq.(19) into Eq.(18) and Eq.(20) into Eq.(17): Ã ! 1−a ρ T 1−a w f,t ρ a be (1−a)t 1−a yt = Akt pt e he,t 1 + T (21) we,t yt = Akta (1 − pt )

1−a ρ

ebf (1−a)t h1−a f,t

Ã

T we,t 1+ T wf,t

! 1−a ρ

(22)

The logarithmic form of Eq.(21) can be estimated econometrically to provide the coefficient values of A, a, ρ and be . It is now straightforward to solve Eq.(22) in terms of hf,t by using the estimated coefficients of Eq.(21) and the growth identity bf,t = d log yt − be After carrying out the numerical calculation of the annual hours of work of the self-employed, we can proceed to merging the three subsectors (households, 16

firms, government) into a comprehensive general equilibrium model in order to determine the employment functions. Starting with he,t , we solve (14a) for we,t , equate it to (6) and rearrange the terms. To facilitate the econometric estimation, we set ∙ ¸σ 1 − pt σ σ σ ωt (22a) [pt he,t + (1 − pt ) hf,t ] = pt he,t 1 + pt where

ωt =

hf,t he,t

(22b)

and à ! ∙ µ bf t ¶ρ ¸ T ¡ b t ¢ρ ¡ be t ¢ρ w h 1 − p e t f,t f,t ρ ρ = pt ebe tρ he,t 1 + T pt e he,t +(1 − pt ) e f hf,t = pt ebe tρ he,t 1 + pt ebe t he,t we,t by using Eq.(20). The employment equation for employees is then given by ⎡ ³ ´ ⎤a1 τt ∙ ½ ¾¸a2 1 − pt ⎢ (1 − a) yt 1 − γ ⎥ ³ he,t = a0 ⎣ ωt ⎦ pt 1 + T ´ wf,t p t ct 1 + wT

(23)

e,t

¡ ¢ 1 wT w 1 σ where a0 = n1 1+σ , a1 = 1+σ , a2 = − 1+σ and wf,t = wf,t ωt . T e,t e,t In determining hf,t , we solve Eq.(14b) for wf,t , equate it to Eq.(7) and rearrange the terms. By using Eq.(19) and carrying out the necessary manipulations, similar to those adopted in deriving Eq.(23), we end up with the employment equation for the self-employed: ⎡ n o ⎤β 1 τt ∙ ¾¸β 2 ½ pt ⎢ (1 − a) yt 1 − (1 − rt ) γπt μt ν t ⎥ −1 ³ ´ ω hf,t = β 0 ⎣ ⎦ (1 − pt ) 1 + wT 1 − pt t ct 1 + we,t T f,t

where β 0 =

1 ¡ 1 ¢ 1+σ

n

(24)

, β1 =

1 , β2 1+σ

σ = − 1+σ and

T we,t T wf,t

=

we,t −1 ω . wf,t t

The coefficient values of the constrained estimation of the model (a0 = β 0 , a1 = β 1 , a2 = β 2 ) will be used throughout the econometric analysis, as these values were found to be closely related to the coefficient values of the unconstrained estimation (a0 6= β 0 , a1 6= β 1 , a2 6= β 2 ). 17

4.2. Estimation method, data measures and GMM results The structural parameters of the model are estimated as follows: The parameter δ is identified by the capital-stock equation (4) E [Kt+1 − (1 − δ) Kt − it ] = 0 The parameter α is identified through the Euler Eq. (8) ¶ µ αyt =0 E rt − Kt

(25)

(26)

The parameters γ and θ are identified from Eqs. (10) and (10a) E [Ty,t − ϑ (T B)γt ] = 0 ¤ £ =0 E τ t − γϑ (T B)γ−1 t

(27)

E [ct+1 − βct (1 − δ + rt+1 )] = 0

(29)

(28)

The parameter β is identified by the intertemporal Euler Eq. (15b)

The following three moment restrictions are employed to estimate the parameters j0 , j1 , j2 by using Eqs. (9) and (10) and the government budget constraint: E (gt − j0 − j1 gt−1 − j2 yt ) = 0

(30)

E [(gt − j0 − j1 gt−1 − j2 yt ) gt−2 ] = 0 ¶¸ µ ∙ • γ =0 E (j0 + j1 gt−1 + j2 yt ) − θ (T B)t + Tt + B t

(31) (32)

Given the production function (5), the ratio of factor payments (19) and the growth identity bf,t = d log yt − be the following three moment restrictions are used to estimate the parameters p, A, be : o n ¡ b £ ¡ be ¢ρ ¢ρ ¤ 1−α a ρ f,t =0 (33) E yt − Akt pt e he,t − (1 − pt ) e hf,t 18

E

´ o n³ ¡ £ ¡ ¢ρ ¢ρ ¤ 1−α ρ yt−1 = 0 yt − Akta pt ebe he,t − (1 − pt ) ebf,t hf,t "

T we,t pt E − T wf,t 1 − pt

µ

ebe he,t ebf,t hf,t

¶ρ #

=0

(34)

(35)

Lastly, the parameters α0 (= β 0 ), α1 (= β 1 ) and α2 (= β 2 ) are identified through the employment Eqs. (23) and (24): ⎧ ⎫ ⎡ ³ ´ ⎤α1 ⎪ τ ∙ µ ¶¸ t a2 ⎪ ⎨ ⎬ 1 − pt ⎢ (1 − a) yt 1 − γ ⎥ ³ ´ =0 p 1 + ω E he,t − a0 ⎣ ⎦ t t T wf,t ⎪ ⎪ p t ⎩ ⎭ ct 1 + T

(36)

we,t

⎧ ⎫ ⎡ ³ ´ ⎤β 1 (1−rt )τ t ⎪ ⎪ ∙ ¶¸ µ β ⎨ 2⎬ pt ⎢ (1 − a) yt 1 − γπt μt ν t ⎥ ³ ´ E hf,t − β 0 ⎣ =0 ⎦ (1 − pt ) 1 + wT ⎪ ⎪ (1 − pt ) ω t ⎩ ⎭ ct 1 + we,t T

(37)

f,t

⎧⎛ ⎫ ⎡ ⎞ ³ ´ ⎤α1 ⎪ ⎪ τt ∙ µ ¶¸ a ⎨ ⎬ 2 1 − pt ⎜ ⎢ (1 − a) yt 1 − γ ⎥ ⎟ ³ ´ ⎦ E ⎝he,t − a0 ⎣ pt 1 + ωt ⎠ he,t−1 = 0 wT ⎪ ⎪ pt ⎩ ⎭ ct 1 + f,t T

(38)

we,t

We have 14 parameters to be estimated (δ, a, γ, θ, β, j0 , j1 , j2 , ρ, A, be , a0 , a1 , a2 ) and 14 moment conditions [Eqs. (25) to (38)], thus forming an exact identification system. These relationships will be used in the GMM (Generalised Method of Moments) to obtain the estimates of the parameters in the sample countries. Sources and definitions for all variables are reported in Appendix B. It should be stressed that data series on hours worked by employees had to be modified to account for the fact that employees are subject to contracts which do not permit deviations from the prevailing working time pattern. To this end, annual hours of work in the labor supply function for employees [Eqs. (36) and (38)] are re-defined to represent the difference between the actual hours of work per worker in manufacturing – as given by the OECD Labor Force Statistics – and the statutory hours of work –as given by the Main Economic Indicators of OECD and the Data Stream. Such a difference may be considered to reflect the

19

working time pattern over and beyond the official contracts (overtime, part-time work, occasional employment, work in agriculture and so on). The application of the GMM requires that each equation includes only stationary variables. Thus, before estimating the model, the order of integration of the variables has to be established. To assess their time-series properties, we carried out the Kwiatkowski-Phillips-Schmidt-Shin (KPSS) test. The results (available on request) suggested that, while the unit root hypothesis could not be rejected for the levels of each of the variables (yt , kt , pt , he,t , hf,t ) in the production function, the corresponding first-differenced series were stationary. Investigation of the univariate stationary properties of the series is only necessary, but not sufficient, for adequately specifying the model. In addition, the number of common trends in the multivariate representations must also be examined. If one or more linear combinations of the variables is drawn from a stationary distribution, the individually integrated variables are said to be cointegrated, thus defining steady-state relationships. Experimentation with the tests of Johansen and Juselius suggested the existence of one cointegrated vector in almost all countries at the 1% or 5% level (two cointegrating vectors for France). Various model evaluation diagnostic tests for the residuals of the cointegrating equation were conducted. They included tests for error autocorrelation, using LM(1) and LM(4) tests, and model misspecification (Ramsey’s RESET test), a residual normality test (Jarque-Beta), the conventional autoregressive conditional heteroscedasticity (ARCH) test and Breusch-Pagan-Godfrey’s heteroscedasticity test. All diagnostic tests indicated that the residuals are Gaussian without any strong evidence of autocorrelation and heteroscedasticity. In the interest rate equation (8), the test statistics for the interest rate and the output-capital ratio showed that the null hypothesis can be rejected in favor of the hypothesis that the series are I(0) at least at the 5% level. Finally, in testing for unit root behavior of the equations for consumption (15b), capital (4), government expenditure (9), tax revenue (10) and employment [(23),(24)], we were in each case unable to reject the unit root null hypothesis at conventional nominal levels of significance. However, putting the series into first difference form did appear to induce stationarity for each of the series. In addition, in almost all of the above relationships, the results of the trace and maximum eigenvalue tests failed to reject the null hypothesis of at least one cointegrating vector. In estimating the model, we applied the estimation technique adopted by Mankiew et al. (1985), who rely heavily on Hansen and Singleton’s (1982) method 20

of manipulating the general case of non-linear rational expectations models with future expectations by using a non-linear instrumental variables procedure. The instruments used were a constant, input prices and tax rates with two and three lags and growth rates of capital, employment, government spending, tax revenue and consumption lagged twice. Lastly, to obtain autocorrelation consistent standard errors, the weighting matrix has been defined as in Newey and West (1987). Model parameter estimates and standard errors for the sample countries are reported in Table 2.

5. Near steady state dynamics of the model In order to examine the dynamic responses of employment to different marginal tax-rate shocks, we first adopt the method of King-Plosser-Rebelo (1990) to determine the near steady state dynamics of the model. In our model, there are two state variables, the capital stock and government spending. For control variables, the households (employees and the self-employed) decide on consumption and working hours. In the following analysis, a transitory shock is considered, i.e. a once and for all increase in the marginal (personal income) tax rate that takes place in the first year of the sample period. Figures 2 to 5 plot the dynamic response of hours worked per employee and self-employed to a one standard deviation shock to the marginal tax rate. A preliminary inference from the inspection of the figures is that the sample countries can be partitioned into two groups: the first containing France and the second the remaining three countries (Italy, Spain, Portugal). Since these groups present remarkable differences as to the relation between work effort and tax adjustments, a more detailed analysis of the employment behavior by country is required. In France, hours worked per employee increase after a transitory shock in the first year and then return to the steady-state level. In contrast, hours worked per self-employed decrease in the first year and then return to the steady state level. The response functions show that a marginal tax rate shock increases the divergence of hours worked per employee from a steady trajectory by 10 per 21

cent but reduces the divergence of hours worked per self-employed from a steady trajectory by 15 per cent. In relative terms, the effect of the tax reform on the working time of the self-employed is one and a half times as strong as that of employees. The positive response of employees may be attributed to the fact that employees are generally ranked at lower income groups (with higher marginal utilities of income) than the self-employed: the average hourly wage rate amounts to FRF 86.4 over the sample period whereas the average hourly compensation of the self-employed is as high as FRF 235.8. As a result, a given tax increase deteriorates the employee’s standard of living more than it does with the selfemployed. Thus, the pressure to recover the tax-induced income losses will be larger for employees than for the self-employed. By a similar reasoning, lower aftertax incomes for employees tend to reduce their demand for all goods, including leisure, to a greater extent than it is the case with the self-employed, so that the income effect for employees tends to dominate the substitution effect. The opposite reasoning can be said to justify the adverse effect of the tax increase on the incentive to work of the self-employed, thus leading to a substitution effect that tends to dominate the income effect. It is not only that the self-employed are free of any kind of contracts and can easily adjust their working time. They are also subject to higher tax rates in the progressive personal income tax scale and the higher tax burden creates a stronger incentive to avoid taxes by working less. An indication of the greater flexibility of the self-employed over their working time schedule is the fact that their response to a tax increase is more than one and a half as strong as that of employees. In Italy, Spain and Portugal, hours worked per employee and self-employed respond differently to a tax-rate shock: Working time is uniformly affected by the shock across these three countries, but in a different way than in France. More specifically, a transient marginal tax-rate increase in Italy, Spain and Portugal does not affect hours worked per employee but reduces hours worked per selfemployed. With tax withholding in these three countries, a statistically insignificant response of employees to income tax-rate increases was to be expected. King et al. (1990) do not suggest any method for directly measuring the statistical significance of any response. An indirect measure, however, can be obtained by comparing the response of employees to that of the self-employed. As becomes evident from the inspection of the relative figures, the response of employees accounts for approximately 18 per cent of the response of the self-employed in Italy, while the corresponding proportions are 12 per cent in Spain and 13 per cent in 22

Portugal. Recall that the relative ratio was found to be 67 per cent in France. A tentative conclusion that can be drawn from the preceding analysis is that, in countries with tax withholding provisions, employees barely react to tax-rate changes compared to both the self-employed in their own country and employees in countries with no tax withholding. On the other hand, the self-employed in all the sample countries respond to tax-rate increases by reducing their working time horizon. A quantification of the effects of tax rate adjustments on employment behavior is taken up in the next sections.

6. Simulation experiments with a modified general equilibrium model The evidence presented in the previous section makes it clear that the steady-state analysis along the lines suggested by King et al. can hardly explain the dichotomous pattern in the response of work effort to marginal tax-rate shocks across the two groups of countries. In what follows, our interest will centre on using other estimation techniques, as well as identifying new factors that can justify the variety of statistical findings across the four countries. The addition of new factors means that the initial data set should be expanded along the lines suggested by OECD (OECD’s Economic Surveys, various issues). These surveys point to a number of institutional reforms and revisions in economic policy which occurred during the period examined in the four countries and may have potentially influenced labor supply. The most important of these factors, defined as country-specific variables, are the following: In France, the unemployment rate – to account for the government’s policy to reduce unemployment via curtailing hours worked – and two dummy variables to capture the two structural changes in the statutory working week (changeover to 39 hours over the period 1981-1982 and to 35 hours over the period 1998-2003). In Italy, a dummy variable for the period 1993-2003, to capture the growing labor market flexibility arising from the labor market reform adopted since the early 1990s (most notably the 1993 agreement between government and social patterns and the so-called Treu Package of 1997); the Treu Package incorporated a number of significant innovations, such as the introduction of temporary employment, a lessening of the sanctions on fixed-term contracts, an extension of apprenticeships and the introduction of private employment agencies. In Spain: (i) the unemployment rate and deviations of employment from trend to account for the labor market reforms of 1997 (aiming at reducing the high levels 23

of both strict employment protection legislation and structural unemployment, through revising permanent contracts, lowering severance payments and cutting social security contributions) and 2001 ( aiming at broadening the 1997 reform measures and making them permanent), (ii) a dummy variable for the period 19852003 to account for the fact that, in the mid-1980s, the authorities addressed the rigidities stemming from strict employment protection legislation by introducing fixed-term contracts with no firing costs. In Portugal: (i) the unemployment rate and employment growth to account for the National Action Plan for Employment in 1998 (improvement in employability fostering a climate favorable to entrepreneurship, enhancing workers’ and business adaptability and promoting equal opportunities), the new legislation of 2001 (tightening the rules of fixed-term employment contracts) and the supplementary legislation of 2002 (encouraging permanent employment), and (ii) a dummy variable for the period 1996-2003 to account for the Social Pact of 1996 (encouraging use of "atypical" work contracts – fixed-term and part-time – to suit new patterns of production). The above country-specific variables were added to the list of the RHS variables of Eqs.(23) and (24), as additional explanatory factors of hours worked per employee and per self-employed. The augmented employment relationships, in conjunction with the remaining equations of the model, were again used in GMM to get new estimates of the parameters. The results are presented in Table 2. The revised estimates will be employed to examine the dynamic response of working time to marginal tax-rate changes. To this end, dynamic simulations of the model are carried out over the sample period. Using exogenous time series but only the starting values of the endogenous variables, the model generated historically simulated values for work effort. We found that these values were close to average historical values, as indicated by the low values of the RMSE test (between 1.2% and 4.3%) for the equations considered. Thus, the model appears to track hours worked closely and provides as a basis run a good representation of the behavior of the four economies in a disturbed sample period. Next, we carried out dynamic stochastic simulations to generate the time path of working time and conduct policy experiments in order to investigate how the model as a whole behaves in response to exogenous shocks to tax-rate adjustments. The dynamic simulations for each country were then compared with the control solution and the dynamic responses of each economy to tax-rate shocks were examined. Figs. 6 to 13 plot the time path of hours worked after the tax-rate 24

shock. A mere inspection of these figures fails to lead to reliable inferences, so that a more comprehensive measure needs to be used. Thus, in Table 3, we present average (over the sample period) estimates of the dynamic responses of work effort to a permanent one standard-deviation shock to marginal tax rates. The general observation to be made from Table 3 is that it portrays significantly different pictures of the relation between marginal tax rates and hours worked for the two groups of countries. On the whole, the results are not at odds with those of the steady-state analysis of the previous section, but they carry superior information. They provide us with numerical estimates of the effects of a one standard-deviation shock to tax rates on work effort: • In France, a marginal tax-rate increase (from 13.5% to 20.5%) raises annual hours (actual minus statutory) worked per employee by 11 per cent (from 134 to 149 hours) and decreases hours worked per self-employed by approximately 2 per cent (from 2123 to 2080 hours) on the average, over the sample period. These changes correspond to a less than half an hour increase in weekly hours worked per employee and a less than one hour decrease in weekly hours worked per self-employed. • In the remaining three countries, changes in working patterns are quantitatively different. The most striking difference is observed in Portugal, where a marginal tax-rate increase (from 7.4% to 9.7%) leads to an over two-hour decrease in weekly hours worked per self-employed. The corresponding reductions are roughly one hour in Italy and less than one hour in Spain (working weeks are assumed to be 48 per year). On the contrary, a one-standard-deviation rise in marginal tax rates results in almost unaltered working patterns for the employees. The results in Table 3 can be summarised as follows: In the absence of tax withholding, private agents may respond to (higher) tax rate shocks either negatively (the self-employed in all the sample countries) or positively (employees in France). With tax withholding provisions, employees do not change their working pattern (Italy, Spain, Portugal). 25

7. Estimation of income and substitution effects. The results in Table 3 give an estimate of the total effect of the tax-rate shock on work effort. The disaggregation of this total effect into its components, i.e. the evaluation of the income and substitution effects, has received relatively scant regard in literature. Of course, the decomposition of a tax-induced change in the supply of labor into a substitution effect and an income effect has been adequately elaborated in mathematical terms. A formal mathematical derivation can, for example, be found in Gilbert and Phouts (1958) and Hanoch (1965). In experimental studies which deal with this issue, it is argued that the labor supply curve without an income effect may slope downward (see, for instance, Dickinson, 1999, and the references cited in his article). Moreover, in their theoretical approach to this issue, Menezes et al. (2005) examine labor supply under wage rate uncertainty and find that the Slutsky income effect is positive while the Slutsky substitution effect is negative. However, a numerical comparison of the income and substitution effects is basically an empirical matter and one cannot be sure that these effects would be at all uniform for employees and the self-employed or from one group of countries to another. In studying the income and substitution effects of tax-induced changes in income, one cannot ignore the vast contribution of the permanent income/life cycle (PI/LC) hypothesis to the subject matter. The PI/LC hypothesis predicts that risk averse consumers will use the capital market to absorb income changes, accumulating assets in booms and dissaving in slumps, in order to smooth lifetime consumption. In other words, consumers take an intertemporal view of their ability to finance consumption by using borrowing and lending strategies to shift purchasing power between periods, so that current consumption varies only in response to permanent changes in expected lifetime wealth. Modern tests of the PI/LC model are usually based on the framework devised by Hall (1978): It is assumed that consumption follows a random walk , possibly with drift, where the current consumption differs from the previous period’s level only by a random error term. This implies that prediction of next period’s consumption is based upon knowledge of current consumption, so that current income carries no additional information that would improve forecasts of future expenditure. In this context, aggregate per capita consumption takes the following form ct = a + θct−1 + εt 26

which corresponds to Eq. (15b) of our model. As becomes evident from the preceding analysis, traditional macroeconomic policies may be incapable of creating the required changes to lifetime income within a PI/LC environment. Consequently, the government’s ability to use fiscal policies to fine-tune the economy may be quite limited (see Deaton, 1992, p.101). More recent versions of the PI/LC theory attempt to relax its strict assumptions by adopting alternative approaches as, for example, • by distinguishing between periods covering the regulated financial systems from periods covering deregulated periods (Olekalns, 1997), • by introducing a variety of additional explanatory variables (cross-section data, average values): demographic variables, such as population age structure, labor force participation rates and retired population (Graham, 1987) or inflation rate and per capita GNP (Koskela and Viren, 1989), • by employing a life cycle labor supply model in which a time-separable utility function of consumption and leisure is maximised subject to a budget constraint (Klevmarken, 2000). In the context of the life cycle labor supply model, labor supply is shown to be a function of the gross wage rate, the marginal tax rate, non-labor income and a number of taste shifters and demographic characteristics (education, age, family status, unemployment rate etc.). However, all of these variables are not derived from a structural economic model; instead, economic theory is called forth to guide the analysis of work behavior and suggest the control variables. Thus, the general equilibrium econometric model of the present study appears to be an extension of the standard life cycle labor supply model in several respects: Intertemporal consumption choices are combined with intra-temporal conditions; estimation results are based on time-series data which permit dynamic simulations; and the relationships (or variables) used have a robust theoretical foundation on a structural model allowing for more realistic estimates of the income and substitution effects. To evaluate the income effect econometrically, the standard microeconomic approach – see, for example, Nickolson (1998), ch. 22 – is adopted (average values of the relative variables over the sample period are employed): • The utility function (1a,b) is taken as the starting point. Consumption is given by Eq.(3), after inserting identities (13a) and (11), and working time 27

is given by Eqs. (23) and (24), after inserting identity (22b). The utility index of the representative household was found to range from 10.1 in Italy to 12.3 in France. • From the maximisation of the utility functions, the first-order necessary conditions for the choice of working time, ∂U = 0, are derived. The solution ∂h with respect to h gives the labor supply as a function of both the non-wage income (nw) and the remaining variables (Z), h∗ = h∗ (nw, Z)

(39)

∂h ∂h ∂h∗ = |U =U +h∗ ∂w ∂w ∂ (nw)

(40)

• Given the Slutsky equation,

the income effect, namely the last term of the RHS of Eq.(40) is calculated as the product of the optimal choice of working time in Eq.(39) and its first derivative with respect to non-wage income. The numerical results of the income effect for employees and the self-employed are presented in Table 4. In quantifying the substitution effects of taxation on work effort, the standard microeconomic approach is of little help, due to the complexity of the utility function (1a,b). Instead, the following alternative procedure is suggested: • First, rearrange the budget constraint (3) for employees to give (nw)t = ct − pt we,t he,t (1 − τ t ) − Zt where ct = pt ce,t + (1 − pt ) cf,t and Zt = it − (1 − pt ) [wf,t hf,t − (1 − rt ) (τ t−1 wf,t−1 hf,t−1 )] − rt kt and maximise (41), subject to the constant-utility constraint (1a,b) µ ¶ n t 1+σ U = β log ct − h 1+σ t 28

(41)

From the Lagrangian for the maximisation, the first-order conditions for the choice of consumption and work effort for employees are ct λ= t β and we,t (1 − τ t ) = λβ t nhσt

Substituting the value of λ into the last relationship, we obtain ct nhσt = we,t (1 − τ t ) or log ct + log n + σ log ht = log we,t + log (1 − τ t )

(42)

• Second, substitute the constant utility constraint log ct =

U n h1+σ t + 1+σ t β

into (42) and rearrange the terms to obtain the revised constant-utility function ∙ ¸ n t 1+σ h U =β − − log n − σ log ht + log we,t + log (1 − τ t ) (43) 1+σ t • Third, differentiate (43) with respect to the wage rate, ∙ ¸ ∂U n ∂h1+σ ∂ log ht ∂ log we,t t t = =β − −σ + ∂we,t 1 + σ ∂we,t ∂we,t ∂we,t ∙ ¶ µ ¶ ¸ µ 1+σ ∂ht ∂he,t n ∂ log ht ∂ht ∂he,t 1 ∂ht t =β − −σ + = 1+σ ∂ht ∂he,t ∂we,t ∂ht ∂he,t ∂we,t we,t ∙ ¸ σ ∂he,t 1 ∂he,t t σ =0 − pt + = β −nht pt ∂we,t ht ∂we,t we,t and rearrange the terms to obtain the substitution effect of a tax-induced change in the wage rate on hours worked per employee, i.e. the first RHS term of the Slutsky equation (40) ∂he,t h ¡ t ¢ = ∂we,t pt we,t σ + nh1+σ t 29

Following a similar procedure, we can determine the substitution effect of a taxinduced change in earnings on hours worked per self-employed. After maximising (41) subject to the constant utility constraint (1a,b) and substituting the value of λ into the first-order condition for the choice of work effort for the self-employed, we obtain µ ¶ (1 − rt ) τ t log ct + log n + σ log ht = log wf,t + log −1 (44) (1 − pt )γπ t μt ν t

In the second stage, we substitute the constant utility constraint into (44) and rearrange the terms to obtain the revised constant utility function ∙ µ U = β log wf,t + log t

¸ ¶ (1 − rt ) τ t n 1+σ h −1 − − log n − σ log ht (1 − pt )γπ t μt ν t 1+σ t

(45)

Lastly, we differentiate (45) with respect to the rewards per self-employed and rearrange the terms by using (13a) to obtain the substitution effect of a taxinduced change in rewards on hours worked per self-employed 1 (1 + B) wf,t ∂hf,t = 1 ∂wf,t B hf,t + (1 − pt )(nhσt +

where B=

σ ) ht

(1 − rt )τ t−1 (1 − rt )τ t−1 − μν

Note that it is only the response of hours worked per self-employed – not per employee – that is expressed in dynamic terms (lagged dependent and independent variables) due to the carry-over provision of the current tax liability for the self-employed. The numerical estimates of the substitution effect for employees and the selfemployed are presented in Table 4. Even though the results in Table 4 are not directly comparable to those in Table 3, both of them convey the same message. The total effect of a tax-induced decrease in the wage rate of employees is negligible in Italy, Spain and Portugal, but it is favorable to work effort in France. On the other hand, tax-induced 30

reductions in the earnings of the self-employed have a significantly negative effect on hours worked in all of the sample countries. In absolute terms, the income effect appears to dominate the substitution effect in France (employees), whereas the substitution effect seems to dominate the income effect for the self-employed in all the sample countries. In the remaining cases, income and substitution effects tend to largely offset each other. As a final test of the ability of our model to identify the true nature of the income tax-work effort relationship, we estimate the effect of the marginal tax rate on working hours. To do this, we differentiate Eqs. (23) and (24) – after replacing the term ct by its equivalent from the budget constraint (3) – with respect to the marginal tax rate, in order to determine the numerical values of both the partial derivatives of hours worked per employee (self-employed) with respect to taxation and the corresponding elasticities. Calculations are carried out on the basis of the mean values of the variables over the sample period. Table 5 displays the results. It should be noted that the results in Table 5 cannot be directly compared to those in Tables 3 and 4. Table 3 displays simulated estimates of the effects of a one standard-deviation shock to tax rates on work effort and Table 4 reports the influence of tax-induced changes in income on work effort by utilising only part of the general equilibrium model, namely the household sector. On the other hand, the estimates in Table 5 relate work effort to marginal tax rate changes by utilising solely the two final employment relationships of the general equilibrium model, while disregarding the remaining equations. Notwithstanding these differences, the estimates in Table 5 are generally in line with the findings reported in the two previous Tables: They point out that a 10 per cent increase in the marginal tax rate exerts a significantly negative effect on hours worked per self-employed, ranging from 3.6 per cent in France to 5.2 per cent in Portugal. As for employees, a 10 per cent rise in the marginal tax rate leads to a 2.8 per cent increase in working time in France but it insignificantly affects working time in Italy, Spain and Portugal. In summary, our findings from both steady-state analysis and empirical investigation may go some way towards explaining the differential inferences about the income tax-working time relationship between the sample countries. Most of the results in the present study lend support to the tax-withholding scenario and 31

provide a clue to explain the shape of the labor supply curve. With tax withholding, the labor supply curve is more or less flat (employees in Italy, Spain and Portugal). In the absence of tax withholding, a tax-induced decline in income was shown to result in an increase in working hours, pointing to a downward sloping or backward bending labor supply curve (employees in France). It is only with the self-employed in the sample countries that the absence of tax withholding is associated with an upward sloping labor supply curve. It should be stressed, however, that whatever conclusions have been reached in the present study should be taken with caution, given the limited number of countries examined. Obviously, future research must be extended to include more countries with varying income tax provisions, labor market conditions and household behavioral patterns.

8. Concluding remarks In this paper, we argue that an analytical approach to the tax-employment relationship that takes into account the distinction between employees and selfemployed helps to generate important insights. To substantiate this argument, we constructed a stochastic general equilibrium model in which employees and the self-employed enter as separate factors into the production process. The underlying reason is that employees in most countries are subject to a tax-withholding system that helps to conceal their actual tax burden, thus minimising their response to tax rate shocks. In contrast, the employment decisions of the self-employed are not influenced by any tax withholding provisions, so that the self-employed are expected to react rather rigorously to tax reforms. The model was estimated and tested for four industrialised countries over the post-1965 period. The main points from both the steady-state analysis and the econometric investigation can be summarised as follows: 1. Marginal income tax-rate increases have significantly negative effects on hours worked per self-employed (no tax withholding), indicating an upward sloping labor supply curve. 2. Adjustments in the income tax regime exert a small and insignificant impact on the working status of employees in countries with tax-withholding provisions (Italy, Spain, Portugal).

32

3. Marginal income tax-rate increases elicit a positive response, via a rise in hours worked per employee in France, where the lack of tax withholding provisions and the concomitant fully identifiable tax-induced reduction in income give rise to an income effect that is stronger than the substitution effect. In each case, our analysis uncovers empirical predictions of the basic general equilibrium model that have not previously been investigated in the literature on the tax-employment relationship. Note, however, that the present analysis should be interpreted as a modest first step towards a more complete empirical assessment of the effects of direct taxation on the working status of important specific groups in the labor force. In fact, although our results appear promising, more work is needed to determine if the inferences reported in this paper are robust to alternative specifications of the model, to larger samples of countries, to varying income tax schedules and to more representative data sets. An interesting extension of our work could also be in the direction of analysing the effects of tax chamges on the equilibrium wage rate.

A. Appendix : Formulating an Aggregate utility function The most commonly used approach to determine the aggregate utility of consumption (for simplicity, we ignore hours of work) over all individuals is to add individual utilities: U1 = E ∗ U(ce ) + F ∗ U (cf ) = E ∗ ln ce + F ∗ ln cf

(A1)

The aggregate utility function, we have opted for in the present study, is of the form U2 = (E + F ) ∗ ln [p ∗ ce + (1 − p) ∗ cf ]

(A2)

E where p = E+F . Both formulae are alternative ways of representing joint consumer preferences on a theoretically sound basis. To prove it, suppose, for simplicity, that the economy is composed solely of one employee and one self-employed, i.e.

E = F = 1, so that p = 0, 50

33

In this case, eqs. (A1) and (A2) collapse to U1 = ln ce + ln cf and U2 = −1, 40 + 2 ln [ce + cf ] Thus, the problem of the most suitable approach centers on whether one opts for the sum of the logarithms of consumption of the two agents or for the logarithm of the sum of their consumption (the numerical terms in U2 are of minor importance for our conclusion). Both approaches can be considered as valid. The econometric estimates should be qualitatively the same with small quantitative differences. These differences may be attributed to the fact that: • The first approach, i.e. eq. (A1), fails to account for the complex behavioral interrelationships between employees and the self-employed, given that the decisions of each type of households are formulated independently of the preferences of the other category of agents in the process of deriving the partial derivatives of the model. On the other hand, this approach allows the optimal time paths for consumption, hours of work and saving to accurately replicate the choices made by the individual households in the model. • The second approach employed throughout the present paper, i.e. Eq. (A2), takes into account the effects of both consumption and working-time choices of each group on the decision making process of the other group. Needless to say, the representative agent model, as given by this approach, cannot accurately reflect the preferences of the two individual types in the economy. Since the marginal utility level of the representative household – Eq. (A2)– differs from the corresponding one of the two individual types –Eq. (A1)– the aggregation of the optimal choices of labor, capital and consumption in the representative agent model will not coincide with those of a model where one solves each individual type’s problem separately. Hence, the representative agent model will not accurately describe the time paths of capital and labor supply in the economy. Notwithstanding these weaknesses, the representative agent model captures the static and dynamic features of the real economy in a better way than the alternative model, through incorporating the interactions in behavior between employees and the self-employed. 34

B. Appendix: Descriptions and sources The time series include Gross Domestic Product at market prices, private consumption expenditure, private capital stock, government consumption expenditure, personal income tax revenue, public debt, private investment, annual compensation of employees (excluding social security contributions) and the operating surplus of the private, unincorporated sector. All the above variables are deflated by the GDP deflator and expressed in per capita terms. Per capita values are obtained by dividing each of these variables by the population defined as the total number of self-employed and employees. The remaining time-series used include the total number of the self-employed, the total number of employees, the lending rate and the weekly hours of work per worker in manufacturing. The annual hours of work of the self-employed are indirectly derived from the production function, as described in Section 4.1. The hourly wage rate is estimated as the ratio of the annual compensation of employees to the product of three arguments: weekly hours of work per worker in manufacturing, total number of employees and the number of working weeks per year (48). The hourly earnings of the self-employed are estimated as the ratio of the operating surplus of the private unincorporated sector to the product of two elements: annual hours of work of the self-employed and their total number. Non-wage income includes such elements as government transfer payments to households, interest payments on public debt to domestic government-bond holders and interest receipts from private deposits with domestic financial institutions. Most of the aforementioned annual data are provided by Data Stream. For some data, however, it was necessary to use additional sources: Flows and Stocks of OECD Countries, OECD, for the capital stock, National Income Accounts of OECD Countries, OECD, for the operating surplus of private unincorporated sector, and Labour Force Statistics , OECD, for hours worked per worker in manufacturing. Missing observations in some of the years were approximated by using interpolation techniques.

References [1] Aronsson, T., Lofgren, K. and T. Sjogren (2002), Wage setting and tax progressivity in dynamic general equilibrium, Oxford Economic Papers 54, 490504. 35

[2] Barro, R. (1987), Government spending, interest rates , prices and budget deficits in the United Kingdom, 1701-1918, Journal of Monetary Economics 20, 221-247. [3] Belfield, C. and J. Heywood (2001), Unionization and the pattern of nonunion wages: Evidence for the UK, Oxford Bulletin of Economics and Statistics 63, 577-598. [4] Bender, K., Donohue, S. and J. Heywood, Job satisfaction and gender segregation, Oxford Economic Papers 57, 479-496. [5] Chung-cheng Lin (2003), A backward-bending labor supply curve without an income effect, Oxford Economic Papers 55, 336-343. [6] Deaton, A. (1992), Understanding consumption, Clarendon Press, Oxford. [7] Devereux, M., A. Head and B. Lapham (1996), Monopolistic competition, increasing returns and the effects of government spending, Journal of Money, Credit and Banking 28(2), 233-254. [8] Dickinson, D. (1999), An experimental examination of labor supply and work intensities, Journal of Labor Economics 17, 638-670. [9] Evans, C.L. (1992), Productivity shocks and real business cycles, Journal of Monetary Economics 29, 191-208. [10] Fiorito, R. and F. Padrini (2001), Distortionary taxation and labor market performance, Oxford Bulletin of Economics and Statistics 63, 173-196. [11] Gilbert, F. and R. Phouts (1958), A theory of the responsiveness of hours of work to changes in the wage rate, Review of Economics and Statistics 40, 116-121. [12] Graham, J.W. (1987), International differences in saving rates and the life cycle hypothesis, European Economic Review 31, 1509-1529. [13] Guo, Jang-Ting (2004), Increasing returns, capital utilisation and the effects of government spending, Journal of Economic Dynamics and Control 28, 1059-1078.

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[14] Hall, R.E. (1978), Stochastic implications of the life cycle-permanent income hypothesis: Theory and evidence, Journal of Political Economy 86(6), 971988. [15] Hanoch, G. (1965), The backward-bending supply of labor, Journal of Political Economy 73, 636-642. [16] Hansen, P. and K. Singleton (1982), General instrumental variables estimation of non-linear rational expectations models, Econometrica 50, 1269-1286. [17] Johnson, G.E. and P. Layard (1986), The natural rate of unemployment: Explanation and Policy, in O. Ashenfelter and R. Layard, eds., Handbook in Labor Economics, Vol. II (Elsevier Science Publishers, Amsterdam), 921-999. [18] King, R.G., Plosser, C.I. and S.T. Rebelo (1990), Production, growth and business cycles: Technical appendix, Memo, University of Rochester. [19] Klevmarken, A. (2000), Did the tax cuts increase hours of work? A statistical analysis of a natural experiment, Kyklos 53, 337-362. [20] Koskela, E. and M. Viren (1989), International differences in savings rates and the life cycle hypothesis, European Economic Review 33, 1489-1498. [21] Langot, F. (1996), Do we need a hysteresis model to explain the unemployment persistence?, Annales d’ Economie et de Statistique 44, 30-57. [22] Mankiw, G., Rotemberg, J., and L. Summers (1985), Intertemporal substitution in Macroeconomics, Quarterly Journal of Economics 100, 225-251. [23] Menezes, C. and H. Wang (2005), Duality and the Slutsky income and substitution effects of increases in wage rate uncertainty, Oxford Economic Papers 57, 545-557. [24] Merz, M. (1995), Search in the labor market and the real business cycle, Journal of Monetary Economics 36, 269-300. [25] Newey, W., and K. West (1987), A simple, positive, semi-definite heteroscedasticity and autocorrelation consistent covariance matrix, Econometrica 55, 703-708. [26] Nickolson, W. (1998), Microeconomic Theory, The Dryden Press, Harcourt Brace College Publishers, Florida, USA. 37

[27] Pisauro, G. (1991), The effect of taxes on labor in efficiency wage models, Journal of Public Economics 46, 329-345. [28] Weiss, A. (1980), Job queues and layoffs in labor market with flexible wages, Journal of Political Economy 88, 526-538. [29] Yellen, J.L. (1984), Efficiency wage models of unemployment, American Economic Review 74, 200-205.

38

Table 1. Labor market and income tax characteristics France Average ratio of employees to total labor 0.84 force (0.06) Tax withholding No Note. Standard deviations within parentheses

Italy 0.64 (0.02) Yes

Spain 0.62 (0.04) Yes

Portugal 0.65 (0.04) Yes

Table 2. Parameter estimates of the general equilibrium model

Standard general equilibrium model δ α J0 J1 J2 θ

France 0.08 (0.006) 0.217 (0.003) -6386 (3075) 0.73 (0.10) 0.07 (0.03) 2x10-7 (1x10-7)

γ

2.05 (0.43) β 0.97 (0.24) A 36.8 (5.4) ρ 0.43 (0.08) be 0.042 (0.002) α0=β0 7.6 (2.13) α1=β1 0.19 (0.08) α2=β2 0.82 (0.12) Unemployment ─ rate Dummy1 ─

Italy 0.09 (0.008) 0.29 (0.10) 1134 (743) 0.87 (0.21) 0.03 (0.01) 0.0035 0.0008) 1.7 (0.06) 0.95 (0.41) 42.3 (13.6) 0.34 (0.15) 0.03 (0.008) 13.7 (2.4) 0.36 (0.21) 0.76 (0.24) ─

Spain 0.05 (0.009) 0.31 (0.04) 364 (168) 0.86 (0.10) 0.13 (0.04) 0.00007 (9x10-6) 1.8 (0.4) 0.96 (0.45) 18.7 (7.3) 0.25 (0.06) 0.04 (0.007) 8.2 (2.4) 0.24 (0.11) 0.63 (0.31) ─

Portugal 0.06 (0.006) 0.32 (0.05) 916 (405) 0.89 (0.18) 0.15 (0.07) 7x10-6 (4x10-6) 1.5 (0.64) 0.98 (0.38) 13.4 (3.6) 0.43 (0.20) 0.004 (0.002) 6.8 (3.2) 0.42 (0.21) 0.45 (0.14) ─

─

─

─

Dummy2

─

─

─

─

Dummy3

─

─

─

─

Continued….

General equilibrium model with country-specific variables France 0.07 (0.009) 0.234 (0.045) -5693 (3126) 0.69 (0.15) 0.13 (0.05) 1x10-6 (2x10-7)

1.89 (0.51) 0.98 (0.32) 22.1 (4.7) 0.46 (0.12) 0.039 (0.007) 8.3 (2.56) 0.24 (0.12) 0.76 (0.24) 263.5 (56.8) 0.83 (0.36) 0.65 (0.28) ─

Italy 0.08 (0.006) 0.28 (0.09) 1056 (784) 0.86 (0.24) 0.02 (0.008) 0.0043 0.0008 1.6 (0.13) 0.94 (0.46) 37.8 (12.9) 0.35 (0.18) 0.025 (0.009) 12.6 (3.4) 0.41 (0.14) 0.72 (0.23) ─

Spain 0.04 (0.007) 0.29 (0.04) 343 (152) 0.81 (0.22) 0.11 (0.03) 0.00005 (7x10-6) 1.6 (0.68) 0.92 (0.37) 16.8 (4.6) 0.24 (0.12) 0.03 (0.009) 7.6 (1.9) 0.25 (0.09) 0.61 (0.30) 96.4 (38.3) ─

Portugal 0.08 (0.009) 0.32 (0.04) 934 (504) 0.78 (0.26) 0.13 (0.05) 6x10-6 (7x10-6) 1.4 (0.61) 0.96 (0.45) 14.7 (4.5) 0.40 (0.22) 0.005 (0.002) 6.5 (2.8) 0.37 (0.19) 0.42 (0.13) 59.2 30.8 ─

─

─

─

2.3 (0.9)

─

─

.…Continued Dummy4

─

─

─

─

─

─

Dummy 5

─

─

─

─

─

─

0.68 (0.52) ─

Employment ─ ─ growth Employment ─ ─ deviation Note. Standard errors in parentheses.

─

─

─

─

─

─

─

─

─

26.5 (9.6)

─ 2.3 (1.8) 83.4 (56.7) ─

Table 3. Dynamic effects of marginal tax rate changes on work effort Hours worked per Hours worked per Marginal (personal employee self-employed income) tax rate Control Dynamic Control Dynamic Control Dynamic solution simulations solution simulations solution simulations France 134 149 2123 2080 0.135 0.205 Italy 225 226 3284 3235 0.104 0.153 Spain 204 200 2538 2497 0.085 0.124 Portugal 126 124 3351 3244 0.074 0.097 Note. All numbers represent average values of hours worked and tax rates over the sample period. Hours worked per employee are estimated as the difference between actual and statutory (annual) working hours.

Table 4. Estimates of income and substitution effects France Italy Spain Portugal Emplo- SelfEmplo- SelfEmplo- SelfEmplo- Selfyees empl. yees empl. yees empl. yees empl. Income -39.4 -80.7 -6.2 -33.2 -9.6 -49.3 -7.4 -40.9 effect Substitution 23.8 112.6 5.3 69.7 10.3 73.5 7.9 82.7 effect Total effect -15.6 31.9 -0.9 36.5 0.7 24.2 0.5 41.8 Note. Hours worked per employee are estimated as the difference between actual and statutory (annual) working hours.

Table 5. Estimates of derivatives and tax elasticity of work effort France Italy Spain Portugal Employees 12.4 0.94 -0.86 -1.8 ∂he / ∂τ elasticity 0.028 0.0002 -0.0004 -0.0009 Self-employed -16.9 -23.2 -28.4 -31.4 ∂hf / ∂τ elasticity -0.036 -0.041 -0.048 -0.052 Note. Hours worked per employee are estimated as the difference between actual and statutory (annual) working hours.

2

Ratio

.92

.88

.84

France

.80

.76

.72

.68

Italy .64

.60

Portugal Spain

.56

Years

.52 60

62

64

66

68

70

72

74

76

78

80

82

84

86

88

90

92

94

96

98

Figure 1. The ratio of employees to the total labor force

00

02

.0010

Hours

.0005 per employee

.0000

-.0005 per self-employed -.0010

-.0015

Years 1965

1970

1975

1980

1985

1990

1995

Figure 2. FRANCE: The effect of a transitory marginal tax-rate shock on hours worked per employee and per self-employed.

2000

.0004

Hours per employee

.0000

-.0004

-.0008

-.0012

per self-employed

-.0016

Years

-.0020 1965

1970

1975

1980

1985

1990

1995

Figure 3. ITALY: The effect of a transitory marginal tax-rate shock on hours worked per employee and per self-employed.

2000

.0002

Hours

.0000 per employee -.0002 -.0004 -.0006 -.0008 per self-employed -.0010 -.0012

Years

-.0014 1965

1970

1975

1980

1985

1990

1995

Figure 4. SPAIN: The effect of a transitory marginal tax-rate shock on hours worked per employee and per self-employed.

2000

.0001

Hours

.0000 per employee

-.0001 -.0002 -.0003 -.0004

per self-employed

-.0005 -.0006 -.0007

Years

-.0008 1965

1970

1975

1980

1985

1990

1995

2000

Figure 5. PORTUGAL: The effect of a transitory marginal tax-rate shock on hours worked per employee and per self-employed.

Hours 250

200

150 he(simulated) he(baseline)

100

50 1960

Years 1965

1970

1975

1980

1985

1990

1995

2000

Figure 6. FRANCE: Simulated changes in hours (actual minus statutory) worked per employee (he) after a one-standard deviation increase in the marginal (personal income) tax rate

hf

3000

hf (baseline)

2000 hf (simulated)

1000 1960

Years 1965

1970

1975

1980

1985

1990

1995

2000

Figure 7. FRANCE: Simulated changes in annual hours worked by self-employed (hf) after a one-standard deviation increase in the marginal (personal income) tax rate

360

Hours

320

280 he (baseline) he (simulated) 240

200

160

120 1960

Years 1965

1970

1975

1980

1985

1990

1995

2000

Figure 8. ITALY: Simulated changes in hours (actual minus statutory) worked per employee (he) after a one-standard deviation increase in the marginal (personal income) tax rate.

4050

4000

3950

3900 hf (simulated) 3850

3800

3750 hf (baseline) 3700 1960

1965

1970

1975

1980

1985

1990

1995

2000

Figure 9. ITALY: Simulated changes in hours worked per self-employed (hf) after a one-standard deviation increase in the marginal (personal income) tax rate.

320

Hours

280

240

200

he (baseline)

160

he (simulated)

120

80 1960

Years 1965

1970

1975

1980

1985

1990

1995

2000

Figure 10. SPAIN: Simulated changes in hours (actual minus statutory) worked per employee (he) after a one-standard deviation increase in the marginal (personal income) tax rate.

2640 Hours

2600

2560

hf (baseline)

2520 hf (simulated)

2480

2440 1960

Years 1965

1970

1975

1980

1985

1990

1995

2000

Figure 11. SPAIN: Simulated changes in annual hours worked per self_employed (hf) after a one-standard deviation increase in the marginal (personal income) tax rate.

240

Hours

200

160

he (baseline)

120

he (simulated)

80

40 1960

Years 1965

1970

1975

1980

1985

1990

1995

2000

Figure 12. PORTUGAL: Simulated changes in hours (actual minus statutory) worked per employee (he) after a one-standard deviation increase in the marginal (personal income) tax rate.

4000

hf hf (simulated)

3800

3600

3400

3200

hf (baseline)

3000

2800 1960

Years 1965

1970

1975

1980

1985

1990

1995

2000

Figure 13. PORTUGAL: Simulated changes in annual hours worked by self-employed (hf) after a one-standard deviation increase in the marginal (personal income) tax rate.

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