European Fiscal Harmonization and the French Economy

The implications of European fiscal harmonization for the French economy are examined using a general equilibrium model. The model extends the overlapping generations, simulation model developed by Auerbach and Kotlikoff in three ways: a well-developed external sector is included; households face constraints in their borrowing; and the population comprises “rich” and “poor” households with different labor productivities. The harmonization policy that involves cuts in VAT and savings taxes leads to welfare losses for both rich and poor approximately equivalent to 1 percent of GDP.

Abstract

The implications of European fiscal harmonization for the French economy are examined using a general equilibrium model. The model extends the overlapping generations, simulation model developed by Auerbach and Kotlikoff in three ways: a well-developed external sector is included; households face constraints in their borrowing; and the population comprises “rich” and “poor” households with different labor productivities. The harmonization policy that involves cuts in VAT and savings taxes leads to welfare losses for both rich and poor approximately equivalent to 1 percent of GDP.

This paper uses a general equilibrium simulation model to gauge the impact of European fiscal harmonization on the French economy. For France, harmonization as currently envisaged will involve two main elements: first, a downward adjustment in value-added tax (VAT) rates compensated for by an increase in direct taxation; and, second, a general reduction in the level of savings taxes.

To gain some idea of the magnitude of the tax reforms such convergence would entail, note that to bring French VAT rates into line with German rates would mean an overall cut approaching 3 percentage points. The change in effective savings tax rates that will emerge from current discussions is harder to estimate, but a reasonable guess is that the general level of taxation on income from savings will fall by 10 percent. The total revenue losses associated with these tax cuts could amount to over 2 percent of gross domestic product (GDP).

Despite the scale of these changes, relatively little attention has been paid to their possible economic impact on European Community (EC) member countries. Initially, tax harmonization was viewed simply as a prerequisite to the broader movement toward a post-1992 single market. Studies such as those in Cecchini (1988) emphasized the economic implications of this integration of markets while ignoring the independent impact of tax harmonization.1

In fact, the planned harmonization raises broad questions concerning the desirability of different tax bases. If VAT rates in member states are to be brought into line, should indirect taxes in countries with high rates be lowered, or should those in countries with low rates be raised? Assuming that income and possibly other taxes are adjusted so that the VAT harmonization is revenue neutral, the answer will necessarily turn upon the relative advantages of different tax bases, in particular consumption versus income or wages.

There is a long tradition in public finance, associated with such authors as Fisher (1937), Kaldor (1955), and Meade (1978), of recommending the use of a consumption tax or VAT rather than income taxes. The basic argument is that taxes on consumption, like taxes on labor income, impose no burden on capital income and, therefore, do not distort a household’s intertemporal choice between consumption in different periods. Furthermore, the introduction of a new consumption tax effectively imposes a once-and-for-all tax on existing wealth, which is equivalent to a lump-sum tax.

Interest in these issues was reawakened by a series of empirical papers beginning with Boskin (1978) that suggested that the elasticity of savings with respect to the real interest rate was much higher than had previously been thought. If this were the case, then the deadweight losses involved in taxing capital income, or in relying on income rather than consumption taxes, would be higher.

As Feldstein (1978) pointed out, however, it is not the absolute level of savings elasticities that matters but, rather, their magnitude relative to labor supply elasticities. While savings taxes distort the choice between consumption at different dates, levying consumption taxes in their place increases the wedge between the prices of goods and leisure (the wage), and thereby exacerbates the distortionary impact of the tax system on labor supply decisions. Only if labor supply elasticities are very low is it possible to say unambiguously that the switch to consumption taxes will enhance welfare.2

Since the relative benefits of a consumption versus an income tax system depend in a more or less complex way on the level of agents’ demand elasticities, more recent work in this area has concentrated, first, on trying to refine estimates of the relevant elasticities and, second, on using general equilibrium simulation models to unravel the various ways in which different tax bases affect welfare.3

Although the above literature is relevant to evaluating the impact of savings tax cuts, it sheds little light on the relative merits of VAT and wage taxation. In a closed economy, VAT is usually superior to a tax on wages, since it generally has a broader base. Consumers’ budget constraints mean that consumption equals the sum of labor income and lump-sum endowments such as bequests, non-means-tested transfers from the government, and income tax allowances. For rational agents, a proportionate tax on consumption is equivalent to a similar proportional tax on wage income plus a lump-sum tax. Since lump-sum taxes are nondistortionary, a consumption tax will generally be preferable to a wage tax raising the same revenue.

However, there are two important qualifications to the above argument. First, in an open economy model, it is possible to show (Perraudin and Pujol (1990a)) that with inelastic demand for the country’s exports, terms of trade effects may divert welfare gains to the rest of the world, so that a lower VAT actually increases welfare. A second qualification to the superiority of VAT concerns the timing of consumption and wage tax liabilities over the life cycle. As Summers (1981) has pointed out, in a steady state with overlapping generations, a government may levy taxes on young or old and still raise the same amount of revenue. However, households will prefer taxes to be levied late in the life cycle, since they have positive discount rates. If wage income should be earned later in the life cycle than consumption expenditures are incurred, then a switch toward wage taxes could improve welfare.

These arguments mean that although the overall presumption must be that wage taxes are inferior to VAT in the excess burden they impose, in a particular case, such as the current French economy, this inferiority remains to be demonstrated. This paper develops a general equilibrium, overlapping generations, simulation model in which such questions may be analyzed.

Early papers that used such models, like Summers (1981), calculated the steady-state utilities of overlapping generations of households under various tax regimes. Summers argued strongly that the potential gains from switching to consumption taxes were extremely large. Unfortunately, steady-state calculations of this kind ignore the burden that policies may impose on households alive during the transition path and the adjustment costs borne by firms that have to revise their investment strategies. As a result, welfare gains may be significantly overstated.

The analysis of Auerbach and Kotlikoff (1987) confirms this criticism of studies that concentrate on steady-state results alone. As they demonstrate, the increase in economic welfare shown by Summers that follows from a switch from income to VAT is, in fact, partly the consequence of welfare transfers between generations. The utility gains of households in the terminal steady state are accompanied by utility losses for households in current generations. However, according to Auerbach and Kotlikoff, switching to income from wage taxes does produce a genuine Pareto improvement.

The approach taken in this study builds on the work of Auerbach and Kotlikoff. The model we develop extends their framework in three ways. First, given that French product and capital markets are closely integrated with those of its neighbors, it makes sense to incorporate a well-developed external sector. The demand for exports and the supply of savings from the rest of the world are assumed to be imperfectly elastic.4

Second, we assume that a fraction of the households in the model are limited in their ability to borrow against future labor income. A substantial body of empirical work points to the presence of such borrowing constraints in markets for consumer loans.5 This assumption may therefore be seen as realistic and is also desirable, given the questions posed by the present study. As Hubbard and Judd (1986) have stressed, if agents earn income late in life while their desired consumption has, say, a flat time profile, then switching from income taxes to VAT is likely to aggravate liquidity constraints leading to a reduction in welfare.

The third extension of Auerbach and Kotlikoff’s work is to incorporate two sorts of households with different levels of labor productivity. Since an important feature of VAT is that it is typically less progressive than income tax, comparisons of the relative merits of consumption versus income tax bases should ideally take distributional issues into account. To do this, it is of course essential to have a model that includes heterogeneous households.

Of the three extensions described above, the assumption of an open economy with variable terms of trade is the one that influences our results the most.6 To understand why this is the case, consider the effects of cutting VAT and savings taxes to a degree consistent with European harmonization and financing this through increases in lump-sum taxation. The primary effect is to make consumption goods more attractive compared to leisure, leading to an increase in labor supply and a significant boost in production. Selling the additional output in international markets necessitates a worsening in the terms of trade, which lowers domestic welfare despite the fact that domestic output has risen.

Results of this kind signal the considerable importance of addressing tax policy questions within an open economy framework. The implications of open economy effects for the relative attractiveness of different tax bases have only recently begun to receive their due recognition. Dixit’s (1985) survey of the theory of tax policy for open economies simply translates the results of Ramsey optimal tax theory into a version applicable to countries with trade. Such an approach ignores both terms of trade effects and the dynamic impact of taxation on savings and investment that have been the primary focus of the literature on consumption and income tax bases described above. More recent contributions by Frenkel and Razin (1987) and Frenkel, Razin, and Symansky (1991) have begun to analyze these topics, but more work in this area is an urgent research priority.

It is important to note that the analysis presented in this paper does not imply that harmonization by itself is necessarily welfare reducing.7 The problem is that harmonization, as currently envisaged, involves EC member countries adjusting their tax rates toward some overall average. The results suggest that if harmonization were achieved by tax changes that included more of a leveling-up of VAT rates in particular, with offsetting reductions in wage income tax, then the benefits to the Community would be distinctly greater.

The remainder of this paper is organized as follows. Section I describes discussions within the EC concerning fiscal harmonization and the design of VAT systems. The likely direct impact of the movement toward harmonization on French public finances is then analyzed. Section II provides a brief summary of the model used in the simulations. Section III reports the results of steady-state simulations of the model under a variety of assumptions about financing and the degree of openness of the economy. Section IV provides information on the short-term impact of tax harmonization by describing the economy’s transition path to the new long-run equilibrium. Section V states the conclusions. A description and solution of the model are provided in Appendix I and Appendix II.

I. Fiscal Harmonization in France

The last few years have seen a lively debate within the EC on the need for tax harmonization within the projected post-1992 single market. At present, wide disparities exist in the degree to which different EC countries rely upon indirect as opposed to direct tax bases. Before the process of tax harmonization began, the disparities were even more striking (see Table 1).8 The tax treatment of savings in different EC member states also varies widely.

Table 1.

Tax Revenue Comparisons

(As a percentage of GDP in 1985)

article image
Source: Organization for Economic Cooperation and Development (1990).

Includes social security contributions.

To a large extent, the need for harmonization depends on the design of the tax system itself. In the case of VAT, two approaches have been suggested.9 Under the so-called destination principle,10 taxes depend upon where a good is consumed, rather than where it is produced. By implication, such taxes do not distort a consumer’s choice between foreign and domestic goods.

Although favored by economists, a system based on the destination principle is difficult to implement. It requires either that firms apply the different tax rates appropriate to the different national markets in which they operate, or that exports be tax exempt and VAT be levied on importers in the country of destination. The first possibility involves firms in onerous administrative expenses and requires a complicated clearinghouse of tax revenues between member states at a national level. The second possibility creates a need for elaborate border controls.

The alternative to a VAT system based on the destination principle is a system based on the “origin principle,” under which tax rates depend on the country of production. Such an approach has the disadvantage of introducing a distortionary wedge between the prices of domestic and foreign goods faced by consumers, but the administrative costs imposed on firms are likely to be significantly lower, and border controls are not necessary.11

The implications of destination-principle or origin-principle VAT systems for harmonization are quite different. If adopted, the origin principle would make it much more difficult for countries to maintain different VAT rates. Imposing a high rate would effectively mean discriminating against one’s own domestic industry and creating large incentives for shopping across borders by tax-bearing purchasers. For countries like France, cross-border shopping on the part of households is of limited significance and would exist whatever the design of the VAT system. VAT-exempt entities, however, such as hospitals, financial institutions, and local government bodies, which cannot subtract VAT charged on their purchases from charges for the goods they supply, represent a large group of potential arbitrageurs and are likely to create problems for high-tax countries.12

The European Commission initially argued strongly in favor of the adoption of a VAT system based on origin, contending that this would reduce firms’ costs, further promote the single market, and allow the elimination of customs tolls. Some member countries, including France, have resisted such a move, arguing that the cost of border controls could be significantly cut from present levels and that the competition between European firms that an origin system would generate would be distorted.13 The outcome of this debate is that, at least in the short run, the destination-principle system will remain. In the longer term, the commitment by all EC members to equalize tax rates will make the distinction immaterial.

Although the overall design of the VAT system has still not been agreed upon, EC member states have decided to reduce the number of VAT rates to two (a normal and a reduced rate). Moreover, the classification of goods into these two categories will be the same in each member state. Thus, for example, refrigerators will bear the normal tax rate in all countries, even though the level of this rate could differ among countries.

Turning now to the impact of harmonization on France, should the origin principle be adopted, four kinds of adjustment to the French tax system are likely to prove necessary. First, the French authorities would not be likely to accept a tax differential with a close neighbor and competitor such as Germany that exceeded 2 percentage points. Assuming that Germany maintains its current rates, this would imply a reduction in the normal French VAT rate of 2.6 percent. Second, special rates, such as those on luxury goods like cars and perfumes, would be abolished.

Third, French indirect taxes on energy would be lowered. As a large net importer of energy, France has a policy of discouraging energy consumption through high taxes, whereas the current EC proposals suggest that energy should be taxed at the reduced VAT rate. Fourth, a number of other special features of the French system would disappear. For instance, part of the VAT paid by firms cannot be deducted from taxes on final sales. The VAT payments in question are mainly those on goods that could represent an implicit perk for employees, such as company cars and business travel allowances.

To give some indication of the scale of these tax harmonization changes, Table 2 shows the French authorities’ estimates of the potential loss in revenues. According to these estimates, the total revenue loss would equal approximately 1.6 percent of GDP.

Table 2.

Revenue Losses

article image
Source: Staff calculations based on information from the French authorities.

From 18.6 percent to 16 percent.

The other major area of fiscal harmonization that has been under discussion within the EC is savings taxation.14 The removal of capital controls, which has largely been completed, raises important issues for savings taxation. The availability of foreign tax havens has obliged EC member governments to make substantial cuts in the level of taxation on savings.

In France, where income on capital has in the past borne a comparatively heavy burden of taxation, two measures have been taken to reduce the outflow of savings to tax havens within the EC. First, incentives, in the form of specific tax allowances, have been provided for French households, provided they hold their savings in domestic financial institutions. The implicit market segmentation implied by these measures partially offsets the liberalization of capital flows.

Second, capital income tax rates have been substantially cut from a range of 25 percent to 30 percent in the past, to a unified rate of 15 percent. Also, new financial instruments, such as the “Sicav de Capitalisation” will allow investors to avoid taxation on capital income up to twice the average net wage. It is therefore possible that the effective reduction could be even greater, leading to decreases in revenue of around 0.5 percent of GDP.

One should note that harmonization could result from competition between tax systems rather than from coordination. EC proposals for a 15 percent withholding tax have been shelved, but other policy initiatives are possible. In the absence of further EC-wide reforms, arbitrage by households and firms has already and will continue to provide a strong impetus for tax cuts in high-tax countries.

A final issue is the likely reaction of the French authorities to the substantial revenue losses involved in harmonization as currently intended. One possibility would be to increase the deficit. However, this would run counter to the government’s firm announced intention to reduce the reduction and hence seems unlikely. A second possibility is that the establishment of the single market will lead to rapid growth, which would then help to finance cuts in VAT and savings taxation. Close examination of the expenditure side of the French budget suggests, however, that the Government has already boxed itself in through past commitments.15

Thus, it is highly likely that direct taxes will have to be raised or will be lowered to a lesser extent than they would have been if the costs of harmonization were not present. In the simulations that we report below, we consider cases in which the harmonization tax cuts are financed either by adjustments in labor income taxes or in lump-sum taxes.16 The latter would be equivalent to, say, increases in income tax allowances, which would have no impact on marginal net wage rates and would therefore influence labor supply decisions only through lump-sum income effects.

II. The Model

The model developed in this paper is similar to the overlapping generations model used by Auerbach and Kotlikoff in their studies of the U.S. economy. However, three major extensions of the Auerbach-Kotlikoff model are incorporated. First, the model describes an open economy facing both a demand curve for its exports and a supply curve for savings from the rest of the world.17 Second, two categories of households are introduced, making it possible to address redistributional issues in a more realistic way. Third, one of the categories of household is assumed to face constraints in borrowing against future labor income.

Household Behavior

The model of households follows the usual life-cycle approach. We suppose that there are two different kinds of households distinguished by their differing labor productivities, and consequently, by the level of wages they receive. For simplicity, the two groups are referred to as “rich” and “poor.” One may think of the higher productivity of the rich as reflecting a larger initial endowment of human capital.18 Since each household is assumed to be adult for ten periods,19 at any given time the household sector includes 20 representative households. In each period, one household in each cohort dies and is replaced by a new young household. Thus, the population remains constant over time.

Each household’s utility function is assumed to be time-separable, with a nested, constant elasticity of substitution (CES) function defined on leisure, a nontradable good, denoted by C1,t, and a composite tradable good, denoted by CT, t. In turn, the composite tradable is assumed to be a CES function of an imported good, C2,t, and a domestically produced good, C3, t. Thus, for a given household, preferences are represented by

U1(11α)Σt=1T1(1+δ)t1ut11/α,(1)

where

ut[Ct11/ρ+α0lt11/ρ]1/(11/ρ)
Ct[α1C1,t11/ρ1+(1α1)CT,t11/ρ1]1/(11/ρ1)
CT,t[α2C2,t11/ρ2+(1α2)C3,t11/ρ2]1/(11/ρ2).

Suppose that all households retire at the start of their ninth period. This assumption is highly plausible in the case of French households, given the uniformity of retirement ages allowed for by pension schemes.20 Households’ marginal labor productivities depend, as mentioned above, on the group to which they belong but also on their ages. Poor households are assumed to face liquidity constraints that prevent them from borrowing against their future labor income. Since poor households’ wages rise relatively rapidly over time,21 these constraints are likely to be binding in the first few periods of their lives.

Taxation and transfers affect households’ behavior through their influence on both income and prices. Lump-sum transfers have a direct impact on income, while VAT affects consumer prices, and direct taxation (including social security contributions) influences interest rates and wages. By optimizing the utility function, households determine labor supply and the respective demand for goods.

Behavior of Firms

The economy in the model contains two domestic industries, denoted 1 and 3, producing a nontradable and a tradable good, respectively, in a perfectly competitive manner. Each sector comprises a representative firm with constant returns to scale and a CES production function of capital,22 Kt, and labor, Lt:

Ft(KtLt)1[0Kt11/+(10)Lt11/]1/(11/).(2)

The long-run constant returns to scale of the production function has various well-known implications. First, in the long run, profits equal zero. Second, profit-maximization leads to the so-called factor-price frontier, a relation between the real costs of inputs, dependent on the parameters of the production function but independent of quantities.23 Since firms are assumed to face quadratic costs of adjusting their inputs, however, returns to scale are decreasing in the short run.

Taxation affects firms’ decisions in various ways. Social security contributions increase the relative cost of labor, thereby reducing labor demand. This tax is assumed to be paid exclusively by employers at a constant rate, denoted by txt. In fact, as long as households’ behavior depends only on net wages, it is immaterial whether contributions are borne by employers or employees.

By adopting simplifying assumptions, we ensure that profit taxes do not distort firms’ behavior. These assumptions include, first, the supposition that scrapping is tax deductible and that the fiscal depreciation rate, d′, equals the amortization rate, d.24 Second, we assume that, at the margin, investment is financed using bonds and that interest payments are tax deductible. It follows (see Auerbach (1983)), that the steady-state user cost of capital, denoted by uc, equals the sum of the scrapping rate and the interest rate divided by the gross interest rate and is, therefore, independent of profit taxes.

Government and Welfare Analysis

In this neoclassical framework, the government performs various tasks including expenditure on goods, the operation of a system of transfers, the collection of taxes, and the issuance of debt. The treatment also implicitly assumes that the government owns the firms and consequently receives their profits in the form of dividends.

The government faces an intertemporal budget constraint, which for given time paths of nominal public expenditures {Gt}t=0 and tax receipts {Tt}t=0, can be written as

Σt=0πtTt=Σt=0πtGt+D0,(3)

where πtΠs=1t1/(1+rs) is the discount factor.

The fact that government expenditure on goods does not contribute to households’ utility or to firms’ production means that any cut in public expenditure allows an uncompensated tax cut and therefore results in increased welfare. The model is therefore inappropriate for studying such questions as the optimal design of expenditure programs or the impact of government debt, D0, on the distribution of wealth across generations. We therefore concentrate in the analysis on tax and transfer policies that can improve social welfare for given levels of public expenditure and given steady-state debt.

Closure of the Model

The model includes several departures from the commonly adopted small country assumption.25 On the real side, it appears quite unrealistic to assume that medium-size industrialized countries can sell unlimited quantities of their exports at constant prices. In the modeling of international capital flows, the assumption that interest rate and borrowing requirements are positively correlated also seems more sensible.

We therefore suppose, first, that the imported good, which is consumed by households and used by firms in their constant coefficient production of capital, has a foreign currency price, P2*, which is assumed to be exogenously fixed. Second, the export good, which is also consumed by domestic households and used as an input to capital by firms, is assumed to be demanded by the rest of the world according to a constant elasticity demand function, X3=X0(P3*)ω, where X3 and P3* are export quantities and their foreign currency prices, respectively. In the base case, ω′ is set to unity, which is consistent with usual macroeconomic estimates.

Third, the supply of savings from the rest of the world is taken to depend positively on the net interest rate26 according to the equation, WROW=ω(rtr¯). When ω = ∞, the interest rate is internationally given and the small country assumption holds for capital markets; if ω′ = ∞, the same is true of the goods market. When ω = 0—that is, the autarky case—the interest rate adjusts to give current account equilibrium with constant capital flows between the domestic economy and the rest of the world. The relevance of these different cases depends on the degree of liberalization of capital flows. The base case value for ω reflects the view that interest rates do not react markedly to an increase in the country’s overall net indebtedness.

Given these closure assumptions, solution of the model requires finding an equilibrium in five different markets (labor, bonds, and the three goods). Choosing the nontraded commodity, good 1, as numeraire, one must determine four prices (wage, interest rate, exchange rate, and export prices) in each period.

Parameterization of the Model

We chose tax parameters for the base case simulations in accordance with national accounts data and the tax rates faced by French households and firms in 1985.27,28 Households’ labor supply and savings elasticities, ρ and α, were calibrated using the results from a number of microeconomic studies of households’ behavior. Labor supply elasticity was set so that it was consistent with a global wage elasticity of 0.4. The elasticity of substitution between tradables and nontradables, ρ1, was chosen on the basis of published estimates of import demand equations. Households’ subjective rate of time preference, δ, was set to 2 percent. All these parameters were assumed to be identical across households.

The firms in the two domestic production sectors were assumed to have identical production function and adjustment cost parameters. The capital-labor substitution elasticity was selected using a combination of micro- and macroeconomic studies, and the adjustment cost parameter was fixed at what appears a reasonable value. A summary of the levels of the most important parameters is provided in Table 3.

Table 3.

Model Parameters

article image

III. Long-Run Results

In this section, we describe the long-run implications for the French economy of the tax changes associated with European fiscal harmonization. Table 4 gives the percentage changes in selected economic variables that follow a cut in VAT from 12.5 percent to 10 percent and a halving of the 20 percent tax on interest income. As argued in a previous section, the resulting shortfall in government revenues is likely to be made up by a rise in labor income taxes, and this is what we assume in the majority of our simulations.29 However, for completeness, we shall also discuss the consequences of financing the harmonization reforms by adjustments in lump-sum taxes.

Table 4.

Long-Run Results

(Percentage changes)

article image
article image
Note: Simulation (1) is the base case involving a cut in VAT rates from 12.5 percent to 10 percent and in saving rates from 20 percent to 10 percent—all financed by increases in wage income taxes; in simulation (2) the tax cuts are financed with changes in lump-sum taxation; in simulation (3) the initial level of public debt is assumed to be zero; in simulation (4) savings taxes are not cut; and in simulation (5) VAT is not cut.

Utility changes are money metric; that is, GDP equivalent.

As a percentage of GDP.

Note that a 5 percent change in the interest rate is equivalent to an annual change of 25 basis points.

The basic findings of the analysis are the results of simulation (1) reported in the fourth column of Table 4. Household utility in total falls by the equivalent of 1 percent of GDP, while the impact on real variables is quite substantial, with output, employment, and the capital stock falling by about 3 percent. In order to analyze these results, it is helpful to consider the VAT and savings tax cuts that make up the harmonization package separately.

Superiority of VAT over Wage Taxes

As Table 4 shows, VAT harmonization financed by changes in labor income tax leads to declines in domestic welfare (see simulation (4)). This result, which is consistent with the findings of Auerbach and Kotlikoff (1987), amounts to saying that consumption taxes distort economic behavior less than wage taxes. An analysis of the household budget constraint sheds some light on the reasons for this ranking. The budget constraint may be written as follows:

Σt=1TΣi=13πtPi,tCi,t=Σt=1TπtWt(1T1,t)(1lt)+Tr,(4)

where Tr is the discounted value of transfers, and T1,t denotes taxes on labor income; Pi,t denotes commodity prices inclusive of consumption taxes; and πt, is a discount factor.

The size and magnitude of transfers, Tr, play a pivotal role in the analysis. In most countries, income tax allowances are sizable and, hence, Tr is large and positive. In France, this is all the more true since the income of a large part of the population is not taxed. It may be noted that if one wishes to include a redistributive element in the income tax system, it is necessary that the tax allowance component of Tr be positive.

Ignoring the complication of forced retirement, the degree of tax distortions may be measured through the ratio RR = (1 – marginal wage tax)/(1 + VAT rate). This ratio may be thought of as the tax wedge between the real net wage faced by households and the wage cost faced by firms. RR appears in the first-order conditions of households (see Appendix I) and will lead to changes in real behavior to the extent that it departs from unity.

With positive transfers, a 1 percent increase in VAT rates leads to higher tax revenues than an increase in wage tax rates of a similar amount. Equivalently, for a given amount of tax revenues, RR is closer to unity and the distortion less severe if one relies on VAT rather than wage taxes. An intuitively plausible way to express this idea is to say that consumption taxes reduce the real value of transfers, thereby imposing a nondistortionary, lump-sum tax. Since the discounted value of transfers is positive, one may expect a Pareto deterioration to result from a shift to wage taxation.

As emphasized by Summers (1981), another possible explanation for the decline in welfare is the time pattern of taxes. As the above budget constraint clearly shows, a given household is better off if taxes are levied later in the life cycle. However, if the population is constant, the amount of revenue collected by the government does not depend on the period in which a given individual pays the tax. To delay tax collection, thereby shifting the burden onto the old, is therefore an improvement in terms of Pareto efficiency. Since income typically precedes consumption over the life cycle (even though the rich dissave slightly for the first two periods of their lives), a consumption tax is preferable to a wage tax. This argument obviously has even more force when agents face binding liquidity constraints. Another consequence of such timing arguments is that since the major part of transfers is paid as pensions after retirement, reductions in interest rates are welfare improving.

The impact of a marginal switch from VAT to wage taxes may be traced as follows. Including social security contributions in the calculation of the effective marginal wage tax, RR equals 0.50 in the base case, falling to 0.46 and 0.48 in simulations (1) and (5) (see Table 4). The decline in the ratio induces households to switch their consumption from goods to leisure, leading to a drop in the supply of labor. To restore labor market equilibrium, wages rise, leading to a substitution of capital for labor, and output in both the tradable and the nontradable sector declines. The reduction in export supply leads to an increase in foreign prices or, equivalently, to an exchange rate appreciation. This, in turn, induces households to switch consumption from domestic to foreign goods. However, because of a marked drop in imports of investment goods, imports fall overall. The terms of trade improvement or, put differently, the effective transfer from the rest of the world to the home economy, is insufficient to offset the initial welfare loss.

As a final point, one should bear in mind that this model probably underestimates the negative impact of wage taxes. A lack of data regarding the distribution of marginal tax rates prevented us from analyzing the impact of the progressivity of income tax. However, it is well known that distortions grow more than linearly with tax rates.30 In the case of France, such nonlinearities could be important given the narrowness of the wage tax base.31

Savings Tax versus Wage Tax: The Influential Role of Government Debt

An important element in the tax harmonization reforms is the substantial cut in the effective rate of tax on savings. In this subsection, we discuss the long-run impact of such cuts financed by increasing labor income taxes. As we shall show, the impact of such a policy depends in a complex way on the relative size of households’ intertemporal substitution and labor supply elasticities and on the initial level of the public debt.

It is often argued that since taxes on interest income amount to levies on future consumption, if the government also imposes a conventional consumption tax, then savings suffer double taxation. Such double taxation, the argument continues, almost certainly represents an excessive burden. However, as Feldstein (1978) argues, this argument ignores a crucial point. If taxes on savings are cut, thereby reducing the distortionary wedge between current and future consumption, some other tax must be increased if the government deficit and spending are to remain fixed.

If the increased tax is, say, a wage or a consumption tax, then the effect in general will be to create another distortionary wedge between the prices of consumption and leisure. In some simple cases, one may show that eliminating savings taxes is nevertheless optimal. For instance, if the utility function is of the form UU(U1(l1 ,.., lT), U2(C1 ,.., CT))—that is, separable in consumption and leisure—where the subfunction U2(.,..,.) is homothetic in consumption, then as Atkinson and Stiglitz (1976) have shown, the optimal savings tax is zero.

In contrast to the above case, the utility functions employed in this study imply no simple rules concerning the optimal level of savings taxes. Nevertheless, one may still gain a better understanding of the results by drawing parallels with the Ramsey analysis of optimal commodity tax. This analysis implies a recommendation to levy relatively high taxes on goods with low demand elasticities.32 Thus, the finding (see simulation (5) in Table 4) that cuts in savings taxes financed by higher wage taxes lower welfare hinges in part on the assumption of a low elasticity of intertemporal substitution in relation to the elasticity of substitution between labor and consumption. In other words, a higher intertemporal elasticity would improve the relative efficiency of a wage tax. From our sensitivity analysis, we found—as did Auerbach and Kotlikoff (1987), who performed a similar analysis—that within an acceptable range of parameter values, saving should be taxed.

Another important factor in determining the impact on welfare of switching from savings to wage taxes is the initial level of the government debt. In the steady state, positive government debt implies that the government must run a primary budget surplus in order to meet interest payments. We assume in the simulations that the value of the debt—that is, minus the ratio of public surplus to net interest rate—is the same before and after the policy change. Increases in the gross interest rate, or, as in the current instance, cuts in savings taxation, imply that the government must increase the size of its surplus in the new steady state. To do this requires raising either wage or lump-sum taxes, depending on the assumptions about financing. These tax increases will leave households worse off.

Given this discussion, it is natural to wonder just how reliable is the assumption regarding the initial debt level and what implications the assumption will have for the welfare changes that follow cuts in savings taxes. Auerbach and Kotlikoff (1987) simplify their analysis by assuming a zero level of government debt. Since the French public debt is probably not zero,33 we did not follow their example in the baseline simulation. However, to gauge the importance of this assumption, we did simulate the model for the basic package of VAT and savings tax cuts, financed by changes in labor income tax, assuming a zero initial level of public debt. The results may be found in the sixth column of Table 4. The analysis shows that with zero public debt, the real impact of the tax changes is to some degree muted (apart from import consumption, which grows by more). Utility falls by somewhat less than in the base case. On the basis of the above arguments, this result could be interpreted as showing that much of the negative impact on utility of the savings tax reduction related to the balanced budget is due to the initial indebtedness of the government and the assumption of an unchanged debt level.

Treatment of the External Sector

To assess the sensitivity of the results to the assumptions about the external sector, we performed a series of simulations in which the elasticities of savings supply and export demand are effectively infinite, or equivalently, foreign prices and interest rates are internationally determined.34 The results of these simulations are given in Table 5. In almost all cases, the different parameterization led to greater welfare losses for domestic households. In the standard case of combined VAT and savings tax cuts financed by higher wage taxes, the decreases in households’ lifetime utility for both rich and poor were over 50 percent higher than in the baseline simulation (1) given in Table 4.

Table 5.

Small Country Results

(Percentage changes)

article image
article image
Note: Simulations (6) through (10) are identical to simulations (1) through (5) in Table 4, except that the export demand and savings supply elasticities of the rest of the world ω and ω′ are set to infinity.

Utility changes are money metric; that is, GDP equivalent.

As a percentage of GDP.

Note that a 5 percent change in the interest rate is equivalent to an annual change of 25 basis points.

Two factors contributed to this result. First, by fixing the exchange rate,35 the small country assumption prevents domestic households from partially shifting onto foreigners the welfare losses due to the tax cuts through an improvement in the terms of trade. Second, the small country assumption also implies a fixed interest rate determined by the rates available in world capital markets. Lower savings taxes raise the after-tax interest rate, leading to a reduction in the present value of households’ transfer payments. As already noted, the timing of income and, particularly, the concentration of transfers in the retirement period mean that interest declines are welfare improving. In the baseline case of Table 4, gross interest rates fell, partly offsetting this effect, but with the small country assumption fixing the pretax rate, this can no longer happen. Partially offsetting this second effect, as one can see by a comparison of simulations (6) and (8), is the fact that with the higher net interest rate, the government need not run such a large steady-state surplus to finance its fixed stock of debt, and steady-state taxes on households are therefore lower.

Apart from the impact upon welfare, the most interesting aspect of the small country results shown in Table 5 is the scale of the changes in the real economy that follow the tax cuts. Output, labor supply, the capital stock, and consumption fall in the basic simulation (6) by about 5 percent, with the consumption of leisure rising by approximately 7 percent. By fixing some prices, the small country assumption reduces the ability of the price system as a whole to equilibrate tax changes and thus leads to quantity responses on this scale.

Credit Constraints

In Table 6, we report the results of repeating the basic simulations of Table 4 but without imposing credit constraints on poor households. The results are interesting mainly because of the small difference that the change makes. It is interesting to note, although not unexpected, that poor households are able to reduce the welfare losses they suffer following the tax changes when borrowing constraints are absent (utility changes for poor households in simulations (11) to (15) are uniformly lower than the utility changes in the corresponding base simulations (1) to (5)). Nevertheless, the magnitude of the differences between the results in Tables 4 and 6 is minor, and the relaxation of borrowing constraints makes no qualitative difference to the welfare impact of the policy changes, which remains uniformly negative.

Table 6.

Results with Unrestricted Borrowing

(Percentage changes)

article image
article image
Note: Simulations (11) through (15) are identical to simulations (1) through (5) in Table 4, except that poor household’s borrowing is unrestricted.

Utility changes are money metric; that is, GDP equivalent.

As a percentage of GDP.

Note that a 5 percent change in the interest rate is equivalent to an annual change of 25 basis points.

In their study of the relative efficiency of different tax bases in the presence of borrowing constraints, Hubbard and Judd (1986) argue that such constraints may radically affect the welfare impact of altering levels of savings taxation. Clearly, such effects will depend on a number of factors, including the degree to which the borrowing constraints actually bite. In this setup, because unconstrained consumption only exceeds income by a slight amount, the reduction in distortion is fairly small.

Lump-Sum Financing of the Reforms

Despite the discussion in Section I, some grounds might still remain for questioning the basic assumption that the package of fiscal harmonization reforms will be financed with higher wage taxes. Certain changes in income tax rules (for example, a general change in tax allowances or a broadening in the tax base) or in expenditures taxes may be better represented as changes in lump-sum taxation. Accordingly, it would be interesting to analyze the results of the reforms under such alternative financing.

In fact, the channels through which the VAT and savings tax cuts affect the economy turn out to be very different under lump-sum as opposed to labor income tax financing. As we discussed above, a shift from VAT to wage taxes may be thought of as increasing the degree of distortion in the economy, whereas one would naturally suppose the opposite in the case of a shift to lump-sum transfers. It may therefore seem paradoxical that the net effect of cutting VAT and savings taxes financed in a lump-sum fashion is still a reduction in utility. This result stems, first, from the relaxation of the small country assumption and, second, from the presence of a nonzero government debt.

As may be seen in column 4 of Table 4, with lump-sum financing, labor supply actually rises. Together with large increases in saving, this stimulates the investment and output of domestic industry. With production outpacing domestic consumption, exports increase. To maintain balance of payments equilibrium, the terms of trade must deteriorate. Though household incomes have benefited from the expansion in domestic output, the worsening in the terms of trade is sufficient to lead to an overall decrease in households’ welfare.36

In the small country case given in simulation (7) (that is, with constant terms of trade), the package of tax cuts still involves a reduction in welfare, but this time it is due more to the cut in the savings tax. Simulations not reported in the paper show that with constant terms of trade, switching from savings taxes to lump-sum taxation lowers welfare significantly when government debt is nonzero but has a negligible impact if the stock of debt is small.

Sensitivity Analysis

An important question to ask is what is the sensitivity of the results described above to the value of certain key parameters. In comparing VAT with wage taxes, it is reasonable to expect that elasticities of substitution between leisure and consumption goods will be important. In evaluating savings tax cuts financed by higher wage taxation, one may expect elasticities of intertemporal substitution, consumption-leisure substitution, and world savings supply to play significant roles. Table 7 shows the percentage changes in GDP and in the lifetime utilities of the two representative steady-state households (in terms of percentages of GDP—that is, money-metric form) for a series of different parameter values.

Table 7.

Sensitivity Analysis of Tax Cuts with Wage Tax Financing

article image
Notes ω ≡ interest derivative of world savings supply; ρ ≡ elasticity of substitution between leisure and consumption; and α ≡ elasticity of intertemporal substitution. All changes are in percentage terms; utility changes are expressed in units of GDP (that is, money metric).

The following observations are suggested by the results in Table 7. First, under all sets of parameter values, the VAT cuts and the combined VAT and savings tax cuts lower GDP and the utility of both households. Second, while the declines in GDP vary widely, the magnitudes of the utility changes tend to be more robust. Third, as one might expect, the welfare costs of cutting VAT are increasing in the leisure-consumption elasticity. However, this effect is remarkably small, only affecting the second decimal place of the percentage changes in utility for the baseline levels of the other parameters. Fourth, the welfare costs of VAT cuts are decreasing in the coefficient of intertemporal substitution, α. The reason for this effect is the asymmetry between the impact of the tax cut on welfare before and after the date of retirement. A lower VAT clearly improves welfare in the post-retirement period, but the policy lowers lifetime utility overall, so welfare before retirement is reduced. The magnitude of the coefficient of intertemporal substitution, α, determines the extent to which the former effect offsets the latter. Fifth, the welfare costs of the combined tax cuts decline quite steeply as α increases, presumably because of the impact of the VAT cuts just referred to and because the reduction in intertemporal distortions from the cut in savings taxation will be all the greater.

IV. Short-Run Results

This section describes the transition path taken by the economy following cuts in VAT and savings taxes financed by higher wage income taxes. Three important points emerge from these simulations. First, even when one takes account of the welfare of generations alive when the policy is implemented, the package of tax cuts is undesirable—that is, it represents a potential Pareto reduction in welfare. Second, the simulations show that the dynamics of the model are influenced primarily by the fact that the existing wealth of households reflects past savings decisions made under the previous tax system. Third, prior announcement of the tax cuts elicits a very different dynamic response from the economy than that obtained if the policy is implemented immediately.

Welfare Effects

Figures 1-3 show the lifetime utilities of the 10 cohorts alive when taxes are cut and of the first 18 cohorts born thereafter. Each figure shows three simulations: a base case simulation without input adjustment costs for firms; a simulation that assumes adjustment cost parameters of 5 percent; and a simulation in which an announcement is made in the first period that the policy will be implemented in the second.

Figure 1.
Figure 1.

Impact of Tax Harmonization: Welfare and Output

Citation: IMF Staff Papers 1991, 001; 10.5089/9781451947076.024.A007

Figure 2.
Figure 2.

Impact of Tax Harmonization: Labor Supply and Consumption

Citation: IMF Staff Papers 1991, 001; 10.5089/9781451947076.024.A007

Figure 3.
Figure 3.

Impact of Tax Harmonization: Interest Rate and Prices

Citation: IMF Staff Papers 1991, 001; 10.5089/9781451947076.024.A007

Since the utility levels from the original steady state were -49.78 for the rich and -54.65 for the poor, one may see that one cohort of poor households and three cohorts of rich are marginally better off following the policy. The reason is intuitively obvious. Switching from VAT to wage taxation benefits households that have built up a stock of savings out of earlier wage income. Given the minor nature of these utility gains, it is clear37 that transferring resources from gainers to losers in such a way as to stabilize the lifetime utilities of the former at their previous steady-state levels will leave some worse off and none better off than before the tax cuts took place. The policy, therefore, is a potential Pareto reduction in welfare.

Source of the Dynamics

The second point to emerge from the simulations is that, given our parameterization, firms’ costs of adjusting inputs play a small role in determining the dynamics. The adjustment cost parameters in the model were set at 5 percent. Though it is difficult to see a priori what value one should choose, this value seemed reasonable. As may be seen in Figures 1 and 2, depicting output and labor supply, the differences between the base simulation and the one with adjustment costs are minor. Instead, the major source of dynamics in the model is that when policies are implemented, households currently alive possess stocks of savings that reflect decisions made under the relative prices of the old steady state. Figure 1, for example, shows that it takes approximately 80 years for prices and stocks to adjust to such a point that the economy is close to its new steady state, although the bulk of the adjustment is achieved within 40 years.

Announcement Effects

The third point to note is that the announcement of policies in advance of their implementation significantly affects the short-term results, reducing the magnitude of households’ welfare losses. Turning to the impact on real demand and supply in the economy, prior announcement of the policy leads to a 1½ percent increase in labor supply in the first period, in contrast to the 3½ percent fall observed in the base case with instantaneous implementation. When the tax cuts are actually carried out in the second period, labor supply falls precipitously by about 5 percent.

From a preannounced reform, one would expect an increase in labor supply and a reduction in consumption reflecting households’ expectations about lower net wages and after-tax prices. This intertemporal substitution does take place in the case of labor but not for consumption because of price changes that offset the impact of the tax reform. Output by domestic firms is boosted by the temporarily higher labor supply, and consumption spending, while lower than in the initial steady state, falls by much less than it does in the first period of the base case simulation. Prices in the economy react to these real shocks in the following way. The temporary escalation in labor resources boosts potential output, leading to an exchange rate depreciation that induces foreigners to absorb the increased net supply of good 3 from the domestic economy. Thus, households substitute domestic consumption for imports (substitution effect), while reducing overall consumption (income effect). The interest rate falls sharply because of the extra savings by households out of their transitorily higher real income. It may seem paradoxical, given this interpretation of the results, that the wage rate in the simulation with prior announcement rises slightly in the first period. The reduction in interest rates and, hence, in the user cost of capital allows firms to pay higher wages while remaining on the factor price frontier. This, in turn, reinforces the incentive for households to supply labor.

V. Conclusions

In this paper, we have used simulation models to analyze the package of measures that France will have to adopt in order to bring its VAT and savings taxes into line with those of its EC neighbors. According to our calculations, these measures could entail significant long-run welfare losses for French households. Tax harmonization may still remain a worthwhile objective for the EC, since, for example, it would permit the virtual removal of frontier controls. However, the results suggest that current proposals that call for all EC members to adjust their different VAT rates toward some overall average rate may be seriously misguided.

Instead, it may be preferable for countries that currently impose relatively heavy direct taxes to use the harmonization as an opportunity to shift their tax systems toward greater reliance upon indirect taxes. Countries like France could then maintain their VAT tax rates at reasonably close to current levels.

An important relevant topic for future research is study of the impact of harmonization on other countries in the EC. If the gains from harmonization for these countries were sufficiently pronounced, then the currently envisaged policy of averaging existing VAT rates might still be desirable, provided that transfer payments could be arranged to compensate losers. A systematic examination of this issue could be performed within a multicountry version of the model described in the present paper.

As a final point, one should note that the conclusions of this study are not sensitive to whether or not VAT tax cuts can be financed out of higher than expected revenues, due to, say, fiscal drag. First, such fiscal drag may involve agents moving into higher wage income tax bands due to increases in the real value of their earnings; from an economic point of view, this is somewhat similar to a rise in wage income tax rates. Second, the most important message of the study concerns differences in tax rates rather than levels. In other words, if revenues grow due to an unforeseen shock, the extra budgetary room for maneuver should be used to lower wage income taxes rather than VAT.

APPENDIX I Model Description

This Appendix provides a derivation of the principal behavioral equations of the model. As mentioned in the text, agents are assumed to possess utility functions of the form

U1(11α)Σt=1T1(1+δ)t1ut11/α
ut=[Ct11/ρ+α0lt11ρ]1/(11/ρ)
Ct=[α1C1,t11/ρ1+(1α1)CT,t11/ρ1]1/(11/ρ1)
CT,t=[α2C2,t11/ρ2+(1α2)C3,t11/ρ2]1/(11/ρ2),

where Ci, t (i = 1, 2, 3) represents the consumption of the three goods in period t. Households face budget constraints given by

Wt=Wt1(1+rt)Σi=13Pi,tCi,t+ItT(wt(1lt),rtWt1)
Itwt(1lt)+rtWt1,

where T(.,.) is a differentiable function giving the level of taxes. We also assume that leisure is constrained to equal unity in the last two periods of the household’s life and that the household cannot borrow against its anticipated future labor income:38

lt=1t=9,10Wt0t=1,2,..,10.

Since there are no bequests, W0 = 0. The Lagrange multipliers associated with the budget, retirement, and liquidity constraints are Ωt, μt, and νt, respectively. The household’s first-order conditions may be rearranged to give

1(1+δ)t+1ut1/ρ1/aCt1/ρ=ΩtPt(1+tt)
1(1+δ)t+1ut1/ρ1/aα0lt1/ρ=Ωt(wt(1T1,t)+μt)
Ωt+1=(Ωt+vt)(1+rt+1(1T2,t+1))
P1,t(1+t1,t)P2,t(1+t2,t)=α11α1(C1,tC2,t)1/ρ1,

where Ti, t denotes the partial derivative of function T with respect to the ith variable in period t, and where the tax-inclusive price index, Pt,(1 + tt), is defined as

Pt(1+tt)[α1ρ1(P1,t(1+t1,t))1ρ1+(1α1)ρ1(PT,t(1+tT,t))1ρ1]1/(1ρ1)
PT,t(1+tT,t)[α2ρ2(P2,t(1+t2,t))1ρ2+(1α2)ρ2(P3,t(1+t3,t))1ρ2]1/(1ρ2).

In formulating the model, the following properties of CES utility functions prove useful (see Dixit and Stiglitz (1977)).

Pt(1+tt)Ct=P1,t(1+t1,t)C1,t+PT,t(1+tT,t)CT,t
PT,t(1+tT,t)CT,t=P2,t(1+t2,t)C2,t+P3,t(1+t3,t)C3,t.

Note that it is not possible to solve the above system analytically, because the shadow wage or Lagrange multiplier to the retirement constraint is not known.

The economy we examine has two production sectors producing goods 2 and 3 using capital and labor inputs. Each industry consists of identical firms with CES production functions of the form

Ft(Kt,Lt)1[0Kt11/+(10)Lt11/]1/(11/).

Firms face convex costs of adjusting their inputs:

CK(It,Kt1)b(ItdKt1)2Kt1
CL(Lt,Lt1)a(LtLt1)2Lt1.

Each firm has a rate of capital depreciation, d, which is assumed to be constant over time. Given these assumptions, the long-run equilibrium will be independent of the adjustment costs.

Though French firms are subject to many different taxes, the most important are the profits tax (whose rate we denote τt) and social security contributions (with rate txt). We assume that social security contributions are paid exclusively by employers. So long as household behavior depends only on after-tax wages, this involves no loss of generality.

We further assume that the fiscal depreciation rate d′ is equal to the rate of economic depreciation, d. Although the actual fiscal rate almost certainly exceeds the economic rate, one may reasonably argue that the benefits to firms are counterbalanced by the fact that the calculation of depreciation allowances is based on nominal values. If rt represents the discount rate for the firm,39 then, for each dollar of investment, the discounted value of the tax deduction implied by the depreciation allowance equals40

Zt=τdΣs=0(1d)sπt,

where

πt=Πj=0t(1+rj).

Since interest costs paid by firms are tax deductible, the Miller-Modigliani theorem does not hold, and it is necessary to specify the financial behavior of the firm. Assume that, at the margin, the percentage of investment financed by debt is θ, and the interest rate on this debt is rt. The expression for Zt should then be modified by multiplying by (d+θrt)/d. The firm’s profit maximization may then be stated as

maxΣt=0πt((1τ)(ptYtwt(1+txt)Lt)qt(1Zt)It),

subject to Kt = (1 - d)Kt - 1 + It, where qt is the price of capital goods. Accordingly, we obtain the first-order conditions:

ptFK=b2pt[(Kt+1Kt)21]+(1+rt)bpt1[KtKt11]+uct
ptFL=wt(1+txt)+(1+rt)apt1[LtLt11]a2pt[Lt2+1Lt21].

The implicit user cost of capital is

uct=1(1τ)(qt(1τZt)(1+rt)qt+1(1τZt+1)(1d)πtπt+1).

It follows that in a steady state, uct = q(1 - τZ)(r + d)/(1 - τ) with the two polar cases: uct = q(r + d) if θ = 1; and uct = q(r′ + d)/(1 - τ), if θ = 0. Only if θ = 1 will firms’ incentives to invest be unaffected by taxation. In the simulations reported in the text, we will assume that marginal investment is debt financed and hence profit taxes are nondistortionary. We assume that profits are paid to the government, which therefore becomes the implicit owner of the firm. This assumption removes the need to include a market in equities and, as we show below, does not necessarily affect households’ budget constraints. Moreover, in the long run returns to scale are constant, so that profits equal zero.

APPENDIX II Solution of the Model

Several approaches to solving general equilibrium models that are static and nonlinear have been discussed in the literature. These include, first, the Scarf algorithm, either in its original form or in one of the more recent improved versions. Second, standard numerical methods for solving nonlinear systems, such as Gauss-Seidel, Gradient, or optimization approaches, have been applied.41 Third, as advocated by Dervis, De Melo, and Robinson (1981), one may adopt techniques that exploit the structure of the particular model concerned.

The solution of multiperiod models presents additional difficulties, since the number of variables for which it is necessary to solve is effectively multiplied by the number of periods. The approach that is generally adopted consists of, first, solving for the initial steady state; second, computing the final steady state after policy changes; and, last, solving the transition path between the two steady states. If one assumes perfect foresight and rational expectations on the part of agents, it will not in general be possible to solve the model recursively over the transition path, since current behavior will depend on variables in future periods, which depend in turn on lagged variables (for instance, capital accumulation). Techniques to deal with this problem have been discussed by Fair and Taylor (1983) (the Fair-Taylor algorithm), by Lipton and others (1982) (multiple shooting methods), and by Spencer (1985) (optimization techniques).

For an application such as ours, the main difficulty is the combination of a nonrecursive dynamic structure and the nonlinear implicit form of many of the equations in the model. In particular, solving the household program with liquidity constraints is computationally costly. For this reason, it seems to be more efficient to solve for the transition path of the model directly, rather than attempting to use the model’s dynamic structure as suggested by, for example, Fair (1984) and Laitner (1984).

Figure 4 shows the algorithm for the steady-state solution of the model. Since prices are constant in the steady state, we only need to find the level of wages, the exchange rate, export prices, and the interest rate. Beginning with a guess for the interest rate, exchange rate, and the level of transfers to households, the optimality conditions of firms are used to establish both relative prices (via the factor price frontier) and the ratios of capital stocks and output to labor demands. Given relative prices, we solve the intertemporal optimization problem of households, including retirement and liquidity constraints, and then aggregate to obtain the aggregate levels of consumption and labor supply. Together with export demand (given by the exchange rate) and the exogenously determined level of government spending, we then have total goods demands and labor supply. Combining these with the capital stock and output ratios mentioned previously yields total output and labor demand in the two domestic industries. Given the total demands for domestic goods, we are then able to calculate the disequilibria in the labor market and the balance of payments and the degree to which government debt diverges from the initially assumed level. Using a Newton procedure, we then perturb the interest rate, exchange rate, and the level of transfers to households in order to reduce these three discrepancies.

Figure 4.
Figure 4.

Steady-State Algorithm

Citation: IMF Staff Papers 1991, 001; 10.5089/9781451947076.024.A007

REFERENCES

  • Atkinson, A.B., and Joseph E. Stiglitz, “The Design of Tax Structure: Direct Versus Indirect Taxation,” Journal of Public Economics, Vol. 6 (July-August 1976), pp. 5575.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Auerbach, Alan J., “Taxation, Corporate Financial Policy and the Cost of Capital,” Journal of Economic Literature, Vol. 21 (September 1983), pp. 90540.

    • Search Google Scholar
    • Export Citation
  • Auerbach, Alan J., and Laurence J. Kotlikoff, Dynamic Fiscal Policy (Cambridge: Cambridge University Press, 1987).

  • Boiteux, Marcel, Fiscalité et Marché Unique Européen, Rapport d’Etape au Ministre d’Etat, Ministre de l’Economic, des Finances et de la Privatisation (Paris: Documentation Francaise, 1988).

    • Search Google Scholar
    • Export Citation
  • Boskin, Michael J., “Taxation, Saving, and the Rate of Interest,” Journal of Political Economy, Part 2, Vol. 86 (April 1978), pp. S3S27.

  • Cecchini, P., The European Challenge, 1992: The Benefits of a Single Market (Brookfield, Vermont: Gower, 1988).

  • De Melo, Jaime, and Sherman Robinson, “Product Differentiation and the Treatment of Foreign Trade in Computable General Equilibrium Models of Small Economies,” Journal of International Economics, Vol. 27 (August 1989), pp. 4767.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Dervis, Kemal, Jaime De Melo, and Sherman Robinson, General Equilibrium Models for Development Policy (Cambridge; New York: Cambridge University Press, 1981).

    • Search Google Scholar
    • Export Citation
  • Dixit, Avinash K., “Tax Policy in Open Economies,” in Handbook of Public Economics, ed. by Alan J. Auerbach and Martin Feldstein (Amsterdam: North-Holland, 1985).

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Dixit, Avinash K., and Joseph E. Stiglitz, “Monopolistic Competition and Optimum Product Diversity,” American Economic Review, Vol. 67 (June 1977), pp. 297308.

    • Search Google Scholar
    • Export Citation
  • Fair, Ray C., Specification, Estimation, and Analysis of Macroeconomic Models (Cambridge, Massachusetts: Harvard University Press, 1984).

    • Search Google Scholar
    • Export Citation
  • Fair, Ray C., and John B. Taylor, “Solution and Maximum Likelihood Estimation of Dynamic Nonlinear Rational Expectations Models,” Econometrica, Vol. 51 (July 1983), pp. 11691185.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Feldstein, Martin, “The Welfare Cost of Capital Income Taxation,” Journal of Political Economy, Part 2, Vol. 86 (April 1978), pp. S29S51.

  • Fisher, Irving, “Income in Theory and Income Taxation in Practice,” Econometrica, Vol. 5 (January 1937), pp. 155.

  • Frenkel, Jacob A., and Assaf Razin, Fiscal Policies and the World Economy (Cambridge, Massachusetts: MIT Press, 1987).

  • Frenkel, Jacob A., and Assaf Razin, and Stephen Symansky, “International Spillovers of Taxation,” IMF Working Paper 91/22 (Washington: International Monetary Fund, February 1991).

    • Search Google Scholar
    • Export Citation
  • Hall, R.E., and F.S. Mishkin, “The Sensitivity of Consumption to Transitory Income: Estimates from Panel Data on Households,” Econometrica, Vol. 50 (March 1982), pp. 46181.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Harberger, Arnold C., “Three Basic Postulates for Applied Welfare Economics: An Interpretative Essay,” Journal of Economic Literature, Vol. 9 (September 1971), pp. 78597.

    • Search Google Scholar
    • Export Citation
  • Harris, Richard G., “Alternative Solution Methods in Applied General Equilibrium Analysis,” OECD Working Paper 53 (Paris: Organization for Economic Cooperation and Development, 1988).

    • Search Google Scholar
    • Export Citation
  • Hayashi, Fumio, “The Permanent Income Hypothesis: Estimation and Testing by Instrumental Variables,” Journal of Political Economy, Vol. 90 (October 1982), pp. 895918.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hubbard, R. Glenn, and Kenneth L. Judd, “Liquidity Constraints, Fiscal Policy and Consumption,” Brookings Papers on Economic Activity: 1 (Washington: The Brookings Institution, 1986), pp. 150.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kaldor, Nicholas, An Expenditure Tax (London: Allen and Unwin, 1955).

  • Keen, Michael, “The Welfare Effects of Commodity Tax Harmonization,” Journal of Public Economics, Vol. 33 (June 1987), pp. 10714.

  • Laitner, J., “Transition Time Paths for Overlapping-Generations Models,” Journal of Economic Dynamics and Control, Vol. 7 (May 1984), pp. 11129.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lebegue, D., La Fiscalité de l’Épargne dans le Cadre du Marché Intérieur Européen, Rapport du Conseil National du Credit (Paris: Direction des Journaux Officiels, 1988).

    • Search Google Scholar
    • Export Citation
  • Lipton, David, James M. Poterba, Jeffrey Sachs, and Lawrence H. Summers, “Multiple Shooting in Rational Expectations Models,” Econometrica, Vol. 50 (September 1982), pp. 132933.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Meade, J.E., and Institute for Fiscal Studies, The Structure and Reform of Direct Taxation (London; Boston: Allen and Unwin, 1978).

  • Organization for Economic Cooperation and Development, Revenue Statistics of OECD Member Countries, 1965–1989 (Paris: OECD, 1990).

  • Pechman, Joseph, “The Future of the Income Tax,” American Economic Review, Vol. 80 (March 1990), pp. 120.

  • Perraudin, W.R.M., and T. Pujol (1990a), “Tax Efficiency in an Open Economy,” IMF Working Paper 90/94 (Washington: International Monetary Fund, 1990).

    • Search Google Scholar
    • Export Citation
  • Perraudin, W.R.M., and T. Pujol (1990b), “European Tax Harmonization and the French Economy,” IMF Working Paper WP 90/96 (Washington: International Monetary Fund, 1990).

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Spencer, Peter D., “Bounded Shooting: A Method for Solving Large Nonlinear Econometric Models Under the Assumption of Consistent Expectations,” Oxford Bulletin of Economics and Statistics, Vol. 47 (February 1985), pp. 7982.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Summers, Lawrence H., “Capital Taxation and Accumulation in a Life Cycle Growth Model,” American Economic Review, Vol. 71 (September 1981), pp. 53344.

    • Search Google Scholar
    • Export Citation
  • Zeldes, Stephen P., “Consumption and Liquidity Constraints: An Empirical Investigation,” Journal of Political Economy, Vol. 97 (April 1989), pp. 30546.

    • Crossref
    • Search Google Scholar
    • Export Citation
*

W.R.M. Perraudin is an Economist in the Research Department.

T. Pujol is an Economist in the European Department.

The authors would like to thank Krister Andersson, Alan Auerbach, Jonathan Skinner, Cuong Le Van, and numerous Fund colleagues for helpful comments.

1

Thus, the Cecchini report concentrates overwhelmingly on the gains from increased competition and economies of scale due to the removal of barriers between national markets.

2

Even then, the presence of liquidity constraints may reduce or even reverse the welfare gain, as we note below.

3

Some authors, such as Pechman (1990), also question the underlying life-cycle framework, which assumes that all income is eventually consumed by households. If this is not the case, then income will represent a broader tax base and a better indicator of ability to pay than consumption.

4

Hence, we do not make the commonly adopted small country assumption.

6

As discussed in Perraudin and Pujol (1990a), allowing for imperfectly elastic supplies of savings and demand for exports from the rest of the world may radically alter the traditional ranking of different tax bases from the point of view of their impact on economic welfare. For example, substituting distortionary VAT for a lump-sum tax may raise domestic welfare by improving the terms of trade.

7

As argued by Keen (1987), since deadweight losses depend on the square of tax rates, one would expect a Pareto improvement from a harmonization of EC rates to the average compensated by lump-sum transfers at an international level.

8

Differences in excise duties across different EC member states are in many instances larger than those in VAT rates. In this study, however, we focus attention only on appropriate levels for VAT rates, since excise duties are largely determined on public health rather than strictly economic grounds.

9

The following discussion of VAT harmonization and its effects on the French economy owes much to the detailed study by Boiteux (1988).

10

This broadly follows the provisions of the General Agreement on Tariffs and Trade relating to commodity taxation.

11

Although a clearinghouse for tax revenues is required.

12

In France, 30 percent of VAT receipts currently comes from the purchases of such organizations.

13

Some EC members might also have been worried by the intricacies of and the lack of control over the clearing system suggested by the Commission. Note again that the distortions referred to here concern tax-exempt firms.

14

For a more detailed account of this issue and how it affects France, see Lebegue (1988).

15

Specifically, to increase expenditure on education and public wages.

16

Note that in our model, broadening the income tax base is equivalent to a reduction in lump-sum taxation.

17

The commonly adopted small country assumption under which interest rates and the prices of traded goods are exogenously given from abroad is a special case of this model.

18

Since households cannot adjust their levels of human capital through, for example, education, this analogy is of only partial relevance. It might be interesting in future work to allow for investment in human capital or, alternatively, to allow households to switch from one category to another.

19

Given average life expectancies in industrialized countries, each period of time in the model is regarded as representing approximately five years.

20

Since retirement payments are contingent upon withdrawal from the labor market, the shadow cost of leisure may be expected to fall dramatically, leading to a sharp drop in the participation rate.

21

Compared with those of the rich.

22

Capital is, in fact, a composite good made up of fixed shares of domestic and imported goods.

23

When this condition holds, the level of production is determined by demand, and any change in the real price of one input must be offset by an opposite change in the real price in the other input.

24

One may justify the latter assumption by saying that an overestimated fiscal rate (d′ > d) offsets the distortions due to the nominal tax regime prevailing in the French system.

25

See De Melo and Robinson (1989) for a careful examination of the treatment of the external sector in general equilibrium models.

26

Note that under our assumptions, a withholding tax is levied on foreign bondholders, which is not affected by changes in the income tax.

27

More details can be found in Perraudin and Pujol (1990b)).

28

Recall that the model is formulated so that one period is equivalent to five years. Given that the tax changes will mostly take effect in the period 1990 to 1995, it seemed reasonable to take 1985 as the base.

29

What is actually held constant by adjusting labor income taxes in the simulations is the level of the government debt.

30

Harberger (1971) proves that distortions depend on the square of marginal tax rates.

31

The proportion of households paying income tax slightly exceeds one half.

32

Such a general description of the Ramsey rule ignores the influence of cross elasticities between goods.

33

Estimating the true” level of government debt is far from easy, given the existence of offsetting items on the government’s balance sheet, such as public corporations and share holdings.

34

In the baseline simulation, these elasticities were set, respectively, to 5 and −1.

35

Strictly speaking, the real exchange rate is not fixed, since changes could in general take place in the relative price of tradables and nontradables. However, in this case, such price adjustments do not occur since the production functions in the two sectors are identical. This means that if firms in sector 1 are on their factor price frontiers, so also are firms in sector 3. This explains why the exchange rate does not change in the simulations reported in Table 5.

36

Interested readers may find a more detailed analysis of this result in Perraudin and Pujol (1990a).

37

And may easily be shown numerically.

38

In the model simulations, we assume that only poor households face such liquidity constraints. The utility maximization problem of rich households is the same as that described here, except that the Lagrange multipliers for the borrowing constraints are identically zero.

39

This will not, in general, equal that of households.

40

In this calculation, we implicitly ignore the potential nonlinearity resulting from different tax treatment of negative profits.

41

For more discussion and a comparison with the other methods mentioned here, see Harris (1988).

IMF Staff papers: Volume 38 No. 2
Author: International Monetary Fund. Research Dept.