A New-Open-Economy Macro Model for Fiscal Policy Evaluation
Author: Mr. Dirk V Muir, Mr. Douglas Laxton, Mr. Dennis P Botman, and Mr. Andrei Romanov

Contributor Notes

Author(s) E-Mail Address: dbotman@imf.org, dlaxton@imf.org, dmuir@bank-banque-canada.ca, aromanov@ssc.wisc.edu
Publication Date:
01 Feb 2006
eISBN:
9781451863055
ISBN:
9781451863055
Language:
English
Keywords:
WP; open economy; shadow price; case home; optimization problem; world real interest rate; equilibrium price
Download PDF (440.5 KB)

We develop a New-Open-Economy-Macro model in which Ricardian equivalence does not hold because of (i) distortionary labor and corporate income taxation; (ii) limited asset market participation; and (iii) because the overlapping-generations structure results in a disconnect between current and future generations. We consider a permanent increase in government debt following a cut in labor or corporate income taxes in a small and large open economy. We analyze the sensitivity of the results to the key structural parameters of the model and argue that under plausible assumptions there will be significant crowding-out effects associated with permanent increases in government debt.

Abstract

We develop a New-Open-Economy-Macro model in which Ricardian equivalence does not hold because of (i) distortionary labor and corporate income taxation; (ii) limited asset market participation; and (iii) because the overlapping-generations structure results in a disconnect between current and future generations. We consider a permanent increase in government debt following a cut in labor or corporate income taxes in a small and large open economy. We analyze the sensitivity of the results to the key structural parameters of the model and argue that under plausible assumptions there will be significant crowding-out effects associated with permanent increases in government debt.

I. Introduction

The crowding-out effect of government debt continues to be an area that is of considerable interest in policy circles. However, the emergence and popularity of the New-Open-Economy-Macroeconomics (NOEM) paradigm has resulted in monetary policy issues becoming the center of studying macroeconomic interdependence across countries while there has been much less attention directed at fiscal issues. Indeed, standard NOEM models typically specify an infinitely lived representative agent in a perfect-foresight setting with nondistortionary taxation implying that the Ricardian equivalence hypothesis holds, and the analysis of fiscal policy is confined to studying the effects of balanced-budget fiscal policies.2 With the reemergence of fiscal deficits in the United States, as well as fiscal policy issues elsewhere, the idea of bringing the rigorous microfoundations of NOEM paradigm to the analysis of fiscal policies is very appealing.3

In this paper we develop a two-region NOEM model suitable for the evaluation of alternative fiscal policies when Ricardian equivalence is not expected to hold. There are three reasons why Ricardian equivalence does not hold in the model. First, the model features an overlapping-generations structure where current generations are disconnected from future generations. Second, both labor and corporate income taxes are distortionary because labor effort and capital formation respond to relative price movements that result directly from tax wedges. Third, it is also assumed that a certain proportion of wage income accrues to rule-of-thumb consumers who vary their consumption one-for-one with their after-tax labor income.

Relative to previous studies that have focused on the crowding-out effects of fiscal policy in economies with only traded goods, the multi-sectoral and multi-regional dimensions of the model provides a richer framework by allowing for additional channels through which fiscal policy can operate to induce changes in relative prices. Specifically, developing a fiscal model within the NOEM framework can bring insights beyond those from Real Business Cycle (RBC) or New Keynesian (NK) models, which face difficulties in adequately replicating the dynamic effects of fiscal policy–for example, see Blanchard and Perotti (2002). In order for an RBC model to capture the dynamic effects of government spending on the real economy, Fatas and Mihov (2001) argue that the model must be extended in order to replicate plausible dynamics by including features such as liquidity constraints, finite horizons, or some sort of myopic behavior. Similar arguments are made by Gali, López-Salido, and Vallés (2003) in their critique of NK models, which argue that inclusion of both nominal rigidities (price stickiness) and non-Ricardian (rule-of-thumb) consumers may be required for NK models to match the reduced-form empirical evidence on the effects of government spending shocks on consumption. This paper incorporates some of these suggestions by relying on a finite-horizon setup with distortionary taxes and rule-of-thumb consumers.

Bringing an overlapping generations setting into a NOEM model has been undertaken by Ghironi (2003a and 2003b) and by Ganelli (2003b).4 The former does not consider the effects of government debt, but shows that an overlapping generations structure following Blanchard (1985) and Weil (1989) ensures the existence of a well-defined steady state for net foreign asset holdings (see also Buiter, 1981). Ghironi, Iscan, and Rebucci (2005) describe how differences in agents’ discount factors across countries gives rise to nonzero net foreign asset positions in the long run.

Our model bears the closest resemblance to Ganelli (2003b), which is the first attempt to analyze alternative fiscal policies in a NOEM model with finite lives. This paper extends Ganelli (2003b) in various directions: (i) the utility function is less restrictive permitting more realistic and smaller values of the intertemporal elasticity of substitution; (ii) the production structure is extended to include endogenous capital formation, which provides an additional channel through which government debt can crowd out economic activity and allows for the consideration of corporate income taxation; (iii) the model features both traded and nontraded goods which allows us to consider the implications of home bias in either consumption or government spending; (iv) the labor supply decision is endogenous and consequently labor income taxes will be distortionary; and (v) the current setup features rule-of-thumb consumers, which provides a third channel through which government debt affects private activity.

The intuition of the resulting model is as follows. In general, a debt-financed reduction in taxes results in an increase in private consumption as agents perceive themselves to be wealthier. The extent to which they perceive this follows from the fact that they are disconnected from future generations, who help finance the interest burden associated with higher levels of government debt. The degree to which they increase consumption depends on their effective planning horizons, which are assumed to be zero for liquidity-constrained consumers and some finite number for other consumers. It also depends on the extent to which taxes are distortionary, which in turn depends on the elasticity of labor supply (for a reduction in labor income taxes) and the elasticity of substitution between capital and labor (in the case where corporate income taxes are being cut).

Twin deficits (government and the current account) emerge as a result of this change in fiscal policy, which implies that the real exchange rate needs to depreciate in the long run to generate the higher trade flows that are necessary to finance the higher stock of net foreign liabilities. Depending on the sensitivity of consumers to changes in the real interest rate (i.e., the intertemporal elasticity of substitution) as well as the size of the home economy in terms of the world economy, the real interest rate adjusts correspondingly in the long run, which affects capital accumulation and output. The exchange rate and interest rate movements, together with trade linkages, are the main channels through which spill-over effects to the rest of the world occur.

Thus, the time profile of taxes and deficits will have effects on labor effort, capital accumulation, and the aggregate savings rate of the economies at home and abroad. This will become clear in the base-case calibration of the model, for which we illustrate the model’s predictions by considering the macroeconomic implications of a debt-financed reduction in labor income taxes and then compare this to a reduction in corporate income taxes.5 In addition, we analyze the sensitivity of the base-case results to the key structural parameters of the model, which include: the planning horizon of agents; the share of rule-of-thumb consumers; the elasticity of labor supply; the elasticity of substitution between capital and labor; the intertemporal elasticity of substitution; and the size of the home economy in terms of world GDP.

The remainder of the paper has five sections. Section II presents the theoretical structure of the model. Section III discusses the base-case calibration of the model and then presents results for a fiscal policy shock where labor taxes are cut for ten years and are financed by issuing government debt. We discuss the effects on the home economy, the spillover effects on the foreign economy, as well as the implications for the nontradables and tradables sectors. As we will assume that wages and prices are perfectly flexible, the main emphasis throughout the paper will be on assessing the medium- and long-term effects of the tax cut rather than on whether the short-run multipliers match those obtained from empirical reduced-form evidence. In Section IV we discuss the sensitivity of the results to variations in the key structural parameters. Section V provides some concluding remarks and outlines possible extensions.

II. The Model

The world consists of two countries, home and foreign. Countries are populated with overlapping generations of agents with finite planning horizons as in Blanchard (1985) and Weil (1989).6 In each period, n individuals are born in the home economy and 1 − n individuals are born in the foreign economy. The assumption of finite lives by itself does not imply any deviations from Ricardian equivalence. However, in combination with the assumption that newly born agents own no financial assets or cash balances, government debt will be perceived as net wealth. Each agent is also assumed to have a planning horizon of 1/(1 − q), where q represents a constant probability of survival. Under the assumption that consumers face identical probabilities of survival that are identical across countries, the relative size of the home economy versus the foreign economy will be equal to n1−n.

There is a unit measure of monopolistic firms in the world producing intermediate goods which are traded internationally, with n of those located in the home economy and 1 − n located abroad. Firms survive forever and each firm specializes in the production of a single differentiated variety. As is customary in these models, the intermediate tradable goods are combined into a final traded good. A similar structure of production exists in the nontraded goods sector.

Asset markets are incomplete. The only assets traded internationally are nominal non-contingent bonds issued by each region. Both bonds are assumed to be denominated in the home currency. There is complete home bias in equity holdings: all shares of domestic (foreign) firms are owned by home (foreign) residents. The same assumption is made for government debt.

A. Households

A representative agent born in period a derives utility from consumption, leisure, and real money balances. Agents are endowed with one unit of time, part of which they spend working (La,s) with the remainder devoted to leisure. A representative agent of age a at time t has preferences that are assumed to be non-separable in consumption and leisure. Lifetime expected utility of home agent a (denoted as Ua,t) is assumed to be:

Ua,t=Εt∑s=t∞(qβ)s−t[(Ca,sη(1−La,s)1−η)1−ρ1−ρ+χ1−ρ(Ma,sPs)1−ρ](1)

where q is the probability of survival, β is the discount rate, ρ > 0 is the inverse of the intertemporal elasticity of substitution, 0 < η < 1 and χ > 0.7

Following Blanchard (1985) we assume the existence of insurance companies, which charge a premium of (1−q)q to those agents who survive each period and in the event of death are assumed to take possession of the agent’s wealth.8 The consumer’s budget constraint in nominal terms is,

PtCa,t+Ma,t+Fa,t+1+StFa,t+1*+Ba,t+1+∫0nVtixa.t+1idi(2)=1q  [Ma.t−1+(1+it)(Fa,t+Ba,t)+(1+it*)StFa,t*]+1q[∫0nDivtixa,tidi+∫0nVtixa,tidi]+Wt(1−τL,t)La.t+Φt

where Aa,t=Fa,t+St−1Fa,t* are net foreign asset holdings; Ba,t is government debt; Vti represents the (ex dividend) value of a claim to all future profits of firm i whereas xa,ti is the share of firm i owned by the representative home agent born in period a in the beginning of period t. Divti is the after-tax amount of dividends paid by firm i in period t; τL,t is the tax rate on labor income and Φt is the revenue from adjustment costs rebated uniformly to all home households in a lump-sum fashion. As taxes are levied on labor income and labor supply is endogenous, changes in tax rates will have distortionary effects on consumption and leisure choices. Also, the assumption of finite lives combined with the assumption that newly born agents arrive without any assets (i.e., no bequests), xt,ti=Mt,t−1=Bt,t=At,t=0, implies that part of government debt will be counted as net wealth. Consequently, government deficits will affect the aggregate savings rate of the economy, resulting in increases in real interest rates when economies are either closed or large and “twin” fiscal and current account deficits when economies engage in international trade.

Together, the agent a’s lifetime expected utility, in tandem with her nominal budget constraint is a concise statement of the consumer’s optimization problem, which results in the following first-order conditions. The optimal supply of labor is determined by the consumption-leisure trade-off and satisfies,

La,t=1−1−ηηPtWt(1−τL,T)Ca,t(3)

where η is a parameter that affects the extent to which labor supply is elastic (lower values of η imply a higher elasticity and when η approaches one labor supply becomes perfectly inelastic). Money demand takes the form,

Ma,tPt=(χη)1ρ(1−ηηPtWt(1−τL,t))(1−ρ)(1−η)(1+it+1it+1)1ρCa,t(4)

whereas the money supply is assumed to be fixed as the central bank is assumed to follow money targeting. The Euler equation that determines consumption or savings is the following.

Ca,t+1=(β (1+it+1)PtPt+1)1ρ  (Wt+1(1−τL.t+1)/Pt+1Wt(1−τL,t)/Pt)(1−1ρ)(1−η)Ca,t(5)

Together with the optimality condition for the holdings of foreign bond holdings, this condition produces the standard uncovered interest parity condition.

1+it+1=(1+it+1*)St+1St(6)

From the life-time budget constraint, eq. (2), and using the above first-order condition for the optimal consumption rule of optimizing agents, the decision rule of optimizing agents, denoted by Ca,topt, can be written as the sum of human wealth and financial holdings,

PtCa,topt.=(7)Dt−1{Ha,t+1q [Ma,t−1+(1+it−1)(Aa,t−1+Ba,t−1+nVa,t−1ixa,t−1i)]}

where Ha,t=∑s=t∞Rt,sqs−t(1−Ψ)[WsLs(1−τL,s)+Φs] denotes (nominal) human wealth of agent a at time t and Ψ is the share of rule-of-thumb consumers and Dt−1 is the marginal propensity to consume out of total wealth. In the general case the inverse of the marginal propensity of consume evolves according to,

Dt=1+1−ηη+(χη)1ρ(1−ηηPtWt(1−τL,t))(1−ρ)(1−η) (it+11+it+1)1−1ρ+(8)q1+it+1pt+1pt(β (1+it+1)ptpt+1)1ρ(wt+1(1−τL,t+1)Pt+1Wt(1−τL,t)Pt)(1−1ρ)(1−η)Dt+1

while in the logarithmic case (ρ =1) this expression reduces to Dt=1+1−ηη+(χη)+qβDt+1, which leads to a constant marginal propensity to consume of 1−qβ1+1−ηη+χη. In what follows we will assume that profits are uniformly distributed among optimizing agents. In this case, the Φt variable includes period profits (dividends) from every domestic firm, distributed equally across agents, besides rebates from adjustment costs. Since there are no shares traded in this case, xa,ti=0, the consumption function can be written as,

PtCa,topt=Dt−1{Ha,t+1q[Ma,t−1+(1+it−1)(Aa,t−1+Ba,t−1)]}(9)

By fixing the total number of shares outstanding issued by firm i at unity and defining the per capita equity value as Vt=nVa,tin1−q=(1−q)Va,ti one can easily aggregate the consumption function for optimizing agents. Also, as a result of the competitive labor market assumption and uniform distribution of transfers, human wealth will be identical across optimizing agents and other per capita variables are easily aggregated as they are linear functions of generation-specific variables.

Total aggregate consumption consists of two components: consumption of optimizing agents and consumption by rule-of-thumb consumers. Thus, aggregate consumption is given by:

Ct=Ctopt+Ctrot(10)

with aggregate consumption of rule-of-thumb consumers given by,

PtCtrot=Ψ(WtLt (1−τL,t)+Φt)(11)

B. Firms

There are two types of firms. A continuum of monopolistic firms indexed by i are assumed to produce a single differentiated good, which is either traded or nontraded, and a set of representative firms that combine the domestically traded good and an imported good with the nontraded good to produce three distinct final goods–a private consumption good Ct, a public consumption good Gt, or a private gross investment good (It + CACt).

Consider final goods production in the home economy. The private consumption good is produced using a CES technology:

Ct=(γ1∈CtT∈−1∈+(1−γ)1∈CtN∈−1∈)∈∈−1(12)

where ε > 0 is the elasticity of substitution between traded and nontraded consumption goods, and 0 ≤ γ ≤ 1 governs the preference for traded over nontraded goods.

The utility-based price index corresponding to this basket has a similar form:

Pt=(γ PtT1−∈+(1−γ)PtN1−∈)11−∈(13)

Pt serves as the consumer price deflator in this model, and is used to define inflation in the model:

Pt/Pt−1=1+πt(14)

Using θN to denote the elasticity of substitution over different varieties of a composite nontraded good we use the following CES aggregator and corresponding price index:

CtN=((1n)1θN∫0nCtN(z)θN−1θNdz)θN−1θN(15)
PtN=(1n∫0nptN(z)1−θNdz)11−θN(16)

As for the traded consumption good CtT, it can be further decomposed into domestically-produced and imported components:

CtT=(α1ϖCtHϖ−1ϖ+(1−α)1ϖCtFϖ−1ϖ)ϖϖ−1(17)

where ϖ>0 is the elasticity of substitution between home and foreign goods and 0 ≤ α ≤ 1 is the home bias parameter.

The equivalent price index for tradable goods in the home economy is:

PtT(H)=(α(ptT,H)1−ω+(1−α)(st*ptT,F)1−ω)11−ϖ(18)

which is a combination of the price of domestically produced tradables, ptT,H, and the price of tradable goods produced in the rest of the world, ptT,F, where st is the nominal exchange rate (defined as the price of home currency in terms of foreign currency). Foreign indices are expressed in foreign units and are analogous to the home indices. The law of one price holds for intermediate traded inputs, but the purchasing power parity (PPP) condition can be violated because of the presence of nontraded goods and home bias in consumption.

As with the nontraded good CtN, the domestically produced traded good CtH has the following demand function and the corresponding price index:

CtH=((1n)1θH∫0nctH(z)θH−1θHdz)θH−1θH(19)
PtH=(1n ∫0nptH(z)1−θdz)11−θH(20)

where θH is the elasticity of substitution over different varieties of the composite domestically produced traded good.

The imported consumption good CtF is produced in the foreign economy, and has analogous demand and price functions to CtH.

The final investment good ItT is produced in the same manner, while the government good Gt is composed uniquely of nontraded goods (home bias is unity in the government sector) so that Gt=GtN and PtG=PtN.

At the level of the intermediate good level, firms produce either traded or nontraded goods. For notational simplicity, the T and N superscripts will be dropped. The remainder of the equations in this section apply equally to all firms producing either traded or nontraded goods.

A firm is assumed to maximize the discounted value of current and all future dividends:

max{Ps(i),Li,s,Ii,s,Ki,s} ∑s=t∞Rt,sPs(Divi,s−τπ,sPsλs(MPKs−δ)Ks)(21)

subject to the production of Ys with a CES production technology,

Yi,s=(μ1ξKi,sξ−1ξ+(1−μT)1ξ (ZsLi,s)ξ−1ξ )ξξ−1(22)

and the law of motion of capital,

Ki,s+1=(1−δ)Ki,s+Ii,s(23)

with Ki denoting the capital stock of firm i, Li the amount of labor the firm employs and Zt is a stochastic process governing productivity. ξ is the elasticity of substitution between the factors of production, while μ is the bias towards the use of capital in the production of. the traded good. Ii represents gross investment and δ represents the depreciation rate on capital. We assume that adjustment of the capital stock is subject to quadratic adjustment costs9:

C ACi,t=ψ2(Ii,t)2Ki,t(24)

The after-tax dividends of a representative firm (which are economic profits) are defined as

Divi,t=(1−τπ,s)[(Pt(i))1−θ(PtH)θYt−WtLi,t−Pt(Ii,t+ψ2(Ii,t)2Ki,t)](25)

where τπ,t denotes the corporate income tax rate.

We can define the shadow price of capital, with some transformation as Tobin’s Q, Qi,t, while the shadow price associated with the production constraint is marginal cost MCi,t. Furthermore, the equilibrium price that arises from profit maximization under monopolistic competition satisfies the familiar pricing rule,

Pi,t=θθ−1MCi,t(26)

where price is a constant markup over (nominal) marginal cost.10

C. Government

We assume that all government consumption Gt is met by the supply of nontraded goods so that PtG=PtN.11 In order to finance its consumption, the government collects taxes (Tt) by imposing a tax rate on labor income (TL,t = τL,tWtLt) and on corporate incomes in the traded and nontraded goods sectors respectively (Tπ.t=τπ,t(ptTYtT−WtLtT−ItT)+τπ,t(ptNYtN−WtLtN−ItN), where YtT and YtN denote total output in the traded and nontraded sectors respectively. Other sources of financing include seigniorage and the issuance of debt. In nominal terms, the government budget constraint takes the form (for both the home and foreign countries):

PtGGt+(1+it)Bt=Tt+(Mt−Mt−1)+Bt+1(27)

Fiscal closure is achieved by specifying a target path for the desired level of government debt as a ratio of GDP (bt*). In the standard version of the model the aggregate tax rate adjusts until the government debt ratio reaches its long-run target level. The tax rate is determined by the following 2 equations,

τt=ϰ1,t(τt+DEBTGAPS)+(1−ϰ1,t) τ¯t(28)
DEBTGAPS=(BtGDPt−υ1bt*−(1−υ1)Bt−1GDPt−1)+υ2(ΔBtGDPt−Δbt*)(29)

where Bt is government debt, GDPt is nominal income (gross national product), ϰ1,t is an exogenous variable that allows temporary fixes of the tax rate at some pre-specified rate τ¯t, and the two parameters (v1,v2) will determine the speed at which the actual government debt to GDP ratio (BtGDPt) is adjusted to its desired path (bt*).12 Note, that when ϰ1,t = 1 the tax rate drops out of equation (28) and the rule becomes a simple error-correction model that gradually closes the gap between the actual and target government debt to GDP ratio.13

BtGDPt=υ1bt*+(1−υ1)Bt−1GDPt−1−υ2(ΔBtGDPt−Δbt*)(30)

When (v1,v2) = (1, 0) the rule would imply that tax rates would be adjusted completely to achieve the desired debt ratio in each period. The problem with such a rule is that it could result in large swings in tax rates when there are significant deviations between actual and the desired debt levels. This problem can be resolved in most cases by imposing a smaller value for v1, that allows for partial adjustment where only part of the debt gap is eliminated over time. The last term in equations (29) and (30) is a flow condition and is included to prevent excessive cycling in the tax rate and the real economy. Experience has shown that this simple rule with (v1,v2)=(0.1, 1.0) seems to work well in practice for conducting experiments that result in permanent shifts in the government debt ratio, without causing excessive cycling in tax rates and the real economy–the only purpose for which the rule has been designed in the experiments considered here.

To illustrate how the tax rule can be used in practice, suppose we are interested in the effects of a cut in taxes for 10 years. Then we would set ϰ1,t = 0 for t = 1, …, 10 and τ¯t will reflect the shock (for example, a one-percentage point of GDP tax cut). After ten years, ϰ1,t =1 and the tax tax rate, τt, is determined by equation (28). There is no particular reason why all of the adjustment has to be imposed on labor taxes and it is straight forward to consider cases where tax rate adjustments are assumed to fall on capital income or government spending, or some combination of capital and labor taxes and spending.

D. Characteristics of “the Rest of the World”

The foreign economy is identical to the home economy, apart from the fact that the internationally traded assets are denominated in the home currency. The current account balance for the home economy is the sum of interest receipts on the stock of net foreign assets plus the trade balance,

CBALt=it−1At−1+TBALt(31)

where TBALt is defined to be equal to nominal exports minus nominal imports. The change in net foreign assets will simply be equal to the current account balance.

At−At−1=CBALt(32)

For the foreign economy the mirror image of this expression will be the following.

At*=−n1−nAtSt(33)

The nominal exchange rate, with RERt denoting the real exchange rate, is given by the following expression.

St=RERtPtPt*(34)

From the uncovered interest parity (UIP) condition, the real exchange rate, with r denoting the real interest rate, will be the following.

RERt+1=RERt1+r1+r*(35)

The equivalent nominal form of the UIP condition is:

St+1=St1+i1+i*(36)

In the steady state, the real exchange rate will be constant, so we know that r = r*. And as long as both regions have the same steady-state inflation rate, it follows that i = i*.

By definition, the home economy can hold its net foreign assets At in either currency as Ft or Ft*. The pure UIP condition insures the same nominal return. For a given holding as either F¯t or n1−nStF¯t*, the real returns are exactly equivalent. By applying the nominal UIP condition to (1 + it) F¯t and (1+it*)n1−nStF¯t* we can see the return is always i*. This means there is no need to differentiate between Ft or Ft*. At and At* will share the same properties for its returns; (1+it)StAt*=−(1+it*)n1−nAt so that net foreign assets will be in zero net supply worldwide.

Finally, the terms of trade is defined as:

TOTt=PtT,HPtT,F/St(37)

where PtT,H is the price of tradables in the home economy and PtT,F is the price of tradables in the foreign economy.

III. The Effects of Tax Cuts in a Small and Large Open Economy

In this section, we discuss the baseline calibration of the model and the implications of tax cuts when the home economy accounts for either a small (1 percent) or a large share of the world economy (60 percent). In the latter case the model is calibrated to equal the share of the OECD membership in world GDP during the 1980s, which was about 60 percent. This allows us to relate the implications of the model to the empirical evidence on the effects of the build-up in government debt in the OECD economies in the 1980s on the world real interest rate.14 The first experiment we consider is a debt-financed cut in labor income taxes, which increases the primary deficit by one percent of GDP for 10 years. Starting in the 11th year, the tax rate is allowed to rise to gradually stabilize the government debt-to-GDP ratio at its new higher steady-state level. An increase in taxes will also be necessary to finance the higher interest rate burden that results from higher levels of government debt.

A. Initial Steady State

The parameter values and steady-state values for the baseline calibration of the model are reported in Tables 1 to 3. For simplicity we assume identical parameters in both countries and as a consequence all relative prices will be equal to one and neither region will be a net debtor nor creditor in the initial steady state. The discount rates for both countries are computed residually to generate a steady-state real interest rate of 3 percent, a value that is close to the average value of real long-term interest rates in the U.S. and other OECD countries over the last 25 years. In general, differences in discount rates across countries determine if a country is a net debtor or creditor in the steady state. In addition to being non-Ricardian, this was another important reason why several modelers adopted the Blanchard (1985) OLG framework and incorporated it into both small open-economy models as well as multi-region models.15 Throughout the experiments, wages and prices are assumed to be fully flexible.16 We assume complete home bias in government spending, but no home bias in private spending. This is clearly an exaggeration, but is an innocuous assumption for examining the effects of tax cuts.

Table1:

Baseline Parameters

article image
Table 2:

Baseline Parameters (Varied Later For Sensitivity Analysis)

article image
Table 3:

Initial Steady-State Ratios

article image

Table 2 shows the key structural parameters of the model whose values will be varied to perform some sensitivity analysis. One of the key structural parameters that will determine the extent of crowding out in the model will be the effective planning horizon (1/q) of consumers. In the baseline calibration of the model, we set this value equal to 10 years, which translates into a value of q equal to 0.90. A value of this magnitude for q is obviously much lower than the probability of survival for most of the population, but it is a simple way of introducing a form of myopia into the model that many others have emphasized is necessary to generate plausible dynamics.17 We assume that labor supply is moderately elastic (η = 0.96 whereas if η was equal to unity, labor supply would be completely inelastic) allowing for a second channel through which taxes can affect the private sector behavior. The share of liquidity-constrained consumers is assumed to be equal to 25 percent of the population, a value that is consistent with estimates from the empirical literature. This combined with a planning horizon of 10 years generates plausible dynamics and correlations between consumption and disposable income.18

The intertemporal elasticity of substitution (1/ρ) is set at 0.20 (ρ = 5). This is around the mid-range of econometric estimates derived from models without habit formation. We also consider the implications of a value for the intertemporal elasticity of substitution of 1/3 (ρ = 3), which is consistent with the upper end of the range of empirical models without habit persistence.19 We set the elasticity of substitution between home and foreign goods (1/ω) equal to 0.40 (ω = 2.5). This is in line with estimates used in NOEM models, but is significantly higher than the mid-point of the range of econometric estimates, which falls closer to one.20 The elasticity of substitution between capital and labor (χ) is set equal to 0.8 and we contrast this to the Cobb-Douglas case when discussing the results from the sensitivity analysis.

Table 3 shows the initial steady-state ratios to nominal GDP for a number of key variables. Again apart from size, the model calibration is symmetric. As a result, the real exchange rate and terms of trade are equal to unity and there is no net international borrowing and lending; the net foreign asset position, trade balance, and current account are all equal to zero. Liquidity-constrained consumers represent one-fourth of the population, but because they do not have any wealth they only account for about one-seventh of total private consumption.

Table 4 reports the fiscal characteristics of the initial steady state. The initial level of government debt is assumed to be zero. Consequently, in the initial steady state there is no interest burden on government debt so aggregate taxes have to be collected to finance only the level of government expenditures. The labor income tax rate is assumed to be higher than the corporate income tax rate. The corporate income tax is applied to a base consisting of capital income as well as pure economic profits that arise because of the assumption of monopolistic competition.21

Table 4:

Initial Steady State of Fiscal Variables

article image

B. Increase in Government Debt from Lower Labor Income Taxes in a Small Economy

A cut of one percentage point of GDP in tax revenue requires a reduction in labor income taxes of about two percentage points–see Figure 1. As a result of the tax cut government debt starts accumulating and the government debt-to-GDP ratio reaches a value that is about 12 percentage points higher than baseline after 10 years. The NFA-to-GDP ratio falls by a similar magnitude, but converges at a slower speed to its new steady-state value.22 Over the first 10 years of the simulation the current account balance declines by around half the amount of the fiscal balance.

Figure 1.
Figure 1.

Effects on the Home Economy: small-open economy case Home: Ten-year 1.0 Percent of GDP Cut in Income Taxes

Deviation From Control

(In percentage points; unless otherwise stated)

Citation: IMF Working Papers 2006, 045; 10.5089/9781451863055.001.A001

In the short run, the real exchange rate appreciates in response to persistently higher real interest rate differentials. This appreciation and increase in real interest rate differentials is consistent with constraining domestic demand forces in response to lower taxes, but is also necessary to generate the current account and trade deficits that are consistent with the preferences of consumers. In this case the appreciation in the currency of the home economy is only a proximate cause of the trade deficit, as the real fundamental cause of the trade deficit is a reduction in savings by the public sector. To service the higher interest payments on the accumulated stock of net foreign liabilities, the home economy will need to generate trade balance surpluses in the new steady state, which is achieved over the medium term and long run by a depreciation in the real exchange rate.

Real GDP, consumption, and labor effort all rise over the first 10 years of the simulation in response to lower labor income taxes, but higher real interest rates crowd out investment.23 Consumption of rule-of-thumb consumers rises by almost 3 percent as their consumption responds fully to lower labor income taxes and the rise in real income that it causes. By contrast, consumption of optimizing forward-looking agents is more muted as these consumers partially account for the future tax burden that will be associated with the tax cut.

Over time, higher taxes, lower profits, and the depreciation of the real exchange rate reduce real wealth of the home economy. Together with the crowding-out effects on investment because of higher interest rates we see that real GDP, the capital stock, and consumption all decline permanently. Despite a large reduction in real wages, labor effort falls only modestly in the long run, reflecting a relatively low elasticity of labor supply. Given the small size of the home economy, the spill-over effects of higher government debt on the rest of the world are negligible and are not reported.

C. Increase in Government Debt from Lower Corporate Income Taxes in a Small Economy

The qualitative results for a cut in corporate income taxes are very similar to the results of a cut in labor income taxes (see Figure 2) and the quantitative spill-over effects to the rest of the world remain small. However, there are two interesting differences. First, real GDP and consumption increase slightly less in the short run. Consumption increases less because liquidity-constrained consumers do not benefit directly from the tax cut as they are assumed to not own capital or any other asset. In this case their rise in consumption is solely a result of higher before-tax labor income, which increases as a result of the real wage.

Figure 2.
Figure 2.

Effects on the Home Economy: small-open economy case Home: Ten-year 1.0 Percent of GDP Cut in Corporate Taxes

Deviation From Control

(In percentage points; unless otherwise stated)

Citation: IMF Working Papers 2006, 045; 10.5089/9781451863055.001.A001

Second, the cut in corporate taxes causes an investment boom in the short run, which is short-lived because of rising real interest rates. Real GDP declines by more in the long run than in the previous exercise because the rise in corporate income taxes necessary to finance the higher debt servicing costs is more distortionary than labor taxes. This is a reflection of the fact that the labor supply elasticity is small, while taxes on corporate income can have significantly larger effects on capital accumulation.

D. Increase in Government Debt from Lower Labor Income Taxes in a Large Economy

An accumulation of government debt in a single large economy, or a large group of smaller economies, caused by lower labor income taxes has a significant permanent effect on the world real interest rate and results in large crowding-out effects (Figure 3). Indeed, for each 12.5 percentage point increase in the government debt ratio, the real interest rate increase by about 100 basis points, suggesting that the 20 percentage point increase in government debt in the OECD countries during the 1980s would have accounted for about a 160 basis point increase in real interest rates in this period. This estimate is similar to reduced-form empirical evidence concerning the increase in world interest rates during this period in countries with integrated capital markets–see Ford and Laxton (1999). As a result of the rise in the world real interest rate, investment declines substantially and results in a smaller short-run output multiplier relative to the earlier case when the home economy was small. The long-run crowding out effects of government debt are substantial both in the home and in the foreign economy (Figure 4). The initial effect on output in the rest of the world is small as the increased demand for their goods is offset by rising interest rates and the negative wealth effect associated with a depreciation of the real exchange rate. While not reported, a cut in corporate income taxes in a large open economy results in a slightly larger increase in the real interest rate and the spill-over effects to the rest of the world are correspondingly greater as well.

Figure 3.
Figure 3.

Effects on the Home Economy: large-open economy case Home: Ten-year 1.0 Percent of GDP Cut in Income Taxes

Deviation From Control

(In percentage points; unless otherwise stated)

Citation: IMF Working Papers 2006, 045; 10.5089/9781451863055.001.A001

Figure 4.
Figure 4.

Spill Over Effects to the Foreign Economy: large-open economy case Home: Ten-year 1.0 Percent of GDP Cut in Income Taxes

Deviation From Control

(In percentage points; unless otherwise stated)

Citation: IMF Working Papers 2006, 045; 10.5089/9781451863055.001.A001

IV. Sensitivity Analysis

In this section we present some sensitivity analysis of the results presented earlier by changing the five key structural parameters of the model. This includes: (1) making the savings rate more sensitive to future tax increases (by lengthening the planning horizon of agents); (2) reducing the supply-side effects of tax cuts (by making labor supply inelastic); (3) reducing the effects of deficits on interest rates (by increasing the intertemporal elasticity of substitution); (4) increasing the effective planning horizon of agents (by setting the share of rule-of-thumb consumers equal to zero); and (5) increasing the substitutability between factors of production (by setting the elasticity of substitution between capital and labor equal to unity, which is the Cobb-Douglas case). The results are reported in Tables 5 to 16.

Table 5:

Sensitivity Analysis: effects on the Home Economy (cut in labor taxes; small-open economy)

article image

Longer planning horizon;

Inelastic labor supply;

Higher intertemporal elasticity of substitution;

Share of rule-of-thumb consumers;

Higher elasticity of subst. between capital and labor.

Table 6:

Sensitivity Analysis: effects on the Home Economy continued (cut in labor taxes; small-open economy)

article image

Longer planning horizon;

Inelastic labor supply;

Higher intertemporal elasticity of substitution;

Lower share of rule-of-thumb consumers;

Higher elasticity of subst. between capital and labor.

Table 7:

Sensitivity Analysis: effects on the Foreign Economy (cut in labor taxes; small-open economy)

article image

Longer planning horizon;

Inelastic labor supply;

Higher intertemporal elasticity of substitution;

Lower share of rule-of-thumb consumers;

Higher elasticity of subst. between capital and labor.

Table 8:

Sensitivity Analysis: effects on the Home Economy (cut in corporate taxes; small-open economy)

article image

Longer planning horizon;

Inelastic labor supply;

Higher intertemporal elasticity of substitution;

Lower share of rule-of-thumb consumers;

Higher elasticity of subst. between capital and labor.

Table 9:

Sensitivity Analysis: effects on the Home Economy continued (cut in corporate taxes; small-open economy)

article image

Longer planning horizon;

Inelastic labor supply;

Higher intertemporal elasticity of substitution;

Lower share of rule-of-thumb consumers;

Higher elasticity of subst. between capital and labor.

Table 10:

Sensitivity Analysis: effects on the Foreign Economy (cut in corporate taxes; small-open economy)

article image

Longer planning horizon;

Inelastic labor supply;

Higher intertemporal elasticity of substitution;

Lower share of rule-of-thumb consumers;

Higher elasticity of subst. between capital and labor.

Table 11:

Sensitivity Analysis: effects on the Home Economy (cut in labor taxes; large-open economy)

article image

Longer planning horizon;

Inelastic labor supply;

Higher intertemporal elasticity of substitution;

Lower share of rule-of-thumb consumers;

Higher elasticity of subst. between capital and labor.

Table 12:

Sensitivity Analysis: effects on the Home Economy continued (cut in labor taxes; large-open economy)

article image

Longer planning horizon;

Inelastic labor supply;

Higher intertemporal elasticity of substitution;

Lower share of rule-of-thumb consumers;

Higher elasticity of subst. between capital and labor.

Table 13:

Sensitivity Analysis: effects on the Foreign Economy (cut in labor taxes; large-open economy)

article image

Longer planning horizon;

Inelastic labor supply;

Higher intertemporal elasticity of substitution;

Lower share of rule-of-thumb consumers;

Higher elasticity of subst. between capital and labor.

Table 14:

Sensitivity Analysis: effects on the Home Economy (cut in corporate taxes; large-open economy)

article image

Longer planning horizon;

Inelastic labor supply;

Higher intertemporal elasticity of substitution;

Lower share of rule-of-thumb consumers;

Higher elasticity of subst. between capital and labor.