How does the debt crisis affect investment and growth? : a neoclassical growth model applied to Mexico

Policy, Research, and Extemal Affairs 1 WORKING PAPERS Debt and International Finance International Economics Department The World Bank April 1990 WPS 378 How Does the Debt Crisis Affect Investment and Growth? A Neoclassical Growth Model Applied to Mexico Patricio Arrau A large-scale neoclassical growth model can provide interesting quantitative policy implications. Growth-oriented reforms can increase the present value of repayment, and the relative impact on growth from alternative government financing can be evalu- ated. The Policy, Research, and External Affairs Cosmplex distributes PRE Working Papers to disseminate the findings of work in progress and to encourage the exchange of ideas among Bank staff and all others interested in development issues. These papers carry the names of the authors, reflect only their views, and should be used and cited accorduingly, The findings, interpretations, and conclusions are the authors' own They should not be attnbuted to the World Bank, its Board of Directors, irs management, or any of its member countries.  Policy, Research, and Extemal Affairs Dotand International Finance l This paper - a product of the Debt and Intemational Finnce Division, Intemational Economics Departnment - is part if a larger effort in PRE to examine the interrelationship between extemal debt and economic growth. A subset of that work deals with the theoretical and empirical underpinning of the debt overhang hypothesis. That hypothesis argues that a large extemal debt discourages investment and adjustment and, ultimately, harms creditors. Copies of the paper are available free from the World Bank, 1818 H Street NW, Washington DC 20433. Please contact Sheilah King-Watson, room S8-025, extension 31047 (46 pages with figures and tables). Most economists and specialists in intemational * Growth-oriented reforms (in the model, tax finance believe that the debt crisis hurts macro- reforms in favor of capital formation) can economic performance, particularly discourag- increase the present value of repayment by ing investment and growth-oriented structural several percentage points of GDP. If these reforms. reforms are negotiated in the context of a debt reduction agreement, the secondary market dis- Identifying the link between the foreign debt count for the remaining debt can be substantially overhang and macroeconomic performance is reduced. essential for assessing what creditors and debtors have to gain from altemative debt Arrau used a neoclassical (life-cycle) model solutions. Having set up a neoclassical growth instead of the simpler Ricardian (infinite- model to study the impact of the debt crisis on horizon) model of growth because Ricardian investment and growth. Arrau concludes: models have recently failed to be supported by the data when their implications were tested The best case for growth is given by infla- against the life-cycle model. The Ricardian tion financing; the worst case, by national debt model also imposes a theoretical limit for issucs financing. In between are different combina- at stake here. The neoclassical model is more tions of income taxation and capital ince-o" flexible because long-run equilibria depend on taxation. (This result is interesting because in- the cumulative effects of the transition caused by flation has been a primary source of financing policy choices. Its main limit is its assumption early in tl'e crisis - but it is not robust because of exogenously supplied labor. the model does not include any inflation disin- centive to invest.) The PRE Working Paper Series disseminates the findings of work under way in the Bank's Policy. Research, and External Affairs Complex. An objective of the series is to get these findings out quickly, even if presentations are less than fully polished. The findings, interpretations, and conclusions in these papers do not necessarily represent official Bank policy. Produced at the PRE Dissemination Center  Contents 1 Introduction ............. ... 1 2 Theoretical and Empirical Background of the Neoclassical Approach 3 2.1 The Limits of the Ricardian View for Policy. 3 2.2 The Keynesian and Neoclassical Views. 5 2.3 Toward a Neoclassical Framework for Policy Evaluation . . . 7 3 The Basic Framework ......... .. 9 3.1 The Individual Optimizadion . . . . . . . . . . . . . . . . . . 9 3.2 Firms .......... .. . .. .. .. . .. .. .. . .. . . 11 3.3 Aggregation and Government ...... . . . . . . . . . . . . 11 3.4 Earnings and Growth ....... . . . . . . . . . . . . . . . 13 4 Calibrating the Model for Mexico ...... .......... . . . . 14 4.1 Parameterization of the Model ...... . . . . . . . . . . . 15 4.2 Summary of the Calibration . . . . . . . . . . . . . . . . . . . 18 5 Debt Crisis, Adjustment and Debt Overhang . .19 5.1 Internal Adjustment .20 5.2 The Secondary Market Price .25 6 Conclusions ..30 *1 would like to thank Bela Balassa, SL.jn Claessens, Ishac Diwan, John Underwood and Sweder van Wijnbergen for very helpful comments.  1 1 Introduction Most economists and specialists in international finance believe that the debt crisis has an impact on the macroeconomic performance of countries, specially discour- aging investment and growth oriented structural reforms. Identifying the linkage between the foreign debt overhang and macroeconomic performance is extremely important to assess the potential gains for creditors as well as debtors in the event of alternative debt solutions. The link, however, is still elusive. Assuming that a country's capacity to pay its debt is bounded above as a fixed proportion of its GDP,1 we set up a neoclassical model of growth to study the impact of the debt crisis on investment and growth. Short-run underutilization of resources (Keynesian effects) are neglected, so that the model can tell us the evolution of potential output through time. If the maximum coupon that the country can pay grows at the rate of output growth, it is of the most importance to study the dynamics of that rate of growth. Why do we use a Neoclassical (life-cycle) model instead of the simpler Ricardian (infinite-horizon) model of growth?.2 Three reasons can be given. First, Ricardian models have been employed before to study the debt crisis, whereas the neoclassical 'An assumption both extremely convenient in our set up and extensively used in the debt over- hang literature. 2'n the context of the modern debate in macroeconomics, the well known Ramsey-Cass-Koopmnans framework, sometimes referred as a neoclassical model, should be renamed Ricardian. See section 2.  2 model has not.3 We do not know what the dynamics look like in this framework. Second, the Ricardian model has recently failed to be supported by the data when its implications have been tested against the life-cycle model. If agents take deci- sions based on finite horizons, policy evaluation exercises based on infinite horizons might be very misleading. Third, the infinite-horizon model imposes a theoretical limitation for the issues at stake here. The long-run level of income (per capita or per efficiency unit), is tied down by the Modified 'olden Rule equilibrium.' The long-run capacity to pay foreign debt is, therefore, very much decided in advance. The neoclassical mode, leads to long-run equilibi;a which depend on the cumulative effects of the transition caused by policy choices, and therefore, it is more flexible. The organization of the paper is as follows. In section 2 we discuss the theo- retical and empirical background of the neoclassical approach. Section 3 describes the model in detail. The model is calibrated to resemble some aspects of the Mex- ican economy in section 4. In section 5 we introduce the debt crisis and present simulations of the internal adjustment to the crisis and the impact of policy on the secondary market price for debt. A final section summarizes the results. 3See for instance Borenztein (1989) and Kaminsky and Pereira (1989). 4The long-run marginal productivity of capital is driven only by structural parameters and the marginal tax on capital formation.  3 2 Theoretical and Empirical Background of the Neoclassical Approach The Life-Cycle proposition advanced by Ando and Modigliani (1963) is a micro- economic proposition about consumptior. and savings. Households would be better off by forgoing consumption early in life to smooth the consumption path over the life-cycle. Savings arise as earnings are not equally distributed over the lifespan. Although there is a revived controversy whether pure "hump" savings (or savings for retirement) can explain aggregate wealth,5 the life-cycle benchmark, when in- troduced in a general equilibrium macroeconomic model, constitutes a powerful framework which has come to be known as the Neoclassical Approach. This frame- work, together with the Keynesian and the Ricardian frameworks, constitutes the core of modern macroeconomics.6 The three models, however, are not on the same plane when it comes to the question of policy recommendations. We first criti- cally review the Ricardian model and its empirical background and then discuss the alternative models. 2.1 The Limits of the Ricardian View for Policy The role of the Modigliani-Miller proposition in corporate finance is comparable to the role of the Ricardian Equivalence proposition in macroeconomics7. Theoreti- 5See Kotlikoff (1988) and Modigliani (1988) for this controversy. 'Bernheim (1989). Bernheim's classification is in the context of the debate on the impact of budget deficit on consumption and savings. 7Barro (1989).  4 cally pure in the context of their own assumptions, both propositions did reshape the debate in their respective fields. By carefully defining the implications of an extreme benchmark, the propositions opened the doors for new research on their shortcomings as empirically relevant guides for decision-making. Barro's (1974) Ricardian Equivalence proposition implies strong neutralities re- garding government policy. The relevant decision-making unit would be the infinite- lived dynasty, as parents and offsprings would be altruistically linked. An attempt by the government to transfer resources through time (say temporary tax cut fi- nanced by government bonds) would be neutral in the aggregate. Living members of the dynasty would offset government decisions in the name of future members, and national savings and consumption would be unaffected. Most empirical evidence contradicting the implications of this strong behavioral assumption is provided in Bernheim (1987). More recently, powerful tests from micro data have been devel- oped by Abel and Kotlikoff (1989) and Altonji, Hayashi and Kotlikoff (1989). The Abel-Kotlikoff test exploits the Ricardian implication that consumption from all cohorts (age groups) should move together. The test rejects that implication when it is performed in first differences. Altonji, Hayashi and Kotlikoff use a sample that allows them to stu' ; direct information from parents and offsprings in order to verify whether the members of the same "dynasty" do share the same budget constraint. The results are also largely in support of the view that the relevant  5 decision-making unit is the finite-lived household (neoclassical approach) and not the infinite-lived dynasty (Ricardian approach). For policy design and planning, the; -.fore, our effort should concentrate on the two alternative frameworks.8 Before leaving this part is extremely important to emphasize that we do not question the power of the infinite-horizon representative-consumer model (Ricar- dian) to provide important qualitative lessons for policy. We also think that the model is extremeiy convenient for partial equilibrium (Euler) estimations. In fact, most of the evidence on the structural parameters which is needed to calibrate a neoclassical model comes from estimations of Euler equations of the representative- consumer framework. What is questioned is the power of the Ricardian framework as a quantitative policy evaluation device.9 2.2 The Keynesian and Neoclassical Views Although Keynesian macroeconomics was founded without much reference to a- gents' optimization, introducing liquid.ty constraints into the agents' optimization problem yields saving and consumption functions strongly dependent on current income, a typical Keynesian assumption. Price rigidities are the second ingredient to Keynesian macroeconomics which yield the quantity adjustment and factor un- 8This view, although it could be considered the 'majority' view (Barro, 1989), is not consensual. See Barro (1989) for a defense of the empirical relevancy of the Rkardian model. 9The extent to which representative-consumer Euler estimations might lead to biased estimates is an open question. Consequently we should be cautious when calibrating a neoclassical model based on estimates coming from Ricardian estimations.  6 derutilization normally observed along the business cycle. Although some recent literature attempt to explain business-cycle fluctuations by using stochastic versions of the representative-consumer optimizing framework"0, the neoclassical approach is generally concerned with the long-run equilibrium around which the economy would be fluctuating.1" The implications for the short run are only limited to the transition impact from or e long-run equilibrium to another when the economy is unexpectedly perturbed by a policy shift or a once-and-for-all shock. Consequently, the model is often presented in certainty frameworks, as it intends to study the econ- omy's reaction to government control variables (policy parameters) or to significant shocks (e.g. external shocks). The neoclassical approach is, therefore, a relevant benchmark for policy evaluation. More importantly, some short-run implications of the model are consistent with some observed reactions of the economy to pol- icy. U'ntil the recent work by Auerbach and Kotlikoff (1987), it was not clear that a model with these characteristics could explain output expansion (capital being crowded in) in response to expansionary fiscal policy (temporary tax cut financed with government bonds). Unlike the Keynesian model however, that is not the end of the story. The model also predicts that capital is crowded out in the long-run by a higher stock of national debt. "0See Plosser (1989), which are models often referred as neoclassical. In our context, these are Ricardian models as they assume infinite-horizon (dynastic) behavior. "This description, and in general the rest of this part, is heavily based in Bernbeim (1989).  7 The Keynesian paradigm can be better understood as a short-run model Jf fine tuning around some long-run equilibrium. The emphasis on flows is an indica- tion of that. The mode' is relevant depending on how good a "fine-tuner" is the government, an issue largely explored but unsettled as yet. On the contrary, the Neoclassical framework puts the emphasis on the level of stocks and the long-run equilibrium around which the economy would be fluctuating. In this sense, and given the current 'state of the art", the neoclassical and Keynesian frameworks should be considered complementary tools for the decision-making process. While the latter seems to track well business cycle fluctuations and is a powerful dtvice for short-term forecasting, the lack of microfoundations for the Keynesian model makes it difficult to judge its power for long-run planning and policy evaluation.'2 2.3 Toward a Neoclassical Framework for Policy Evaluation The seminal work by Diamond (1965) constitutes the basic framework of the neo- classical approach. The two period version of the model, however, can not provide quantitative results and it is uninteresting as a policy design tool. The two period life-cycle or overlapping generaticns model implies that the relevant unit of time is roughly 30 years. From the point of view of the policymaker, this is extremely inconvenient. That amount of years not only is close to the whole political lifespan '2This is Lucas' (1976) critique. Since then, an important economic research agenda, known as 'New Keynesian' economics, has taken the micro considerations seriously. See Fischer (1988) and Mankiw (1988).  8 of a policymaker, but it exceeds by several times the life of most gnvernments. A large-scale version of the Neoclassical framework is needed for policy design and evaluation. Our model is strongly based on the neoclassical simulation model developed by Auerbach and Kotlikoff (1987). The latter is a large-scale simulation model which put special care in modelling individual life-c, * variables to study the dynamics of the economy in response to fiscal policy. Profiles of consumption, earnings, labor supply and wealth accumulation over the life cycle are fairly realistic. Policy instruments like taxes and national debt are also included. No attempt has been made, as far as we know, to extend the domain of this framework to other policy issues like monetary policy. We set up a monetary version of the model, neglecting labor supply decisions. A few words are appropriate regarding the monetary version we implement here. While any particular introduction of money is bound to be controversial, the issue cannot be avoided. Money seigniorage constitutes a non negligible part of govern- ment revenue in many developing countries."3 Money is necessary if the model is expected to be a reasonable characterization of those countries. A Money in the Utility Function Model is used for this purpose. "3See Fischer (1982) for estimates.  9 3 The Basic Ftramework The purpose of this section is to develop a monetary neoclassical model. We first describe the optimization problem of individuals and firms and then the equilibrium solution and growth. 3.1 The Individual Optimization Individuals have a lifespan from adult-age one through fifty five (actual age 21 through 75). In what follows we describe the optimization problem for the particular cohort age 1. The individual maximizes the time separable utility function U I 1+ - (1 + 6) ('tl-/) (1) use= (Ct'- + tmi-lXp)TII/ (2) subject to the budget constraint at+, = (1 + rt)at + mt - (1 + irt+i)mt+l + wtet - ct - r(rtag + wtet) (3) where ce is consumption, mg is real monetary balances, wgee is labor income (effi- ciency unit wage wg times the units of human capital at age t et), r is the income tax, at is the stock of real assets, 7rt+l is the inflation rate (Pt+1/Pt - 1) and rt+1 is the real domestic interest rate between period t and t + 1.  10 From (1) and (2) it can be verified that the intratemporal elasticity of substitu- tion between consumption and liquidity services is equal to dlog(c/m) = (4) d/Jog (ut&/u,) and the mntertemporal elasticity of substitution is equal to dIog(u,+i/ut) _5 dIog(U.,/U.,+1) 7 (5) The C.E.S. formulation in (2) is more general than the formulations which have been used in most empirical investigations of this type (which use the Cobb- Douglas). Allowing the intratemporal elasticity of substitution to be different than one fits better the observed co-movement of consumption and money in response to inflation.14 Besides, the Cash-in-Advance model implies no sensitivity of money demand to the nominal interest rate,15 and therefore p is equal to zero. In this sense, we are collapsing the two basic benchmarks on intertemporal monetary economics into one.'6 The details of the individual optimization problem are relegated to an Appendix. :4See Arrau (1989b). 'Fixed velocity when the scale variable is consumption. "6The above paragraph requires some qualifications. Our money in the utility function model nests only simple versions of the cash-in-advance model. If only a fraction of consumption goods is "cash goods" (Lucas and Stokey, 1987) then velocity would be sensitive to inflation when it is defined with respect to total consumption (or income), and fixed only when defined with respect to the "cash' good. We also assume that the cash-in-advance constraint is binding whenever the nominal interest rate is positive. This is not necessary the case when individuals must choose money balances before they know the realization of a shock relevant to choose current consumption (Svensson, 1985).  11 3.2 Firms Assuming many atomistic firms with identical technologies of production, we can express the firm's problem in aggregate terms. Firms hire nondepreciating and homogeneous capital and effective units of labor until factor prices and marginal rates of substitution are equalized. Firms face the Cobb-Douglas technology Yt = Kt-L (6) where Kt and Lg are aggregate physical capital and effective labor respectively (hereafter an uppercase letter indicates aggregate variables in real terms). The first order conditions for the firm's problem are (Lt) rt p (K Q)- ) 3.3 Aggregation and Government Aggregate financial assets at period t are 55 At = E a,(1 + n)ts8+l (9) .=1 where x4 means variable x at year t for cohort age s, and n is a fixed and exogenous rate of population growth. Now we need to keep track of both age and year inde- pendently. Notice in the expression above that we have implicitly normalized the  12 size of cohort age 1 at year 0 to be equal to 1. Aggregate financial assets are the sum of national debt Bt and equity or claims on firms' cash flow. Capital therefore is Kt = At - Bt (10) and labor can be expressed as 56 L= Ee(1 + n)t (11) 8=1 Definition. A sequence {wt, rg} represents an equilibrium if it satisfies the individ- ual optimization problem (Appendix), the firm problem (7)-(8) and the equilibrium conditions (10)-(11). Furthermore, in a 'steady state" (or balanced growth) equi- librium the sequence {wt, rt} is constant for all t > 0. Next we define the government budget constraint which determines the envi- ronment for agents optimization and the supply of outside assets. We treat the government as a consolidated unit with coordinated decisions between the mone- tary and fiscal authority. The flow budget constraint can be expressed as Bt+j-Bt+(1+ 7rt+)Mt+l+Mt =Gt+r.Bt-r(W