Fiscal policy and indeterminacy in models of endogenous growth

This paper investigates the dynamic behavior of two-sector models of endogenous growth with sector-specific external effects, and government expenditure financed by distortionary taxation. When this type of external effect is combined with a sufficient degree of capital taxation in a Lucas-Uzawa endogenous growth model, continua of equilibria will emerge in the region of the balanced growth paths. By contrast, indeterminacy is not possible when either sector-specific external effects or factor taxation are added to the model in isolation. In the second part of the paper, we demonstrate that if labor supply is endogenous, indeterminacy can be consistent with much lower degrees of increasing returns to scale. Furthermore, certain types of fiscal policy will be associated with multiple balanced growth paths and the existence of a poverty trap. Finally, in the last part of the paper, we demonstrate that if physical capital is employed in both sectors of the economy, indeterminacy will emerge for varying combinations of factor taxation and external effects, even when returns to scale are constant at the social level.     

Equilibrium Growth and Nonlinear Dynamics in Continuous-Time Models

Building on recent work on equilibrium growth models with externality, I re-examine earlier results from multi-sector growth models in the continuous-time framework, and study the structural relationship between technology and local dynamics. It is shown that it is very easy to construct large classes of economies that exhibit Hopf bifurcations or indeterminacy with constant returns to scale in multi-sector frameworks.
JEL Classification Numbers: C41, E32, O41.     

Multiple transitional growth paths in endogenously growing open economies

This paper extends research in indeterminacy literature to a small open economy, two-sector endogenous growth model. It shows that a continuum of equilibria exist in two situations, (i) the production functions exhibit social constant returns to scale with very small or even negligible externalities; and (ii) the production functions are standard constant returns to scale without externalities but the government implements asymmetric tax policies across sectors.     

Indeterminacy and cycles in two-sector discrete-time model

Summary. We consider a discrete-time two-sector Cobb-Douglas economy with positive sector specific external effects. We show that indeterminacy of steady states and cycles can easily arise with constant or decreasing social returns to scale, and very small market imperfections. This is in sharp contrast with most of the contributions in the literature in which increasing social returns are required to generate indeterminacy. Received: July 31, 2000; revised version: June 5, 2001     

SEARCH EXTERNALITIES IN MACROECONOMIC THEORY

The paper gives a survey of the basic features of macroeconomic models with search externalities. It presents a simple static general equilibrium model with search externalities. Within this context the main results characterizing steady state in dynamic search models are reproduced in a simple context. Specifically, the link between transaction technology and strategic complementarity is analysed. It is shown that increasing returns to scale in the transaction technology create feed-back effects and multiple, Pareto-ranked equilibria may arise. With economies of scale in matching, fluctuations in the economy can be large even with a low elasticity of search activity. The formal equivalence to models with investment externalities is analysed. In an application to the labour market, the allocative role of wages in the presence of search frictions and hysteresis effects are discussed. General conditions are given under which the set of welfare ranked equilibria is described by a closed loop. Finally, it is shown that with a more general transaction technology, even with constant returns to scale multiple equilibria may occur in the presence of externalities.     

Ruling Out Multiplicity and Indeterminacy: The Role of Heterogeneity

It is well known that economies of scale that are external to the individualdecision makers can lead to self-fulfilling prophecies and the multiplicityor even indeterminacy of equilibrium. We argue that the importance of thissource of multiplicity and indeterminacy is overstated in representativeagent models, as they ignore the potential stabilizing effect ofheterogeneity. We illustrate this in a version of Matsuyama's (1991)two-sector model with increasing returns to scale. Two main results areshown. First, sufficient homogeneity with respect to individual productivityleads to the instability and non-uniqueness of a given stationary state andthe indeterminacy of the corresponding stationary state equilibrium. Second,sufficient heterogeneity leads to the global saddle-path stability and theuniqueness of a given stationary state and the global uniqueness ofequilibrium.     

Are Progressive Income Taxes Stabilizing?

We assess the stabilizing effect of progressive income taxes in a monetary economy with constant returns to scale. It is shown that tax progressivity reduces, in parameter space, the likelihood of local indeterminacy, sunspots and cycles. However, considering plausibly low levels of tax progressivity does not ensure saddle‐point stability and preserves as robust the occurrence of sunspot equilibria and endogenous cycles. It turns out that increasing progressivity, through its impact on after‐tax income, makes labor supply more inelastic. However, even when large, tax progressivity does not neutralize the effects of expected inflation on current labor supply which may lead to expectation‐driven business fluctuations.     

The comparative statics of cumulative distribution function changes for the class of risk averse agents

We examine the connection between Walrasian equilibria of a limit economy (with infinitesimal firms) and the noncooperative (Cournot) equilibria of approximating finite economies (with significant firms). Following earlier work of Novshek and Sonnenschein we allow for set-up cost and permit a minimal form of mixed strategies. We depart from them by requiring that the aggregate production set exhibits some degree (however small) of decreasing returns. Contrasting with their results, it is shown that a (regular) Walrasian equilibrium of a limit economy can always be approximated by a sequence of noncooperative equilibria for the tail of the approximating (finite) economies. Thus, there is a surprising qualitative discontinuity when one passes from the Novshek-Sonnenschein case of aggregate constant returns to scale of the decreasing returns case of this paper.     

Econometric Cost Structure Estimates for Cellular Telephony in the United States

This article estimates economies of scale for a sample of five cellular telephony firms in the United States. We reject constant returns to scale for all but the smallest firm studied; the remaining firms exhibit decreasing returns to scale. This finding suggests that scale economies cannot be used to justify the current regulated duopoly structure of United States cellular markets.     

Returns to scale and externalities in the consumption and investment sectors

Using data on US manufacturing, I estimate internal returns to scale and external effects for the consumption and investment sectors. I construct panels of data at the industry level and use results of gross output production function estimation to derive implied estimates in a value added specification. For the investment sector, returns to scale appear to be slightly increasing, with evidence of a positive external effect. For consumption, the evidence indicates decreasing to constant returns to scale. I discuss the implications of these results for the empirical plausibility of indeterminacy in recent multi-sector models of the business cycle.     

Indeterminacy,capital maintenance expenditures and the business cycle

This paper examines how maintenance expenditures affect the occurrence of indeterminacy in a two-sector model economy, motivated by the empirical fact that equipment and structures are maintained and repaired. McGrattan and Schmitz's (1999) survey on ‘Capital and Repair Expenditures’ in Canada indicates that maintenance expenditures account for a substantial fraction of output and new investment. It is shown that the endogenous maintenance expenditures reduce the requirement of the degree of increasing returns to scale to generate sunspot equilibria. In fact, the minimum level of the returns to scale required could be as low as 1.0179. This aspect is important since empirical works such as Basu and Fernald (1997) suggest that returns to scale is close to constant.     

On characterizing equilibria of economies with externalities and taxes as solutions to optimization problems

Summary We characterize equilibria of general equilibrium models with externalities and taxes as solutions to optimization problems. This characterization is similar to Negishi's characterization of equilibria of economies without externalities or taxes as solutions to social planning problems. It is often useful for computing equilibria or deriving their properties. Frequently, however, finding the optimization problem that a particular equilibrium solves is difficult. This is especially true in economies with multiple equilibria. In a dynamic economy with externalities or taxes there may be a robust continuum of equilibria even if there is a representative consumer. This indeterminacy of equilibria is closely related to that in overlapping generations economies.An earlier version of this paper, entitled Externalities and Taxes in General Equilibrium, was presented at the North American meetings of the Econometric Society, June 1988, at the University of Minnesota. We are grateful to David Backus, Kenneth Judd, Patrick Kehoe, and Rodolfo Manuelli for helpful conversations. National Science Foundation grants SES 86-18325 and SES 87-08616 provided financial support.The views expressed herein are those of the authors and not necessarily those of the Federal Reserve Bank of Minneapolis or the Federal Reserve System.     

On the plausibility of sunspot equilibria

This paper presents a one-sector business cycle model with variable capacity utilization and externalities that stem from aggregate economic activity. It uses a new formulation of the endogenous capital utilization rate in which utilization costs appear in the form of variable maintenance expenses. Indeterminacy arises at approximate constant returns to scale. This result challenges the viewpoint that indeterminacy is empirically implausible. Sunspot driven model fluctuations duplicate a number of stylized facts of the business cycle. Plausible parameter space contains regions in which stationary sunspot equilibria are stable under learning.     

External Economies of Scale and Optimal Plant Location

This paper departs from earlier work on location theory by introducing external economies of scale into the Weber–Moses location model. It is shown that under Cournot–Nash competition, when external economies prevail, constant returns to scale at the firm level is not a sufficient condition for ensuring the invariance of the firm's optimal location with respect to a change in market demand, regardless of whether or not free entry is allowed. Moreover, when free entry is allowed and the production function exhibits decreasing returns to scale, but with very strong external economies, the optimal location moves towards or away from the market as demand increases according to whether the demand function is convex or concave. These results are different significantly from the conventional wisdom.     

Enterprise diversification in US dairy: impact of risk preferences on scale and scope economies

Enterprise diversification has recently become a prominent feature of US dairy farms. Scope economies and risk aversion are two forces that simultaneously determine diversification. We jointly estimate scope economies and determine risk preferences under price uncertainty. We reject risk neutrality in favour of Increasing Absolute Risk Aversion (IARA) and Increasing Relative Risk Aversion (IRRA). Scope economies are significant, but diminish with farm size. Increasing returns to scale exist in the production of multiple enterprises and diminish with size. Large farms operate under decreasing returns to scale. Ignoring risk preferences, a common practice in empirical work, results in an underestimate of the effect of scope economies for large farms.     

Imperfect competition and capital accumulation: the role of price normalization

We consider a capital-accumulation model with infinitely lived households and two production sectors. The intermediate-good sector is characterized by perfect competition, a constant-returns-to-scale technology, and production externalities. The final-good sector is a monopoly operating under constant returns to scale. We analyze the general equilibrium in the sense of Gabszewicz and Vial [Journal of Economic Theory (1972) 4: 381–400] for this economy and different price-normalization rules. It is shown that the qualitative behavior of the equilibrium paths depends crucially on the chosen normalization rule. In particular, whether equilibria are monotonic or oscillating and whether indeterminacy occurs or not may depend on the choice of the numeraire.     

UNIQUENESS AND INDETERMINACY OF THE EQUILIBRIUM GROWTH PATH IN THE UZAWA‐LUCAS MODEL WITH SECTOR SPECIFIC EXTERNALITIES*

We introduce sector specific external effects of human capital on production in an otherwise Uzawa‐Lucas model of endogenous growth; and show that the problem of indeterminacy of the competitive equilibrium growth path does not exist even if the production function satisfies the increasing returns to scale at the social level.     

Tax Rate Variability and Public Spending as Sources of Indeterminacy

We consider a constant returns to scale, one sector economy with segmented asset markets of the Woodford type. We analyze the role of public spending, financed by labor income and consumption taxation, on the emergence of indeterminacy. We find that what is relevant for indeterminacy is the variability of the distortion introduced by government intervention. We show that the degree of public spending externalities in preferences affects the combinations between the tax rate and its variability under which indeterminacy occurs. Moreover, we find that consumption taxes can lead to local indeterminacy when asset markets are segmented.     

Walrasian equilibria as limits of noncooperative equilibria. Part II: Pure strategies

We examine the connection between Walrasian equilibria of a limit economy (with infinitesimal firms) and noncooperative (Cournot) equilibria of approximating finite economies (with significant firms). Nonconvex production sets, decreasing returns in the aggregate, and endogenous determination of the number of active firms are allowed. A Walrasian equilibrium is a limit of pure strategy noncooperative equilibria only if a condition (loosely analogous to downward sloping demand in the partial equilibrium constant returns to scale case) holds. The condition is also sufficient to guarantee the existence of a robust sequence of pure strategy noncooperative equilibria which converges to the Walrasian equilibrium.