Lucas Model Research Articles

Occupational Choice, Number of Entrepreneurs and Output: Theory and Empirical Evidence with Spanish Data

This paper extends the Lucas (1978) model of occupational choices by individuals with different skills, beyond the simple options of self-employment or wage-employment, by including a second choice for the self-employed. That is, an option to hire employees and so become self-employed with employees (SEWEs), or to be self-employed without employees (SEWNEs). We solve for the market equilibrium and examine the sensitivity of relative sizes of occupational groups, and of the level of productivity, tochanges in the exogenous parameters. The results show that the positive (negative) association between number of SEWEs (SEWNEs) and productivity, observed in the Spanish data, can be explained, under certain conditions, as the result of cross-region and time differences in average skills. These findings point to the importance of distinguishing between SEWEs and SEWNEs in drawing valid conclusions concerning any link between entrepreneurship and economic development.

Human Capital and Regional Development *

AbstractWe investigate the determinants of regional development using a newly constructed database of 1,569 subnational regions from 110 countries covering 74% of the world’s surface and 97% of its GDP. We combine the cross-regional analysis of geographic, institutional, cultural, and human capital determinants of regional development with an examination of productivity in several thousand establishments located in these regions. To organize the discussion, we present a new model of regional development that introduces into a standard migration framework elements of both the Lucas (1978) model of the allocation of talent between entrepreneurship and work, and the Lucas (1988) model of human capital externalities. The evidence points to the paramount importance of human capital in accounting for regional differences in development, but also suggests from model estimation and calibration that entrepreneurial inputs and possibly human capital externalities help understand the data.

State-dependent pricing and the non-neutrality of money

Golosov and Lucas (2007) have challenged the view that infrequent price adjustments by firms explain why money has aggregate real output effects. The basis of their challenge is the ‘selection effect’ – re-setting firms are not selected at random, they are those firms whose prices are furthest from the optimal reset price. Because of this the aggregate price level is sufficiently flexible for monetary neutrality. In this paper I add price review costs to an otherwise standard Golosov and Lucas model. This weakens the selection effect and restores monetary non-neutrality.

Optimal taxation in the Uzawa–Lucas model with externality in human capital

In this paper we study the optimal policy in the Uzawa–Lucas model with externality in human capital when agents value both consumption and leisure. We find that the government pursuing the first best can achieve its goal by a subsidy which depends on foregone earnings while studying and which is financed through a lump sum tax. Anyway, the optimal policy, that should be designed to provide incentives for agents to devote more time to schooling and cut both on leisure and working, is not unique. There exists an infinite number of combinations of consumption, capital income, labor income and lump sum taxes that can decentralize the first best.

Population dynamics and utilitarian criteria in the Lucas–Uzawa Model

This paper introduces population growth in the Uzawa–Lucas model, analyzing the implications of the choice of the welfare criterion on the model's outcome. Traditional growth theory assumes population growth to be exponential, but this is not a realistic assumption (see Brida and Accinelli, 2007). We model exogenous population change by a generic function of population size. We show that a unique non-trivial equilibrium exists and the economy converges towards it along a saddle path, independently of population dynamics. What is affected by the type of population dynamics is the dimension of the stable manifold, which can be one or two, and when the equilibrium is reached, which can happen in finite time or asymptotically. Moreover, we show that the choice of the utilitarian criterion will be irrelevant on the equilibrium of the model, if the steady state growth rate of population is null, as in the case of logistic population growth. Then, we show that a closed-form solution for the transitional dynamics of the economy (both in the case population dynamics is deterministic and stochastic) can be found for a certain parameter restriction.

The two sector endogenous growth model: An atlas

In this paper we investigate the underlying structure of the Lucas (1988) endogenous growth model. We derive analytically, the restrictions on the parameter space that are necessary and sufficient for the existence of balanced growth paths and saddle-path stable local dynamics. We demonstrate that in contrast to the original model, with the addition of an external effect and depreciation in the human capital sector, the Lucas model can be made consistent with the high degrees of intertemporal elasticities of substitution increasingly estimated in the empirical literature—even if there is a significant degree of increasing returns to scale in the physical production sector of the economy. Finally we demonstrate that for a given baseline rate of steady state growth, with the inclusion of modest degrees of depreciation and external effects to the human capital production process, the model can accommodate the widest possible range of economies—including those characterized by low discount factors, high elasticities of intertemporal substitution, increasing returns in the final goods sector, and also both the high rates of population growth and steady state per-capita output growth we observe in many parts of the world today.

THE EQUITY PREMIUM IN CONSUMPTION AND PRODUCTION MODELS

In this paper we use a simple model with a single Cobb–Douglas firm and a consumer with a CRRA utility function to show the difference between the equity premia in the production-based Brock model and the consumption-based Lucas model. With this simple example we show that the equity premium in the production-based model exceeds that of the consumption-based model with probability 1.

Cognitive Capital and Islands of Innovation: The Lucas Growth Model from a Regional Perspective

Knowledge triggers regional growth. Evidence suggests that skilled labor force concentrates in islands of innovation, determining an advantage for innovative regions and a challenge for lagging ones. We address the role of knowledge in shaping effective markets for skilled labor. Estimates are based on the Lucas (1988) model, with EVS and EUROSTAT data. The externality driving growth in the model is cognitive capital. Empirical tests show that a higher endowment of cognitive capital generates increasing returns to knowledge, favoring the emergence of islands of innovation; regions with a high endowment of cognitive capital attract knowledge spillovers from neighbors.

Growth and the diffusion of ideas

In a recent model of growth developed by Lucas (Lucas, R., 2009. Ideas and growth. Economica 76, 1–19), a continuum of people interact in a random manner and copy each other’s productive ideas when it is economically beneficial to do so. This paper extends the Lucas model by assuming that each person’s productivity also experiences random shocks due to individual discovery. A nonlinear partial differential equation is derived for the distribution of income, which admits a traveling wave solution representing a growing economy. The growth rate is an increasing function of the rate of imitation. The growth rate is also an increasing but concave function of population size and reaches a plateau in the continuum limit. Hence the scale effect is bounded. The model is extended to account for a nonzero cost of imitation, with similar results. The mathematical tools presented in this paper should prove useful in developing idea-based models of growth.

Diameter growth models for mixed-species stands of Coastal British Columbia including thinning and fertilization effects

In this study, diameter growth models for three species growing in mixed-stands of Coastal British Columbia (BC), Canada, under a variety of silvicultural treatments were developed. The three species were: Douglas-fir ( Pseudotsuga menziesii var. menziesii (Mirb.) Franco), western hemlock ( Tsuga heterophylla (Raf.) Sarg.), and western redcedar ( Thuja plicata Donn). A Box and Lucas model (1959) was initially fitted to the diameter growth series for each tree, as this model is very flexible and was based on processes reflective of the metabolic processes governing tree growth. Next, a random coefficients modelling approach (i.e., parameter prediction approach) was used to modify the estimated parameters for each species using functions of tree size and stage of development, site productivity, and inter-tree competition variables, while accounting for temporal correlation within trees. Impacts of fertilization on diameter growth were estimated by including the time since fertilization as an additional variable. Since state variables that are changed as a result of thinning were already in the model, accurate results post-thinning were obtained with no changes to the model. For the combined effects of thinning and fertilization, a two-step additive approach was used, where the state variables were changed following thinning and the diameter increment was modified for fertilization using the time since fertilization variable. Results indicated that multiple treatments sustain a change in growth for a longer time period following treatment than thinning or fertilization alone.

Stochastic technology shocks in an extended Uzawa–Lucas model: closed-form solution and long-run dynamics

We add stochastic technological progress, modelled as a geometric Brownian motion with drift, to an augmented Uzawa–Lucas growth model. Under a particular combination of parameters we derive a closed form solution to the model and analytical expressions which show that uncertainty reduces the optimal levels of consumption and increases the proportion of human capital devoted to producing new human capital.

WHAT DETERMINES ENTREPRENEURIAL CLUSTERS?

We contrast two potential explanations of the substantial differences in entrepreneurial activity observed across geographical areas: entry costs and external effects. We extend the Lucas model of entrepreneurship to allow for heterogeneous entry costs and for externalities that shift the distribution of entrepreneurial talents. We show that these assumptions have opposite predictions on the relation between entrepreneurial activity and firm-level TFP: with different entry costs, in areas with more entrepreneurs firms' average productivity should be lower; with heterogeneous external effects it should be higher. We test these implications on a sample of Italian firms and unambiguously reject the entry costs explanation in favor of the externalities explanation. We also investigate the sources of external effects, finding robust evidence that learning externalities are an important determinant of cross-sectional differences in entrepreneurial activity.

Consequences of local Allee effects in spatially structured populations

The ideal free distribution model incorporating the Allee effect was published by Fretwell and Lucas (1970), but went almost unnoticed within the ecological literature. The model is relevant to populations distributed among patchy habitats. It predicts a sporadic but substantial decline in populations at high densities, which in turn induces the rapid growth of new populations. In this paper, I show that the simple process explained by this model can be used to change our view of several phenomena within the field of population ecology, behavioural ecology and conservation. The ecological consequences of the model are well known. A key feature of Fretwell and Lucas's model is what I call the "Allee paradox:" there is a range of local population densities at which local individual fitness is less than the potential mean gain that could be obtained in the environment; however, individuals cannot disperse. This paradox can be used to explain why helping appears before suitable breeding areas are fully occupied, and why breeding females aggregate when male coercion is a reproductive cost. The model also predicts high clustering between related populations, and, in conservation biology, it can identify unfounded concerns about the dangers of extinction, delays in recolonisation processes after human-induced population decline, and latency periods in the initial phases of expansion of invasive species.

Solow or Lucas? Testing speed of convergence on a panel of OECD countries

We test whether the growth experience of a sample of 21 OECD countries over the past three decades is more consistent with the augmented Solow model or the Uzawa–Lucas model, by exploiting the different non-linear restrictions implied by them as regards the relationship between factor shares and speed of convergence. Using cross-country/time-series data, we specify our growth regression without imposing cross-country homogeneity restrictions on the speed of convergence and short-run parameters. Indeed, both theoretical models imply that the speed of convergence to the steady state differs across countries due to heterogeneity in population growth, technical change or progressiveness of income taxes. Our estimated speed of convergence is too fast to be compatible with the augmented Solow model, but is consistent with the Uzawa–Lucas model with constant returns to scale. Our main findings are robust to several robustness tests.

Lucas meets Baumol and Tobin

Many issues that were traditionally analyzed using the Baumol-Tobin model can also be analyzed, perhaps more easily, using the Lucas (1980) cash-in-advance model where money serves both as a medium of exchange and as a store of value. This is illustrated by three examples (implications) of the Lucas model: (i) the velocity of money is time varying, volatile, and inflation-dependent; (ii) transitory money injections have expansionary real effects on output and employment; and (iii) the welfare cost of anticipated inflation is a couple of orders larger than the conventional estimates.

Managing Expectations and Fiscal Policy

Working Paper 2009-29 October 2009 Abstract: This paper studies an optimal fiscal policy problem of Lucas and Stokey (1983) but in a situation in which the representative agent's distrust of the probability model for government expenditures puts model uncertainty premia into history-contingent prices. This situation gives rise to a motive for expectation management that is absent within rational expectations and a novel incentive for the planner to smooth the shadow value of the agent's subjective beliefs to manipulate the equilibrium price of government debt. Unlike the Lucas and Stokey (1983) model, the optimal allocation, tax rate, and debt become history dependent despite complete markets and Markov government expenditures. JEL classification: D80, E62, H21, H63 Key words: Ramsey plan, misspecification, robustness, taxes, debt, martingale, expansion 1 Introduction Optimal policy design problems heavily exploit the rational expectations assumption that attributes a unique and fully trusted probability model to all agents. That useful assumption precludes carrying out a coherent analysis that attributes fears of model misspecification to some or all agents. It seems natural to ask the question: How should we approach policy design problems in macroeconomics when at least some agents distrust the model? This question is not just of academic interest but of particular practical relevance. Lack of confidence in models seems to have become pronounced in the recent financial crisis and has entered policy discussions. Caballero and Krishnamurthy (2008), for example, impute sets of probability models and a max-min criterion to private agents as a way to model Knightian uncertainty when a lender of last resort copes with flights to quality, whereas Uhlig (2009) appeals to uncertainty aversion to justify pessimism during bank runs. Our approach can be viewed as putting a particular structure on a decision maker's set of models and thereby on his pessimism. This additional structure opens up channels of influence for policy makers not present in the analyses of Caballero and Krishnamurthy (2008) and Uhlig (2009). (1) This paper features a notion of expectation management that is absent from the standard rational expectations paradigm. We formulate an optimal policy problem in which private agents' fears of model misspecification cause them to adjust their expectations in ways that a Ramsey planner recognizes and exploits, bringing the household's endogenous beliefs into the forefront of an optimal policy design problem because they affect equilibrium prices. We study a Ramsey fiscal policy problem in which a planner knows that a representative household distrusts a probability model for exogenous sequences of government expenditures, while the planner still trusts it. We start with the complete-markets economy without capital analyzed by Lucas and Stokey (1983), but modify the representative household's preferences to express his concerns about misspecification of the stochastic process for government expenditures. The planner can use a distortionary tax on labor income and issue state-contingent debt in order to finance the exogenous government expenditures. Our household expresses distrust of his model by ranking consumption plans according to the multiplier preferences of Hansen and Sargent (2001); when a multiplier parameter assumes a special value, the expected utility preferences of Lucas and Stokey (1983) emerge as a special case in which the decision maker completely trusts his probability model. (2) The Lucas and Stokey (1983) environment isolates essential dimensions of an optimal macroeconomic policy design problem in which a representative household's ambiguity about its statistical model creates an avenue that motivates the planner to manipulate the household's beliefs, because they affect equilibrium Arrow-Debreu prices. …

The US Productivity Slowdown, the Baby Boom and Management Quality

This paper examines whether management changes caused by the entry of the baby boom into the workforce explain the US productivity slowdown in the 1970s and resurgence in the 1990s. Lucas (1978) suggests that the quality of managers plays a significant role in determining output. If there is heterogeneity across workers and management skill improves with experience, an influx of young workers will lower the overall quality of management and lower total factor productivity. Census data shows that the entry of the baby boom resulted in more managers being hired from the smaller, pre baby boom cohorts. These marginal managers were necessarily of lower quality. As the boomers aged and gained experience, this effect was reversed, increasing managerial quality and raising total factor productivity. Using the Lucas model as a framework, a calibrated model of managers, workers, and firms suggests that the management effects of the baby boom may explain roughly 20 percent of the observed productivity slowdown and resurgence.

Regional External Economies and Economic Growth under Asymmetry

In this article, we explore the impact of regional external economies from human capital accumulation on economic growth. In particular, we allow the extent of local and regional spillovers to vary between the home and foreign economies. Our analysis yields novel insights regarding the diffusion of knowledge across countries. In contrast to the standard, closed‐economy Lucas (1988) model, spillovers within the home country may adversely affect growth in the presence of substantial knowledge flows from the foreign country.

Homoclinic bifurcation and global indeterminacy of equilibrium in a two‐sector endogenous growth model

This paper considers an endogenous growth model that belongs to the same family as the Lucas model. In the Lucas model an external effect appears in the physical‐goods sector, whereas in our model, it appears in the educational sector. In our model, this external effect yields multiple balanced growth paths. Our model undergoes a homoclinic bifurcation and exhibits global indeterminacy of equilibrium.

Equilibrium Illusion, Economic Complexity and Evolutionary Foundation in Economic Analysis

It is widely believed that an equilibrium framework based on simple models, such as the representative agent and bilateral bargaining, in a frictionless economy provides a consistent framework in micro, macro, finance, and institutional economics. However, equilibrium believes in self-stabilizing market and institutional convergence broken down when inherent instability and non-predictable uncertainty emerge under nonlinear and social interactions. Equilibrium illusions in economics and econometrics are pretty in math modeling but dangerous in policy decision. Known examples are the Frisch model of noise-driven cycles, the Lucas model of microfoundations, and the Coasian world of zero transactions. These models not only violate basic laws in science but also lack evidence in economic history. Their common problem is associated with linear Hamiltonian economics with symmetric information without history. Economies are dissipative systems in nature, characterized by symmetry breaking, information flow, a time arrow, and history. The many-body problem is fundamentally different from the one-body and two-body problem in mathematics. Both computational and natural experiments, such as a stock market crash and a transitional depression, reveal the severe limitations of equilibrium thinking and structural changes from evolutionary dynamics. The new science of complexity offers new tools of nonlinear dynamics and non-stationary time series analysis. Existing puzzles in equilibrium economics, such as persistent cycles, interruptive crises, market resilience, social movements, and organizational diversity, can be better understood by nonlinear dynamic models. Like the paradigm shift after Einstein in physics, the evolutionary perspective provides a general framework, while equilibrium models serve as its special cases, since the equilibrium picture is an approximation of economic complexity in a short-time window taken from a long-term historical current.