Indeterminacy in discrete-time infinite-horizon models with non-linear utility and endogenous labor

We consider a discrete-time two-sector model with sector specific externalities in which the technologies are given by CES functions with asymmetric elasticities of capital–labor substitution, and the preferences of the representative agent are given by a CES additively separable utility function defined over consumption and leisure. We first show that when the labor supply is infinitely elastic, the steady state is always saddle-point stable, no matter what the elasticity of intertemporal substitution in consumption and the size of externalities are. We then prove that when the elasticity of intertemporal substitution in consumption is sufficiently large, local indeterminacy requires a low enough elasticity of the labor supply.     

The modified golden rule of a multi-sector economy

We consider an n-good model of optimal accumulation determined by a technology, a utility function, and a discount factor. A technology is δ-productive if it contains an input-output pair such that the discounted output vector strictly dominates the input vector. We show that a δ-productive technology has a non-trivial modified golden rule. We also report a counter- example of David Starrett showing that the modified golden rule need not have turnpike properties, and that there may exist non-trivial periodic optimal consumption plans even when there is no non-trivial modified golden rule.     

Consumption paths under prospect utility in an optimal growth model

This paper studies the Cass-Koopmans-Ramsey model of optimal economic growth in the presence of loss aversion and habit formation. The representative agent's preferences for consumption can be gradually varied between the standard constant intertemporal elasticity of substitution (CIES) case and Kahneman and Tversky's prospect utility. We find that the transitional dynamics of optimal consumption paths differ distinctly from the standard model, in particular consumption smoothing is more pronounced. We also show that prospect utility can cause the economy to remain in a steady state with low consumption and low capital.     

Business cycle fluctuations and learning-by-doing externalities in a one-sector model

We consider a one-sector Ramsey-type growth model with inelastic labor and learning-by-doing externalities based on cumulative gross investment (cumulative production of capital goods), which is assumed, in accordance with Arrow (1962), to be a better index of experience than the average capital stock. We prove that a slight memory effect characterizing the learning-by-doing process is enough to generate business cycle fluctuations through a Hopf bifurcation leading to stable periodic orbits. This is obtained for reasonable parameter values, notably for both the amount of externalities and the elasticity of intertemporal substitution. Hence, contrary to all the results available in the literature on aggregate models, we show that endogenous fluctuations are compatible with a low (in actual fact, zero) wage elasticity of the labor supply.     

Local and global indeterminacy in two-sector models of endogenous growth

We consider a two-sector endogenous growth model where the productions of the final good and human capital require economy-wide external effects. Assuming constant returns to scale at the private and social levels, we show that local and global indeterminacy of equilibrium paths are compatible with any values for the elasticity of intertemporal substitution in consumption and any sign for the capital intensity difference across the two sectors. We also show that for any value of the elasticity of intertemporal substitution in consumption, poverty traps may occur when the final good sector is capital intensive in human capital.     

Age-dependent investing: Optimal funding and investment strategies in defined contribution pension plans when members are rational life cycle financial planners

A defined contribution pension plan allows consumption to be redistributed from the plan member's working life to retirement in a manner that is consistent with the member's personal preferences. The plan's optimal funding and investment strategies therefore depend on the desired profile of consumption over the lifetime of the member. We investigate these strategies under the assumption that the member is a rational life cycle financial planner and has an Epstein–Zin utility function, which allows a separation between risk aversion and the elasticity of intertemporal substitution. We also take into account the member's human capital during the accumulation phase of the plan and we allow the annuitisation decision to be endogenously determined during the decumulation phase.We show that the optimal funding strategy involves a contribution rate that is not constant over the life of the plan but is age-dependent and reflects the trade-off between the desire for current versus future consumption, the desire for stable consumption over time, the member's attitude to risk, and changes in the level of human capital over the life cycle. We also show that the optimal investment strategy during the accumulation phase of the plan is ‘stochastic lifestyling’, with an initial high weight in equity-type investments and a gradual switch into bond-type investments as the retirement date approaches in a way that depends on the realised outcomes for the stochastic processes driving the state variables. The optimal investment strategy during the decumulation phase of the plan is to exchange the bonds held at retirement for life annuities and then to gradually sell the remaining equities and buy more annuities, i.e., a strategy known as ‘phased annuitisation’.     

On the Ramsey equilibrium with heterogeneous consumers and endogenous labor supply

In this paper, we address the stability issue, stressing the role of labor supply, in a Ramsey model with heterogeneous households subject to borrowing constraints. Making labor supply endogenous leads us to prove the existence of two kinds of steady state: the one where everybody supplies labor, the other where only the most patient agent refrains from working. Going beyond models with inelastic labor supply, we show how preferences of impatient agents affect the saddle-path stability of each type of steady state and the occurrence of endogenous cycles. When their elasticity of intertemporal substitution in consumption exceeds one, instability and cycles are less likely, requiring lower degrees of capital-labor substitution. Conversely, elasticity values below one promote the emergence of fluctuations. We end the paper by showing the existence of the intertemporal equilibrium under market incompleteness, using a local approach based on the first-order conditions.     

Uncertain horizon and stability: Analysis in an optimal growth model

In a one-sector optimal growth model with uncertainty about production optimal capital stocks converge in distribution to a stochastic modified golden rule [see, for example Brock and Mirman (1972, 1973)]. We show that such a result cannot be obtained, in general, if in addition to the random one-period shocks to production there is also a lasting shock to the production function at some random date in the future; however, the conditional optimal capital stocks ‘bunch together’ over time, i.e., a turnpike result for optimal programs is proved.     

Capital–labor substitution and equilibrium indeterminacy

This paper examines the quantitative relationship between the elasticity of capital–labor substitution in production and the conditions needed for equilibrium indeterminacy (and belief-driven fluctuations) in a one-sector growth model. With variable capital utilization, the substitution elasticity has little quantitative impact on the minimum degree of increasing returns needed for indeterminacy. However, when capital utilization is constant, a below-unity substitution elasticity sharply raises the minimum degree of increasing returns because it imposes a higher effective adjustment cost on labor hours. Overall, our results show that empirically-plausible departures from the Cobb–Douglas production specification can make indeterminacy more difficult to achieve.     

Optimal dynamic tax evasion

We study optimal dynamic tax evasion in the framework proposed by Lin and Yang (2001) and Dzhumashev and Gahramanov (2011) with some modifications: a more flexible utility function, a more realistic audit process, and a penalty function which can be defined both on evaded income and evaded taxes. In the former case the elasticity between tax rate and tax evasion is positive, unless the subsistence consumption level is higher than a given threshold. In the latter case the relationship is usually negative , but the value of elasticity depends on the form of absolute risk aversion. In particular we show that for increasing relative risk aversion, for a tax rate higher than 50%, the elasticity may even become positive. US data are consistent with IRRA preferences.     

Existence in undiscounted non-stationary non-convex multisector environments

An omission in growth theory concerns the existence of optimal programs in models that simultaneously include non-stationary non-convex technologies, non-convex preferences, multisectors and undiscounted utility sums. Non-stationarities rule out the classical route employing golden rule programs; non-convexities vitiate classical duality methods based on separating hyperplane theorems; multisectors destroy the regularity in the dynamics of the one-sector growth model; and divergent utility sums render inapplicable the Weierstrass approach based on compactness-continuity arguments. This paper proves the existence of optimal programs in such generally specified models, by utilizing the non-convex duality theory of Balder to replace the bilinear functional that links a topological dual pair by a class of non-linear functions that are of needle type at the origin of the commodity space.     

Equilibrium asset pricing with Epstein-Zin and loss-averse investors

We study multi-period equilibrium asset pricing in an economy with Epstein-Zin (EZ-) agents whose preferences for consumption are represented by recursive utility and with loss averse (LA-) agents who derive additional utility of gains and losses and are averse to losses. We propose an equilibrium gain-loss ratio for stocks and show that the LA-agents are more (less) risk averse than the EZ-agents if their degree of loss aversion is higher (lower) than this ratio. When all the agents have unitary relative risk aversion degree and elasticity of intertemporal substitution, we prove the existence and uniqueness of the equilibrium and the market dominance of the EZ-agents in the long run. Finally, we extend our results to the case in which the LA-agents use probability weighting in their evaluation of gains and losses.     

Optimal money supply in models with endogenous discount factor

This paper studies the Friedman rule for the optimal quantity of money in money in the utility (MIU) and cash–credit models while considering two specifications for the endogenous discount factor. In the first specification, the discount factor depends directly on the utility level. In the second, the discount factor depends on every component of the utility function. We show that under the former specification the Friedman rule is the optimal policy. Under the latter, however, while the Friedman rule is optimal for the MIU model, it is not optimal for the cash–credit model.     

A time series analysis of real wages,consumption and asset returns

This paper re-examines whether the time series properties of aggregate consumption, real wages, and asset returns can be explained by a neoclassical model. Previous empirical rejections of the model have suggested that the optimal labour contract model might be appropriate for understanding the time series properties of the real wage rate and consumption. We show that an optimal contract model restricts the long-run relation of the real wage rate and consumption. We exploit this long-run restriction (cointegration restriction) for estimating and testing the model, using Ogaki and Park's (1989) cointegration approach. This long-run restriction involves a parameter that we call the long-run intertemporal elasticity of substitution (IES) for non-durable consumption but does not involve the IES for leisure. This allows us to estimate the long-run IES for non-durable consumption from a cointegrating regression. Tests for the null of cointegration do not reject our model. As a further analysis, our estimates of the long-run IES for non-durable consumption are used to estimate the discount factor and a coefficient of time-nonseparability using Hansen's (1982) Generalized Method of Moments. We form a specification test for our model à la Hausman (1978) from these two steps. This specification test does not reject our model. © 1996 John Wiley & Sons, Ltd.     

Long-run growth and welfare effects of public policies with distortionary taxation

In a one-sector growth model with infrastructure investment, we study the impact of fiscal policies on growth. The government collects taxes on labor income and profits. The government uses these revenues to purchase infrastructure investment, provide utility enhancing government services, and to provide transfer payments to the households. We show that the balanced growth rate is an increasing function of the percent of government revenues that goes to infrastructure. We find that the growth maximizing mix of taxes depends on the elasticity of substitution between inputs. In particular, with distortionary taxes, the growth maximizing tax rate on capital is higher the lower the elasticity of substitution between private physical capital and public capital. In addition, the growth maximizing size of the government is higher when the elasticity of substitution between public and private inputs is low. We also investigate welfare effects of other public expenditures as well. Depending on the elasticity of substitution in production, the welfare implications of different public policies can be substantial.     

An estimation of US industry-level capital–labor substitution elasticities: support for Cobb–Douglas

A key parameter that determines the distributional impacts of a policy shift in general equilibrium models is the elasticity of substitution between capital and labor. Despite the importance of this parameter in applied modeling, its identification continues to pose a challenge. Given the structure of most growth models, we posit that the true relationship between capital and labor is likely to be close to Cobb–Douglas. Using a rich new data set from the Bureau of Economic Analysis (BEA), we estimate substitution elasticities for 28 industries that cover the entire economy, and provide an indication of the long- and short-run ranges of those estimates. We fail to reject the Cobb–Douglas specification in 20 of the 28 industries. These findings lend support to the Cobb–Douglas specification as a transparent starting point in simulation analysis.     

A two sector endogenous growth model with habit formation

In this paper, we study an endogenous growth model with physical and human capital in which consumption habits enter the utility function multiplicatively. We show that although the utility function with multiplicative habits is nonconcave and unbounded, an interior optimal growth path still exists, it is uniquely determined and it converges to a balanced growth path. We also find that habit formation in consumption lowers the convergence speed of the optimal path toward the balanced growth path.     

Influence measurement of rapid urbanization on agricultural production factors based on provincial panel data

The proportion of agricultural output value is continuously decreasing because of the process of rapid urbanization, but it is still the basis of economic development and urban construction. Agricultural production factors are at the core of agriculture, and have an important influence on the agricultural output value. In the period of rapid urbanization, high technical and capital investment improved agricultural production efficiency and increased the income of farmers. However, in recent years it also introduced serious problems for agricultural production, including aging farmers and weakening labor markets, farmland conversion, and soil pollution. In this study, we estimated the elasticity coefficients of agricultural production factors, including labor, capital and technique, using the improved Cobb–Douglas production function and provincial panel data from 2000 to 2015, and measured the effects of urbanization on elasticity coefficients using the Euclidean metric and gravity model. The results were as follows. (1) In time, the elasticity coefficient of labor was stable, and with a low increase from 0.238 to 0.304. However, the elasticity coefficients of land and capital had been increasing since 2000, by 1.125 and 0.140, respectively. The higher elasticity coefficient of agricultural production factors was gradual from labor to capital, with the growth of urbanization level. (2) In space, the elasticity coefficients were the space distribution, as urbanization divided into east, central and west: the elasticity coefficients of labor and land in the eastern regions were higher, and the elasticity coefficient of capital in the central regions was higher. (3) Economic urbanization had a larger positive influence on the elasticity coefficient of capital, and the population had a larger negative influence on elasticity coefficients of labor. The quantitative results were similar to the development status, but there were different influences on elasticity coefficients in different provinces. (4) Finally, the study put forward suggestions for agricultural sustainable development according to the function mechanism of urbanization on agricultural production factors, including increasing the attention paid agriculture, ensuring a stable market environment, and optimizing the industrial structure, with reference to scientific, green and healthy agriculture.     

Measuring Scale Efficiency from a Translog Production Function

In parametric analysis based on a frontier production function, usually the scale elasticity rather than scale efficiency level is reported. In this paper we show how one can use an estimated translog production function to obtain output- and input-oriented measures of scale efficiency at an observed input bundle. We also show how the estimated model can be used to determine the optimal quantity of labor input for an exogenously fixed quantity of capital.     

Optimal consumption under uncertainty,liquidity constraints,and bounded rationality

I study how boundedly rational agents can learn a “good” solution to an infinite horizon optimal consumption problem under uncertainty and liquidity constraints. Using an empirically plausible theory of learning I propose a class of adaptive learning algorithms that agents might use to choose a consumption rule. I show that the algorithm always has a globally asymptotically stable consumption rule, which is optimal. Additionally, I present extensions of the model to finite horizon settings, where agents have finite lives and life-cycle income patterns. This provides a simple and parsimonious model of consumption for large agent based models.