Cobb-Douglas Technology Research Articles

Inspecting the Mechanism Exactly: A Closed-form Solution to a Stochastic Growth Model

This paper considers the canonical stochastic growth model with CRRA utility and Cobb-Douglas technology. It obtains a closed-form solution for the case where capital's share is equal to the reciprocal of the intertemporal elasticity of substitution. This provides a useful benchmark that illuminates the transmission mechanism under uncertainty. In particular, it highlights the complicated ways in which risk and nonlinearities interact, via Jensen's inequality, to affect the steady state capital stock.

On human capital formation with exit options: comment and new results

Katz and Rapoport (2005) conclude that with linear production technology and the possibility of unilateral migration, region-specific shocks may increase the average level of education. Previously, Poutvaara (2000) derived a corresponding result with Cobb–Douglas technology and migration which may go in both directions. This paper extends the analysis to all strictly concave production functions, and shows how the effect of the region-specific shocks depends on the shape of the production function. Also, the paper establishes when the presence of exit option increases and when it reduces investment in education. The results are robust to allowing for migration costs.

ENDOGENOUS FLUCTUATIONS IN TWO-COUNTRY MODELS

This paper investigates the interlinkage in the business cycles of large-country economies in a free-trade equilibrium. We consider a two-country, two-good, two-factor general equilibrium model with Cobb-Douglas technologies and linear preferences. We also assume decreasing returns to scale in the consumption good sector. We first identify the determinants of each country’s global accumulation pattern in autarky equilibrium, and secondly we show how a country’s business cycles may spread throughout the world once trade opens. We thus give capital intensity conditions for local and global stability of competitive equilibrium paths.

Improving the estimation of total factor productivity growth: capital operating time in a latent variable approach

Measuring labor and capital services accurately is essential to obtaining reliable estimates of production functions and total factor productivity (TFP) growth. Using data on the operating time of capital, a series that exists for the French business sector, greatly improves the measurement of effective capital services in production. The ensuing estimation results are consistent with Cobb–Douglas technology under constant returns to scale, with the factor elasticities not statistically different from their income shares. In the same framework, TFP growth is estimated as a latent variable and found to be less volatile than accounting residuals, negatively correlated with employment, and free of cyclicality. It is statistically best estimated as a first-order autoregressive process, with an autoregressive coefficient of 0.95. Total factor productivity growth was estimated to have declined steadily between the mid-1970s and mid-1990s, but the rate of decline has diminished since then.

DIFFERENTIAL DEPRECIATION AND THE 2 x 2 MODEL OF DISTRIBUTION, PRICING AND PRODUCTION

In a two-sector model it is entirely arbitrary to take the depreciation rate to be the same in both sectors; capital is being used differently in the two sectors! With differential depreciation rates factor-intensity-reversal can arise even when both sectors have a Cobb–Douglas technology. Efficient allocations do not involve mutual tangency points between consumption–good and capital–good isoquants.

On Human Capital Formation with Exit Options: Comment and New Results

Katz and Rapoport (2005) conclude that with linear production technology and the possibility of unilateral migration, region-specific shocks may increase the average level of education. Previously, Poutvaara (2000) derived a corresponding result with Cobb-Douglas technology and migration which may go in both directions. This paper shows that the exit option may reduce human capital formation with a quadratic production technology.

Endogenous fluctuations in unionized economies with productive externalities

We discuss the effects of unions on steady-state multiplicity and welfare, and on the existence of endogenous fluctuations. We consider an OG economy with productive capital externalities and we focus on underemployment equilibria. We find that for wide regions in the parameter space, including an arbitrarily small degree of externalities and a Cobb-Douglas technology, unions increase steady state employment and welfare, and local indeterminacy (sunspots) emerges. Moreover with a CES technology multiplicity of steady states is only possible in the presence of unions. Our results also show that the role of unions in shaping local dynamics and bifurcations depends on technology (externalities and factor’s substitutability).

Transitional dynamics and the distribution of assets

We study the evolution of the distribution of assets in a discrete time, deterministic growth model with log-utility, a minimum consumption requirement, Cobb-Douglas technology, and agents differing in initial assets. We prove that the coefficient of variation in assets across agents decreases monotonically in a transition to the steady state from below, if (i) the consumption requirement is zero, or (ii) the consumption requirement is not too big and the initial capital stock is large enough. We also show how a positive consumption requirement or a small elasticity of substitution between capital and labor can generate non-monotonic paths for inequality.

THE FIRM AS A NEXUS OF STRATEGIES

This paper replaces the standard view of the firm as a nexus of contracts with a repeated game framework where input contributions and side payments are self-enforced. General production technologies and flexible transfers among team members are allowed. When an incentive constraint binds, input demand and output supply are influenced by the discount factor, the probability of exogenous team dissolution, and the aggregate value of outside options. When this incentive constraint does not bind, the firm maximizes profit in the usual way. I discuss examples involving the Cobb-Douglas technology, firms with a single residual claimant, and partnerships.

Model for Analysing and Forecasting Short Term Developments

MASCOTTE is the new version of the Banque de France's macro-econometric forecasting model. Following the last rebasing of National Accounts (currently at 1995 price), the previous version of the model was simplified, re-specified and re-estimated. The model is essentially used for making macro-economic projections of the French economy over a two-to-three year horizon, which requires an accounting framework as close as possible to the French National Accounts. The main agents are companies, households, general government and the rest of the world. The new version now includes a supply block derived from the explicit optimisation behaviour of companies using a Cobb-Douglas technology under imperfect competition, and a new Wage Setting schedule. Full homogeneity of the nominal side of the model ensures the independence between the nominal equilibrium and the real equilibrium, the latter being only determined in the long run by relative prices. Furthermore, as regards the specification of equations, special attention was paid to the consequences of changes in short-term interest rates.

A note on the determinants of labour share movements

Adjustment costs cause movements of the labour share if the economy experiences demand or wage shocks. With linear adjustment costs and Cobb–Douglas technology, these movements are independent of the size of these shocks and depend only on the size of the adjustment costs.

Public services and endogenous growth

We investigate the role of fiscal policy when composite (non-utility-enhancing) public services complement private capital in production. In this case, taxes finance public capital investment and non-capital flow expenditure. This structure is embedded in a simple endogenous growth framework with capital adjustment costs and transitional dynamics. The Barro (1990) rule of optimal fiscal policy is generalised and shown to maximise steady-state growth under Cobb-Douglas technology. It is also welfare-optimal in a model without capital in the generation of services. In the general case, whilst the rule delivers too high rates of tax and public investment for welfare maximisation, the associated loss in utility may not be prohibitively high.

Capital Operating Time and total Factor Productivity Growth in France

Data on the weekly operating time of capital improve the measurement of effective capital input in production. The production function of the French business sector is found to be consistent with a Cobb-Douglas technology under constant returns to scale. Total factor productivity growth, estimated as an unobservable variable, has declined steadily since the late 1970s, but more slowly since 1994. During the 1990s, a secular increase in shift work raised the operating time of capital and began to contribute positively to growth, albeit only slightly.

Capital Operating Time and Total Factor Productivity Growth in France

Data on the weekly operating time of capital improve the measurement of effective capital input in production. The production function of the French business sector is found to be consistent with a Cobb-Douglas technology under constant returns to scale. Total factor productivity growth, estimated as an unobservable variable, has declined steadily since the late 1970s, but more slowly since 1994. During the 1990s, a secular increase in shift work raised the operating time of capital and began to contribute positively to growth, albeit only slightly.

Productivity measurement in Swedish departments of gynecology and obstetrics

The rapid growth of public spending and the need to assess its impact on the welfare system has made the studies of productivity in the public sector an important subject. This paper is concerned with the specification and estimation of total factor productivity growth using the primal panel data approach. The total factor productivity growth is decomposed into technical change and scale components. Several competing models are used to explore whether there are any similarities in the estimates of total factor productivity growth and technical change among these models. The models are estimated using different estimation methods. Some of the models, although assuming a Cobb–Douglas technology, exhibit firm-specific technical change. These models are used to measure productivity growth in departments of gynecology and obstetrics in Sweden. Empirical results show evidence of large and negative rate of productivity growth. In comparison among different specifications proposed, the level and the time pattern of productivity measures vary substantially across models and estimation methods.

Growth Regressions and Economic Theory

In this note we show that the standard, loglinear growth regression specification is consistent with one and only one model in the class of stochastic Ramsey models. This model is highly restrictive: it requires a Cobb-Douglas technology and a 100% depreciation rate and it implies that risk does not affect investment behavior.

Factor prices and the factor content of trade revisited: what’s the use?

This paper examines and extends a result of Deardorff and Staiger (An interpretation of the factor content of trade. Journal of International Economics 1988;24:93–107) (D–S), who showed how the factor content of trade may indicate the factor price adjustments that can be attributed to that trade. It elaborates on what this means, and also extends it beyond several of the assumptions that D–S used. The strongest result, in D–S only for Cobb–Douglas technology, is extended to common constant elasticities of substitution and, for small changes, more general technologies. Also, the assumption of nonspecialization is shown to be unnecessary with Cobb–Douglas technology. More generally, noncompeting imports equate with Hicks-neutral technological improvements.

Factor Prices and the Factor Content of Trade Revisited: What's the Use?

This paper examines the usefulness of a result of Deardorff and Staiger (1988), who showed that the factor content of trade can be interpreted under certain assumptions as indicating the nature of the factor price adjustments that can, in a specified sense, be attributed to that trade. This paper elaborates on the sense in which this result says anything about the factor market effects of trade. It also examines several of the assumptions that were used by Deardorff and Staiger to determine whether they can be relaxed. These include the assumption, used for only one of Deardorff and Staiger's several results, of Cobb-Douglas technology, which is shown here to be easily extended to Constant Elasticity of Substitution. Also examined is the assumption of nonspecialization, or that all imported goods are produced or producable in the domestic economy. With Cobb-Douglas technology that assumption is shown not to be needed. With more general technology, however, the presence of non-competing imports requires a reinterpretation of the factor content of trade. Whereas without noncompeting imports, trade itself is analogous, in terms of its effects on factor markets, to a change in factor endowments equal to the factor content of trade, with noncompeting imports trade has an additional effect analogous to a Hicks-neutral technological improvement enabling those noncompeting imports to be produced competitively.

Capital Precommitment and Competition in Supply Schedules

Although the Cournot and Bertrand equilibrium concepts have dominated economic analysis of oligopoly problems, neither has a compelling theoretical rationale. However,notions of capacity commitment have been used to rationalize the Cournot equilibrium. At the same time, the idea of competition in supply schedules under uncertainty has been used by Klemperer and Meyer to derive an equilibrium concept intermediate between Cournot and Bertrand, In this paper, we combine these two approaches and show that under the assumptions of Cobb-Douglas technology and constant elasticity demand, an equilibrium in markups can result.

Wage risk and the Lee, Liaw, and Rahman model

In an article in this journal, Lee, Liaw, and Rahman assumed systematic price uncertainty and a generalized Cobb-Douglas technology to show that β is negatively related to firm market power and capital intensity. They also showed that market power mitigates the negative effect of capital intensity. This paper demonstrates that these results stem from assuming that price uncertainty is the only source of systematic risk. With wage uncertainty introduced, all the relationships derived by the authors may reverse direction. Furthermore, restriction to a Cobb-Douglas technology is unnecessary because the relationships apply to any homothetic transform of a homogeneous function.