Trends in the extraction of non-renewable resources: The case of fossil energy

This paper considers a strategy for the extraction and production of non-renewable resources that are finite in quantity. Specifically, we illustrate empirical data on reserves, production, consumption, and price evolution for fossil fuel. Our model is an intertemporal model of a short decision time horizon with a monopolistic resource producer extracting non-renewable resources. The model is solved numerically using a finite horizon solution method called Nonlinear Model Predictive Control (NMPC), which approximates well models with a longer decision time horizon. Consistent with the results of recent empirical studies, our numerical solution method shows a U-shaped path for the price and an inverted U-shaped path for the extraction rate, in the case of modest initial stock of proved reserves.     

Intertemporal substitution and the liquidity effect in a sticky price model

The liquidity effect, defined as a decrease in nominal interest rates in response to a monetary expansion, is a major stylized fact of the business cycle. This paper first confirms that, with separable preferences, a low degree of intertemporal substitution in consumption is a necessary condition for the existence of the liquidity effect. In contrast to this result, in a model with non-separable preferences and capital accumulation it takes an implausibly high elasticity of intertemporal substitution to produce a liquidity effect. The robustness of these results to alternative degrees of nominal rigidities, capital adjustment costs and stochastic monetary processes is also analysed. We conclude that price stickiness, by itself, does not guarantee the existence of a liquidity effect.     

The trade balance and the terms of trade in a two-country two-sector OLG economy

We consider a two-country, two-sector OLG model. It is shown that the trade balance and the relative price of exports are always positively related when exports are labor intensive regardless of the elasticity of intertemporal substitution in consumption. A large response of savings to future prices becomes a sufficient condition for an inverse relation between these variables only if exports are capital intensive. In this case, a rise in the terms of trade can be followed by a trade balance decline if consumption goods are capital intensive and the income effect implied on savings is negative and large.     

Intertemporal production and intertemporal substitution in output supply and input demand

This article presents an intertemporal model of production with multiple inputs to investigate substitution opportunities facing firms over time. The firm’s intertemporal profit maximization problem is characterized with the familiar cost function, and various intertemporal substitution elasticities are delineated for output supply and input demand. The absence of intertemporal substitution in production can imply production smoothing, and allowance for intertemporal substitution in labour demand reinforces the prediction of the real business cycle model. For aggregate US manufacturing, we find substantial substitution in output supply and labour demand over time due to intertemporal changes in output price and wage rates.     

A closed-form solution to the Ramsey model with logistic population growth

In this paper, we consider the Ramsey growth model with CIES utility function, Cobb–Douglas technology, and logistic-type population growth law. We show the model to have a unique non-trivial steady-state equilibrium (a saddle point) and prove the optimal path to be non-monotonic over time. Moreover, we derive a closed-form solution for the case where capital's share is equal to the reciprocal of the intertemporal elasticity of substitution.     

Income and wealth distribution in a simple model of growth

Summary. This paper studies a deterministic one-sector growth model with a constant returns to scale production function and endogenous labor supply. It is shown that the distribution of capital among the agents has an effect on the level of per-capita output. There exists a continuum of stationary equilibria with different levels of per-capita output. If the elasticity of intertemporal substitution is large, a higher output level can be achieved when income inequality is great, that is, when the income distribution is strongly dispersed. If the elasticity of intertemporal substitution is low, the reverse relation holds. The paper shows that countries with identical production technologies and identical preferences may have different GDP levels because wealth is distributed differently among their inhabitants. Received: January 29, 1999; revised version: October 4, 1999     

Renewable energy subsidies: Second-best policy or fatal aberration for mitigation?

This paper evaluates the consequences of renewable energy policies on welfare and energy prices in a world where carbon pricing is imperfect and the regulator seeks to limit emissions to a (cumulative) target. The imperfectness of the carbon price is motivated by political concerns regarding distributional effects of increased energy prices. Hence, carbon prices are considered to be temporarily or permanently absent or endogenously constrained by their effect on energy prices. We use a global general equilibrium model with an intertemporal fossil resource sector and calculate intertemporally optimal policies from a broad set of policy instruments including carbon taxes, renewable energy subsidies and feed-in-tariffs, among others. If carbon pricing is permanently missing, mitigation costs increase by a multiple (compared to the optimal carbon pricing policy) for a wide range of parameters describing extraction costs, renewable energy costs, substitution possibilities and normative attitudes. Furthermore, we show that small deviations from the second-best subsidy can lead to strong increases in emissions and consumption losses. This confirms the rising concerns about the occurrence of unintended side effects of climate policy – a new version of the green paradox. Smart combinations of carbon prices and renewable energy subsidies, however, can achieve ambitious mitigation targets at moderate additional costs without leading to high energy price increases.     

Superneutrality, indeterminacy and endogenous growth

In this paper, we explore the possibility of having money as a source of indeterminacy in endogenous growth models. We adopt the simple Ak model of endogenous growth to be the main analytical vehicle whose balanced growth paths do not display local indeterminacy. Money is introduced via either a general cash-in-advance (CIA) constraint or a pecuniary transactions costs (PTC) technology. It is shown that local indeterminacy of the dynamics is due to the presence of an intertemporal substitution effect on capital accumulation that works against and dominates the conventional inflation effect of Tobin [1965, Money and economical growth. Econometrica 33(4), Part 2, 671]. If money is growth-rate superneutral, then the intertemporal substitution effect is absent so that local indeterminacy cannot occur. Finally, the strength of the intertemporal substitution effect depends positively on the intertemporal elasticity of substitution in consumption.     

Nominal debt as a burden on monetary policy

We characterize the optimal sequential choice of monetary policy in economies with either nominal or indexed debt. In a model where nominal debt is the only source of time inconsistency, the Markov-perfect equilibrium policy implies the progressive depletion of the outstanding stock of debt, until the time inconsistency disappears. There is a resulting welfare loss if debt is nominal rather than indexed. We also analyze the case where monetary policy is time inconsistent even when debt is indexed. In this case, with nominal debt, the sequential optimal policy converges to a time-consistent steady state with positive—or negative—debt, depending on the value of the intertemporal elasticity of substitution. Welfare can be higher if debt is nominal rather than indexed and the level of debt is not too high.     

Savings, Volume of Trade, and Growth

This paper develops a two-country dynamic general equilibrium model with endogenous growth to analyze the effects of international trade on steady-stage growth. The two countries differ both in preferences and in technologies. It is shown first that both countries cannot simultaneously experience increases in consumption growth from trade. It is then shown that trade can increase output growth for both countries if the attitude towards saving matches the change in the terms of trade in each country. A country facing a decline (rise) in its output price grows faster if its intertemporal elasticity of substitution is sufficiently low (high).     

Duopoly models with a joint capacity constraint

The paper proposes a two-stage mixed duopoly model of exhaustible resource market where at the first stage the government decides on the degree of privatization of public firm and at the second stage the public and private firms decide simultaneously on the two-period extraction paths. It is demonstrated that if the two firms have symmetric technologies with increasing marginal extraction costs and the same resource stocks, then neither full nationalization of any of the two firms nor full privatization will be socially desirable. It is shown that the presence of a semi-public firm improves intertemporal allocation of the fixed resource stock. Thus, partial privatization is optimal even under exogenously fixed total outputs of each firm. For asymmetric cost case, when the public firm is less efficient than the private firm, we derive the conditions under which full nationalization or full privatization is optimal.     

Intertemporal Labor Supply and Human Capital Accumulation*

We solve and estimate a dynamic model that allows agents to optimally choose their labor hours and consumption and that allows for both human capital accumulation and savings. Estimation results and simulation exercises indicate that the intertemporal elasticity of substitution is much higher than the conventional estimates and the downward bias comes from the omission of the human capital accumulation effect. The human capital accumulation effect renders the life‐cycle path of the shadow wage relatively flat, even though wages increase with age. Hence, a rather flat life‐cycle labor supply path can be reconciled with a high intertemporal elasticity of substitution.     

Private consumption,public consumption and liquidity constraints in developing countries: some empirical evidence

This paper extends the empirical work of Giovannini (1983, 1985) in seeking to identify the elasticity of substitution in consumption in developing countries using the Euler equation approach. Allowing for liquidity constraints in capital markets which force a percentage of aggregate consumption growth to track income growth to track income growth, we report static and time-varying estimates of this percentage and the elasticity of intertemporal substitution, as well as estimates of substitution between private and public consumption and implied utility function parameters. Our results suggest that liquidity constraints are a pervasive feature of developing country consumption data and that the elasticity of intertemporal substitution is near-zero for the majority of countries considered.     

Preference for output price uncertainty by the non-renewable resource extracting firm

We establish a general preference for price uncertainty by the price-taking, risk-neutral, non-renewable resource extracting firm with orthodox convex extraction costs. We prove that the relevant value function for profits over an interval is convex in output price.     

Monetary Policy with Parameter Uncertainty in Small-Open Economy

This paper computes optimal robust monetary policy in a new Keynesian small-open economy model with Knightian uncertainty about the degree of price stickiness and the elasticity of substitution between domestic and foreign goods. Due to the simple model structure used in the paper, I can derive analytical results for the min–max solution under discretion and assess how a robust optimal Taylor rule must be set in small-open economy. I find that, in an optimal robust discretionary equilibrium, the central bank should assume that the degree of price stickiness and the elasticity of substitution between domestic and foreign goods take on their highest numerical values. In terms of interest rate setting, if the optimal discretionary robust equilibrium is implemented with a Taylor rule, the policy rate should react to inflation in a less aggressive way than in the case of complete information.     

Money Illusion and the Double Dividend in the Short Run

Abstract. In their seminal paper, Bovenberg and de Mooij (1994) elucidate why an ecological tax reform will not yield a double dividend, i.e. fails to increase the efficiency of the tax system. The present paper slightly modifies the Bovenberg and de Mooij model by introducing money illusion. With this modification, an environmental tax reform that raises the price level may generate a double dividend, since the additional tax on the dirty good does not reduce labor supply. A prerequisite for the double dividend to occur is a sufficiently small elasticity of substitution between clean and dirty consumption. Moreover, accounting for money illusion always reduces the intertemporal gross cost of the tax reform.     

Commodity Rates of Interest and Intertemporal Substitution in Commodity Demand and Consumption

This paper examines the role of commodity own rates of interest in intertemporal analysis of consumer behaviour and presents a disaggregate analysis of intertemporal substitution in commodity demand and consumption. Commodity rates of interest are defined from the Euler equations implied by the intertemporal consumer choice problem. The relationship between commodity own rates and the real interest rate is derived, and the conditions for equality of commodity own rates are discussed. The intertemporal commodity substitution elasticities are characterised using commodity rates of interest, and the intertemporal substitution elasticity of consumption is derived from its constituent commodity demands. Evidence from estimation of the demand system and the consumption function reveals high intertemporal substitution for consumer goods as well as consumption.     

新《劳动合同法》的实施对劳动力供给的影响研究

新<劳动合同法>的实施引起社会各界的广泛关注,新法对劳动力供给究竟产生何种影响,目前国内尚无此问题微观角度的实证分析.本文采用个体跨期最优模型,通过计算劳动力供给跨期弹性,分析新法对劳动力供给的影响.结果发现,在新<劳动合同法>实施后,劳动力的跨期弹性变小.新法的实施达到了建立和谐稳定的劳动关系和稳定劳动力供给的目的.     

Intertemporal Substitution and Terms-of-Trade Shocks

The paper examines the relationship between transitory terms‐of‐trade shocks and private saving. Using a model allowing for nonseparability between the consumption of tradables and nontradables, the paper estimates the intertemporal elasticity of substitution while accounting for the intratemporal elasticity of substitution between the consumption of tradables and nontradables. Empirical analysis of data for five industrial countries indicates that in response to transitory terms‐of‐trade shocks, intertemporal substitution of consumption and intratemporal substitution of consumption between tradables and nontradables both have large effects on private saving.     

Price Stability in Open Economies

This paper studies the theoretical conditions under which price stability is the optimal policy in a two-country open-economy model with imperfect competition and price stickiness. Special conditions on the levels of country-specific distortionary taxation and the intratemporal and intertemporal elasticities of substitution need to be satisfied. These restrictions apply to both cooperative and non-cooperative settings. Importantly, we show that cooperative and non-cooperative solutions do not coincide despite market completeness and producer currency pricing. We study the conditions under which quadratic approximations of single countries' welfare can be correctly evaluated by relying only on log-linear approximations of the equilibrium conditions.