A model of banknote discounts

Prior to 1863, state-chartered banks in the United States issued notes—dollar-denominated promises to pay specie to the bearer on demand. Although these notes circulated at par locally, they usually were quoted at a discount outside the local area. These discounts varied by both the location of the bank and the location where the discount was being quoted. Further, these discounts were asymmetric across locations, meaning that the discounts quoted in location A on the notes of banks in location B generally differed from the discounts quoted in location B on the notes of banks in location A. Also, discounts generally increased when banks suspended payments on their notes. In this paper we construct a random matching model to qualitatively match these facts about banknote discounts. To attempt to account for locational differences, the model has agents that come from two distinct locations. Each location also has bankers that can issue notes. Banknotes are accepted in exchange because banks are required to produce when a banknote is presented for redemption and their past actions are public information. Overall, the model delivers predictions consistent with the behavior of discounts.     

基于随机贴现因子的人民币与新台币汇率定价

基于随机贴现因子定价理论,采用无套利定价法,推导出人民币与新台币的即期汇率与随机贴现因子、远期汇率之间的关系,并利用人民币和新台币的无本金交割远期外汇作为远期汇率,对人民币与新台币的即期汇率进行定价。实证研究结果显示,人民币与新台币的汇率主要受中国大陆地区和台湾地区的股票市场和债券市场波动的影响。用本文模型定价模拟的即期汇率与真实汇率的变动趋势较为一致,这表明本文模型可为人民币与新台币之间的双向直接兑换提供依据,进而有助于建立两岸货币清算机制。     

Short-term eurocurrency rate behavior and specifications of cointegrating processes

This article presents empirical evidence on short-term behavior based on seven Eurocurrency market rates. Empirical analysis suggests that there is two-dimensional cointegration. First, the domestic short-term interest rate is cointegrated with longer-term interest rates within a particular country. Second, the domestic short-term interest rate is cointegrated with the comparable foreign short-term interest rate adjusted for the foreign exchange forward premium (discount). The empirical evidence confirms that an error-correction model combining both dimensional market-correcting processes better explains short-term interest rate movements.     

Exchange Rate Expectations and the Risk Premium: Tests For A Cross Section of 17 Currencies*

Survey data on a broad cross section of 17 currencies are used to determine whether the forward discount moves primarily in response to changes in expectations of depreciation, or in the risk premium. We find that, in contrast to earlier studies involving developed country exchange rates, variation in the risk premium is a quantitatively significant factor in movements of the forward discount. However, changes in expectations also have a substantial effect.     

An Efficient Avoided Cost Pricing Rule for Resale of Local Exchange Telephone Services

The Telecommunications Act of 1996 requires incumbent local exchange telephone companies to make their retail telecommunications services available to resellers at a discount that reflects the costs that will be avoided by providing the services at wholesale rather than at retail. In this article, we develop a pricing methodology to apply to such wholesale services. The methodology, which we label the Avoided Cost Pricing Rule, is designed to generate an economically efficient discount that may be applied to the incumbent local exchange carriers' services that are offered to resellers.     

The Neutrality of the Resource Rent Tax

Although less distorting than conventional royalties and income tax, the resource rent tax is strictly neutral only if the interest rate at which losses are carried forward relates correctly to the discount rate employed by investors in project evaluation. Thus it is possible in principle to design a resource rent tax that is strictly neutral only if parameters are set independently for each minerals investment. Such attempts to tailor parameters to each investment would make great demands on information and would increase business uncertainty. The paper suggests expedients to reduce the costs of non-neutrality when resource rent tax is applied with parameters that are of general application and discusses their use in Australia.     

Forward discount dynamics in integrated markets

This paper models the excess return or forward discount (premium) dynamics in integrated markets. Its decomposition at different time frequencies suggests that both stochastic and fundamental processes, as well as exogenous random shocks, are relevant for the determination of the forward discount (premium) over time. A stochastic process within a time-dependent parabolic well appears to capture the empirical findings of the literature and provides the means for the derivation of the equilibrium pricing formula for the forward discount. The mathematical solution that determines the relationship between the stochastic process and the trend allows for an interpretation of the reasons why, in some cases, expectational error appears to be correlated with the forward discount (premium) but not with the forward risk premium. Finally, estimations of the forward discount are carried out using the proposed model, which seems to support the data well.     

Do retirement planning strategies alter the effect of time preference on retirement wealth?

An individual’s willingness to accumulate retirement wealth is influenced by their preference for intertemporal consumption. People with a strong preference for current consumption (high personal discount rate) may choose to save less and face the risk of decreased retirement preparedness. A negative relation between a high personal discount rate and retirement wealth may be reduced when individuals engage in some form of retirement planning. Using the National Longitudinal Survey of Youth, we provide evidence that respondents with a high personal discount rate accumulated 37% less retirement wealth, on average, between 2004 and 2008, when compared with respondents with a low personal discount rate. However, when retirement planning strategies were included in the model, there was no statistical difference in retirement wealth between people with high and low personal discount rates. The retirement planning strategies included calculating a retirement income need, hiring a financial planner for retirement or engaging in both of these activities.     

On the long and short run relationship between the forward rate and the interest parity

The interest parity theory postulates that a one percentage point increase in the interest differential favoring a currency will be accompanied by an increase in the discount on that currency in the forward market of one percentage point as well. Using Canadian data we find that the forward rate responds to the interest differential with a lag. Moreover, a unit increase in the differential favoring the U.S. was accompanied in the long run by a rise in the discount on the forward U. S. dollar which was not significantly different from unity.     

利率互换的定价模型及其实证研究

本文研究利率互换的定价模型，以及利率互换的定价过程。从选取债券到拟合理论即期利率曲线、远期利率曲线，最后拟合出互换利率曲线，并对上述的定价模型和过程进行实证研究。对拟合结果与目前市场报价的相同点和差异进行分析，并对国内利率互换的套期保值策略进行实证研究。     

Discounting and divergence of opinion

Agents impatience rate and their anticipations about the future of the economy, are two essential determinants of the equilibrium discount rate, as illustrated by the Ramsey formula. Heterogeneity in time preference rates and in anticipations is widely acknowledged. Our objective is to determine the equilibrium discount rate when this heterogeneity is taken into account. Among others we tackle the following questions: As an additional risk or uncertainty, can dispersion in agents' characteristics lead to lower discount rates? What is the asymptotic behavior of the discount rate in such a setting? More generally, what is the shape of the yield curve?     

Covered interest parity: The untestable hypothesis

Although post Keynesian economists advocate the realistic bankers’ view of the forward exchange rate, neoclassical economists formulate (CIP) as a testable hypothesis. In reality, CIP represents a formula used by bankers to calculate the forward rates they quote to their customers. This article provides arguments for the post Keynesian view of the forward exchange rate and suggests that CIP is not a theory, that it is a microeconomic relation, and that it is a hedging rather than an arbitrage condition. An empirical illustration shows that deviations from CIP are observed whenever published data are used, but these deviations disappear when transaction data are used instead. It is concluded that CIP is an untestable hypothesis.     

OPTIMAL EXPORT AND HEDGING DECISIONS WHEN FORWARD MARKETS ARE INCOMPLETE

This paper examines the behaviour of the competitive firm that exports to two foreign countries under multiple sources of exchange rate uncertainty. There is a forward market between the home currency and one foreign country's currency, but there are no hedging instruments directly related to the other foreign country's currency. We show that the separation theorem holds when the firm optimally exports to the foreign country with the currency forward market. The full‐hedging theorem holds either when the firm exports exclusively to the foreign country with the currency forward market or when the relevant spot exchange rates are independent. In the case that the relevant spot exchange rates are positively (negatively) correlated in the sense of regression dependence, the firm optimally opts for a short (long) forward position for cross‐hedging purposes.     

Cost-benefit analysis of alien vegetation clearing for water yield and tourism in a mountain catchment in the Western Cape of South Africa

Economic analysis is used to assess the costs and benefits of restoration following clearing of invasive alien trees in the floristically rich Fynbos mountainous area near Franschhoek, Western Cape of South Africa. The Groot Drakenstein, Franschhoek and Jonkershoek mountains receives more rainfall than the surrounding areas and is an important source of water for the city of Cape Town. The costs of alien invasive plant removal, gully-erosion repair and reseeding with indigenous plants are considered in a case-study cost-benefit analysis of restoration, in terms of the water and tourism benefits derived. Three different options of restoration (comprehensive, moderate, basic) were analysed under three different economic scenarios (optimistic, realistic, pessimistic) and the costs of which have been weighted up against the income derived from the supply of water and tourism. The results have shown that despite the high costs of restoration, the basic restoration option costs were out-weighed by the water and tourism benefits derived. This was also true of the moderate restoration option, when evaluated under the optimistic scenario and using an 8% discount rate, or a 3% discount rate under any scenario. However, this was not the case in the moderate restoration option when using an 8% discount rate in conjunction with the realistic and pessimistic scenarios. Neither was it the case when using a 12% discount rate, irrespective of the scenario. Under no scenario was the cost of a comprehensive restoration option outweighed by the benefits quantified, irrespective of the discount rate used. It was concluded that further restoration, in addition to the mere clearing of alien invasive plants, would be economically viable under certain assumptions and conditions.     

The Ethics of Intertemporal Distribution in a Warming Planet

This paper evaluates, from the ethical viewpoint, current work by economists on intergenerational resource allocation in the presence of global warming. We begin by attempting to elucidate the debate that has recently occurred on the appropriate choice of the discount rate. We offer three justifications for maximizing the discounted sum of generational utilities, and find only one of these to be a satisfactory justification of that practice: the possibility that the human species may become extinct. This implies that a very small discount rate (large discount factor) should be used. We argue that the justification for discounting, inherent in the approaches taken by many economists, is that of ‘the present generation of hegemon,’ which is unacceptable. The role of the Ramsey equation in deducing the discount rate in these theories is explained. As an alternative to discounted utilitarianism, we propose a principle of sustainability; we describe optimal paths that have been calculated for the sustainabilitiarian (Rawlsian) objective function, and paths that will sustain growth in welfare, at a positive rate. We report results concerning optimal paths when the uncertainty of existence of future generations is taken into account. In sharp contrast to the utilitarian model, it turns out that under some conditions, the ‘sustainabilitarian’ can ignore the uncertainty regarding the date at which humans become extinct. There is a striking difference between the solutions of the discounted utilitarian program and the sustainabilitarian program under uncertainty.     

Ecological discounting

Which rates should we use to discount costs and benefits of different natures at different time horizons? We answer this question by considering a representative agent consuming two goods whose availability evolves over time in a stochastic way. We extend the Ramsey rule by taking into account the degree of substitutability between the two goods and of the uncertainty surrounding the economic and environmental growths. The rate at which environmental impacts should be discounted is in general different from the one at which monetary benefits should be discounted. We provide arguments in favor of an ecological discount rate smaller than the economic discount rate. In particular, we show that, under certainty and Cobb-Douglas preferences, the difference between the economic and the ecological discount rates equals the difference between the economic and the ecological growth rates. Using data about the link between biodiversity and economic development, I estimate that the rate at which changes in biodiversity should be discounted is 1.5%, whereas changes in consumption should be discounted at 3.2%.     

On recursive utility and the superneutrality of money

This paper investigates whether a change in the growth rate of the money supply enhances the rate of capital accumulation in a cash-in-advance monetary model with recursive utility. Although money is superneutral in the steady state, the effect of the growth rate of money supply on the speed of capital accumulation depends not only on the curvature of the felicity, but also on the slope and curvature of the discount rate function. We find that when the discount rate decreases with consumption and the elasticity of marginal utility is greater than unity, inflation yields a slower speed of capital accumulation.     

汇率制度能影响外汇市场压力和央行干预吗

按照Stavarek（2007）的方法和标准,分别计算了2002年1月到2011年12月期间人民币对美元的外汇市场压力及中央银行干预指数。结果显示,人民币实行参考一篮子货币的汇率制度与盯住美元的汇率制度相比,不仅没有减轻外汇市场压力,反而加大了外汇干预压力。汇率制度不是影响外汇市场压力的决定因素,但不同的汇率制度却对我国央行外汇市场干预程度产生了较大的影响。在人民币实行参考一篮子货币的汇率制度下,央行干预程度明显降低,汇率决定的市场化程度相应提高。     

Discounting the Distant Future: An Experimental Investigation

We use a laboratory experiment to elicit discount rates over a 20-year time horizon using government savings bonds as a payment vehicle. When using a constant (exponential) discount rate function, we find an implied average discount rate of 4.9 %, which is much lower than has been found in previous experimental studies that used time horizons of days or months. However, we also find strong support for non-constant, declining discount rates for longer time horizons, with an extrapolated implied annual discount rate approaching 0.5 % in 100 years. There is heterogeneity in discount rates and risk preferences in that people with more optimistic beliefs about technological progress have higher discount rates. These findings contribute to the debate over the appropriate discount rate to use in comparing the long-term benefits of climate change mitigation to the more immediate costs.     

Non-convex aggregate technology and optimal economic growth

This paper examines a model of optimal growth where the aggregation of two separate well behaved and concave production technologies exhibits a basic non-convexity. First, we consider the case of strictly concave utility function: when the discount rate is either low enough or high enough, there will be one steady state toward which the convergence of the optimal path is monotone and asymptotic. When the discount rate is in some intermediate range, we will find sufficient conditions for having either one equilibrium or multiple equilibria steady state. Depending to whether the initial capital per capita is located with respect to a critical value, we show that the optimal paths monotonically converge to one single appropriate equilibrium steady state. Second, we consider the case of linear utility and provide sufficient conditions to have either unique or two steady states when the discount rate is in some intermediate range. In this range, we give conditions under which the above critical value might not exist, and the economy attains one steady state in finite time, then stays at the other steady state afterward. P. Michel passed away when this research was completed. This paper is dedicated to his memory as a friend and colleague. N. M. Hung and C. Le Van thank the referee for vey helpful remarks and criticisms. They are grateful to Takashi Kamihigashi for very fruitful discussions. They also thank J.-F. Leclerc for editing the final version of this paper.