Discount rates and shadow prices for public investment

This paper extends the Harberger–Sandmo–Drèze model for public discount rates to a many-good economy. It derives a formula for discount rates which are specific to each public enterprise or agency and used by them to discount future outputs and inputs evaluated at market prices. Such an approach is shown to be more efficient than that of simply using a single rate for all public projects. It is also more practical than asking each public firm to use second-best shadow prices in their analyses of investment projects.The general results are first provided; then, simple cases are considered and numerical examples presented to help interpret our formula and analyse its main determinants.     

Joint estimation of discount rates and willingness to pay for public goods

We analyze willingness to pay (WTP) for environmental programs whose time periods of benefit and repayment differ, using a net present value framework that identifies parameters of both WTP and personal discount rates. Respondents to a contingent valuation survey focusing on protection of critical habitat buffer zones for the endangered Steller Sea Lion in Alaska were asked their willingness to pay for 1-, 5-, and 15-year repayment periods. We jointly estimate the personal discount rates and WTP via maximum likelihood, and compare with a model assuming a fixed, market discount rate.     

Optimal taxation and discount rate for public investment in a growth setting

This paper studies the optimal policy of a government which maximizes intertemporal social welfare using such instruments as taxes on interest income and wages, and debt in conjunction with public investment. In doing so, it has to face a decentralized economy where in each generation individuals and firms are free to maximize their own objectives subject to their own private constraints. The welfare function is a sum of discounted generational utilities and its maximization is handled by using dynamic programming. From the first order conditions so derived, it appears that an optimal policy of taxation and public capital accumulation is that which sets the tax rates according to Ramsey's optimal taxation structure and which equates the rate of return on public investment to the rate of social time preference.     

Empirical and public choice evidence for hyperbolic social discount rates and the implications for intergenerational discounting

The derivation of the correct discount rate for intergenerational projects in Cost Benefit Analysis is particularly contentious. Public choice has resulted in lower discretionary exponential discount rates for many intergenerational projects in Britain and the USA. This is shown to be strong indirect evidence that the true social discount rate may be a hyperbolic (rather than an exponential) function. There is also empirical evidence for this hypothesis. The hyperbolic nature of discounting is also a standard finding in the behavioural sciences. For intergenerational time frames hyperbolic discount rates should be employed together with exponential discount rates in cost-benefit sensitivity analyses.Sincere thanks to Maureen Cropper and Paul Portney for supplying their survey results and to Elaine Barrow and Phillip Judge for graphics assistance. Two anonymous referees also provided valuable comments.     

License prices for financially constrained firms

It is often alleged that high auction prices inhibit service deployment. We investigate this claim under the extreme case of financially constrained bidders. If demand is just slightly elastic, auctions maximize consumer surplus if consumer surplus is a convex function of quantity (a common assumption), or if consumer surplus is concave and the proportion of expenditure spent on deployment is greater than one over the elasticity of demand. The latter condition appears to be true for most of the large telecom auctions in the US and Europe. Thus, even if high auction prices inhibit service deployment, auctions appear to be optimal from the consumers’ point of view.      

Determining output shadow prices for a cost-constrained technology

We develop a method for computing output shadow prices when total cost and input prices are exogenous, using the indirect output distance function of Shephard (1974). We show that indirect distance function shadow price imputations for output prices are the same to a proportional constant as marginal cost imputations. We motivate our results by relating them to the problem of valuing the output of nonprofit institutions, to some measurement issues for noncompetitive industries, and to a problem of imputing sales of the commercial banking industry to consuming sectors of the economy in the national income accounts.Thanks are due to a very informed and helpful referee.Rolf Färe supported by IHE, Lund, Sweden.     

Stock prices and inflation hedged firms

As the Federal Reserve continues its near-zero rate policy, the threat of inflation remains a concern among both policymakers and businesses. This article uses over 30 years of accounting data and stock returns to examine how publicly traded firms respond to increasing inflation expectations. We first examine whether firms make balance sheet adjustments in response to expected inflation. We then examine whether these activities have a positive effect on stock prices. We find that firms increase inventory, increase capital expenditures and reduce long-term debt when there is an increased expectation of inflation. We then find that firms that increase inventory in this economic regime are rewarded in the market. Markets also reward firms that increase their cash positions and reduce long-term debt possibly suggesting investor flight to safety.     

Schooling choices: Preferences, discount rates, and rates of return

This paper develops an empirical model to identify the structural parameters of schooling preferences and human capital production. Our model distinguishes between consumption and investment motives with regard to schooling. The results show that both motives matter. Preferences for schooling vary with social background and ability. Children from poorer social backgrounds and of lower ability have a lower preference for schooling. The discount rate that enters the net value of lifetime income varies with social background as well. The marginal rate of return to schooling decreases with ability and schooling. On average the marginal rate of return is 7.3 per cent, which can be contrasted with a `Mincerian' rate of return equal to 4.8 per cent. This indicates that the usual OLS estimate underestimates the true rate of return. First version received: November 1997/Final version received: February 1999     

Debt policy, corporate taxes, and discount rates

This paper applies the standard risk-neutral valuation framework to tax shields generated by dynamic debt policies. We derive a partial differential equation (PDE) for the value of the debt tax shield. For a class of dynamic debt policies that depend on the asset's free cash flows, value, and past performance, we obtain closed-form solutions for the PDE. We also derive the tax-adjusted cost of capital for free cash flows and analyze the conditions under which the weighted average cost of capital is an appropriate discount rate. Finally, we derive closed-form solutions for equity betas, which differ from the formulas that have traditionally been used to lever and unlever equity betas.     

Intertemporally consistent shadow prices in an open economy: Estimates for Cyprus

In the practical estimation of shadow prices, the assumption that the economy is on a steady-state growth path is often invoked, usually implicitly. Most developing countries are far from this trajectory. We derive shadow prices where the dynamic evolution of the economy is endogenously determined, important influences being initial conditions and the constraints on foreign borrowing. Hence, the resulting (dated) shadow prices of tradeables, nontradeables, labor and the accounting rate of interest (ARI) are mutually consistent. Estimates for the Republic of Cyprus show that derivations from steady-state growth can be significant, leading to large fluctuations in the ARI and thereby making the timing of investment projects crucial.     

Temporal insensitivity of willingness to pay and implied discount rates

A number of studies have defined and tested the temporal sensitivity of willingness to pay to payment schemes and the resulting implied discount rates for environmental projects. We demonstrate that those studies have imposed restrictive assumptions on the structure of the willingness to pay function and the underlying decision process. We investigate the temporal sensitivity of willingness to pay using a new temporal willingness to pay function applied to a proposed oyster reef restoration program. We find that (1) holding the length of the project constant, the temporal willingness to pay for the project is the same across different payment schemes, (2) temporal willingness to pay does not vary significantly across projects of varying lengths, and (3) estimated discount rates are low relative to previous studies, but vary significantly across payment schemes and project lengths.     

Empirical measures of factors affecting social rates of discount

Economists have long considered possible divergences between private and social rates of time preferences. In this paper, we investigate factors hypothesized to affect this potential divergence. Results indicate that time preferences of individuals may be influenced by: 1. whether the resource in question is publicly or privately managed (respondents tend to have lower rates of time prefernce for publicly managed resources); and 2. the type of good being managed (respondents tend to have lower rates of time preference for income derived from a forest than for income derived from a portfolio of stocks and bonds). Additional factors which may influence the revealed rate of time preference include the pattern of benefits derived over time and various personal characteristics of the respondent. Although numerous methodological problems cloud the issues, our results suggest that capital markets may fail to aggregate utility over individuals and between goods, and that it may therefore be appropriate for governments to consider using lower rates of discount than the private sector, and to vary the rate used according to the type of good being evaluated.     

Economic efficiency and shadow prices in an infinite horizon model: Reply

Journal of Economics -     

Optimal fiscal and monetary policy under sticky prices

This paper studies optimal fiscal and monetary policy under sticky product prices. The theoretical framework is a stochastic production economy. The government finances an exogenous stream of purchases by levying distortionary income taxes, printing money, and issuing nominal non-state-contingent bonds. The main findings of the paper are: First, for a miniscule degree of price stickiness (i.e., many times below available empirical estimates) the optimal volatility of inflation is near zero. Second, small deviations from full price flexibility induce near random walk behavior in government debt and tax rates. Finally, price stickiness induces deviation from the Friedman rule.     

Estimates of optimal public capital stocks in Japan using a public investment discount rate framework

The purpose of this paper is to empirically assess the optimality of the level of public capital in Japan. We use a methodological approach based on Burgess's (1988) procedure for calculating the public discount rate. This approach involves estimating a production function, but does not necessarily require utility function estimation. The results indicate that, although the Japanese economy experienced a public capital deficiency over the period 1960–1982, public capital moved toward optimal levels throughout the period. First version received: March 1997/final version received: June 1998