Rates of return to public and private capital: new estimates using nonlinear Euler equations

Abstract

Results obtained by Otto and Voss show that public investment undertaken in Australia over recent decades satisfies conditions for intertemporal efficiency. This paper confirms this result, although lower output elasticities and rates of return to private and public capital are obtained. The reason for these results is that the earlier work is extended by estimating the parameter related to the elasticity of intertemporal substitution that was earlier restricted to a specific value. In fact, it is shown here that it is possible to obtain an economically reasonable (and statistically significant) estimate of this parameter by assuming that the stochastic discount factor for the representative firm is the same as for the representative consumer and equal to a gross real interest rate.

Acknowledgements

The authors acknowledge the financial support from CICYT grants SEC2002-00266 and SEC2002-00667. We are indebted to Javier Andrés and Ramón Ruiz for their helpful comments. Any remaining errors are the authors’ responsibility.

Notes

 Notice that in this simplified economy, public capital is a given input for the firm that is provided by an optimizing public sector, that is taking private capital as given.

 Notice that this is the standard approach followed in the empirical consumption literature.

 As OV we do not include a measure of technical efficiency, because we are interested in the relative sectoral returns and these can be expressed independently of the usual specifications of technical progress.

 The next section discusses some econometric considerations in order to properly estimate the system of Equations 3′.

 The empirical investigation of consumption with aggregate data has not been very fruitful in providing a generally accepted value for the elasticity of intertemporal substitution. For the US case, Hall (1988) obtains a value near to zero and Epstein and Zin (1991) obtain a value near to 1. Campbell and Mankiw (1989) obtain intermediate values, after allowing consumption growth to be affected by income changes. On the other hand, the empirical investigation of consumption with microeconomic data produces higher values for this elasticity (ranging between 2 and 3). This is the case, for instance, in Attanasio and Weber (1989) or Shea (1995) after controlling for individual characteristics.

 Data sources and details about construction are available at the following Internet address: http://www.economics.unsw.edu.au/staff/voss.html.

 The nominal interest rate used in this work is the long-run interest rate available in the OECD Economic Outlook. It is a rate for long-run assets with an approximated maturity of 10 years.

 Recall that 1/(1 − σ) is the intertemporal elasticity of substitution.

 The only difference with OV is due to the fact that the sample period is 1969:01–1992:02, instead of 1960:04–1992:02. The reason is that there is available interest rate data only from 1969:01 onwards.

 In both cases we depict results obtained with Instruments Set 4.

 As emphasized by OV, the rates of return depend on the evolution of the output capital ratios that display some trend behaviour in Australia, the depreciation rates that are constant and the investment output relative prices. Obviously, the stationarity of the return series is due to the inclusion of the price series in the estimated models.

 Notice also that the estimated residuals in our models are dominated by the return component, so if R _{t  + 1} are stationary so are the estimated residuals.

 In fact, we tried some of these methods, but always obtained lower average ex ante real interest rates than with our method.