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Exogenous versus endogenous rates of return: The user cost of capital in Statistics New Zealand's multifactor productivity measures

Statistics New Zealand Working Paper No 10–03

Nairn MacGibbon

Abstract

Objectives

Capital (together with labour), is one of the primary inputs in productivity analysis. Statistics New Zealand constructs indexes of industry capital services input as Törnqvist indexes. A Törnqvist index is where the geometric mean of assets’ two-period productive capital stock ratios are weighted exponentially by each asset’s mean two-period share of the industry’s value of capital costs. An asset’s cost of capital is estimated as its user cost (rental price) multiplied by its flow of capital services (proxied by the productive capital stock). The user cost of capital could theoretically be observed as a market rental price for the asset concerned. Given however that capital rental markets are often very sparse (if not non-existent), the user cost is approximated by an implicit rental that owners of capital are inferred to be charging themselves.

The choice of methodology used to derive the user cost of capital services can significantly impact on relative weights assigned to the various asset capital services that provide an input into the production function of an industry. In particular, choosing whether an endogenous or exogenous rate of return is used (or some hybrid thereof), and how capital gains are treated, can markedly impact the resulting asset capital services weights.

Methods

International recommendation (and theory) gives many alternative methodologies in formulating the user cost of capital, recognising that what suits the unique circumstances of each country will affect choice.

While the preferred method in much of the literature is for an endogenous nominal rate of return with capital gains on assets (excluding land and buildings), a number of factors render the resulting time series of weights in the New Zealand situation economically implausible. This paper presents an analysis of the different methods that could be used to calculate the user cost of capital, and assesses each of the methods against a range of criteria.

Findings

The use of an exogenous real rate of return (set at 4 percent) and excluding capital gains from the formulation of the user cost of capital provides more economically plausible results in the New Zealand context. The industry asset-weights derived from this method provide a superior representation of the underlying production function of many of the industries. They also display markedly less volatility, and hence are a more realistic representation of the change in the aggregate industry production functions over time. Consequently, this method has been used by Statistics NZ to construct the capital services indexes in the published estimates of multifactor productivity.

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Citation

MacGibbon, N (2010). Exogenous versus endogenous rates of return: The user cost of capital in Statistics New Zealand's multifactor productivity measures (Statistics New Zealand Working Paper No 10–03). Available from www.stats.govt.nz.

ISBN 978-0-478-35378-5 (online)
ISSN 1179-934X (online)

Published December 2010

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