A univariate model of aggregate labour productivity

Abstract

In this article, we set out a model of labour productivity which distinguishes between shocks which change productivity permanently and shocks which have transient affects on productivity. We show that this model is a type of unobserved components model – a random walk with drift plus noise model. The advantage of this approach is that it provides a coherent framework to identify the deterministic trend growth component and also the productivity enhancing (or technology related) stochastic components. The model is applied to aggregate labour productivity in Australia and the time series of technology shocks extracted is used to shed some light on the contributions of policy reforms to productivity.

Keywords:

• labour productivity
• technological change
• economic growth

JEL Classification::

• O47
• C22
• O40

Notes

¹ Although the presence of measurement errors and frequent revisions in national accounts data does provide a prima facie case for considering models which allows for both types of shocks.

² For further discussion on the constancy of the capital-output ratio in conditions of equilibrium growth, see Dixon (2003, 2006).

³ See also Shapiro and Watson (1988, p. 114).

⁴ In the context of the Solow–Swan growth model, the equilibrium level of output per worker is derived as , where s is the savings propensity, n is the rate of population growth (assumed exogenous and equal to the rate of growth in labour supply and employment), g (=γ) is the rate of technological progress and d is the depreciation rate. When s, n, g and d are assumed to be constant over time, then taking logs we find that φ is equivalent to log(s/(n + g + d)).

⁵ Nontechnology shocks will include measurement errors.

⁶ Harvey (1989, 2006) has a good discussion of the time-series characteristics of the model. See also Harvey et al. (2007) and Oh et al. (2008). Enders (2004, p. 164) refers to this model as a ‘trend plus noise model’.

⁷ If Equation 9 is the true model and an equation for y_t were to be estimated without including the second last term on the RHS of Equation 9, the estimate of γ would be biased. Further, if Equation 9 is the true model, then any forecast should take into account both the deterministic and the stochastic trend components and should not rely only on the former.

⁸ The ‘market sector’ is defined as comprising 12 of the 17 ANZSIC divisions. The divisions included in the market sector are: Agriculture, forestry and fishing, Mining, Manufacturing, Electricity, gas and water, Construction, Wholesale trade, Retail trade, Accommodation, cafes and restaurants, Transport and storage, Communication services, Finance and insurance and Cultural and recreational services. Excluded are: Property and business services, Government administration and defence, Education, Health and community services and Personal and other services.

⁹ The (seasonally adjusted) data have been downloaded from the ABS website for 5206.0 Australian National Accounts: National Income, Expenditure and Product and is contained in the spreadsheet 5206001_key_aggregates.xls. The series ID's are A2304192L and A2304194T. A description of the way in which the data are compiled may be found in ABS (2005).

¹⁰ That is, where production is valued at labour cost.

¹¹ Our results also show that average technology shocks were −0.0015 in the period 1979:Q1 to 1989:Q4 and +0.0012 in the period 1992:Q1 to 2007:Q4 (we have chosen the start and end dates for these segments so as to avoid the recession of the early 1990s – the period of negative growth was 1990:02 to 1991:03).

¹² But our evidence does not rule out the possibility that they do reflect instead increases in the ‘intensity of work’ as Quiggin (2000) has proposed.