5.3  Output (GDP)

Definitions of Output

Productivity measures can be based on different definitions of output, gross output and value-added based measures. Gross output and value added can be thought of as different representations of the production process. Gross output measures the goods or services that are produced within an economic unit and that become available for use outside the unit. It represents the value of sales and net addition to inventories but does not factor out the purchase of intermediate inputs. Value added takes gross output as a starting point and deducts the purchase of intermediate inputs. The following discussion draws heavily on the OECD’s Productivity Manual (2001).

Consider the following production function, which relates the maximum quantity of gross output (Q) that can be produced from all inputs.

(22)      ⇒

Inputs consist of primary inputs (comprising labour and capital) and intermediate inputs . The parameter captures shifts in what the OECD calls disembodied technology. However, given Carlaw and Lipsey’s critique that was discussed in Section 2.2, it is more appropriate to think of this as TFP or MFP and not technology. Consequently technological change should be thought of as the growth in MFP. To maintain consistency with the source, the terminology used by the OECD is used throughout this section, but the difference between technological change and MFP or TFP should be kept in mind. Technological change has been assumed to be ‘Hicks-neutral’. One way to think of technical change is the rate at which the production function shifts over time (ie, ). With Hicks-neutral technological change equals.[22] The OECD productivity manual calculated MFP growth as the difference between the growth rate of a Divisia index of output and a Divisia index of inputs. The Divisia index of inputs is made up of the logarithmic rates of change of primary and intermediate inputs, weighted by their respective shares of total input cost (denoted and ). Consequently:

(23)    

where equals the percentage growth rate in MFP based on a gross output measure of output.

Instead of defining a production function, one may define a value added function that illustrates the maximum amount of current price value added that can be produced, given a set of primary inputs and given the prices of intermediate inputs and output , ie:

(24)    

If we define productivity change as the shift in the value added function and measure this as the difference between the growth rate of Divisia volume index of value-added and the growth rate of the Divisia index of primary inputs we can write:

(25)    

where equals the percentage growth rate in MFP based on a value added measure of output.

There is a direct relationship between the two MFP growth measures outlined in and , with this relationship being shown below:

(26)    

where is the nominal share of value-added in gross output. As, MFP growth measures based on value added will be greater than MFP growth measures based on gross output.

How should these two different MFP measures be interpreted? When production technology is Hicks neutral the gross output based productivity measure is a valid representation of disembodied technical change, however this is not the case for the corresponding value added based measure. Technology change in the value-added based measure reflects the ability to translate technical change into income and into a contribution in final demand (OECD, 2001). This interpretation is dependent on equation being a valid representation of the production process. If technological change only operates on primary inputs then this is no longer the case and the value-added based measure becomes the valid measure of technical change and the gross output measure loses its significance.[23] When the unit of interest, such as a firm or industry, is subject to vertical integration and outsourcing, the gross output based TFP measure is usually considered superior as this measure gives a better indication of how much extra delivery to final demand per unit of primary inputs a firm or industry generates.

Extrapolation

In order for productivity measures to be valid it is important that price and quantity indices of output are constructed independently of price and quantity indices of inputs. An example of when this independence assumption is breached is when quantity indices of outputs are based on extrapolation of input series.

From the perspective of productivity measurement, the independence of statistics on inputs and outputs is key. Input-based indicators that are used to deflate output series generate an obvious bias in productivity measures: (labour) productivity growth will either be zero by construction or will reflect any assumption about productivity growth made by statisticians. Occurrences of input-based extrapolation are concentrated in activities where market output prices are difficult to observe. This may create a case for excluding from productivity measurement those industries that are characterised by a large share of non-market producers and thereby avoiding potential biases in output measurement.

OECD, 2001: 33

This paper does not go into detail on how New Zealand output measures are constructed but it should be noted that extrapolation based on input measures is important for measuring output in some industries. For example, the contribution to gross domestic product made by the government services industry involves extrapolation by an employment volume indicator.