3  Approaches to measuring productivity

This section summarises four prominent approaches to productivity measurement: the growth accounting approach; the index number approach; a distance function approach; and the econometric approach.

3.1  Growth accounting

Growth accounting enables output growth to be decomposed into the growth of different inputs (typically capital and labour) and changes in total factor productivity. Growth accounting requires the specification of a production function that defines what level of output can be produced at some particular time given the availability of a certain level of different inputs and total factor productivity.

The production function is written as:

where is output at time t, represents total factor productivity at time t, is the capital stock at time t, and is a measure of the labour available at time t.

The growth accounting approach is based on several important assumptions. The first is that the technology or total factor productivity term, , is separable as in (3). The second is that the production function exhibits constant returns to scale. Third, it is assumed that producers behave efficiently in that they attempt to maximise profits. Finally, it is assumed that markets are perfectly competitive with all participants being price-takers who can only adjust quantities while having no individual impact on prices.

Differentiating with respect to t gives[12]:

(4)    

where the dots indicate a first partial derivative with respect to time. Dividing by gives:

(5)    

The elasticity of output with respect to labour and the elasticity of output with respect to capital can be written as:

and therefore (5) can be rewritten as:

(6)     

Solving (6) for (),the growth rate of TFP, gives:

(7)     

Thus TFP growth is a residual, in that it represents that part of the total growth of real output that cannot be explained by growth in labour or capital inputs alone.

To apply (7), estimates of and (the output elasticities) are required. These are typically not readily available. However, if it is assumed that the production function takes a Cobb-Douglas form with constant returns to scale:

(8)     

and that the factors of production are paid their marginal products, then , is equal to the share of income paid to capital and equals the share of income paid to labour. From equation (7) it is apparent that if we have data on the growth rate of real output (), the growth rate of the capital stock (), the growth rate of labour inputs () and capital and labour’s share of income (which correspond to and ) then we have enough information to obtain an estimate of TFP growth ().

The use of an underlying production function other than a Cobb-Douglas function will often mean that it is not appropriate to equate output elasticities with factor income shares. Consequently the use of a different production function yields different results compared with TFP estimates based on a Cobb-Douglas production function.