4.5  Labour market

4.5.1  Employment and participation

(i) Steady-state equations

The labour force (nts) is equal to the product of the participation rate and the working-age population. In steady state, the participation rate (partt, based on filtering historical data, see Section 7.3) is an exogenous assumption, as is the working-age population.

where rpop3_eq is the ratio of Household Labour Force Survey (HLFS) working-age population to Statistics New Zealand estimated resident working age population.

In steady state, unemployment (urt) is set equal to the NAIRU which is exogenous. Guy and Szeto (2004) provided evidence that the NAIRU may change over time depending on the structure of the economy and government policy. This and an exogenous assumption with respect to government employment (ngg_eq) form an identity with private sector employment (nsr):

If we multiply private sector employment by an exogenous hours paid per week assumption (prhr_eq) (multiplied by 13 to get hours paid per quarter) we get aggregate hours paid in the private sector (nthpr1), which is used as an input into the production block.

(ii) Dynamic equations

The main driver of hours paid (nthpr1) in the economy is the firm's demand for hours from the dynamic production block (ie, the medium-run profit-maximising value, nthsr ). This adjustment term towards the production block value and a lag (nthpr1(-1)) are used to introduce a sluggish response towards the firms' profit maximising number of hours paid. The reason hours paid do not immediately match the firm's demand in the model can be justified by the presence of search costs (time and effort it takes to find new workers) introducing frictions into the labour market. The profit margin, as proxied by the profit-maximising price of the domestic good relative to the current price of the domestic good (rpydmr), is included to capture the idea that when profits are high, firms will demand more labour.

Knowing aggregate hours paid, and using an exogenous assumption of hours paid per person per week (prhr_a; multiplied by 13 to get hours paid per person per quarter), we can calculate the number of people employed in the private sector (nsr) using the following identity:

Adding government employment to this (an exogenous assumption) we get the number of people employed in the whole economy.

To derive the labour force, we need to know the participation rate. In the dynamic model, the participation rate depends on its lag, adjustment toward its steady-state value as well as the extent to which unemployment is above or below the NAIRU -capturing the idea that a labour market with relatively more unemployment will mean fewer people participating due to a discouraged worker effect.[12]

We can calculate the labour force using equation (4.5.1). Unemployment can be calculated using the identity that unemployment is equal to the labour force minus those employed.

4.5.2  Wages

The steady-state value of real average earnings (rwa) is based on the hourly wage (rhw) from the production block (see Section 3.1) and an exogenous hours paid per week(prhr_eq; multiplied by 13 to get hours paid per quarter).

In the dynamic model, wage growth (inf_hw) depends on:

• an exogenous labour productivity assumption (a1, see section 8.3 for how this is determined) − if the marginal product of labour increases, labour should be paid more
• the ratio of the profit-maximising price level of ydo to its actual level (rpydmr)[13] - this variable is used as a proxy for the profitability of firms (ie how close the current price of the domestic good is to its profit-maximising price). Relatively low values of rpydmr mean firms can afford to pay workers more
• previous inflation (inf, second lag) and inflation expectations (infe, first lag) - to reflect the role inflation plays in wage setting, note both these variables are lagged to reflect the fact that wage bargaining tends to be backward looking
• tightness of the labour market (proxied by the derivation of unemployment from the NAIRU) - this is a proxy for the bargaining power of workers, and
• an equilibrium adjustment term (rhw/erhw).