RDP 2003-10: Productivity and Inflation Appendix E: Reverse Causal Flow

Table 4 presented the results for the model of inflation's effect on productivity growth. Table E1 reports the results for the reverse direction of productivity's effects on inflation.

Table E1: Productivity Growth to Inflation Model
Industry productivity growth's causal effect on IPDs, with two lags on price and productivity variables: 1967–2002
  From labour
productivity to IPDs
  From multifactor
productivity to IPDs
Coefficient R2 Coefficient R2
Mining 0 0.20   0 0.19
Manufacturing + 0.42   +** 0.55
Utilities 0 0.38   +* 0.46
Construction 0 0.10   +* 0.12
Wholesale & retail trade +* 0.52   +** 0.54
Transport, storage & communications 0 0.31   +** 0.37

Notes: Number of observations = 34; number of parameters = 5.

We see that there is little relationship for labour productivity but a predominant positive effect from MFP to inflation. Intuitively this doesn't make a lot of sense and it is also at odds with the results that show higher inflation causing lower productivity. Nonetheless, following an idea from Lowe (1995) we consider whether this may reflect the operation of a third, omitted factor: wages. Lowe argues that higher nominal wage growth is associated with faster productivity growth, and conversely that when an industry's real product wages[44] fall, that industry's labour productivity will also fall as it employs more workers, particularly more marginal workers. Further, Lowe argues nominal wages should also explain the IPDs. For this reason we re-estimate the model reported in Table E1 with an added wages measure.[45]

Our measure of wage growth excludes the cyclical elements of employee compensation, such as overtime payments and bonuses.[46] At risk of stating a truism, these cyclical elements are closely correlated with the business cycle in a way that is different from the underlying growth in wages. For example, hourly overtime rates are greater than ordinary time rates, which means faster than underlying growth in hourly wages during upswings when more overtime hours are worked. We wish to assess the hypothesis that productivity growth affects underlying wage growth, which in turn drives the IPDs, not simply the story that wage growth explains the industry IPDs through cyclical co-movement. And so it is important that the wage growth measure we use only incorporates the productivity-related part of wage growth, and is ‘cleaned’ of the purely cyclical elements.

Adding wage growth to our model of productivity growth's effect on price growth has only a marginal effect on the productivity growth coefficients, although the wage growth coefficients are uniformly of the expected sign and significant in all but one equation. Table E2 reports the results of interest.[47]

Table E2: Productivity Growth and Inflation Model with Wages' Growth
Relationship between IPDs and industry productivity growth with ordinary time wage growth: 1967–2002
Labour productivity to IPDs model:
Ait = αi + β1Ait−1 + β2Ait−2 + β3Pit−1 + β4Pit−2 + β5Yit + β6Wit−1 + εit,
where A is labour productivity growth, W is growth ordinary time earnings
Coefficient Productivity Wages' growth R2
Mining 0 +** 0.32
Manufacturing 0 +** 0.78
Utilities 0 +** 0.56
Construction 0 +** 0.56
Wholesale & retail trade +** +** 0.62
Transport, storage & communications + +** 0.48
Multifactor productivity to IPDs model:
Ait = αi + β1Ait−1 + β2Ait−2 + β3Pit−1 + β4Pit−2 + β5Yit + β6Wit−1 + εit,
where A is MFP growth, W is growth ordinary time earnings
Coefficient Productivity Wages' growth R2
Mining 0 +** 0.34
Manufacturing +** +** 0.80
Utilities +** +** 0.63
Construction 0 +** 0.56
Wholesale & retail trade +** +** 0.63
Transport, storage & communications +** +** 0.52

Notes: Number of observations = 34; except utilities equations where number of observations = 29.
Number of parameters = 6.
Like Table 4, this table contains the results from two tests. The signs indicate whether the lagged independent coefficients sum to a sign significant at the 10 per cent confidence level. A 0 indicates the coefficients have no determinable sign. * and ** represent the results from the conventional Granger causality tests, on the joint significance of the lagged coefficients. * and ** indicate the relevant lagged explanators are jointly significant at the 10 per cent and 5 per cent levels, respectively. Utilities' wages data only commence in 1974. As the SUR estimation does not manage unbalanced data, the results in this table come from excluding utilities from the SUR, then running a second SUR including utilities to observe the relationship for that sector.

The wage growth coefficient is significant in all but one equation and of the expected sign. However, adding wage growth has only a marginal effect on the labour productivity and multifactor productivity growth equations. For labour productivity there was not much of a relationship to start with so this is unremarkable. For MFP it shows that the problem remains.

These results clearly show that wages affect inflation. However, the wages' growth variable does not account for the curious causal relationship between growth in multifactor productivity and the IPDs. We added a range of other variables and tried alternative but intuitively sensible models, but were unable to explain the results in Table E2. Given the odd relationship predominately appears in the multifactor productivity growth equations, a possible explanation may be the measurement issues with our multifactor productivity growth series. Measuring multifactor productivity growth as a residual of an output function means the series also captures the measurement error in capital – which is especially hard to measure accurately – and the aggregate hours and real and nominal GVA series. However, this explanation is unconvincing given multifactor productivity growth behaved similarly to labour productivity growth in the model observing price growth's effect on productivity growth. So, in sum, the results for MFP growth remain anomalous, and a potential area for future research.


Lowe (1995) defines real product wages as nominal wage growth deflated by the IPD. For clarity, contrast this with real consumption wages, which are nominal wages deflated by the CPI – Lowe (1995) argues this version of wages should not effect employment, hence productivity. [44]

Madsen and Damania (2001) find empirical support for a positive relationship between wages and productivity in OECD countries. [45]

The measure used is the growth in average weekly ordinary time earnings per hour worked, for full-time, non-managerial adult males in both private and public sectors, using averages for the year-to-August where possible. This series was the only wage information running the full length of our productivity series clean of business cycle variations.
There is an alternative labour compensation measure, namely the labour income measure in the national accounts. Although this measure also runs the full length of the sample, it has two disadvantages: a) it does not fully remove the cyclical component of employee compensation (e.g., bonuses, overtime payments, etc); and b) the series is used to calculate industry GVA and hence is highly correlated with the productivity measures. An independently calculated series seems preferable. [46]

When included in the equations explaining productivity growth, the sign on wages is less well behaved and appears to have a less determined effect on the lagged IPD coefficients. This is not inconsistent with Lowe's (1995) thesis. (Results are available upon request from the authors.) [47]