RDP 2003-10: Productivity and Inflation 6. Robustness

There are two principle ways we test our findings' robustness: one splits the sample; the other includes additional control variables that may substitute for inflation in the productivity-inflation relationship. The test is whether a significant relationship remains despite including these alternative controls. There are a number of factors that limit the testing we can do. First, we have limited observations: 34 in the full sample, 17 when we split it, leaving 9 degrees of freedom if we include alternative controls in the sub-samples. Second, we are estimating this system over six industries, across three periods, using two measures of productivity growth, so we would expect some of our results to be incorrect when applying a 10 per cent confidence level. These considerations mean we use the following discussion to suggest where the weight of evidence lies rather than focusing on individual results.

6.1 Robustness to Sample Period

First we assess the relationship's robustness across different periods. The Australian inflation-productivity growth experience is unlike those of the G7 countries studied elsewhere as productivity growth does not slow until the 1980s (see Table 1). Yet the relationship remains when limited to observations over different samples (Table 7).

Table 7: Productivity Growth and Inflation Model: Robustness Tests
Relationship between IPDs and industry productivity growth
IPDs to labour productivity model:
Ait = αi + β1Ait−1 + β2Ait−2 + β3Pit−1 + β4Pit−2 + β5Yit + εit,
where A is labour productivity growth
  1967–2002   Pre-1986 sample   Post-1985 sample
Coefficient R2   Coefficient R2   Coefficient R2
Mining ** 0.45   ** 0.68   +** 0.69
Manufacturing 0 0.08   0 0.29   0 0.32
Utilities ** 0.20   ** 0.43   0 0.09
Construction +** 0.26   +** 0.64   0 0.13
Wholesale & retail trade ** 0.46   ** 0.75   ** 0.59
Transport, storage
& communications
0 0.21   0 0.53   0 0.39
IPDs to multifactor productivity model:
Ait = αi + β1Ait−1 + β2Ait−2 + β3Pit−1 + β4Pit−2 + β5Yit + εit,
where A is MFP growth
  1967–2002   Pre–1986 sample   Post–1985 sample
  Coefficient R2   Coefficient R2   Coefficient R2
Mining ** 0.41   ** 0.39   0 0.69
Manufacturing 0 0.25   0 0.36   0 0.44
Utilities 0 0.39   ** 0.58   0 0.61
Construction +* 0.20   +** 0.68   0 0.28
Wholesale & retail trade ** 0.47   0 0.72   ** 0.54
Transport, storage & communications 0 0.30   0 0.62   0 0.31

Notes: 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. Number of observations: full sample = 34; pre-1986 sample = 17; post-1985 sample = 17. Number of parameters = 5.

When the sample is split only 12 degrees of freedom remain, and this is likely to have a non-trivial effect on the significance of our results. Furthermore, there is less variation in inflation in the post 1986 sample and, correspondingly, relatively more noise. Nonetheless, where the sub-sample results are significant, they are generally of the same sign as the full sample results.

6.2 Robustness to Additional Control Variables

Other variables may be more closely related to productivity growth than inflation, and hence reduce the significance in our model. There are three groups of possible variables other than inflation that we consider. The first group focuses on the uncertainty aspect of higher inflation rates. We know higher levels of inflation are associated with more variance in the inflation rate,[27] hence with greater cyclical volatility (Blanchard and Simon 2001). Perhaps a range of variables measuring output and aggregate inflation variability would also predict productivity growth. A second group of variables focuses on the business cycle aspect of inflation. The final group looks at agents' predictions of aggregate inflation, with the premise that agents determine their behaviour more by these than the actual inflation outcomes.

Returning to first principles, the primary role of prices is as an efficient means of transmitting information about relative supply and demand conditions in diverse parts of the economy. By definition, inflation is a period of rising prices. But prices generally do not rise smoothly; instead, there is an iterated process of prices jumping levels. These changes do not necessarily happen in a coordinated or consistent way. And therein lies the problem for agents. Because the relative prices of a firm's inputs and outputs change faster during inflations, the firm has to be able to distinguish between a change in relative scarcities and a rise in the overall price level. Thus the firm's essential function of determining optimal input and output combinations becomes more complex.

We can test this theory and observe whether it offsets the IPDs' role in explaining productivity growth in a variety of ways. One approach is to focus on the effects of uncertainty in general. To do this we treat uncertainty and volatility as synonymous. We can observe the relationship between productivity growth and variability in real output, the CPI, and inflation expectations as measured by the Economic Group Bond Market Inflation Expectations series and by the Melbourne Institute-Westpac inflation expectations survey. ‘Variability’ is measured in two ways: the standard deviation of the quarterly data across a window of the previous 5 years, and as the error in the predicted level of the variable from an autoregressive model, run from 9–16 quarters prior to time t.[28] We chose the 2-year lag between the autoregressive system and the actual inflation outcome to approximate the lead-time between a business decision (e.g., investment in a new technology or organisational structure) and its appearance in the firm's productivity performance.

Over the full sample, the only consistent effect of including the standard deviation of the GDP deflator, CPI inflation and bond market inflation expectations is to make the standard errors of our Granger causality coefficients larger, but generally not so as to make the IPDs insignificant. This outcome is not unexpected given adding these variables means two more parameters are being estimated, hence 2 fewer degrees of freedom are available. The coefficients of the alternative variables are generally insignificant, with parameter estimates varying widely as different lags are included in the estimates. The best performing addition is the standard deviation of the GDP deflator,[29] but it shared the other variables' inability to perform better than the IPDs at explaining productivity growth. For example, CPI inflation's standard deviation only significantly explained productivity growth in the utilities equation. The autoregressive CPI predictions based on past CPI inflation and bond market inflation expectations were even less effective in our models.[30] In sum, the IPDs consistently outperform intuitively sensible alternatives at explaining productivity growth.[31]

A criticism of earlier studies is that they ignored cyclically as a driver of the apparent prices and productivity growth relationship.[32] While the model estimated in Table 7 does include an industry-specific output gap, some other variable may be more appropriate. We consider interest rates (both nominal and real), growth of industry and aggregate value added, and the change in the ratio of capital to labour inputs. None of these emerge as significant.[33]

In summary, the model seems to pass the robustness tests as well as could be expected given the limitations created by the number of observations. Our results suggest that, at the least, something that is highly correlated with inflation causes changes in the rate of productivity growth.[34] Furthermore, this is something that has remained correlated through some quite substantial monetary policy regime changes. Section 7 proceeds on the basis that inflation is, in fact, causing the changes in productivity growth. On these foundations, it suggests a means of tying down the transmission mechanism, building on insights from the various industries' differing experiences.


There is a succession of important papers on this point, dating from Okun (1971); Taylor (1981) is a classic reference. [27]

Both these approaches require quarterly data, thus excluding the only annually available IPDs. [28]

This explained IPD growth in the productivity-to-prices equations (see Appendix E) for mining, manufacturing and utilities at the 5 per cent confidence level, which tells us that higher IPDs are associated with greater volatility in the aggregate inflation measures – not a remarkable result. [29]

This result does not imply that uncertainty does not play a role in inflation's effect on productivity growth. Instead, this merely indicates that we have not been able to locate a better proxy for this uncertainty than our IPDs. [30]

All of these results are available upon request from the authors. [31]

See especially Sbordone and Kuttner (1994). [32]

The exception is the change in the industries' respective real GVA, which was significant and negative, but generally did not dramatically alter the IPDs' coefficients and standard errors. This result is limited to the multifactor productivity growth equation. Again, all of these results are available upon request from the authors. [33]

A possible alternative explanator relates to variations in labour's relative share of total output. However, this variable is not significant when added to our model, and does not materially affect the coefficients on the IPDs. Again, these results are available from the authors. [34]