RDP 9509: Australian Wage and Price Inflation: 1971–1994 3. Estimation of the Price and Wage Equations

3.1 The Long-Run Price Equation

Following from the imperfect competition model outlined above, we propose in our price and wage model that firms desire a constant ratio of price on unit costs in the long run with short-run deviations in the ratio the result of shocks and the economic cycle. Assuming that demand does not impact on prices in the long run (i.e. β₁ = 0) and the competitive environment is unchanged then the long-run real wage equation (4) can be interpreted as a simple markup model where prices P are a constant multiple Q of unit costs. For an open economy, these costs include import prices and the long-run price equation can be written as:

where W/Φ is unit labour costs with W the average compensation per employee, Φ labour productivity and P_M is the price per unit of imports. The coefficients β and 1 − β are the long-run price elasticities with respect to unit labour costs and import prices respectively. Long-run homogeneity is imposed with these coefficients summing to unity.

Before we estimate price and wage equations we need to analyse the impact of import prices on the domestic price level. In addition, two issues raised above need be addressed: how to model the large and persistent changes in income shares which have occurred over the past 25 years; and whether or not separate price and wage equations exist. Each of these issues is dealt with in turn before we proceed to estimate the price and wage equations.

3.1.1 The impact of import prices on the domestic price level

Defining the markup as the ratio of price to unit labour costs (equivalent to the inverse of labour's income share), equation (5) can be rearranged to show that the markup is dependent in the long run on the relative price of imports and unit labour costs which we loosely characterise as the real exchange rate (RER):^[12]

Permanent movements in the real exchange rate will result in a shift in the markup and, equivalently, in a shift in labour's long-run income share. Factor shares of income are, therefore, not necessarily stationary (or constant in the long run) but depend on the behaviour of the real exchange rate.

Figure 4 illustrates the real exchange rate as defined above where a rise represents a real depreciation. It is clear that the exchange rate experiences prolonged deviations from its mean level exhibiting cycles of around ten years. Yet it also appears that it reverts to its mean in the long run.^[13] This suggests that shocks to the real exchange rate should have no permanent effect on the markup and labour's share of income but can exert an important influence on income shares and prices for an extended period of time. If the defined real exchange rate is indeed stationary, there must exist a second long-run relationship between import prices and unit labour costs. This relationship is not formally modelled in this paper.

3.1.2 Modelling Australia's changing income shares

In the ten years following the wage shocks in the early 1970s labour's income share was on average around 6½ per cent higher than during the four years prior to the wage shocks (see Figure 2). With the wage restraint associated with the wages pause and the Accord, labour's income share is now not substantially different from its pre-shock level.

This persistent movement in labour's income share suggests long cycles in the relationship between real wages and productivity though labour's income share appears mean reverting over the sample considered.^[14] However, over shorter samples, the mean reverting (or stationary) characteristics of the series are not revealed and the long-run relationship which is identified may be erroneous. By choosing the starting period for the estimation prior to the 1974 wage shocks, labour's income share is mean reverting in a statistical sense and this allows a ‘correct’ characterisation of the long run. While a number of characterisations of the persistent movement in income shares are possible we have chosen the ‘slow adjustment to shocks’ option. In addition, although the relationship between real wages and productivity was subject to a series of potential shocks, the econometric results which follow suggest that OPEC 1 in 1973 and the metal trades decision in 1974 are the only shocks necessary for understanding the observed disequilibrium in income shares.

3.1.3 Identification and the imperfect competition model

Whether or not the wage and price equations of the imperfect competition model are identified was raised in Section 2. In order to estimate separate wage and price equations, variables are required which only appear in one of these equations. Unfortunately, these variables are difficult to discover. Possible candidates, such as unemployment benefits, union strength, and strike activity are themselves endogenous variables and in a bargaining model will impact directly on the behaviour of both labour and firms.

Manning (1994) considers the identification problem and points out that the usual practice is to add dynamics to the model and omit one or more variables (or lags thereof) in one of the equations. This will technically identify the equations so that the system can be estimated but fails to identify the economically important variables which separate the demand and supply curves in the wage-price decision. However, we find that it is prices and not wages which respond to deviations from the long-run markup and this identifies the wage and price equations in an important way.^[15] The estimated model describes a world where firms respond to disequilibria from the long-run markup by adjusting their price (possibly because they set prices after wage costs are known) and labour responds to past inflation and labour market conditions.^[16] We believe that this model is a reasonable representation of the Australian economy.

3.2 The Price and Wage System

The estimation of the price and wage system is based on a vector error correction version of equation (6). The price equation is shown as equation (7) and incorporates inflationary pressures from petrol prices and the business cycle. Also included is the real exchange rate which is considered exogenous for the purpose of estimation.^[17] As noted earlier, the inclusion of a real exchange rate variable implies a long-run relationship between prices, unit labour costs and import prices.

where:

• p^fc private consumption deflator at factor cost;^[18]
• ulc Treasury's national accounts measure of non-farm unit labour costs;
• output gap measured as the log of the ratio of actual to potential non-farm output;
• rer real exchange rate;
• p_m import price deflator; and
• pet petrol prices.

The output gap measure is constructed using potential output as used in the 1994 Reserve Bank Annual Report (Wilkinson 1994) and is defined as the ratio of actual to potential output with an index value of 100 representing full capacity.

The wage equation is shown in equation (8) and relates changes in wages to past changes in both wages and prices as well as labour market pressures with the latter captured by the unemployment rate and strikes.^[19],^[20]

where:

• w average non-farm wages measured on a national accounts basis;
• p private consumption deflator at market prices;
• IU inside unemployment defined as the unemployed with at least 2 weeks of full time work in the past 2 years taken as a percentage of employment plus insider unemployment; and
• stks strikes measured as working days lost as a proportion of employed full and part-time persons.

The standard unemployment rate is a poor measure of labour market pressure because it has suffered structural shifts since the early 1970s. Inside unemployment is a better measure since it does not exhibit these structural shifts and can simply be interpreted as those actively seeking employment with up to date employment skills. Unfortunately, this series begins in March 1979 while the wage and price equations should be estimated from before the wage shocks in the early 1970s to ensure that income shares are stationary. The unemployment gap ratio, however, can be produced for the entire estimation period but has no clear economic interpretation.^[21]

Both these series are presented in the top panel of Figure 5. Over the most recent period, the unemployment gap ratio closely tracks the inside unemployment rate, and can, therefore, be considered a proxy for inside unemployment. This information is utilised to construct an ‘inside unemployment’ or ‘labour market pressure’ series for the entire sample period.^[22] This new labour market pressure variable is illustrated in the bottom panel of Figure 5.

Prior to estimation, the time series properties of the data were considered using the augmented Dickey-Fuller tests along with the test proposed by Kwiatkowski, Phillips, Schmidt and Shin (1992) and the results are reported in Appendix B. These tests generally suggest that, for the sample considered, the level of prices, wages and unit labour costs contain unit roots and the remaining exogenous variables are best characterised as stationary.

From equation (6) it is expected that prices and unit labour costs will move one-for-one in the long run.^[23] The long-run relationship between prices and unit labour costs was investigated using the Johansen (1988), Phillips and Hansen (1990) and unrestricted error correction techniques. In all cases it was found that the normalised long-run coefficient on unit labour costs was insignificantly different from unity and that prices and unit labour costs are cointegrated. These results, therefore, strongly support the view that the markup is stationary over the sample and that there is full pass-through of unit labour costs into prices in the long run.

A theoretically correct systems approach to estimating the price and wage equations would allow for the non-stationary characteristics of the data. The Johansen (1988) vector error correction estimation is one such approach. This procedure however has a number of well known drawbacks. In particular, the estimation requires the same variables to enter each regression of the system.

An alternative approach which overcomes some of the drawbacks is to estimate the wage and price system using the seemingly unrelated regressions (SUR) technique. Because the statistical properties of a SUR with non-stationary variables are unknown, the markup and the real exchange rate were used in the SUR estimation as they are stationary. Comparison of the results from a system estimated by the Johansen technique with one estimated using the SUR technique indicates that the SUR technique does not provide economically different coefficients but generates an improved fit.

The results of the SUR estimation of the wage and price system are reported in the first two columns of Table 1 where insignificant variables were excluded after joint and individual tests of their significance. In order to allow for the expected very fast pass through of cost increases into prices, the contemporaneous change in unit labour costs is included in the inflation equation and the system is estimated using three stage least squares.

Since the markup does not enter the wage equation, the estimates suggest that prices, and not wages, respond to a disequilibrium in the markup.^[24] The coefficient on the markup in Table 1 is significant and represents the speed of adjustment to deviations from the long-run markup. It is almost 14% per quarter and this implies that half of the adjustment to the long run is achieved in the first 4 to 5 quarters.^[25]

The real exchange rate has a significant impact on inflation. Depreciations in the real exchange rate (i.e. rises in rer) lead to an increase in the rate of inflation but a fall in the real wage relative to productivity. Changes in the real exchange rate often persist for a number of years (see Figure 4) and over this time have had a sizeable effect on inflation.^[26] While this is clearly relevant to the setting of policy, the impact eventually disappears as the real exchange rate returns to its long-run value.

Two measures of capacity utilisation are used in the price and wage system. The first is the potential output gap which is found not to significantly explain price inflation conditional on unit labour costs.^[27] This result conforms with the general view that firms do not ‘price to demand’ and the markup is independent of the business cycle given the level of costs.^[28] The second measure is inside unemployment. Interestingly, it is changes and not the level of inside unemployment which significantly impact on wage inflation even though this measure of labour market conditions already incorporates some form of hysteresis in the labour market by excluding the long-term unemployed from affecting the wage outcome.^[29] In addition, the strikes variable is significant in the wage equation with the expected positive sign.

A number of dummies were incorporated in the initial estimation to capture the sometimes erratic nature of the wage process and the possible non-linear response of firms to surges in wages and costs. Somewhat surprisingly, dummies to capture the mining wage boom, OPEC 2, the wage pause and the Accord were all insignificant. Two dummies remain in the final specification and capture the turbulence of the years surrounding OPEC 1. In the price equation the June and September 1973 dummy has a positive impact on prices. This implies that prices rose by more than the model would otherwise predict. However, even given the increased price response of firms, the price rises were not sufficient to fully absorb the cost increases in the period and the markup fell.

The second dummy appears in the wage equation and coincides with the timing of the Metal Trades decision in September 1974. This dummy does not appear in the price equation which suggests that the model successfully predicts firms' price responses to the wage shock in that period.

3.3 Steady State Inflation

It is important that the price and wage system allows a range of possible inflation rates in the steady state. This property of the system can be achieved in a number of ways. Consider the following simplified version of our estimated price and wage system:

where Γ_p and Γ_w are the constants and the other exogenous variables from the price and wage equations respectively. Long-run linear homogeneity between prices and unit labour costs is imposed in equation (9) through the markup where π = p − ulc.

The steady state properties of the model depend on the short-run coefficients δ₁ and λ₁ on the price and wage inflation terms in the model. Using this simplified model we can distinguish between homogeneity in price and wage levels and homogeneity in price and wage inflation rates. The former is imposed in the model due to the long-run linear homogeneity condition. In this case, the markup is unaffected by a doubling of the level of prices and unit labour costs leaving steady state inflation unchanged and no real effects. Homogeneity in price and wage inflation rates, which we will refer to as short-run homogeneity, exists if δ₁ = 1 and λ₁ = 1 in the model. Consequently, if inflation is doubled in the steady state then the markup is unaffected and again there are no real effects.

The system displays distinctly different steady state properties depending on whether δ₁ and/or λ₁ are equal to unity. Three relevant combinations of these coefficients are considered in Table 2. When δ₁ = 1 and λ₁ = 1, short-run homogeneity is present along with the imposed long-run homogeneity and the system displays the properties of a standard macroeconomic model.^[30]

The second combination corresponds to our unrestricted system estimated above where we find both δ₁ < 1 and λ₁ > 1. In this case, the system displays the undesirable property of a unique rate of inflation in the steady state which conflicts with standard theory.^[31] This undesirable property disappears in the third combination of the coefficients when δ₁ < 1 and λ₁ = 1. In the empirical analysis of the unrestricted system, the restriction that δ₁ = 1 is comprehensively rejected in the price equation yet λ₁ = 1 is accepted for the wage equation. The price and wage system was, therefore, re-estimated having imposed a coefficient of unity on lagged inflation in the wage equation. Estimation results of this restricted model are reported in columns 3 and 4 of Table 1. As may be expected there is little impact on the coefficients of the price and wage equations providing some indication of the ready acceptance of the restriction.

The restricted model now displays a range of possible inflation rates in the steady state. However, the model differs in an important way from the standard model in that the markup and inflation are negatively correlated in the steady state (see column 3 of Table 2). This result follows because δ₁ < 1 in the price equation.

The nature of long-run linear homogeneity is subtly changed in the restricted model. In the standard macroeconomic model, increases in unit labour costs are fully reflected in higher prices in the long run irrespective of the rate of steady state inflation. This is in contrast with the restricted model where increases in unit labour costs are fully reflected in higher prices only if there is no change in steady state inflation. As the markup and inflation are negatively correlated in the steady state, increases in unit labour costs which are associated with a shift in steady state inflation imply the markup has also changed and, therefore, the cost increase is not fully passed through into prices.

Inflation in the restricted model consistent with a given markup and with all the exogenous variables at their steady state values is illustrated as the solid line in Figure 6. Also shown as a scatter plot are the actual combinations of annual inflation and the markup. The negative correlation between inflation and the markup in the steady state is apparent in the estimated restricted model (the solid line) and in the data. This steady state relationship appears important. It is estimated that a 1 percentage point increase in annual steady state inflation is associated with a reduction in the markup by 1 percentage points.

The years 1973/74 and 1974/75 are two obvious outliers on Figure 6 and coincide with the wage shocks at the time of OPEC 1. By following the annual observations in chronological order in the figure we see the persistence of the shocks to the markup. Starting with the 1972/73 observation, the real wage shocks saw the markup fall and inflation rise dramatically. The markup slowly recovers and inflation slightly declines after 1975/76 until real wages again rise substantially relative to productivity in the early 1980s. The wage pause and Accord complete the process begun with OPEC 1 and the markup finally recovers to around its initial level in the late 1980s.

While the negative correlation between inflation and the markup conflicts with standard macroeconomic models, two explanations are offered in the literature. Bénabou (1992) explains the negative correlation through a reverse chain of causality, arguing that higher inflation increases search in customer markets which leads to greater competition and this results in a lower markup. Bénabou supports this view by showing that expected and unexpected inflation significantly reduce the markup using United States retail sector data. Alternatively, Russell (1994, 1995) explains the reduced markup when inflation increases as the cost that non-colluding price setting firms pay to avoid the repercussions of poor price coordination as they respond to changes in demand and costs. Russell demonstrates that the negative correlation in the steady state between inflation and the markup is also present in the data for the United States, the United Kingdom, Japan and Germany.

In Figure 6 the dispersion of the data points around the steady state inflation line is due to the lags in the data, the impact of the exogenous variables on inflation and shocks to the system. The exogenous variables also impact on the markup due to the different timing and response of wages and prices to these variables. As mentioned above, one of the difficulties encountered when estimating price and wage inflation is the sustained shifts in income shares over the sample. It is of interest, therefore, to see whether the system can accurately predict these shifts in income share. More importantly, as inflation and the markup are negatively correlated in the steady state then if the model fails to explain the observed range in the markup it also fails to explain the observed range in steady state inflation. To this end, Figure 7 shows the actual markup and the markup predicted by the restricted price and wage system using a dynamic forecast.^[32] While the predicted markup appears to forecast movements in the markup fairly well, there are periods when there are discrete shifts in the level of the actual markup which are not captured by the model. This is made evident by the relatively low correlation between the predicted and actual level of the markup (0.57) compared with the correlation between the changes in these series (0.62). Particularly obvious is the range of the predicted markup is considerably less than that of the actual markup. It appears, therefore, that there are periods when some non-model influence impacts significantly on the level of the markup. However, the model does well at explaining movements in the markup given these unexplained shifts in the level of the markup.

3.4 The Impact of Inside Unemployment, the Real Exchange Rate and Strikes on Inflation

For the estimated system, the exogenous variables impact on inflation directly and indirectly by causing the markup to vary. The lower three panels of Figure 8 show the estimated contributions to inflation of changes in inside unemployment, the real exchange rate and strikes for a given markup.^[33] We see that changes in inside unemployment can explain up to 1½ percentage points in annual inflation in short lived episodes over the sample. In contrast the impact of the real exchange rate on inflation is more persistent and powerful. For example, as a result of the depreciation in the real exchange rate in the mid 1980s, it is estimated that this led to inflation being around 3 percentage points higher than its steady state level in September 1987. The bottom panel shows the dramatic reduction the impact strikes have had on inflation since the onset of the wages pause and Accord.

Footnotes

This definition of the real exchange rate may not be as ‘loose’ as first thought. It is similar to the measure of the relative price of traded and non-traded goods used by Swan (1963) in his classic article. [12]

Although the graphical evidence of stationarity of the real exchange rate is apparent in Figure 4 the statistical evidence is less clear. The augmented Dickey-Fuller (ADF) (Said and Dickey (1984)) and the Kwiatkowski, Phillips, Schmidt and Shin (1992) (KPSS) tests provide conflicting results. See Appendix B. While using a different measure of the real exchange rate, Gruen and Shuetrim (1994) support the finding of stationarity. [13]

The KPSS test and graphical analysis support the view that labour's income share is stationary. However, the ADF test contradicts this result. See Appendix B and Figure 2. [14]

The impact of disequilibrium from the long-run markup on prices and wages was investigated within the Johansen framework. It was found that the speed of adjustment coefficient was significant in the price equation yet insignificantly different from zero in the wage equation. See Johansen (1991). [15]

This result is not always found. Franz and Gordon (1993) find disequilibria in the markup impacts on price but not wage adjustment for the US. In contrast, Franz and Gordon (1993) using German data and Cozier (1991) using Canadian data find the reverse relationship exists. Mehra (1993) using US data finds conflicting results depending on whether prices are measured by the GDP deflator or CPI. [16]

The price equation is similar to that estimated by de Brouwer and Ericsson (1995) but excludes the level of petrol prices in the long-run relationship. [17]

The indirect tax rate was calculated as non-farm indirect taxes plus subsidies as a proportion of non-farm GDP at factor cost. To provide a price series at factor cost the consumption deflator was divided by 1 plus the indirect tax rate. [18]

Unemployment benefits were also investigated as a source of inflationary pressure. Unfortunately this series does not exist prior to December 1976. The variable was included in a number of forms to reflect its possible role as a measure of the opportunity cost of work or leisure but remained insignificant over the shorter sample from December 1976. [19]

For a survey of work on Australian wage equations see Lewis and MacDonald (1993). [20]

The unemployment gap ratio is defined as the difference (or gap) between actual unemployment and unemployment ‘smoothed’ by a Hodrick Prescott filter divided by smoothed unemployment. The scaling of the unemployment gap by smoothed unemployment was thought necessary as the structural shifts impact on the unemployment gap as well as the level of unemployment. This can easily be observed during the three recessions in the sample. These recessions are of roughly similar size but the unemployment gap in the 1974/75 recession is very small in absolute terms compared with the following two recessions. It appears, therefore, that the unemployment gap not only depends on the business cycle but is also related to the level of unemployment. [21]

The spliced inside unemployment rate was obtained by first estimating the relationship between inside unemployment and the unemployment gap ratio for the period from 1979:Q1 to 1994:Q2 as a simple distributed lag model. Back-casts of inside unemployment are then produced for the period prior to 1981:Q2 and finally this new series is spliced with the actual inside unemployment data. [22]

This result is expected given that the real exchange rate is stationary and enters as a separate and exogenous variable. An alternative modelling strategy is to introduce import prices as a separate variable in which case we expect the sum of the coefficients on unit labour costs and import prices to be unity. [23]

The null hypothesis that the speed of adjustment coefficient in the wage equation is zero was tested within the Johansen framework. The likelihood ratio test statistic is = 0.56 (Prob. value = 0.46) and the null hypothesis is not rejected at the 5% level of significance. This suggests that if the price equation described the full set of the parameters of interest, wages could be described as weakly exogenous and a single equation approach pursued for modelling inflation. Since it remains the objective of this paper to estimate both wage and price equations, a systems approach was preferred. [24]

The median lag is calculated as − log2/log(1 + γ) = 4.7 where γ = −0.137 is the speed of adjustment coefficient. [25]

An equivalent representation of the long-run relationship relates prices to unit labour costs and import prices as in equation (5). Rearranging the estimates in Table 1, the implied long run in this form is price = 0.76 unit labour costs + 0.24 import prices. This implies that a 10 per cent increase in import prices will eventually increase the price level by 2.4 per cent given the level of unit labour costs. These long-run coefficients may be interpreted as the response of prices to changes in costs if the real exchange rate were not to adjust back to its pre-shock level. [26]

Detrended private final demand was also investigated as a measure of excess demand and found not to impact significantly on price inflation. This result is in contrast with that of de Brouwer and Ericsson (1995) where they find that detrended final demand impacts on inflation. However, their model does not include a wage equation and is over a shorter sample. [27]

Layard, Nickell and Jackman (1991) conclude after surveying the mixed empirical findings on the impact of demand on prices that prices are relatively unresponsive to demand. See also the references cited in footnote 5. [28]

In standard models, hysteresis is identified by a significant coefficient on changes in total unemployment. [29]

This follows in any standard model which incorporates a vertical long-run Phillips curve. [30]

Because the unrestricted system has a unique inflation rate in the steady state, the markup is also unique. [31]

The dynamic forecast was calculated using the exogenous variables and the forecasted endogenous variables. [32]

The lower three panels of Figure 8 show the contributions to the change in inflation rather than the level of inflation. The unexplained component of the change in inflation is conceptually due to unexplained shocks to the markup. [33]