1 B&W s derivation of the Phillips curve Wage and price setting. Slides for 26. August 2003 lecture Ragnar Nymoen University of Oslo, Department of Economics Ch 12.3: The Battle of the mark-ups as a framework for understanding inflation. Using the notation in B&W we have W P =(1+θ) (Y/L) price setting (12.4 ) W/P e =(1+γ) Y, wage setting (12.5 ) L θ represents firms setting prices as a mark-up on unit labour costs, and γ represents workers and union strive to set the expected real wage as a markup on average productivity. If we substitute W in (12.4 ) from (12.5), we obtain August 26, 2003 1 P =(1+θ)(1 + γ)p e, (12.6) the price level depends only on the price expected by wage negotiators which hence becomes a nominal anchor in this model. 2 From level to dynamics: P 1=(1+θ)(1 + γ)( P e 1) + (1 + θ)(1 + γ) 1 P 1 P 1 P 1=(1+θ)(1 + γ)( P e 1) + θ + γ + θγ P 1 P 1 Introducing: π = P 1 P 1 for inflation, and π = P e 1 P 1 for core inflation we obtain: π =(1+θ)(1 + γ) π + θ + γ + θγ = π + θ + γ + θ π + γ π + θγ π + θ + γ Next B&W hypothesize that the mark-up moves pro-cyclically: θ + γ = a(y Ȳ )= b(u Ū) (12.7) where Ȳ is the trend component of output (or GDP), whereas Ū is the equilibrium level of the unemployment rate. The right hand side equality is referred to as Okun s Law (cf Ch 11). Thus we can draw this Phillips curve either in a π, Y diagram (AS schedule) or on a π, U (Phillips curve) diagram, see Fig 12.5. To either version of the story, B&W add (additive supply) shocks, denoted s, hence we have π = π + a(y Ȳ )+s (12.11) = π b(u Ū)+s 3 4
What is on B&W s mind? Are the static equations (12.4 ) and (12.5) meant to be interpreted as behavioural relationships or as long-run steady state relationships? Either interpretation has its drawbacks/inconsistencies. 1. Behavioural equations: But then, for given expectations, prices and wages are reacting without lags to changes in productivity (and changes in the mark-up). We know that this is not even approximately true: In the real world there are substantive lags. 2. Long-run steady state relationships: Inconsistent then to include price expectations. In a steady-state, there is no room for expectation errors. Before we return to B&W we will take a detour into a more coherent approach to wage-price dynamics, where we build on the insight that relationships between wage and price levels are best interpreted as hypothetical long-run relationships.atthesametimewewillconcentrateonwageandpricesetting of small open economies. 5 2 The Norwegian main-course model The Scandinavian model of inflation was formulated in the 1960s, by the Norwegian economist Odd Aukrust. It became (an still is!) the framework for both medium term forecasting and normative judgements about sustainable centrally negotiated wage growth in Norway. In its day the Scandinavian model and the Phillips curve were views as alternative models. No doubt that the Phillips curve won. Pity, since Odd Aukrust s (1977) model can be reconstructed as a consistent set of propositions about long-run relationships and causal mechanisms. The reconstructed Norwegian model of inflation serves as a reference point for, and in many respects also as a corrective to, the modern models of wage formation and inflation in open economies. The Phillips curve is a special case! 6 2.1 A model of long-run wage and price setting Central to the model is the distinction between a tradables sector where frims are price takers, and a non-tradables sector where firms set prices as mark-ups on wage costs. Notation: w e,t denotes the nominal wage in the tradeable or exposed (e) industries. q e and a e are the product price and average labour productivity of the exposed sector. w s, q s and a s are the corresponding variables for the sheltered (s) sector. p is the consumer price. All variables are in logs, so e.g., w e =log(w e ). w e q e a e = m e (1) w e = m es + w s (2) w s q s a s = m s (3) p = φq s +(1 φ)q t, 0 <φ<1. (4) 7 m i (i = e, s) are means of the wage shares in the two industries and m es denotes the mean of the relative wage. φ is a coefficient that reflects the weight of non-traded goods in private consumption. Equation (1) has two implications: First, it defines the exposed sector wage share w e,t q e,t a e,t as a constant. Second, since both q e and a e show trendlike growth: the nominal wage w e is also trending (upwards). Thus, we define the main-course variable: mc = a e + q e (5) Aukrust clearly meant equation (1) as a long-run relationship between the e-sector wage level and the main-course made up of product prices and productivity. 8
The relationship between the profitability of E industries and the wage level of E industries that the model postulates, therefore, is a certainly not a relation that holds on a year-to-year basis. At best it is valid as a long-term tendency and even so only with considerable slack. It is equally obvious, however, that the wage level in the E industries is not completely free to assume any value irrespective of what happens to profits in these industries. Indeed, if the actual profits in the E industries deviate much from normal profits, it must be expected that sooner or later forces will be set in motion that will close the gap. (Aukrust, 1977, p 114-115). For example The profitability of the E industries is a key factor in determining the wage level of the E industries: mechanism are assumed to exist which ensure that the higher the profitability of the E industries, the higher their wage level; there will be a tendency of wages in the E industries to adjust so as to leave actual profits within the E industries close to a normal level (for which however, there is no formal definition). (Aukrust, 1977, p 113). Aukrust goes on to specify three corrective mechanisms, namely wage negotiations, market forces (wage drift, demand pressure) and economic policy. 9 10 log wage level "Upper boundary" Main course There are two other main hypothesis contained in (2) and (3): w-sector wage leadership, and normal cost pricing in the s-sector. To summarize, the three basic long-run propositions of the reconstructed maincourse model are: H1 mc we q e a e = m e, H2 mc we ws = m es, H3 mc ws qs a s = m s "Lower boundary" where the indicates the three endogenous long-run level variables. a e and a s are exogenous productivity trends. q e is also an exogenous variable, reflecting that e-sector firms are price takers (due to fierce competition from foreign firms) and that the exchange rate is independent of domestic prices and wages. 0 time Figure 1: The Wage Corridor in the Norwegian model of inflation. 11 A plausible generalization of H1 mc is represented by H1 gmc we = m e,0 + mc + γ e,1 u + γ e,2 D, where u t is the log of the rate of unemployment and D is a catch-all for other factors than u t which can lead to shifts in the mean of the wage share, thus in H1 gmc. 12
2.2 Causality The main-course model specifies the following three hypotheses about causation: H4 mc mc we, H5 mc we ws, H6 mc ws qs p, where denotes one-way causation. In his 1977 paper, Aukrust sees the causation part of the theory (H4 mc -H6 mc )asjustasimportantasthelong term relationships (H1 mc -H3 mc ). From a modern viewpoint this seems to be something of a strait-jacket, in that the steady state part of the model can be valid even if one-way causality is untenable. For example H1 mc, the main course proposition for the exposed sector, makes perfect sense also when the nominal exchange rate, together with wage adjustments are stabilizing the wage share around a long-run mean. 2.3 The Norwegian model and the Battle of the Mark-ups In a way,...,the basic idea of the Norwegian model is the purchasing power doctrine in reverse: whereas the purchasing power doctrine assumes floating exchange rates and explains exchange rates in terms of relative price trends at home and abroad, this model assumes controlled exchange rates and international prices to explain trends in the national price level. If exchange rates are floating, the Norwegian model does not apply (Aukrust 1977, p. 114). 13 Chapter 12.3 in the book by B&W contains a general framework for thinking about inflation. 1. firms typically attempt to mark-up up their prices on unit labour costs, 2. workersandunionsonformulaterealwageclaimswhichareamark-upon productivity. 14 Hence there is a conflict between workers and firms: both care about the real wage, but they have imperfect control: Workers influence the nominal wage, while the nominal price is determined by firms. The Norwegian model of inflation fits right into this (modern) framework. Hence, using H1 mc H3 mc abovewehavethat w = m e + q e + a q, qs = m s + w a s. The desired wage level is a mark up on prices and productivity, exactly as in equation (12.5 ) in B&W. The s-sector price level is a mark-up on unit-labour costs (as in B&W s equation (12.4 ). There are however two differences: First: don t have the full circular process emphasized by B&W (see p 287), but if the Norwegian model is extended to incorporate also effects of consumer prices (which would be an average of q e and q s ), in e-sector wage setting, full circularity would result. Second, B&W present the battle of mark-ups model in a static setting.this of course runs against our main message, namely that actual wage and prices are better described by a dynamic system. 15 16
2.4 Dynamic adjustment If e-sector wages deviate too much from the main-corse, forces will begin to act on wage setting so that adjustments are made in the direction of the maincourse. We can use the autoregressive distributed lag model, ADL, to represent this: w e,t = β 0 + β 11 mc t + β 12 mc t 1 + β 21 u t + β 22 u t 1 + αw e,t 1 + ε t. (6) There are now two explanatory variables ( x-es ): the main-course variable mc t and u t. Assume (first) that both mc t and u t are exogenous variables. We will then see that corrective forces are at work even at any constant rate of unemployment. This is a thought provoking contrast to natural rate models which dominates modern macroeconomic policy debate, and which takes it as a given thing that unemployment has to adjust in order to bring about wage and inflation stabilization. 17 Using the same 1-1 transformation as explained before: and w e,t = β 0 + β 11 mc t + β 21 u t (7) +(β 11 + β 12 )mc t 1 +(β 21 + β 22 )u t 1 +(α 1)w et 1 + ε t w e,t = β 0 + β 11 mc t + β 21 u t (8) ½ (1 α) w e,t 1 β 11 + β 12 1 α mc t 1 β ¾ 21 + β 22 1 α u t 1 + ε t Using H1 gmc,withγ e,2 = 0 since equation (6) omits other shift variables than unemployment, this can be expressed as w e,t = β 0 + β 11 mc t + β 21 u t (9) (1 α) n o w e.t 1 mc t 1 γ e,1 u t 1 + εt as long as also the following restriction is imposed in (6) β 11 + β 12 =(1 α) (10) 18 rate of unemployment (10) embodies that the long-run multiplier implied by (6) is unity. The shortrun multiplier is β 11, which can be considerably smaller than unity without violating the main-course hypothesis H1 gmc. The formulation in (9) is often called an equilibrium correction model, ECM for short. In fact, we can write wage level t 0 time w e,t = β 0 0 + β 11 mc t + β 21 u t a (1 α) {w e. w } t 1 + ε t b where w e is given by the left hand side of the extended main course relationship H1 gmc (simplified by setting γ e,2 =0). t 0 time Figure 2: The main course model: A permanent increase in the rate of unemployment, and possible wage responses. 19 20
Two final remarks Exercise 2.1 Is β 22 > 0 a necessary and/or sufficient condition for path b to occur? Exercise 2.2 What might be the economic interpretation of having β 21 < 0, but β 22 > 0? Exercise 2.3 Assume that β 21 + β 22 =0. Try to sketch the wage dynamics (in other words the dynamic multipliers) following a rise in unemployment in this case! 1. First, looking back at the consumption function example, it is clear that the dynamics there also has an equilibrium correction interpretation. 2. Below we will show that also the Phillips curve has an ECM interpretation. The main difference is the nature of the corrective mechanism: In Aukrust s model there is enough collective rationality in the system to secure dynamic stability of wages setting at any rate of unemployment (also very low rates). Wage growth and inflation never gets out of hand or out of control. In the Phillips curve model on the other hand, unemployment has to adjust to a special level called the natural rate and/or NAIRU for the rate of inflation to stabilize. 21 22 3 The Phillips curve 3.1 The long-run, causality and the Phillips curve natural rate In the 1970s, the Phillips curve and Aukrust s model were seen as alternative, representing demand and supply model of inflation respectively. However, as pointed at by Aukrust, the difference between viewing the labour market as the important source of inflation, and the Phillips curve s focus on product market, is more a matter of emphasis than of principle, since both mechanism may be operating together. Without loss of generality we concentrate on the wage Phillips curve, and recall that according to Aukrust s theory it is assumed that 1. w e = m e + mc, i.e., H1 mc above. Moreover, modern derivations give the Phillips curve a supply side interpetation!. We now show formally how the two approaches can be combined. 2. u t = m u, i.e., unemployment has a stable long-run mean m u. 3. the causal structure is one way as represented by H4 mc and H5 mc above. 23 24
A Phillips curve ECM system is defined by the following two equations w t = β w0 + β w1 mc t + β w2 u t + ε w,t, (11) β w2 0, u t = β u0 + α u u t 1 + β u1 (w mc) t 1 + ε u,t (12) 0 <α u < 1, wherewehavesimplified the notation somewhat by dropping the e sector subscript. On the other hand, since we are considering a dynamic system, we have added a w in the subscript of the coefficients. Note that compared to (7) the autoregressive coefficient α w is set to unity in (11) this is of course not a simplification but a defining characteristic of the Phillips curve. Equation (12) represents the basic idea that low profitability causes unemployment. Hence if the wage share is too high relative to the main-course unemployment will increase in most situations, i.e., β u1 0. 25 To establish the natural rate of unemploym,ent in this model (which we can call the main-course rate of unemployment), rewrite first (11) as w t = β w1 mc t + β w2 (u t ŭ)+ε w,t, (13) where ŭ = β w0 (14) β w1 is the rate of unemployment which does not put upward or downward pressure on wage growth. Next, consider a steady state situation where mc t = g mc. From assumption 1, we that w g mc =0where w. i Then (13) defines the defines the main-course equilibrium rate of unemployment which we denote u phil : 0=β w2 [u phil ŭ]+(β w1 1)g mc. or u phil =(ŭ + β w1 1 g mc ), (15) β w2 u phil represents the unique and stable steady state of the dynamic system. 26 wage growth The slope of the long-run Phillips curve represented one of the most debated issues in macroeconomics in the 1970 and 1980s (this is not reflected in B&W Ch 12, though). Long run Phillips curve w 0 g mc u 0 phil u log rate of unemployment In the context of an open economy this discussion appears as somewhat exaggerated, since a long-run trade-off between inflation and unemployment in any case does not follow from the premise of a downward-sloping long-run curve. Instead, as shown in figure 3, the steady state level of unemployment is determined by the rate of imported inflation m mc and exogenous productivity growth. Neither of these are normally considered as instruments (or intermediatetargets)ofeconomicpolicy. Figure 3: Open economy Phillips curve dynamics and equilibrium. 27 28
It is important to note that the Phillips curve needs to be supplemented by an equilibrating mechanism in the form of an equation for u t. Without such an equation in place, the system is incomplete and we have a missing equation. The question about the dynamic stability of the natural rate (or NAIRU) cannot be addressed in the incomplete Phillips curve system. Conversely: The main-course model can be extended with an equation for u t without inconsistencies! If u t depends on wages as in (12), we are essentially adding one more of Aukrusts corrective mechanisms, meaning that adjustment to the main-course will be faster than in the case with exogenous u t! 29