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1 B&W’s derivation of the Phillips curve Ch 12.3: The Battle of the mark-ups as a framework for understanding inflation. Wage and price setting. Slides for 26. August 2003 lecture Ragnar Nymoen University of Oslo, Department of Economics Using the notation in B&W we have P = (1 + θ) W (Y /L) price setting (12.4’) Y W/P e = (1 + γ) , 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 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. 1 2 From level to dynamics: P Pe − 1 = (1 + θ)(1 + γ)( − 1) + (1 + θ)(1 + γ) − 1 P−1 P−1 Pe P − 1 = (1 + θ)(1 + γ)( − 1) + θ + γ + θγ P−1 P−1 Introducing: π= for inflation, and π̄ = for core inflation we obtain: P −1 P−1 Pe −1 P−1 π = (1 + θ)(1 + γ)π̄ + θ + γ + θγ = π̄ + θ + γ + θπ̄ + γ π̄ + θγ Next B&W hypothesize that the mark-up moves pro-cyclically: θ + γ = a(Y − Ȳ ) = −b(U − Ū ) 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 = π̄ + a(Y − Ȳ ) + s = π̄ − b(U − Ū) + s ≈ π̄ + θ + γ 3 (12.7) 4 (12.11) 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. At the same time we will concentrate on wage and price setting of small open economies. 5 2.1 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 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: we,t denotes the nominal wage in the tradeable or exposed (e) industries. qe and ae are the product price and average labour productivity of the exposed sector. ws, qs and as are the corresponding variables for the sheltered (s) sector. p is the consumer price. mi(i = e, s) are means of the wage shares in the two industries and mes 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 we,t − qe,t − ae,t as a constant. Second, since both qe and ae show trendlike growth: the nominal wage we is also trending (upwards). Thus, we define the main-course variable: mc = ae + qe (5) All variables are in logs, so e.g., we = log(We). we − qe − ae = me (1) ws − qs − as = ms (3) we = mes + ws p = φqs + (1 − φ)qt, 7 (2) 0 < φ < 1. 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. (4) 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 There are two other main hypothesis contained in (2) and (3): w-sector wage leadership, and normal cost pricing in the s-sector. log wage level "Upper boundary" Main course where the ∗ indicates the three endogenous long-run level variables. ae and as are exogenous productivity trends. qe 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. "Lower boundary" 0 To summarize, the three basic long-run propositions of the reconstructed maincourse model are: H1mc we∗ − qe − ae = me, H2mc we∗ − ws∗ = mes, H3mc ws∗ − qs∗ − as = ms time Figure 1: The ‘Wage Corridor’ in the Norwegian model of inflation. A plausible generalization of H1mc is represented by H1gmc we∗ = me,0 + mc + γe,1u + γe,2D, where ut is the log of the rate of unemployment and D is a catch-all for other factors than ut which can lead to shifts in the mean of the wage share, thus in H1gmc. 11 12 2.2 Causality The main-course model specifies the following three hypotheses about causation: H4mc mc → we∗, H5mc we∗ → ws∗, H6mc ws∗ → qs∗ → p∗, where → denotes one-way causation. In his 1977 paper, Aukrust sees the causation part of the theory (H4mc-H6mc) as just as important as the long term relationships (H1mc-H3mc). 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 H1mc, 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). Chapter 12.3 in the book by B&W contains a general framework for thinking about inflation. 13 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 H1mc−H3mc above we have that 1. firms typically attempt to mark-up up their prices on unit labour costs, 2. workers and unions on formulate real wage claims which are a mark-up on productivity. 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 qe and qs), in e-sector wage setting, full circularity would result. w∗ = me + qe + aq , qs∗ = ms + w∗ − as. 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’). 15 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. 16 2.4 Dynamic adjustment Using the same 1-1 transformation as explained before: 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: we,t = β0 + β11mct + β12mct−1 + β21ut + β22ut−1 + αwe,t−1 + εt. (6) There are now two explanatory variables (“x-es”): the main-course variable mct and ut. Assume (first) that both mct and ut 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. (7) ∆we,t = β0 + β11∆mct + β21∆ut + (β11 + β12)mct−1 + (β21 + β22)ut−1 + (α − 1)wet−1 + εt and (8) ∆we,t = β0 + β11∆mct + β21∆ut ½ ¾ β11 + β12 β21 + β22 − (1 − α) we,t−1 − mct−1 − ut−1 + εt 1−α 1−α Using H1gmc, with γe,2 = 0 since equation (6) omits other shift variables than unemployment, this can be expressed as ∆we,t = β0 + β11∆mct + β21∆ut n o − (1 − α) we.t−1 − mct−1 − γe,1ut−1 + εt (9) β11 + β12 = (1 − α) (10) as long as also the following restriction is imposed in (6) 18 17 rate of unemployment (10) embodies that the long-run multiplier implied by (6) is unity. The shortrun multiplier is β11, which can be considerably smaller than unity without violating the main-course hypothesis H1gmc. The formulation in (9) is often called an equilibrium correction model, ECM for short. In fact, we can write t time 0 wage level 0 ∆we,t = β0 + β11∆mct + β21∆ut a − (1 − α) {we. − w∗}t−1 + εt b where we∗ is given by the left hand side of the extended main course relationship H1gmc (simplified by setting γe,2 = 0). t0 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 β22 > 0 a necessary and/or suﬃcient condition for path b to occur? Exercise 2.2 What might be the economic interpretation of having β21 < 0 , but β22 > 0? 1. First, looking back at the consumption function example, it is clear that the dynamics there also has an equilibrium correction interpretation. Exercise 2.3 Assume that β21 + β22 = 0. Try to sketch the wage dynamics (in other words the dynamic multipliers) following a rise in unemployment in this case! 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 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. Moreover, modern derivations give the Phillips curve a supply side interpetation!. We now show formally how the two approaches can be combined . The long-run, causality and the Phillips curve natural rate Without loss of generality we concentrate on the wage Phillips curve, and recall that according to Aukrust’s theory it is assumed that 1. we∗ = me + mc, i.e., H1mc above. 2. u∗t = mu, i.e., unemployment has a stable long-run mean mu . 3. the causal structure is “one way” as represented by H4mc and H5mc above. 23 24 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 A Phillips curve ECM system is defined by the following two equations ∆wt = βw0 + βw1∆mct + βw2ut + εw,t, βw2 ≤ 0, ∆ut = βu0 + αuut−1 + βu1(w − mc)t−1 + εu,t (11) (12) 0 < αu < 1, where we have simplified 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 αw is set to unity in (11)–this is of course not a simplification but a defining characteristic of the Phillips curve. ∆wt = βw1∆mct + βw2(ut − ŭ) + εw,t, (13) where βw0 (14) −βw1 is the rate of unemployment which does not put upward or downward pressure on wage growth. ŭ = Next, consider a steady state situation where ∆mct = gmc. From assumption 1, we that ∆w∗ − gmc = 0 where ∆w∗. i Then (13) defines the defines the main-course equilibrium rate of unemployment which we denote uphil : 0 = βw2[uphil − ŭ] + (βw1 − 1)gmc. or 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., βu1 ≥ 0. 25 β −1 gmc), uphil = (ŭ + w1 −βw2 (15) uphil represents the unique and stable steady state of the dynamic system. 26 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). wage growth Long run Phillips curve ∆ w0 g mc u 0 u phil 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 mmc and exogenous productivity growth. Neither of these are normally considered as instruments (or intermediate targets) of economic policy. 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 ut. 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 ut without inconsistencies! If ut 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 ut! 29