Labor Market Institutions and the Effects of Monetary Policy

Transcription

1 1 Douglas Hbbs Macro Theory II, c2 Labor Market Insttutons and the Effects of Monetary Polcy Consder two Labor Market Insttutonal Regmes; n each regme labor unons have monoploy wage settng power: 1. Rgd : Unons contract nomnal wages n advance for at least one perod (longterm contractng). They nternalze the central bank s known reacton to ther wage polces. 2. Flexble : Unons do not sgn bndng contracts, and are able to adjust wages n every perod. Both unons and the monetary authorty nteract smultaneously, takng realzatons of m (money) and (nomnal wages), respectvely, as gven. w Under both flexble and rgd wage settngs, frms are super leaders whose prce settng behavor ncorporates realzatons of wages and the money supply, perceved by backward nducton of solutons to the (determnstc) optmal programs of unons and the central bank. Graphcally, the sequences of moves s: Unons Central Bank ( Stackelberg ) Frms Unons & Central Bank ( Nash ) Frms A Boler Plate Economy (lower case letters denote logs of correspondng upper case letters) There are n unons of equal sze, and a contnuum of monopolstc frms of mass one, each producng a dfferentated good or servce. Wages are set by unons whch are ndexed by. All frms assocated wth unon n wage barganng are ndexed by j. Output Technology: Y j = α 0,1 L α j

2 2 Proft functon: P Π = Y P W P L j d j j j Frm level demand: Y d j η Pj M M =, η > 1, = Aggregate Demand P P P Under monopolstc competton frms set prce by equatng margnal revenue to margnal cost, gvng frm prce and labor demand as ( 1 ) pj p= θ α m p + α w p d j l = θ m p w p η, 1 θ = > 0 α + η α ( 1 ) It follows that unon-level unemployment s proportonal to: U = θ η w p m p. The foregong mply (settng some nessental constants to zero) that the macroeconomc prce level and unemployment rate are: ( 1 α) p = αw+ m U = w m Usng the soluton for p, frm/unon-level unemployment s: ( 1) U = θ ηw w α η m The economy-wde log nomnal wage level s

3 3 ( 1 ) w= w + w σ σ 1 σ = s the relatve sze of unon s membershp (whch s equvalent to the degree n of unon centralzaton), and w s the average log nomnal wage set by other unons. It follows that U can be expressed: U {( ( 1) ) w ( 1 )( 1) } = θ η ασ η α σ η w m. When settng the nomnal wage, unon faces two opposte effects: 1. By rasng ts wage, t decreases the demand for labor and, thus, employment due to the hgher labor costs mposed on the frm. 2. By rasng ts wage, the unon ncreases the economy-wde wage, whch by tself makes frm j more compettve. The former effect naturally domnates the latter. Optmal Polces The central bank s problem: Set m to Maxmze 2 2 U CB =, ( 0, ), = ( p p 1) = p β π β π 2 2 The resultng optmal wage-contngent monetary polcy rule s: ( ) ( α) 2 α 1 α β 1 m= φw, φ = 1 β + 1. The reacton parameter φ defnes the central bank s degree of conservatveness, wth lower bound -1 and upper bound α /(1 α): When φ < 0, wage ncreases are at least partly accommodated; the central bank s lberal or populst. As β goes to ts lower bound of zero, φ approaches the lower

4 4 bound, -1. The central bank s ultra-lberal. Its objectve functon s only mnmzaton of unemployment, and monetary polcy full accommodates wage ncreases. When φ > 0, and the central bank s conservatve, wth polcy desgned to offset at least partly wage-nduced ncreases to nflaton. As β goes to ts upper lmt, φ approaches ts upper bound, α /(1 α), and we observe the ultra-conservatve central bank that ams only to mnmze nflaton (or deflaton). At β = α 1 ( 1 α ), the reacton coeffcent φ = 0. The central bank s passve, and monetary polcy s nether accommodatng nor non-accommodatng. The unons problem Set w to Maxmze The frst order condton for unon s: 2 U TU = γ ( w p), γ > 0 2 p U FOC γ 1 U = 0, w w After substtuton for the endogenous varables π and U we shall obtan the correspondng optmalty condtons n terms of parameters and gven varables. Macroeconomc Outcomes Flexble labor markets Each unon fnds the nomnal wage that maxmzes ts objectves by dfferentatng p and U wth respect to ts control varable w, takng both m, and the wages of other unons, condton. w, as gven, and substtutng these dervatves nto the frst-order optmalty The wage polcy reacton functons obtaned are: w ( 1) ( 1 )( 1) m ( 1) ( 1) η α η α σ η = + η ασ η η ασ η ( 1) ( 1) η α η + γ ( 1 ασ) > 0 η ασ η 2 w

5 5 The Nash equlbrum s found by mposng the symmetry condton w= w = w, gvng the macroeconomc nomnal wage: ( 1) 1 η α η w = 1 ασ γ > 0 1+ φ η ασ η 1 After substtuton of w nto m, p( π ) and U : ( 1 ασ )( η α ( η 1) )( α φ + αφ ) ( η ασ( η 1) )( 1+ φ) π = γ "nflaton bas" 0 U ( 1 ασ ) η α ( η 1) η ασ( η 1) = γ > 0 "excess U". Note: Snce the conservatveness parameter, φ, s the only term dependent on the central bank s preferences, monetary authorty cannot affect the real economy, (U). Therefore, monetary polcy s neutral. Unemployment goes to the compettve equlbrum U = 0, and the nflaton bas goes to zero, only when unons wth monopoly wage power place no weght on achevng a real wage above that warranted by productvty, that s, only when γ = 0. See Table 1 for addtonal, mportant comparatve statcs Rgd labor markets Each unon solves ts problem by nternalzng the central bank s reacton functon and the gven wage clams of other unons. After substtuton of the approprate wage dervatves nto the frst-order optmalty condton, we obtan:

6 6 w κ w 2 = + κ1 κ1 γ w p w U w wth κ = η ασ( η ) θ + σφ, 1 1 κ 2 = α 1 σ η 1 θ 1 σ φ. The mpled economy-wde equlbrum log nomnal wage s: ( 1 ( α φ+ αφ) σ) ( α + ( 1 α) η) ( η ( 1 σ ( α φ + αφ )) + ασ ( 1+ φ ))( 1+ φ ) w = γ > 0. Inflaton and unemployment n the macroeconomy mpled by w are: ( 1 ( + ) )( + ) + ( 1 ) { η ( 1 σ ( α φ + αφ )) + ασ ( 1+ φ )}( 1+ φ ) α φ αφ σ α φ αφ α α η π = γ 0 nflaton bas U ( 1 ( + ) ) + ( 1 ) 1 ( + ) + 1+ α φ αφ σ α α η = γ > η α φ αφ σ ασ φ excess U 0 Note: (See Table 1 ahead) Monetary polcy now affects the real economy, (U); monetary polcy s nonneutral. Conservatve monetary polcy s able to acheve both lower nflaton and lower unemployment when wages are pre-commtted vs-à-vs monetary polcy. As before unemployment goes to the compettve equlbrum U = 0, and the nflaton bas goes to zero, only when unons wth monopoly wage power place no weght on achevng a real wage above that warranted by productvty, that s, only when γ = 0.

7 7 Comparatve Statcs: Summary of Effects Table 1. Parameter effects on nflaton and unemployment n varous settngs * Parameter effects (a) Flexble wage regme (Nash) (b) Rgd wage regme (Stackelberg) (c) Sngle unon ( σ = 1) (d) Perfect competton (η = ) π U π U π U π U Central Bank conservatveness φ Product market competton η N N N N N Unon centralzaton σ N N Unon real wage weght γ * The table reports the sgn of the effect of ncreases n the parameters n the frst column on nflaton (π) and unemployment (U). N ndcates no effects. The outcomes assocated wth cases (c) and (d) are ndependent of the wage regmes. The comparatve statcs yeld standard results, wth a couple of wrnkles: Row 1: the degree of central bank conservatveness always affects nflaton, but has capacty to affect unemployment (the real economy) only f a multplcty of uncoordnated unons pre-commt wages n an economy wth less than perfectly compettve product markets. Rows 2 and 3: Increasng ether product market competton or unon centralzaton reduces both nflaton and unemployment n the both flexble and rgd wage regmes. The degree of unon centralzaton of wage settng affects macroeconomc outcomes only f frms exert market power over product prces, η <. The degree of market competton affects outcomes only f there s a multplcty of unons, σ < 1. Absent ether a multplcty of unons or mperfect product competton, monetary polcy s neutral.

8 8 Row 4: The greater the weght placed on the (net of productvty) real wage relatve to unemployment, the hgher are both unemployment and nflaton under any combnaton of labor and product markets. The overall pattern of results s therefore qute standard: A low unemployment and low nflaton macroeconomy are promoted by conservatve, ant-nflaton central bankers, hghly compettve product markets, and hghly centralzed unons that place relatvely small weght on real wage premums as compared to unemployment. Model Calbraton and Quanttatve Effects Parameter Settngs: α = 23 η : baselne settng of 1.3; values o spannng 1.1 to 2.0. σ baselne settng 0.4; values spannng 0.20 to 0.8. γ : baslne settng 0.125; vaules spannng φ : full theoretcal range, 1, α 1 α = 2

9 9 Smulaton Graphs Fgure 1. Inflaton and Unemployment n Rgd- and Flexble-Wage Regmes as Monetary Polcy Conservatveness Increases * (1a) (1b) * Data are expressed as log approxmatons to percentage nflaton rates and percentage ponts of unemployment Inflaton and were generated by parameter settngs α = 23, γ = 0.125, σ = 0.4 and η = 1.3 as φ goes from ts lower bound, 1, to ts upper lmt, α ( 1 α) = 2. The ultra-lberal lower bound of conservatveness s truncated n 1(a) because π as 1 Fgure 1: φ. In both rgd and flexble wage regmes nflaton declnes wth central bank conservatveness. However, when monetary polcy s lberal or populst, φ < 0, a flexble wage regme generates lower nflaton than a rgd wage regme, and conversely, f polcy s conservatve. But that the dfferences are small to vanshng for plausble parameter settngs. When polcy s passve and does not respond to nomnal wage developments, φ = 0, nflaton converges across wage formaton regmes.

10 10 Inflaton outcomes also converge to zero when polcy approaches the ultraconservatve maxmum, φ = α 1 α. When monetary polcy s lberal, unemployment equlbrums are always hgher n Stackelberg, rgd wage envronments than n Nash, flexble wage regmes; when monetary s conservatve, the reverse s true and rgd wage systems yeld superor unemployment (employment) outcomes. Intutve Explanatons: Under monopolstc prce competton and a multplcty of atomstc unons, the contrbuton of unon-specfc wages to the general prce level s small by comparson to wage effects on product prces. Each uncoordnated unon ratonally explots the wedge between log real consumpton wage receved by ts members, ( w frms, ( w p j ) p ), and the log real product wage faced by ndvdual, by ncreasng nomnal wages n order to acheve hgher real wages, dscountng the mpact of ts behavor on the general prce level and, therefore, on the real wages of other unons. All unons behave n lke fashon; the ensung ncrease to the general prce level reduces aggregate demand va the negatve effect on real money balances, whch yelds hgher economy-wde unemployment. In a flexble wage Nash regme, unons nteract smultaneously wth the central bank, and take the money supply, along wth the wages of other unons, as gven. Unon wage polces are therefore unaffected by the central bank s reactons to wage changes Hence, even a Draconan ant-nflaton monetary polcy s unable to overcome any of the unemployment costs created by the wage behavor of uncoordnated ndvdual trade unons. By contrast, n a rgd wage Stackelberg regme, unons nternalze the systematc reacton of the central bank to wage ncreases, and ths affects ther strategc calculatons. The unemployment effects of unon wage polces are aggravated or mtgated, dependng on the posture of polcy.

11 11 Fgure 2. The Effects of Monetary Polcy Conservatveness on Unemployment by Varaton n Centralzaton of Wage Settng * * Relatve nflaton and unemployment are log approxmatons to percentage pont rates and were generated by parameter settngs α = 23, γ = and η = 1.3 as φ goes from ts lower bound, 1, to ts upper lmt, α ( 1 α) = 2 for varous degrees of unon centralzaton σ. Rgd wage outcomes are depcted by the convex graph lnes; flexble wage outcomes by the parallel lnes. Fgure 2: When unons are bg and therefore set wages for a large fracton of the labor force, they understand that ther wage polces have great mpact on the general prce level and, consequently, that the wedge between product real wages and consumpton real wages opened up by nomnal wage ncreases s correspondngly small. Hence, n both flexble and rgd wage envronments, large unons correctly perceve that the real wage return to aggressve wage polces s comparatvely small, especally relatve to the utlty cost of wagenduced ncreases n unemployment among unon members. Unon sze therefore tempers optmal wage aspratons, yeldng lower frm-level prce rses and lower unon-level unemployment as centralzaton In rgd wage systems, however, the effects of unon centralzaton nteract wth the restrctveness of monetary polcy. At any gven degree of centralzaton, the nternalzaton of lberal polces by unons that must precommt nomnal wages leads to wage polces that become more aggressve as

12 12 monetary polcy becomes more accommodatng, whch yelds rates of nflaton and unemployment that always exceed the correspondng rates n flexble wage regmes, where the money supply s taken as gven. The otherwse benefcal effects of centralzaton are eroded completely as polcy approaches the ultra-lberal lmt φ = 1. The reverse s true n rgd wage labor markets when polcy s conservatve, and the central bank contracts the money supply n proporton to nomnal wage ncreases. The bgger are unons, the greater s the nternalzaton of antnflaton monetary polces, and the lower are rates of unemployment (and nflaton) by comparson to outcomes n flexble wage labor markets. At the lmt, when all wages are set by one all-encompassng unon (.e as σ 1), monetary polcy no longer affects unon wage polces because a sngle unon nternalzes fully the macroeconomc consequences of t s wage behavor on ts own. Fgure 3. The Effects of Monetary Polcy Conservatveness on Unemployment by Varaton n Product Market Competton * * Relatve nflaton and unemployment are log approxmatons to percentage pont rates and were generated by parameter settngs α = 23, γ = and σ = 0.4 as φ goes from ts lower bound, 1, to ts upper lmt, α ( 1 α) = 2, for varous elastctes of prce competton, η. Rgd wage outcomes are depcted by the convex graph lnes; flexble wage outcomes by the parallel lnes. Fgure 3:

13 13 In rgd wage systems monetary polcy exerts less potent effects as product markets become more compettve the convex graph lnes get flatter as η ncreases. The reason s that relatvely small values of η (less market competton) yeld relatvely hgh monopoly rents to frms and, therefore, hgher wages to unonzed workers, whch n turn rases unemployment. In rgd wage labor markets, where monetary polcy has capacty to nfluence unon wage clams, polcy actvsm therefore can worsen unemployment f populst, or mprove t f conservatve. Although a prce elastcty of product demand of 2.0 s probably a reasonable upper lmt, f competton were to become much fercer, for example, because of government polces that dramatcally reduced costs of market entry and barrers to trade, monetary polcy would loose most of ts relevance to unemployment n rgd wage regmes, where otherwse t exerts great effects. Frms chargng non-compettve prces would be drven to bankruptcy, and labor would be reallocated to survvng producers, no matter what the wage nflaton posture of the central bank. The ensung unformty of product prces would elmnate the wage wedge and, therefore, elmnate the ncentve of unons to pursue wage polces explotng the gap between the real consumpton wage and the real product wage.

14 14 Fgure 4. The Effects of Monetary Polcy Conservatveness on Unemployment by Varaton n Unon Real Wage Weghts * * Relatve nflaton and unemployment are log approxmatons to percentage pont rates and were generated by parameter settngs α = 23, σ = 0.4 and η = 1.3 as φ goes from ts lower bound, 1, to ts upper lmt, α ( 1 α) = 2, for varous magntudes of unon real wage utlty weghts, γ. Rgd wage outcomes are depcted by the convex graph lnes; flexble wage outcomes by the parallel lnes. Fgure 4: In prncple γ can nterpreted to be a behavoral parameter, rather than a deep, structural parameter such as α. Hence, n prncple the weght unons attach to real wages n the determnaton of nomnal wage polces s subject to planned adjustment. Unemployment outcomes are very senstve to unon real wage goals. Across plausble settngs for γ, unemployment rates shft by as much as 7 percentage ponts. γ s a parameter that dstorts compettve outcomes n labor markets, n that t represents the wllngness of unons to mpose wage levels exceedng the underlyng productvty of the (gven) labor force, whch n turn drves unemployment above the perfect competton equlbrum U = 0.

15 γ s therefore drectly analogous to the status of η n product markets, and t nteracts wth monetary polcy conservatveness n much the same fashon as η. Hence monetary polcy exerts greatest effects when unon goals are most dstortng that s, at the larger values of γ. As γ gets small unon wage behavor corresponds more on ts own to compettve behavor, and the condtonng effects of restrctve polcy dsspate, just as s the case product prce competton, η gets large. 15