NEW DEVELOPMENTS IN PRICE DYNAMICS² Wage Dynamics: Reconciling Theory and Evidence By OLIVIER BLANCHARD AND LAWRENCE F. KATZ * U.S. macroeconometric evidence shows a options (as opposed to match-speci®c negative relation between the rate of change productivity) in wage determination. of wages and the unemployment rate, con- (ii) In the light of this condition, we reinter- ditional on lagged price in¯ation. This pret the presence of an ``error correc- (wage) Phillips-curve relationship can be in- tion'' term in macroeconometric wage terpreted as a negative relation between the relations for most European economies expected rate of change of the real wage and but not in the United States. unemployment. (iii) We also show that whether this condition In contrast, most theories of the natural holds or not has important implications rate of unemployment imply what David for the effects of a number of variables, Blanch¯ower and Andrew Oswald (1994) from real interest rates to oil prices to have labeled a ``wage curve,'' that is, a neg- payroll taxes, on the natural rate of ative relation between the level of the real unemployment. wage and unemployment, given the reserva- tion wage and (if rent-sharing matters for I. The Phillips Curve and the Wage Relation wage determination) the level of productivity. For example, models of unemployment based The relation between aggregate (annual) on ef®ciency wages, matching (or bargaining) time-series data on wage in¯ation, price in¯a- models, and competitive wage determination tion, and unemployment in the United States all generate such a wage-curve relation is reasonably well represented by a textbook (Blanchard and Katz, 1997). Phillips curve of the following form: How can one reconcile the empirical Phillips-curve relation and the theoretical (1) wtt0 w 0 1 Å awt/ (p 0 1 0 pt 0 2 ) wage-curve relation? In this paper, we address this question and make three main 0 butt/ « points: where p and w are, respectively, the logarithms (i) We derive the condition under which one of the price level and nominal wage, u is the can go from the theoretical relation to a unemployment rate, aw is a constant, and « is wage Phillips-curve speci®cation that an error term. The usual interpretation of this matches the U.S. empirical evidence. We equation is that the lagged in¯ation term (pt 0 1 0 show the constraints that such a condi- pt 0 2 ) proxies for expected current in¯ation e tion imposes on the determinants of (p t 0 pt 0 1 ). Under this interpretation, we can workers' reservation wages as well as the rewrite (1) to yield relative importance of workers' outside e (2) (wtt0 p ) Å a w/ (w t0 1 0 pt 0 1 ) ² Discussants: Edmund Phelps, Columbia University; 0 butt/ « . Alan Blinder, Princeton University. The macroeconomic empirical wage equation * Department of Economics, Massachusetts Institute of Technology, Cambridge, MA 02139, and Department of implies that the (expected) log real wage de- Economics, Harvard University, Cambridge, MA 02138, pends on the lagged log real wage (with a co- respectively. ef®cient of 1) and the unemployment rate. A low 69 / 3y16 my11 Mp 69 Friday Nov 05 04:01 PM LP±AER my11 70 AEA PAPERS AND PROCEEDINGS MAY 1999 unemployment rate leads to an increase in the lagged wages. Much psychological re- expected real wage, and a high unemployment search, and fairness models of wage de- rate leads to a decrease in the expected real termination, also suggest that workers' wage. aspirations in job search and wage bargain- Turn now to theory. Almost all theoretical ing are likely to be shaped by their previous models of wage-setting generate a strong core earnings. The reservation wage depends on implication: the tighter the labor market, the what the unemployed do with their time, higher is the real wage, given the workers' res- what is typically called the utility of leisure ervation wage. Most ef®ciency-wage or bar- but which also includes home production gaining models deliver a wage relation that can and earnings opportunities in the informal be represented (under some simplifying as- sector (the black and gray economies). A sumptions about functional form and the appro- plausible benchmark is that increases in priate indicator of labor-market tightness) as productivity in the informal and home pro- duction sectors are closely related to those e (3) (wtt0 p ) Å mb t/ (10 m)y t0 bu tt/ « in the formal market economy. The reser- vation wage ®nally depends on nonlabor in- where b is the log reservation wage and y is come. It also seems reasonable, at least with the log of labor productivity. The (expected) Harrod-neutral technological progress, for real wage depends on both the reservation productivity increases to lead to equal pro- wage (the wage equivalent of being unem- portional increases in labor and nonlabor ployed) and the level of productivity. The income. parameter m ranges from 0 to 1. In some Together, these factors suggest that the res- ef®ciency-wage models, such as the shirking ervation wage is likely to depend on both pro- model of Carl Shapiro and Joseph Stiglitz ductivity and lagged wages. The empirically (1984), productivity does not affect wages reasonable condition that technological pro- directly, so that m Å 1. In bargaining models gress does not lead to a persistent trend in the ( e.g., Dale Mortensen and Christopher unemployment rate puts an additional restric- Pissarides, 1994), m is typically less than 1 tion on this relation, namely, that the reserva- since wages depend on the surplus from a tion wage be homogeneous of degree 1 in the match and, thus, on productivity. real wage and productivity in the long run. Inspection of the empirical wage equation Rather than work with a general distributed lag (2) and the theoretical wage equation (3) relation, let us assume, for illustrative pur- shows two important differences. First, the poses, the following simple relation among the reservation wage and level of productivity en- reservation wage, the real wage, and the level ter (3) but not (2). Second, the Phillips curve of productivity: gives a relation between the change in the real wage and unemployment, whereas the theo- (4) bttÅ a / l(w 0 1 0 pt 0 1 ) / (1 0 l)yt retical model implies a relation between the level of the real wage (given the reservation where l is between 0 and 1. Substituting this wage and productivity) and unemployment. expression for the reservation wage into the These two distinctions are in fact intricately wage relation (3) and rewriting gives related. They point to the need to look at the e determinants of the reservation wage, to see (5) (wtt0 p ) Å ma / ml(w t0 1 0 pt 0 1 ) whether and when one can reconcile the two speci®cations. / (1 0 ml)yttt0 bu / « . The reservation wage depends ®rst on the generosity of unemployment bene®ts and A comparison of equations (2) and (5) the other forms of income support individ- implies that the theoretical wage relation is uals can expect to receive if unemployed. consistent with the Phillips-curve represen- The institutional dependence of unemploy- tation if and only if ml Å 1. This can only ment bene®ts on previous wages suggests occur if two conditions are simultaneously that reservation wages will move with satis®ed: / 3y16 my11 Mp 70 Friday Nov 05 04:01 PM LP±AER my11 VOL. 89 NO. 2 NEW DEVELOPMENTS IN PRICE DYNAMICS 71 (i) There is no direct effect of productivity on Wage in¯ation depends not only on expected wages given the reservation wage (m Å 1). in¯ation and the unemployment rate, but also (ii) There is no direct effect of productivity on an error correction term, de®ned as the dif- on the reservation wage (l Å 1). ference between the lagged real wage and lagged labor productivity. That this is in gen- Both conditions are extreme but cannot be ruled eral a theoretically more appropriate speci®- out. For example, the Shapiro-Stiglitz ef®ciency- cation of the wage relation than the Phillips wage model, plus the assumption that the res- curve was a point ®rst made by J. D. Sargan ervation wage depends only on unemployment as early as 1964. Equations along the lines of bene®ts, which are in turn proportional to the (6) have since been estimated for various previous wage, yields both conditions. The OECD countries by a number of researchers strong performance of a standard wage Phillips- (e.g., OECD, 1997). curve speci®cation on U.S. data therefore These speci®cations differ in various ways, suggests that ml Å 1 may be a reasonable ap- in particular in their construction of labor pro- proximation for the United States.1 ductivity (trend or actual) and of expected in- ¯ation. For our purposes, however, they II. The United States versus Europe consistently yield one main conclusion. The coef®cient on the error correction term for the It has been known for some time that there is United States is close to zero with point esti- a striking difference between the empirical wage± mates that are typically wrong-signed (i.e., im- unemployment relations in the United States and plying a positive effect of the lagged real wage Europe. The difference, which might appear at adjusted for productivity on current wage in- ®rst to be rather esoteric, is the presence of an ¯ation), but small and insigni®cant. Put an- error correction term in the European but not in other way, the Phillips-curve speci®cation, the U.S.