How Sticky Wages In Existing Jobs Can Affect Hiring

Transcription

1 How Sticky Wages In Existing Jobs Can Affect Hiring Mark Bils University of Rochester NBER Yongsung Chang University of Rochester Yonsei University February 5, Sun-Bin Kim Yonsei University Abstract We consider a matching model of employment with wages that are flexible for new hires, but sticky within matches. We depart from standard treatments of sticky wages by allowing worker effort to respond to the wage being too high or low, rendering the effective wage (wage divided by output) more flexible. Shimer (4), Pissarides (9), and others have illustrated that employment in the Mortensen-Pissarides model does not depend on the degree of wage flexibility in existing matches. But this is not true in our model. If wages of matched workers are stuck too high in a recession, then firms will require they provide more effort. In turn, this lowers the value of additional labor, reducing new hiring. Keywords: Unemployment, Sticky Wages, Effort JEL Classification: E, E4, J

2 . Introduction There is much evidence that wages are sticky within employment matches. For instance, Barattieri, Basu, and Gottschalk () estimate a quarterly frequency of nominal wage change, based on the Survey of Income and Program Participation (SIPP), of less than., implying an expected duration for nominal wages greater than a year. On the other hand, wages earned by new hires show considerably greater flexibility. Pissarides (9, Tables II and III) cites eleven studies that distinguish between wage cyclicality for workers in continuing jobs versus those in new matches, seven based on U.S. data and four on European. All these studies find that wages for workers in new matches are highly procyclical and more cyclical than for those in continuing jobs. This greater wage cyclicality for new hires is typically sizable, especially for the studies on U.S. data. Reflecting such evidence, we consider a Mortensen-Pissarides matching model of employment with wages that are flexible for new hires, but are sticky renegotiated infrequently within matches. For our benchmark, nominal wages are fixed for a year at a time. But we depart from the sticky-wage literature by allowing that firms and workers must, at least implicitly, bargain over worker effort more frequently than these wage rates are altered. Specifically, we treat firms and workers as bargaining each period on the output, and hence effort, expected by the worker. To an extent, this renders wages flexible within matches despite nominal rigidities. Suppose that after a negative shock a worker s wage, if flexible, would fall by percent. If the wage is stuck in the short run, our model predicts that the firm will require the worker to produce more. In fact, if worker preferences over effort are sufficiently elastic, we find under Nash bargaining that the worker will be expected to produce at nearly a percent higher effort and output, yielding an effective wage (per unit of labor productivity) that does decline by percent. For salaried workers this extra effort could be viewed as spending more hours at work or taking work home. For hourly-paid workers it could be viewed as increasing the pace of work. In both cases the key is that extra effort and production is not directly accompanied by any wage compensation. Shimer (4) and Pissarides (9), among others, illustrate that the behavior of employment in the Mortensen-Pissarides matching model does not depend on the degree of wage flexibility in existing matches. We show below that this result does not hold in our

3 model with effort choice. Consider a negative shock to aggregate productivity. If existing jobs exhibit sticky wages, then firms will ask more of these workers. To the extent that aggregate labor demand is downward sloping in the short run, in turn this will lower the marginal value of adding labor, lowering the rate of vacancy creation and new hires. Note this impact on hiring does not reflect the price of new hires, but is instead entirely a general equilibrium phenomenon. Because capital is relatively fixed in the short-run, the greater effort asked of current workers reduces the aggregate capital-labor ratio, reducing the demand for new hires. Our model is particularly consistent with events during the great recession. Wage stickiness acts to raise productivity in a recession, relative to a flexible or standard sticky wage model, assuming the sticky wage for current matches is held above its flexible counterpart. Thus it helps to understand why from 7 to 9, the brunt of the great recession, the economy exhibited a percent decline in hours work, compared to only a 6 percent decline in real output (BLS data on program Multifactor Productivity). It also is consistent with a wide set of anecdotal evidence that firms have required more tasks from their workers since the onset of the recession, rather than expand their workforces. We consider two versions of our model. We first allow firms to require different effort levels across workers of all vintages, as dictated by Nash bargaining subject to the sticky wages of past hires. This may require very different effort levels across workers. For instance, during a recession the efficient contract for new hires may require low effort at a low wage, while matched workers, whose wages have not adjusted downward, work at an elevated pace. Alternatively, we impose a technological constraint that workers of differing vintages must operate at a similar pace. For instance, it might not be plausible to have an assembly line that operates at different speeds for new versus older hires. We find that the latter model generates considerable wage inertia and considerably greater employment volatility. Again consider a negative shock to productivity, where the sticky wage prevents wage declines for past hires. The firm has the ability and incentive to require higher effort from its past hires, in lieu of any decline in their sticky wages. But, if new hires must work at that same pace, this restricts the contracting terms for new hires to high effort as well. For reasonable parameter values we find that firms will choose to distort the contract for new hires, rather than give rents (high wages without high effort) to its current workers. This

4 acts to produce much greater aggregate wage stickiness. The sticky wage for past hires drives up their effort and thereby the effort of new hires. But, because high effort is required of new hires, their bargained wage, though flexible, will be higher as well. In subsequent periods this dynamic will continue. High effort for new hires drives up their wage, because their wage is sticky, driving up their effort in subsequent periods, driving up effort and wages for the next cohort of new hires, and so forth. This model can generate a great deal of (counter)cyclicality in effort. As a result, it can make vacancies and new hires much more cyclical. In fact, for our benchmark calibration it causes unemployment to be more than twice as volatile as under a standard sticky-wage model. Our paper proceeds as follows. In Section we present our matching model of employment under sticky wages and endogenous effort. We calibrate a version of the model in section (to be added). In section 4 (to be added) we illustrate how our calibrated model responds to aggregate shocks that affect labor demand (e.g., productivity) or labor supply. In particular, we show that sticky wages for current matches exacerbate cyclicality of vacancy creation and hiring. Section 5 (to be added) considers a number of empirical predictions of our model across aggregate, industry, and individual data. At the industry level we show that relative cyclical movements in wages across industries are associated with corresponding large movements in relative industry TFP. We ask whether this relationship is better explained by industry wages affecting TFP, as suggested by our model, or the other way around. As one example, we instrument for industry wage stickiness by looking at wage changes for stayers in the CPS and the SIPP data, then ask if industries with stickier wages display different cyclicality in TFP. At the individual level we exploit data from the American Time Use Survey to look at work and the leisure features of workers during the great recession. For example, we ask if workers in industries that displayed high TFP growth, but big employment declines during the great recessions were more likely to report longer hours (such as taking work home) or displayed leisure choices consistent with having exerted greater effort at work.

5 . Model Transitions between employment and unemployment are modeled with matching between workers and firms, as in the standard Diamond-Mortensen-Pissarides (DMP) framework, but allowing for an choice of labor effort at work... Environment Household: There is a contiuum of identical households whose mass is normallized to one. Each housholds consists of a continuum of infinitely lived workers whose mass is also one. Each worker has preferences defined by: E t= { β t c t + ψ ( e t) γ }, γ where c denotes consumption and e the effort level at work. The time discount factor is denoted by β. It is assumed that the market equates ( ), where r is the rate of +r return on consumption loans, to this discount factor; so consumers are indifferent to consuming or saving their wage earnings. Each period, an individual worker is either employed or unemployed. When employed (or matched with a firm), a worker is paid with wage w t and exerts the effort e t. The parameter γ reflects the worker s willingness to substitue effort levels over time. When unemployed, a worker engages in job search and is entitled to collect unemployment insurance benfits b. Naturally, an unemployed worker s labor effort is assumed to be zero. Firm: There is a continuum of identical firms. A firm maintains multiple jobs, either filled (or matched with a worker) or vacant. Each firm produce output accordintg to a Cobb-Douglas production technology: Y t = z t L α t K α t, where Y t denotes output, z t the aggregate productivity, K t capital which is assumed to be fixed in the short run at K. For simplicity, we assume that the capital is owned by This household (or family) assumption is innocuous given the linear utility in consumption and separability between consumption and leisure. One can show that the allocation of this economy is identical to that where all workers act individually and form a labor union (when they bargain with firms on the choice of effort) which assigns an equal weight on its members. 4

6 households. The total labor services (efficiency unit of labor including the effort and labor hours), L t, is provided by matched pairs of workers and jobs. There are N t active matches in a period and each worker in a match exerts the effort level e t, hence the total labor services is L t = e t N t. Each period existing matches break at the exogenous rate δ and a firm posts vacancies with the unit cost κ to recruit workers. Matching Technology: New matches are formed through an aggregate matching technology: M(u t, v t ) = χu η t v η t, where u t denotes the total number of unemployed workers and v t the total number of vacancies. Thanks to the CRTS property of the matching function, the matching probabilities for an unemployed worker, denoted by p, and for a vacancy, q, can be described as only a function of the labor market tightness θ as follows: p(θ) = χθ η, q(θ) = χθ η. Staggering Wage Contract: Wages for a match are determined through the Nash bargaining between the worker and firm at the first period of employment and will be fixed for T periods as long as the match survives the exogenous match separation shocks. At any period, matches can be categorized into T cohorts according to the age of contract (i.e., the number of periods since the wage contract is negotiated). The number of workers whose contract is j period old is denoted by N j,t, where j =,,,, T. Thus, there is a distribution of matches over the space of T distinct wage contracts. A measure N t = µ(w t ) captures this distribution of matches, where w t denotes a vector of wages (in the order of age) and N t a vector of corresponding matches. Choice of Labor Effort: The effort level is also determined through the Nash bargaining (to maximize the match surplus) between the involved workers and firm given the contracted wages. In our benchmark mode, workers choose the common level of labor effort (due to strong complementarity among labors). We also consider a model where workers choose the effort level individually (by cohort). 5

7 .. Value functions and choices for labor effort and wages For simplicity, time suscripts are omitted: variables are understood to refer to time period t, unless marked with a prime ( ) denoting period t +. The value function for a typical households is: T W (z, µ) = N j w j + ( N)b + r K T + (N j ψ ( e) γ ) + βe [ W (z, µ ) z ] γ j= j= = N w + ( N)b + Nψ ( e) γ + βe [ W (z, µ ) z ] () γ subject to z F (z z) = Prob(z t+ z z t = z) () µ = T(µ, z). () where N = T j= N j is the total number of employed workers and w = T N j= N jw j is the average wage of the household. The transition operator T is characterized as: w w (z, µ ) w. = w., (4) w T w T N N. N T ( δ)n T + M(u, v) = ( δ)n., (5) ( δ)n T where the newly-employed worker s wage in the next period is denoted by w (z, µ ). The value function for a typical firm is written as follows: J(z, µ) = zl α K α N w r K κv d K + βe [ J(z, µ ) z ] (6) subject to () and (). Here, for simplicity, we assume that the capital stock, K is fixed over time and there is a constant replacement investment, d K each period. Given the perfectly Given the linear utility and separability (between consumption and leisure), the value of family is simply the sum of value of individual workers. Without famility assumption, the value of a worker in cohort j, denoted by W j, is simply W j = W Nj. 6

8 competitive rental market for capital, the real rate of return (r) is the marginal product of capital net of depreciation: J(z, µ) K = r(z, µ) + d = ( α)k α (7) Firms post vacancies (v) until the expected value of hiring a worker equals the cost of vacancy: J(z, µ) v = κ = q(θ)βe [ J (w ; z, µ ) z ], (8) where k = K/L is capital per efficiency unit of labor, and J j = J(z,µ) N j for j =,,, T, denotes the additional value to the firm of hiring a worker of j th cohort. whose wage contracts are already specified, i.e., for j =,,, T : For the matches J j (w j ; z, µ) = αzk α e w j + β( δ)e [ J j+ (w j ; z, µ ) z ]. (9) For the match whose wage will be negotiated in the next period (i.e., j = T ) J T (w T ; z, µ) = αzk α e w T + β( δ)e [ J (w ; z, µ ) z ]. () Analogously, the additional value to the household of having an additional worker in j th cohort employed is denoted by W j = W (z,µ) N j. For the matches whose contracts are already specifed, i.e., for j =,,, T : W j (w j ; z, µ) = w j b + ψ ( e) γ γ + β( δ)e [ W j+ (w j ; z, µ ) z ] βp(θ)e [ W (w ; z, µ ) z ]. () For the match whose wage will be newly negotiated in the next period (j = T ): W T (w T ; z, µ) = w T b + ψ ( e) γ γ + β ( δ p(θ) ) E [ W (w ; z, µ ) z ]. () The wage for new matches w (z, µ) is determined through the Nash bargaining between the household to which the worker belongs and the firm to which the job belongs: ( ) η ( η. w (z, µ) = argmax J (w; z, µ) W (w; z, µ)) w In the definition of J j, we include explicitly w j in the list of state variables to reflect the sticky wage contract assumed in (4). 7

9 The first order condition for w (z, µ) is ( η)j (w ; z, µ) = ηw (w ; z, µ) () The effort level is also assumed to be determined through the Nash bargaining between the household to which the worker belongs and the firm to which the job belongs. Since the effort levels they exert when working are the same across cohorts while wages are different across cohorts, the household and the firm bargain over the total marginal contributions of all cohorts given the specified wage contracts. Specifically, given the wage contracts, the common effort level, e(z, µ), is determined through the Nash bargaining between the household and the firm according to: ( ) η ( η, e (z, µ) = argmax J N (e; z, µ) W N (e; z, µ)) e where J N = J(z,µ) N and W N = W (z,µ) N are the marginal contributions to the firm and household, respectively, of having an additional worker employed from each cohort: 4 and J N (e; z, µ) = αzk α e w + β( δ)e [ J N (e ; z, µ ) z ] (4) W N (e; z, µ) = w b + ψ ( e) γ γ This yields the following first order condition for e (z, µ): + β ( δ p(θ) ) E [ W N (e ; z, µ ) z ]. (5) ( η)j N (e ; z, µ)ψ( e ) γ = ηw N (e ; z, µ)αzk α. (6) Finally, when the effort levels are chosen individually (by cohort), e j (w j, z, µ) is determined through the Nash bargaining between the workers and the firm according to: ( ) η ( η e j(w j, z, µ) = argmax J j (e j ; z, µ) W j (e j ; z, µ)) for j =,,..T. e j This yields the following first order condition for e j(w j, z, µ): ( η)j j (e j; z, µ)ψ( e j) γ = ηw j (e j; z, µ)αzk α for j =,,..T. (7) 4 Without family assumption, the bargaining for the choice of common effort is equivalent to the bargaining between the firm and labor union which assign an equal weight on its members. This leads to the exactly the same formula as above because W N J N = J N = J j= J j Nj N. = W (z,µ) N = J j= W j Nj N. 8 Note also that the firm s surplus is

10 . Calibration: Benchmark Imposed Parameters The period is a quarter. The discount factor, β is set to.99, implying an annualized real interest rate of 4%. The Frisch elasticity of labor effort γ( e)/e, reflects both the parameter γ and the level of effort. Given the average effort (by choosing ψ accordingly) to be / in the steady state, we set γ = so that the Frisch elasticity is one. The exogenous aggregate productivity shock follows an AR() process in logs: log z t+ = ( ρ z ) log z + ρ z log z t + ɛ t+, ɛ t+ N(, σ z), where ρ z =.95 and σ z =.7, following Kydland-Prescott. The unconditional mean of the aggregate productivity (log z) is chosen to normaize the steady state output to one. In our benchmark, the duration of wage contract is one year (four quarters): T = 4. The real interest rate (%) combined with capital depreciation rate, d =.5%, the marginal product of capital r +d is.5%. The labor share in the production function: α =.64. The elasticity of new matches with respect to unemployment, η, which is identical to the worker s share in Nash bargaining, is set to /. Targeted Parameters Other parameters are chosen to match the following targets in the steady state. The labor-market tightness (θ = v/u) is normalized to one. The match efficiency (χ =.6) is chosen so that the job finding rate is p(θ) = χθ η is 6% in steady state. The job separation rate (δ = 4%) is chosen so that the unemployment rate is 6.5% in the steady state. The utility parameter for leisure (ψ) is chosen to generate the steady state effort level of.5 e =.5. In steady state wages of all cohorts are the same and equation () holds for all j =,,, T and hence for j = N. From equation (6), ( ) α ( α ψ = αk α ( e) γ α ) = α ( e) γ r The vacancy posting cost (κ) is chosen to satisfy the free entry condition in (8). Given the steady-state wage w ss =.6787, the unemployment benefit (b) is chosen to match the / ( ) replacement rate (in terms of utility) b w ss + ψ ( e) γ is 75%. γ 4. Results [To Be Added] 9

11 4.. Business Cycle Properties 4.. Impulse Responses 5. Evidence from Industry Data [To Be Added]

12 Table : Benchmark Parameter Values Parameter T = 4 α =.64 β =.99 γ =. δ =.4 η =.5 χ =.6 r =.5 ρ z =.95 σ z =.7 log z = 7.8 ψ =.686 b =.54 κ =.4754 Description Duration of wage contract Labor share in production function Discount factor Reciprocal of labor supply elasticity Job separation rate Elasticity of matching w.r.t. unemployment Scale parameter in matching function User cost of capital Persistence of aggregate productivity Std. dev. of innovation to aggregate productivity Normalization of output to one Scale parameter for utility from leisure Unemployment insurance benefits Vacancy posting cost

13 Figure : Impulse Responses to Technology Shock Output (Y) Interest Rate (R) Labor Productivity (A) Unemployment (U) 5 Vacancies (V) 5 Labor Market Tightness (TH) Employment (N) Effort (E) Aggregate Labor Input (L) : e() : e() : e() : e(4) New Matches (M) Wage for New Matches (W()) Aggregate Wage (Wagg)

14 Figure : Impulse Responses to Preference Shock Output (Y) Interest Rate (R) Labor Productivity (A) Unemployment (U) Vacancies (V) Labor Market Tightness (TH) Employment (N) Effort (E) Aggregate Labor Input (L) : e() : e() : e() : e(4) New Matches (M) Wage for New Matches (W()) Aggregate Wage (Wagg)