A General Equilibrium Model of Variable Scheduling Preliminary Version NICK FRAZIER Rice University nfrazier@rice.edu January, 2017 ABSTRACT: A salient feature of the U.S. labor market is the large fraction of jobs with week-to-week variability in hours and compensation. A recent movement to limit employer control over scheduling aims to reduce that variation and improve employee welfare. Understanding the full economic consequences of such policies, however, requires a model of both why such jobs exist and why individuals accept them. I present a search model with productivity shocks and worker and firm heterogeneity that generates labor contracts that match observed patterns in variable hours and compensation. The model includes the firm s hiring decisions, choice over volatility in hours, and labor contracting to capture equilibrium effects of restricting the contracting environment. I present my identification strategy and discuss the difficulty of separately identifying the primitives of the firm and worker problems using typical data sources. I then estimate the model using a mixture of stated preference, panel, and aggregate firm data and evaluate the consequences of several relevant policies on employee welfare. I am grateful to Flávio Cunha and Ken Wolpin for helpful comments and suggestions. 1
Nick Frazier 2 I. INTRODUCTION Technological advances in on-demand scheduling offer firms increasingly finer control over employee hours but have also induced a backlash against the perceived externalities created by fluctuating hours and unpredictable work schedules. The resulting pressure has caused firms to change their policies, see Nassauer (2016), White (2015), Tabuchi (2015), but also motivated policies that directly regulate such contracts as in San Francisco, Seattle, and Portland. These policy changes are supported by survey evidence describing the prevalence of such jobs in the United States and the negative consequences of variability in earnings, hours scheduling, and employee turnover. 1,2 However, without a model describing why these jobs exist and why individuals accept them, any characterization of the net welfare consequences of these policies remains partial. For example, prohibiting variability in week-to-week hours seemingly makes employed individuals better off but could also change levels of employment, hours, and compensation. These net economic consequences may ultimately represent a welfare reduction for workers. One important consideration motivated at least in part in the above survey evidence is how to model the source of volatility in hours. A standard neoclassical labor supply model has the employee choosing hours free of constraints from the firm. Such models can generate both fixed and variable hours but struggle to replicate the mixture observed in U.S. data. The further implication that observed labor hours are then necessarily optimal labor hours implies the new policies decrease welfare and stand at odds with survey evidence suggesting that workers would accept pay cuts to control their hours. The literature incorporating search frictions provides a way to generate sub-optimal contracts but often treats hours as of secondary importance in a job contract. I propose a general equilibrium model where heterogeneity in worker preferences interacts with firms responding to productivity shocks to generate a mixture of jobs resembling that found in the U.S. labor market. Similar to Bloemen (2008) my model has firms offer a combination of hours and compensation to potential employees through meetings subject to search frictions. However, offers here are a joint distribution of hours and wages where the choice to work is based on ex ante expected utility but the pay-offs are based on ex post outcomes. I further incorporate directed search so that workers who differ in degrees of risk aversion can choose whether to apply to jobs where the joint distribution is degenerate (fixed hours) or non-degenerate (variable hours). Productivity shocks motivate firms to offer variable schedules, where 1 The prevalence of such jobs is documented in Lambert et al. (2014) using the nationally representative National Longitudinal Survey of Youth 1997 to estimate that around three-quarters of workers in their early thirties experience at least some fluctuation in weekly hours. 2 Reviews of survey evidence are Lambert et al. (2014) and Golden (2015). Works that use survey responses include Golden et al. (2013), Henly and Lambert (2014), Ingre et al. (2012), Lambert (2008), Lambert et al. (2012), Reynolds and Aletraris (2006), Reynolds (2003), and Stewart and Swaffield (1997).
Nick Frazier 3 hours adjustments are possible, but heterogeneity in worker preferences tempers their use. Evidence for this dynamic includes Mas and Pallais (2016) who use a field experiment where participants chose between contract types found a willingness-to-pay that ranges from 0% to around 20% of wages to avoid the type of variable contracts considered here. In estimation, I use stated preference data to identify variation in worker preferences that resembles that used in Eriksson and Kristensen (2014) who also find a large degree in variation in employee willingness-to-pay. In my model firms employ at most one worker but make decision ranging from the type of vacancy to offer, the optimal labor contract, and production decisions in the fact of uncertainty. Workers have types that reflect their degree of risk aversion and choose whether to apply to variable or fixed type jobs and then whether to accept offered contracts. I estimate the model s primitives of worker preferences, firm revenue functions, and productivity shocks using data from a survey instrument designed to elicit preferences over similar contracts, panel data on observed jobs, and aggregated information on firm hiring, separations, and fluctuations in production. A detailed discussion of data requirements for identification is included. The general equilibrium nature of the model allows us to study the economic consequences of restricting the contracting space. A typical restriction would be limiting the amount of variability permissible. Such a policy potentially affects the firm s decision to offer jobs, how they set wages and hours, and overall employment levels. Using estimated primitives I provide evidence on the resultant changes in the labor market and provide some limited characterizations of optimal policies. These include ones similar to those proposals described above. The plan of the paper is as follows. In Section 2, I develop my model of variable scheduling. Section 3 discusses identification given data and details my approach. Section 4 describes my approach to estimating degrees of worker heterogeneity. Section 5 contains the econometric framework and approach used to estimate the general equilibrium model. In Section 6 I present the results of estimation and in Section 7 I use these estimates to characterize the welfare costs of various policies. Section 8 concludes. II. MODEL Two types of agents populate the economy: firms and workers. Firms produce the economy s consumption good using the labor hours input of at most one worker. Firms act independently when making personnel and production decisions and take aggregate equilibrium outcomes, such as the unemployment rate, as given. They face an i.i.d. productivity shock each period that affects firm revenue such that firms prefer to respond by adjusting labor hours. Firms are heterogeneous in the variance of this shock. Workers are characterized by their type which determines the degree risk aversion in their preferences. The combination
Nick Frazier 4 drives heterogeneity in the production and cross-sectional variation in observed jobs in the economy. Firms enter a period as either matched with an worker or not. Whether they are matched and the type of the employee if matched represent the principle state variable of the firm s problem. Each period begins with some economy-wide exogenous separations. Afterwards, any unmatched firm may post a vacancy to one of two markets. The first market specifies the worker s hours before realization of the productivity shock which I refer to as a fixed contract. Firms may also post a vacancy for a variable contract which permits adjusting hours to the shock. Equivalently, the variable contract specifies a menu of labor hours for all possible realized productivity shocks. Workers face a symmetric choice to search for a specific type of vacancy. This feature suggests the markets may differ in job-filling rates and expected types of workers and firms. Further, the terms of the contract will depend on both the firm-specific distribution of the productivity shock and the worker-specific degree of risk aversion. Conceptually, both contracts can be thought of as joint distributions in hours and compensation. The variable contract fixes a wage before production in return for working a set number of hours the random shock determined by the shock. Thus, the contract specifies a joint distribution of labor hours and compensation, equal to the fixed wage times hours. Fixed contracts offer degenerate distributions since both wage and hours are fixed before realization of the productivity shock. Worker and firm types drive expected returns and generate variation in labor contracts which in turn influences the composition of jobs in the economy. Firms post vacancies subject to a non-convex cost structure discussed below. Upon meeting a worker, the firm makes a take-it-or-leave-it offer to the worker but with the contract type as specified in the market where they met. The type of contract may not change for the duration of the match and since neither the firm s or the worker s individual types evolve the same contract will occur for every period of the match. Meetings do not imply matches as a contract given the firm and worker types may not be expected profit maximizing from the firm s point of view. Failed meetings result in the firm and worker remaining unmatched for the period. Unemployed workers also choose whether to apply in the fixed or variable market. They meet firms with posted vacancies through a search process and then choose to accept or reject an offered contract. Both parties know the worker may lose their job in a subsequent period. Meetings are assumed to occur with probability each period that is exogenous to the agents but determined in equilibrium. The worker accepts the job when the expected value of working meets their participation constraint or the value of unemployment. Mechanically, every period consists of three phases. The first phase is a labor force adjustment where exogenous separations occur followed by the opportunity for unmatched firms and workers to participate in the search market. Any pairing with an expected value less than the reservation value for either the firm or worker is dissolved and both continue unmatched. The second phase is the contracting phase where labor
Nick Frazier 5 contracts for all current matches are determined. The third and final phase is production where the random productivity shock is realized and production occurs followed by consumption. Firms and workers discount at the same rate between periods. A. Workers Workers exist in one of two states: employed or unemployed. Employed workers supply labor and receive compensation in accordance with their contract. Unemployed workers receive b, the guaranteed value of home production. Workers are risk-averse and have preferences over consumption and total hours supplied in any period. Workers vary by belonging to one of two types which captures their degree of risk-aversion. Their type is fixed across time. Let there be π κ proportion of workers of type κ L and 1 π κ of type κ H. Since job contracts amount to a ex ante joint distribution of possible compensation and total labor hours, this preference shock affects their decision to accept or reject a given job. Formally, preferences over hours and consumption are described by the per-period utility function Z( ) where risk-aversion depends on κ Z(C, L; κ) = C1 ρ c(κ) 1 ρ c (κ) γ L1 ρl(κ) 1 ρ l (κ). (1) By assumption ρ j (κ L ) < ρ j (κ H ) for j = 1, 2 so that low types are less risk averse than high types. Workers also face a budget constraint such that total consumption in any period, C, is less than or equal to total labor compensation, wl, or their value of home production if total hours worked, L, is zero. Equivalently, C wl + 1 [L=0] b(κ). (2) By assumption, the values of home production (b(κ L ), b(κ H )) satisfy Z(b(κ L ), κ L ) = Z(b(κ H ), κ H ). In other words, all workers receive the same utility from home production. In doing so, I abstract away from trying pinning down heterogeneity in the utility value of home production, not the least of which is taking a stance on whether risk-averse workers prefer home production. Notice that this assumption is not intrinsically different than assuming a single value of home production for homogeneous workers and affects the dynamics only in that individuals are ceteris paribus equally likely to reject a job offer. Each period initially unemployed workers become employed with some positive probability. Let J and U represent the value of entering the production phase as employed and unemployed, respectively. The
Nick Frazier 6 period pay-off is a realization from the joint distribution of compensation and total labor so the ex-ante is in expected utility and a continuation value. Specifically, the value of holding a job with a variable schedule is J v (κ) = E [Z(C, L; κ)] + β E [(1 q)j v (κ) + qu(κ)] (3) where β is the discount rate and q is probability of job loss. The value of a job with a fixed contract, J f (κ), follows symmetrically except it has a non-random contracted pay-off such that E [Z(C, L, κ)] = Z(C, L, κ). An unemployed worker may costlessly choose to search in either the fixed or variable contract market. Both markets have equilibrium job finding rates that depend on the number of workers, U, and firms, V participating in that market. Workers take these values as given. Let the job-finding rate for the fixed and variable markets be φ f and φ v, respectively. The firm a worker of type κ potentially meets comes from a continuum of firm types, σ i R +, where for some sufficiently large value of σ i either the worker or the firm would prefer remaining unmatched. This behavior occurs in behavior as a worker will potentially participate in a market if other firms can produce profitable matches. Since the worker s type drives the cut-off I denote the probability of this occurrence as τ(κ). 3 Consider the value of unemployment when entering the period and participating in the fixed market, U f (κ) = φ f (U f, V f )τ(κ) E J f (κ) + (1 φ f (U f, V f ) + φ f (U f, V f )(1 τ(κ)))(z(b, κ) + β E U f (κ)). (4) The first term is the expected return to working where integration is over the set of firm types that participate in the fixed market. The second term is continuation value from a failed match but the discounted continuation value of unemployment and is weighted by the probability of a failed search and a failed meeting after a successful search. Notably, the state variable does not change. The absence of aggregate uncertainty implies a steady state equilibrium wherein if a worker applies to jobs in the fixed market in one period they will do so in all future periods. This property is seen in the worker s choice between the fixed and variable markets is described by the value of unemployment U(κ) = max{e U f (κ), E U v (κ)} (5) where since a worker s type does not change, neither does there decision rule. 3 I derive a formal expression when discussing the matching technology below.
Nick Frazier 7 B. Firms Firms use a production technology that converts labor hours into the consumption good. Firms are risk neutral and consume any profits. The production technology of firm i in period t is described by y it = ε it l α it (6) where l is labor, ε is a productivity shock, and α is a curvature parameter to allow for diminishing returns to scale due to abstraction away from fixed factors of production. I assume ε it LogN(1, σi 2 ) such that firms differ in the variance of their productivity shocks which I further denote as the firm s type. Though the productivity shock each period is an independent draw from the firm s distribution, the firm s type, σ i, is drawn from F σ upon entry and fixed for the life of the firm. The firm s type will largely determine whether it prefers to offer a fixed or variable vacancy. Intuitively, firms with large values of σ i will prefer to respond to these shocks by their adjusting labor hours which is permitted by the terms of variable contracts but not by fixed contracts. Firms enter a period either unmatched or matched with a worker of particular type. The period begins with the exogenous destruction of matches with probability δ. The probability of exogenous destruction is independent of all firm and worker characteristics. Unmatched firms then post vacancies and hire through a process described below. Importantly, the type of contract used in the match, whether fixed or variable, is determined during hiring process and persists through the duration of the match. Each period and after hiring, all matched firms contract with their workers through a take-it-or-leave-it offer with full information. Therefore, both parties know the worker and firm type and all aggregate variables. This setting implies workers will receive their expected reservation value in the case of variable contracts and true reservation value for fixed contracts. The decisions of firms are largely driven by the expected value of production. This process begins with whether, given their type, they prefer to post a vacancy in the fixed or variable market. The decision depends on the expected types and number of workers in that market and the expected productivity of any match. To help build intuition I first discuss the production decision of the firm and work backwards to the hiring decision. B.1. Production under Fixed Contracts As a first case, I consider the production decision for a worker employed in a fixed contract. Both hours and wage are set in negotiations occurring before the realization of the productivity shock. In particular, the firm
Nick Frazier 8 seeks to maximize expected profit but because contracting occurs in a full information environment with take-it-or-leave-it offers, the firm need only keep the worker indifferent between working and unemployment. Formally, the wage must satisfy the following inequality, E[Z(wl, l; κ) + βj f (κ, σ i )] Z(b, 0; κ) + βu(κ) [ ] w (1 ρ c)(b + β E U(κ) J f (κ, σ i ) ) [ ] E l 1 ρ c γ 1 ρ l l 1 ρ l 1 1 ρc. (7) [ ] Define H f (κ, σ i ) = b + β E U(κ) J f (κ, σ i ) which roughly represents the expected return to quitting. The careful reader will notice that J f (κ, σ i ) = J f (κ) and H f (κ, σ i ) = H f (κ) σ i as the scale of productivity is normalized across firms and the worker is perfectly insured against shocks. The firm s problem simplifies to maximizing profit subject to the worker s participation constraint. Notice that for a fixed contract hours worked are set independent of ε and so the constraint further simplifies to following problem, l f (κ) = max l E [ε i l α wl] s.t. w ( (1 ρc )H f l 1 ρ c γ 1 ρ l l 1 ρ l ) 1 1 ρc where by the convexity of the problem the constraint binds and the solution provides both a l f (κ) such that knowing the worker type perfectly determines fixed labor and compensation. The offer is independent on time and the firm s type. The wage offer, w f (κ) is a consequence of substituting the labor demand into the participation constraint. One final consideration for firms operating with fixed labor contracts is the occurrence of a productivity shock small to cause negative profit. Formally, any ε it < w f l 1 α f will generate negative profit for the firm. I assume the firm cannot break the contract and factors in this possibility when both setting fixed contracts and choosing between variable and fixed contracts. An analogous assumption is made about not needing to satisfy the variable worker s participation constraint ex-post. The reasoning behind these assumption is discussed in Section III. B.2. Production under Variable Contracts The production decision of a firm with a worker employed in a variable contract has a slightly different structure as the wage is determined separately from hours. To illustrate, given a contracted wage w, the
Nick Frazier 9 profit maximizing labor demand is the solution to ł v (κ, ε it ) = max l ε it l α wl l v = ( αεit ) 1 1 α w where intuitively conditional labor demand is increasing in the productivity shock and decreasing in the wage. Notably, for ε > 0 the firm always produces a positive amount so that there would never be a reason for the firm to terminate a match during production. Furthermore, even if the worker s participation constraint is not satisfied by the ex-post wage and labor demand combination, I make the assumption that the worker cannot break the contract. This assumption is symmetric to that made in the section above. Though the firm sets labor optimally given the realization of ε, the wage is set during the contracting phase before its realization with regard to expected production. Since contracting occurs in a full information environment with take-it-or-leave-it offers, the firm need only keep the worker indifferent between working and unemployment as specified by (7). Here the wage is set to expected hours for which I substitute in the labor demand conditional on κ and ε to yield w (1 ρ c )(b + β E [U(κ) J v (κ, σ i )]) [ ] ( E αεit ) 1 ρc 1 α w γ ( αεit ) 1 ρ l 1 α 1 ρ l w 1 1 ρc (8) which has an implicit solution for w. Notably, the expected total labor depends on the firm s type, σ i, which appears in the integration in the denominator. The worker s type enters the determination through ρ c, ρ l, U, and J v which are all functions of κ. Here the constraint also binds and the above equation determines w v (κ, σ i ) for any firm worker pair. The implication of a matched worker/firm pair in a variable contract is a series of realizations that resemble the week-to-week variation in worker schedules observed in the data. B.3. Determining Employment Firms enter each period as either matched, and with employee s type or as unmatched. Before the adjustment phase jobs are exogenously destroyed at rate δ. This feature replicates structural unemployment and affects variable and fixed jobs equally by assumption. Next, all unmatched workers and firms participate in a matching process where firms post a vacancy to either the fixed or variable market and workers apply to one of the two markets. The cost to a firm of a vacancy is k and vacancies must be re-posted each period. Any filled vacancy is characterized by a pairing {σ i, κ} which is fixed for the duration of the match. The existence of two search markets requires that they have separately determined aggregate conditions.
Nick Frazier 10 I make the assumption that they are subject to the same technology of matching. Let U v and U f be the number of workers applying to the variable and fixed markets respectively. Let V v and V f be the number of vacancies firms post to the variable and fixed markets, respectively. The existence of search frictions imply meetings happen with some probability. Since both workers and firms vary in their type, the meeting of any two pairings is also probabilistic. Let ψ v and ψ f be the probability of meeting a worker in the variable and fixed markets, respectively. Though I have only two types of workers, firms are continuous in type, and so given a large value of σ i some firms may meet a worker of type κ high enough that they would prefer to continue unmatched. This probability depends on σ i and density of types that participate in the market which is constant over time in steady state. Let the probability of such a successful meeting be η(σ i ). Then the value of posting a variable vacancy to a firm is [ ] Q v (σ i ) = k + ψ v (U v, V v )η v (σ i ) E V f + (1 ψ v (U v, V v ) + ψ v (U v, V v )(1 η v (σ i ))) E [Q v ]. (9) The expectation is taken over both ε and the distribution of worker types participating in the market conditional on the meeting being successful. The continuation value of a failed search is Q v as without an evolution of the state variable and a steady state market the firm will always choose the same market. The value of posting a fixed vacancy is analogous. When making decisions firms take labor market conditions as given. The firm s decision to post a vacancy in one market over the other is driven by expected return. Formally, the value of posting a vacancy is Q(σ i ) = max{e Q v (σ i ), E Q f (σ i )} (10) where because of the equal costs the problem reduces to the expected return as a function of aggregate vacancy-filling rates and the expected return to production for the two types of contracts. The firm also takes as given the behavior of workers who also choose which market to participate in given their own type. The worker may costlessly apply to either market and chooses the highest expected return given their type. Similar to the discussion in A, the value of applying to the variable market for an unmatched worker is U v (κ) = φ v (U v, V v )τ(κ) E J v (κ) + (1 φ v (U v, V v ) + φ v (U v, V v )(1 τ(κ)))(z(b, κ) + β E U v (κ)). (11) where the expectation for J v is taken over both firm type conditional on an accepted match and future possible shocks given σ i. Again, a worker who applies to the variable market in one period would always apply to the same market in all future periods.
Nick Frazier 11 In the absence of aggregate shocks the economy rests in a steady state across periods. I therefore assume a simple matching function that provides the same equilibrium contact rate in every period. The vacancy filling rate for market k, ψ k (U k, V k ), depends on θ v = V k U k which is a state of the aggregate labor market variable that is determined in equilibrium but taken as given by all agents when making decisions. Giving the set-up, unemployment in each market is constant in equilibrium and defined by the flows in U k = (1 U k)q(u k, V k ) + (1 ψ(u k, V k ))U k. (12) I also assume a matching function with a Cobb-Douglas technology with a constant returns to scale specification. Formally, matches in any period are equal to M(U k, V k ) = µu ν k V1 ν k (13) where U k is the level of unemployment, V k is the number of vacancies, q is the separation rate equal to quits plus fires, φ k = M(U k, V k )/U k is the job finding rate, and ψ k = M(U k, V k )/V k represents the vacancy filling rate. C. Equilibrium The ingredients for equilibrium in this economy are the optimization behavior of firms and workers and worker-flow conditions. Firm behavior must specify an optimal labor contract for hours and wage for the fixed market subject to the worker s type-specific participation constraint. There must be an equilibrium state-contingent hours schedule which solves the profit maximization problem for variable contracts and an attendant wage pairing that satisfies the worker s type-specific participation constraint for all feasible matches in the variable market. Unmatched firms and unmatched workers must have a decision rule for which market they will post and apply to, respectively. Workers must also have a decision rule on whether to accept or reject any contract. The consistency of the worker flow conditions requires that the vacancy filling rate, taken as given in the firm s problem, be consistent with the aggregate market tightness in equilibrium. Steady state equilibrium also requires that unemployment follow (12). D. Discussion Firm heterogeneity in the variance of the productivity shock drives variation in the desirability of adjusting labor to the shock. Heterogeneity in worker preferences over degree of risk aversion tempers observed
Nick Frazier 12 contracts so that some firms will prefer to offer fixed hour contracts at a lower wage. Search frictions induce mis-matches in the sense of not all high variance firm types will match with less risk-averse workers and vice versa. Since wages are set before production and ex post observed hours vary for some jobs the model generates both a mixture of jobs with fixed hours and compensation as well as variation in hours and compensation conditional on variable contracts. Increasing the heterogeneity in worker types would provide for a greater range of observed wages for both types. Increasing the heterogeneity of firm types also produces more variation in wages for variable contracts. In estimation both of these types would likely be continuous. The model further generates cross-sectional variation across workers and firm through productivity shocks. Even identical variable matches, up to firm and worker type, may produce different worker outcomes through productivity shocks. Identical fixed matches will produce the same observed compensation and hours. III. IDENTIFICATION Given my intent to evaluate the general equilibrium consequences of policies that restrict contractual variation in hours I require a model of optimizing firms and workers. I choose to model the source of varying hours as the result of firm-specific productivity shocks and worker heterogeneity. These allow for an exogenous driver of variation in hours while allowing for the possibility of mis-match where some workers have variable contracts despite preference for fixed contracts. The gains, then, from the counter factual policies I consider will often hinge on the degree of mis-match which is turn driven by general equilibrium effects of search frictions. Given my premise that observed hours are often not optimal hours from the perspective of the employee, I require data beyond the typical panel of observed jobs familiar to the literature. This conflict results from the inability, even given the full set of characteristics for observed jobs, to separate the influence of firm optimizing behavior from worker optimizing behavior. Firm s maximize profit given available technology through production and labor force adjustment subject to stochastic productivity and search frictions which generate the desirability of variable contracts from the firm s perspective. Workers maximize utility but through search frictions do not have direct control over the details of their hours schedule or compensation. Thus, an observed job with high variability could be from a strong demand from the firm or relatively low disinclination from the worker. Clearly, separating the role of these mechanisms has strong implications for the overall effect on welfare. Without the primitives of both the firm s and the worker s problem any evaluation of the general equilibrium effect of these policies. The model permits adjustments by firms on the extensive and intensive
Nick Frazier 13 margins of labor scheduling while still allowing estimation of welfare impact. To separately identify worker preferences, I propose using a purpose made survey instrument to elicit preferences from a sample of workers for whom the kinds of jobs I consider would be relevant. I can then further re-weight my non-representative sample using the representative sample from the National Longitudinal Survey of Youth 1997 (NLSY97). This matching is facilitated by the collection of demographic and employment information similar to that solicited by the NLSY97. As discussed below, these survey instruments can be used to trace out preferences over the kinds of jobs and contracts used in my model. A similar approach is used in Eriksson and Kristensen (2014). The controlled environment of stated preferences data even allows us to estimate the compensating differentials workers would require between various contracts. Given both relative values and the distribution of preferences, I then estimate the general equilibrium model using the (1) characteristics from pertinent jobs in the NLSY97, which notably collects information on the distribution of usual hours, and aggregate data on firm behavior such as that available in JOLT. The observed jobs will be used to pin down the hours, wages, and compensation of jobs in my economy. The data on hiring, firing, and job openings from sources like JOLT will discipline the labor force adjustment technology where correlations reveal fixed costs and movements determine structural and transitory flows. This largely leaves the firm s production technology and the economy s stochastic productivity shock process to resolve remaining variation in observed jobs and firm outcomes with the intention that the primitives be estimated with as little structure as possible given their importance to the consequences of the policy changes under consideration. IV. ESTIMATION I would prefer matched employer-employee data but the countries that have this don t have these types of jobs. Estimation of the model closely follows the identification argument. I first estimate preferences using the functional forms supplied above while allowing for heterogeneity in risk aversion and controlling for other job attributes. The second step estimates the general equilibrium model using the simulated method of moments taking preferences as given. The procedure simulates the economy and attempts to match a set of chosen moments that replicate patterns in the data. In practice this may also require some parameters to be calibrated. The survey was conducted in January 2016 with estimation using the above specifications currently underway.
Nick Frazier 14 V. ESTIMATION OF PREFERENCES Each individual n N at choice set j J has a utility specified for alternative i {1, 2, 3} such that utility Z( ) is given by Z nji = C1 ρ n 1 ρ n γ L1 τn 1 τ n + φx nji + ε nji (14) where ln ρ n = ρ + κ n and ln τ n = ρ + κ n for κ n N(0, σ 2 κ ). This induces correlation between risk aversion in hours and consumption while maintaining a reasonably parsimonious three parameters. ρ: mean risk-version in consumption τ: mean risk-version in hours X nji : vector of other characteristic for alternative Fixed effect for different degrees degree of flexibility degree of advanced notice ρ: vector of valuations for other job characteristics κ n : type of person n Mixed Logit Model ε nji ε njk < Z njk Z nji ε i.i.d extreme value type 1 Z njk Z nji logistic distribution κ n allows arbitrary correlation across j and i and correlation for risk-aversion in consumption and hours A. Data Description Survey Data Commission a survey targeted at recovering preferences Vignette: 2 job offers and an unemployment value Jobs the 6 attributes in a discrete set of values
Hours Variation in hours Wage Variation in wage (productivity pay) Scheduling flexibility Advanced notice Dimension Values Notes Advanced Notice 1 week You will learn your schedule each week 1 2 Weeks You will learn your schedule 1-2 weeks before 3+ weeks You will learn your schedule at least 3 weeks in advance Scheduling Flexibility None. Starting and finishing times are decided by your employer and you cannot change them on your own A little. Starting and finishing times are decided by your employer but with your input Some. You can decide the time you start and finish work, within certain limits A lot You are entirely free to decide when you start and finish work Hours 10 hours per week 20 hours per week 30 hours per week 40 hours per week Variance in Hours Fixed e.g. always h hours/week ±20% Hours vary between.8h, h, 1.2h ±50% Hours vary between.5h, h, 1.5h Pre-Tax Wage Low 0.9 w i,p + 0.1 w i,r Pessimistic Mid1 0.6 w i,p + 0.4 w i,r Low Mixture Mid2 0.4 w i,r + 0.6 w i,o High Mixture High 0.1 w i,r + 0.9 w i,o Optimistic Variance in Pay Fixed Always w per hour. ±10% Pay varies between.9w, w, 1.1w Table 1: A full description of the attributes for each job used in my vignettes.
Figure 1: An example of a vignette from my survey instrument used to elicit preferences. Nick Frazier 16
Nick Frazier 17 B. Estimation of General Equilibrium Model SMM or indirect inference similar to Cooper et al. (2007). Using observed jobs and moments for aggregate workforce.
Nick Frazier 18 REFERENCES Bloemen, Hans G., Job Search, Hours Restrictions, and Desired Hours of Work, Journal of Labor Economics, 2008, 26 (1), pp. 137 179. Cooper, Russell, John Haltiwanger, and Jonathan L. Willis, Search frictions: Matching aggregate and establishment observations, Journal of Monetary Economics, 2007, 54, pp. 56 78. Eriksson, Tor and Nicolai Kristensen, Wages or Fringes? Some Evidence on Trade-Offs and Sorting, Journal of Labor Economics, 2014, 32 (4), pp. 899 928. Golden, Lonnie, Irregular Work Scheduling and Its Consequences, Economic Policy Institute, 2015, Briefing Paper No. 394., Julia R. Henly, and Susan Lambert, Work Schedule Flexibility: A Contributor to Happiness?, Journal of Social Research and Policy, 2013, 4 (2). Henly, Julia R. and Susan J. Lambert, Unpredictable Work Timing in Retail Jobs: Implications for Employee Work-Life Outcomes, Industrial and Labor Relations Review, 2014, 67 (3), pp. 986 1016. Ingre, Michael, Torbjörn Åkerstedt, Mirjam Ekstedt, and Göran Kecklund, Periodic self-rostering in shift work: correspondence between objective work hours, work hour preferences (personal fit), and work schedule satisfaction, Scandinavian Journal of Work, Environment & Health, 2012, 38 (4), pp. 327 336. Lambert, Susan J., Passing the Buck: Labor Flexibility Practices that Transfer Risk onto Hourly Workers, Human Relations, 2008, 61 (9), pp. 1203 27., Anna Haley-Lock, and Julia R. Henly, Schedule Flexibility in Hourly Jobs: Unanticipated Consequences and Promising Directions, Community, Work and Family, 2012, 15 (3), pp. 239 315., Peter J. Fugiel, and Julia R. Henly, Precarious Work Schedules among Early-Career Employees in the US: A National Snapshot, Technical Report 2014. Mas, Alexandre and Amanda Pallais, Valuing Alternative Work Arrangements, Working Paper 22708, National Bureau of Economic Research 2016. Nassauer, Sarah, Wal-Mart Rolls Out a New Worker Scheduling System, Wall Street Journal, August 2016. Reynolds, Jeremy, You Can t Always Get the Hours You Want: Mismatches between Actual and Preferred Work Hours in the U.S., Social Forces, 2003, 81 (4), pp. 1171 1199. and Lydia Aletraris, Pursuing Preferences: The Creation and Resolution of Work Hour Mismatches, American Sociological Review, 2006, 71 (4), pp. 618 638. Rosen, Sherwin, The Theory of Equalizing Differences, in O. Ashenfelter and R. Layard, eds., Handbook of Labor Economics, Vol. 1 of Handbook of Labor Economics, Elsevier, 1987, chapter 12, pp. pp. 641 692. Stewart, Mark B. and Joanna K. Swaffield, Constraints on the Desired Hours of Work of British Men, The Economic Journal, 1997, 107 (441), pp. 520 535. Tabuchi, Hiroko, Abercrombie & Fitch to End On-Call Shifts for Workers, New York Times, August 2015. White, Gillian B., The Very Real Hardship of Unpredictable Work Schedules, The Atlantic, April 2015.
Figure 2: Taken from Lambert et al. (2014). Highlights the high degree of week-to-week variability in hours.