Flexibility, investment, and growth

s_I__

JOURNALOF

__

I!B

Monetary

Journal of Monetary Economics 34 (1994) 2 I.5238

ELSEVIER

Flexibility,

investment, Giuseppe

ECONOMICS

and growth

Bertola

(Received September 1991; final version received June 1994)

Abstract

This paper proposes a model of growth with diversifiable microeconomic uncertainty and uses it to study the efficiency costs and distributional effects of obstacles to labor mobility. Labor mobility costs reduce private and social returns to irreversible investment decisions, decrease the speed of capital accumulation, and lower a representative agent’s welfare. They can however shift income distribution towards ‘workers’, or individuals who own no accumulated factors of production and have no incentives to save any portion of their income flows in balanced-growth equilibrium. This may help explain why labor’s political representatives often favor provisions which decrease socially desirable labor mobility. Kc_laWV&

Job security;

JEL c’las.s(fication:

Firm-level

uncertainty;

Factor-income

distribution

D92; E24; E25

1. Introduction

This paper addresses open issues in two recent lines of research: (a) that concerned with the effects of job-security provisions in partial-equilibrium models of dynamic labor demand and (b) that focused on theoretical and empirical interactions among market structure, income distribution, and capital accumulation (or ‘endogenous growth’). Contributions to the first strand of

Previous versions were circulated as CEPR discussion paper #422 and NBER working paper #3864. Corrado Benassi. Samuel Bentolila, Avinash Dixit, Gene Grossman. a referee, and seminar and conference participants gave helpful comments on earlier drafts. I also thank I.I.E.S. (Stockholm) and I.G.I.E.R. (Milan) for hospitality and the National Science Foundation for financial support.

0304.3932;94i$O7.00 SSDI 030439329401

‘c) 1994 Elsevier Science B.V. All rights reserved 156 Z

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literature find that labor turnover costs have asymmetric effects on employment peaks and troughs. Inasmuch as firms discount future cash flows, in fact, firing costs tend to increase the average long-run labor intensity of production at given wages. This may rationalize the favor accorded by workers’ political representatives to ‘job-security’ legislation and to contractual provisions which make it costly or difficult for employers to shed labor in response to cost and/or demand shocks, without necessarily providing direct monetary benefits to redundant workers. [See Bentolila and Bertola (1990) and Bertola (1992) for specific formal models, and also Emerson (1988) and Piore (1986) for institutional information on the stringency and character of job-security provisions in different countries, sectors, and periods.] Insights from recent theoretical work on the institutional determinants of an economy’s growth rate become relevant when this type of reasoning is brought to bear on a general-equilibrium framework of analysis. An economy’s rate of growth is determined on the one hand by the aggregate propensity to save (rather than consume) currently available resources, on the other by the efficiency with which aggregate savings are used in furthering the economy’s production possibilities; the institutional structure of factor and output markets is obviously relevant to both aspects. Recent work by Bencivenga and Smith (1991), Greenwood and Jovanovic (1990), Levine (1991), and others emphasizes the growth implications of capital-market imperfections. This paper takes a complementary point of view, allowing capital markets to perfectly diversify all idiosyncratic uncertainty, and focuses on the growth implications of the dynamic structure of the market for labor, a nonaccumulated factor of production. Like other constraints on firms’ profit maximization programs, job-security provisions discourage investment, the more so if they are associated to a large share of nonaccumulated factors in disposable income. In dynamic general equilibrium, a slower pace of capital accumulation feeds back into the labor market to depress the dynamics of equilibrium wages. Recent work on the institutional determinants of equilibrium growth is also relevant to a second issue raised by partial-equilibrium models of dynamic labor demand. The conflicts of interest between ‘firms’ and ‘workers’ noted by such models need not be well-defined in general equilibrium models where individual agents draw income from both capital and labor. As noted in Bertola (1993) however, wages grow at the same rate as individual and aggregate consumption along a path of balanced growth sustained by infinite-horizon optimal saving decisions. Thus, realistic factor-income heterogeneity across individuals is self-sustaining in models which generate steady investment-driven growth equilibria, as any agent who happens to own no capital (a ‘worker’) will never have incentives to accumulate any. Bertola (1993) studies the politico-economic implications of such a stable ‘class’ structure for growth-oriented policies which have no distortionary effects other than those on private incentives to save (and, therefore, preserve the economy’s static production efficiency). Here, a similar

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perspective is applied to the welfare implications of institutions which, like job-security legislation, are probably motivated by a desire to redistribute income across classes of agents, but also burden the economy with a loss of static and dynamic efficiency. To explore such issues, the present paper models an economy which may be characterized by different degrees of flexibility in (re)allocating labor across heterogeneous production sites, or ‘firms’, in response to idiosyncratic shocks. Section 2 presents a benchmark dynamic general equilibrium model. As in Romer (1987, 1990) and Grossman and Helpman (1991) capital accumulation is modeled as a rational decision to create new, differentiated opportunities for production and employment (or ‘firms’). Here, each differentiated good is produced by a unit of capital, irreversibly allocated to a specific variety, and by a stochastically varying amount of a factor, ‘labor’, which is in exogenously given aggregate supply. Section 3 characterizes the economy’s equilibrium under costly labor mobility. Quite intuitively, constraints on employment flexibility reduce production efficiency and the value of firms, with adverse effects on private incentives to invest and, in equilibrium, on the level and rate of growth of product demand and wages. Section 4 discusses the effects of idiosyncratic uncertainty and labor mobility costs. As in partial-equilibrium models, turnover costs may increase the labor intensity of production and the equilibrium share of labor in aggregate income. Agents who draw income only from labor may find such level effects attractive, and lobby for job-security legislation. In dynamic general equilibrium, however, the welfare of the economy’s consumer-investors and workers is harmed - to a degree which depends on factor-income composition ~ by lower profitability of existing capital, reduced capital accumulation, and slower growth of productivity and wages. Section 5 concludes.

2. Idiosyncratic

uncertainty and labor mobility

The model economy features a continuously divisible labor force, whose total size is normalized to unity, and a continuum of production sites (‘firms’) of total measure M, at time t. The aggregate production flow at time r equals l/(1

Y, =

-a)

)

a
(1)

where xit denotes the output of the firm indexed by i E [0, M,] at time t. Each unit of the flow index (1) may be either consumed, or applied to physical investment and research so as to enlarge by one unit the measure of existing firms. Thus, output is allocated to aggregate consumption and investment according to Y, =

c, + hi,.

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Econon~ic.s 34 ( IYY4) 215- 238

Each existing firm employs labor in proportion to its production. The unit labor requirement of variety i is denoted l/rli in what follows, and will be assumed to fluctuate randomly in stationary fashion. With x < 1, individual varieties are imperfectly and symmetrically substitutable to each other, marginal returns to an individual firm’s production are decreasing in terms of aggregate output, and the index (1) rewards variety in its composition. On the consumption side, the aggregate Y may be seen as a Dixit and Stiglitz (1977) subutility function, attributing a taste for variety to the final consumers themselves, or as a CES function yielding a single consumable good from a list of intermediate inputs {xi) as in Romer (1987). On the investment side, the technology which makes it possible to produce previously unavailable varieties {xi) may be taken to use all existing intermediate inputs {.~i) and to become more efficient when many different such inputs are available. Inasmuch as an interpretation of (1) as a subutility function is appropriate, vi may represent a variety-specific taste parameter as well as purely technological productivity. Thus, this parameter is a generic index of an individual firm’s business conditions. The l/( 1 - 2) exponent applied to the integral of individual firms’ production reflects increasing aggregate returns to scale external to every firm. This functional form models in a simple way the idea that capital accumulation increases production efficiency in ways that can only partially be appropriated by individual investors, and makes it possible for the economy to grow endogenously at a nondecreasing rate even though production of accumulated factors requires a factor of production (labor) in given aggregate supply. Various rationalizations of similar assumptions have been proposed by Romer (in, e.g., 1986, 1990), Grossman and Helpman (1991), and others. For this paper’s purposes, what is essential is that growth be endogenously determined and that labor be necessary for production of each individual variety: the exact form of the externalities and the specific channels through which they operate are inconsequential for the results.’ 2.1. Instantaneous

equilibrium

A continuum of firms of infinitesimal size simplifies derivation of equilibria in two crucial respects: first, there are no integer constraints on the equilibrium ‘number’ of firms, M, and second, sources of uncertainty which are independently

I Increasing specialization and the production function’s ‘taste for variety’ suffice to sustain endogenous growth in the model proposed by Romer (1987). which however cannot accommodate an analysis of labor allocation since only the accumulated factor is used in production of differentiated goods. Endogenous productiwty growth might equivalently be modeled as a learning externality, under the assumption that the consumption price of investment is inversely related to M, (see Grossman and Helpman, 1991).

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and identically distributed across firms yield deterministic The price of variety i is proportional to

-715- -738

aggregate

219

outcomes.

the constant of proportionality being determined by choice of numeraire. Choosing output Y as the numeraire, it is easy to verify that the price of variety i is Z f .xy- ‘, where the index of ‘disembodied’ productivity, z/(1 -1) Z,r

Mt -uf !S

0

di

= Y:,

(3)

1

is taken as given by each infinitesimally small, independently managed firm, but is endogenous and, in equilibrium, grows along with aggregate output2 Firm i takes as given the competitively determined wage rate W, and chooses employment and production to maximize its cash flow. Under costless labor mobility, we have a sequence of static optimization problems: omitting time subscripts,

Xi

=

X(Wi,rli,Z)

=

arg max x, ( ZXi x --Xi1

)=

(~)‘~“~“.

For simplicity, let vi take only two values, qs and qb, with qs > qb. ‘Good’ firms enjoy favorable business conditions, indexed by qs, while ‘bad’ ones experience the low productivity and/or depressed demand state, indexed by qb.3 Denoting with rc the proposition of good firms, the full-employment condition for the (unitary) labor force can be written M

nx(Ws>Z) (

+(1

-7r)

X(w, qb? qb

‘Is

This and (4) yield the market-clearing tt’=

az((nij,

+ (1 - n)&,)h’f)1-2,

1

z, !

=

wage level (5)

‘The index of aggregate activity relevant to disembodied productivity’s level and dynamics is thus output rather than capital as in the Romer (1986) model of competitive firms with Cobb-Douglas production functions. While output and capital are proportional to each other in balanced growth, the formulation used here allows for static externalities through the level of Y as well as for standard investment-driven externalities. ‘Only unessential complications would be introduced if more than two 1, levels were allowed for. In particular, it would not be difficult to model product obsolescence, interpreting q as a taste parameter and allowing absorption at zero with positive probability.

G. Bertola JJournal qf’ Monetary

220 where

jj. =

product’is

Economics 34 (1994)

215-23X

pf” ’ mu) for typographical

equalized

convenience. When the marginal revenue across firms at this level, using (5) and (4) in (1) yields

Y = (7cFjs + (1 - rr)jlb)M,

(6)

and the shares of wage and profit income

are, respectively,

c( and 1 - M.

2.2. Gvo~c~th Under perfect labor mobility, the static equilibrium’s Cobb-Douglas reduced form is easily embedded in a dynamic growth model. According to (2) one unit of output may be exchanged for the perpetual right to produce a new differentiated commodity. To address issues of idiosyncratic uncertainty and labor mobility, let each currently good firm turn into a bad one with constant probability intensity 6 per unit time, and let it be impossible to transform existing firms back into consumption goods - as might of course be desirable after a negative business conditions shock is realized.4 Thus, bad firms remain in existence and wait for a positive business-conditions shock, which. occurs with constant probability intensity y. It is convenient to let a newly created firm be good with probability y/(6 + r), i.e., with the (ergodic) probability that an indefinitely old firm enjoys good business conditions, and to take all stochastic events to be independently distributed across firms: then, all uncertainty washes out in the aggregate, subject to the technical qualifications in Judd (1985) and the actual fractions rr and (1 - rc) of good and bad firms in the continuum [0, M] coincide, at all times, with the long-run probabilities of good and bad states for an individual firm.’ To model savings and consumption decisions, let wages and operating profits (in the form of dividends) accrue to agents with possibly different wealth, but identical objective functions

rem@(“l_, s l-0

~({c,})

E

’ dt,

CJ >o.

(7)

0

4The irreversibility constraint 6f, 2 0 is not binding at the aggregate level in a steadily growing economy. It has macroeconomic relevance, however, since it implies that idiosyncratic shocks to business conditions are reflected in existing firms’ value (to an extent that, in the next section, will depend on the flexibility of labor reallocation). 50ne might prefer to let new firms to be always ‘good’ instead. The proportion of good firms would then tend to be larger the faster is growth, and the economy would exhibit (nonstochastic) off-steadystate dynamics. It might be equally plausible to let q = nb for all new, inexperienced firms, however, and the nontrivial analytic complications introduced by either assumption are best left to further research.

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Let these agents interact in a perfect capital market where all idiosyncratic uncertainty can be costlessly diversified away, and the instantaneous lending/borrowing rate is r. In equilibrium, the interest rate r equals the private return to an optimally diversified portfolio of existing firms, which is indeed riskless since the market portfolio contains constant shares rt and (1 - 7~) of good and bad firms. Inserting (5) and (4) and averaging across firms, the constant dividend yield of existing firms is r = (1 - X)(rrq, + (1 - x)&).

(8)

Inasmuch as the probability that a new firm be good is the same as the fraction of good firms among the existing ones, the expected rate of return from investment in new firms is also given by the expression in (8) which is thus the appropriate cost of capital from the point of view of decentralized investment activity. Along a consumption path which maximizes (7) the Euler condition fr/c, = (r - p)/o holds for each individual’s consumption and, in the aggregate,

C,_r-p c, Inserting

CT’ (8) in (9) recalling

d”l=y__c dt

’

the aggregate

accumulation

constraint

!!!3>()

I’

dt

’

and noting that equilibrium output is proportional to M by (6) it is easy to verify that the economy’s equilibrium features balanced growth at rate

3_ Iii, Y*-M,=c,

c,=

1 ,((I

- tx)(7+, + (1 - X)jjb) - P) = 9,

(10)

if the parameters are such that 3 > 0 - to imply that irreversibility constraints do not bind in the aggregate - and that (1 - a) 9 < p ~ to imply that the integral in (7) converges and the consumers’ transversality condition is satisfied. The parameters introduced above yield r = 8.33% and, with p = 3% and 0 = 1 (logarithmic utility), 9 = 5.3%.

3. Costly labor mobility Labor moves across firms for two reasons in the previous section’s dynamic equilibrium. First, a firm’s employment changes discretely when it is hit by a business conditions shock. Second, a ‘creative destruction’ mechanism is at work: the growing measure M, of potential employers bids up the wage at rate 9 and, as Z grows at the slower rate cr9 in (4) every firm’s production and

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employment decline at exponential rate 9 throughout spells of unchanging business conditions, thus releasing labor for employment in new firms. This section proceeds to derive the economy’s dynamic equilibrium under the assumption that a real resource cost is incurred whenever one firm’s employment decreases and another’s increases. Recalling that firms’ products are differentiated along some dimension, these costs may represent firm-specific training or relocation expenses. Over and above such technological costs, labor mobility may also be hampered by the labor market institutions noted in the Introduction. It is convenient to let the incidence of all such mobility costs fall on firms, whether in the form of hiring costs (e.g., relocation allowances and training) or of firing costs (e.g., redundancy payments, which might of course offset the portion of relocation and retraining costs paid by fired workers rather than by their next employer, and dead-weight costs such as court procedures and sour industrial relations). As mobility is thus costless from the workers’ point of view, to prevent arbitrage opportunities the wage rate must be equalized across firms at every point in time.6 Retracing the previous section’s steps, the following subsections derive first the economy’s instantaneous equilibrium, and then its aggregate dynamic evolution. Under costly labor mobility, however, firms’ optimal labor-demand policies are forward-looking and take into account the economy’s rates of interest and growth. Thus, instantaneous clearing of the labor market and dynamic clearing of saving and investment paths are not independent of each other, and the model needs to be solved recursively. 3.1. Dynamic labor demand It is realistic and convenient to let the cost of reallocating one unit of labor increase at the same rate as labor’s average productivity, so that, in equilibrium, hiring and firing costs are proportional to wages: at time t, hiring a unit of labor at time t entails a cost hw, to each expanding firm, while contracting firms pay ,fw, per dismissed worker. In reality, training and relocation are labor-intensive activities and redundancy benefits are indexed to wage rates, and the assumed strict proportionality ensures that labor mobility costs remain relevant along a path of balanced growth.

‘Under the maintained assumption of perfect capital markets, the value of firms and the economy’s growth path depend on the total real cost of moving one unit of labor, regardless of its incidence on firms rather than on workers. Only minor algebraic complications would arise if workers were to bear some (net) mobility costs. Wages paid by good firms would be higher than those paid by bad firms, to induce labor mobility and finance the workers’ portion of mobility costs. Firms’ employment policies would take into account the expected present value of such wage differentials which. absent arbitrage, should coincide with the workers’ portion of labor mobility costs.

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Consider then the optimal labor demand policy the wage w,, the productivity index Z,, the growth It is shown in the Appendix that, if h andf‘are turnover, then the value-maximizing employment given by 1, = l,e- ‘I, that of a currently ‘bad’ firm satisfy: sz,@;-’

= W,(l + 9,f+

6(h +.1’) + rh),

XZ, q;: I;- ’ = W,(l + s.l’-

g(h +f’) - rf’).

34 11994)

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223

of a firm which takes as given rate 8, and the interest rate r. not so large as to prevent all level of a currently ‘good’ is by 1, = lb e - 9r, where 1, and Ib

(11)

Firms should adjust employment so as to equate the marginal revenue product of their employees, on the left-hand sides of (1 l), to the wage rate if h =f= 0, and to more complex expressions which capture the effects of turnover costs and of uncertainty if h and/orSare not zero. During spells of unchanging business conditions, firms continuously shed labor at proportional rate 9 because wages are steadily bid up by new entrant firms, hence the 9.f term. Firms whose business conditions have improved (and new firms) regard the annuity value of the hiring cost, rh, as part of the wage; symmetrically, firms which experience a negative shock shed less labor if rfis positive. The terms 6(h +.f) and y(h +f‘) reflect the cautiousness of firms’ hiring and firing policies in the presence of uncertainty. For example, I, is larger the smaller is 6, i.e., the more permanent is a positive business conditions shock: firms refrain from responding fully to positive shocks because with probability (1 - emdd’) = 6 dt the favorable developments may be immediately reversed, causing a loss of +f on the marginal employment decision. To characterize labor-market equilibrium, it is convenient to denote with p the proportion of the unitary labor force employed by the measure rcM of good firms. In full employment equilibrium, the complementary fraction 1 - p is employed by bad firms, and the employment levels of good and bad firms are given by

lg=&,

(1 -PI /,=(I

-7r)M

(1-a

Subtracting term-by-term in (1 l), we see that turnover costs drive a wedge of size (r + 6 + y)(h +f)w between labor’s marginal revenue product at firms in different business conditions. Fig. 1 illustrates the equilibrium relationship between turnover costs and labor allocation, plotting the marginal revenue product functions of good and bad firms as functions of p. Quite intuitively, labor is more readily reallocated from bad to good firms if mobility costs are small. Fig. 1 is drawn under roughly realistic parametric assumptions: 6 = y = 40%, so that spells of good and bad business conditions on average last a little more than two units of time (years) on average; x = 5, to obtain a realistic share of labor in total output; and 6, + ijb = f, to obtain a capital/output ratio of about fout

G. Berrola /Journal qf Monetary Economics 34 (1994)

0

0.4

0.5

0.6

0.7

0.8

215

0.9

1.0

P Fig. I. Labor market equilibrium. Marginal revenue product of labor at good firms (downward-sloping) and at bad firms (upward-sloping) as functions of the proportion of the labor force employed by good firms. The vertical line represents the wedge induced by mobility costs.

finally, qs/qr, = 5, a large value which reflects the empirical importance of idiosyncratic uncertainty noted by, e.g., Davis and Haltiwanger (1990) and ensures that labor turnover is positive for even very large mobility costs7 Turnover costs drive a wedge between the marginal revenue product of labor at good and bad firms, and obviously reduce the (static) efficiency of labor allocation. The definition (1) yields the expression Y, =

M,(7r-“p”q;

+ (1 - &a(1

- p)“#/‘l-~)

(13)

for the equilibrium output flow as a function of p. Taking term-by-term ratios of the two dynamic labor demand schedules in (11) and rearranging yields (14) where

WE

1 + l!Jf+ 6(h +f) 1+9f-::(h+f.)-rJ21

+ rh

‘By Eq. (12) firm-level employment responds to business condition shocks (I, > I,) as long as p > z, and this inequality implicitly defines the set in parameter space that is consistent with ongoing labor reallocation and a dynamic labor market equilibrium. Quite intuitively, labor mobility is more likely to be the equilibrium outcome the larger is rig/q,,, the more frequent are transitions between the two states (i.e., the larger are y and c?),and the steeper are marginal revenues as a function of employment.

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225

(in proportional terms) the wedge between labor’s marginal revenue at good and bad firms. It is readily shown that (13) is maximal at

Pm =

J.$J/((l - +ib + @g),

(15)

which corresponds to the equilibrium labor allocation implied by firms’ optimizing behavior only when labor mobility is costless and o = 1. To complete the derivation of instantaneous equilibrium for given M,, given r, and given 8, Eqs. (12) and (14) can be inserted in (11) to obtain an expression for the equilibrium wage rate: w, =

‘UM:-“Z,[(l

- 7c)jlb + 7rfigw1’(~-1)]1-S

1 1 + Sf-

$I

+f)

- rf’

(16) Recognizing from its definition in (3) that Z, = Y;, (13) and (14) can be used in (16) to express w, in terms of the parameters. Equilibrium wages increase at the same rate as production, consumption, and M, along a path of balanced growth. 3.2. Growth The previous subsections’ optimality and equilibrium relationships were conditioned on specific values of Yand 9, but the rates of interest and growth are endogenous to the economy’s dynamic equilibrium. This subsection closes the model considering the no-arbitrage conditions relevant to creation of new firms (and employment opportunities) and to the consumption/saving tradeoff. An entrepreneur who contemplates creating a new firm knows that its initial business conditions will be good with probability II and bad with probability (1 - rr). As these are idiosyncratic and diversifiable events, the total ex ante expected cost of creating a new firm must be equal to its expected value in equilibrium:

1 + (~4 + (1 - 4bJhw = ~W,,~,,O) + (1 - ~1f’(h,~ltnO),

(17)

where V(., ., .) denotes the value of a firm as a function of employment, business conditions, and time. Expressions for such value functions are derived in the Appendix. Higher hiring costs increase the cost of creating a new firm, and the cash flow of existing firms is reduced by the firing costs paid to reduce employment in the face of rising wages. A bit less obviously, idiosyncratic uncertainty enhances the impact of imperfect flexibility on private returns to investment, as mobility costs worsen the trade-off between revenue losses and costly turnover optimized by the employment policy (11) in the face of firm-level uncertainty and rising wages: firms’ cash flows suffer from lower operating revenues due to the relatively inefficient allocation of labor on the one hand, and from turnover cost payments on the other.

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G. Bertola/Journal41 Monetury Economics 34 11994) 215 238

/

Z-

T such

-

that

I+(rrla+(l-n)r,)wh=~v~~l~~~v~.

/

\

zd

with: /

‘\

/

h=O.O.

f=O.O

h=0.3,

f=0.3

h=0.4.

f=0.4

h=0.5,

f=0.5

/ / / Ed

/ / -6%

x/

89


0

./

5: x

0.025

0.035

0.045

0.055

0.065 d

Fig. 2. No-arbitrage conditions. The dashed line plots the interest rate as a function of consumption growth, and is based on the optimality condition for consumption/saving choices. Other lines plot the rate of return that equates a firm’s expected value to its creation cost in balanced-growth equilibrium. for various levels of labor mobility costs.

It can be shown that Eq. (17) is satisfied by a unique rate of return r for each growth rate 9. Such loci in r, 9 space are plotted as solid lines in Fig. 2, using the baseline parameters above and a variety of hiring and firing cost parameters. The economy is in dynamic equilibrium at the intersection of the relevant no-arbitrage locus with the r, 8 relationship implied by (9) r = p + 09,

(18)

plotted in the Fig. 2 as a dashed line. Since l,, lb, W, and V(.) are all highly nonlinear functions of r and LJ,no closed-form solution is available, but a simple iterative procedure on the expressions resulting from insertion of (18) in (17) readily yield numerical solutions for any admissible set of parameter values.

4. Welfare implications In the costless-mobility equilibrium of Section 2, the accumulation constraint C, = Y, - 9A4, and Eq. (6) set the initial level of aggregate consumption at CO = (rr(q, - &,) + ij6 - 9)Mo. As long as private investment opportunities are those considered above, the distribution across agents of consumption levels is irrelevant to the economy’s dynamic equilibrium: the constant-elasticity utility function that sustains steady aggregate growth also ensures that the each individual’s consumption path, however large or small at any given point in

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time, grows at the same rate as the aggregate economy’s, This section evaluates the impact of labor mobility costs on each individual’s initial consumption level, on the aggregate growth rate 9, and hence on the welfare measure obtained by integration of (7).

Consider first a ‘representative’ individual, i.e., one whose factor endowments and income streams are scaled-down version of the aggregate economy’s. Such an individual faces the same tradeoff between higher initial consumption and faster growth as the aggregate economy; the implied welfare measure is of course the only relevant one for an economy inhabited by identical agents, and would also be the appropriate objective for an economy-wide social body with access to lump-sum redistribution. As in other models where positive production externalities sustain steady endogenous growth in the presence of nonaccumulated factors of production, decentralized supply and investment decisions which take as given the level and dynamic behavior of {Z,) only partially internalize social returns to accumulation, and the representative individual’s welfare could be increased if investment and savings subsidies were used to decrease initial consumption and increase its growth rate. As to the specific extensions proposed in this paper, it may be interesting to note that diversifiable firm-level uncertainty per se need not decrease welfare. In costless-mobility equilibrium, the level and growth rate of output are convex in qs and qb if r > $: in this case, by Jensen’s inequality, an ergodic-mean-preserving spread of firm-level productivity increases expected profits per unit time, enhances production, makes investment more attractive, and has a positive effect on growth and welfare.’ Further, larger values of 6 and y, which imply more unstable business conditions for any given ergodic mean, have no effect on output, growth, and welfare as long as the proportion 7c of good firms in the economy is unchanged. An increase in turnover costs, conversely, reduces the level of production at all points in time, decreases the growth rate, and unambiguously worsens the representative individual’s welfare. Even in the absence of business conditions variability (qs = qb), labor mobility costs are relevant since labor needs to be steadily reallocated from existing to new firms; if qs > Q,, the growth and welfare effects of low flexibility are stronger the more variable are individual firms’ business conditions, i.e., the larger are y and 6. To isolate these effects from the functional-form-dependent ones based on Jensen’s inequality, it

‘The profit function of a competitive firm is always convex in prices and wages (Hartman, 1972). The firms in the economy under consideration are monopolistically competitive, and cost and demand uncertainties may or may not increase their expected profits, depending on how they are measured and on functional forms.

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Table 1 Growth rate (9)

6 6 6 6 6

= = = = =

0. I i’ = 0.2 *(zz 0.3 ;>= 0.4 ‘/ = 0.5

7’ =

f=O

.1’= 0.2

./= 0.5

.f= 1.0

,f = 1.5

0.0533 0.0533 0.0533 0.0533 0.0533

0.0527 0.0521 0.0509 0.049 1 0.0463

0.0512 0.0475 0.0397 0.0268

0.049 1 0.0397 0.02 10

0.0458 0.0276

Missing entries indicate that there is no labor mobility; 6, ;J denote the probability intensity per unit time of negative and positive firm-level shocks; ,f denotes dismissal costs per unit worker, as a proportion of consumption wage per unit time.

suffices to consider mean-preserving spreads of the marginal-revenue indexes jls and Pjb,defined below Eq. (5) which enter linearly in (6) and (8). Thus measured, higher uncertainty is completely irrelevant in the costless-mobility case, and unambiguously welfare-decreasing when labor mobility is costly. To evaluate the quantitative relevance of these results, the growth rate can be solved numerically from (17) and the level of aggregate consumption can be computed subtracting from aggregate production the resources spent on labor reallocation and capital accumulation. 9 Table 1 reports the equilibrium level of output for various levels of turnover cost and idiosyncratic uncertainty parameters, fixing the other parameters at the baseline values discussed above and setting M, = 1, h = 0. Table 2 reports the corresponding growth rates, and Table 3 reports the implied levels of the representative individual’s welfare. For realistic levels of idiosyncratic uncertainty, the growth and level effects of labor mobility costs are far from negligible: both the level and the growth rate of output fall by about half before labor mobility is shut down. The welfare measure is also drastically reduced by the resulting downward shift of the consumption path. In equilibrium, there are no incentives to speed up labor mobility, as the optimality conditions on which the above derivations are based exhaust all decentralized market interactions between atomistic workers and firms. Like direct subsidies to investment and savings, policy measures intended to reduce labor mobility costs and/or idiosyncratic business conditions variability may only be implemented through government intervention (or other forms of

‘Per unit time, 9 units of labor move from old to new firms, and (lyt - Ibl) 6nM, from existing firms turned bad to existing firms turned good. The cost of these flows in terms of output is (h +.f) w, per unit of labor. Thus, C, = Y, - 9 M, - (h +/‘) W, (9 + K M,6(19, - jr,,)). Since rvlr Y,, and M, grow at rate Sand Igf and I,, decline at the same rate, the proportion of output spent on labor reallocation is constant in steady growth equilibrium.

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Table 2 output

fi=y=O.l 6 = ;’ = 6 = ^, = 6 = .I = 6 = .I, =

(Yo)

0.2 0.3 0.4 0.5

j-=0

f = 0.2

f=OS

J=

0.250 0.250 0.250 0.250 0.250

0.249 0.248 0.245 0.239 0.23 1

0.247 0.237 0.215 0.178

0.242 0.217 0.163

1.0

f=

1.5

0.236 0.185

Missing entries indicate that there is no labor mobility; S,r denote the probability intensity per unit time of negative and positive firm-level shocks; f denotes dismissal costs per unit worker, as a proportion of consumption wage per unit time.

Table 3 Representative

(j = 6 = 6= 6= 6=

.,’ = 0.1 ;’ = 0.2 .,’x 0.3 .,’= 0.4 .,’= 0.5

agent welfare: cumulative

discounted

.f=O

f‘= 0.2

5.05 5.05 5.05 5.05 5.05

2.46 0.55 - 1.90 ~ 5.15 ~ 9.49

utility from c, = Y, - 9,&f, ,f = 0.5 - 1.02 ~ 1.53 - 18.7 - 36.2

J=

1.0

- 4.19 - 18.6 - 43.9

.f = 1.5 - 9.12 - 34.7

Missing entries indicate that there is no labor mobility; 8,~ denote the probability intensity per unit time of negative and positive firm-level shocks; .f denotes dismissal costs per unit worker, as a proportion of consumption wage per unit time.

cooperative behavior). Such measures would improve firms’ cash-flows and, if financed by lump-sum or consumption taxes, would beneficially distort private choices towards faster capital accumulation. Thus, the externality that makes endogenous growth possible in the presence of a nonaccumulated factor of production not only magnifies the welfare effects of imperfect flexibility, but also justifies policies tending to improve flexibility.” 4.2. Income

distribution

and excess

turnover

costs

If flexibility is so desirable in the context of the proposed model, why does real-life legislation often tend to restrict labor mobility, and why do measures

“‘If static and intertemporal markets were perfect and complete, conversely, the decentralized equilibrium with adjustment costs would achieve a constrained optimum, and adjustment assistance would not improve the representative individual’s welfare (a point made by Mussa, 1978, and others in different contexts).

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intended to reduce job security encounter fierce opposition? The question might of course be answered invoking many realistic features left out of the model outlined above, such as wage bargaining, search unemployment, capital-market imperfections, and worker heterogeneity. However, labor mobility costs in excess of technologically given ones may also be rationalized recognizing that they may positively affect the income and welfare of agents other than ‘representative’ ones and that, inasmuch as if lump-sum redistribution is unfeasible, such individuals’ welfare is in general relevant to the politico-economic process by which institutions are formed. Consider first the distributional impact of turnover costs on the labor market’s instantaneous equilibrium. Turnover costs inhibit both hiring and firing and, as emphasized by the partial-equilibrium studies referenced in the Introduction, may or may not decrease a given firm’s long-run average labor demand. The insight is directly relevant to the present paper’s equilibrium framework of analysis: as uncertainty is purely idiosyncratic and new firms are spread across states with the ergodic probabilities, in fact, the cross-sectional average labor demand function coincides with the long-run mean over time for a representative firm. At given wages, labor mobility costs reduce labor demand by firms in good business conditions, but increase labor demand by firms in bad business conditions, and in long-run equilibrium the endogenous full-employment wage rate may be an increasing or decreasing function of turnover costs. Indeed, the market-clearing wage in (16) is a U-shaped function of turnover costs for given r, 9, M,, and Z,. On the right-hand side of (16), the term in square brackets is a decreasing function of the wedge tr) between the marginal revenue product of labor at different firms, which in turn is larger for larger turnover costs. Quite intuitively, the market-clearing wage is lower, in output terms, when labor is less efficiently allocated across firms of different productivity. Since r must exceed 9 for any admissible set of parameters, however, the last term on the right-hand side of (16) increases in each of h and ./; and does so at an increasing rate. The equilibrium wage rate is then an increasing function of turnover costs when their positive effect on the last term more than offsets their negative effect on the efficiency of labor allocation. Fig. 3 plots the equilibrium wage as a function of turnover costs, using the baseline parameter values discussed above. In the figure, w starts increasing in fatf% 0.9 if h = 0: thus, lower flexibility increases the wage if firing costs exceed 11 months of wages. Conversely, iff= 0, then N begins to increase in h only at h z 1, and not very strongly. While the point at which the wage effect of mobility costs changes sign depends on the parameters in complex ways, the tendency of average labor demand and equilibrium wages to increase more as a function of firing than of hiring costs holds in some generality, and is due to the discounting efSeect discussed in Bentolila and Bertola (1990) and Bertola (1992). When hiring, firms take into account the full annuity value of hiring costs, but only the expected discounted value of firing costs from the time of the next adverse shock

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4_ d

@=z:

w

=I_

h=O)

/

d /

/

3_ d

/ / /

w

2 6

(h=z;

f=O)

L

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3 2

1.4

1.5

(=f.h)

Fig. 3. Equilibrium wage and turnover costs. The dashed line plots the wage that equates labor demand to (given) labor supply as a function of firing costs per unit worker, measured as a fraction of the wage, assuming that hiring costs are zero. The solid line plots the same as a function of hiring costs, for zero firing costs.

to business conditions; as the converse applies at times when firing decisions are taken, higher firing (hiring) costs tend to discourage labor shedding more (less) than job creation. As to the other parameters, the net effect of more job security is more likely to be positive the larger is the difference between the interest rate and the rate of growth, the less convex is marginal revenue product as a function of employment, and the more persistent are spells of good business conditions. 4.3.

Workers

us. incestors

Organized labor may have incentives to lobby against flexibility-oriented measures if labor mobility costs have (locally) positive effects on equilibrium wages. In dynamic general equilibrium, however, higher wages and lower efficiency affect firms’ current profitability on the one hand, and forwardlooking investment decisions on the other. To analyze the distributional impact of such indirect effects, it is helpful to note that the model features balanced growth sustained by constant income shares for accumulated and nonaccumulated factors of production and by infinite-horizon saving decision. Thus, the model economy belongs to the class analyzed by Bertola (1993) and can accommodate realistic heterogeneity in factor endowments. Along a full-employment growth path, every unit of labor contributes wt to its owner’s income at every time t and, as the rate of growth of wage income is the same as the desired rate of growth of consumption, no part of labor income is ever saved.

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Any initial dispersion of factor incomes across agents is perpetuated by different saving propensities out of wages and profits and, as in Bertola (1993) it is then meaningful to study how ‘classes’ of labor-income and capital-income earners may be differently affected, in welfare terms, by institutional and market features which alter the economy’s growth rate. Consider for example the effects of job security provisions on the welfare of ‘workers’, i.e., agents who own only labor. Such individuals earn no capital income, hence they are indifferent to the decrease in interest and profit rates caused by limited labor mobility. If the level and dynamic behavior of disembodied productivity {Z,} is viewed as exogenous as would be appropriate in the context of the Solow (1956) model of growth ~ workers have apparent incentives to slow. down labor reallocation if the economy is on the upward-sloping portion of the relationships in Fig. 2. In dynamic equilibrium, however, a higher income share for labor discourages capital accumulation and, as in Bertola (1993) decreases the growth rate of labor productivity and wages. Moreover, and inasmuch as higher wages are accompanied by worse efficiency of labor allocation, limits to employment flexibility have not only distributional, but also dead-weight-loss effects on aggregate production and on the productivity index Z. While external to every agent’s decision problem, such effects should of course be taken into consideration by social bodies, such as unions and workers’ political representatives. Constraints on labor mobility can conceivably increase the welfare of a typical worker, i.e., the integral of (7) with c, = w,. For this to be the case, however, not only must their effect on income distribution be favorable to labor, as is the case on the upward-sloping portion of the wage schedules in Fig. 3, but it must also be stronger than their negative effect on the level and rate of growth of output and ‘disembodied’ productivity, Z. For this paper’s functional forms and baseline parameter values, the welfare impact of higher labor mobility costs is negative for workers as well as for firm-owners and representative individuals. Table 4 reports the wage, Table 5 the share of labor in income, and Table 6 the Table 4 Wage level (wO)

6 6 6 6 6

= = = = =

7= 7= 7= ‘r =

0.1 0.2 0.3 0.4 )’ = 0.5

f‘=o

J= 0.2

./= 0.5

.f=

0.167 0.167 0.167 0.167 0. I67

0.156 0.149 0.143 0.137 0.131

0.146 0.134 0.122 0.108

0.139 0.123 0.103

1.0

1’= 1.5 0.132 0.111

Missing entries indicate that there is no labor mobility; 6,,-1denote the probability intensity per unit time of negative and positive firm-level shocks; f denotes dismissal costs per unit worker, as a proportion of consumption wage per unit time.

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Journal~$'Monrtur~ Economies 34 (lY94) 215-238

Table 5 Share of wages in output .f‘=o

.f = 0.2

.f= 0.5

f=

1.0

j=

1.5

;’ = 0.1 6 z i'= 0.2 6 = i'= 0.3

0.667

0.624

0.591

0.573

0.562

0.667

0.602

0.566

0.564

0.598

0.667

0.584

0.566

0.635

6=y=O4 g = ;'= 0.5

0.667

0.571

0.608

0.667

0.565

6=

Missing entries indicate that there is no labor mobility; ii,; denote the probability intensity per unit time of negative and positive firm-level shocks; .f denotes dismissal costs per unit worker, as a proportion of consumption wage per unit time.

Table 6 Worker welfare: cumulative

discounted

.f= 0 6 =

6 6 g 6

= = = =

;’

=

;’ = ;’ = ;’ = ;‘ =

0.1

0.2 0.3 0.4 0.5

-

0.466 0.466 0.466 0.466 0.466

utility from ct = w,e”. .f= 0.2 - 3.42 ~ 5.56 - 8.26 - 11.8 ~ 16.4

.f = 0.5 - 7.26 - 14.3 - 26.0 - 44.4

.f=

1.0

~ 11.3 - 25.9 - 52.4

j.=

1.5

- 16.5 - 42.7

Missing entries indicate that there is no labor mobility; S, 7 denote the probability intensity per unit time of negative and positive firm-level shocks; ,f denotes dismissal costs per unit worker, as a proportion of consumption wage per unit time.

welfare of a unit-sized worker, using the baseline parameters of Section 2, various turnover cost, and different levels of idiosyncratic uncertainty. Even though more job security may increase the share of labor (as shown in Fig. 2) its negative effect on the productivity indicator Z is such as to make the wage a decreasing function of turnover costs over all the range of parameters considered. Thus, manipulation of turnover costs may make it possible for ‘labor’ to extract a larger share of a (smaller) producer’s surplus but, when all general equilibrium interactions are taken into account, stringent job security provisions yield decentralized equilibria that are worse, even for individuals who own only labor, than those implied by technological mobility costs.

5. Conclusions This paper proposes a model of aggregate growth with a detailed microeconomic structure, and uses it to study the general equilibrium effects of costly

234

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labor mobility. Labor mobility costs decrease the economy’s efficiency. From the point of view of a representative individual, the same market imperfections that make endogenous growth possible in the presence of nonaccumulated factors of production would justify subsidies to labor mobility (as an alternative to direct investment subsidies). Obstacles to labor reallocation also affect the share of wages in aggregate income, however, and this may induce individuals who own only labor to lobby for stringent job security provisions. The model departs from representative-agent analyses in two key respects: production sites are heterogeneous and institutions are viewed as the possibly rational result of politico-economic conflicts between classes of agents with different factor endowments. The interaction of endogenous growth and idiosyncratic uncertainty is crucial to the results. If all firms were the same, constraints on labor mobility would still be relevant, as in a growing economy an exogenously given supply of labor needs to be relocated from old to new productive activities, but would have no effect on equilibrium wages. Conversely, if the level and growth rate of productivity were exogenously given, then lower profit rates would not feed back into wage determination, and would be a matter of indifference to workers. Workers never save along a path of steady, endogeneous growth, hence it is meaningful to analyze their ‘class’ preferences regarding growth-relevant institutions. Inasmuch as wage growth depends (through external effects) on the pace of capital accumulation, however, low-flexibility/low-growth equilibria may yet be bad ones for workers as well as for investors and ‘representative’ agents. The results might be read as providing a new explanation for different growth rates in different countries and different historical periods. For a given intensity of technological idiosyncratic shocks, the model predicts less labor mobility and slower growth if labor has substantial bargaining or political power in a polarized society.’ ’ If it were possible to control for every other source of systematic variation in growth rates, we would expect larger intersectoral employment flows to be associated to faster growth, and stronger union power to be negatively correlated with both growth performance and labor mobility. The comparative experiences of Far Eastern economies analyzed by Young (1989) give some support to such relationships, and further (at least) anecdotal evidence could certainly be gathered. However, so many features of an economic system are relevant for growth (and so few data on long-run growth are available) that it might be misleading to focus narrowly on any given one. This paper’s contribution may also be read as

I I In the context of the model. .f’measures mobility costs across products, which may or may not correspond to mobility costs across corporation. The Japanese system of lifetime employment and frequent retraining corresponds to low 1; while constraints on labor redeployment inside the firm such as those noted by Piore (I 986) would increase 11

G. Bert&

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235

an extension of previous partial-equilibrium work on dynamic labor demand, offering theoretical insights into realistic interactions of growth and accumulation with labor-market equilibrium, politico-economic institutions, and industrial structure. Further work could relax several simplifying assumptions made above. In principle, the model could accommodate realistic business conditions processes with more than two states, search unemployment, mobility costs borne by labor, and off-steady-state dynamics due to quality differences between new and existing productive opportunities. It might also be interesting to explore how some aspects of the above analysis may be applicable to markets for other nonaccumulated factors, such as land and energy, which are often subject to stringent static and dynamic institutional constraints.

Appendix: Firm-level value and policy functions In steady-growth equilibrium, the rate of return is constant wages and unit turnover costs grow at rate 9; and disembodied grows at rate 9’~ Denote with V(/, q, t) the value of a firm 1 workers and whose business conditions index is q, at time employment policy is optimal, the value function must solve the equations

and equal to r; productivity Z, which employs t. If the firm’s pair of Bellman

(A.11 rv(I,,~,,

t)dt = max(Z,e”“‘(tl,l,)” It

- \~0e29’(It - h&l’

+f‘[j,]-))dt

(A.9 where [xl+ = max(x, 0), [x] = min(x, 0), and .t denotes the left time derivative of Y. In words, the required return on the value of the firm over a small time interval dt must equal the sum of the cash flow (the term multiplied by dt) and of the expected capital gain or loss per unit time, computed considering that over a time interval dt a good firm becomes bad with probability (1 - emad’) = 6 dt and a bad one becomes good with probability (1 - eC ydf)= 7 dt. By inspection of (A.l) and (A.2), the value function is independent of time if employment decreases exponentially at rate 9 in the absence of business

236

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condition changes, i.e., if 1, = 1,e - ” when ylt = qs and 1, = &e - ” when Q = y]b. In this case, (A.l) and (A.2) are equivalent to

- V(l,,vg,O) -

(1,- l,)fw)),

(A.3)

-

(lb -

(A.4)

~(lb>~b,o)

-

lb) hw)}.

Along optimal employment paths, (A.l) and (A.2) hold identically (without the max operator), hence may be differentiated with respect to 1, (the resulting equations set to zero the value of a ‘feasible perturbation’ that varies employment by a small amount). Equivalently, under exponential decline of employment, (A.3) and (A.4) may be differentiated with respect to 1, and lb respectively. This yields a pair of linear relationships between the possible (detrended) levels of labor’s marginal revenue product and marginal value:

with solutions (r +

6 + y)rv,

= (r + y)(xZq~l~ml - (1 + Sf) w)

+ 6(aZigl;-’ (r +

)’ +

- (1 +

9f’)W)>

(A.3

d)rvb = (r + 6)(xzv]~l~-’ - (1 + $f)w) + y(aZrg-’

- (1 + Sf) w).

(A.6)

If the parameters are such that 1, > lb, then the firm’s employment jumps at times when business conditions change, and for such jumps to be optimal it must be the case that vg = h, vb = -f, or that the marginal value of hired/fired labor be equal to (marginal) hiring or firing costs. These conditions and (A.5) (A.6) form a linear system of equations, whose solution is given as Eq. (11) in the main text. (If h andfare large relative to y, 6, and qs/qb, the solution may lie outside of the region where 1, > lb. The employment path is then piecewise constant or declining at rate 9, with neither hiring nor firing at times when business-condition shocks are realized. This special case is not relevant to the subject matter of the paper, and details are omitted.)

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231

Using I, and lb from (11) in (A.3) and (A.4), it is straightforward to obtain time-invariant expressions for the value of firms in ‘good’ and ‘bad’ business conditions:

Z(q,I,)” - w(l,(l + 8.f) + W,, vs, t) = (r + Y) r(r + 1: + 6) +

Ib)f)

gmblb)a - WUb(l+ Sf) + YU,- lb)h 1 r(r +

+

w, -

tr

+

S)Z(qbib)l

-

w(lb(l r(r

(A.7)

6)

‘/ +

+ +

gf) y +

+ 6)

y(l,

-

lb)

/‘I ) OW

References Bencivenga, Valerie R. and Bruce D. Smith, 1991, Financial intermediation and endogenous growth, Review of Economic Studies 58, 195-209. Bentolila, Samuel and Giuseppe Bertola, 1990, Firing costs and labour demand: How bad is eurosclerosis?, Review of Economic Studies 57, 381402. Bertola, Giuseppe, 1992, Labor turnover costs and average labor demand, Journal of Labor Economics 10, 389411. Bertola. Giuseppe, 1993, Factor shares and savings in endogenous growth, American Economic Review 83, 118441198. Davis, Steven J. and John Haltiwanger, 1990, Gross job creation and destruction: Microeconomic evidence and macroeconomic implications, in: O.J. Blanchard and S. Fischer, eds., NBER macroeconomics annual 1990 (MIT Press, Cambridge, MA) 1233168. Dixit, Avinash K. and Joseph P. Stiglitz, 1977, Monopolistic competition and optimum product diversity, American Economic Review 67, 297-308. Emerson, Michael, 1988, Regulation or deregulation of the labor market, European Economic Review 32, 775817. Greenwood, Jeremy and Boyan Jovanovic, 1990, Financial development, growth, and the distribution of income, Journal of Political Economy 98, 1076-l 107. Grossman, Gene M. and Elhanan Helpman, 1991, Innovation and growth (MIT Press, Cambridge, MA). Hartman, Richard, 1972, The effects of price and cost uncertainty on investment, Journal of Economic Theory 5, 238-266. Judd. Kenneth L., 1985, The law of large numbers with a continuum of IID random variables, Journal of Economic Theory 35, 19-25. Levine, Ross, 1991, Stock markets, growth, and tax policy, Journal of Finance 46, 1445-1465. Mussa, Michael, 1978, Dynamic adjustment in the HeckscherOhlin-Samuelson model, Journal of Political Economy 86, 775-791. Piore, Michael, 1986, Perspectives on labor market flexibility, Industrial Relations 25, 146166. Romer, Paul M., 1986, Increasing returns and long-run growth, Journal of Political Economy 94, 100221037.

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Romer, Paul M., 1987, Growth based on increasing returns due to specialization, American Economic Review Papers and Proceedings 77. 56-72. Romer, Paul M., 1990, Endogenous technological change, Journal of Political Economy 98, S71-SlO2. Solow, Robert M., 1956, A contribution to the theory of economtc growth, Quarterly Journal of Economics 70, 65 94. Young, Alwyn, 1989, Hong Kong and the art of landing on one’s feet: A case study of a structurally flexible economy. Unpublished Ph.D. dissertation (Fletcher School of Law and Diplomacy, Medford, MA).