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Determinants of long-run unemployment.



1. Introduction

Although a high rate of economic growth and a low rate of unemployment are two major goals of most governments, the relationship between these two goals is not well understood. For example, Pissarides (1990) shows that the long-run adj. 1. relating to or extending over a relatively long time; as, the long-run significance of the elections s>.

Adj. 1. long-run
 unemployment rate and growth rate are always negatively correlated cor·re·late  
v. cor·re·lat·ed, cor·re·lat·ing, cor·re·lates

v.tr.
1. To put or bring into causal, complementary, parallel, or reciprocal relation.

2.
, whereas Aghion and Howitt Howitt could refer to:
  • Howitt Hall a hall of residence at Monash University, Australia.
  • Mount Howitt a mountain in the Alpine National Park, Victoria, Australia.
  • Alfred William Howitt an Australian anthropologist and naturalist.
 (1994) conclude that the former can be an inverted inverted

reverse in position, direction or order.


inverted L block
a pattern of local filtration anesthesia commonly used in laparotomy in the ox.
 U-shaped function of the latter. More recent studies by Eriksson The surname Eriksson (also spelled Erikson or Ericsson) is a historically famous Scandinavian appellation. The most famous bearer of this name was Erik the Red, father of Leif Erikson, who found the Americas before Christopher Columbus's supposed discovery; though  (1997) and Falkinger and Zweimuller (2000) suggest that growth can either increase or decrease unemployment depending on the sources of economic growth. The empirical evidence on this issue is equally ambiguous. Bean and Pissarides (1993) find that there does not exist any significant relationship between unemployment and growth across OECD OECD: see Organization for Economic Cooperation and Development.  countries. Caballero cab·al·le·ro  
n. pl. cab·al·le·ros
1. A Spanish gentleman; a cavalier.

2. A man who is skilled in riding and managing horses; a horseman.
 (1993) finds that these two series are weakly weak·ly  
adj. weak·li·er, weak·li·est
Delicate in constitution; frail or sickly.

adv.
1. With little physical strength or force.

2. With little strength of character.
 positively correlated in the UK and United States United States, officially United States of America, republic (2005 est. pop. 295,734,000), 3,539,227 sq mi (9,166,598 sq km), North America. The United States is the world's third largest country in population and the fourth largest country in area. . However, Muscatelli and Tirelli (2001) find that though unemployment has a significant negative effect on growth in Canada Canada (kăn`ədə), independent nation (2001 pop. 30,007,094), 3,851,787 sq mi (9,976,128 sq km), N North America. Canada occupies all of North America N of the United States (and E of Alaska) except for Greenland and the French islands of , France, Germany Germany (jûr`mənē), Ger. Deutschland, officially Federal Republic of Germany, republic (2005 est. pop. 82,431,000), 137,699 sq mi (356,733 sq km). , Italy Italy (ĭt`əlē), Ital. Italia, officially Italian Republic, republic (2005 est. pop. 58,103,000), 116,303 sq mi (301,225 sq km), S Europe. , Norway Norway, Nor. Norge, officially Kingdom of Norway, constitutional monarchy (2005 est. pop. 4,593,000), 125,181 sq mi (324,219 sq km), N Europe, occupying the western part of the Scandinavian peninsula. , Japan, and Sweden Sweden, Swed. Sverige, officially Kingdom of Sweden, constitutional monarchy (2005 est. pop. 9,002,000), 173,648 sq mi (449,750 sq km), N Europe, occupying the eastern part of the Scandinavian peninsula. , its impact is not significant in Australia Australia (ôstrāl`yə), smallest continent, between the Indian and Pacific oceans. With the island state of Tasmania to the south, the continent makes up the Commonwealth of Australia, a federal parliamentary state (2005 est. pop. , Austria Austria (ô`strēə), Ger. Österreich [eastern march], officially Republic of Austria, federal republic (2005 est. pop. 8,185,000), 32,374 sq mi (83,849 sq km), central Europe. , the UK, and the United States.

Aghion and Howitt (1994) and Pissarides (1990) are two influential theoretical studies that have investigated the long-run effect of growth on employment. (1) In Pissarides (1990), the long-run growth rate is exogenous Exogenous

Describes facts outside the control of the firm. Converse of endogenous.
. Because higher productivity growth raises the rate of return from job creation, and hence increases the exit rate from unemployment, the unemployment rate and growth rate are always negatively correlated in his model. To reconcile the conflict between the model prediction and the empirical evidence, Mortensen Mortensen is a surname of Danish origin, meaning son of Morten. It is currently the 20th most common surname in Denmark. [1]

It may refer to the following people:
  • Carlos Mortensen
  • Christian Mortensen
  • Henry Mortensen
  • Dale T.
 and Pissarides (1998) incorporate renovation costs into a model similar to that of Pissarides (1990). (2) They show that the relationship between the unemployment rate and growth rate depends on the renovation costs. That is, they are negatively correlated if the renovation costs are low and positively correlated if the renovation costs are high.

Aghion and Howitt (1994) identify two competing effects of growth on unemployment. On the one hand, as in Pissarides (1990), an increase in growth increases the returns from job creation, which reduces the unemployment rate (the capitalization capitalization n. 1) the act of counting anticipated earnings and expenses as capital assets (property, equipment, fixtures) for accounting purposes. 2) the amount of anticipated net earnings which hypothetically can be used for conversion into capital assets.  effect). On the other hand, an increase in growth shortens the duration of job matches. Because shorter duration of job matches directly raises the job separation rate and indirectly discourages job creation (the creative destruction effect), a higher growth rate could increase the unemployment rate. The results (Propositions 1 and 2) in Aghion and Howitt (1994) suggest that the unique equilibrium equilibrium, state of balance. When a body or a system is in equilibrium, there is no net tendency to change. In mechanics, equilibrium has to do with the forces acting on a body.  unemployment rate can be represented as an inverted U-shaped function of the growth rate whenever the entry cost is positive but sufficiently small sufficiently small - suitably small .

Because productivity growth is exogenous in Pissarides (1990) and Mortensen and Pissarides (1998), the cross-country cross-coun·try  Abbr. XC or X-C
adj.
1. Moving or directed across open country rather than following tracks, roads, or runs: a cross-country race.

2.
 variations in economic growth cannot be explained. In contrast, the long-run growth rate is endogenously en·dog·e·nous  
adj.
1. Produced or growing from within.

2. Originating or produced within an organism, tissue, or cell: endogenous secretions.
 determined in Aghion and Howitt (1994). However, they do not explicitly examine the impact of labor market labor market A place where labor is exchanged for wages; an LM is defined by geography, education and technical expertise, occupation, licensure or certification requirements, and job experience  parameters such as unemployment benefits and hiring costs on the unemployment rate and growth rate. (3) Consequently, Aghion and Howitt (1994) cannot answer some important questions such as whether differences in institutional settings between Europe Europe (yr`əp), 6th largest continent, c.4,000,000 sq mi (10,360,000 sq km) including adjacent islands (1992 est. pop. 512,000,000).  and the United States are accountable for the differences in their unemployment rates. Because, as shown by Mortensen and Pissarides (1998), the relationship between the unemployment rate and growth rate can turn from negative to positive as the renovation costs rise, an explicit examination of the impact of labor market parameters is important to understanding the cross-country differences in the long-run growth rate and unemployment rate.

To examine the determinants of long-run unemployment and economic growth simultaneously, we extend the endogenous endogenous /en·dog·e·nous/ (en-doj´e-nus) produced within or caused by factors within the organism.

en·dog·e·nous
adj.
1. Originating or produced within an organism, tissue, or cell.
 growth framework of Howitt and Aghion (1998) to allow for a more general treatment of the labor market in the spirit of Pissarides (1990). The major distinction between Pissarides (1990) and Mortensen and Pissarides (1998) and our model is whether growth is endogenously determined. (4) Endogenizing economic growth enables us to explicitly analyze the impact on unemployment of factors that are commonly considered as determinants of growth, but are largely overlooked by the unemployment literature, such as the productivity of research and development (R&D) and the speed of technological spillovers. Our model differs from Aghion and Howitt (1994) in that the impact of several important institutional factors, such as unemployment benefits and workers' bargaining power, on growth and unemployment is explicitly examined. Our model generates several interesting findings that are absent from Aghion and Howitt (1994), Mortensen and Pissarides (1998), and Pissarides (1990). (5)

First, we find that the long-run growth rate depends not only on the regular preference and technology parameters, as in the literature on endogenous growth with full employment, but also on certain labor market parameters; symmetrically sym·met·ri·cal   also sym·met·ric
adj.
Of or exhibiting symmetry.



sym·metri·cal·ly adv.

Adv. 1.
, we find that the unemployment rate depends not only on the labor market parameters, but also on other factors that affect growth. Second, consistent with the empirical evidence, our model predicts that a rise in the growth rate can either increase or decrease the unemployment rate, depending on the model's parameters. Third, different types of government policies that directly or indirectly promote long-run growth can have opposite effects on the unemployment rate.

The remainder of the paper is organized as follows. The next section describes the environment and sets up the model. Section 3 derives the steady-state equilibrium conditions and the major results and discusses the policy implication of these results. Some concluding remarks are given in the last section.

2. The Model

This section develops the basic model. Our model extends the Schumpeterian endogenous growth model of Howitt and Aghion (1998) to allow for a more general treatment of the labor market in the spirit of Pissarides (1990).

Technologies

The economy is populated pop·u·late  
tr.v. pop·u·lat·ed, pop·u·lat·ing, pop·u·lates
1. To supply with inhabitants, as by colonization; people.

2.
 with a continuum Continuum (pl. -tinua or -tinuums) can refer to:
  • Continuum (theory), anything that goes through a gradual transition from one condition, to a different condition, without any abrupt changes or "discontinuities"
 of identical households with measure one. Each household consists of many infinitely lived members whose time endowment A transfer, generally as a gift, of money or property to an institution for a particular purpose. The bestowal of money as a permanent fund, the income of which is to be used for the benefit of a charity, college, or other institution.  is normalized to unity. There are five types of production activities in this economy: final good production, intermediate good production, search in the labor market, physical capital accumulation Most generally, the accumulation of capital refers simply to the gathering or amassment of objects of value; the increase in wealth; or the creation of wealth. Capital can be generally defined as assets invested for profit. , and R&D. It is assumed that in the intermediate sectors, producers are assumed to have temporary monopoly power, and in the labor market, wage rates are determined through Nash bargaining.

Final Good Production

Following Pissarides (1990), we make the following two assumptions: (i) there is a continuum of identical final-good producing firms with measure one and (ii) each firm employs many workers and is large enough to eliminate all uncertainty about the flow of labor. An individual firm uses a continuum of intermediate goods i [member of] [0, 1] and labor as its inputs subject to the following production technology:

Y = [N.sup.1 - [alpha]] [[integral].sup.1.sub.0] [A.sub.1][x.sup.[alpha].sub.i] di, 0 < [alpha] < 1, (1)

where Y is the output; N is the number of workers employed; (6) [x.sub.i] is the flow of intermediate good i used: [alpha] is a parameter (1) Any value passed to a program by the user or by another program in order to customize the program for a particular purpose. A parameter may be anything; for example, a file name, a coordinate, a range of values, a money amount or a code of some kind.  that measures the contribution of the intermediate good to the final-good production, and its inverse (mathematics) inverse - Given a function, f : D -> C, a function g : C -> D is called a left inverse for f if for all d in D, g (f d) = d and a right inverse if, for all c in C, f (g c) = c and an inverse if both conditions hold.  measures the intermediate-good producer's market power; and [A.sub.i] s the productivity coefficient coefficient /co·ef·fi·cient/ (ko?ah-fish´int)
1. an expression of the change or effect produced by variation in certain factors, or of the ratio between two different quantities.

2.
 of intermediate good i that is determined by the technology from R&D.

Final output is allocated among consumption C, investment in R&D Q, expenditures on hiring in the labor market [GAMMA The way brightness is distributed across the intensity spectrum by a monitor, printer or scanner. Depending on the device, the gamma may have a significant effect on the way colors are perceived. ], and investment in physical capital K:

Y = C + [??] + Q + [GAMMA]. (2)

We implicitly assume that each unit of consumption good foregone fore·gone
v.
Past participle of forego1.

adj.
Having gone before; previous.

Usage Note: The word foregone has recently developed a new meaning as a truncation of the phrase
 can be used to produce one unit of capital and that there is no capital depreciation. Throughout this paper, the final good is used as a numeraire.

Search in the Labor Market

To produce final output, the final-good producers have to search for workers. Because N is the number of workers that are matched with jobs in the final good sector, 1 - N is the number of unemployed workers. Job-worker pairs are assumed to separate at a constant rate s, with 0 < s < 1. (7) To find a suitable employee, a firm has to incur To become subject to and liable for; to have liabilities imposed by act or operation of law.

Expenses are incurred, for example, when the legal obligation to pay them arises. An individual incurs a liability when a money judgment is rendered against him or her by a court.
 a hiring cost [GAMMA]. We assume that the hiring cost is proportional proportional

values expressed as a proportion of the total number of values in a series.


proportional dwarf
the patient is a miniature without disproportionate reductions or enlargements of body parts.
 to the wage rate W, that is, [GAMMA] = [gamma]W, where [gamma] > 0. The rate at which new jobs and workers match is governed gov·ern  
v. gov·erned, gov·ern·ing, gov·erns

v.tr.
1. To make and administer the public policy and affairs of; exercise sovereign authority in.

2.
 by the constant-returns-to-scale aggregate matching technology

M (v, 1 - N) = M (v, u), (3)

where v is the number of vacancies, and u [equivalent to] 1 - N is the number of unemployed workers. Because the labor force is normalized to unity, v and u are also respectively the vacancy VACANCY. A place which is empty. The term is principally applied to cases where an office is not filled.
     2. By the constitution of the United States, the president has the power to fill up vacancies that may happen during the recess of the senate.
 rate and the unemployment rate. With the matching technology (3), the instantaneous in·stan·ta·ne·ous  
adj.
1. Occurring or completed without perceptible delay: Relief was instantaneous.

2.
 probability of a vacancy being filled is m([theta Theta

A measure of the rate of decline in the value of an option due to the passage of time. Theta can also be referred to as the time decay on the value of an option. If everything is held constant, then the option will lose value as time moves closer to the maturity of the option.
]) [equivalent to] M(v, u)/v = M(1, 1/[theta]) with m'(*) < 0, where [theta] [equivalent to] v/u is the vacancy-unemployment ratio that is outside the control of firms. As a result, the employment of an individual firm evolves according to according to
prep.
1. As stated or indicated by; on the authority of: according to historians.

2. In keeping with: according to instructions.

3.
 (8)

N = m([theta])v - sN, (4)

where a dot over a variable represents the time change rate of that variable. Equation 4 states that the net change of employment N is the difference between the inflow in·flow  
n.
1. The act or process of flowing in or into: an inflow of water; an inflow of information.

2.
 of workers m([theta])v and the outflow of workers sN. Given the matching technology (3), the wage rate determined through Nash bargaining W, and the prices of intermediate goods [p.sub.i], the final-good producer chooses the number of vacancies v and quantities of intermediate inputs [x.sub.i] to maximize its discounted expected profit (9)

[[integral].sup.[infinity infinity, in mathematics, that which is not finite. A sequence of numbers, a1, a2, a3, … , is said to "approach infinity" if the numbers eventually become arbitrarily large, i.e. ].sub.0] [e.sup.rt][[pi].sub.Y]dt, [[pi].sub.Y] = [N.sup.1 - [alpha]] [A.sub.i][x.sup.[alpha].sub.i] di - WN - [GAMMA]v - [[integral].sup.1.sub.0][p.sub.i] [x.sub.i] di, (5)

subject to the dynamic employment of Equation 4. In Equation 5, [p.sub.i] is the price of intermediate good i in terms of final good. The current-value Hamiltonian Ham·il·to·ni·an  
n. Abbr. H
A mathematical function that can be used to generate the equations of motion of a dynamic system, equal for many such systems to the sum of the kinetic and potential energies of the system expressed in terms
 function for the final-good producer's maximization problem is

[H.sup.f] = [N.sup.1 - [alpha]] [[integral].sup.1.sub.0] [A.sub.i] [x.sup.[alpha].sub.i] di - WN - [GAMMA]v - [[integral].sup.1.sub.0] [p.sub.i][x.sub.i] di + [xi][m([theta])v - sN],

where [xi] is the co-state variable associated with this maximization problem. The first-order first-order - Not higher-order.  conditions are

[partial derivative partial derivative

In differential calculus, the derivative of a function of several variables with respect to change in just one of its variables. Partial derivatives are useful in analyzing surfaces for maximum and minimum points and give rise to partial differential
][H.sub.f]/[partial derivative][x.sub.i] = [alpha][A.sub.i][x.sup.[alpha] - 1.sub.i][N.sub.1 - [alpha]] - [p.sub.i] = 0, (6)

[partial derivative][H.sub.f]/[partial derivative]v = -[GAMMA] + [xi]m([theta]) = 0, (7)

[MATHEMATICAL EXPRESSION A group of characters or symbols representing a quantity or an operation. See arithmetic expression.  NOT REPRODUCIBLE re·pro·duce  
v. re·pro·duced, re·pro·duc·ing, re·pro·duc·es

v.tr.
1. To produce a counterpart, image, or copy of.

2. Biology To generate (offspring) by sexual or asexual means.
 IN ASCII ASCII or American Standard Code for Information Interchange, a set of codes used to represent letters, numbers, a few symbols, and control characters. Originally designed for teletype operations, it has found wide application in computers. ], (8)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (9)

Note that in Equation 8, as discussed in Shi SHI Sumitomo Heavy Industries, Ltd. (Japan)
SHI Samsung Heavy Industries
SHI Social Health Insurance (Europe)
SHI Statutory Health Insurance
SHI Samsung Heavy Industries Co, Ltd
 and Wen (1997), that the difference between the marginal product In economics, the marginal product or marginal physical product is the extra output produced by one more unit of an input (for instance, the difference in output when a firm's labour is increased from five to six units).  of labor (1 - [alpha])[[integral].sup.1.sub.0] [A.sub.i][([x.sub.i]/N)sup.[alpha]] di and the wage rate W is the final-good producer's surplus 1. (Polit. Econ.) Any profit above the normal rate of interest and wages accruing to a producer on account of some monopoly (temporary or permanent) of the means or materials of production; - called also Producer's rent.  from hiring an additional worker. Solving the first-order conditions gives the conditions that determine the final-good sector's demand for labor and intermediate good i:

(1 - [alpha]) [[integral].sup.1.sub.0] [A.sub.i] [([x.sub.i]/N)sup.[alpha]] di = W + (s + r - [g.sub.w])[GAMMA]/m([theta]), (10)

[alpha][A.sub.i][x.sup.[alpha] - 1.sub.i] [N.sup.1 - [alpha]] = [p.sub.i] [for all]i [member of] [0,1], (11)

where [g.sub.w] [equivalent to] W/W W/W Wall to Wall
W/W Wire Wrap (electronics)
W/W Weight to Weight
. Equation 10 equalizes the marginal benefit (the left-hand side left-hand side nizquierda

left-hand side left nlinke Seite f

left-hand side nlato or
) and the marginal cost Marginal cost

The increase or decrease in a firm's total cost of production as a result of changing production by one unit.


marginal cost

The additional cost needed to produce or purchase one more unit of a good or service.
 (the right-hand side right-hand side nderecha

right-hand side right nrechte Seite f

right-hand side nlato destro 
) of employing an additional worker. The marginal cost of using an additional worker consists of two parts: the wage cost W and the expected hiring cost (s + r - [g.sub.w])[gamma]/m([theta]). Similarly, Equation 11 states that the marginal benefit (the left-hand side) and the marginal cost (the right-hand side) of using an additional unit of intermediate good i must be equalized. In the steady-state balanced growth equilibrium, [??] = 0. Then, the unemployment rate is determined by

s + s/[theta]m([theta]). (12)

Equation 12 implies that the unemployment rate depends positively on the job separation rate s and negatively on the vacancy-unemployment ratio [theta] and the matching efficiency m([theta]). (10)

Intermediate Good Production

Following Howitt and Aghion (1998), we assume that only capital is needed to produce intermediate goods. The production technology for intermediate good i is assumed to take the following form:

[x.sub.i] = [K.sub.i]/[A.sub.i], (13)

where the capital input [K.sub.i] is deflated de·flate  
v. de·flat·ed, de·flat·ing, de·flates

v.tr.
1.
a. To release contained air or gas from.

b. To collapse by releasing contained air or gas.

2.
 by the productivity parameter [A.sub.i] to reflect the fact that higher-quality intermediate goods are more difficult to produce. Given the rental rate r and the final-good sector's demand for intermediate goods (Equation 11), intermediate good producer i chooses output level [x.sub.i] to maximize its monopoly profit In economics, a firm is said to reap monopoly profits when a lack of viable market competition allows it to set its prices above the equilibrium price for a good or service without losing profits to competitors.  flow

[[pi].sub.i] = [p.sub.i][x.sub.i] - r[K.sub.i] = [alpha][A.sub.i] [x.sup.[alpha].sub.i]][N.sup.1 -[alpha]] - r[A.sub.i][x.sub.i], (14)

where [[pi].sub.i] is the monopoly profit flow for intermediate good producer i. Then the first-order condition for this maximization problem is

r = [[alpha].sup.2] [([x.sub.i]/N).sup.[alpha]-1], (15)

which yields intermediate-good sector i's optimal output

[x.sub.i] = x [equivalent to] N [([[alpha].sup.2/r)sup.1/(1 - [alpha]) (16)

Because both the marginal revenue Marginal revenue

The change in total revenue as a result of producing one additional unit of output.


marginal revenue

The extra revenue generated by selling one additional unit of a good or service.
 and marginal cost of each intermediate monopolist are proportional to the quality of its product, every intermediate monopolist produces the same amount of output regardless of the quality of its product. From Equation 16 and the capital market equilibrium condition [[integral].sup.1.sub.0] [K.sub.i] di = [[integral].sup.1.sub.0] [A.sub.i][x.sub.i] di = Ax = K, where A [equivalent to] [[integral].sup.1.sub.0] [A.sub.bi] di is the average productivity of intermediate goods, we have

x = K/A K/A Knowledge and Abilities  = kN, and r = [[alpha].sup.2][k.sup.[alpha] -1], (17)

where k [equivalent to] K/(AN) is the productivity-adjusted capital-labor ratio. Correspondingly, the intermediate monopolist's maximum profit is

[[pi].sub.i] = [A.sub.i][alpha](1 - [alpha])[k.sup.[alpha]]U. (18)

Substituting the quantity of each intermediate input given in Equation 17 into Equation 1 yields the output of final good

Y = A[k.sup.[alpha]] N. (19)

Note that Equation 19 is the standard neoclassical ne·o·clas·si·cism also Ne·o·clas·si·cism  
n.
A revival of classical aesthetics and forms, especially:
a. A revival in literature in the late 17th and 18th centuries, characterized by a regard for the classical ideals of reason, form,
 production function.

R&D

R&D is targeted at specific intermediate products. It is assumed that each successful innovation creates an improved version of the existing product, which replaces the existing product. As a result, the innovator becomes a temporary monopolist until the next innovation in that sector. Assume that innovations follow a Poisson process A Poisson process, named after the French mathematician Siméon-Denis Poisson (1781 - 1840), is a stochastic process which is used for modeling random events in time that occur to a large extent independently of one another (the word event  and that the arrival rate in any sector is

[phi] = [lambda]q, [lambda] > 0, (20)

where [lambda] is the R&D productivity parameter, and q = [Q/A Q/A Question and Answer
Q/A Quality Accounting
.sup.max] is the (leading-edge) productivity-adjusted expenditure on R&D in each sector, where [A.sup.max] = max{[A.sub.i], i [member of] [0, 1]} is the productivity of the leading-edge technology. The reason for deflating R&D expenditure by the leading-edge productivity parameter is that the complexity of innovation increases proportionally pro·por·tion·al  
adj.
1. Forming a relationship with other parts or quantities; being in proportion.

2. Properly related in size, degree, or other measurable characteristics; corresponding:
 as technology advances. An R&D firm chooses its R&D expenditure Q to maximize its expected return Expected Return

The average of a probability distribution of possible returns, calculated by using the following formula:
 {[phi][PI] - Q}, where [PI] is the expected value Expected value

The weighted average of a probability distribution. Also known as the mean value.
 of an innovation. The expected value of an innovation is given by [PI] = [[integral].sup.[infinity].sub.t] [[A.sup.max][alpha](1 - [alpha])[k.sup.[alpha].sub.[eta]][N.sub.eta] exp exp
abbr.
1. exponent

2. exponential
 [- [[integral].sup.[eta].sub.t] ([r.sub.[tau]] + [[phi].sub.[tau]]) [d.sub.[tau]]] d[eta] (where [eta] is a time subscript (1) In word processing and scientific notation, a digit or symbol that appears below the line; for example, H2O, the symbol for water. Contrast with superscript.

(2) In programming, a method for referencing data in a table.
), which yields

[PI] = [A.sup.max] [alpha](1 - [alpha])[k.sup.[alpha]]N/r + [lambda]q. (21)

Equation 21 shows that the discount rate is the sum of the interest rate r and the arrival rate [lambda]q of innovation. The arrival rate of innovation in the discount rate implies that the higher the arrival rate of innovation, the shorter the period during which the intermediate monopolist can enjoy its monopoly profits. The first-order conditions for an R&D firm's maximization problem are

[lambda][PI]/[A.sup.max] [less than or equal to] 1, Q [greater than or equal to] 0, and Q ([lambda][PI]/[A.sup.max] -1) = 0. (22)

Because we will consider only interior solutions Q > 0, the first-order conditions (Equation 22) reduce to

[lambda][PI]/[A.sup.max] = 1. (23)

Equation 23 states that the expected marginal benefit of R&D (the left-hand side) equals the marginal cost of R&D (the right-hand side).

Knowledge Spillovers

Following Caballero and Jaffe Jaffe is a surname, and may refer to:
  • Al Jaffee, cartoonist
  • David Jaffe, a video game designer and director
  • Eliezer Jaffe, a professor
  • Harold Jaffe, U.S. author
  • Harold Jaffe, AIDS researcher
  • Jerome H.
 (1993) and Howitt and Aghion (1998), we assume that growth of the leading-edge productivity [A.sup.max] comes from knowledge spillovers produced by innovations. Specifically,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (24)

where [sigma] is a parameter that measures the marginal impact of each innovation on the stock of public knowledge. Howitt and Aghion (1998) have shown that the ratio of the leading-edge productivity [A.sup.max] to the average productivity A converges monotonically to the constant 1 + [sigma]. Since we are interested only in the steady-state balanced growth path, we assume that [A.sup.max]/A = 1 + [sigma] for all t, so the average productivity A also grows at the same rate as the leading-edge productivity, i.e., [??]/A = [g.sub.a].

Preferences

As mentioned above, the economy is populated with a continuum of identical households, and each household consists of many infinitely lived members. Each household member spends his time working if he is employed or searching for a job if he is unemployed. Unemployed household members are randomly matched with job vacancies. To simplify our analysis, we follow Shi and Wen (1997) to assume that each household consists of a continuum of members who care only about the household's welfare. As a result, there is no uncertainty in the household's income and consumption. The representative household's preferences are given by

U(C) = [[integral].sup.[infinity].sub.0] [e.sup.[rho]t] ([C.sup.1 - [epsilon]]/1 - [epsilon]) dt, (25)

where C is consumption; [rho] is the constant rate of time preference; [member of] is the elasticity of marginal utility marginal utility

In economics, the additional satisfaction or benefit (utility) that a consumer derives from buying an additional unit of a commodity or service. The law of diminishing utility implies that utility or benefit is inversely related to the number of units
; and t represents time. Note that the time subscript is omitted whenever no confusion can arise. The household's budget constraint A Budget Constraint represents the combinations of goods and services that a consumer can purchase given current prices and his income. Consumer theory uses the concepts of a budget constraint and a preference ordering to analyze consumer choices.  is

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (26)

where r is the rate of interest, W the wage rate, K the household's capital assets capital assets n. equipment, property, and funds owned by a business. (See: capital, capital account) , N the fraction of employed household members, [[pi].sub.Y] the profit from the final-good production, Z the unemployment benefits, and T the lump-sum tax. (1l) We assume that the employment benefits are proportional to the wage rate, i.e., Z = zW, where z > 0. The household chooses consumption C to maximize its utility (Equation 25) subject to its budget constraint (Equation 26) and the following law of motion for N:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (27)

Equation 27 states that the net change of the number of employed members in each household is the difference between the flow of job matches [theta]m([theta])(1 - N) and the flow of job separations sN. The current-value Hamiltonian function for the household's maximization problem is

[H.sup.c] = [C.sup.1 -[epsilon]/1 - [epsilon] + [eta] [rK + [[pi].sub.Y] + WN + Z (1 - N) - C - T] + [zeta][[theta]m([theta]) (1 - N) (1 - N) - sN], (28)

where [eta] and [zeta] are the co-state variables associated with this maximization problem. The first-order

[partial derivative][H.sup.c]/[partial derivative]C = [C.sup.[epsilon]] - [eta] = 0, (29)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (30)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (31)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (32)

Solving the above first-order conditions gives conditions are

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (33)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (34)

Equation 33 states that the growth rate of consumption depends positively on the interest rate r and negatively on the subjective discount rate 9 and the elasticity of marginal utility [epsilon]. In Equation 34, the difference between the wage rate W and the unemployment benefit Z is the worker's surplus from employment.

Wage Determination

Now we consider the determination of wage rates. We assume that the wage rates are determined by Nash bargaining. As in Shi and Wen (1997), a matched worker (who cares only about the household's welfare) negotiates with the firm. (12) The wage rates derived from the Nash bargaining solution maximize the weighted surpluses of the household and the firm, (13)

[(W - Z)sup.[beta] [[(1 - [alpha])A[k.sup.[alpha]] - W].sup.1 - [beta]], 0 < [alpha] < 1, (35)

where [beta] is the workers' bargaining power. The first-order condition for this maximization problem is

[beta]/W - Z = 1 - [beta]/(1 - [alpha])A[k.sup.[alpha]] - W, (36)

which gives the following solution:

W = A[beta](1 - [alpha])[k.sup.[alpha]]/1 - (1 - [beta])z. (37)

From Equation 37, we can see that the equilibrium wage rate depends positively on the average productivity A of intermediate goods, the productivity-adjusted capital-labor ratio k, the workers' bargaining power [beta], and the unemployment benefit z.

3. Steady-State Equilibrium and Results

We focus our discussion on steady-state balanced growth equilibria. In a steady-state balanced growth equilibrium, the values of the interest rate r, the productivity-adjusted capital intensity k, the vacancy rate v, the unemployment rate u, and the vacancy-unemployment ratio [theta] are all constant, and output Y, consumption C, capital stock K, investment in R&D Q, the wage rate W, the leading-edge productivity [A.sup.max], and the average productivity A all grow at the same constant rate g, i.e., [g.sub.y] = [g.sub.c] = [g.sub.k] = [g.sub.q] = [g.sub.w] = [g.sub.a] = g, where [g.sub.y] = [??]/Y, [g.sub.k] = [??]/K, and [q.sub.q] = [??]/Q. (14) Now we derive equilibrium conditions. First, we obtain the usual positive relationship between the interest rate and the growth rate from Equation 33:

r = [epsilon]g + [rho]. (38)

Note that this relationship is exactly the same as in the literature, with an exogenous growth rate and an endogenous interest rate. Given the growth rate g, a higher elasticity of marginal utility (i.e., a lower elasticity of intertemporal substitution Substitution
Arsinoë

put her own son in place of Orestes; her son was killed and Orestes was saved. [Gk. Myth.: Zimmerman, 32]

Barabbas

robber freed in Christ’s stead. [N.T.: Matthew 27:15–18; Swed. Lit.
) gives rise to a higher interest rate. Second, Equation 17 is rewritten as

k = [([[alpha].sup.2]/r).sup.1/(1 - [alpha]), (39)

where the productivity-adjusted capital intensity k depends negatively on the interest rate. The intuition intuition, in philosophy, way of knowing directly; immediate apprehension. The Greeks understood intuition to be the grasp of universal principles by the intelligence (nous), as distinguished from the fleeting impressions of the senses.  behind this is that a higher interest rate increases the cost of capital, thus reducing the demand for capital. Third, combining Equations 21, 23, 24, and 38, we rewrite re·write  
v. re·wrote , re·writ·ten , re·writ·ing, re·writes

v.tr.
1. To write again, especially in a different or improved form; revise.

2.
 the optimal R&D condition as

[lambda][alpha](1 - [alpha])[k.sup.[alpha]](1 - u)/g([epsilon] + 1/[sigma]) + [rho] = 1. (40)

Fourth, Equations 10, 16, and 37 lead to

s + r - g/m([theta]) = (1 - [beta])(1 - z)/[beta][gamma]. (41)

Using the unemployment rate given by Equation 12, i.e.,

u = 1/s + [theta]m([theta]), (42)

we know that the vacancy-unemployment ratio 0 depends positively on the separation rate s and negatively on the unemployment rate u, that is,

[theta] = f(u, s) with [partial derivative]f/[partial derivative]u < 0 and [partial derivative]f/[partial derivative]s > 0. (43)

Combining Equations 41 and 43 gives

m[f(u, s)] = [beta][gamma](s + r - g)/(1 -[beta])(1 - z). (44)

Since m'(x) < 0 and [partial derivative]f/[partial derivative]u < 0, the unemployment rate u depends negatively on the difference between the growth rate and interest rate (g - r). If the interest rate r is fixed or the elasticity of marginal utility [epsilon] < 1, then an increase in the growth rate g reduces the unemployment rate u; if the interest rate is endogenous and [epsilon] > 1, then the effect reverses. Finally, substituting Equations 38 and 39 into Equations 40 and 44, we obtain the following two equations that determine the steady-state values of the unemployment rate u and growth rate g:

u = 1 - [([epsilon] + 1/[sigma])g + [rho][([epsilon]g + [rho]).sup.[alpha]/(1 - [alpha])]/ [lambda] (1 - [alpha])[[alpha].sup.(1 + [alpha])/(1 - [alpha])], (R)

m[f(u, s)] = [beta][gamma][s + ([epsilon] - 1)g + [rho]]/(1 - [beta])(1 - z). W

Equation R is essentially the optimal R&D condition. We can easily see that this equation indicates a negative relationship between the unemployment rate and the growth rate. The reason is that an increase in the unemployment rate decreases the profit flow of a successful innovator, which reduces the value of innovation. As a result, investment in R&D drops, and the growth rate falls.

Equation W is the wage determination condition. This equation implies that the relationship between the unemployment rate and the growth rate depends on the magnitude of the elasticity of marginal utility (see the proof of Proposition 1). The unemployment rate increases with (is independent of, decreases with) the growth rate if the elasticity of marginal utility [epsilon] is greater than (equal to, smaller than) unity. The reasons are as follows. As discussed in Pissarides (1990), the unemployment effects of changes in the growth rate are related to technological progress and the intertemporal nature of the final-good producers' employment decisions. On the one hand, the final-good producers have to incur hiring costs now to hire workers who bring profits to the final-good producers in the future. Since the hiring cost increases proportionally with profits as technology advances, the final-good producers have the incentive to economize e·con·o·mize  
v. e·con·o·mized, e·con·o·miz·ing, e·con·o·miz·es

v.intr.
1. To practice economy, as by avoiding waste or reducing expenditures.

2.
 on future hiring costs by bringing forward some hiring provided that the interest rate remains the same. As a result, given the interest rate, the final-good producers increase (decrease) the number of vacancies as the growth rate rises (falls) in order to economize on the hiring costs (the growth effect).

On the other hand, the final-good producers discount the future hiring costs and profits at the equilibrium interest rate. As the equilibrium interest rate rises, the final-good producers have less (more) incentive to bring forward (postpone post·pone  
tr.v. post·poned, post·pon·ing, post·pones
1. To delay until a future time; put off. See Synonyms at defer1.

2. To place after in importance; subordinate.
) hiring because future hiring becomes less expensive relative to current hiring (the interest rate effect). These two effects offset each other: the growth effect decreases unemployment while the interest rate effect does the opposite. The net effect depends on which effect dominates.

From the equilibrium relationship between the interest rate and the growth rate, r = [epsilon]g + [rho], we have [partial derivative]r/[partial derivative]g = [epsilon] . As discussed in Eriksson (1997), the strength of the interest rate effect relative to the growth effect depends on the elasticity of marginal utility: If the elasticity of marginal utility [epsilon] > (=, <) 1, then the interest rate effect is stronger than (as strong as, weaker than) the growth effect. Accordingly, the unemployment effect of an increase in the growth rate depends on the elasticity of marginal utility. With an increase in the growth rate, the equilibrium unemployment rate increases (remains unchanged, decreases) if the elasticity of marginal utility is greater than (equal to, less than) unity.

[FIGURE 1 OMITTED]

Figure 1 shows the two curves that illustrate the relationships between the unemployment rate and the growth rate determined by Equations R and W. The R&D curve (R) is always downward-sloping Adj. 1. downward-sloping - sloping down rather steeply
declivitous, downhill

descending - coming down or downward
, whereas the wage determination curve (W) is upward-sloping (horizontal, downward-sloping) if the elasticity of marginal utility is greater than (equal to, less than) unity.

Now we investigate the properties of steady-state equilibria by examining the above two equilibrium conditions, R and W. First, we look at the conditions for the existence of steady-state equilibria. Let [u.sub.1] be the solution to Equation W with g = 0 (thus [u.sub.1] > 0) and B be the expected marginal benefit of R&D when g = 0, that is, B = (1 - [u.sub.1])[lambda](1 - [alpha])[[alpha].sup.(+ [alpha]/(1 - [alpha])][[rho].sup.1/[alpha] - 1)] (see Equation 40), then the condition for the existence of equilibria is given by:

PROPOSITION 1. If B [less than or equal to] 1, then there exists a unique steady-state equilibrium with [u.sup.*] = [u.sub.1] and [g.sup.*] = 0 (a development trap equilibrium); if B > 1, then there exists a unique steady-state equilibrium with [u.sup.*] > 0 and [g.sup.*] > 0.

PROOF: From Equation R, we have

[partial derivative]u/[partial derivative]g < 0, [u|.sub.g = 0] = [u.sub.2] [equivalent to] 1 - [[rho].sup.1]/(1 - [alpha])]/[lambda](1 - [alpha])[[alpha].sup.(1 + [alpha])/(1 - [alpha])], (46)

and u = 0 if g is sufficiently large In mathematics, the phrase sufficiently large is used in contexts such as:
is true for sufficiently large
. From Equation W, we obtain

[partial derivative]u/[partial derivative]g = [beta][gamma]([epsilon] - 1)/[psi PSI - Portable Scheme Interpreter ], (47)

where [psi] [equivalent to] (1 - [beta])(1 - z)m'(x) [partial derivative]f/[partial derivative]u) > 0 because [partial derivative]f/[partial derivative]u < 0 and m'(x) < 0. Because the denominator denominator

the bottom line of a fraction; the base population on which population rates such as birth and death rates are calculated.

denominator 
 [psi] is always positive, the sign of [partial derivative]u/[partial derivative]g depends on the sign of ([epsilon] - 1). As a result, we have [partial derivative]u/[partial derivative]g > (=, <) 0 if [epsilon] > (=, <) 1. Furthermore, [u|.sub.g = 0] = [u.sub.1] > 0, and u > 0, [mu] g > 0. The properties of these two equations imply that if [u.sub.2] [less than or equal to] [u.sub.1], then the two curves R and W given by these two equations do not intersect In a relational database, to match two files and produce a third file with records that are common in both. For example, intersecting an American file and a programmer file would yield American programmers.  each other; if [u.sub.2] > [u.sub.1], then these two curves have a unique intersection intersection /in·ter·sec·tion/ (-sek´shun) a site at which one structure crosses another.

intersection

a site at which one structure crosses another.
 point. Note that the condition [u.sub.2] [less than or equal to] (>) [u.sub.1] is equivalent to the condition B [less than or equal to] (>) 1. QED QED
abbr.
Latin quod erat demonstrandum (which was to be demonstrated)


QED which was to be shown or proved [Latin quod erat demonstrandum]

Noun 1.
.

This proposition is intuitive. The condition B [less than or equal to] 1 implies that the expected marginal benefit of R&D is less than or equal to the marginal cost (the marginal cost = 1). In this case, R&D firms do not have incentives to invest in R&D. As a result, there is no growth ([g.sup.*] = 0). This is a development trap equilibrium. In this equilibrium, unemployment still exists because job-worker separation always occurs, and it is costly to match workers with jobs. From the definition of B, we can see that the expected marginal benefit B of R&D (when g = 0) depends positively on the productivity of R&D [lambda], and negatively on the subjective discount rate [rho] and the unemployment rate [u.sub.1]. The unemployment [u.sub.1] in turn depends positively on the separation rate s, the subjective discount rate [rho], the hiring cost [gamma], the unemployment benefits z, and the workers' bargaining power [beta]. As a result, the development trap equilibrium occurs if one or more of the following happen: (i) the productivity of R&D) [lambda] is too low, (ii) the subjective discount rate [rho] is too large, (iii) the separation rate s is too high, (iv) the hiring cost 7 is too high, (v) the unemployment benefits z are too generous, and (vi) the workers' bargaining power [beta] is too strong.

The condition B > 1 indicates that the expected marginal benefit of R&D is greater than the marginal cost if there is no investment in R&D. Obviously, it is optimal for the R&D firms to invest in R&D to the extent that the expected marginal benefit and the marginal cost of R&D are equalized. The rest of the paper will focus on the unique steady-state equilibrium with positive unemployment and growth (i.e., B > 1). The steady-state equilibrium growth rate exhibits the following comparative statics Comparative statics is the comparison of two different equilibrium states, before and after a change in some underlying exogenous parameter. As a study of statics it compares two different unchanging points, after they have changed. : (15)

PROPOSITION 2. The equilibrium growth rate [g.sup.*] depends positively on the productivity of R&D [lambda] and the effectiveness of knowledge spillovers [sigma], and negatively on the separation rate s, the hiring cost [gamma], the unemployment benefits z, the workers' bargaining power [beta], the subjective discount rate [rho], and the elasticity of marginal utility [epsilon].

PROOF: From Equation R, we can easily see that

[partial derivative]u/[partial derivative][lambda] > 0, [partial derivative]u/[partial derivative][sigma] > 0, [partial derivative]u/[partial derivative][epsilon] < 0, and [partial derivative]u/[partial derivative][rho] < 0 . (48)

Similarly, from Equation W, we obtain

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (49)

where [partial derivative]/[partial derivative]u < 0 and [partial derivative]f/[partial derivative]s > 0. The conditions in Equations 48 and 49 imply [partial derivative][g.sup.*]/[partial derivative][lambda] > 0, [partial derivative][g.sup.*]/[partial derivative][sigma] > 0, [partial derivative][g.sup.*]/[partial derivative]s < 0, [partial derivative][g.sup.*]/ [partial derivative][gamma] < 0, [partial derivative] [g.sup.*]/[partial derivative]z < 0, [partial derivative] [g.sup.*]/[partial derivative][beta] < 0, [partial derivative][g.sup.*]/[partial derivative][epsilon] < 0, and [partial derivative][g.sup.*]/[partial derivative][rho] < 0. QED.

[FIGURE 2a OMITTED]

[FIGURE 2b OMITTED]

[FIGURE 2c OMITTED]

The growth effects of changes in the model's parameters can be easily shown graphically. Changes in the parameters shift either the curve R or the curve W or both. For example, though an increase in the productivity of R&D [lambda] does not affect the curve W, it shifts the curve R upward to the right. Hence, the equilibrium growth rate increases (see Figure 2a). A rise in the separation rate s shifts the curve W upward to the left while leaving the curve R unchanged. As a result, the equilibrium growth rate decreases (see Figure 2b). An increase in the subjective discount rate [rho] decreases the equilibrium growth rate by shifting the curve R downward and the curve W upward (see Figure 2c). The effects on the equilibrium growth rate of changes in other parameters can also be seen graphically.

The comparative-static results concerning those regular parameters ([alpha], [lambda], [sigma], [rho], [epsilon]) remain the same as those in the literature on endogenous growth with full employment (e.g., Aghion and Howitt 1998). Changes in these parameters affect the equilibrium growth rate by directly influencing the expected marginal benefit of R&D. (16) For example, an increase in the productivity of R&D [lambda] directly increases the expected marginal benefit of R&D by increasing the probability of success, leading to an increase in the monopolists' expected profits.

However, different from the endogenous growth literature with full employment, the labor market parameters ([beta], z, [gamma], s) also affect the equilibrium growth rate by indirectly influencing the expected marginal benefit of R&D. The growth effects of the labor market parameters can be easily seen from the two equilibrium conditions R and W in the benchmark case with [epsilon] = 1 (i.e., log utility). (17) With [epsilon] = 1, Equation W becomes m[f(u, s)] = [beta][gamma](s + [rho])/[(1 [beta])(1 - z)]. Since m'(x] < 0, [partial derivative]f/[partial derivative]u < 0, and [partial derivative]f/[partial derivative]s > 0, an increase in any of the four parameters ([beta], z, [gamma], s) raises the unemployment rate u. This is because an increase in any of the four parameters reduces the final-good producers' profits (an increase in the hiring cost [gamma] or the separation rate s directly decreases the final good producers' profits while an increase in the workers' bargaining power [beta] or the unemployment benefits z reduces the final-good producers' profits indirectly by raising the wage rate) and thus lowers the final-good sector's employment, leading to a higher unemployment rate. From Equation R, we can see that a higher unemployment rate u lowers the growth rate g. The reasons are as follows: A lower level of employment in the final good sector reduces the final good sector's demand for intermediate goods, which reduces the profits of intermediate monopolists and hence reduces the expected marginal benefit of R&D.

The result that the labor market parameters also indirectly affect the long-run growth rate has important policy implications. Although those policies that promote R&D activities (direct growth-promoting policies) play a critical role in increasing long-run growth, those policies that ensure a well-functioning labor market (indirect growth-promoting policies) are equally important. Moreover, as we will see in Proposition 3, the indirect growth-promoting policies are "better" than the direct growth-promoting policies in the sense that, although both of them promote growth, the former always reduce unemployment, whereas the latter may do the opposite.

Now we turn to the determinants of the steady-state equilibrium unemployment rate. The determinants of the equilibrium unemployment rate are summarized by: (18)

PROPOSITION 3. (i) The equilibrium unemployment rate [u.sup.*] increases with the separation rate s, the hiring cost [gamma], the unemployment benefits z, the workers' bargaining power [beta], and the elasticity of marginal utility [epsilon], regardless of the value of the elasticity of marginal utility [epsilon]; (ii) the equilibrium unemployment rate [u.sup.*] increases with (decreases with, is independent of) the productivity of R&D [lambda] and the effectiveness of knowledge spillovers [sigma] if the elasticity of marginal utility [epsilon] > 1 ([epsilon] < 1, [epsilon] = 1); and (iii) the equilibrium unemployment rate increases (decreases) with the subjective discount rate 9 if the elasticity of marginal utility [epsilon] = 1 ([epsilon] < 1).

PROOF: The results in Proposition 3 come from the conditions in Equations 48 and 49. QED

As mentioned above, changes in the model's parameters shift either the curve R or the curve W or both (see Figures 2a-c). For example, an increase in the hiring cost [gamma] shifts the curve W upward while leaving the curve R unchanged, thus raising the equilibrium unemployment rate. The responses of the equilibrium unemployment rate to changes in other parameters can also be seen easily by examining the curves R and W.

The effects of the labor market parameters, such as the separation rate, the hiring cost, and the unemployment benefits, on the equilibrium unemployment rate are very intuitive. For

example, an increase in the workers' bargaining power [beta] or the unemployment benefits z increases the equilibrium unemployment rate by raising the equilibrium wage rate. Similarly, a rise in the job separation rate s increases the equilibrium unemployment rate by reducing the labor market tightness and by increasing the number of unemployed workers during a given period.

However, the unemployment effects of those parameters that directly affect the equilibrium growth rate (such as the productivity of R&D and the effectiveness of knowledge spillovers) are less straightforward. We start from the case with a fixed interest rate (e.g., for a small open economy). As discussed earlier (after Equation 44), a change in any of the growth-related parameters (e.g., an increase in the productivity of R&D) that raises the growth rate always reduces the unemployment rate. This is the growth effect on unemployment discussed in Pissarides (1990).

Now consider the case with an endogenous interest rate (i.e., r = [epsilon]g + [rho]). In this case, in addition to the growth effect, changes in growth also affect unemployment through the interest rate channel: an increase in the growth rate increases the unemployment rate by raising the interest rate. This is the interest rate effect on unemployment discussed in Eriksson (1997), Pissarides (2000), and Falkinger and Zweimuller (2000). As a result, a change in any of the growth-related parameters has two offsetting effects on unemployment: the growth effect and the interest rate effect. The growth effect decreases the unemployment rate while the interest rate effect does the opposite. (19) The net effect depends on the relative strength of the two effects: (20) (i) if the elasticity of marginal utility c < 1 and thus the interest rate effect is relatively weak, then the unemployment effects of the growth-related parameters remain quantitatively the same as in the case with a fixed interest rate; (ii) if the elasticity of marginal utility [epsilon] = 1 and thus the interest rate effect exactly offsets the growth effect, then changes in the growth-related parameters do not affect unemployment; and (iii) if the elasticity of marginal utility [epsilon] > 1 and thus the interest rate effect is relatively strong, then a change in any of the growth-related parameters that raises the growth rate always increases the unemployment rate. As a result, for example, an increase in the productivity of R&D increases (does not affect, decreases) the unemployment rate if the elasticity of marginal utility is greater than (equal to, less than) unity.

Propositions 2 and 3 show that the relationship between the unemployment and growth rates Growth Rates

The compounded annualized rate of growth of a company's revenues, earnings, dividends, or other figures.

Notes:
Remember, historically high growth rates don't always mean a high rate of growth looking into the future.
 depends on the model's parameters. For example, an increase in the productivity of R&D [lambda] always increases the equilibrium growth rate, but the effect on the equilibrium unemployment rate depends on the elasticity of the marginal utility: the equilibrium unemployment rises (remains unchanged, falls) if the elasticity of marginal utility [epsilon] > (=, <) 1. As a result, it is possible to have various combinations of unemployment and growth: (i) high growth and high unemployment; (ii) low growth and low unemployment; (iii) high growth and low unemployment; and (iv) low growth and high unemployment. More formally, we have:

COROLLARY corollary: see theorem. . In response to exogenous changes in the model's parameters, the unemployment rate may or may not change. If the unemployment rate does change, it may rise or fall with the growth rate.

Although we do not explicitly investigate the impact of various government policies on the unemployment rate and growth rate, it can be verified ver·i·fy  
tr.v. ver·i·fied, ver·i·fy·ing, ver·i·fies
1. To prove the truth of by presentation of evidence or testimony; substantiate.

2.
 that government policies can affect the equilibrium unemployment and growth rate in the same way as changes in the model's parameters. (21) For example, the unemployment and growth effects of a subsidy subsidy, financial assistance granted by a government or philanthropic foundation to a person or association for the purpose of promoting an enterprise considered beneficial to the public welfare.  to R&D are similar to those of an increase in the productivity of R&D. Similarly, the effects of government-funded employment services on unemployment and growth are also similar to those of a decrease in the hiring costs. Because of this, we can derive some policy implications from the comparative-statics results in Propositions 2 and 3.

The first policy implication comes directly from the corollary. That is, high growth does not necessarily come at the expense of high unemployment. In other words Adv. 1. in other words - otherwise stated; "in other words, we are broke"
put differently
, it is possible for a country to achieve both high growth and low unemployment, even in the long run, as long as the right government policies are used. For example, any policies that can shift the curve W downward and keep the curve R unchanged would be able to raise the growth rate and lower the unemployment rate.

Related to the first implication, the second policy implication is that government policies aimed at promoting growth may cause the unemployment rate to rise or fall depending on the nature of the policies and the nature of the economy. The determinants (including government policies) of the equilibrium unemployment and growth rate summarized in Propositions 2 and 3 can be divided into three groups: (i) parameters that appear in growth models with full employment (e.g., the productivity of R&D [lambda] and the effectiveness of knowledge spillovers [sigma] (ii) preferences parameters (e.g., the subjective discount rate [rho] and the elasticity of marginal utility [epsilon]); and (iii) labor market parameters (e.g., the separation rate s, the hiring cost [lambda], and the unemployment benefit z). There is an important difference between those determinants in the first group and those in the last two groups: changes in the determinants in the last two groups have in general definite effects on the equilibrium unemployment and growth rate; changes in those determinants in the first group also have definite effects on the equilibrium growth rate, but they have indefinite INDEFINITE. That which is undefined; uncertain.

INDEFINITE, NUMBER. A number which may be increased or diminished at pleasure.
     2. When a corporation is composed of an indefinite number of persons, any number of them consisting of a majority of those
 effects on the equilibrium unemployment rate. For example, an R&D subsidy will increase growth, but it may increase or decrease the unemployment rate depending on whether individuals' elasticity of marginal utility is greater or smaller than unity. In contrast to the R&D subsidy, government-funded employment services will raise growth and lower unemployment by reducing the hiring costs.

In terms of promoting growth, the direct policies such as R&D subsidies and the indirect policies such as government-funded employment services are both helpful. (22) However, in terms of reducing unemployment, the indirect policies can serve the purpose but the direct policies may do the opposite. In this sense, the indirect policies that affect the labor market efficiency are "better" than the direct growth-promoting policies.

4. Conclusions

This paper develops a model of endogenous growth with unemployment to investigate the determinants of and the relationship between long-run unemployment and growth. Our framework incorporates the spirit of Pissarides' (1990) search model into Howitt and Aghion's (1998) endogenous growth model with both innovation and capital accumulation. In our model, both long-run growth and unemployment are endogenously determined.

We find the following results. First, both the long-run growth rate and unemployment rate depend not only on factors, such as the productivity of R&D and the elasticity of marginal utility, that affect long-run growth as in those endogenous growth models with full employment, but also on the labor market parameters, such as the unemployment benefits and the hiring costs.

Second, the relationship between long-run growth and unemployment depends on the model's parameters. That is, various combinations of growth and unemployment are possible. This may explain why previous empirical studies Empirical studies in social sciences are when the research ends are based on evidence and not just theory. This is done to comply with the scientific method that asserts the objective discovery of knowledge based on verifiable facts of evidence.  cannot detect any deterministic 1. (probability) deterministic - Describes a system whose time evolution can be predicted exactly.

Contrast probabilistic.
2. (algorithm) deterministic - Describes an algorithm in which the correct next step depends only on the current state.
 link between these two variables.

Third, both policies that directly provide incentives for investment in R&D and policies that indirectly encourage investment in R&D through the labor market promote long-run growth. However, these two types of policies may affect the unemployment rate differently. Indirect policies can reduce the unemployment rate while direct policies may raise it. As a result, in terms of reducing unemployment, indirect policies that improve the labor market efficiency are better than direct growth-promoting policies. We believe that these results can help us to further understand the determinants of long-run unemployment.

Received May 2005; Accepted November November: see month.  2006.

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European bat lyssavirus
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European beech tree
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1 City (1990 pop. 25,186), seat of Boone co., central Iowa, on the Des Moines River; inc. 1865. It is a railroad and industrial center with plants making machinery, steel fabrications, and plastic signs.
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(2) To reduce equipment and associated costs by switching to a less-expensive system.

(jargon) downsizing
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Another Charles Bean is the Chief Economist of the Bank of England


Charles Edwin Woodrow Bean (November 18, 1879 – August 30, 1968), usually known during his career as C.E.W.
 and Chris CHRIS Chemical Hazards Response Information System (US DoD)
CHRIS California Historical Resources Information System
CHRIS Computerized Human Resources Information System
CHRIS Command Human Resources Intelligence System
 Pissarides. European Economic Review 37:855-9.

Caballero, R. J., and A. B. Jaffe. 1993. How high are the giants' shoulders: An empirical assessment of knowledge spillovers and creative destruction in a model of economic growth. NBER NBER National Bureau of Economic Research (Cambridge, MA)
NBER Nittany and Bald Eagle Railroad Company
 Working Paper No. 4370.

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Evans Ev·ans , Herbert McLean 1882-1971.

American anatomist who isolated four pituitary hormones and discovered vitamin E (1922).
, D. J. 2005. The elasticity of marginal utility of consumption: Estimates for 20 OECD countries. Fiscal Studies 26:197-224.

Falkinger, J., and J. Zweimuller. 2000. Learning for employment, innovating for growth. Journal of Institutional and Theoretical Economics 156:455-72.

Gordon Gordon, river in W Tasmania, Australia, 125 mi (200 km) long. Flowing from mountains to the W coast, its main tributaries are the Franklin and Denison from the N, and Serpentine and Olga to the S. , R. J. 1997. Is there a trade-off between unemployment and productivity growth? In Unemployment Policy, edited by D. J. Snower and G. de la Dehesa La Dehesa is a neighborhood located in the Chilean municipality of Lo Barnechea, in northeastern Greater Santiago. It is inhabited by mid-high to high-income families.

La Dehesa is located in a valley, in the north bank of the Mapocho River.
. Cambridge, UK: Cambridge University Press Cambridge University Press (known colloquially as CUP) is a publisher given a Royal Charter by Henry VIII in 1534, and one of the two privileged presses (the other being Oxford University Press). , pp. 433-66.

Hall, R. E. 1988. Intertemporal substitution in consumption. Journal of Political Economy 96:339 57.

Hoon hoon Austral & NZ slang
Noun

a loutish youth who drives irresponsibly

Verb

to drive irresponsibly
, H. T., and E. S. Phelps Phelps may refer to:

In places in the US:
  • Phelps (village), New York
  • Phelps (town), New York
  • Phelps, Kentucky
  • Phelps (town), Wisconsin
Other:
  • USS Phelps (DD-360), a US Navy destroyer
People with the surname
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Merz Merz may refer to:
  • Merz Apothecary, a historic German health care store in Chicago
  • Merz Pharma, an international healthcare company
  • Merz Peninsula, an irregular, ice-covered peninsula near Antarctica
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British-born American physician who was the first woman to be awarded a medical doctorate in modern times (1849).
.

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pertaining to or emanating from analysis.


analytical control
control of confounding by analysis of the results of a trial or test.
 results. Journal of Economic Dynamics and Control 21:1747 76.

(1) Some other studies on this issue include Bean and Pissarides (1993), Boone (2000), Brecher, Chen, and Choudhri (2002), Daveri and Tabellini (2000), Gordon (1997), Hoon and Phelps (1997), Manning (1992), and Mortensen and Pissarides (1998).

(2) The renovation costs consist of the expenditure on updating machinery and the cost to train workers to operate this new equipment.

(3) More recently, Aghion and Howitt (1998) explicitly consider how the labor market parameters affect the long-run growth rate and unemployment rate in a modified version of the model in Aghion and Howitt (1994) with a simplifying formulation formulation /for·mu·la·tion/ (for?mu-la´shun) the act or product of formulating.

American Law Institute Formulation
 of the labor market. We follow the spirit of Pissarides (1990) to model the labor market; in particular, wages paid to workers are determined through Nash bargaining between workers and firms. Our results confirm the findings in Aghion and Howitt (1998).

(4) Another important difference between Pissarides (1990) and Mortensen and Pissarides (1998) and our model is the assumption about firms and workers' attitudes toward risk. In their models, both firms and workers are risk-neutral Risk-neutral

Insensitive to risk.
. However, in our model, workers are risk-averse Risk-averse

Describes an investor who, when faced with two investments with the same expected return but different risks, prefers the one with the lower risk.
 while firms are still risk-neutral. Because of this difference, those asset-pricing type of equations concerning wage determination in Pissarides (1990) and Mortensen and Pissarides (1998) cannot be used in our model. To avoid analytical complexity arising from the fact that individuals face risk in the labor market, we follow Merz (1995) and Shi and Wen (1997) to adopt the "large household" assumption that each household consists of a continuum of members who care only about the household's welfare; as a result, individual risks in the labor market are completely smoothed within each household.

(5) Job destruction is exogenous in our model. The models in Aghion and Howitt (1994) and Mortensen and Pissarides (1998) can be used to study the impact of growth on unemployment, but the analysis will be more complicated because the influence goes through both job creation and job destruction.

(6) An alternative interpretation is that, in the production function (1), the variable N is actually rain[N, K], where K is the capital stock and v [equivalent to] K - N [greater than or equal to] 0 is the number of vacancies.

(7) The assumption that the separation rate is constant may not be realistic. The separation rate may depend on the rate of technological progress. An interesting extension of this paper is to examine whether the main results in the paper will still hold true if the separation rate depends on the rate of technological progress.

(8) Because we assume that there are a continuum of identical firms with measure one, this is also the law of motion for the aggregate employment.

(9) Because we will focus on the steady state, steady-state conditions In telecommunication, the term steady-state condition has the following meanings:
  • In a communications circuit, a condition in which some specified characteristic of a condition, such as a value, rate, periodicity, or amplitude, exhibits only negligible change over an
 (e.g., [r.sub.t] = r) will be used when we derive relevant expressions and equations.

(10) The unemployment rate depends negatively on the vacancy-unemployment ratio [theta] because [theta]m([theta]) is increasing in [theta].

(11) We assume that the unemployment benefits Z are financed by the lump-sum tax T and that the government's budget is balanced at each point in time, that is, Z(1 - N) = T.

(12) Alternatively, the Nash bargaining game The Nash bargaining game is a simple two player game used to model bargaining interactions. In the Nash Bargaining Game two players demand a portion of some good (usually some amount of money).  can be reinterpreted as one between the matched worker's household (on behalf of the matched worker) and the firm.

(13) Note that the firm and the worker in this bargaining game are assumed to be myopic my·o·pi·a  
n.
1. A visual defect in which distant objects appear blurred because their images are focused in front of the retina rather than on it; nearsightedness. Also called short sight.

2.
 because only the current surpluses are shared (rather than the present-discounted values as in more general search models). As discussed earlier, the worker's surplus is (W - Z), whereas the firm's surplus is [(1 - [alpha])[[integral].sup.1.sub.0] [A.sub.i][([x.sub.i]/N).sup.[alpha]] di]. Using the definition A = [[integral].sup.1.sub.0] [A.sub.i] di and [x.sub.i] = x = kN from Equations 16 and 17, we rewrite the firm's surplus as [(1 - [alpha])A[k.sup.[alpha]] - W].

(14) In equilibrium, the hiring cost [GAMMA], the unemployment benefits Z, and the lump-sum tax T also grow at the constant rate g.

(15) Note that the effect of [alpha] on the expected marginal benefit of R&D is ambiguous. This can be seen from the determinants of the intermediate-good producer's profit. The intermediate-good producer's profit (Equation 18) can be rewritten as [[pi].sub.i] = [[A.sub.i](1/[alpha] - l)r]x, where [A.sub.i](1/[alpha] - 1)r is the profit per unit of output and x = N[([[alpha].sup.2]/r).sup.1/(1 - [alpha])] is the optimal output. An increase in a has two offsetting effects on the profit hi. On the one hand, the increase in [alpha] reduces the profit by decreasing the price [A.sub.i]r/[alpha] and thus lowering the profit per unit of output. On the other hand, the increase in [alpha] raises the optimal output x by increasing the capital input. The net effect on the profit depends on which of the above two effects dominates. As a result, the growth and unemployment effects of changes in [alpha] are ambiguous.

(16) Note that the marginal cost of R&D is normalized to 1.

(17) In the case with [epsilon] [not equal to] 1, the growth effects of the labor market parameters remain qualitatively the same. However, the magnitudes of these growth effects will depend on the feedback effects of growth on unemployment.

(18) If the elasticity of marginal utility [epsilon] > 1, then the effect of the subjective discount rate [rho] on the equilibrium unemployment is ambiguous. As will be discussed in Proposition 3, this is due to the fact that changes in [rho] have two offsetting effects: the growth effect and the interest rate effect.

(19) As a result, a rise in the elasticity of marginal utility increases the unemployment rate by strengthening the interest rate effect.

(20) The relative strength of the two effects is determined by the elasticity of marginal utility [epsilon]. The larger the elasticity of marginal utility, the stronger the interest rate effect. Empirical studies find that the elasticity of marginal utility is in general greater than unity (see, e.g., Evans 2005; Hall 1988).

(21) Actually, some of the model's parameters are directly or indirectly related to government policies. For example, the unemployment benefits are directly affected by the government's unemployment insurance policies, and the hiring costs are indirectly related to the government's labor market regulations.

(22) Here, direct (indirect) policies refer to those policies that directly (indirectly) affect long-run growth.

Haoming Liu, Department of Economics, National University of Singapore The National University of Singapore (Abbreviation: NUS) is Singapore's oldest university. It is the largest university in the country in terms of student enrollment and curriculum offered. , Singapore Singapore (sĭng`gəpôr, sĭng`ə–, sĭng'gəpôr`), officially Republic of Singapore, republic (2005 est. pop. 4,426,000), 240 sq mi (625 sq km).  117570; E-mail ecsliuhm@nus.edu See .edu.

(networking) edu - ("education") The top-level domain for educational establishments in the USA (and some other countries). E.g. "mit.edu". The UK equivalent is "ac.uk".
.sg.

Jinli Zeng, Department of Economics, National University of Singapore, Singapore 117570; E-mail ecszjl@nus.edu.sg; corresponding author.

We would like to thank two anonymous referees for valuable comments and suggestions and the National University of Singapore for financial support (under Academic Research Grant R-122-000-037-112). All remaining omissions and errors are our own.
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Title Annotation:trends in labor market and whole economy due to unemployment
Comment:Determinants of long-run unemployment.(trends in labor market and whole economy due to unemployment)
Author:Liu, Haoming; Zeng, Jinli
Publication:Southern Economic Journal
Article Type:Author abstract
Geographic Code:1USA
Date:Jan 1, 2008
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