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Federal Reserve Bank of Chicago
Labor Market Transitions and
Self-Employment
Ellen R. Rissman
WP 2007-14
Labor Market Transitions and Self-Employment
By
Ellen R. Rissman*
Economic Research
Federal Reserve Bank of Chicago
230 S. LaSalle St.
Chicago, IL 60604
erissman@frbchi.org
11/30/2007
Preliminary
*
I wish to thank Gadi Barlevy and Eric French for their excellent comments and suggestions, and Kyung
Park for his research assistance on this project. The views expressed here a not necessarily those of the
Federal Reserve Bank of Chicago or the Federal Reserve System.
Abstract
The self-employed are a heterogeneous group. Some are self-employed because they are
good at it, while others are self-employed because they cannot find a better paying
salaried job. Data from the CPS for prime age males show that workers are almost twice
as likely to enter self-employment from unemployment as from paid employment.
Furthermore, almost 22% of workers exit self-employment within the year with most
returning to paid employment. This paper develops a framework for examining
transitions between the labor market states of unemployment, paid employment, and selfemployment. The self-employed fall into two groups: those who continue to seek paid
employment in the wage and salary sector and those whose value from self-employment
exceeds the expected value from continued search. The calibrated model is used to
examine the effects of business startup costs on labor market transition rates. Doubling
startup costs has very little impact on these rates.
Even a fool can have one good idea in a thousand.
Chinese proverb∗
Introduction:
Entrepreneurs are thought to hold a unique position in our economy. Creating
both employment opportunities and encouraging technological progress, they are viewed
as the engine of growth. While studying entrepreneurship may provide insight into
economic growth and development, entrepreneurs themselves are difficult to study
directly—partly because of a lack of data and partly because entrepreneurs are difficult to
identify ex ante.
New and richer datasets are being developed that address some of the
shortcomings of existing datasets. Specifically, Davis et al. (2006) are making progress
in merging the employer and nonemployer universes in the Integrated Longitudinal
Business Database (ILBD). Efforts are also under way at the U.S. Census Bureau to
integrate business and household data in the Longitudinal Employer–Household
Dynamics (LEHD) Program. Abowd, Haltiwanger, and Lane (2004) discuss this dataset.
The University of Michigan’s Panel Study of Entrepreneurial Dynamics (PSED) follows
a group of individuals who are considering starting a business and tracks them over time
to determine the steps and outcomes of their decisions. Campbell and DeNardi (2007)
have recently evaluated the first wave of this panel. These relatively new datasets should
provide much needed depth in our understanding of small business creation and growth
and shed light on the determinants of entrepreneurial success.
∗
The Columbia World of Quotations. 1996.
Identifying someone who is self-employed as being an entrepreneur is tricky.
Not everyone who starts a business is an entrepreneur. In fact most small businesses do
not survive for long.1 This problem in identifying entrepreneurial talent from a field of
wannabes encumbers the study of business formation and growth. Understanding how
businesses grow can lead to better-targeted policies aimed at helping small nascent
ventures. For venture capitalists and investment bankers this issue is even more
pertinent.
The difficulty in identifying individuals who are entrepreneurs stems from two
issues. First, there is a great deal of uncertainty surrounding any new business venture.
Consequently, some businesses will thrive while others fail independent of
entrepreneurial talent. This uncertainty means that it is difficult to identify entrepreneurs
within a pool of businesses started at the same time. To the extent that entrepreneurs are
more likely to succeed, then tautologically entrepreneurs are those who tend to own
businesses that survive. This is not a very illuminating way of thinking about
entrepreneurs. One way to narrow the field of business owners to something potentially
more akin to entrepreneurs is to evaluate the owner’s employment history. If
entrepreneurs have some kind of talent that makes them better-suited to starting a
business, we would perhaps think that entrepreneurs who fail at one business go on to
start another until eventually they succeed. This of course assumes that the entrepreneur
possesses some reasonable degree of accuracy surrounding his own innate abilities as an
entrepreneur and the necessary capital to implement the business strategy.
1
Rissman (2006), using the NLSY, finds that over 40 percent of males over the age of 24 who are selfemployed in one year are not self-employed the following year.
To further complicate things, some people start businesses not because they have
some particular talent or marketable insight, but just the opposite. They start a business
as a way to supplement or replace income lost while unemployed or employed at a lower
wage than desired. These individuals are not drawn to self-employment because of the
income it can generate, but are rather pushed into self-employment because they are
unable to find what they would consider to be an adequate paying job in the wage sector.
Alba-Ramirez (1994) and Rissman (2003) among others argue that unemployment
increases the likelihood of self-employment. Furthermore, monetary returns to selfemployment do not appear to be large. Hamilton (2000) finds that nonpecuniary benefits
must be large in order to explain the observation that entrepreneurs have lower initial
earnings and lower earnings growth than their paid employment peers. These factors
make it even more complicated to determine who exactly is an entrepreneur.
Many researchers have noted that entrepreneurs account for a disproportionate
amount of wealth in the economy. Entrepreneurs hold a large share of their net worth in
the form of equity in their business. Liquidity constraints are thought to play an
important role in explaining these observations. Evans and Jovanovic (1989), Quadrini
(2000), and Cagetti and DeNardi (2006) have modeled transitions to and from selfemployment while focusing on the role of liquidity constraints. In these models wealth is
disproportionately accumulated by entrepreneurs who may face a liquidity constraint.
The importance of these liquidity constraints is found to be limited in Uusitalo (2001)
who shows that capital constraints have only a minor influence on new business startups.
Bhidé (2000) estimates startup costs of around $10,000. Hurst and Lusardi (2004) also
provide evidence that liquidity constraints to do not bind for most small business owners.
The model analyzed here, which is a variant of the standard two-state search
model presented in Ljungqvist and Sargent (1995), is also interested in understanding the
transitions between paid employment and self-employment. However, rather than
seeking to explain the concentration of wealth by entrepreneurs, the goal is to model the
transitions among the three labor market states of unemployment, paid employment, and
self-employment.2 A definition of who is an entrepreneur is a natural outcome of the
model. It also provides a way to assess the impact of startup costs in business creation.
Business creation is certainly a complicated process. However, all businesses
start first with an idea or concept.3 Not all ideas are worth pursuing, however. It is
assumed that each idea is associated with some random payoff that, once known,
continues for the life of the business once the startup cost is incurred. If a paid employee
receives a profitable enough entrepreneurial idea, he will leave paid employment and
move to self-employment. The likelihood of moving to self-employment is declining in
the wage rate earned from paid employment. Exits to wage work from self-employment
are decreasing in the profit of the business. There is some threshold level of profitability
that, once attained, makes wage work less attractive than continued self-employment.
These individuals—the ones who have no reason to continue to search for wage sector
employment—are entrepreneurs in the sense that they remain self-employed indefinitely.
The model is calibrated to capture salient features of the US economy. Given
assumptions about the underlying parameters, the model is solved to generate transition
rates across states. The steady state fraction of paid employment, self-employment, and
2
Nonparticipation is also permitted.
The model presented here is not meant to be a detailed analysis of how these ideas are generated. One can
imagine that past exposure and experience could be important determinants. In order to build a better
mousetrap the entrepreneur most understand the shortcomings of the currently produced one. These
interesting questions are not explored here.
3
unemployment are calculated. For reasonable parameters the model does a good job of
capturing transitions from unemployment to paid employment and from unemployment
to self-employment. It also does well at capturing transitions from paid employment to
unemployment and self-employment. However, it overstates transitions from selfemployment to unemployment and understates transitions from self-employment to paid
employment leaving the retention rate in self-employment close to that observed in the
data. The result is that for reasonable parameter values the steady state level of selfemployment is too high relative to that observed in the U.S. economy.
The role of business start-up costs is examined in more detail. Specifically, the
model is used to determine the effect of increasing business start-up costs on steady state
self-employment. The results suggest that start-up costs are not important determinants
of the steady state level of self-employment with the calculated transition rates being
changed very little by a doubling of business startup costs. The model is introduced in
Section I followed by a fuller discussion of paid employment, unemployment, and selfemployment respectively. Calibration results are found in Section II and conclusions are
in Section III.
Section I: The Model
A worker can be in one of three distinct states: employed in the wage sector,
unemployed, or self-employed. A worker who is employed in the wage sector is said to
be a paid employee. Paid employment is characterized by a wage w that the worker
earns each period he is a paid employee. There is a probability of layoff each period
given by q where q ∈ (0,1) . This probability of layoff is fixed and known to the worker.
To keep the model simple, workers are not permitted to search for alternative paid
employment while on the job.
Wage sector jobs are obtained through a search process. Search is both costly and
time-consuming. It is assumed that only those who are unemployed or self-employed can
engage in job search. It costs c each period to search for a wage sector job.4 The
process of search elicits a wage offer with probability λ ∈ (0,1) . Wage offers are drawn
from a known cumulative distribution function F ( w) where w ∈ [ w, w] , w > 0 and
w < w ≤ B . (A tilde over a lower case letter indicates that it is a random variable. The
same lower case letter without the tilde refers to the realization of that random variable.)
The worker must decide whether to accept the job offer or not. Rejected offers cannot be
recalled.
The process of becoming self-employed is different from that generating paid
employment. Self-employment requires the worker to first have an entrepreneurial idea.
These ideas occur randomly and without cost. Each period there is a fixed probability ρ
of a person receiving an idea where ρ ∈ (0,1] . Ideas occur regardless of whether the
worker is employed, unemployed, or self-employed. The attractiveness of this new idea
depends upon the worker’s current labor market state and income. Ideas are nontransferable and expire after one period. Hence, ideas cannot be stored for later use.5
The idea is associated with a profit opportunity of π , which is drawn from a cumulative
density function given by G (π ) , where π ∈ [π , π ] , π > 0 and π < π ≤ Π . The
4
The cost of job search is likely to differ depending upon whether the worker is unemployed or selfemployed. For the self-employed, actively looking for wage work takes time away from his or her venture.
So the costs of search may be greater for them. On the other hand, searching while self-employed may be
more efficient since employment opportunities may be encountered in the normal course of business.
5
This assumption makes the state space more manageable. Otherwise, the value functions associated with
various states would depend upon the best idea received to date.
realization of π is drawn before the worker determines whether to start the business or
not. Once he knows how profitable it will be, he decides whether to implement his idea.
Businesses have a known startup cost of k which does not depend upon past history or
the magnitude of the profit associated with the business idea.6
Both the idea and the profit it generates is unique to that individual. The
opportunity cannot be transferred to another person or firm—just as a job in the wage
sector cannot be sold to another worker.7 The entrepreneurial opportunity is assumed to
last for only one period and cannot be stored. However, the opportunity, once taken,
generates profit indefinitely, ceasing only when the worker exits self-employment. It is
given value only by combining the specific worker with the idea.
The individual observes π but cannot take advantage of it unless he is selfemployed. He cannot be working in the wage sector or unemployed while also selfemployed.8 Self-employment is a full time endeavor requiring the worker to exit either
unemployment or paid employment. Additionally, an entrepreneur is assumed to be able
to take advantage of only one entrepreneurial idea at a time. If another idea arrives that
the entrepreneur chooses to pursue, it entails shutting the current operation, foregoing the
6
This is an obvious abstraction. We can imagine, for example, that costs decline as the number of
businesses the worker starts increases. Furthermore, more profitable ventures are likely to be larger in
scale and therefore require larger startup costs. These complications have been omitted from the model to
keep it as simple and tractable as possible.
7
By assumption, the businesses permitted in this model do not have a value to anyone other than their
owner. This rules out the possibility of a worker selling his business to others to operate. You can imagine
the business as one in which the owner is an integral part, conveying value to the venture. An alternative
way to think about it is that there is some value of a business that is common to all businesses and the profit
that is drawn from the profit distribution is the value added to the business by that specific entrepreneur.
Once that entrepreneur separates from the business, the value of the business declines to only the common
value.
8
Obviously, this precludes “moonlighting” as an option available to the worker. Campbell and DeNardi
(2007) find that a large proportion of nascent entrepreneurs are employed in the wage and salary sector at
the time they are starting their own business. The model presented here assumes that all businesses take
one period to implement.
profits it generates, and starting a new one at a cost of k . The self-employed worker can
continue to generate entrepreneurial ideas and may continue to search in the wage sector.
There is no uncertainty associated with a specific idea once the profitability of the
idea is known. However, these entrepreneurial endeavors randomly fail at a rate γ > 0,
where γ ∈ (0,1) . The failure of a small business can occur for many reasons that are not
expressly considered here.9 The key assumption here made for tractability is that events
can occur that are outside the entrepreneur’s control that influence the success or failure
of the enterprise. In this case the event permanently reduces the business’s profit to zero,
effectively making continued self-employment an unattractive option. The worker then
becomes unemployed unless a wage sector job is found. This failure rate makes
continued search for paid employment an important option.
While unemployed, each period the individual receives the value of leisure given
by . He must decide whether to optimally search for wage work or, alternatively, wait
for an entrepreneurial idea to occur. A person may optimally choose to be a
nonparticipant. These are individuals whose expected value of waiting for an acceptable
entrepreneurial idea exceeds the expected value of a strategy involving actively searching
for a wage sector job. In previous work Rissman (2003) showed that transitions to selfemployment depend upon the structure of the unemployment compensation system. As
unemployment benefits expire, the tradeoffs among unemployment, self-employment,
and wage work change. In the model presented here features of the unemployment
compensation system are omitted.
9
It may be that the likelihood of failure is individual-specific. Some people may intrinsically be better
entrepreneurs than other. The likelihood of failure may also have to do with experience. Those having
more labor market or entrepreneurial experience may be less likely to fail. Another possibility is that many
individuals may be competing in the same market and competition drives some out. For example, a local
store may find its profitability limited by the introduction of a Wal-Mart to the area.
The simple model described above generates transitions among the three states of
paid employment (PE), unemployment (U), and self-employment (SE).10 There are six
(3x2) possible transitions. A worker can transition from wage work directly to selfemployment only if the entrepreneurial idea is lucrative enough after having paid startup
costs, appropriately valuing the current job and layoff probability. A worker can
transition from unemployment to self-employment, appropriately weighing the potential
value of a wage sector job. Transitions from self-employment to employment in the
wage sector can occur if the entrepreneur engages in search and receives a high enough
wage offer. Transitions from self-employment to unemployment occur only if the current
business fails. Transitions from unemployment to paid employment and from paid
employment to unemployment are standard in the labor search literature.
One implication of the model is that, as time progresses, a self-employee will tend
to have increasing income conditional on his or her remaining either self-employed or
employed in wage work. The reason for this is straightforward. Once a business is
started, an entrepreneur can either stay employed in that same business, transition to
wage work if a good enough wage sector job becomes available, start up an even more
profitable business, or become unemployed if the business fails. Given that he remains
self-employed, income should be rising over time.
There is some level of profitability beyond which a self-employed person will not
actively engage in wage sector job search. This observation offers a natural definition of
an entrepreneur: An entrepreneur is a worker who is self-employed whose income from
self-employment is sufficiently high so as to make wage sector job search unattractive.
According to this definition, entrepreneurs may find themselves back in the wage sector
10
A fourth state of nonparticipation can easily be incorporated.
or unemployed—but only after the business fails. A richer model would include the
possibility of the entrepreneur selling his business and becoming a wage worker. This
possibility is precluded in the current model.
Evaluation of Paid Employment
Let W ( w) be the optimal value of a worker currently employed in the wage sector
at a wage w . The worker receives w for the current period and will continue to receive
w indefinitely until either he becomes self-employed or is laid off and becomes
unemployed. Layoffs occur at a rate of q each period and imply nothing about the
worker’s abilities.
To become self-employed, the worker must first have an entrepreneurial idea.
These ideas arrive at a rate ρ that is independent of past history and the worker’s ability.
It takes time and is costly to implement a new idea. It is assumed that the idea cannot be
implemented until next period and only after paying the initial startup cost of k . The
entrepreneurial payoff π accrues each and every period for which the worker is selfemployed, but the startup cost occurs only once at the business’s inception. Let V (π ) be
the optimal value of an entrepreneurial idea paying π . The value of the entrepreneurial
idea net of startup costs is then V (π ) − k . The future is discounted at a rate given by β .
The optimal value of unemployment is given by U .
The value of employment at the wage w can be expressed as:
{
(1.1)
}
W ( w) = w + β q ρ E ⎡ max {V (π ) − k , U }⎤ + q (1 − ρ )U + (1 − q ) ρ E ⎡ max {W ( w), V (π ) − k}⎤ + (1 − q )(1 − ρ )W ( w) .
⎢ se ',u
⎥
⎢ e, se '
⎥
⎣
⎦
⎣
⎦
This period the worker receives a wage of w . The following period, which is discounted
at a rate β , one of four possible outcomes may occur. First, the worker may be laid off
and also receive an entrepreneurial idea. Second, the worker may be laid off but does not
receive an entrepreneurial idea. Third, the worker is not laid off but still receives an
entrepreneurial idea. Fourth, the worker is laid off and does not receive an
entrepreneurial idea.
Each one of these possibilities is addressed in succession. The first term in
brackets in equation (1.1) gives the optimal value for the situation in which the worker is
laid off but receives an entrepreneurial idea. This situation occurs with probability q ρ .11
Once he receives the idea, the profitability of that idea is drawn. The worker observes the
associated profit π and selects the better of two alternatives: unemployment and selfemployment. Unemployment has an associated optimal value of U and selfemployment has a net optimal value of V (π ) − k . In evaluating the value of wage work
the wage worker does not know the actual payoff from the potential self-employment
idea but does know the distribution of potential payoffs. He therefore values the
possibility of being laid off and receiving an entrepreneurial idea in terms of the expected
value of the better alternative, E max [V (π ) − k , U ] .
The second term inside the brackets gives the value to the worker if he is laid off
but receives no entrepreneurial idea. This happens with probability q(1 − ρ ) . The worker
becomes unemployed, behaving optimally, and receives the value of unemployment
given by U .
11
It is assumed that layoffs and ideas are independent events.
The third term in brackets expresses the decision facing the worker if he is not
laid off but still has an entrepreneurial idea. This event occurs with probability (1 − q ) ρ .
He weighs the optimal value of maintaining his wage sector job, given by W ( w) , against
the optimal net value of self-employment after startup costs, given by V (π ) − k . In
evaluating this option the worker does not know the draw from the profit distribution but
instead must evaluate the expected value of the better alternative.12
Finally, the last term in brackets gives the outcome that occurs when the worker is
neither laid off nor in receipt of an entrepreneurial idea. In this case he remains
employed and receives the optimized value of the wage sector job, W ( w) , with
probability (1 − q )(1 − ρ ) .
*
Define π u , se as the level of profits for which the worker is indifferent between
*
remaining unemployed and becoming self-employed. In other words π u , se solves:
*
U = V (π u , se ) − k .
(1.2)
It is assumed that the distribution of profits is such that there exists some level of
entrepreneurial profit for which the worker prefers self-employment over unemployment.
The level of profits required to induce a worker to exit unemployment for selfemployment is rising in the cost of starting a business k .
*
Now define π e, se as the level of profits for which the worker is indifferent
between remaining employed at wage w and becoming self-employed. It solves the
following expression:
12
The decision facing the worker is similar to the decision a worker would face with successful on-the-job
search. In that event the worker must choose between continued employment at the current job versus
incurring the search cost and moving to a new job.
*
W ( w) = V (π e, se ) − k .
(1.3)
The level of profitability required to induce a worker to leave his current job in the wage
sector to become self-employed rises with the wage currently earned and with the cost of
starting a business.
Evaluation of unemployment
The decision facing a worker who is unemployed depends upon whether he opts
to search for a wage sector job or not. In most models of job search, it is assumed that
the expected value of searching is too high to induce workers to select unemployment
without search as the optimal strategy. In this model, the search decision is complicated
by the possibility that an unemployed worker can receive an entrepreneurial idea
costlessly. In order to induce the unemployed worker to search for a job in the wage
sector, either the arrival rate of ideas has to be low enough or the expected value of the
entrepreneurial idea has to be low enough to make wage sector search the better
alternative for an unemployed worker. If the unemployed worker has no better
alternative than to wait for entrepreneurial ideas to arrive, eventually no one would work
in the wage sector and wages would adjust upwards. This is clearly not sustainable so the
parameters must be set so as to make the worker at least indifferent between searching
and not searching.
Unemployment provides the worker with a given base level of income denoted by
. This can be thought of as the value of leisure or the value of leisure combined with
the value of the unemployment insurance he receives. If the unemployed worker opts not
to search, the following period one of two things can occur: he can either receive an
entrepreneurial idea with a probability of ρ or he can have no idea. If he receives an
idea, he must decide whether to pursue it and become self-employed or to remain
unemployed until the next idea occurs. In other words, he must select the better of selfemployment or unemployment. Of course if he does not receive an entrepreneurial
opportunity, he will simply remain unemployed.
The value of searching for a wage sector job from unemployment is a little more
complicated. Search entails a cost c and is successful in generating a wage offer with
probability λ . One of four possible outcomes can occur. First, the worker receives both
a wage offer and an entrepreneurial idea. Second, the worker receives a wage offer but
no entrepreneurial idea. Third, the worker’s job search does not generate a wage offer,
but he does receive an entrepreneurial idea. Fourth, the worker receives neither a job
offer nor an entrepreneurial idea.
The expression below gives an expression for the optimal value of
unemployment.
(1.4)
⎧λρ E ⎡ max V (π ) − k , W ( w), U ⎤ + ⎫
}⎥ ⎪
⎪
⎢ se ', pe ',u {
⎣
⎦
⎪
⎪
⎧
⎫
⎪ λ (1 − ρ ) E ⎡ max {W ( w),U }⎤ + ⎪ ⎪ ρ E ⎡ max {V (π ) − k , U }⎤ + ⎪
⎪
⎪
⎢ se ',u
⎥ ⎬}
⎢ pe ',u
⎥
⎣
⎦
⎣
⎦
U = + max {−c + β ⎨
⎬, β ⎨
search , nosearch
⎪
⎪
(1 − ρ )U
⎡
⎤ ⎪ ⎪
⎩
⎭
⎪ (1 − λ ) ρ E ⎢ max {V (π ) − k , U }⎥ + ⎪
⎣ se ',u
⎦
⎪
⎪
(1 − λ )(1 − ρ )U
⎪
⎪
⎩
⎭
The worker receives the value of leisure and optimally decides whether to search actively
for a wage sector job or not. Unlike the traditional search literature in which the only
way to escape unemployment is to search for a job, an unemployed worker can improve
his position by waiting for an entrepreneurial idea. The distribution of wage offers is
such that it benefits workers to engage in search. In this model in order for the worker to
be rewarded for search from unemployment the distribution of wage offers must be high
enough relative to the distribution of profit payouts or the probability of receiving an idea
must be low relative to the probability of a wage offer. Furthermore, the cost of search
cannot be too high.
While the worker is unemployed, he receives a benefit from leisure valued at .
He also must decide whether to search for a wage sector job or not. The value of not
searching depends upon whether he receives an entrepreneurial idea. 13 He receives an
idea with probability ρ . Conditional on receiving this idea, he then optimally decides
between one of two alternative actions: he can either enter self-employment and receive
the profit stream associated with this idea, or he can optimally choose to remain
unemployed. The self-employment opportunity has an optimal value of V (π ) given the
realization of the payoff to the idea. However, at the time the worker is making his
search decision, this payoff is not realized and the worker weighs the expected value of
the self-employment net of startup costs, E[V (π )] − k against the value of
unemployment. There is a probability (1 − ρ ) that the worker will not receive any
entrepreneurial idea and remain unemployed. This option is valued at (1 − ρ )U .
Now we can address the value of job search to the unemployed worker. This is
given by the first term within brackets. The cost of search each period is given by c but
is not always successful in generating a wage offer. Wage offers occur with probability
λ . There are four possible outcomes: (1) search generates an offer and an
entrepreneurial idea becomes available; (2) search generates an offer and no
13
The value of not searching for a wage sector job is expressed by the last term within brackets.
entrepreneurial idea occurs; (3) search does not generate an offer and the worker receives
an entrepreneurial idea; and finally (4) search does not generate an offer and the worker
does not receive an entrepreneurial idea.
If a wage offer occurs and an entrepreneurial idea strikes, the worker chooses the
best of three alternatives: working in the wage sector, entering self-employment, or
remaining unemployed. If search results in a wage offer but no entrepreneurial idea
presents itself, the worker optimally weighs the value of the wage offer against the value
of remaining unemployed. If search is not successful in generating a wage offer but an
entrepreneurial idea occurs, the individual optimally weighs the self-employment
opportunity against the value of remaining unemployed. Finally, if neither a wage sector
nor self-employment opportunity arises, the worker remains unemployed.
*
Define the reservation wage wu ,e as the wage offer that would induce the
unemployed worker to work in the wage sector. The reservation wage solves the
following expression:
*
W ( wu ,e ) = U .
As the level of benefits rises, the reservation wage also increases. Combining the
expressions for the reservation wage and reservation level of profit gives:
*
*
W ( wu ,e ) = V (π u , se ) − k .
The value of self-employment at the reservation profit level must exceed the value of
wage work at the reservation wage by the amount of startup costs.
Evaluation of Self-Employment
The value of self-employment depends upon whether the worker continues to
search for a wage sector job or not once he is self-employed. Consider the decision the
entrepreneur makes when he is already self-employed with entrepreneurial payoff π .
There is a probability γ each period that the entrepreneur’s business will fail. Once this
happens, the business disappears and the worker has the option of returning to
unemployment unless another opportunity becomes available. Let V (π ) be the optimal
value of the firm earning π to the worker.
(1.5)
⎧
⎡ λ ρ (1 − γ ) E m ax ′ {W ( w ), V (π ), V (π ) − k } + ⎤
pe ', se , se
⎪
⎢
⎥
⎪
⎢ λ ργ E m ax {W ( w ), V (π ) − k , U } +
⎥
pe ', se ′ , u
⎪
⎢
⎥
⎪
⎢ (1 − λ ) ρ (1 − γ ) E m ax {V (π ), V (π ) − k } + ⎥
se , se ′
⎪
⎢
⎥
⎪
⎢ (1 − λ ) ργ E m ax {V (π ) − k , U } +
⎥,β
V ( π ) = π + m ax ⎨ − c + β
search , nosearch
se ′ , u
⎢
⎥
⎪
⎢ λ (1 − ρ )(1 − γ ) E m ax {W ( w ), V (π )} +
⎥
⎪
pe ', se
⎢
⎥
⎪
⎢ λ (1 − ρ ) γ E m ax {W ( w ), U } +
⎥
⎪
⎢
⎥
pe ', u
⎪
⎢ (1 − λ )(1 − ρ )(1 − γ )V (π ) + (1 − λ )(1 − ρ ) γ U ⎥
⎥
⎪
⎢
⎩
⎣
⎦
⎫
⎪
⎪
⎪
ρ (1 − γ ) E m ax {V (π ), V (π ) − k } + ⎤ ⎪
⎡
se , se ′
⎢
⎥⎪
⎪
⎢ ργ E m ax {V (π ) − k , U } +
⎥⎬
′,u
se
⎢
⎥⎪
⎢ (1 − ρ )(1 − γ )V (π ) + (1 − ρ ) γ U ⎥ ⎪
⎣
⎦
⎪
⎪
⎪
⎪
⎭
The entrepreneur receives profit π this period. He must decide optimally whether to
search for a wage sector job or not. The value of the search option is found in the first
term within brackets. Searching for a wage sector job entails incurring a search cost c
this period.14 The following period which is discounted at a rate β , he optimally weighs
his options, which depend upon whether his job search is successful, whether another
self-employment opportunity becomes available, and whether his current entrepreneurial
14
The cost of search is assumed to be independent of the worker’s current state. Such an assumption may
not be warranted. It is plausible that searching while self-employed is more costly than search from
unemployment since it takes time away from the business. This assumption is made in Rissman (2003).
Alternatively, it may be the case that search is more efficient while self-employed as being in the business
world increases the contact the worker has with other businesses and makes search less time-consuming or
alternatively increases the likelihood of any particular search generating an offer.
activity remains profitable. The likelihood of a wage offer and an entrepreneurial idea
both occurring is given by λρ . The term λρ (1 − γ ) is the probability that job search is
successful in generating a wage offer, he also has another entrepreneurial opportunity,
and the current entrepreneurial activity remains profitable. In this event, the entrepreneur
selects the best of three alternatives: He can accept a job in the wage sector; he can
continue to work in the current self-employment job receiving V (π ) ; or he can pay the
startup fee of k and start a new business based upon the new idea. The second term
describes the optimal decision of the worker who has generated both a wage offer and has
a new entrepreneurial idea, but whose current entrepreneurial endeavor has failed. In this
case, he weighs the value of wage work, the new entrepreneurial idea net of start-up
costs, and unemployment.
Now suppose that job search does not elicit a job offer but he still receives a new
entrepreneurial idea, and his old self-employment opportunity remains profitable. In this
event he chooses between remaining self-employed in the current job receiving V (π ) or
paying a startup cost and starting a new firm. If the current self-employment endeavor
disappears, he weighs the value of the new opportunity against the value of
unemployment.
The next two terms evaluate the decision the worker faces if his wage sector
search generates a job offer but no other entrepreneurial opportunity aside from the
current one presents itself. In this case the worker weighs the wage sector job against the
value of the current self-employment opportunity if that opportunity still exists. And if
the current self-employment endeavor becomes bankrupt, the worker optimally weighs
the wage sector job against unemployment.
Finally, if search does not generate a job offer and he receives no new
entrepreneurial idea, the worker stays at his current self-employment job, earning V (π ) if
the business does not go bankrupt. If it does, he receives the value of unemployment.
The entrepreneur’s other option is not to search for a wage sector job. This option
is examined in the second term within brackets. In this case, the worker may still receive
an entrepreneurial idea with probability ρ . He then selects between two options: He can
either remain in the same self-employment position he is currently in and earn V (π ) , or
he can pay the startup fee of k and earn the value of the new self-employment
opportunity. If no idea presents itself, he continues to remain self-employed at a value of
V (π ) .
There is some level of self-employment profit beyond which wage sector search
will no longer occur. This result suggests a natural definition for distinguishing between
“entrepreneurs” and those who are “interim-preneurs” for lack of a better term.
Entrepreneurs are those workers whose earnings from self-employment are so high that
they have no incentive given their current profit level to seek work in the wage sector.
For them, the value of self -employment exceeds the expected value of searching for
employment in the wage sector. Entrepreneurs have a lasting attachment to selfemployment so long as the business does not fail and, in this simple model, have no
incentive to ever return to wage work. Interim-preneurs are those who are currently selfemployed but continue to search for wage sector employment. For these workers,
continued search for wage sector employment, if successful, would induce the interimpreneur to transition from self-employment to wage work.
Define π * as the reservation profit level at which the worker is indifferent
between continued wage sector search and remaining self-employed in the current
opportunity, i.e. it is the level of profits for which the worker is indifferent between being
an entrepreneur and an interim-preneur. For profit levels in excess of π * the
entrepreneur has no incentive to engage in wage sector search. Thus, he will remain selfemployed until the business fails. It is possible that the entrepreneur can encounter
another business opportunity whose profitability exceeds his current profit level. If this
occurs, he will remain self-employed, closing his existing business, but starting a new
venture if the increased profit merits it.
Given that the current business has a level of profit π associated with it that
exceeds π * , the entrepreneur will start a new firm if the value of doing so net of costs
exceeds the optimal value of staying in the current opportunity. The reservation level of
ˆ
profit π (π ) is defined such that:
ˆ
V (π ) = V (π (π ) ) − k for π ≥ π * .
ˆ
Since V (π ) is increasing in π , it follows that π (π ) ≥ π .
Section II: Calibration
The model described in the previous section can be calibrated assuming parameter
values for k , ρ , , β , γ , λ , c and distributions G (π ) and F ( w). Some of these
parameters have precedents in the literature whereas others are more difficult to quantify.
In the results that follow the unit of time is taken to be a year. Transitions to and from
self-employment should be low frequency events.
In order for the calibration exercise to be meaningful, the parameter values are
chosen to reflect certain attributes of the data. The March Current Population Survey
provides an opportunity to examine transitions between the various labor market states.
Since January 1994 the survey asks those who are employed the following question:
"Last month, were you employed by government, by a private company, a nonprofit
organization, or were you self-employed?" Individuals in the CPS who respond that they
are employed by government, a private company, or a nonprofit organization are
classified as wage and salary workers. Individuals who respond that they are selfemployed are asked: "Is this business incorporated?" Individuals who respond "yes" are
classified as wage and salary workers and are treated as employees of their own
businesses. The "no" responses are classified as unincorporated self-employed—the
measure that typically appears in Bureau of Labor Statistics publications.
It is not clear what the conceptual distinction is between incorporated and
unincorporated self-employment. The BLS definition implies that incorporated
businesses treat their self-employed owners as wage and salary workers. The model
presented above does not make a distinction between incorporated and unincorporated
self-employment. In accordance, the descriptive statistics presented below treat selfemployment as those who are either self-employed and incorporated or non-incorporated.
Table 1 gives the fraction of males ages 21 to 54 for each year from 1976 to 2006
in unemployment, paid employment, self-employment, and nonparticipation. Farm
workers have been excluded from the analysis. Approximately 76% of males are in paid
employment over this time period. Self-employment accounts for just under 11% of the
population studied. Around 5.5% of the group are unemployed and nonparticipants
account for roughly 8.5%. Table 1 also gives averages by decade. Paid employment
rates have varied little. Self-employment rates have declined from 11% to 10% over the
past 30 years. Unemployment rates for this population have fallen as well, whereas
nonparticipation rates have risen almost 2.5%.15 Figure 1 exhibits this data in a graphical
form.
The CPS provides an opportunity to examine transitions between labor market
states from one year to the next. Of those who are interviewed in March of year t, some
respondents will be asked the same set of questions again in year t+1. For those who
appear in the March CPS for two consecutive years, we are able to examine transition
rates between labor market states.16
Table 2 below gives estimates of the average transition rates from 1977 to 2006
among the labor market states of paid employment, self-employment, and
unemployment. Nonparticipants have been omitted from the computation for two
reasons. First, nonparticipants are likely to be disabled or full time students. The labor
supply decisions for them are much more complicated than for the “typical” male. The
model discussed above does not formally address these individuals and they should be
omitted from the analysis. Second, although the model presented includes the option of
nonparticipation, for nonparticipants the only transition possible is directly to selfemployment. While some workers may optimally select nonparticipation, the model is
15
This increase in nonparticipation rates has been noted by many others.
Of course respondents can drop out of the sample from one March to the next. This attrition bias is only
important if the attrition rate differs depending upon labor market status. Neumark and Kawaguchi (2004)
have studied attrition bias and their effect on estimates of union wage differentials and the male marriage
wage premium. They conclude that the advantages of using matched CPS panels to obtain longitudinal
estimates are likely to far outweigh the disadvantages from attrition biases.
16
calibrated to ensure that searching while unemployed is the better alternative for prime
age males. Consequently, no one ever chooses nonparticipation as the optimal strategy.
The larger values along the diagonal in Table 2 indicate that once an individual
enters a particular state, he tends to stay in that state. For example, a respondent who was
interviewed in year t and determined to be in paid employment at that time is found to be
in paid employment again in year t+1 93.5% of the time. Compared with paid
employment, the other labor market states are less sticky in the sense that those who enter
these other states are more likely to exit than if they were in paid employment. Selfemployment has a retention rate of 78.3%. Unemployment is the most transitory state,
with 34.2% of those unemployed in one year observed to be unemployed the following
year. People enter self-employment from both paid employment and unemployment.
Only 3.3% of those employed in one year are found to be self-employed the following
year whereas 6.5% of those unemployed in a given year are subsequently found to be
self-employed.17 Although unemployment is an important source of inflows to selfemployment, because unemployment accounts for a smaller percentage of the work force
most inflows into self-employment come from paid employment.
Assumptions
The model is calibrated to match seven moments. These include the six transition
rates found in Table 2 where i ≠ j. . The seventh moment is the average observed
earnings from paid employment in year t given that the worker was unemployed in year t17
We do not observe a continuous job history between period t and period t+1. Therefore, it is possible
that interim transitions are made that are unobserved. These interim transitions may bias transition rate
estimates with the estimates consistently underestimating true transition rates. See Shimer (2005) for a
discussion and estimates of monthly transition rates.
1 and is employed in paid employment in year t. This is computed to be $23,711.37 in
2004 dollars for males ages 21-54, excluding farm workers and nonparticipants. The
objective is to choose parameter values to match as closely as possible deviations of the
model’s computed transition matrix from the actual observed in the data and the
percentage difference in the conditional wage this period given that the worker was
unemployed last period.
In the results that follow it is assumed that both wages and profits are generated
by a Gamma distribution.18 The Gamma distribution is a two parameter family of
continuous distributions defined over the positive real numbers. It has both a scale
parameter and a shape parameter. The exponential, chi-square, and normal distributions
are all special cases of the Gamma distribution.
Obtaining estimates of business startup costs is difficult. In his book Bhidé
(2000) estimates business startup costs in 2000 of $10,000. This figure is adjusted to
$10,946.20 in 2004 dollars.19 Uusitalo (2001) finds that the role of startup costs is
limited in new business formation. Similarly, Hurst and Lusardi (2004) find that the
probability of entering entrepreneurship is flat over a large range of the wealth
distribution, rising only for the richest workers. In contrast, Cagetti and DeNardi (2006)
show that the presence of liquidity constraints can generate this same pattern so the
unresponsiveness of entrepreneurship to wealth cannot be taken as evidence that liquidity
constraints are unimportant. The model presented above abstracts from liquidity
constraints.
18
Other distributions were also evaluated. These include lognormal and Pareto. Only the results for the
Gamma distribution are reported here.
19
The 2004 figure adjusts for inflation using the GDP chain-type price index.
In keeping with what appears to be acceptable practice in the literature, the
discount rate β is set to 0.97. The cost of job search c is parameterized as c = α * wm
where α is a parameter and wm is the wage from the wage offer distribution such that
5% of all offers generated are lower. Thus, the cost of job search is a fraction of the
lowest wage from the wage offer distribution and can be thought of as the cost necessary
to obtain any wage offer. The layoff probability, q, is set equal to 0.035 as is estimated
by Shimer (2005).
In the model presented above the job finding rate is a constant parameter λ . In
reality the job finding rate may be a function of the intensity with which a worker
searches, which itself is endogenous. If unemployment is particularly costly, then
workers will have an incentive to increase their job search efforts so as to increase their
likelihood of obtaining an offer. This is not the focus of the current exercise. Instead, the
notion of a job offer employed here is the minimum amount of effort that is likely to
generate some job offer. In the results presented here the job offer rate is given as
λ = 0.96 . A wage offer is generated 96% of the time by incurring a search cost of
c = α * wm .
Typically the value of leisure
is thought to be positive. Initial calibration
results were very sensitive to this assumption. The reason for this seems to be that selfemployment is a valuable alternative. The cost of unemployment is the foregone
earnings it entails. Given reasonable assumptions about the arrival rate of entrepreneurial
ideas, the foregone earnings are overwhelmed by the potential value of self-employment.
In order to make unemployment less attractive there must be a substantial cost to it.
Although
can be interpreted as the value of leisure, it can also be thought of as the loss
in the value of skills incurred each period of unemployment. In the results presented
below
= −$20, 000.
Rissman (2006) estimates that more than 40% of all classified as self-employed in
one year are not self-employed the following year. This does not imply that the failure
rate is in excess of 40%, however. The model presented above suggests that workers
self-employed at one point in time may transition to both unemployment and paid
employment. Transitions to paid employment are determined by the optimal search
strategy and are only partially determined by business failures. Even if the business does
not fail, the worker may continue to search for paid employment and if the wage an offer
generates exceeds some threshold, the worker will close his business and move to paid
employment. Thus, the failure rate should be less than 40%.
The idea rate is difficult to quantify. However, the CPS provides some
information as to its magnitude. According to the model, nonparticipants transition from
nonparticipation to self-employment only if they receive an entrepreneurial idea and if
that idea generates profit in excess of the level of profit that would induce him to exit
unemployment given that he is not currently looking for a job in the paid sector. In the
CPS the rate at which nonparticipants become self-employed is 0.035. According to the
model, the likelihood of transitioning from nonparticipation to self-employment is given
by
ˆ
Pr( SEt | NPt −1 ) = ρ G (π > π ) =0.035
ˆ
where π is the threshold level of profits that would induce someone to exit
ˆ
nonparticipation for self-employment. With G (π > π ) ≤ 1 the parameter ρ , which is the
rate at which new ideas are formed, is at least 0.035.
Results
The results of the calibration exercise are found in Tables 3 and 4. In Table 3 the
lower half of the table gives the parameters assumed given outside the model. These
include the discount rate, value of leisure, wage offer rate, business startup cost, and
layoff rate. The other seven parameters are free. These include the idea rate, business
failure rate, and the parameters of the wage offer and profit opportunity distributions.
A grid search method was used to minimize the objective function. The objective
is to choose parameter values to match as closely as possible seven moments of the data.
These moments are taken to be the six transition rates from state i to state j where
i, j = u, pe, se and i ≠ j. The seventh moment is the average wage observed in year t
given the worker was unemployed in year t-1 and is in paid employment in year t.20 In
practice this entails minimizing the squared deviations of the moments generated from
the model from those observed in the data.
PijA is the actual transition rate from state i = u, pe, se to state j = u, pe, se . These
are found previously in Table 2 and reproduced in Table 4. Pij* is the transition rate
generated by the model where again i, j = u , pe, se . The percentage difference between
the actual and expected wage in period t given that the worker was unemployed in period
t-1 is also given in Table 4.
The model clearly does a good job of capturing some transition rates better than
others. The model predicts a transition rate of 0.5883 from unemployment to paid
employment against an observed rate of 0.6030. It also does a good job of capturing
transitions from unemployment to self-employment and from paid employment to
20
This last moment is scaled as a percentage difference from the data.
unemployment. It overpredicts the transition from paid employment to self-employment
(0.0601 versus 0.0330) and from self-employment to unemployment (0.0633 versus
0.0190) and underpredicts the transition from self-employment to paid-employment
(0.1651 versus 0.2070). However, it closely matches the wage moment with less than a
0.02% difference.
The calibrated idea rate is 0.065. The business failure rate is calibrated to be
18%. Comparing the business failure rate to the job separation rate of 3.5%, selfemployment is quite a bit riskier. This translates into higher calibrated transition rates
back to unemployment from self-employment than from paid employment. Thus workers
are willing to give up a certain level of income in return for a more steady job. Because
the cost of unemployment is so high, given the wage and profit distribution assumptions,
workers always search from self-employment. Thus, in the economy modeled here, the
fraction of those who are self-employed who are entrepreneurs is 0. Only if the tail of the
profit distribution is thicker will a person be an entrepreneur. Given the simple
assumptions of this model, the tails of the distribution are not pinned down. Further work
remains to be done.
The model’s projected transition rates can be used to generate steady state levels
of unemployment, paid employment, and self-employment. Results are found in Table 5.
The model overpredicts the steady state level of self-employment and underpredicts the
steady state level of paid employment.
Business startup costs
The model provides a way to evaluate the effect of doubling the cost of starting a
business on the steady state levels of unemployment, paid employment, and self-
employment. This can be thought of as a partial equilibrium analysis in that anything that
affects the flows of people into labor market states will in a more general framework also
affect the distribution of wage offers. In the model presented here the wage offer
distribution is assumed to be given. As shown in Cagetti and DeNardi (2006), liquidity
constraints can explain the disproportionate wealth accounted for by entrepreneurs. The
model presented here does not explicitly consider asset accumulation and consumption.
However, it is still possible to determine the effect of doubling business startup costs on
the labor market states in equilibrium.
The model is solved assuming the same parameters as calibrated in Table 3 with
the exception that business startup costs are doubled. The results of this exercise are
found in the last row of Table 5. Increasing startup costs decreases the net value of selfemployment. It increases steady state unemployment, increases steady state paid
employment, and decreases steady state self-employment. However, the effects are quite
small. Doubling startup costs raises equilibrium unemployment by 60 basis points, raises
equilibrium paid employment by 27 basis points, and lowers equilibrium selfemployment by 86 basis points. It also increases the expected wage given that a person
transitions from unemployment to paid employment.
The bottom part of Table 4 looks more closely at the calculated transition
matrices. Doubling startup costs tends to raise unemployment because it decreases
transitions from unemployment to paid employment and also decreases the transition rate
from unemployment to self-employment. Steady state self-employment falls
predominantly because doubling startup costs increases transitions from self-employment
to unemployment with only a minor increase in flows from self-employment to paid
employment. These relatively minor effects do not mean that liquidity constraints are
unimportant. It simply shows that in this model where there are no liquidity constraints
business startup costs do not have a large impact on the steady state.
Section III: Conclusions
The model of labor market transitions presented above is fairly good at explaining
some of the transitions we observe in the data. However, it fails to match all moments of
the data. In particular it tends to overstate equilibrium self-employment and understate
equilibrium paid-employment under some common assumptions for parameter values.
One possible reason for the model’s failure to match all the moments selected is
that the calibration is done while fixing some of the parameters and searching for the best
possible values of the other parameters. The estimates obtained are likely associated with
a local minimum of the value function. A more thorough search of the parameter space
may yield better results. Similarly, the five fixed parameters may be inconsistent with
matching the model moments to the data. A less restrictive parameterization may be
necessary.
The model seems to provide a close approximation to reality but suggests that a
richer model may be better able to capture certain features of the data. One possibility is
to permit self-employment to entail learning on the job. Thus, failures would occur
earlier in the life of a business and those that survive would have lower failure rates.
Furthermore, the model as formulated here has a very simple process for idea generation.
In reality, ideas may be born of experience. The more experience a worker has in paid
employment, the more exposure he may have to self-employment opportunities. This
would encourage people to work in the wage sector as a means of obtaining entrée into
self-employment. It also suggests that life cycle events may be important determinants
of labor market transitions.
The model provides a framework for thinking of entrepreneurs as those who have
such a high value in self-employment that they do not continue searching for wage work.
In fact, according to the strict view of the model entrepreneurs never return to wage work
except when their business fails. Ideally, the calibration exercise would provide an
estimate of the fraction of self-employed who are entrepreneurs in this sense. However,
the calibrated parameters are such that there are no entrepreneurs. This most certainly
stems from a high calibrated business failure rate. With almost 20% of all businesses
failing each period, the self-employed worker optimally chooses to continue to search for
a wage sector job as insurance against business failure. In order to generate
entrepreneurs who do not search, a richer model of self-employment needs to be
developed.
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longitudinal employee–employer data for the United States,” U.S. Census Bureau,
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Table 1: Fraction of males ages 21 to 54 by labor market state, excluding farm
workers, 1976 to 2006*
Source: March CPS
Year
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
1976-1986
1987-1996
1997-2006
Paid Employment Self-Employment Unemployment Nonparticipant
0.774
0.093
0.061
0.076
0.762
0.111
0.059
0.072
0.771
0.112
0.048
0.073
0.776
0.115
0.044
0.069
0.756
0.120
0.056
0.071
0.750
0.116
0.066
0.071
0.729
0.117
0.087
0.073
0.716
0.109
0.103
0.078
0.745
0.110
0.072
0.078
0.754
0.109
0.065
0.078
0.760
0.105
0.065
0.076
0.759
0.108
0.061
0.077
0.753
0.115
0.054
0.083
0.773
0.109
0.045
0.076
0.770
0.109
0.047
0.078
0.746
0.114
0.068
0.079
0.740
0.108
0.074
0.083
0.738
0.110
0.072
0.086
0.747
0.105
0.060
0.093
0.763
0.101
0.049
0.092
0.758
0.102
0.051
0.092
0.761
0.105
0.046
0.092
0.771
0.104
0.040
0.090
0.777
0.098
0.033
0.095
0.780
0.097
0.034
0.092
0.775
0.097
0.038
0.093
0.760
0.095
0.053
0.096
0.747
0.099
0.055
0.103
0.746
0.099
0.051
0.107
0.750
0.101
0.046
0.107
0.757
0.102
0.042
0.103
0.754
0.755
0.762
0.111
0.108
0.100
0.066
0.058
0.044
0.074
0.084
0.098
* Paid employment includes those who responded affirmatively to the employment question and are
employed by government, a private company, or a nonprofit organization. Those who are self-employed
have responded affirmatively to the employment question and also indicate that they are self-employed.
No distinction is made between incorporated and unincorporated self-employment. A person is
characterized as unemployed if they have been actively seeking work. Those who are nonparticipants
include all others.
Figure 1: Labor force composition, males 21-54 yrs, 1976-2006
0.80
0.12
0.78
0.10
0.76
0.08
0.74
0.06
0.72
0.04
Semp
Source: March CPS, 1976-2006.
Unemp
nilf
Emp, Not SE
2006
2004
2002
2000
1998
1996
1994
1992
1990
1988
1986
1984
1982
0.68
1980
0.00
1978
0.70
1976
0.02
Paid employment
Self-employment, Unemployment,
Nonparicipation
0.14
Table 2: Transtions between labor market states, nonfarm males ages 21-54, 1977-2006.
Source: March CPS
Time t
u
pe
se
Time t+1
u
0.342
0.033
0.019
pe
0.603
0.935
0.207
se
0.065
0.033
0.783
Note: Nonparticipants have been omitted from the calculations.
Table 3: Parameter assumptions for calibration
Definition
Idea rate ρ
Business failure rate γ
Shape parameter for wages
Shape parameter for profits
Scale parameter for wages
Scale parameter for profits
Job search cost c
Free
x
x
x
x
x
x
x
Fixed
Value
Discount rate β
Value of leisure
x
x
0.065
0.18
9.3
2.1
1,914
25,000
$470.15=.05*wmin
0.97
-$20,000
Wage offer rate λ
Business startup cost k
Layoff rate q
x
x
x
0.96
$10,946
0.035
Table 4: Calibration results
Ut
PEt
Ut −`1 ⎡ 0.3320 0.6030
A
Pij = PEt −1 ⎢0.0330 0.9340
⎢
SEt −1 ⎢ 0.0190 0.2070
⎣
SEt
0.0650 ⎤
0.0330⎥ .
⎥
0.7740 ⎥
⎦
Ut
PEt
SEt
Ut −`1 ⎡0.3516 0.5883 0.0602⎤
*
P = PEt −1 ⎢0.0309 0.9090 0.0601⎥
ij
⎢
⎥
SEt −1 ⎢0.0633 0.1651 0.7717 ⎥
⎣
⎦
[(wt | u t −1, pet ) − E(wt | u t −1, pet )] /(wt | u t −1, pet ) =
0.0002
Table 4A: Doubling startup costs
Ut
PEt
SEt
U t −1 ⎡0.3964 0.5442 0.0594 ⎤
*
Pij = PEt −1 ⎢0.0309 0.9098
0.0593⎥
⎢
⎥
SEt −1 ⎢0.0714 0.1664 0.7623 ⎥
⎣
⎦
[( wt | u t −1 , pet ) − E ( wt | u t −1 , pet )] /( wt | u t −1 , pet ) = -0.0173
Table 5: Steady state results
Unemployment
Actual
Calibrated
Doubling
Startup
costs
0.0444
0.0554
0.0614
Paid
Employment
0.8227
0.7362
0.7389
SelfEmployment
0.1329
0.2084
0.1998
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@FedFRASER