A Dynamic Model of Entrepreneurship with Borrowing
Constraints (Job Market Paper)
Abstract
This paper studies the interaction between individuals’ savings and the
decision to become an entrepreneur in a multi-period model with borrowing
constraints. Able individuals who start with wealth above a threshold purposely
save to become entrepreneurs, while those who start below this threshold fall
into a ’poverty trap’ and remain wage earners forever. Using the model and
evidence from US data the importance of poverty traps and the welfare cost of
borrowing constraints are found to be significant. For example, individuals that
could earn up to 18% more as entrepreneurs remain workers if they start with
zero wealth. The model generates a well-defined transition of individuals from
wage earners to entrepreneurs - a major focus of recent empirical work.
Although the probability of becoming an entrepreneur as a function of wealth is
increasing for low wealth levels - as predicted by standard static models - it is
decreasing for higher wealth levels. The predictions about saving rates,
consumption growth and the transition into entrepreneurship are compared
with US data and limited support is found for the model.
1 Introduction
In the recent development literature occupational choice is at the center of the
development process (e.g. Banerjee and Newman (1993), Galor and Zeira (1993)). In
these models, borrowing constraints or other financial frictions affect productivity
and the distribution of income by restricting agents from profitable occupations that
require capital, such as entrepreneurship. Able individuals who start poor are
doomed to remain poor.
To make these models tractable often the analysis is either carried out under
strong assumptions or the models are solved numerically. In particular, generations
are assumed to live for a single time period and the evolution of wealth is
determined by a warm-glow bequest motive that is not forward-looking. These
assumptions have proven useful for understanding the rich dynamics of the wealth
distribution across generations and for studying general equilibrium effects.
However, these assumptions have made quantitative understanding of these
models’ implications elusive. Indeed, the models rule out one potentially important
and interesting mechanism with which able individuals may overcome borrowing
constraints and thus escape poverty traps: life-cycle savings.
As a backdrop, note that borrowing constraints and other financial frictions have
played an important role in intertemporal consumption models where individuals
experience income shocks. One insight from this literature (e.g. Deaton (1992),
Aiyagari (1994), Carroll (1997)) is that individuals facing borrowing constraints will
make an effort to overcome them by saving and, as a result, may be able to
accomplish a significant amount of consumption smoothing by accumulating and de-
accumulating assets. Whether the same logic can be extended to models of
occupational choice and whether welfare cost of borrowing constraints to
entrepreneurship remain large once individuals can save to overcome them remains
an open question.
One purpose of this paper is to construct a tractable dynamic model of
occupational choice with life-cycle savings. The model is then used to understand
the importance of poverty traps and the welfare cost of borrowing constraints.
, Having a tractable model of the life-cycle occupational choice transitions is also
important because they are a major focus of a large and recent empirical literature
(e.g. Evans and Jovanovic (1989), Holtz-Eakin et. al. (1994), Paulson and Townsend
(2002)). Most of the empirical literature on entrepreneurship and borrowing
constraints had focused on measuring the effect of wealth on the likelihood that an
individual becomes an entrepreneur. A positive relationship is then seen as evidence
in favor of the direct effects of borrowing constraints. Understandably, many
researchers have expressed the concern that wealth and ability, which is
unobservable, may them be positively correlated making such an interpretation
difficult. A better understanding of models in which wealth and entrepreneurship
are jointly determined is thus needed to understand the data.
There are four main ingredients to the model: (1) a discrete occupational choice
between being a wage earner and an entrepreneur; (2) borrowing constraints; (3)
standard intertemporal preferences; (4) heterogeneity in wealth and talent.
The discrete occupational choice introduces a non-convexity into the dynamic
problem of households. Fortunately, despite this non-convexity, the continuous time
framework allows a simple characterization of the savings problem. The optimal
decision to save has a simple threshold property. Able individuals who start with
wealth above the threshold but below that needed to start a profitable business
save to become entrepreneurs; able individuals who start with wealth below the
threshold have low savings and will remain workers. In this sense, individuals with
wealth below the threshold are in a poverty trap.
The model is used to investigate the importance of poverty traps as a function of
several parameters of interest. More able entrepreneurs are less likely to be in a
poverty trap. Indeed, there exists a threshold ability level such that individuals above
this threshold are never in a poverty trap regardless of their wealth. Poverty traps
are more likely if the intertemporal elasticity of substitution is lower and the
discount rate is higher, since these two parameters affect the costs of a high savings
plan. Interestingly, the effects of the interest rate and a given worker’s wage rate are
ambiguous. A higher interest rate and a higher wage make it easier for able
individuals to save the capital needed to start a profitable business, but, at the same
time, a higher interest rate and higher wage raise the costs of being in business and
make the option of being a wage earner relatively more attractive.
Turning to quantitative implications, I find significant poverty traps and welfare
costs of borrowing constraints for a large set of parameter values consistent with
those used in the literature. For example, individuals who could earn up to 18%
higher income as entrepreneurs will remain workers if they start with zero wealth.
Even for workers who do not find themselves in a poverty trap welfare is
reduced for two reasons. First, although they eventually become entrepreneurs their
entry into entrepreneurship is delayed relative to the case without borrowing
constraints. Second, their need to save to overcome the borrowing constraint is
costly in terms of utility because it requires an uneven consumption path and
individuals prefer smooth consumption. I show how calculations based on U.S. data
can yield measures for the welfare costs of borrowing constraints. The consumption
of the median entrant into entrepreneurship in the data must be increased
permanently by 24% to make her indifferent between living in the economy with
credit constraints and in an economy with perfect capital markets.
From these quantitative exercises I conclude that, borrowing constraints can
remain important in models where agents can potentially overcome them by saving.
The model has strong predictions that can be compared to the data: (1)
individuals who expect to become entrepreneurs have higher savings rates than
individuals who expect to remain workers; (2) the growth rate of consumption of
newer entrepreneurs is higher than that of workers and older entrepreneurs; (3) the
1
,relationship between the probability of entry into entrepreneurship and wealth is
not monotone.
The first prediction summarizes nicely the essential ingredient of the model: that
workers can save up to overcome their borrowing constraints to become
entrepreneurs. As discussed above, depending on their relative skills some workers
will choose to never become entrepreneurs, either because it is not productively
efficient or because the savings required to overcome the constraints requires too
large a sacrifice. Others find that becoming an entrepreneur will have a large enough
surplus and consequently save more. Intuitively, saving is valued because it reduces
the time at which they obtain the surplus from entrepreneurship. Thus, workers who
expect to become entrepreneurs will save more than those that expect to remain
workers.
The second prediction follows from the fact that new entrepreneurs are still
constrained with respect to their capital level and consequently have a higher
marginal product of capital than older entrepreneurs and higher than the market
interest rate.
The last prediction follows from the fact that wealth and entrepreneurship are
jointly determined in the model. For low wealth levels, entry into entrepreneurship
increases with wealth because it relaxes the borrowing constraint; this is just as
predicted by standard static models. But, for high wealth levels, entry into
entrepreneurship and wealth become negatively related. This negative relationship
reflects the fact that over time individuals with high entrepreneurial skills are
selected out of the pool of workers and that this selection effect increases with
wealth. Intuitively, if an individual is rich and still works for a wage then it is unlikely
that he has a high entrepreneurial skill and thus it is most likely to be a bad
entrepreneur and thus to remain a worker.
The same reasoning implies that the coefficient of wealth in a regression of entry
into entrepreneurship may underestimates the impact of an exogenous wealth
transfer on the likelihood that individuals become entrepreneurs. In other words, a
regression may not correctly identify the actual parameter of interest for certain
transfer policies that have been considered to promote entrepreneurship. A precise
statement of this is given in the paper.
No single U.S. data set contains all the variables stressed by the model. Because
of this, I compare these three predictions to the data using three U.S. data sets: the
Panel Study of Income Dynamics (PSID), the Survey of Consumer Finances (SCF) and
the Consumers Expenditure Survey (CES). As predicted by the model, future
entrepreneurs that start poor do save more than poor those that remain workers.
There is some evidence that the consumption growth of entrepreneurs is higher
than that of workers, although that of newer entrepreneurs is not particularly high.
Finally, the relationship between entry into entrepreneurship and wealth is hump-
shaped for individuals with low wages and individuals who enter labor-intensive
industries.
The rest of the paper is organized as follows. Section 2 discusses the related
literature. Section 3 describes the individual’s dynamic occupational choice problem
and Section 4 characterizes its solution. Section 5 examines the quantitative
importance of poverty traps and the welfare cost resulting from borrowing
constraints implied by the model. Section 6 presents the implications of the model
for the average relationship between wealth and the likelihood of a transition to
entrepreneurship. Section 7 discusses two extensions of the model: stochastic
business opportunities and incorporating an additional sector with a labor-intensive
technology. Section 8 tests the predictions of the model using data from the PSID,
the SCF and the CEX. Section 8 concludes and discusses directions for future
research.
2
, 2 Related Literature
There is a large and recent literature studying models of occupational choice and
credit market frictions. Papers in this literature include Banerjee and Newman
(1993), Galor and Zeira (1993), Aghion and Bolton (1997), Lloyd-Ellis and Bernhardt
(2000), Caselli and Gennaioli (2002), Matsuyama (2000, 2003), Mokeerjee and Ray
(2002, 2003), Galor and Moav (forthcoming). The main objective of these papers is
to shed light on complex general equilibrium interactions that arise between wealth
distribution and the development process. In a similar venue, Greenwood and
Jovanovic (1990) study an economy where individuals face an option to join a
financial coalition after paying a fixed cost.
This paper follows the original contributions by Skiba (1978) and Brock and
Dechert (1983), who study optimal control problems with non-convex technology
sets, to study the dynamics of wealth and occupational choices. Majumdar and Mitra
(1982) and Dechert and Nishimura (1983) study the discrete time version of the
optimal growth problem with convex-concave production function. Related,
Matsuyama and Ciccone (1999) study an economy where an aggregate convex-
concave production function arises endogenously from demand complementarities
at individual level.
Steps toward understanding the quantitative implications of models of
occupational choice with borrowing constraints are taken by Quadrini (1999), Li
(2002) and Cagetti and De Nardi (2003) for the US and Gine and Townsend
(forthcoming) and Jeong and Townsend (2003) for developing countries. Quadrini
(1999) and Cagetti and De Nardi (2003) find that a model with entrepreneurs and
borrowing constraints does a good job in fitting the right tale of the US wealth
distribution, while Li (2002) quantitatively studies the effects of government credit
subsidies in the US. Gine and Townsend (forthcoming) study the role of financial
liberalization in explaining the growth and the evolution of inequality in Thailand.
Jeong and Townsend (2003) go one more step further and compare the performance
of alternative models of growth and inequality: the model of occupational choice of
Lloyd-Ellis and Bernhardt (2000) and the model of financial deepening by Greenwood
and Jovanovic (1990).
A large empirical literature studies the causal effect of wealth on the likelihood of
becoming an entrepreneur. See Hurst and Lusardi (forthcoming) for a recent
contribution and a critical discussion of the literature. Paulson and Townsend
(forthcoming, 2002) are recent exemplary empirical studies of occupational choice
and financial constraints for developing countries. Banerjee and Duflo (2002) study
the causal effect of wealth on investment by entrepreneurs using a policy change in
India.
3 The Model Economy
Time is continuous and there is a continuum of agents facing a constant probability
of dying p. The probability that an agent is alived at age t equals e−pt. At each instant
a cohort of size p is born. The offspring of a given agent is born when the agent dies.
Agents do not derive utility from the welfare of their offspring: they are not
altruistic, but agents’ wealth is inherited by their offspring. There are no annuity
markets.
There are two sectors in this economy: an informal and a formal (or corporate)
sector. In the informal sector households can produce a single consumption good
using an agent specific technology that is indexed by a household-specific ability e.
Alternatively, households can work for the corporate sector. The corporate sector
hires capital and labor from the households to produce the single consumption good
using a neoclassical technology.
3
Constraints (Job Market Paper)
Abstract
This paper studies the interaction between individuals’ savings and the
decision to become an entrepreneur in a multi-period model with borrowing
constraints. Able individuals who start with wealth above a threshold purposely
save to become entrepreneurs, while those who start below this threshold fall
into a ’poverty trap’ and remain wage earners forever. Using the model and
evidence from US data the importance of poverty traps and the welfare cost of
borrowing constraints are found to be significant. For example, individuals that
could earn up to 18% more as entrepreneurs remain workers if they start with
zero wealth. The model generates a well-defined transition of individuals from
wage earners to entrepreneurs - a major focus of recent empirical work.
Although the probability of becoming an entrepreneur as a function of wealth is
increasing for low wealth levels - as predicted by standard static models - it is
decreasing for higher wealth levels. The predictions about saving rates,
consumption growth and the transition into entrepreneurship are compared
with US data and limited support is found for the model.
1 Introduction
In the recent development literature occupational choice is at the center of the
development process (e.g. Banerjee and Newman (1993), Galor and Zeira (1993)). In
these models, borrowing constraints or other financial frictions affect productivity
and the distribution of income by restricting agents from profitable occupations that
require capital, such as entrepreneurship. Able individuals who start poor are
doomed to remain poor.
To make these models tractable often the analysis is either carried out under
strong assumptions or the models are solved numerically. In particular, generations
are assumed to live for a single time period and the evolution of wealth is
determined by a warm-glow bequest motive that is not forward-looking. These
assumptions have proven useful for understanding the rich dynamics of the wealth
distribution across generations and for studying general equilibrium effects.
However, these assumptions have made quantitative understanding of these
models’ implications elusive. Indeed, the models rule out one potentially important
and interesting mechanism with which able individuals may overcome borrowing
constraints and thus escape poverty traps: life-cycle savings.
As a backdrop, note that borrowing constraints and other financial frictions have
played an important role in intertemporal consumption models where individuals
experience income shocks. One insight from this literature (e.g. Deaton (1992),
Aiyagari (1994), Carroll (1997)) is that individuals facing borrowing constraints will
make an effort to overcome them by saving and, as a result, may be able to
accomplish a significant amount of consumption smoothing by accumulating and de-
accumulating assets. Whether the same logic can be extended to models of
occupational choice and whether welfare cost of borrowing constraints to
entrepreneurship remain large once individuals can save to overcome them remains
an open question.
One purpose of this paper is to construct a tractable dynamic model of
occupational choice with life-cycle savings. The model is then used to understand
the importance of poverty traps and the welfare cost of borrowing constraints.
, Having a tractable model of the life-cycle occupational choice transitions is also
important because they are a major focus of a large and recent empirical literature
(e.g. Evans and Jovanovic (1989), Holtz-Eakin et. al. (1994), Paulson and Townsend
(2002)). Most of the empirical literature on entrepreneurship and borrowing
constraints had focused on measuring the effect of wealth on the likelihood that an
individual becomes an entrepreneur. A positive relationship is then seen as evidence
in favor of the direct effects of borrowing constraints. Understandably, many
researchers have expressed the concern that wealth and ability, which is
unobservable, may them be positively correlated making such an interpretation
difficult. A better understanding of models in which wealth and entrepreneurship
are jointly determined is thus needed to understand the data.
There are four main ingredients to the model: (1) a discrete occupational choice
between being a wage earner and an entrepreneur; (2) borrowing constraints; (3)
standard intertemporal preferences; (4) heterogeneity in wealth and talent.
The discrete occupational choice introduces a non-convexity into the dynamic
problem of households. Fortunately, despite this non-convexity, the continuous time
framework allows a simple characterization of the savings problem. The optimal
decision to save has a simple threshold property. Able individuals who start with
wealth above the threshold but below that needed to start a profitable business
save to become entrepreneurs; able individuals who start with wealth below the
threshold have low savings and will remain workers. In this sense, individuals with
wealth below the threshold are in a poverty trap.
The model is used to investigate the importance of poverty traps as a function of
several parameters of interest. More able entrepreneurs are less likely to be in a
poverty trap. Indeed, there exists a threshold ability level such that individuals above
this threshold are never in a poverty trap regardless of their wealth. Poverty traps
are more likely if the intertemporal elasticity of substitution is lower and the
discount rate is higher, since these two parameters affect the costs of a high savings
plan. Interestingly, the effects of the interest rate and a given worker’s wage rate are
ambiguous. A higher interest rate and a higher wage make it easier for able
individuals to save the capital needed to start a profitable business, but, at the same
time, a higher interest rate and higher wage raise the costs of being in business and
make the option of being a wage earner relatively more attractive.
Turning to quantitative implications, I find significant poverty traps and welfare
costs of borrowing constraints for a large set of parameter values consistent with
those used in the literature. For example, individuals who could earn up to 18%
higher income as entrepreneurs will remain workers if they start with zero wealth.
Even for workers who do not find themselves in a poverty trap welfare is
reduced for two reasons. First, although they eventually become entrepreneurs their
entry into entrepreneurship is delayed relative to the case without borrowing
constraints. Second, their need to save to overcome the borrowing constraint is
costly in terms of utility because it requires an uneven consumption path and
individuals prefer smooth consumption. I show how calculations based on U.S. data
can yield measures for the welfare costs of borrowing constraints. The consumption
of the median entrant into entrepreneurship in the data must be increased
permanently by 24% to make her indifferent between living in the economy with
credit constraints and in an economy with perfect capital markets.
From these quantitative exercises I conclude that, borrowing constraints can
remain important in models where agents can potentially overcome them by saving.
The model has strong predictions that can be compared to the data: (1)
individuals who expect to become entrepreneurs have higher savings rates than
individuals who expect to remain workers; (2) the growth rate of consumption of
newer entrepreneurs is higher than that of workers and older entrepreneurs; (3) the
1
,relationship between the probability of entry into entrepreneurship and wealth is
not monotone.
The first prediction summarizes nicely the essential ingredient of the model: that
workers can save up to overcome their borrowing constraints to become
entrepreneurs. As discussed above, depending on their relative skills some workers
will choose to never become entrepreneurs, either because it is not productively
efficient or because the savings required to overcome the constraints requires too
large a sacrifice. Others find that becoming an entrepreneur will have a large enough
surplus and consequently save more. Intuitively, saving is valued because it reduces
the time at which they obtain the surplus from entrepreneurship. Thus, workers who
expect to become entrepreneurs will save more than those that expect to remain
workers.
The second prediction follows from the fact that new entrepreneurs are still
constrained with respect to their capital level and consequently have a higher
marginal product of capital than older entrepreneurs and higher than the market
interest rate.
The last prediction follows from the fact that wealth and entrepreneurship are
jointly determined in the model. For low wealth levels, entry into entrepreneurship
increases with wealth because it relaxes the borrowing constraint; this is just as
predicted by standard static models. But, for high wealth levels, entry into
entrepreneurship and wealth become negatively related. This negative relationship
reflects the fact that over time individuals with high entrepreneurial skills are
selected out of the pool of workers and that this selection effect increases with
wealth. Intuitively, if an individual is rich and still works for a wage then it is unlikely
that he has a high entrepreneurial skill and thus it is most likely to be a bad
entrepreneur and thus to remain a worker.
The same reasoning implies that the coefficient of wealth in a regression of entry
into entrepreneurship may underestimates the impact of an exogenous wealth
transfer on the likelihood that individuals become entrepreneurs. In other words, a
regression may not correctly identify the actual parameter of interest for certain
transfer policies that have been considered to promote entrepreneurship. A precise
statement of this is given in the paper.
No single U.S. data set contains all the variables stressed by the model. Because
of this, I compare these three predictions to the data using three U.S. data sets: the
Panel Study of Income Dynamics (PSID), the Survey of Consumer Finances (SCF) and
the Consumers Expenditure Survey (CES). As predicted by the model, future
entrepreneurs that start poor do save more than poor those that remain workers.
There is some evidence that the consumption growth of entrepreneurs is higher
than that of workers, although that of newer entrepreneurs is not particularly high.
Finally, the relationship between entry into entrepreneurship and wealth is hump-
shaped for individuals with low wages and individuals who enter labor-intensive
industries.
The rest of the paper is organized as follows. Section 2 discusses the related
literature. Section 3 describes the individual’s dynamic occupational choice problem
and Section 4 characterizes its solution. Section 5 examines the quantitative
importance of poverty traps and the welfare cost resulting from borrowing
constraints implied by the model. Section 6 presents the implications of the model
for the average relationship between wealth and the likelihood of a transition to
entrepreneurship. Section 7 discusses two extensions of the model: stochastic
business opportunities and incorporating an additional sector with a labor-intensive
technology. Section 8 tests the predictions of the model using data from the PSID,
the SCF and the CEX. Section 8 concludes and discusses directions for future
research.
2
, 2 Related Literature
There is a large and recent literature studying models of occupational choice and
credit market frictions. Papers in this literature include Banerjee and Newman
(1993), Galor and Zeira (1993), Aghion and Bolton (1997), Lloyd-Ellis and Bernhardt
(2000), Caselli and Gennaioli (2002), Matsuyama (2000, 2003), Mokeerjee and Ray
(2002, 2003), Galor and Moav (forthcoming). The main objective of these papers is
to shed light on complex general equilibrium interactions that arise between wealth
distribution and the development process. In a similar venue, Greenwood and
Jovanovic (1990) study an economy where individuals face an option to join a
financial coalition after paying a fixed cost.
This paper follows the original contributions by Skiba (1978) and Brock and
Dechert (1983), who study optimal control problems with non-convex technology
sets, to study the dynamics of wealth and occupational choices. Majumdar and Mitra
(1982) and Dechert and Nishimura (1983) study the discrete time version of the
optimal growth problem with convex-concave production function. Related,
Matsuyama and Ciccone (1999) study an economy where an aggregate convex-
concave production function arises endogenously from demand complementarities
at individual level.
Steps toward understanding the quantitative implications of models of
occupational choice with borrowing constraints are taken by Quadrini (1999), Li
(2002) and Cagetti and De Nardi (2003) for the US and Gine and Townsend
(forthcoming) and Jeong and Townsend (2003) for developing countries. Quadrini
(1999) and Cagetti and De Nardi (2003) find that a model with entrepreneurs and
borrowing constraints does a good job in fitting the right tale of the US wealth
distribution, while Li (2002) quantitatively studies the effects of government credit
subsidies in the US. Gine and Townsend (forthcoming) study the role of financial
liberalization in explaining the growth and the evolution of inequality in Thailand.
Jeong and Townsend (2003) go one more step further and compare the performance
of alternative models of growth and inequality: the model of occupational choice of
Lloyd-Ellis and Bernhardt (2000) and the model of financial deepening by Greenwood
and Jovanovic (1990).
A large empirical literature studies the causal effect of wealth on the likelihood of
becoming an entrepreneur. See Hurst and Lusardi (forthcoming) for a recent
contribution and a critical discussion of the literature. Paulson and Townsend
(forthcoming, 2002) are recent exemplary empirical studies of occupational choice
and financial constraints for developing countries. Banerjee and Duflo (2002) study
the causal effect of wealth on investment by entrepreneurs using a policy change in
India.
3 The Model Economy
Time is continuous and there is a continuum of agents facing a constant probability
of dying p. The probability that an agent is alived at age t equals e−pt. At each instant
a cohort of size p is born. The offspring of a given agent is born when the agent dies.
Agents do not derive utility from the welfare of their offspring: they are not
altruistic, but agents’ wealth is inherited by their offspring. There are no annuity
markets.
There are two sectors in this economy: an informal and a formal (or corporate)
sector. In the informal sector households can produce a single consumption good
using an agent specific technology that is indexed by a household-specific ability e.
Alternatively, households can work for the corporate sector. The corporate sector
hires capital and labor from the households to produce the single consumption good
using a neoclassical technology.
3
