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No matter how many tears I cry
No matter how many years go by
I still can't say goodbye

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[This summary was prepared by Larry Blakeley]

For purposes of this article, the authors classify as “entrepreneurs” the households who:

1. declare owning a business (or a share of one),

2. have an active management role in it, and

3. own at least $5,000 in actively managed businesses.

in order to isolate people who have made a significant up-front investment in their business.

(The exact question is, “Do you, or does anyone in your family living here have an active management role in any of these businesses?”)

We call these GH entrepreneurs.

Although the role of financial constraints on entrepreneurial choices has received considerable attention, the effects of these constraints on:

• aggregate capital accumulation, and

• wealth inequality

are less known.

Entrepreneurship is an important determinant of:

• capital accumulation, and

• wealth concentration,

and, conversely, the distribution of wealth affects: entrepreneurial choices in the presence of borrowing constraints.

We construct a model that matches wealth inequality very well, for both entrepreneurs and non-entrepreneurs; and find that more restrictive borrowing constraints:

• generate less wealth concentration; but also

• reduce average firm size,

• reduce aggregate capital, and

• reduce the fraction of entrepreneurs.

We also find that voluntary bequests are an important channel that allows some high-ability workers to establish or enlarge an entrepreneurial activity.

With accidental bequests only, there would be:

• fewer large firms,

• fewer entrepreneurs, and

• less aggregate capital, but also

• less wealth concentration.

1 Introduction

Many empirical studies find that potential and existing entrepreneurs face borrowing constraints and that the decision to become an entrepreneur or expand one’s firm depends on:

• asset ownership,

• availability of collateral, and

• receipt of bequests.

In the presence of borrowing constraints:

• the decision to invest,

• the fraction of entrepreneurs, and

• the size distribution of firms

depend on the distribution of assets in the economy.

The data show that wealth holdings are extremely concentrated, much more than labor earnings and income, and that entrepreneurs are an important force driving wealth concentration and aggregate capital accumulation.

In this paper we analyze the role of borrowing constraints as determinants of:

• entrepreneurial decisions (entry, continuation, investment, and saving), and

their effects on:

• wealth inequality, and

• aggregate capital accumulation,

in a framework that matches the observed wealth inequality very closely.
Because of the interaction between borrowing constraints and asset holdings, it is key to perform such an analysis in a model that matches well the extreme concentration of wealth observed in the data.

We find that more restrictive borrowing constraints:

generate less inequality in wealth holdings,

but also reduce:

• average firm size,

• the number of people engaging in entrepreneurial activities, and

• aggregate capital accumulation.

These findings are based on a quantitative life-cycle model with altruism across generations and entrepreneurial choice, in an environment in which debt repayment cannot be perfectly enforced.

The amount that entrepreneurs can borrow depends, therefore, on their observable characteristics, and the entrepreneurs’ assets act as collateral for their debts.

Since the implicit rate of return for entrepreneurs is higher than the rate for workers, and consistently with the data, entrepreneurs have a higher saving rate.

We show that our model with entrepreneurial choice matches very well the observed distribution of wealth, for both entrepreneurs and non-entrepreneurs.

2 Empirical evidence on entrepreneurship, borrowing constraints, and wealth

This section discusses the evidence indicating that entrepreneurs:

• are liquidity constrained, and

• have a higher saving rate than non-entrepreneurs.

It also highlights the key role of entrepreneurship in generating a skewed wealth distribution.

We use data from the 1989 Survey of Consumer Finances (SCF).

Unlike other data sets (such as the Panel Study of Income Dynamics and the Health and Retirement Survey), the SCF over samples rich households and thus provides important advantages:

First, it gives a better picture of the concentration of wealth and of the asset holdings of richer households, which include a large share of entrepreneurs; and

Second, the total wealth implied by the SCF is very close to the total wealth implied by aggregate data (such as the Federal Reserve Board flow of funds accounts), the SCF can thus be used to calibrate aggregates (for instance, the share of entrepreneurial wealth and the percentage of entrepreneurs) in a general equilibrium model such as the one developed in this paper.

In our model, an entrepreneur invests his own wealth in the entrepreneurial activity, and his income is primarily the return from this activity.

2.1 Entrepreneurship and borrowing constraints

Contrary to the intuition that only the poor might face borrowing constraints, Holtz-Eakin, Joulfaian, and Rosen [23] find that even in their sample:

• the receipt of a bequest (and thus an increase in wealth) increases the probability of starting a business.

Even more interestingly, they find that existing sole proprietors who receive a bequest:

• are more likely to stay in business, and

• experience a substantial increase in the enterprise’s receipts.

Their explanation for this finding is that:

• entrepreneurial businesses are undercapitalized because of liquidity constraints, and

• capital market imperfections exert an important influence on business and capital formation.

The probability of switching into self-employment increases with asset ownership.

(Note: More recently, however, findings seem to indicate that this correlation is probably more important for the richest than for the poor would-be entrepreneurs.)

This evidence thus suggests that entrepreneurs face borrowing constraints and that the possibility of becoming entrepreneurs and the level of possible borrowing are related to the level of entrepreneurs’ wealth.

The need to accumulate assets in the presence of such constraints may also generate high saving rates among entrepreneurs (or households planning to become entrepreneurs). In fact, entrepreneurs have higher saving rates than the rest of the population.

Another fact that is interpreted by many as evidence of borrowing constraints is that the portfolios of entrepreneurs, even the richest ones, are very undiversified.

Business wealth constitutes a large share of the entrepreneur’s total wealth, and even the entrepreneur’s own assets are often used as collateral.

In the SCF, the median ratio of business wealth to net worth (for the business owners who have more than $5,000 in business assets in 1989) is 48%, the third quartile is 77%, and the top decile is 96%.

Approximately half of the net worth is constituted by business wealth for entrepreneurs both in the top and in the bottom of the distribution.

....the percentage of entrepreneurs who have more than 75% and 90% of net worth invested in their own assets stays high even for the richest entrepreneurs.

In the survey, 33% of entrepreneurs declare that they currently use their own assets as collateral.

Within this group:

• the median amount of collateral is $36,000,

• the top decile is $300,000,

• the top 5% is $570,000; and

• the median ratio of collateral to business value is 21%,

• the top decile is 77%, and

• the top 5% is 100%.

These fractions do not change significantly across quantiles of the wealth distribution, thus suggesting that many businesses need to put up collateral in order to borrow, regardless of their size.

These numbers are just an indication, because they include the use of only personal assets (other than the business itself) and do not indicate the relation between the amount borrowed and the size of the business, nor the amount of borrowing desired by the entrepreneur.

2.2 Entrepreneurship and the wealth distribution

Even though entrepreneurs are only a small fraction of the population, they hold a large share of total net worth.

GH entrepreneurs, for example,

• constitute 8.7% of the population,

• hold 39% of total net worth,

• constitute a large share of the richest households.

The richest households own a large fraction of wealth even among the richest, for example:

• the households in the top 1% of the wealth distribution hold around 30% of total net worth (60% are entrepreneurs or self-employed and hold 69% of the wealth held by this group), and

• those in the top 5% hold more than half of the total net worth (almost 50% are entrepreneurs or self-employed and hold 60% of the wealth held by this group).

2.3 More about entrepreneurs

The percentage of households whose head declares himself self-employed is around 10%, similar to the percentage of entrepreneurs.

However, only around two-thirds of the self-employed have business assets, and only slightly more than one-half of them have more than $5,000 invested in a business.

There is thus a difference between being self-employed and owning business assets. Some self-employed households do not invest any of their (nonhuman) wealth in their activity, or invest only a very small amount.

The difference between those two groups is highest in the lower quantiles of the wealth distribution, where the self-employed tend to be poorer than the entrepreneurs, and many of them have no business assets.

For the higher quantiles, however, the two groups are almost the same. For instance, most (from 85% to 90%, depending on the year) of the self-employed who are in the top 5% of the overall wealth distribution are also entrepreneurs according to the GH definition.

As for the distribution by type of business, roughly:

• one-half of the businesses are sole-proprietorships,

• one-quarter are partnerships, and

• one-quarter are incorporated.

While a few of those who have a management role in a corporation should be classified as managers rather than entrepreneurs who invest their own wealth, the previous section shows that most entrepreneurs have a significant share of their own wealth invested in their businesses.

In fact, the ratio of business assets to total net worth and the fraction of entrepreneurs who have collateralized loans are very similar across these various groups, as well as across various types of business activities.

3 The model

3.1 Demographics

We adopt a life-cycle model with intergenerational altruism.

Households go through two stages of life, young and old age:

• a young person faces a constant probability of aging during each period, and

• an old person faces a constant probability of dying during each period. When an old person dies, his offspring enters the model, carrying the assets bequeathed to him by the parent.

3.2 Preferences

To study the role of bequests, our model nests life-cycle and fully altruistic households as two extreme cases.

In the purely life-cycle version of the model individuals put no weight on the utility of their descendants.

In the perfectly altruistic version, individuals care about their descendants as much as themselves.

We assume exogenous labor supply.

3.3 Technology

Many firms are not controlled by a single entrepreneur and are not likely to face the same financing restrictions that we stress in our model.

Entrepreneurs thus face decreasing returns from investment, as their managerial skills become gradually stretched over larger and larger projects.

Hence, while entrepreneurial ability (defined as the capacity to invest capital more or less productively) is exogenously given,

the entrepreneurial rate of return from investing in capital is:

• endogenous, and

• a function of the size of the project that the entrepreneur implements.

We assume that the entrepreneurs work on their own projects without hiring labor and that all of the workers are hired by the non-entrepreneurial sector.

3.4 Credit market constraints

The borrowing constraints are endogenously determined in equilibrium and stem from the assumptions that contracts are imperfectly enforceable.

Imperfect enforceability of contracts means that the creditors will not be able to force the debtors to fully repay their debts as promised, but that the debtors fully repay only if it is in their own interest to do so.

Since both parties are aware of this feature and act rationally, the lender will lend to a given borrower only an amount (possibly zero) that will be in the debtor’s interest to repay as promised.

In our framework, instead, the higher is the amount of an entrepreneur’s own wealth invested in the business,

• the larger is the amount that the creditor is able to recover, and

• the larger is thus the sum that creditor is willing to lend to the entrepreneur.

Hence, the entrepreneur’s assets act as collateral.

As a result, not all potentially profitable projects receive appropriate funding. Households with little wealth can borrow little, even if they have high ability as entrepreneurs.

Since the entrepreneur forgoes his potential earnings as a worker, he will choose to become an entrepreneur only if the size of the firm that he can start is big enough; that is, he is rich enough to be able to borrow and invest a suitable amount of money in his firm.

3.5 Households - [Very technical economic equations and calculations]

3.6 Equilibrium - [Very technical economic equations and calculations]

3.7 Calibration

The probability of aging and of death are such that the average length of the working life is 45 years, and the average length of the retirement period is 11 years.

We assume that the income and the entrepreneurial ability processes evolve independently.

We use these six parameters to pin down the following moments generated by the model:

1. the capital-to-output ratio,

2. the fraction of entrepreneurs in the population,

3. the fraction of entrepreneurs exiting entrepreneurship during each period,

4. the fraction of workers becoming entrepreneurs during each period,

5. the ratio of median net worth of entrepreneurs to that of workers, and

6. the fraction of people with zero wealth.

Given the features matched in the calibration, we analyze how well:

• the model matches the overall distribution of wealth and

• the distributions of wealth for entrepreneurs and workers.

We then study the role of borrowing constraints and voluntary bequests.

3.8 Results

The notion of capital that we use includes residential structures, plant, equipment, land, and consumer durables, and it implies a capital-output ratio of 3 for the period 1959.

The ratio of average wealth to average income is also about 3.

The data pertaining to the distribution of wealth come from the 1989 SCF. The waves for other years are similar.

3.8.1 The model without entrepreneurs

These results thus refer to a model economy with labor earnings risk and a simplified life-cycle structure.

This model economy produces a distribution of wealth that:

• is much less concentrated than that in the data and

• that, in particular, does not explain the emergence of the large estates that characterize the upper tail of the distribution of wealth.

While the data on wealth display a fat tail, in the model without entrepreneurial choice all households hold less than $1.1 million.

3.8.2 The model with entrepreneurs

These pictures reveal two important features of the baseline model.

• First, and consistently with the data, the distribution of wealth for the population of entrepreneurs displays a much fatter tail than the one for workers.

• Second, contrary to the model without entrepreneurial choice, the baseline model generates distributions of wealth for both entrepreneurs and non-entrepreneurs with a significant mass of people who have more than $1.1 million.

Those with low entrepreneurial ability (who are thus workers) exhibit bufferstock saving behavior:

• if their assets are low, they save because they are experiencing a high ability level as workers and want to build up their buffer-stock

• if their assets are high enough, they dissave, and the richer they are, the higher their rate of dissaving.

In this simulation, the asset level at which the saving rate goes from positive to negative is below $1 million.

The people with high entrepreneurial ability, as explained in section 3.4, become entrepreneurs only if their wealth is above a certain level.

The saving rate of those with high entrepreneurial ability who do not own enough assets to become entrepreneurs is higher than the one for the workers because ability is persistent, and the workers with high entrepreneurial ability save to have a chance to start a business in the future.

The saving rate of those with high entrepreneurial ability and enough assets to become entrepreneurs is positive and considerably higher than that for workers.

The return on the entrepreneurial activity is high, and the entrepreneur would like to increase the size of the firm by borrowing capital.

However, the borrowing constraint limits the size of the firm.

In order to expand the business, the entrepreneur must in part self-finance the increase in capital.

The combination of higher returns from the business together with the budget constraint thus generates a very high saving rate for entrepreneurs.

As the firm expands, the returns decrease. Therefore, the saving rate will also eventually decrease.

3.8.3 The borrowing constraints

In this section, we examine the effect of changing the tightness of the borrowing constraints.

To make the constraints more stringent, we increase f, the fraction of working capital that cannot be seized by creditors, from 0.75 to 0.85. The less the creditors can get back, the less they lend to the entrepreneur.

This increase in f could be interpreted as:

• less efficient enforcement of property rights by the courts, or

• as more lenient bankruptcy laws.

In both economies (baseline model and the model with more restrictive borrowing constraints) the entrepreneurs with few assets cannot borrow.

The amount of collateral necessary to borrow a positive amount in the two economies coincides at low levels of assets.

The entrepreneur with the lowest ability level as a worker must have at least $16,000 in order to borrow some funds; this amount increases to $266,000 for the entrepreneur with the highest ability level as a worker.

This happens because a more able worker is better off in case of default; therefore, he has to provide more collateral.

The key difference in the two economies is that richer entrepreneurs can borrow and invest less in the economy with more restrictive borrowing constraints. For this reason they need more initial assets to implement a project of a given size, and it takes them longer to become rich and own and run a large firm.

If the entrepreneur is rich enough, he is unconstrained.

An increase in the tightness of the borrowing constraint forces entrepreneurs, and in particular rich ones, to borrow less and run smaller firms.

They make fewer total profits and save less, and, as a result, they are poorer.

The distribution of wealth becomes less concentrated; for instance:

• the share of total net worth held by the richest 1% decreases from 30% in the baseline calibration to 26%, and

• the share of total net worth held by entrepreneurs decreases from 34% to 30%.

Hence, as the collateral requirements rise, wealth inequality falls, but this comes at the expense of lower capital accumulation and output.

3.8.4 Bequests

In the baseline economy households are altruistic toward their offspring; therefore, the total amount of bequests includes both voluntary and accidental bequests due to life-span risk.

We use our model to study what happens to entrepreneurial choice and to wealth inequality when households do not care about their descendants and all bequests are accidental.

The absence of the voluntary bequest motive reduces the incentives to accumulate capital and run larger and larger firms.

On the one hand, younger people are bequeathed less wealth, and in the presence of borrowing constraints, this means that young potential entrepreneurs have fewer resources to start and increase their businesses.

On the other hand, the equilibrium interest rate increases to 8.7%, thus allowing more high-ability individuals to use the increased proceedings from their earnings to start a business activity.

The net effect on the total fraction of entrepreneurs is a small decrease from 8.7% to 8.5%

The effects on aggregate capital accumulation are large: in the absence of a voluntary bequest motive to save, the total capital of the economy would decrease from 3.0 to 2.6.

The concentration of wealth would also drop substantially: the Gini coefficient of inequality would go from 0.83 to 0.78, and the fraction of wealth held by the richest 1% from 31% to 23%.

Voluntary bequests are fundamental in explaining the concentration of wealth.

In this model economy, voluntary bequests provide an additional incentive to save to rich entrepreneurs and also generate the intergenerational transmission of large fortunes (and firms) across generations.

To better understand the role of voluntary bequests, we run another experiment, in which we increase the discount factor ß to match a capital-output ratio of 3.0.

The fraction of entrepreneurs increases compared to the baseline model, from 8.7% to 9.1%. This effect is due to an increase in the general equilibrium interest rate, which has the same effect we have discussed above, and to the increase in the household’s discount factor.

In this calibration, households have no bequest motive, but are more patient.

This implies that the younger households accumulate more wealth than in the baseline model, while the old decumulate faster, and thus keep less wealth, because of the lack of altruism.

More people of working age become entrepreneurs, and the old have fewer incentives to continue and expand the entrepreneurial activity and pass to their offspring less wealth and smaller firms.

This reduces the number and the size of large firms.

For these reasons, the wealth concentration generated by this experiment is lower than the one in the benchmark economy; for instance, the share of total net worth held by the richest 1% drops to 26%, down from 31%.

4 Conclusions

We developed and solved numerically a model of wealth accumulation and bequests in which entrepreneurs face an endogenous borrowing constraint that limits the amount that they can borrow.

The entrepreneur’s wealth acts as collateral, so that the richer the entrepreneur, the higher the amount he can borrow.

We show that this setup can generate a wealth distribution that matches the one observed in the data, with a small number of very rich households, many of whom are entrepreneurs. Because of the relation between wealth and borrowing limits, entrepreneurs, although richer, have higher saving rates than workers.

We also show that the tightness of borrowing constraints and voluntary bequests are key forces in determining the number of entrepreneurs and the size of their firms, as well as the overall wealth concentration in the population.

These results have implications for policy analysis, such as subsidized loans to entrepreneurs and estate taxes.

Subsidized loans would make it cheaper for the entrepreneurs to borrow, but would also change their incentives to default, making the effects of this policy a priori ambiguous.

Taxing bequests may decrease inequality, while at the same time reduce the amount of entrepreneurial wealth that could be used as collateral, and thus reduce both the number of entrepreneurs and the total capital of the economy.

We leave these issues for future research.

- "Entrepreneurship, Frictions, and Wealth," Marco Cagetti (University of Virginia) and Mariacristina De Nardi (University of Minnesota and Federal Reserve Bank of Minneapolis), Federal Reserve Bank of Minneapolis, Research Department, Staff Report 322, September, 2003. http://minneapolisfed.org/research/sr/sr322.pdf