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We investigate the implications of time inconsistent preferences on the entrepreneurial decision making. We use a time varying preference model to capture the optimal liquidation choice and investment allocation for the averse risk agent in the incomplete market. Compared to standard entrepreneurial dynamic framework, our model shows that inconsistent preferences may lead to under investment when the entrepreneur faces liquidity constraint and over investment when his liquid wealth is far away from the liquidation boundary. Moreover, the possibility of changing to the future stage has ambiguous influences on the exit decision and optimal investment.

Entrepreneurs face high uncertainty and liquidity constraints, both of which have significant influences on the business decision making process. These uncertainty and constraints are important determinants for capital ac- cumulation, exit decision and asset allocation. Since [

In the standard optimization model framework, it is assumed that agents have a constant rate of time pre- ference. However, virtually every experimental research on time preference indicates that this assumption is unrealistic. The most relevant effect of time inconsistent is the preference change with time. Usually, an agent has different preferences at different stages. In this article, we focus on the entrepreneurs’ decision making under non-constant preference.

In our paper, we try to focus on the following interesting questions: What is the impact of time inconsistent preference on the entrepreneurial valuation? How could the time varying discount rate affects the liquidation choices? How would the entrepreneur allocate the wealth between investment, consumption and public equity? We extend the entrepreneurial optimization model in [

Our model gives three main contributions. First, the time inconsistent agent will under invest when his liquid wealth is close to liquidation boundary and over invest when the agent is far away from the exit threshold. Second, time inconsistent preferences weaken the effects of risk aversion on the liquidation decisions. Third, increasing the possibility of the birth of the future stage with utility discount has ambiguous influences on the exit decision and investment strategy and finally the decisions approach the steady result in the future stage.

Our research relates to the literature about time inconsistency model and its application. [

The remainder of the paper proceeds as follows: Section 2 presents the model; Section 3 derives the solutions; Section 4 provides the quantitative results and Section 5 concludes.

In this section, we set out the framework for the basic model of entrepreneurial optimization problem. The liqui- dation option is described and followed by a discussion of the nature of time inconsistent preferences.

Time is continuous and horizon is infinite. There is a single perishable consumption good. The agent derives utility from a consumption process

where

of relative risk aversion.

for

Consider the setting for a standard entrepreneurial problem as in [

where

measures the degree of the adjustment cost.

The entrepreneur has an option to liquidate capital at any moment. Liquidation is irreversible and gives a terminal value

The agent can invest in risk free asset and public equity. These two financial asset represent the standard investment opportunities in the classical [

ratio for the public equity is:

and the entrepreneurial business. The non diversifiable risks

Let

After exiting from the business, the agent retires and

The agent is allowed to borrow against capital at all times in our model. To make sure the debt is risk free, we set the liquidation value of the capital

The optimization problem of the agent involves the maximization of the utility defined as (3). First, before liquidation

As a benchmark, we consider the case in which the entrepreneurial preference is time consistent. The constant preference case reduces to [

Proposition 1. The entrepreneur operates the business if and only if

the following ordinary differential equation (ODE):

where

approaches the complete-markets solution given by

The ODE (8) satisfies the following boundary conditions at endogenous liquidation choice

capital ratio

Consider the case of an entrepreneur who makes decisions under the belief that future selves act in the interest of the current self. This assumption has been analyzed in [

Assume the entrepreneur is in the present stage where the value function takes the form as (3). The standard dynamic programming argument implies that the agent’s optimal consumption, investment and public equity allocation solve the following Hamilton-Jaobi-Bellman (HJB) equation of value function

where

Let

Proposition 2. The scaled CE wealth

When

the valuation in complete-market.

optimal liquidation choice

The consumption, investment and public equity allocation are given by

Parameter choices. Where possible, we borrow the parameters from [

significant in time inconsistent case. Therefore,

The magnitude of utility discounting parameter

The time inconsistency affects not only the liquidation choice but also the wealth and operation strategies.

time inconsistent case. Panel C plots the investment decision and indicates that there exist both over- and under- investment in time inconsistent case compared to the constant preference. The entrepreneur will invest less when his liquid wealth approaches the liquidation threshold. In a higher level of liquid wealth, on the other hand, the inconsistent preference agent will invest more than standard model. Panel D presents the consumption in two preference settings. The inconsistent agent will consume less and this reflects their precautionary saving con- sidering the utility discount in the future stage.

agent’s liquid wealth equals the capital

This paper extends the entrepreneurial dynamics model to account for time inconsistent preferences. Entrepreneurs need to formulate the investment decisions taking into account the possibility of future stage with utility discount. This sets up a conflict between two opposing forces. First, the agent desires to take advantage of the option to exit, and also has an incentive to invest more and longer to offset the utility discount in future stage. Second, the time inconsistent preference lead to motivation of precautionary saving and thus reducing the investment. We extend the model of [

We find that time inconsistency leads to under investment when the entrepreneurial liquid wealth is close to the liquidation boundary and over investment when the liquid wealth is far away from the exit threshold. For further analysis, we study the effects of some key factors in our model. Inconsistency weakens the effects of risk aversion which accelerates the liquidation. The effects of the correlation between the firm and the public equity are ambiguous and non monotonic in both cases, but the inconsistent setting delays the exit decision compared to consistent model. The magnitude of Poisson process intensity

Jinqiang Yang acknowledges support by Natural Science Foundation of China (#71202007 #71472117), New Century Excellent Talents in University (#NCET-13-0895) and Chen Guang Project of Shanghai Municipal Education Commission and Shanghai Education Development Foundation (#12CG44).