Optimal Subsidization of Business Start‐Ups

• Author: HAKKI YAZICI
• Published date: 01 August 2016
• DOI: http://doi.org/10.1111/jpet.12194
• Date: 01 August 2016

OPTIMAL SUBSIDIZATION OF BUSINESS START-UPS

HAKKI YAZICI

Sabanci University

Abstract

This paper studies efficient allocation of resources in an economy in

which agents are initially heterogeneous with regard to their wealth

levels and whether they have productive ideas or not. An agent with an

idea can start a business that generates random returns. Agents have

private information about (1) their initial types, (2) how they allocate

their resources between consumption and investment, and (3) the re-

alized returns. I show that, under informational frictions, a society that

targets productive efficiency should subsidize poor agents with ideas,

and choose the amount and timing of subsidies carefully in order to

ensure that other agents do not mimic poor agents with ideas and re-

ceive subsidies. Then, I provide an implementation of the start-up sub-

sidies in a market framework that resembles the U.S. Small Business

Administration’s Business Loan Program.

1. Introduction

Starting a business requires two main ingredients: a productive idea and resources to

invest in that idea. Unfortunately, it is not necessarily the case that whoever has one of

these ingredients also has the other one. Consequently, there is a potential mismatch

among individuals in a society in terms of who holds productive resources and who can

use them most efficiently. In a frictionless world, a solution to this mismatch is provided

by private markets: those with ideas (potential start-ups) can borrow from those with re-

sources, invest, and then pay back. This paper explores how a society should cope with

this mismatch in an environment in which informational frictions limit the market’s

ability to finance investment in productive ideas. I show that, under informational fric-

tions, a society that targets productive efficiency has to (1) subsidize agents with ideas,

Hakki Yazici, Sabanci University, FASS, Orhanli, Tuzla 34956, Istanbul, Turkey (hakkiyazici@

sabanciuniv.edu).

An earlier version of this paper was previously circulated as Minneapolis Fed working paper no. 665,

under the title “Business Start-Ups and Productive Efficiency.” I am grateful to Narayana Kocherlakota

and Chris Phelan for their valuable advice and encouragement throughout the project. I also want to

thank Cristina Arellano, V. V. Chari, John T.Dalton, Seda Ertac, Kenichi Fukushima, Turkmen Goksel,

Larry E. Jones, Patrick Kehoe, Tommy Leung, Fabrizio Perri, Facundo Piguillem, Paul Povel, Anderson

Schneider, Ctirad Slavik, Adam Slawski, Richard Todd, Cengiz Yazici, Kuzey Yilmaz, the members of

the Public Economics workshop at the University of Minnesota, and seminar participants at the Federal

Reserve Bank of Minneapolis and the SED meetings in Cambridge for their comments and suggestions.

Special thanks to Tommy Leung and Kevin Wiseman for helpful discussions and detailed comments.

Received November 26, 2013; Accepted December 16, 2014.

C2016 Wiley Periodicals, Inc.

Journal of Public Economic Theory, 18 (4), 2016, pp. 589–609.

589

590 Journal of Public Economic Theory

and (2) choose the amount and timing of transfers carefully in order to ensure that

agents without ideas do not mimic those with ideas and receive subsidies. Then, I pro-

vide an implementation of the start-up subsidies in a market framework that resembles

the U.S. Small Business Administration (SBA)’s Business Loan Program.

Individuals in the model economy live for two periods and are risk-neutral. In pe-

riod one, agents are heterogeneous with respect to wealth levels and whether they have

ideas or not. Agents with ideas can create businesses that generate risky returns in pe-

riod two. The returns depend on the amount of capital invested and there is diminishing

marginal returns to capital. In the absence of informational frictions, efficient resource

allocation involves two separate steps: (1) productive efficiency requires transferring re-

sources to poor and productive agents in period one to ensure that they all can invest

at the socially efficient level; (2) distributive efficiency then requires making transfers

between agents so as to achieve the desired consumption distribution, which depends

on the welfare criterion of the society.

Unfortunately, it is hardly the case that all relevant information about business start-

ups are known publicly.1The paper assumes that agents’ ex ante types (wealth-idea),

how they allocate their resources, and ex post returns to business start-ups are private

information. Under the unobservability of the returns, productive efficiency implies

poor agents with ideas should be subsidized so as to get them operate their businesses at

the efficient scale. The assumption that agents’ wealth-idea types are private information

implies that the government might be limited in the amount of subsidies it can transfer

to agents with ideas: large transfers might induce people without ideas to mimic agents

with ideas and receive transfers. The constrained efficient level of start-up subsidies arise

from this productive efficiency versus incentives trade-off.

In order to understand the intuition for the subsidy result, one first needs to know

what society cares about in this economy. I assume the social welfare function to be util-

itarian with equal weights on every agent. This assumption, together with risk neutrality

of agents, implies that society has a preference only for the amount of total consump-

tion, not for how it is distributed across agents. The society is only concerned about

agents making right amounts of investment. Therefore, the problem that the society is

facing is maximizing production subject to incentive compatibility and feasibility.

The intuition for the subsidy result is simple. Since there are diminishing marginal

returns to investment in start-ups, there is a socially efficient level of investment in each

start-up. However, since returns to start-ups are unobservable, agents cannot write con-

tracts with state-contingent repayment schedules. This market incompleteness then im-

plies that agents can, at most, borrow an amount that they can pay back the next period

in the lowest return state.2This borrowing constraint binds for poor agents with ideas

1See Hubbard (1998) for a survey of the literature on informational problems in capital markets.

2Observe that I do not allow for default in the model. Following Diamond (1984), one can add default

to this model by assuming that if a start-up continues to operate after period two, this brings a continu-

ation value to the owner; if not, then at least some strictly positive fraction of this value gets destroyed.

Then, agents can write state-contingent contracts by conditioning the continuation of a start-up busi-

ness on the level of repayment. The fear of losing a fraction of the continuation value can make the

agent make the payment associated with her true return level. In such a world, θlstate can be inter-

preted as a default state. Even though in such a model poor agents with ideas would be able to borrow

more than they can in the original model, one can show that this level would still be strictly less than

the amount they need to finance socially efficient investment level. Therefore, the subsidy result would

still be true under this alternative model. The reason why such an extension can be interesting is be-

cause it can make the details of the efficient social contract more realistic, giving rise to a more realistic

implementation. A paper along these lines is currently work in progress.