A Dynamic Model of the Firm: Structural Explanations of Key Empirical Findings

• Date: 01 August 2015
• Published date: 01 August 2015
• DOI: http://doi.org/10.1111/fire.12070

The Financial Review 50 (2015) 341–361

A Dynamic Model of the Firm: Structural

Explanations of Key Empirical Findings

Natalia Lazzati∗

University of Michigan

Amilcar A. Menichini

Naval PostgraduateSchool

Abstract

We derive a dynamic model of the firm in the spirit of the trade-off theory of capital

structure that explains firm behavior in terms of firm characteristics. We show our model

is consistent with many important findings about the cross-section of firms, including the

negative relations between profitability and leverage, and between dividends and investment-

cash flow sensitivities. The model also explains the existence of zero-debt firms and their

observed characteristics. These results have been used to challenge the trade-off theory and

the assumption of perfect capital markets. We revisit these critiques and provide structural

explanations for the regularities we replicate.

Keywords: dynamic model of the firm, trade-off theory, zero-debt firms, investment-cash

flow sensitivity, dynamic programming

JEL Classifications: G31, G32

∗Corresponding author: Department of Economics, University of Michigan, 611 Tappan Street, Ann

Arbor, MI 48109-1220; Phone: (734) 764-2355; Fax: (734) 764-2769; E-mail: nlazzati@umich.edu.

We thank Steve Hansen, Chris House, Zafer Yuksel, the journal editor, and two anonymous referees for

helpful comments.

C2015 The Eastern Finance Association 341

342 N. Lazzati and A. A. Menichini/The Financial Review 50 (2015) 341–361

1. Introduction

During the last decades, the empirical literature in corporate finance has re-

ported a few regularities regarding leverage, dividends, and investment decisions

across firms. Some of these findings have been used to challenge the validity of cen-

tral economic theories. For instance, the negative relation between profitability and

leverage, which has been confirmed by numerous studies, has been used to cast doubt

on the trade-off theory of capital structure, and to support alternative, competing

theories, such as the pecking order model of financing decisions.1Another contro-

versial result is the robust evidence of a negative association between dividends and

investment-cash flow sensitivities, often used to question the validity of the perfect

capital markets assumption.2We construct a simple dynamic model of the firm in

the spirit of the trade-off theory that can replicate these, as well as other, important

empirical findings, in a unified way. We explain how firm behavior depends on firm

characteristics and how heterogeneity across firms can easily generate the empiri-

cal regularities we replicate. In doing so, we revisit some of the doubts cast on the

trade-off theory as well as the functioning of capital markets.

In our dynamic model, investment and leverage are the choice variables of the

firm.3In each period, the firm receives a (mean-reverting) shock to profits and, to

maximize share price, it decides how much to investfor the next period, as well as how

to finance that investment (i.e., with debt and/or equity). We initially assume the firm

chooses the optimal level of debt within the range of values in which it can be repaid

in full with certainty. This condition aims to capture the phenomenon of debt con-

servatism shown by Graham (2000) and allows us to solve the model in closed-form.

(We show in Section 4 that our results remain valid even if we allow for risky debt.)

We use Compustat data to calibrate the model parameters (e.g., volatility of profits,

capital depreciation rate, etc.) for different Standard Industrial Classification (SIC)

industries. We then use the analytic model equations to simulate the evolution over

time of the endogenous variables of interest (e.g., leverage, dividends, profitability,

etc.) for representative firms in each of those SIC industries. Finally, with the panel

of firms’ choices constructed from these simulations, we run the regressions typically

used in the empirical literature in corporate finance (e.g., pooled ordinary least squares

[OLS]). Weshow that our model can replicate many regularities reported by that litera-

ture and provide structural explanations for each of them.4Weexplain why we believe

those findings do not provide direct evidence against either the trade-off theory or

1See for example, Fama and French (2002) for a discussion on this and other related issues.

2See for example, Fazzari, Hubbard and Petersen (1988) for a detailed description of this result.

3The simple model we use in this article is sufficientto reproduce several empirical results. For this reason,

we do not add cash holdings or firm exit.

4Furthermore, Lazzati and Menichini (2014b) use this model successfully for firm valuation.For instance,

it prices firms consistently and explains more than 70% of the cross-sectional variation in stock prices.