The Net Worth Trap: Investment and Output Dynamics in the Presence of Financing Constraints

Round 1

Reviewer 1 Report

 Attached I send my review

Comments for author File: Comments.pdf

Author Response

Please see attachment

Author Response File: Author Response.pdf

Reviewer 2 Report

I really tried to read all of this paper.  However, the grammatical constructions too often leave me in doubt as to the logic.

I therefore turned to the equations per se to understand the paper, but I cannot understand why the authors persist in using a linear model to explain events in non-normal and normal contexts?  They admit to the need for nonlinear modeling -- I think -- during such contexts, at least for certain circumstances?

For example, in the Abstract: "Decline of net worth reduces investment and, if firms can rent capital to unconstrained
outside investors, can create a ‘net worth trap’ with both investment and output falling below normal levels for long time periods."  Should the word 'they' be inserted before 'can create'; otherwise the concept of 'if ... then' is missing?

In Section 1, they explain the necessity for nonlinear models: "The resulting dynamics of corporate output and investment are highly non-linear, ..." but this is disregarded in their model as defined in Eqs. (1a) and (1b)?  Admittedly, boundary conditions often introduce nonlinear constructs, but this does not appear to explain any nonlinearities in this paper?

In the Conclusions Section 5, they invoke a ‘phase
change’, but does this arise from their linear(!) model or from boundary conditions.  In this Section they also admit "Our model does not capture potential further feedbacks. "  Note that "phase changes" arise from nonlinearities, else their use of this term is incorrect?

In Section 3, they also admit "In the rest of the paper we neglect discussion of idiosyncratic shocks and refer to
‘the firm’. [$sigma$] is thus the instantaneous standard error of remaining aggregate economic shocks whose
impact cannot be diversified away."  ([$sigma$] is my insert to capture their Greek letter.)

 What then is the point of this paper if they are not capturing important aspects of contexts they themselves cite: "In times of financial and economic stress, such as followed the great depression of the 1930s, global financial crisis of 2007-2008 and now re-emerging as a result of the Covid-19 pandemic, the
situation is quite different."  Why do they think their model addresses the rest of this paragraph: "Paying down debt or recapitalisation becomes difficult or impossible. As
our Figure 4 illustrates such an adverse change in the economic environment can lead to a ‘phase change’, with a shift to a regime where the net worth trap emerges."

Author Response

Please see the attachment

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Congratulations, it's a great paper

Author Response

We again thank the two reviewers.

This second round of reviews only asks for one further change, a clarification of the abstract to highlight that our contribution is not a model for empirical implementation, but rather developing intuitive insight.

In response we have amended the abstract slightly. It now reads as follows:

This paper investigates investment and output dynamics in a simple continuous time setting, showing that financing constraints substantially alter the relationship between net worth and the decisions of an optimizing firm. In the absence of financing constraints net worth is irrelevant (the 1958 Modigliani-Miller irrelevance proposition applies). Incorporating financing constraints, a decline in net worth leads to the firm reducing investment and also output (when this reduces risk exposure). This negative relationship between net worth and investment is already examined in the literature. The contribution here is providing new intuitive insight: (i) showing how large and long lasting the resulting non-linearity of firm behavior can be, even with linear production and preferences; and (ii) highlighting the economic mechanisms involved, the emergence of shadow prices creating both corporate prudential saving and induced risk aversion. The emergence of such pronounced non-linearity, even with linear production and preference functions, suggests that financing constraints can have a major impact on investment and output; and this should be allowed for in empirical modelling of economic and financial crises (for example the great depression of the 1930s, the global financial crisis of 2007-2008 and following the Covid-19 pandemic of 2020).

Reviewer 2 Report

The revised paper reads much better than the original, and adds clarity as to role of the boundary conditions even with their nonlinear model.

I still am uncertain as what can be learned in times of great stress on these systems, since as they admit the model being used is likely not appropriate.  I suggest that even in the abstract they add something like what they have said in their response to my review:

"The purpose of our modelling is not to develop a model for empirical implementation, but rather to develop intuitive insight ."

Author Response

We again thank the two reviewers.

This second round of reviews only asks for one further change, a clarification of the abstract to highlight that our contribution is not a model for empirical implementation, but rather developing intuitive insight.

In response we have amended the abstract slightly. It now reads as follows:

This paper investigates investment and output dynamics in a simple continuous time setting, showing that financing constraints substantially alter the relationship between net worth and the decisions of an optimising firm. In the absence of financing constraints net worth is irrelevant (the 1958 Modigliani-Miller irrelevance proposition applies). Incorporating financing constraints, a decline in net worth leads to the firm reducing investment and also output (when this reduces risk exposure). This negative relationship between net worth and investment is already examined in the literature. The contribution here is providing new intuitive insight: (i) showing how large and long lasting the resulting non-linearities of firm behaviour can be, even with linear production and preferences; and (ii) highlighting the economic mechanisms involved, the emergence of shadow prices creating both corporate prudential saving and induced risk aversion. The emergence of such pronounced non-linearity, even with linear production and preference functions, suggests that financing constraints can have a major impact on investment and output; and this should be allowed for in empirical modelling of economic and financial crises (for example the great depression of the 1930s, the global financial crisis of 2007-2008 and following the Covid-19 pandemic of 2020).