# Impact of working capital constraints onto output

I'm looking for empirical evidence (optimally from natural experiments, as described below) of the impact of working capital constraints onto firm output, and the differentials of firm size.

I suppose that generally, stricter working capital constraints are bad for output, and typically these constraints are stronger for smaller firms (measured in output) and younger firms. However, I couldn't manage to find (a) paper(s) to establish that fact yet.

Where by working capital constraint I mean something along the lines of Kiyotaki&Moore (1997)

$$L, K: f(wL, rK) \leq \psi(F(K,L))$$

, for example, for some constant $\psi_0$,

$$wL + rK \leq \psi_0 \cdot F(K,L)$$

where $F(\cdot)$ is the production function, and $f$ and $\psi$ can be whatever.

I have, in other environments, seen that some people take bank liquidity to approximate $\psi$ and argue that for example the last recession was a natural experiment on a change of $\psi$.

So, one type of useful regression table would be (on the firm level)

• dependent variable: output
• independent variables:
• Increase of financial constraint (here, decrease of $\psi_0$)
• Dummy for firm size (or different size bins)
• And/Or: Dummy for firm age (or different age bins)

One example would be Chodorow-Reich (2014, QJE). The two downsides with that paper are that

• He uses employment, not output as dependent variable (but that's tolerable)
• He does not actually list the coefficients on the dummies for size. He just includes them as controls.
• I'm having a hard time understanding what you mean by "working capital constraints." The constraint written seems really general and so I'm having a hard time imagining an example of what you might mean. Could you maybe give a more explicit example? – jmbejara Jan 24 '15 at 5:34
• @jmbejara : I hope my update helped clearing it up – FooBar Jan 25 '15 at 18:21
• With your equation $$wL + rK \leq \psi_0 \cdot F(K,L)$$, do you have in mind a setting where a firm would like to spend more on inputs to production but is constrained? Because that situation sounds a lot like "time to build" models of productive capacity. – BKay Jan 26 '15 at 19:16
• @BKay Yes, they're constraint, but not due to technology, but rather a liquidity shock, if you will. Cash-in-Advance, with insufficient cash at hands. – FooBar Jan 26 '15 at 19:29
• So, I understand that you're looking for empirical evidence for this kind of thing. Do you have any theory papers that describe in more detail the mechanism that might cause the drop in production? – jmbejara Jan 30 '15 at 4:44