Tobin’s q Is Not a Comparability Filter

EdgarStat excludes zombie firms from the comparables used to benchmark a tested party’s operating margin. A zombie is a mature firm whose operating profits fail to cover its interest expense for consecutive years; it survives on creditor forbearance, not on its own earning capacity.

Two definitions of interest coverage circulate. The OECD definition of McGowan, Andrews and Millot (2018) rests on interest coverage and age. The BIS definition of Banerjee and Hofmann (2018, 2022) adds a market criterion: Tobin’s q below the median of the firm’s sector. We adopt a modified version of the first (we use EBITDA instead of EBIT) and reject the second. A reference is not an authority to be obeyed; it is a set of claims to be examined, and we examined them.

1. The Definitions Side by Side

The 2018 BIS paper takes the OECD test as its broad definition. The equity shares market criterion is the only point of difference, and the 2022 paper uses it in place of the age condition.

2. Why the Filter Was Introduced

The BIS authors state the motive. Under the broad definition, the median Tobin’s q of zombie firms exceeds that of non-zombie firms. They call this an “anomaly” and write that the narrow measure is “designed to purge” it (Banerjee and Hofmann 2018, p. 70).

Their footnote 4 on the same page supplies the explanation: equity can be viewed as a call option on the value of the firm, so if zombies are riskier, their q can be higher. On that reasoning, a high q among highly indebted, low-coverage firms is the expected result, not an anomaly. The shareholders of such a firm hold the upside while creditors bear the downside.

An observation that contradicts the expected pattern was removed by adding a condition, and the condition was not subjected to an independent test. In the vocabulary of Lakatos (1970), this is an ad hoc or auxiliary hypothesis: it protects the expected pattern and predicts no new fact. The filter excludes from the zombie class the firms whose equity the market prices as an option on recovery, which are the firms most dependent on the forbearance that defines a zombie.

3. What Is Measured as q

Tobin (1969) defines q as the market value of capital over its replacement cost (as a practical matter, over its book equity value). The BIS papers describe the variable in three ways:

Replacement cost is named but not measured. The computed variable is a market-to-book ratio whose numerator adds a market price of equity to a book value of liabilities. It combines two valuation bases in one aggregate, and the denominator is historical cost. A comparability criterion should state what it measures and measure what it states.

4. Who Cannot Be Classified

The q criterion requires a traded price of equity. The BIS authors acknowledge the restriction. The 2018 paper covers “only listed companies for which we can observe stock market valuations” (p. 69). The 2022 working paper states that its analysis “does not cover unlisted small and medium-sized enterprises” and that zombie shares may be understated as a result (pp. 5, 8).

For a macroeconomic study of listed firms, that restriction is a disclosed limitation. For a transfer pricing analysis it is disqualifying. The criterion cannot be computed for private companies, for subsidiaries of groups, for SEC registrants with public debt and private equity, or for most foreign comparables. In most cases the tested party is itself a private subsidiary. Applied to a comparable set, the filter converts listing status into a comparability factor. Treas. Reg. 1.482-1(d)(1) enumerates functions, contractual terms, risks, economic conditions, and property or services. Listing status is not among them. As an aside, establishing the entities’ uncontrolled status or independence, that the accounts are audited and free of intercompany eliminations, and that accounting footnotes and textual management disclosures are also decisive.

5. What the Filter Adds to the BIS Results

Under the broad definition, the BIS estimate of the zombie share in 14 advanced economies rose from about 2 percent in the late 1980s to about 12 percent in 2016; under the narrow definition, from 1 percent to about 6 percent (Banerjee and Hofmann 2018, p. 70). The q condition halves the count; it does not alter the trend.

The 2022 working paper reports the same result. With the OECD definition in place of its own, the authors “obtain an upward ratcheting pattern of the zombie share over time” similar to their baseline (p. 11). Their principal finding does not depend on q.

The sector median is a rank, not a threshold. In each sector and year, half of all firms lie below it by construction, whatever their solvency. A criterion that classifies by rank cannot certify non-viability; it can only sort the data.

6. The Question a Comparability Analysis Asks

The BIS paper states that the q criterion captures expected future profitability, and that its purpose is to avoid classifying as zombies firms that make losses today but may earn profits later, such as start-ups (Banerjee and Hofmann 2022, pp. 8–9). The OECD age condition serves that purpose without a market price: a firm of 10 or more years is not a start-up.

A comparability analysis asks a narrower question: could the uncontrolled firm meet its interest expense obligations as an operating entity during the tested years? The answer comes from the income statement and the audit report. The expectations of equity investors, inferred from share prices, belong to a different inquiry and carry no information about the arm’s length price or profit of the tested party’s transactions.

7. The EdgarStat Protocol

We measure coverage with operating income before depreciation and amortization F=\mathrm{OIBDP} in Compustat, against interest expense R=\mathrm{XINT}, since the test asks whether operations generate the funds to pay interest as it falls due:

\quad
(1)\qquad
\mathrm{ICR}(i,t)=\frac{F(i,t)}{R(i,t)},
\qquad
R(i,t)>0

\quad
(2)\qquad
D(i)=\begin{cases}
1 & \text{if }\ \mathrm{ICR}(i,t)<1\ \text{ for }\ t=T-2,\,T-1,\,T
\\[2pt]
& \text{and }\ G(i)\geq 10
\\[2pt]
0 & \text{otherwise}
\end{cases}

Since \mathrm{OIBDP}=\mathrm{OIADP}+\mathrm{DP} and \mathrm{DP}\geq 0, a firm with \mathrm{OIBDP}/\mathrm{XINT}<1 also has \mathrm{OIADP}/\mathrm{XINT}<1. Every firm our test classifies as a zombie is a zombie under the published EBIT definition. The second test is the going-concern opinion: an auditor’s explanatory paragraph under PCAOB AS 2415, or an ASC 205-40 disclosure of substantial doubt that management’s plans do not alleviate, in the Form 10-K for any year of the window. A firm that fails either test is excluded. Both tests apply to every comparable that files financial statements, listed or not.

8. Conclusion

The BIS market criterion was introduced to remove an observation its authors’ own footnote explains. It measures an equity shares market-to-book ratio under the name of replacement cost (really equity book account), it cannot classify unlisted firms, and it does not change the BIS findings. Our disagreement is with its use as a comparability filter, not with the BIS research program. The coverage-and-age definition, joined to the going-concern opinion, is observable, verifiable from EDGAR, and neutral as to listing status. We cite the literature after reading it, and we adopt from it what survives examination.

References

Banerjee, R. and B. Hofmann (2018). “The Rise of Zombie Firms: Causes and Consequences.” BIS Quarterly Review, September, 67–78. Broad and narrow definitions (p. 69); the q “anomaly” and footnote 4 (p. 70).

Banerjee, R. and B. Hofmann (2022). “Corporate Zombies: Anatomy and Life Cycle.” Economic Policy 37(112), 757–803. Working paper version: BIS Working Papers No. 882 (2020, revised 2022), cited for page references.

FASB (2014). Accounting Standards Update No. 2014-15, Presentation of Financial Statements, Going Concern (Subtopic 205-40). Norwalk, CT: Financial Accounting Standards Board.

Lakatos, I. (1970). “Falsification and the Methodology of Scientific Research Programmes.” In I. Lakatos and A. Musgrave (eds.), Criticism and the Growth of Knowledge, 91–196. Cambridge: Cambridge University Press. Ad hoc auxiliary hypotheses.

McGowan, M. A., D. Andrews and V. Millot (2018). “The Walking Dead? Zombie Firms and Productivity Performance in OECD Countries.” Economic Policy 33(96), 685–736. Coverage-and-age definition on Orbis data, including unlisted firms.

PCAOB. AS 2415, Consideration of an Entity’s Ability to Continue as a Going Concern. Washington, DC: Public Company Accounting Oversight Board.

Tobin, J. (1969). “A General Equilibrium Approach to Monetary Theory.” Journal of Money, Credit and Banking 1(1), 15–29. Definition of q as market value over replacement cost.

U.S. Treasury. Treas. Reg. 1.482-1(d)(1), Comparability. Code of Federal Regulations, Title 26.