Intangible Capital and the Investment-q relation, Peters and Taylor 2016

Intro: The neoclassical theory of investment was developed when firms mainly owned physical assets, hence empirical tests of the theory have focused on physical capital. Since then the US economy has shifted toward service and technology based industries in which intangible assets are important.

The question: is the theory still relevant in an economy increasingly dominated by intangible capital? How well does Q work?

The authors find that the classic q, despite being designed to explain physical investment, also helps explain intangible investment. One contribution this paper makes is that they provides a new Q proxy that accounts for intangible capital. The new proxy captures firms’ investment opportunities better than other popular proxies.

Main findings: Even though the classical q works at least as well for intangible capital as for physical capital, when intangible capital is excluded, it typically delivers lower R-square values. The within-firm correlation between physical and intangible investment is 31% but drops to 17% after controlling for total q. Regardless of how we measure investment, total q is better at explaining physical, intangible, and total investment as well as R&D investment, and CAPX.

Since the OLS gives biased estimates, the authors try the cumulant estimator, which produces unbiased slopes and measure how close the q proxy is to the true unobservable q. They find when they include intangible capital in the investment-q regression, Tau-square is much higher implying their new q is closer to the true q.

Slope coefficients of investment on total q help measure capital adjustment costs. The inverse q-slope for physical (intangible) investment measures the convex component of physical (intangible) capital’s adjustment costs. They find intangible capital’s convex adjustment costs are twice as large as those for physical capital.

They find the classic q theory fits data better in firms and years with more intangible capital. However, it is unclear why this is happening. There is no evidence that high-intangible firms are closer to the perfect competition and constant returns to scale. And, their main results are even stronger in the aggregate time-series setting (much higher R-squared values)

Intangible Capital and the Neoclassical Theory of Investment:

Prediction 1: Physical and intangible capital share the same marginal q. Marginal q equals average q.

Prediction 2: The physical and intangible investment rates, both scaled by total capital, vary with total q.

Prediction 3: Total q helps explain all three investment measures, and it shows that the OLS slops identify the adjustment cost parameters. The firm and year fixed effects are needed.

Prediction 4: When intangible capital is excluded in q, it generated downward bias, meaning it produces upward-biased estimates of adjustment-cost parameter.

Prediction 5: Assuming the physical and intangible capital have the same linear adjustment-cost parameters and purchase prices, then a firm holds relatively less intangible capital if intangible capital is costlier to adjust.

Data & Measure

Firm’s market value V= MVE of outstanding equity + BV of debt – Current assets

Replacement cost of intangible capital is sum the firms’ externally purchased and internally created intangible capital. The external one is easy to find in the balance sheet, but the internal one is hard to define. The authors accumulate past intangible investment, as reported on firms’ income statements. They define the stock of internal intangible capital as the sum of knowledge capital and organization capital.

They talk about the variables in detail. Accounting knowledge is kind of required slightly. When hit some topic like this, definitely come back to the paper.

Researchers often discard observations with q > 10 since it is unrealistically large. The total q here is a more relatable measure in that only 1% of the observations exceeds 10.

Full-sample results

In OLS with fixed effects, the authors focus on R-square since coefficients are likely to be biased due to the measurement error. Generally, the total q generates much higher R-square than the standard q does, and the differences are statistically significant. One implication of their theory is that physical and intangible investment should co-move strongly within firms, since the two capitals have the same marginal productivity, and hence, the same marginal q. This co-movement must decrease if we remove the effects of total q. They find the correlation between these two regressions’ residuals is lower after controlling for the total q. In sum, total q explains intangible investment slightly better than physical investment, and it explains total investment even better.

Bias-corrected results: The reason we need total q when we can correct biases using the cumulant estimator. By ignoring intangibles, the measurement error is multiplicative, not additive. And the measurement errors (from q and inv) are correlated with each other, violating the cumulant estimators’ assumption. And they show using the cumulant estimator for q and total q provides different results.

SG&A rather than R&D is highly sensitive to cash flow, so the bias-corrected results even speaks investment is sensitive to cash flow while their theory doesn’t say it. One possible explanation is that the SG&A is measured with errors biasing the cash flow coefficient upward.

Comparing Subsamples

To see the relation between the total q and investment in different time and industries, they have subsample tests. Digging deep into the theory, they find violating the assumption about quadratic adjustment costs is unlikely to generate the empirical patterns in Table 4(subsampled by intangible capital). Differences in economies of scale, or competition could theoretically explain some of the patterns in the table. But empirically they fail to find the supporting evidence. A summary of findings here: as firms hold more intangible capital, the explanatory power of total q increases. And interestingly, the standard q is able to explain investment in physical as well as intangible, though the power is smaller than the total q’s. Next, high tech industries fit their theory of total q well. Lastly, in late years, the q seems to explain the investment opportunities well than early days.

Firms using more intangibles have physical capital that exhibits larger convex adjustment costs, vice and versa. Alternatives to the different adjustment costs: Differences in purchase prices can explain why some firms use more intangible capital, but they don’t explain why firms have different slopes. Differences between the two capital types’ economies of scale do not necessarily drive them to use more of one capital type and do not make their q-slopes different. Candidates: difference in depreciation rates, and adjustment-cost convexities between the two capitals types may make sense, but hard to show empirically.

Macro results

One advantage of the macro data: it does not rely on an assumption about the fraction of SG&A representing an investment. Except in a few subperiods, q explains investment relatively poorly. Relation between total q and physical investment is still week. Total q and intangible investment is strongly related. Total investment and total q also strongly related.

Growth options affect stocks more than bonds, and growth options affect intangible investment more than physical investment. Thus, bond q could be a better proxy for physical capital’s marginal q, while the traditional q measures intangible capital’s marginal q. Another explanation is firms with more intangible investment hold less debt.

In sum, at the macro level, including intangibles makes q explain the investment much better. Bond q is still better at explaining physical investment.


Total q explains physical and intangible investment roughly equally well in different sample periods, different industries, and different holding of intangible capital. The total q is a better proxy for true q, especially in firms with the most intangible capital, and it holds across industry and year subsamples.

Change in lambda value (% of representation of intangible investment) does not change the results. 30% lambda seems proper. Variations of definition of intangible capital also do not change the results.

Takeaway: Traditional measure of q is seriously biased in that it does not account for intangible capital even though US economy has shifted toward more intangible investment economy. Including the intangible capital into q can mitigate the measurement error, so we need to use the total q from now.