Abstract
This chapter evaluates the heterogeneity of capital stock and investment behavior by focusing on and contrasting between heterogeneity across capital goods categories and heterogeneity across acquisition modes. Four categories of capital goods (buildings and structures, machinery and equipment, vessels and vehicles, and land) and three modes of acquisition (new construction, second-hand acquisitions, and large-scale repairs) are mutually matched using microdata from the Cabinet Office and the Development Bank of Japan. Based on the investment rate data by resulting segment (capital good × acquisition mode), we conduct analyses using two approaches: an estimation using the Multiple q investment function that presupposes a convex adjustment cost function, as is assumed in Tobin’s q theory, and a factor analysis that allows for a non-convex adjustment cost function. The results of the factor analysis show that regardless of the type of capital good, the factor loadings are similar in segments with common acquisition modes. Furthermore, the parameter values for the investment adjustment costs are more affected by the acquisition mode than they are by the type of capital good. These results, along with those for the Multiple q investment function, reveal that the investment behavior around new construction can be explained (to some extent) by the convex adjustment cost function assumed by Tobin’s q theory. However, the results also suggest the existence of a non-convex adjustment cost function for second-hand acquisition and large-scale repair modes. In addition, the results suggest that new construction has the strongest relationship with the replacement investment ratio (or corporate growth).
This chapter is a shortened and reorganized version of Tonogi, Nakamura, and Asako (2017). The content of and opinions in this chapter are solely attributable to the authors and are unrelated to any organizations with which the authors are affiliated.
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Notes
- 1.
In Eq. (6.4), in theory, similarly to the investment rate, this parameter can take a value in the range \(a_{j}^{h} \le 1/(1 - \delta_{j} )\), inclusive of negative values.
- 2.
The transaction price of equipment is likely to be higher in the case of new construction than the second-hand acquisitions. However, note that this price difference only reflect a real factor, namely, the difference in remaining life. In other words, considering the relationship between the price of capital goods and the rental cost, we should use a capital goods price (price per unit of service) that is common to new construction and second-hand acquisitions in deflating the capital amount. By using the same capital goods price to compute the real amount of equipment for the case of new construction (with higher transaction prices) and second-hand acquisitions (with lower transaction prices), we find a smaller result for the second-hand case reflecting its shorter remaining life. For further details, see Appendix 1 of Tonogi et al. (2017).
- 3.
- 4.
In other words, communality and uniqueness correspond to the contribution rates to the non-standardized variances of common and individual factors, respectively.
- 5.
The survey set five tiers for random sampling based on capital: greater than 30 million yen and less than 50 million yen, greater than 50 million yen and less than 100 million yen, greater than 100 million yen and less than 1 billion yen, greater than 1 billion yen and less than 5 billion yen, and greater than 5 billion yen. However, all companies with capital over 1 billion yen are included as survey targets.
- 6.
- 7.
In Tonogi et al. (2014), vessels have a different factor loading than other capital goods but are aggregated with vehicles into one category owing to the very small number of observations with positive values for vessels.
- 8.
We calculate the composition ratio for each item with respect to the total value of the three items. However, because all land acquisitions relate to existing properties, there are only two survey items for land: second-hand acquisition costs and large-scale repairs (i.e., land conditioning and forming costs).
- 9.
The Book-Value and Proportional methods calculate investment amounts that take retirement and sales values (negative investments) into consideration. For this figure to be multiplied by the ratio of new construction, second-hand acquisitions, and large-scale repairs, in calculating invest amounts for each acquisition mode, we need to make a strong assumption that the residual value of the assets to be retired or sold have the same breakdown in terms of the acquisition mode as that of new acquisitions.
- 10.
According to this priority order, in all relevant tables in this chapter, the Zero method is referred to first, and the Book-Value and Proportional methods follow, if necessary.
- 11.
Tonogi, Nakamura, and Asako (2010) report that, since the late 1990s, cases of individual companies’ average q values exceeding 100 become more prominent, particularly among ICT-related industries, such as software and computer-related information services, with these values exceeding 1,000 in some cases. ICT-related businesses require few tangible fixed assets, and mostly their corporate values come from intangible assets, such as innovative business models and customer networks. In addition, the values of these intangible assets are often not recognized as assets in corporate accounting. Thus, for these companies, a large numerical value is obtained for the average q when it is calculated based on the conventional definition because the denominator is close to zero and the corporate value in the numerator is inflated by intangible assets. However, our analysis targets investment behaviors for tangible assets. Thus, we do not believe it is problematic to exclude companies with extremely high average q values from our analysis because their main sources of corporate value are derived from intangible assets. See also the discussion in Chap. 7.
- 12.
Meanwhile, the corresponding opposing inequality turns out to be: \(m \ge \{ 2n + 1 + \sqrt {8n + 1} \} /2\), which implies \(m \ge 16.2\) for \(n = 11\).
- 13.
The eigenvalue represents each factor’s level of dominance with respect to all items and signifies the number of dependent variables in the analysis that can be explained by the factor. In this study, we exclude factors with negative eigenvalues.
- 14.
The factor analysis results do not vary greatly even when excluding observations with 100% new construction in the investment/retirement survey.
- 15.
Here, the total capital depreciation rate refers to physical depreciation (not tax depreciation). It is calculated as the weighted average of the capital depreciation rates for each capital good, using the real capital stock values as weight. We refer to Hulten and Wykoff (1977, 1981) for the values of the capital depreciation rate for each capital good. The total investment rate used for comparison is calculated based on the total investment figure, including land.
- 16.
The capital spending survey aggregates data using the following steps:
(i) Each company returns a survey response of their composition ratios on investment motives.
(ii) The investment amount by investment motive is calculated by multiplying the composition ratios of the investment motives by the total investment amounts (including land) for each company.
(iii) The overall ratios for investment motives are calculated by dividing the investment amount totaled for each investment motive by the total investment amount (including land).
That is, the value is congruent to the weighted average of each company’s response on the component ratios of investment motives calculated over the total investment amount (including land).
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Asako, K., Nakamura, Ji., Tonogi, K. (2020). Extensions of the Multiple q Model: (II) Heterogeneity by Mode of Acquisition. In: Multiple q and Investment in Japan. Springer, Singapore. https://doi.org/10.1007/978-981-15-2981-8_6
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