RDP 2005-12: Financial Constraints, the User Cost of Capital and Corporate Investment in Australia 3. Data
December 2005
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3.1 Sample Selection
The data are from the financial accounts of Australian companies available on the Bloomberg database. The sample covers companies publicly listed on the Australian Stock Exchange and includes some firms that have been delisted in the past five years. The sample period covers the financial years from 1990 to 2004. Before estimation, the sample was cleaned as follows:
- banks, financial services, insurance and property trusts were removed (as the monetary policy transmission mechanism is likely to operate in a different manner for firms in the financial sector);
- firms with at least three consecutive years of financial accounts data within the sample period were retained; and
- for each variable in the model, the top and bottom 2 per cent of the distribution were trimmed to minimise the impact of outliers. However, for two variables, the investment rate and cash flow (as a share of capital), both the top and bottom 3 per cent of the distribution were trimmed.^{[10]}
As will be seen, the estimation method also requires differencing the data, so that the first year of observations are lost. Controlling for possible endogeneity by using variables lagged over two years as instruments results in a final (unbalanced) panel of around 300 firms and 1,700 firm-year observations.
The non-random selection of the sample is likely to introduce several problems. For instance, the use of mainly listed companies means that the sample will be skewed towards larger firms. Assuming that larger firms are less likely to be constrained on average, this is likely to lower the estimated sensitivity of investment to cash flow. However, as will be seen in Section 4, it is not clear that this is necessarily the case.^{[11]}
Sources of company accounts data are also often subject to ‘survivor bias’. This occurs when delisted firms are removed from the sample, potentially giving a misleading picture of the corporate sector. However, this paper has the advantage over earlier Australian studies in that it includes some delisted companies. This minimises survivor bias and may better capture the effects of cash flow on firms that are probably financially distressed.^{[12]}
Another potential problem in measuring investment with company accounts data is that firms that enter the sample satisfy certain selection criteria that may depend on unobservable factors that are likely to be correlated with investment and the business cycle. However, as will be discussed in Section 4, the econometric approach adopted should be able to control for these effects.
3.2 Variables in the Model
Appendix A summarises the construction of most of the variables used in the model. However, some variables are worth highlighting given their relative importance. The dependent variable is the investment rate, measured as the percentage change in the capital stock (after adding back depreciation). The explanatory variables include real sales (measured as firm-level sales revenue divided by the aggregate GDP deflator), cash flow and the real user cost of capital.
The calculation of the user cost of capital variable is relatively complex and is adapted from the measure constructed by Hall and Jorgenson (1967). The formula can be derived from neoclassical investment theory – a profit-maximising firm will accumulate capital up to the point where the marginal revenue from an extra unit of capital is just equal to the cost of employing that unit for the user. The user cost of capital incorporates not only the firm-specific cost of financing the purchase of capital (for example, through borrowing or new equity issues) but also sector-specific running costs (for example, depreciation rates) and other economy-wide variables (for example, corporate tax rates).
It is helpful to build the user cost of capital in a number of steps. First, assume that a representative firm finances the purchase or hire of capital through external funding, whether it be debt or equity. The (nominal) cost of debt (r^{D}_{i,t}), including any credit risk premium, is simply:
where τ_{t} is the average corporate tax rate at time t and i^{D}_{i,t} is the nominal interest rate for firm i at time t. When the average tax rate is zero, the cost of debt corresponds to the conventionally defined nominal interest rate. However, the nominal interest rate is multiplied by (1−τ_{t}) because interest payments are deductible from taxable income.^{[13]} The cost of debt is relatively easy to estimate with the nominal interest rate being directly observable as the average rate of interest on the firm's stock of net debt.^{[14]}
The cost of equity (r^{E}_{i,t}) is:
where EY_{s,t} is the earnings yield (total earnings before interest and tax divided by market capitalisation) for industry s at time t. The cost of equity is measured as an ex post rate of return because the shareholder's expected ex ante rate of return on equity investment is generally not observable. I do not measure the earnings yield on a firm-level basis because a significant number of firms report negative gross earnings which results in an earnings yield below zero for these firms. In the model this would imply a very low cost of capital which seems counterintuitive. Instead, the earnings yield is measured on an industry-level basis, which can be thought of as a ‘hurdle rate of return’ that firms within a given industry must achieve in order to satisfy investors. By recognising the inherent (industry-specific) risk related to equity investment, this measure should better reflect the cost of equity than simply using a long-term government bond rate, as in other studies (Gaiotti and Generale 2001; Chatelain and Tiomo 2001; Chatelain et al 2003). It also provides more cross-sectional variation in the data.^{[15]}
The overall cost of finance (r^{C}_{i,t}) is simply taken to be the weighted average of the cost of debt and the cost of equity, where the weights on debt (D) and equity (E) are their respective (stock) shares in the total (book) value of the firm:
The real user cost of capital (UC_{i,t}) then becomes the cost of finance plus depreciation costs, adjusted for the effects of corporate taxes, subsidies and inflation:
where δ_{s,t} is the rate of economic depreciation; Z_{s,t} is the present value of depreciation allowances per dollar invested; p^{K}_{t} is the price deflator for property, plant and equipment investment; p^{GDP}_{t} is the price deflator for GDP and π^{e}_{t} is the expected appreciation of the price of capital goods from t to t+1 taken at time t.^{[16]} The tax system affects the user cost of capital in several ways. Firstly, by taxing the revenue stream generated by an incremental unit of capital, the marginal product of capital declines by (1−τ). This is akin to an increase in the cost of capital of 1/(1−τ), which would tend to discourage investment.^{[17]} However, the tax system also allows various deductions that reduce the cost of capital and hence encourage investment. As we have already noted, corporate interest payments can be deducted for tax purposes, lowering the cost of debt. Also, the purchase price of a unit of capital is reduced by tax-depreciation allowances that can be claimed over time. Denoting the present value of deductions by Z_{s,t}, the reduction in taxes is then given by (1−τZ_{s,t}).^{[18]}
The user cost of capital is also affected by movements in capital goods prices. First, a higher price for capital goods relative to output prices increases the cost of installing the new capital, as captured by the term, p^{K}_{t}/p^{GDP}_{t}. Second, if capital goods prices are expected to increase over the coming period, then it pays to purchase the capital in the current period when it is cheaper. The firm can then benefit from the expected capital gain and, all other things being equal, this would reduce the user cost of capital for the firm. Expected capital goods price inflation is captured by the term, π^{e}_{t}, which, in practice, is approximated by actual capital goods price inflation (Von Kalckreuth 2001).
3.3 Sample Characteristics and Comparisons to Aggregate Data
Before moving on to the econometric modelling, it is useful to examine the characteristics of the underlying sample of firms and to compare the firm-level data with data available at a more aggregated level. In terms of the number of firms, the final sample is about five times larger and covers a wider range of industries than previous Australian studies.^{[19]} The firm-level measures of investment, sales, user cost of capital and cash flow can also be compared with similar concepts at the aggregate level in order to assess the relative importance of this sample for aggregate investment and overall economic activity.
The (nominal) fixed investment, gross earnings and sales of firms in the sample constitute up to 70 per cent of their respective aggregate concepts, as reported in the national accounts.^{[20]} Hence, these firms appear to explain a significant share of overall economic activity. It is also helpful to examine how investment, real sales, cash flow and the user cost of capital have moved at the aggregate level over the sample period and to compare these relationships with the measures at the firm level. The firm-level data are based on the median value for each year in order to minimise the impact of outliers.
Not surprisingly given the smaller coverage, there tends to be more variability in the sample data than in the aggregate data. Still, movements in the firm-level measures of real sales growth and the rate of investment roughly appear to approximate the movements in the equivalent concepts at the aggregate level (Figure 5). Both measures appear to track the business cycle, with the firm-level measures clearly capturing the recession at the beginning of the sample period.
We can also see that the median user cost of capital has generally fallen over the 1990s, reflecting the gradual downward trend in borrowing rates, as illustrated by the business indicator rate in Figure 6.
There is a clear difference in the levels of, and movements in, the user cost of capital and the business indicator rate, reflecting the fact that the user cost of capital incorporates other costs such as depreciation and changes in capital goods prices. Stripping out these other factors and focusing just on the average interest rate embedded in the user cost measure, we can see a clearer correspondence with the indicator rate. Finally, there is also a fairly broad co-movement between the aggregate and firm-level measures of cash flow (Figure 6).
In summary, the aggregate and firm-level data appear reasonably well correlated over the sample period. As such, any significant relationships between investment, sales, cash flow and the user cost of capital uncovered at the microeconomic level are likely to provide insights into corresponding relationships at the macroeconomic level.
Footnotes
The additional trimming of these variables was needed to control for strong merger and takeover activity and the information technology boom that occurred during the 1990s which affected the reported capital stock and profit figures of numerous companies. The extent of trimming is comparable to that seen in other overseas studies (for example, Von Kalckreuth 2001). [10]
It is not immediately clear that the assumption of an inverse relationship between firm size and the level of financial constraints is a valid one. Recall that a financially constrained firm is one whose retained earnings are insufficient to match its investment opportunities. As a firm grows larger, it is not clear that a firm's retained earnings will necessarily grow faster than its investment opportunities. However, economies of scale in credit management arguably imply that larger firms are less likely to be constrained on average. Also, smaller firms are more likely to be start-ups with little credit history, more subject to idiosyncratic risk and less likely to have developed a reputation with investors (Schiantarelli 1996). [11]
However, the improved coverage in the latter part of the sample introduces significant heteroskedasticity in the data. This is controlled for in the estimation procedure. [12]
Note that interest payments can only be claimed as a tax deduction if the firm is earning positive income. For firms earning negative cash flow the average tax rate is set equal to zero. For simplicity, I ignore the fact that these firms could carry the tax deductions forward. [13]
The rate of interest that is needed in principle is the effective rate of interest on marginal borrowing, and not the average interest rate on the firm's outstanding stock of debt. This can complicate attempts to identify the direct effects of interest rate changes. The firm-specific interest rate in a given year is the weighted average of past interest rates (with the weights being given by the composition of debt). So a given change in current interest rates will not necessarily translate directly into a change in the average interest rate. [14]
I also experimented with a firm-level CAPM Beta measure for the cost of equity, though this was only a cross-sectional measure as I could not obtain a time series. Such a measure did not appreciably affect the overall results. [15]
See Appendix B for details on the construction of the depreciation allowances variable. [16]
This cost of capital measure does not account for the dividend imputation system in place since 1987 in Australia. However, this is unlikely to have a significant impact in the model to the extent that dividend imputation means that the choice between distributing dividends and retaining earnings is virtually equivalent from a shareholder's perspective. [17]
The cost of capital is also effectively reduced by investment tax credits. However, these are generally unavailable for investment in plant and equipment in Australia and so the tax credit is set equal to zero in the equation. [18]
Details of the industry composition of the sample can be found in Appendix A. [19]
The aggregate concepts referred to are, specifically, gross investment in property, plant and equipment, gross operating surplus for private non-financial corporations and GDP. The measure of GDP excludes government consumption and imputed dwelling rent in order to better approximate a measure of activity relevant to private non-financial corporations. The relative sizes of the sample aggregates vary on an annual basis, being generally lower in the earlier years because of poorer sample coverage. [20]