3. Performance measurement

08/01: Some Rise by Sin, and Some by Virtue Fall: Firm Dynamics, Market Structure and Performance

Richard Fabling (Reserve Bank of New Zealand), Arthur Grimes (Motu Economic & Public Policy Research), Lynda Sanderson (Ministry of Economic Development), Philip Stevens (Ministry of Economic Development)

[ Last Updated 14 March 2008 ]

This paper focuses on a small number of performance variables, namely sales, total employment, merchandise exporting, profitability, labour productivity and multi-factor productivity (MFP).¹⁷ The first three are trivially calculated, respectively, as BAI total sales; an average of the twelve monthly (PAYE) employee counts in the year¹⁸ combined with a count of working proprietors from LEED; and free-on-board Customs exports. Profitability is measured as the ratio of (IR10) taxable profit to (BAI) sales. Our productivity measures require the construction of value-added, defined as gross output less intermediate consumption, and approximated by:

VA = sales – (purchases – Dstocks) (1)

where sales and purchases are sourced from the BAI & changes in stocks are sourced from IR10s.¹⁹^,²⁰ BAI data is used for sales and purchase data due to concerns over under-reporting of IR10 purchases (Cox 2006), and because BAI coverage is superior.²¹ Prior micro analysis has not had access to IR10 data, and thus the stock adjustment has not factored into earlier firm-level productivity calculations. The effect of this adjustment is, in general, minor. For approximately three fifths (61.5%) of value-added observations the stock adjustment is zero, almost exclusively because opening and closing stocks are both reported as zero. Weighted by total employment, the mean (median) relative contribution of the stock adjustment is 7.2% (0.2%) of value-added.²² The correlation between the labour productivity measures with and without a stock adjustment is 0.959 in levels and 0.903 in growth rates. All this suggests that, while improving the conceptual accuracy of the value-added measure, such an adjustment is unlikely to undermine the results of previous authors who have been unable to make such an adjustment. We retain the adjustment in the remainder of the paper, noting that the use of IR10 data decreases the number of observations of value-added.

Table 5 sets out the number of productivity observations we have. Initially we lose 28.5%²³ of observations simply from the fact that many firms have zero employment – that is, they have neither employees nor working proprietors. A large number of these zero employment firms are in the finance & insurance, and property & business services industries (table 4), perhaps a sign of a large number of "shell" or asset-holding companies in our data. Next we lose a relatively modest 3.0% of observations from the absence of BAI data. As we noted in the prior paragraph, another major loss of observations (15.0%) comes from requiring the stock adjustment to the labour productivity calculation. Finally, because distributions of firm performance are highly skewed, labour productivity is reported as the log difference between value-added and employment. Taking logs of value-added results in another 9.6% of observations being dropped from labour productivity calculations because value-added is zero or negative. As with missing data, non-positive value-added is disproportionately associated with entering and exiting firms. ANZSIC divisions A, B, D & K also have higher rates of negative value-added.²⁴ Overall, we are left with 1,228,322 observations of labour productivity (corresponding to 43.9% of economically active firms).

Table 6 shows correlations comparing our key value-added measure against the measure derived from postal responses to AES.²⁵ In general the correlation of log-levels is very respectable with the finance and insurance industry showing the weakest correlation (at 0.6227). Turning to growth rates, we find that both short-term and longer-term growth rates are more weakly linked across data sources.²⁶ Growth rate comparison is made difficult by the selective nature of any AES longitudinal sample (biased towards the largest firms). However, for industries where large numbers of observations are available the four-year growth rates show significant positive correlation across the data sources. Overall, the results in table 6 give us some confidence that the LBD value-added variable is plausible and fit for research purposes.

MFP is calculated by way of regression assuming a Cobb-Douglas production function in labour (RME) and depreciation expenses (from IR10s) with industry-specific coefficients (a mix of one- & two-digit ANZSIC), year-specific dummies, and the potential for non-constant returns to scale. MFP is the residual of this estimation with industry average and year effects added back. That is, MFP is the component of value-added that is not explained in our model by capital and labour inputs.

The use of depreciation costs rather than a "true" capital services measure is forced on us by the absence of capital stock (and/or capital investment) data.²⁷ The number of MFP observations is lower (38.8%) due to reported zero depreciation (table 5). We lose 7.8% of the value-added and 7.5% of the employment associated with the labour productivity measure (ie, of the sub-population with positive value-added).

Appendix A presents the regression coefficients from the MFP calculation. Some coefficients seem implausible, particularly because of the relative contributions of labour and capital, and the implied rate of increasing returns in some industries. Specifically, we might expect the contribution of capital would be higher (a third being a ballpark figure from macroeconomic estimates) with only mildly increasing returns to scale, together implying lower labour coefficients than those estimated. For this exploratory paper, we treat these estimates as adequate, noting that the MFP calculation needs further investigation.²⁸ One approach to be looked at in more detail is using alternative specifications, particularly a generalised CES production function (see, for example, Grimes 1983).

¹⁷ Because IR10 data constitutes a reasonably full set of financial accounts, the data would allow the construction of additional financial performance measures such as financial solvency. These are not covered in the paper for the sake of brevity, but should be considered as potential avenues for further research.

¹⁸ Known as rolling mean employment (RME). The measure of RME used in this paper differs from that used in official LEED outputs as it excludes working proprietors that receive PAYE income (to avoid double counting of their employment).

¹⁹ GST is removed from sales & purchases data so that value-added is estimated at factor cost, rather than market prices. Most other financial data, including survey responses, are collected on a GST-exclusive basis.

²⁰ All results in this paper are nominal. Potential methods for adjusting to real output all involve applying industry average input and output producer price indices that may help conceal data issues. Appropriate adjustment methods are discussed in the caveat section.

²¹ Comparison of similar variables across data sources often yields some inconsistency. It is hard, in such cases, to disentangle the relative effects of definitional & timing differences, the respondent’s ability to answer accurately, and other sources of potential error such as apportionment or aggregation. Work within the IBULDD project suggests that most IRD-sourced variables correlate well to like variables collected through postal AES returns (Smith 2006).

²³ These percentages are susceptible to the order in which they are calculated.

²⁴ ANZSIC A is Agriculture, Forestry & Fishing; ANZSIC B is Mining; D is Construction; ANZSIC K is Finance & Insurance.

²⁵ Due to sample size, all years are pooled together. Because the comparison is on log levels and differences we lose 14,997 observations with non-positive value-added in at least one of the measures (in 67% of dropped cases the AES measure is non-positive, similarly 52% for the LBD measure).

²⁶ To attempt to smooth potential short-term mismeasurement issues, the four year growth rate is calculated as the difference between the two-year average of value-added in the last and first years of the dataset.

²⁷ We do have closing book values of fixed assets. To a certain extent, the use of depreciation costs should not be too problematic since tax-deductible depreciation rates in New Zealand tend to have an economic basis. However, our depreciation cost should be supplemented by the cost of debt or equity to derive a full cost of capital. We assume this full cost of capital to be correlated to the depreciation cost and, therefore, ignorable in this preliminary paper. A cost of capital component will be investigated in future.

²⁸ In a parallel analysis, Dixon (2007) found similar results using an unbalanced panel of AES/IR10 data with total fixed assets as the capital input and aggregate, rather than industry-specific, coefficients.

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Printed: 26/11/2009