Abstract
This paper examines the determinants of total factor productivity (TFP) using a British plant-level dataset. It considers the role of the following four plant characteristics: internal and external knowledge; foreign ownership; multi-plant economies of scale and competition; and spatial spillovers and ‘place’ effects. A wide range of results are obtained, most of which confirm earlier results in the literature, such as that undertaking R&D is positively associated with TFP and most foreign ownership groups have higher than average TFP. The results also confirm the very small number of studies in the literature that have shown that the age of the plant is negatively related to TFP and therefore that vintage effects outweigh any learning-by-doing effects. The inclusion of a wide range of determinants of TFP allows comment on the relative importance of different groups of TFP determinants; knowledge creation is found to be the most important determinant of TFP (especially in manufacturing), with spatial location impacts overall the next largest determinant. Foreign-ownership is founded to be (overall) the least important determinant of TFP although this is partly the consequence of the relatively small size of the foreign-owned sector.
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Notes
A longer version of this paper discusses these determinants in more detail. See Harris and Moffat (2014).
The notion of ‘absorptive capacity’ was initially put forward by Cohen and Levinthal (1990), who argued that the firm’s “prior related knowledge confers an ability to recognize the value of new information, assimilate it and apply it to commercial ends” and “these abilities collectively constitute what we call a firm’s ‘absorptive capacity’”. Thus, in simple terms, absorptive capacity is the firms’ ability to internalise external knowledge.
As Gittleman et al. (2006) show “… the correction of productivity growth for the vintage effect requires an estimate of the obsolescence and depreciation parameters on the basis of age data…(then) the use of capital stock in efficiency units does cause some smoothing of total factor productivity growth over time” (p. 306).
Martin (1993) develops a model that shows the opposite; greater competition results in a smaller payoff from increasing marginal efficiency and therefore the less it is in the interest of the owner to put in place an incentive structure that induces the manager to reduce marginal cost. Spence (1984) similarly shows that as the number of firms in the market increases (and the expected sales of each firm decreases) then the incentive to invest in cost reduction falls.
As pointed out to us by an Associate Editor, this implied relationship between competition, efficiency and profits ignores the intervening effects of economies of scope and scale. In a single-input single-output non-constant returns-to-scale production frontier, the point of maximum average product (TFP) is the point of tangency between the frontier and a ray from the origin; except in special cases like perfect competition, this is not the point of maximum profits.
For a detailed description of the ARD and discussion of several issues concerning its appropriate use, see Oulton (1997), Griffith (1999), and Harris (2002, 2005a). Analysis using the database covers a range of areas: cf. Disney et al. (2003a, b), Harris and Drinkwater (2000), Harris (2001, 2004), Collins and Harris (2002, 2005), Harris and Robinson (2002, 2003, 2004a,b), Harris and Hassaszadeh (2002), Harris et al. (2005), and Chapple et al. (2005).
For most of these industries we have no data on capital stocks, or they are only partially covered by the ARD.
More details on the UK Data service are available at http://ukdataservice.ac.uk/get-data/secure-access.aspx.
Note, BERD data captures firms that ‘regularly’ undertake R&D, and this could potentially underestimate R&D in smaller firms and/or those in low-tech sectors.
A major problem with the BERD is that the ONS use a different system of enterprise codes for some respondents.
We have experimented with different agglomeration and diversification measures (but note unlike the literature covered in Kominers 2008, we are not measuring whether an industry is agglomerated spatially by using an aggregated industrial agglomeration measure; rather we are trying to capture MAR-spillovers by measuring the percentage of output located in each local authority district for each 5-digit industry). With regard to agglomeration Devereux et al. (2007) used a variable measuring the number of plants in each industry in each county-year, which is significantly correlated with our measure but which we believe to be inferior (as it ignores plant size and thus the relative amount of output produced by an industry at a particular location). For diversification, there are also several different approaches, from the simple measure used by Baldwin et al. (2010) of the population size of an area, to using a locational Herfindahl index, calculated using employment shares for disaggregated industries for each area in each year, excluding a plant’s own industry (e.g. Devereux et al. 2007). These two alternative measures of diversification were strongly correlated with the one used here; the correlation with population density (we prefer this to actual population numbers to allow for the spatial size of the district) is 0.55, and with the locational Herfindahl index we had an overall correlation of 0.67 (it differs by year, but never falls below 0.48). We also believe our diversification index is ‘better’ since using 5-digit industries and 408 local authorities, the mean of the locational H-index (subtracted from 1) was 0.98 with a standard deviation of 0.012 (i.e., most local authorities are very disaggregated); our measure has a mean of 55.3 (standard deviation of 8.1)—see Table 1.
A major issue is at what level of industry disaggregation should the analysis be undertaken. To avoid the imposition of common coefficients across potentially heterogeneous industries, we have used a detailed level of disaggregation, but (as pointed out to us by a referee), such aggregation/disaggregation requires justification. We provide this in the “Appendix”.
Regions are defined as the standard administrative (or Government Office) regions. They equate to NUTS1 definitions and there are 11 regions in Great Britain.
Dividing these numbers into 1 gives the ‘numbers-equivalent’ of equal-sized firms on average operating in each sector. Note, the Herfindahl index was obtained using the following formula: Herfindahl jt = \(\sum\nolimits_{i} {\left( {y_{ij,t} /\sum\nolimits_{i} {y_{ij,t} } } \right)^{2} }\) where j refers to each 4-digit industry, i refers to a plant ∈j, t refers to year, and y refers to real gross output.
The inclusion of fixed effects is necessary as empirical evidence using plant- and firm-level panel data consistently shows that plants are heterogeneous (productivity distributions are significantly ‘spread’ out with large ‘tails’ of plants with low TFP) but more importantly that the distribution is persistent—plants typically spend long periods in the same part of the distribution. Evidence using the ARD has been presented in, for example, Haskel (2000) and more recently Martin (2008). Evidence from other countries is presented in Baily et al. (1992), Bartelsman and Dhrymes (1998). Such persistence suggests that plants have ‘fixed’ characteristics (associated with access to different path dependent (in)tangible resources, managerial and other capabilities) that change little through time, and thus need to be modelled.
In theory the production function should relate the flow of factor services to the flow of goods and services produced; in practice we rarely have data on capital and labour utilization at the micro-level, and this measurement error is included in ε it .
Using more familiar notation, TFP here is defined as A it in the standard Cobb-Douglas production function:
$$Y_{it} = A_{it} E_{it}^{{\alpha_{E} }} M_{it}^{{\alpha_{M} }} K_{it}^{{\alpha_{K} }}$$(3)and thus:
$$A_{it} = Y_{it} /(E_{it}^{{\alpha_{E} }} M_{it}^{{\alpha_{M} }} K_{it}^{{\alpha_{K} }} )$$(4)Note, lnTFP is defined here by replacing lnA it with the last term in Eq. (2). TFP is this determined by (i) the variables captured in X it (which account for plants being ‘on’ or ‘inside’ the current ‘best-practice’ technology); (ii) the time trend (which shifts the ‘best-practice’ frontier generally outwards); and (iii) plant-level fixed effects and idiosyncratic shocks captured by the error term. TFP is not affected directly by returns-to-scale \((\alpha_{E} + \alpha_{M} + \alpha_{K} )\) since any changes in the denominator on the right-hand-side of (4), as factor inputs change, is matched by changes in output, with A it unchanged.
Output, intermediate inputs, labour, capital, R&D, ‘brownfield’ FDI and competition (the Herfindahl index) are treated as endogenous. Thus lagged (predetermined) values of these variables are used as instruments and tested for in terms of their validity (see next footnote).
The validity of the instruments (i.e., that they are correlated with endogenous regressors but are not correlated with the production function error term—and hence productivity) can be tested, but system-GMM (which exploits more moments conditions than other GMM approaches) can still face the problem of weak instruments, and it is well-known by those that use the approach that the parameter estimates obtained (and the ability to pass diagnostic tests) is sensitive to the instrument set used. See also Roodman (2006) for practical guidance on applying the system-GMM approach.
The results are available in an online “Appendix”: https://dl.dropboxusercontent.com/u/72592486/Online%20appendix.xlsx.
However, it is important to emphasize that the underlying results based on all 220 industries are very diverse.
Based on running a large number of regressions with different lags of the instruments for different endogenous variables, no general pattern on which lag-lengths should be used was found across both variables and the220 models estimated, other than lagged instruments starting from t − 4 or longer were generally needed for all endogenous variables (often longer in the case of instruments for the capital stock). In all instances the null hypothesis for the Hansen test is that the instruments used are exogenous (i.e., that they are correlated with endogenous regressors but are not correlated with the production function error term—and hence productivity); this null was accepted in all models.
Parameter estimates for dummy variables need to be converted using the formula: exp(\(\hat{\beta } - 1\)).
That is, given the persistence of heterogeneity (such that plants are expected to occupy similar positions in the distribution of TFP for long periods of time), it might be expected that relative inefficiency levels change slowly and changes in the productivity distribution are more likely in short periods to be dominated by rightward shifts caused by technical change.
The sectors were not exactly the same as those used in our study (high-tech in EU KLEMS is SIC30-33; medium high-tech is SIC29, 35-35; medium low-tech is SIC23-28; low-tech is SIC15-22, 36-37; and services comprised sectors G, H, I, SIC60-64, K and O). Note we weighted individual industry results by their share in total GVA for each year 1997-2006 to obtain the overall TFP figures reported here.
It is important to reiterate how we define ‘greenfield’ and ‘brownfield’ when modeling of TFP using Eq. (1): the former is not just for the year in which the plant begins operation, but applies throughout 1997–2008 if at any time during this period a new plant was established.
Note, the size of the plants operated by single- and multi-plant enterprises may be similar (due to internal—technical—economies of scale in production); but the size of the firm is usually larger in multi-plant enterprises. Plant size is taken into account when estimating Eq. (1) by the inclusion of factor inputs; firm size could have been entered directly as an additional variable but for single-plant enterprises this would have resulted in enterprise and plant employment being the same (and entered twice with associated multicollinearity problems). Hence we chose to include dummy variables representing whether the plant belonged to a single-plant firm, and whether it belonged to a multi-plant firm operating in more than one region.
For example, it has been argued that using competition measures such as firm-level market shares and/or price–cost margins is problematic; as Brouwer and van der Wiel (2010) show increases in competition intensity can result in the reallocation of market shares from inefficient firms (with low mark ups) to efficient firms (with high mark ups), and thus increasing mark-ups are associated with more (not less) competition. Thus we have a preference for the Herfindahl index, that includes the entire distribution of market share across firms, in the expectation that this should mitigate against (although perhaps not entirely alleviate) this problem. It is also interesting to note that Martin (2010) found a significant positive correlation between TFP and firm mark-ups (firms with higher TFP charge higher mark-ups) in Chile, although he also found that over time that when competition increased mark-ups declined as productivity distributions moved to the right.
The formula is given in the notes to Table 4; as an example, the result for the high-tech manufacturing sector is 15.9 %; i.e., 100 × [0.224 × (exp(0.105) − 1) + 0.038 + (−0.084 × ln(3.131))].
Note, this approach is preferable to the use of Chow tests because of the latter's requirements that the variance of the error term is equal across the two groups.
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Acknowledgments
This work contains statistical data from ONS which is Crown copyright and reproduced with the permission of the controller of HMSO and Queen’s Printer for Scotland. The use of the ONS statistical data in this work does not imply the endorsement of the ONS in relation to the interpretation or analysis of the statistical data. This work uses research datasets which may not exactly reproduce National Statistics aggregates. It was also carried out as part of an ESRC Grant (RES-591-28-0001). We would also like to acknowledge the helpful comments provided by the editors and referees, although the authors retain sole responsibility for the contents of this paper.
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Appendix
Appendix
1.1 Disaggregation issues
While the imposition of common coefficients on industries that operate with different technologies is generally understood to be undesirable in the production function estimation literature, the appropriate level at which the data should be disaggregated is rarely tested. The approach taken in this paper is to disaggregate by 4-digit SIC industries and therefore in this section results are provided using a simple test of whether a more aggregated approach would be appropriate. Following Elhorst (2008), let A and B denote two production functions, where \(\hat{\beta }\) represents the parameters estimates and V refers to the variance–covariance, then a Wald test of the null hypothesis that the parameter estimates are the same across the two regressions is used to produce the following statistic:Footnote 35
Using the 4-digit SIC’s that belong to the high-technology manufacturing sector, Table 7 compares system-GMM regessions across pairs of industries (Tables 5, 6).
In all cases, the null of equality of coefficients is rejected at the 95 % level (there is only one pair of industries in which the null of equality of coefficients cannot be rejected at the 99 % level). This therefore provides support for our approach of estimating the models at the SIC 4-digit level.
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Harris, R., Moffat, J. Plant-level determinants of total factor productivity in Great Britain, 1997–2008. J Prod Anal 44, 1–20 (2015). https://doi.org/10.1007/s11123-015-0442-2
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DOI: https://doi.org/10.1007/s11123-015-0442-2