3 Technical efficiency and finance constraints
3.4 The econometric results
Table 3.6 presents the Maximum Likelihood Estimates of the production frontier for the eight industries.5For each industry, I have estimated two separate pro- duction functions where either DAR or ICR has been introduced among the z- variables. The reason for choosing this estimation strategy can be described as follows: the two variables DAR and ICR can have a different impact on tech- nical efficiency. As specified above, DAR is a measure of how much a firm is constrained in its expansion and therefore it is expected to have a positive impact on technical efficiency: if a firm is constrained in its access to external resources, then the only way to expand is by reducing internal inefficiencies.
The picture is different for the ICR. The impact of this variable on efficiency is more ambiguous. An important aspect to consider in this respect is whether the negative shock is considered to be permanent or temporary: if the negative shock is permanent, then an obvious way to increase internal resources is to reduce inefficiency. However, if the shock is deemed to be temporary, the firm may not want to start an internal re-organization in face of a temporary decrease of financial resources and may rather shed workers and investments temporarily.
Therefore, given the potential different impact of DAR and ICR on technical efficiency, it is possible that technical efficiency change may go in different directions according to whether either DAR or ICR is included in the model.
Before estimating the production function, I have mean-corrected the data so that the first-order coefficients listed in Table 3.5 can be interpreted as elastici- ties, evaluated at the sample means. The main results can be summarized as follows. The value of the γparameters (i.e. the ratio of σ2uto the sum of σ2uand σ2v) is significantly greater than zero across all sectors, indicating that the use of frontier estimators (rather than OLS estimators) is justified. First-order coeffi- cients have the expected signs on behalf of the economic behaviour. The coeffi- cients of the time trend variables (both as the second-order polynomial and associated with inputs) show that the sectors have experienced some sort of technical regress throughout the considered sample period, with the sectors of Extraction of Metals, Transformation of Metals, Textiles and Leather having a negative coefficient of the linear time trend and the sectors of Tobacco and Paper having a negative coefficient of the squared time trend. To test the significance of the coefficients of the technical change variables, I have con- ducted a likelihood ratio test which involves the calculation of:
)]
( ) ( [
2 LLF H0 LLF HA
LR=− −
Table 3.6 Maximum likelihood estimates by sector
Variables Parameters t-ratio Parameters t-ratio
Extraction of metals
Constant 8.74 88.04 8.69 121.38
K 0.25 4.86 0.26 4.76
L 0.57 6.89 0.56 6.66
K2 0.093 8.04 0.092 6.86
L2 0.014 3.95 0.012 3.06
T −0.12 −1.93 −0.11 −2.28
t2 0.02 2.15 0.02 2.52
tK −0.01 −0.66 −0.01 −0.74
tL 0.04 1.81 0.04 1.95
KL 0.04 2.5 0.04 2.58
Constant −4.88 −1.09 −7.06 −1.69
ICR −2.2 −1.66 – –
DAR – – 4.02 1.8
σ2 1.18 1.38 0.86 2.22
γ 0.9 11.69 0.85 11.95
λ1 29.6 – 26.6 –
λ2 9.88 – 10.56 –
Mean efficiency 0.84 – 0.87 –
Average technical change −0.056 –0.056 –
Transformation of metals
Constant 3.7 239.69 3.7 237.41
K 0.11 10.72 0.11 11.3
L 0.36 37.14 0.34 25.29
K2 0.007 0.007 0.005 0.004
L2 0.004 0.004 0.004 0.003
t −0.01 −0.03 –0.01 –0.34
t2 0.01 1.07 0.01 1.39
tK −0.01 −3.01 −0.01 −3.47
tL 0.01 2.28 0.01 2.79
KL 0.01 0.25 0.01 0.16
Constant −7.23 −6.16 −6.21 −6.57
ICR −1.68 −6.39 – –
DAR – – −1.01 −6.61
σ2 0.8 6.61 0.79 7.08
γ 0.99 387.64 0.99 354
λ1 19.72 – 17.84 –
λ2 33.52 – 35.68 –
Mean efficiency 0.9 – 0.9 –
Average technical change 0.118 – 0.118 –
Food
Constant 8.91 151.19 8.92 142.75
K 0.3 4.9 0.3 4.59
L 0.69 8.39 0.7 7.68
K2 0.03 1.27 0.029 1.28
L2 0.09 2.22 0.01 2.35
continued
Table 3.6 continued
Variables Parameters t-ratio Parameters t-ratio
t 0.03 0.98 0.03 0.93
t2 0.01 0.4 0.01 0.36
tK −0.03 −1.89 −0.03 −1.7
tL 0.04 2 0.04 1.64
KL 0.05 3.11 0.05 3.21
Constant −14.86 −1.23 −16.26 −1.67
ICR −4.86 −1.27 – –
DAR – – −0.02 −0.08
σ2 3.33 1.25 3.98 1.72
γ 0.99 86.86 0.99 151.54
λ1 38.08 – 30.58 –
λ2 20.94 – 19.426 –
Mean efficiency 0.81 – 0.81 –
Average technical change 0.344 – 0.344 –
Tobacco
Constant 8.54 109.04 8.52 113.22
K 0.4 7.11 0.4 7.01
L 0.64 9.27 0.64 9.06
K2 0.04 2.66 0.043 2.68
L2 0.039 1.13 0.04 1.15
t 0.09 1.81 0.09 1.94
t2 −0.01 −0.83 −0.01 −0.89
tK −0.03 −1.95 −0.03 −1.88
tL 0.02 0.91 0.02 0.83
KL 0.01 0.3 0.01 0.15
Constant −10.23 −2.41 −3.46 −2.76
ICR −3.22 −2.17 – –
DAR – – −4.03 −2.53
σ2 1.69 2.84 0.98 3.67
γ 0.92 27.51 0.85 18.21
λ1 2.3 – 3.1 –
λ2 26.24 – 26.04 –
Mean efficiency 0.86 – 0.88 –
Average technical change −0.903 – −0.903 –
Textiles
Constant 8.97 75.95 8.96 78.92
K 0.34 3.93 0.34 4.04
L 0.72 7.67 0.72 7.95
K2 0.061 2.37 0.062 2.38
L2 0.11 3.62 0.13 3.65
t −0.03 −0.38 −0.02 −0.25
t2 0.01 1.02 0.01 0.92
tK −0.04 −2.04 −0.04 −1.99
tL 0.02 0.97 0.02 0.95
KL 0.01 0.76 0.01 0.74
Constant −21.48 −1.08 −11.42 −0.62
continued
Table 3.6 continued
Variables Parameters t-ratio Parameters t-ratio
ICR −4.86 −0.93 – –
DAR – – –7.54 –0.59
σ2 6.93 1.13 5.42 0.63
γ 0.98 67.27 0.98 32.41
λ1 16.86 – 19.54 –
λ2 15.82 – 26.06 –
Mean efficiency 0.76 – 0.76 –
Average technical change −0.545 – −0.545 –
Leather
Constant 8.72 220.25 8.73 193.04
K 0.34 12.78 0.35 13.99
L 0.61 17.81 0.62 17.96
K2 0.039 4.86 0.036 4.67
L2 0.073 4.55 0.069 4.37
t −0.07 −2.55 −0.07 −2.53
t2 0.01 3.29 0.01 3.29
tK −0.03 −4.27 −0.03 −4.54
tL 0.03 2.94 0.03 2.89
KL 0.01 1.09 0.01 1.03
Constant −13.89 −20.56 −12.8 −4.27
ICR −0.01 −1.02 – –
DAR – – −0.77 −2.53
σ2 3.03 21.86 2.9 4.48
γ 0.97 453.32 0.96 96.19
λ1 65.9 – 68.94 –
λ2 39.1 – 40.88 –
Mean efficiency 0.83 – 0.83 –
Average technical change 0.746 – 0.746 –
Wood
Constant 8.14 157.68 8.15 154.42
K 0.35 11.7 0.35 11.85
L 0.66 16.54 0.66 16.77
K2 0.008 1.11 0.007 1.13
L2 0.019 1.14 0.018 1.24
T 0.02 0.59 0.02 0.48
t2 0.01 0.37 0.01 0.49
tK −0.02 −2.53 −0.02 −2.59
tL 0.01 0.67 0.01 0.73
KL 0.01 0.08 0.01 0.07
Constant −17.75 −2.95 −15.76 −3.85
ICR −0.33 −2.73 – –
DAR – – −1.58 −3.91
σ2 4.88 3.13 4.61 4.16
γ 0.97 99.62 0.97 134.8
λ1 92.5 – 92.8 –
λ2 30.38 – 30.28 –
continued
Table 3.6 continued
Variables Parameters t-ratio Parameters t-ratio
Mean efficiency 0.79 – 0.79 –
Average technical efficiency 0.017 – 0.017 –
Paper
Constant 8.13 149.89 8.14 141.32
K 0.23 6.95 0.23 7.05
L 0.82 16.62 0.82 16.73
K2 0.05 6.39 0.049 6.35
L2 0.07 3.83 0.05 3.56
T 0.05 1.3 0.04 1.22
t2 −0.01 −0.55 −0.01 −0.42
tK −0.02 −2.9 −0.02 −2.96
tL 0.03 2.77 0.03 2.75
KL 0.01 0.13 0.01 0.29
Constant −14.47 −3.19 −12.91 −3.89
ICR −0.27 −3.4 – –
DAR – – 2.51 4.06
σ2 3.17 3.37 2.54 4.21
γ 0.98 117.08 0.97 112.49
λ1 75.4 – 75.12 –
λ2 47.64 – 26.92 –
Mean efficiency 0.83 – 0.83 –
Average technical efficiency −0.258 – −0.258 –
where LLF(H0),LLF(HA) are the values of the log-likelihood function under the null and the alternative hypotheses, respectively. This statistic has an asymptotic Chi-square distribution, with degrees of freedom equal to the number of restric- tions. The results of the tests are shown in Table 3.5. Generally speaking, technical change variables are significant for all sectors. Interestingly, the coeffi- cients of the embodied technical change show that for all the sectors under consideration the technical change related to the stock of capital has been negat- ive (Scott, 1991). These results point to the fact that for some sectors there has been some sort of technical regress. This is confirmed by looking at the average technical change experienced by the sectors over the sample period which is reported at the bottom of each table.6Interestingly, most sectors report a negat- ive technical change. This result can be understood by recalling that in the sample period Italian manufacturing was affected by a sharp recession that hit the economy in the period 1992–1993. It is well known that during recessions the productive structure of an economy goes through a process of change where old techniques are eliminated and substituted by new techniques, mostly embod- ied in the stock of capital in both cases (Caballero and Hammour, 1994, 1996).
In this case, during recessions, both the rates at which new techniques are either created or destroyed change and what it is observed in the aggregate is the net
result of these two contrasting forces. Obviously it may happen that the process of destruction is faster than the one of creation and this implies that the sector is experiencing “negative” technical change (or technical regress). This is exactly what has happened in the sectors experiencing technical regress: during the recession the destruction of old techniques has been the prevalent force over cre- ation. In a sense, these results hint that tighter finance constraints do not have any bearings on technical change, which is an important dimension of a company’s performance. Indeed, during a recession when the availability of financial resources is scarce, a firm prefers to reduce technical inefficiency rather than to engage in changes of the technology to compensate the reduction in financial resources. Interestingly, the size of technical regress varies across sectors. This can be imputed to different speeds of destruction of old techniques across sectors. These in turn can depend on several factors, namely the speed of technology transfer, the existing workers’ skills and the managerial capabilities.
In some sectors, new technologies can be adopted faster in all plants if both workers and managers have the “right” skills and capabilities and therefore cre- ation will eventually counterbalance destruction with a limited technical regress observed in the sector. If a sector is more segmented, then it is possible that old techniques coexist with new techniques; therefore destruction offsets creation and therefore the sector can experience a considerable technical regress.
The estimated coefficients (in absolute value) of the z-variables are listed in the last rows of Table 3.7. It is important to notice that in the context of the Battese and Coelli (1995) model a negative (positive) sign of the DAR or ICR coefficient implies that firms with high DAR or ICR are more/less efficient.
From these estimates, it is possible to see that both DAR and ICR influence pos- itively efficiency in most sectors but the Extraction of Metals. In particular in Table 3.7 Average marginal effects of measures of finance constraints by sector
Variable Sector Marginal effect
ICR Extraction of metals 0.42
Transformation of metals 0.28
Food 1.17
Tobacco 0.95
Textiles 0.29
Leather 0.0004
Wood 0.04
Paper 0.02
DAR Extraction of metals 1.4
Transformation of metals 0.1
Food 0.0007
Tobacco 0.54
Textiles 0.29
Leather 0.06
Wood 0.09
Paper 0.23
this sector, ICR affects positively technical efficiency while DAR does not. This result can be explained by reminding that firms in this sector can have access to external financial resources (thanks to government incentives) aimed in particu- lar at the relaxing of the long-run constraint. So firms cannot really be con- sidered debt-constrained and therefore tightening of the budget constraint cannot have an impact on efficiency. To test the significance of either DAR or ICR, I use the likelihood ratio testing procedure. The hypothesis test has been con- ducted with the unrestricted translog production function as the model under the null hypothesis. The likelihood ratio tests (in Table 3.6) show that both DAR and ICR are significant apart from the Tobacco sector.
The coefficients of either DAR or ICR do not tell directly the magnitude of the effect of changes in the DAR or ICR upon technical efficiency. Therefore, I have computed the partial derivatives of the technical efficiency predictor (or marginal effects) with respect to DAR first and ICR afterwards using the formula in Coelli (2003). They measure how reactive firms in the sector are in reducing their inefficiencies when there is a negative shock to their finances. The marginal effects are listed in Table 3.7. It is possible to see that, for instance, 1 per cent increase in DAR will increase the average technical efficiency score by 0.29 points in the Textiles sector. While in most sectors variations in finance constraints affect positively technical efficiency, it is interesting to notice that the size of the effect varies across sectors and within the same sector according to the whether the long-run or the short-run measure of finance constraints is considered. Consider the example of Food: a 1 per cent increase in ICR will increase efficiency by 1.17 points, while the same increase in DAR has a negli- gible impact on technical efficiency. This difference can be explained by looking at the composition of the sector. Small and medium-sized firms with scarce interest in expansion dominate the Food sector: these fund their activities mostly with internal resources and therefore they are very sensitive to changes in ICR.
The same argument applies to the Leather sector but in the opposite direction: as larger firms with more cash-flow and more interest into expansion populate the sector, changes in ICR do not necessarily trigger an internal re-organization to release internal resources. However, the tightening of the long-run constraint may have an adverse impact on the potential expansion of firms and therefore start a process of technical inefficiency reduction.