The De nition of the Grading Scales in Banks' Internal Rating Systems

Transcription

1 Economic Notes by Banca Monte dei Paschi di Siena SpA, vol. 30, no , pp. 421±456 The De nition of the Grading Scales in Banks' Internal Rating Systems A. FOGLIA ^ S. IANNOTTI ^ P. MARULLO REEDTZ An internal risk rating system can be de ned as the process used to classify bank borrowers into categories of different credit riskiness. Most of the related literature has investigated various aspects of this process, but the problem of de ning the categories and the distribution of borrowers into the different classes or grades has received rather less attention, other than noting that the number of grades and their dispersion should achieve a meaningful differentiation of risk. An appropriate de nition of the grading scale is of primary importance because the probability of default associated to each grade is the key inputs of capital allocation systems at many best-practice banks and is the core of the January 2001's new proposal of the Basel Committee for the calculation of capital requirements. Statistical techniques such as cluster analysis can help in identifying distinct subgroups of borrowers possessing the same creditworthiness. We use a logit model to estimate individual default probabilities for four categories of borrowers and apply cluster analysis to assign borrowers to each grade. However, since cluster analysis is not a purely mechanical process, but requires examination of the nature of observations and of the objective of clustering, the ultimate choice of the most appropriate grading scale for a given portfolio relies on empirical grounds. A suf cient granularity and an appropriate quanti cation of risk must be balanced. (J.E.L.: G21, G22, G33). 1. Introduction An internal risk rating system can be de ned as a process assessing the credit quality of individual borrowers or assets. Although rating systems' design and implementation are in uenced by a broad range of factors, and Banco d'italia, Banking and Financial Supervision Via Nazionale 187, Roma. Tel.: ; Fax: ; ; foglia.antonella@insedia.interbusiness.it; marulloreedtz.paolo@insedia.interbusiness.it. The views expressed herein are the authors' and do not necessarily re ect those of the Bank of Italy. We thank Ulderico Santarelli for useful discussions on the statistical analysis and Andrea Sihoni and Michael Gordy for helpful comments on a previous version of the paper. Published by Blackwell Publishers, 108 Cowley Road, Oxford OX4 1JF, UK and 350 Main Street, Malden, MA 02148, USA.

2 422 Economic Notes : Review of Banking, Finance and Monetary Economics various approaches are adopted by different banks in designing their own rating systems, it is possible to reduce the structure of an internal rating system to three basic elements: 1 The assignment of an indicator of credit quality to a particular borrower 2 The distribution of the rated borrowers among classes or grades 3 The measurement of the riskiness in any given grade Most of the related literature has investigated the various methodologies used in addressing points 1 and 3. The problem of de ning the grading scale has received rather less attention, other than noting that the number of grades and their dispersion should achieve a meaningful differentiation of risk. This is likely due to the wide range of practices used by banks, which has been interpreted as showing that an `appropriate' distribution of exposures among grades varies according to the size of the bank, the type of loan portfolio and the different applications of the rating system within the bank's risk management process. One of the most common practices is to adopt the rating scales used by the rating agencies. The question is of primary importance in the context of the Basel `Internal-rating Based Approach' to capital regulation. The calculation of capital requirements based on the allocation of borrowers across different risk categories assumes that borrowers are different in terms of creditworthiness across classes and homogeneous within the same rating class. Statistical techniques such as cluster analysis can help to identify distinct subgroups of borrowers possessing the same creditworthiness. We use a logit model to estimate individual default probabilities of Italian banks' corporate borrowers and apply cluster analysis to assign borrowers to each grade. This procedure is used to simulate and compare different rating scales. Section 2 reviews the literature on internal rating systems. Section 3 discusses the problem of de ning a rating scale. Section 4 describes the scoring system we used to assign individual risk scores and the sample of rated bank borrowers. Section 5 applies cluster analysis to de ne three grading scales with a different number of classes. Section 6 discusses the various options when facing the choice of a particular grading scale and quanti es the probability of default per grade. Section 7 summarises the main ndings. An appendix describes the basic notions of cluster analysis and presents the method used in this paper. 2. Related Literature Recent literature on banks' credit risk rating systems has tended to focus on describing the range of practices at the largest international banks. English and Nelson (1999) present the results of telephone consultations with more than 100 US banks; Tracey and Carey (2000) survey the 50 largest

3 A. Foglia ± S. Iannotti ± P. Marullo Reedtz: The De nition of the Grading Scales US banking organizations; a report from the Basel Committee (2000) contains information on 30 institutions across the G-10 countries identi ed as having well-developed internal rating systems. For the Italian banking system, De Laurentis (2000) describes the systems used by ve large Italian banks; a paper from the Italian Banking Association (ABI, 2000) describes the results of a survey of the internal rating systems of 13 Italian banks of various sizes and business focuses. Krahnen and Weber (2001) discuss internal rating systems currently used in Germany. Carey and Hrycai (2001) empirically examine methods to measure the riskiness of each grade. In describing the rating systems, information is provided on the different components of the surveyed systems and, in particular: whether they are based on an obligor dimension or a facility dimension whether the process serving to identify the riskiness of the individual borrower relies on quantitative techniques, personal experience or the expertise of loan of cers, or a mixture whether the quanti cation of the default probability per grade is obtained by the scoring model itself, by using the historical loss experience of the bank's own portfolios or on publicly issued bonds rated by the rating agencies the aims and the applications of the rating systems (monitoring, pricing, economic capital allocation, setting of credit limits). As to the number and meaning of grades, English and Nelson (1999) report that smaller banks have generally less detailed systems than larger banks; in particular, larger banks are more likely to have rating systems with a large number of Pass categories. Banks with large business loan portfolios averaged 8.7 possible ratings, while those with small portfolios averaged 7.2 categories; the number of Pass categories ranges from 4.8 for the bigger business lenders to 3.4 for the smaller ones. Tracey and Carey (2000) observe that banks using ratings mainly to identify problem loans may nd that a rating scale with relatively few grades is adequate, whereas ner distinctions of risk are more valuable if they are used as inputs for capital allocation and pricing models. Banks with a signi cant share of their commercial business in the large corporate market tend to have more grades for low risk (investment-grade) borrowers. All banks consider it important to distinguish risk in the below-investment grade range, since default rates rise rapidly as the grade worsens. They conclude that different scales are appropriate for different banks, and that the optimal number of grades may vary according to their size and other organizational features. The banks surveyed in their paper report ve Pass grades (median) and three or four problem-asset grades. Among the ten largest banks, the median number of Pass grades is six. Even for banks with a more granular scale, the distribution of borrowers among grades is highly concentrated: about one-third

4 424 Economic Notes : Review of Banking, Finance and Monetary Economics of the 45 largest banks assign half or more of their rated loans to a single risk grade. According to the report from the Basel Committee (2000), the average number of grades covering good quality loans is ten (including `auxiliary' grades), with a range between two and 20. The average number of problem grades is approximately three, ranging from six to zero. On average, the banks surveyed have a maximum of 30 per cent of rated exposure within a single grade, ranging from 70 per cent to 16 per cent. For the Italian market, De Laurentis (2000) reports 9±10 grades as the solution almost uniformly adopted, with 3±4 grades for problem loans; 50 per cent of loans/borrowers are classi ed in at least three grades. According to a survey of the Italian Banking Association (ABI, 2000), the average number of grades is 10, ranging from 5 to 22. The major universal German banks surveyed in Krahnen and Weber (2001) have typically from six to ten rating classes. Building on the practice observed at these banks, the authors propose a set of rules that sound rating systems should observe; they suggest that `the rating system should always be as ne as necessary', depending on its intended use and on the possibility for the bank to perform back-testing procedures. Carey and Hrycai (2001) examine methods currently used to estimate average default probabilities by grade, a subject that is closely related to that of de ning a rating scale, as discussed in the next section. 3. Discussion When the creditworthiness of individual borrowers is assessed by measuring their probability of default (PD), the de nition of the rating scale amounts to nding a mapping of individual PDs into a discrete number of classes, and estimating a `pooled' or average PD for each grade, so that all borrowers within that grade can be treated as having the same PD. In principle, the most exact result would model each PD as being a grade; in practice, in an organizational context, a less detailed rating system would be suf cient and more appropriate. An average PD for each internal grade, rather than estimates of PDs for each borrower, is, in fact, the input which currently drives portfolio credit risk models and capital allocation systems at many best-practice banks; moreover, the banks' own estimates of the PDs associated to each internal grade are the core inputs of the IRB approach for the calculation of regulatory capital requirements proposed by the Basel Committee on Banking Supervision in January 2001 (BCBS, 2001). Average PDs per grade can be considered reliable as long as each grade

5 A. Foglia ± S. Iannotti ± P. Marullo Reedtz: The De nition of the Grading Scales represents an underlying population of borrowers that is relatively homogeneous. 1 The main question in choosing an appropriate grading scale, therefore, is how to achieve an adequate combination between a meaningful differentiation of borrowers according to their level of risk and the required degree of homogeneity among them in each grade. The more granular a bank's grading system, the more likely each grade includes borrowers with a similar level of risk. On the other hand, there is a point beyond which more ne-grained distinctions are no longer meaningful, because raters would not be able to distinguish reliably borrowers that are just one or two grades apart (Tracey and Carey, 2000). Moreover, as noted by Krahnen and Weber (2001), there is no use de ning a large number of rating categories if a bank is not able to back-test consistently, owing to lack of data. According to the requirements speci ed by the Basel Committee in its proposal of January 2001, to be eligible to use the IRB approach banks' risk rating systems must have a minimum of 6±9 grades for performing borrowers and a minimum of two grades for non-performing borrowers. 2,3 Carey and Hrycai (2000) examine at length the properties of various methods used to estimate average default probabilities by grade. They simulate the grade assignments by dividing the [0,1] interval into ve ranges of probability, `such that the simulated grades cover ranges of default probability roughly similar to the actual rates shown in Moody's study for borrowers rated AAA-A3, Baa, Ba, B, Caa1 and riskier'. Using this scale, they evaluate three methods of quanti cation of the loss characteristics per grade by examining the accuracy of estimated average default rates per simulated grade. Evidence of potential problems of bias, instability and gaming is presented. In particular, biased average PD measures may arise as a by-product of the bucketing process inherent in rating assignment; in addition, banks may have an incentive to deliberately distort or game the boundaries of internal rating grades in a manner that reduces average PDs per grade. 1 `The Committee believes that banks adopting the IRB approach should have risk rating systems that effectively distinguish the level of credit risk across the entire spectrum ± from borrowers that are virtually risk-free to those in default. Risk rating systems that have overly broad grade de nitions, which result in borrowers of signi cantly different risk characteristics being assigned the same grade, are not acceptable. Likewise, risk rating systems that materially assign borrowers of comparable risk to different grades are also unacceptable' (BCBS, 2001). 2 The range for the minimum number of grades aims to meet the needs of banks with different lending activities that may use specialized rating schemes for different types of borrowers, products or market segments. Individual supervisors will have discretion in determining whether a bank's risk rating system meets this requirement. However, the minimum of six performing borrower grades and two non-performing borrower grades represents a oor, which cannot be modi ed (BCBS, 2001). 3 A further requirement is that there should not be excessive concentration in any particular grade, speci cally that no more than 30 per cent of the exposures should fall in any one borrower grade. However, a higher degree of concentration might be due to business practice and/or be related to lending to high-quality borrowers; some comments to this proposal note that it could create incentive to migrate exposure to fewer quality grades.

6 426 Economic Notes : Review of Banking, Finance and Monetary Economics Statistical techniques such as cluster analysis may help to identify an objective rating assignment process that can produce reliable measures of average PD for each grade. 4. The Scoring System and the Sample of Rated Borrowers To discriminate between sound and unsound rms, multivariate statistical techniques are often used to produce a scoring function by aggregating several pieces of information on borrower characteristics; for an excellent survey, see Varetto (1999). The most widely used statistical methods are discriminant linear analysis and probit/logit regressions, generally combining individual accounting ratios. The logit analysis, in particular, is used to predict the probability of borrower default. It assumes that the default probability takes a logistic functional form and the score is therefore constrained to fall between zero and one. In the linear logistic model, the dependent variable is the log of the oddratio, which is assumed to be linearly related to the explanatory variables. 4 The performance of the statistical model can be ascertained in two ways. One way is by verifying the classi cation accuracy, that is the ability to identify the sound and unsound rms in the estimation sample. The second way is by verifying the predictive power ex post, by comparing the speci cation prediction with the actual outcome on a different sample (either out-of-sample or out-of-time on the same sample). Classi cation accuracy can be measured by the misclassi cation of failed rms (Type I error), or the misclassi cation of healthy rms (Type II error); overall accuracy is a combination of both. In the framework of the Italian economy, Borgioli (1999) estimates a logistic model aiming at identifying potentially unsound rms on the basis of balance sheet ratios and variables indicating the status of the credit relationships. The balance sheet database is collected from the CERVED Register, the most comprehensive database on Italian corporations, based on nancial statements collected by local Chambers of Commerce. The total number of nancial statements rose from 408,800 in 1993 to around 630,000 in 1999, approximately 80 per cent of the total number of joint stock companies. The nancial statements are classi ed according to the various economic activities of the corporations (11 macrosectors are considered) and are supplemented with other data about the corporations (number of employees, years of economic activity, etc.). 4 The main advantage of the logistic regression is that it does not require restrictive statistical hypotheses regarding the variables. In addition, it is possible to assess the relative importance of the different ratios included in the function, using a simple t-test. The main problem is that an increase/decrease in the probability does not always correspond to the same deterioration/improvement in the economic situation of the rm. It is understated when the probability values lie near zero or one; it is overstated when the probability values lie near 0.5.

7 A. Foglia ± S. Iannotti ± P. Marullo Reedtz: The De nition of the Grading Scales The source of information regarding credit relationships is the Central Credit Register. This database is run by the Bank of Italy for the purpose of supplying aggregate information on individual borrowers' total indebtedness to the banking system. It includes and aggregates information from each bank and nancial intermediary in the system on individual loans above $71,000. The logistic function estimated by Borgioli uses balance sheet variables related to pro tability, liquidity, leverage and nancial structure. In addition to the usual nancial ratios, two indicators of tension in credit lines are included, which are expected to be positively correlated with the default risk. The rst indicator is a yearly average of the quarterly ratio between the amount of credit effectively drawn by the rm and the total credit granted. The second variable is a dummy which is equal to 1 if the ratio lies over 1 at least in one quarter and 0 otherwise. The estimation sample is composed of 3343 rms which `failed' in 1997, i.e. were classi ed among bad debts by a bank for the rst time. Insolvent rms were matched by an equal number of normally operating rms, randomly drawn from the CERVED Register. 5 The performance of the model was also tested out of the sample. The rms were divided into 16 subsets, according to four sectors of activity (manufacturing, constructions, trade and other services) and four geographic areas. For every sample subset, the nal model was selected using a stepwise procedure and excluding all the variables with estimated sign in contrast with a priori expectations. The models that we use in this paper have been estimated on balance sheet data for 1995 and Credit Register data for The introduction of credit variables into the logistic model improves the quality of the estimate. The overall percentage of correct classi cation (using a cut-off point of 0.5) is 72 per cent in sample (71 per cent for safe rms and 73 per cent for failed rms), and 68 per cent out of sample (70 per cent and 66 per cent respectively). From these models, credit risk scores have been computed for an average of 180,000 rms from 1995 to 1998 (credit register data from 1996 to 1999), accounting for around 50 per cent of total loans to the corporate sector. 5 The choice of a balanced sample enables to better separate rms belonging to the two groups and to decrease the variance of the estimates of coef cients; the main disadvantage is that a balanced sample does not re ect the true proportion between unsound and sound rms: when the function is applied out of the estimation sample the resulting score is a measure of individual risk, but it is not per se a probability of default. A second stage of analysis is needed to correct the logit score to take account of the different composition of the estimation sample. See Varetto (1999) for a discussion on the choice of the sample and on possible methods to move from scores to probabilities.

8 428 Economic Notes : Review of Banking, Finance and Monetary Economics 5. The De nition of the Grading Scale using Cluster Analysis Cluster analysis is usually applied to classify individuals/objects into groups on the basis of several characteristics/variables observed for each individual. Text books suggest keeping the number of such variables low ± by using, for instance, principal component analysis ± so as to avoid multicollinearity and operating complexity. Credit scoring systems pre-identify key factors that determine the likelihood of a borrower's default and combine or weight them into a quantitative score. Thus, clustering bank borrowers according to their credit scores is equivalent to using all the available quantitative information on their creditworthiness. We applied the k-means clustering methodology described in the Appendix to bank borrowers scored in the four years from 1995 to 1998, divided into the four sectors of activity. The clustering was repeated for seven, ten and fteen clusters (k ˆ 7, 10, 15). Tables 1a±1c show the seven-, ten- and fteen-cluster solutions for rms belonging to the manufacturing sector; similar results (not shown) are obtained for rms belonging to the other three sectors of activity (construction trade and other services). The tables are divided into two panels. The left-hand panel shows the distribution of the rms belonging to the four sectors for the four years into 7, 10 and 15 intervals approximately equally spaced, by dividing the [0,1] interval into 7, 10 and 15 ranges of values of approximately equal size. The mean values of the p score for each interval are taken as the initial seeds of the cluster procedure. The right-hand panel shows the solutions obtained using the k-means clustering algorithm. Here the mean values of the p score are the nal seeds or centroids for each cluster obtained after the iteration process has converged. The means of the clusters are very stable across the four years for each of the four sectors and for all values of k, a sign of the robustness of the clustering solutions. Table 2 lists the statistics discussed in the Appendix that can help to assess the validity of the results. They suggest that there is a very low within-cluster variability for all the 48 solutions obtained. The R 2 values are all very high, ranging from to The pseudo F-statistics are also very high, even if we cannot attach any statistically signi cant level to them. In particular, for each of the four sectors, the statistics are again very similar across the four years, indicating that the distribution of rms according to their score has remained stable for the period 1995±98. If all the clusters obtained are reliable, how do we determine the number of clusters and, hence, the numbers of grades of a rating system? As mentioned, the within-group sum of squares (and the within-group standard

9 Table 1a: Manufacturing, 7-cluster solution Year Initial seeds selection Cluster solution Interval Sup Inf Mean p Freq. Cum. freq. Perc. Cum. perc. Cluster Sup Inf Mean p Freq. Cum. Freq. Perc. Cum. perc continued overleaf 429

10 Table 1a: (continued ) 430 Year Initial seeds selection Cluster solution Interval Sup Inf Mean p Freq. Cum. freq. Perc. Cum. perc. Cluster Sup Inf Mean p Freq. Cum. Freq. Perc. Cum. perc

11 Table 1b: Manufacturing, 10-cluster solution Year Initial seeds selection Cluster solution Interval Sup Inf Mean p Freq. Cum. freq. Perc. Cum. perc. Cluster Sup Inf Mean p Freq. Cum. freq. Perc. Cum. perc continued overleaf 431

12 Table 1b: (continued) 432 Year Initial seeds selection Cluster solution Interval Sup Inf Mean p Freq. Cum. freq. Perc. Cum. perc. Cluster Sup Inf Mean p Freq. Cum. freq. Perc. Cum. perc

13 Table 1c: Manufacturing, 15-cluster solution Year Initial seeds selection Cluster solution Interval Sup Inf Mean p Freq. Cum. freq. Perc. Cum. perc. Cluster Sup Inf Mean p Freq. Cum. Freq. Perc. Cum. perc continued overleaf 433

14 434 Table 1c: (continued ) Year Initial seeds selection Cluster solution Interval Sup Inf Mean p Freq. Cum. freq. Perc. Cum. perc. Cluster Sup Inf Mean p Freq. Cum. Freq. Perc. Cum. perc

15

16 436 Table 2: Summary statistics for the various cluster solutions Manufacturing Cluster Total STD Within STD R pseudo F-stat F(7, 10) a ± F(10, 15) b n Construction Cluster Total STD Within STD R pseudo F-stat F(7, 10) a ± F(10, 15) b n

17 Trade Cluster Total STD Within STD R pseudo F-stat F(7, 10) a ± F(10, 15) b n Other services Cluster Total STD Within STD R pseudo F-stat F(7, 10) a ± F(10, 15) b n a Compared with F(3, n 10) d.f. at 5% signi cance ˆ 2.6 b Compared with F(5, n 15) d.f. at 5% signi cance ˆ

18 438 Economic Notes : Review of Banking, Finance and Monetary Economics deviation) is by itself an indicator of the minimum value that has been obtained. On the other hand, the F test suggested by Beale and applied to compare the results obtained for k ˆ 7, 10, 15 clusters solutions is never signi cant at the 5% level. This implies that no signi cant improvement is achieved when moving to a higher number of clusters. Therefore, as suggested by statisticians, `interpreting the results from a clustering algorithm is often dominated by personal intuition and insight; the investigator must make sense of the clusters produced'; `cluster analysis is not a purely mechanical process, but has an empirical character which will, in the nal stage, require examination in the light of our general knowledge of the situation'. A nal decision may come from examining the performance of the different cluster solutions as a whole, by comparing the (ex-post) realized default frequencies for each solution. 6. The Simulated Internal Grading System and the Quanti cation of the PD for each Grade We noticed above that the ranges of the p values de ning each cluster are approximately the same across the years; this is true for the 7-, 10- and 15- cluster solutions and for all the four sectors. The stability of the clustering solutions allows us to de ne a single grading scale for each sector; for each grade, the range is de ned by the cut-off values observed across the years. When not entirely equal, the range is de ned by the mean p values of the respective cut-offs for the four years. Table 3 shows for each sector the three grading scales with 7, 10 and 15 grades. It also shows the distribution of borrowers per grade. For the scale with 15 grades, some groups account for only 2±3 per cent of the borrowers. For the scale with 7 grades, the distribution is more balanced without being too skewed: the largest class accounts for 27 per cent of the borrowers; the smallest grades for 6±7 per cent. More nely grained rating systems are preferable in terms of their ability to differentiate among customers for pricing and management purposes. On the other hand, the larger the number of internal grades, the more dif cult it becomes to distinguish the relative riskiness of borrowers in adjacent grades. This is true especially for the least risky borrowers, who do not show any actual or potential problem in repaying the loans. In other words, in implementing an internal rating system, there could be a potential trade-off between differentiation across grades and homogeneity within grades. With a higher number of grades, disparities across borrowers in the same grades are limited and borrowers are homogeneous in each grade. However, the `dissimilarity' or the statistical difference among borrowers in different grades in terms of their relative riskiness could be enhanced when a lower number of grades is considered.

19 Table 3: Three grading scales Grade Sup Inf Average freq. Perc. Grade Sup Inf Average freq. Perc. Grade Sup Inf Average freq. Perc. Manufacturing continued overleaf 439

20 Grade Sup Inf Average freq. Perc. Grade Sup Table 3: (continued) Inf Average freq. Perc. Grade Sup Inf Average freq. Perc. 440 Construction Trade

21 Other services

22 442 Economic Notes : Review of Banking, Finance and Monetary Economics Therefore, when de ning a grading system, the question to ask is not only whether Grade 3 and Grade 4 can be distinguished but also whether the performance of the system as a whole can be improved with ner grading. Historical default data have been used to quantify the default probability for counterparties assigned to each grade, i.e. by computing average default rates from the actual default experience of borrowers in each internal grade over the years (the so-called `actuarial' approach). The default rate for each year is the number of defaults observed in each grade by the end of the year as a share of total borrowers belonging to that grade. 6 For good actuarial estimates, a relative long series of data is needed; this means that the bank should have recorded internal default data for many years, but also that the process underlying the internal rating system should not have changed. With regard to our simulated internal rating system, since accounting data for rms recorded in the CERVED database ± and the resulting scores ± are only available from 1995 to 1998, default rates have been computed for four years. Tables 4, 5 and 6 report the results of the PD quanti cation respectively for 7, 10 and 15 grades, showing the default rate recorded for each grade in the years from 1996 to 1999 and their average; Figure 1 shows the grading scales for the four sectors using seven grades. Table 7 summarizes these results, showing the average PD per grade (the default rates computed by Standard and Poor's for its rating scale are also shown for comparison in Table 8) and the minimum and maximum values observed for each grade in the four years. To test the consistency of the rating scale, one would ideally like to observe average default frequency values which are statistically different across grades. With a suf ciently long time series of actual default rates, encompassing at least an entire economic cycle, this test can be performed by observing: that each annual default rate realization for each grade lies in a range of possible values which uniquely de nes the riskiness of that particular grade that the average default rate is monotonically increasing by grade. With only four years of observation, annual default rate realizations can be in uenced by systematic risk so it is not possible to draw any clear-cut 6 If the logit scoring model were estimated on a sample re ecting the true proportion of failed vs. safe rms in the population, averages of tted default probabilities could have been used directly as the estimate of the PD for that grade. See discussion in section 4.

23 Table 4: PD Quanti cation for 7 Grades Grade Sup Inf Average freq. Perc. DF 1995 DF 1996 DF 1997 DF 1998 PD % (mean) Manufacturing Construction continued overleaf 443

24 Table 4: (continued) 444 Grade Sup Inf Average freq. Perc. DF 1995 DF 1996 DF 1997 DF 1998 PD % (mean) Trade Other services PD% (mean) Manufacturing Construction Trade Other Services

25 Table 5: PD Quanti cation for 10 Grades Grade Sup Inf Average freq. Perc. DF 1995 DF 1996 DF 1997 DF 1998 PD % (mean) Manufacturing Construction continued overleaf 445

26 Table 5: (continued) 446 Grade Sup Inf Average freq. Perc. DF 1995 DF 1996 DF 1997 DF 1998 PD % (mean) Trade Other services