SELECTION OF CONVERSION FACTORS FOR STUMPAGE PRICE COMPARISONS. January 17, 2002

Transcription

1 SELECTION OF CONVERSION FACTORS FOR STUMPAGE PRICE COMPARISONS January 17, 2002 Michael Stone Susan Phelps René Samson Industry, Economics and Programs Branch Canadian Forest Service Natural Resources Canada

2 Table of Contents 1. Introduction 4 2. A Primer on Scaling Methods 5 3. The Conversion Factor Required to Meet the DOC s Intended Use A Comparison of the Available Conversion Factors Further Comment on the Briggs Study The Search for the Origins of the 4.53 m 3 /mbf Conversion Factor A Caveat on What Conversion Factors Can Do Conclusion 37 References 38 2

3 Forward This report was one of a number of reports prepared by the CFS as part of Canada s legal defence during the fourth Canada/US Softwood Lumber Dispute. It formed part of the legal record used in the NAFTA and WTO dispute resolution proceedings. 3

4 SECTION 1 INTRODUCTION 1.1 Background On January 7, 2002, the petitioner in this case, the Coalition for Fair Lumber Imports Executive Committee, filed a report by David G. Briggs titled Department of Commerce s Selection of a Conversion Factor in the Softwood Lumber Case. In the petitioner s report, Professor Briggs criticises the various log-to-log conversion factors previously put forward for use in this case, whether by the petitioner, the respondents or the Department of Commerce ( DOC ) in the preliminary determination. The Briggs Report argues that all of these proposed conversion factors are too low, and that the DOC should instead use a factor of 4.53 m 3 /mbf. However, the DOC has a very specific purpose for which it needs log-to-log conversion factors, and the factor proposed in the Briggs report is entirely inappropriate for this purpose. To understand why, it is necessary to review the appropriate means of developing conversion factors and assess the suitability of the available conversion factors for the DOC s purposes. 1.2 Purpose of the Report The purpose of this report is to: Provide a brief primer on scaling methods and scaling rules. Discuss the DOC s intended use for the conversion factor and thus determine the criteria an accurate conversion factor must have in order to meet the DOC s intended use for the conversion factor. Compare the ability of the available conversion factors to meet DOC s needs. Review the petitioner s submission (Briggs, 2002) that critiques both the conversion factor used by the DOC in its preliminary CVD determination and the conversion factors recommended by the provincial respondents. The report also presents the results of our search for the origin of the conversion factor recommended by the petitioner s study. Some caveats and limitations on what an accurate conversion factor can do in facilitating a cross-border stumpage price comparison are also presented. The report ends with some conclusions. 4

5 SECTION 2 A PRIMER ON SCALING METHODS Although a seemingly simple task conversion between two rules is highly variable. (Briggs, 1994, p. 29) 2.1 Introduction Given the inordinate amount of confusion that the conversion of log scaling measures generates, a brief introduction to scaling methods is called for. This is followed by an explanation of (1) the variation in conversion factors caused by differences in the log scaling rules being converted and (2) the sensitivity of the conversion factors to differences in the characteristics of the actual logs that are being measured. In addition, when cross jurisdiction conversions are being conducted, the conversion factors must account for differences in log measurement conventions and utilization requirements. 2.2 Background on Scaling A tree is a living organism, and as such, each tree is unique in shape and timber characteristics. The trunks of trees are rarely perfectly straight, rarely perfectly round and rarely of constant taper. The shape a tree has at a given age is determined not only by the genetic makeup of the tree, but also by the inherent productivity of the site on which the tree is growing, the number of surrounding trees that are competing for water and nutrients, and the history of pests, diseases, fire and wind damage that may have affected the tree s growth. It is not surprising, then, that the logs cut from the trunks of trees can also vary greatly in terms of size and shape. This variability is what makes scaling, the practice of measuring log volume, such a challenge. Faced with this variability in log shapes, log scalers have developed a plethora of log scaling rules to estimate log volumes. Indeed a U.S. Forest Service publication documents nearly 200 log scaling rules that are or have been used in North America (FPL, 1974). These rules have been developed to meet specific scaling needs at the time the scale was developed and contain assumptions about the shape of the log or the desired portion of the log that is to be measured. These assumptions are made to allow the log volume to be estimated based on as few log measurements as possible. The accuracy of the scale will be determined by how closely the log shape assumed by the scaling rules matches the actual shape of the log being measured. In addition, log scaling rules typically include rules to reduce the estimated log volume to account for loss of recoverable product due to log defects. These defects can include rot, shattered ends, forks, sweep, conk, and twists (see British Columbia (2001a) for example descriptions of defects and volume deduction methods). Scaling rules may also have different conventions for taking measurements of the log when being scaled plus volume rounding practices that can also affect total volume estimates. 5

6 2.3 Board Foot and Cubic Volume Based Scaling Rules Log scaling rules can be broken down into two main variants: board foot log scales and cubic volume log scales. A board foot is a volume 12 inches wide, 12 inches long and one inch thick. Board foot log scales are a product based log measurement system. That is, they were designed to predict the volume of lumber that could be cut out of a given log based on the sawing technology and practices at the time the rules were developed. Cubic volume log scales attempt to estimate the total firmwood content of the log. Board Foot Log Scales Board foot log scales differ in the portion of the log that is assumed to be able to produce lumber, the date of the technology that was assumed to be used to cut out the lumber, and the dimensions of the lumber that would be produced from the log. The three major board foot scales used in the U.S. are: Scribner Decimal C Developed in 1846 by the Rev. J.M. Scribner, the Scribner rule assumes that saws with a ¼-inch kerf are producing 1-inch thick boards that are 4 inches wide or wider. (FPL, 1974, p. 33). Kerf is the thickness of the material removed by the saw blade during the sawing of the log into lumber. This rule further assumes that lumber can only be cut from a cylinder that extends along the axis of the log. The diameter of the cylinder is equal to the log s small end diameter. Thus, this rule makes no allowance for the taper of the log. The wood outside of this cylinder is ignored, as presumably it would have been waste material in an 1846 sawmill. The Scribner Decimal C variant of this rule rounds the estimated board foot log volume to the nearest 10 board feet. Scribner is the dominant scaling rule used in the U.S. west and other areas of the U.S. International ¼-Inch J.F. Clark introduced this rule in 1917 (FPL, 1974, p. 23). The rules assume that lumber one-inch thick is produced with a saw kerf of ¼ inch. The rule accounts for log taper by assuming a taper of one inch per eight lineal feet. The portion of the log being cut out is assumed to be a series of cylinders four feet long. The first cylinder s width is the log s small end diameter with the diameters of successive cylinders increased by ½ inch for every additional four feet of log length. The rule also makes deductions for slabs and edgings. The International is considered by many to be the most accurate of the board foot scaling rules (Briggs, 1994, p. 24) and is the official statute rule in many eastern U.S. states (FPL, 1974, p.25). Doyle This rule, developed by E. Doyle, dates back to at least 1837 (FPL, 1974, p. 18). The rule assumes that a single square cant is being cut from the log. To estimate the size of the cant, the rule first reduces the small end diameter by four inches, irrespective of log s small end diameter, and then reduces the cant volume by 25% to allow for saw kerf and shrinkage. This rule is notorious for significantly underestimating the volume of small logs and also overestimating 6

7 the volume of large logs. The Doyle log rule is reported to be commonly used in the U.S. South (Briggs, 1994, p. 25). Figure 1 graphs the board foot volume estimates under the Scribner Decimal C, International ¼-Inch, and Doyle log scales for a 16-foot long log with an assumed taper of 1 inch in eight lineal feet (data from Nielson et al., 1985 and Briggs 1994). Not surprisingly, the International rule produces the highest volume estimate over most of the log diameter range shown, as it assumes that a greater portion of the log will yield lumber than do the other two rules over this range of log diameters. The Doyle rule, as expected, yields a significantly lower volume estimate at small log diameters. The Scribner Decimal C rule, because it is diagram-based, produces board foot volume estimates that do not increase in smooth steps across log diameters. For example, the Scribner rule predicts that both a five and six inch diameter 16-foot long log will produce 20 board feet of lumber and that a seven and eight inch diameter log would both produce 30 board feet of lumber. International 1/4 Inch Doyle Scribner Board Feet Log Small End Diameter (inches) Figure 1 Comparison of Volume Estimates for Board Feet Log Scales for a 16 Foot Log It is important to note, however, that none of these board foot log scales will yield an accurate estimate of the lumber recovery possible in a modern sawmill (Hartman et al. 1976). 7

8 Cubic Volume Log Scales As noted earlier, cubic volume log scales attempt to estimate the total wood content of the log. The rules typically do not assume that any given product is to be produced from the log. Cubic volume rules differ in the assumed geometric shape of the log implied by the cubic formula used, the points at which log measurements are taken, plus measurement conventions and conventions on the rounding of the volume estimate. The three most common volume formulas used in forest measurement are (FPL, 1974): Smalian The assumed log shape is that of a truncated paraboloid. Required measurements in small and large end diameters (D 1, D 2 ) and length (L). The formula is: 2 2 V = c (D1 + D 2 ) L / 2 where c is a constant equal to if the volume is measured in cubic feet and if volume is in cubic metres. Huber A cylinder is the assumed log shape under this rule, but the cylinder diameter is taken at the midpoint of the log (D m ), which is assumed to produce the average cross section area of the log. The formula is: 2 V = c (D m ) L where c is the constant noted above. Newton This formula can account for the volume produced by the frustrum of a paraboloid, neiloid or a cone. The formula is: V = c (D1 + 4D m + D 2 ) L / 6 where c is the constant noted above. Both FPL (1974) and Briggs (1994) agree that the Newton formula will produce the most accurate estimate followed by the Huber formula and then the Smalian formula. However, the practicality of the first two formulas is limited by the requirement to measure the diameter inside bark at the midpoint of the log. The assumption, under the Huber formula, that the midpoint of the log will provide the average cross section area may also not always be correct. When selecting which formula to use, there will be a trade-off between accuracy and the number of measurements needed. As Hartman et al. (1976, p.6) state: Some trade-off between accuracy and expediency must be made for operational scaling of large numbers of rough logs. Figure 2 shows the estimated cubic volumes for a 16-foot log with a taper of one inch per eight lineal feet. The volume estimates are remarkably consistent compared to the differences in the board foot log rules examined earlier. However, the diagram somewhat overstates the similarity in volume estimates, as the logs were assumed to have a smooth taper. In particular, the Smalian formula would overestimate volumes for logs with large butt swell. 8

9 Smalian Huber Newton Cubic Metres Log Small-End Diameter (inches) Figure 2 Comparison of Volume Estimates for Cubic Volume Log Scales for a 16 Foot Log with a Taper of One Inch per Eight Lineal Feet 2.4 Conversion of Board Foot Log Measurements to Cubic Volume Measurements We now turn to the surprising difficulty in finding a non-controversial conversion factor for translating volumes measured in board foot log scale into cubic volumes. After all, the conversion factor is simply the volume measured in one log scale divided by the volume measured in another log scale. How difficult can it be? As it turns out, very. The first major difficulty in converting board foot scales arises because the portion of total log volume included in a board foot log measure varies both by the log scale chosen and by the characteristics of the logs being measured. This is shown in Figure 3, which shows the percent of total log volume included in the board foot measurement for the three board foot log scales examined earlier. The total metric volume in this example was calculated using the Smalian formula for a 16-foot log and assumed that the log had a taper of one inch for every eight lineal feet. The conversion factor, which is the ratio of cubic meter volume to board foot volume, will decline as the percentage of log volume contained in the board foot measure increases-that is, as the denominator of the ratio increases. This means that the typical small-end diameter of the log sample will greatly affect the conversion factor for that sample. This in turn means that for a conversion factor to be accurate, it must be representative of the characteristics of the logs that made up the total board foot log volume being converted by the conversion factor. 9

10 The percent of total volume included in the board foot measure increases with small-end diameter relatively smoothly for the International and Doyle log scales, but with the Scribner scale, the pattern is highly erratic. The diagram clearly indicates that the conversion factor needed to translate board foot volume into a cubic measurement should vary greatly depending on the typical diameter size of the logs measured under the board foot log scale. The diagram also shows that the board foot log scale used will affect the magnitude of the conversion factor. 80 Percent of Total Cubic Volume Scribner International 1/4 inch Doyle Log Small End Diameter (inches) Figure 3 Percent of Total Cubic Volume Contained in a Board Foot Volume Measure Under Three Board Foot Log Scales Figure 4 plots the metric conversion factors for each log scale across the small-end log diameters shown in Figure 1. Once again, the conversion factor is simply the ratio of the cubic volume to the board foot volume for each board foot log scale. The metric conversion lines are relatively close at large small-end log diameters but diverge significantly at diameters below 18 inches. Note the highly erratic path that the metric conversion line follows for the Scribner board foot log scale. The conversion factor for the Doyle log scale continuously exceeds the conversion factors of the other two board foot log scales. Figure 4 clearly demonstrates that a metric conversion factor is highly sensitive to the board foot log scale being converted. For example, the horizontal dashed line in the 10

11 figure is set at 4.53 m 3 /mbf, the conversion factor recommended in a petitioner s study (Briggs, 2002). The implied average log small end diameter for this conversion factor can be approximated for a given log sample by noting where this line intersects the conversion line for each board foot log scale. Thus, the example conversion factor would imply a volume weighted average small-end log diameter of over 10 inches for the International ¼-Inch scale, approximately 15 to 17 inches for the Scribner Decimal C log scale and over 18 inches for the Doyle log scale. Note that these implied diameters are only applicable to defect free 16-foot logs with a 1-inch taper in eight lineal feet. As will be shown below, the implied diameters can be significantly higher if these assumptions are relaxed. Further, these conversion factors would be for defect-free logs. Defect deductions, as discussed later, can extend the upper range of the conversion factors significantly. Nevertheless, the diagram suggests that unless all of the logs scaled under the different board foot log rules had very large small-end diameters, the averaging of conversion factors across log scale methods would lead to a potentially wildly incorrect average conversion factor. m³/mbf Scribner International 1/4-Inch Doyle Log Small-End Diameter (inches) Figure 4 Comparison of Metric Conversion Factors for Three Board Foot Log Scales for 16-Foot Logs of Different Small End Diameters 11

12 2.5 Sensitivity of Metric Conversion Factors to Average Log Length and Log Taper Metric conversion factors are also sensitive to log length and log taper as shown in Figures 5 through 8. This sensitivity varies with the board foot log scale employed. Figure 5 shows the metric conversion factor for the International ¼-Inch log rules, the most well behaved board foot log scale, for logs 12, 16 and 20 feet in length, with log small-end diameters of 4 to 30 inches and log taper of one inch in eight lineal feet. While this is thought to be the most accurate of the board foot log scale rules, its volume rounding conventions lead to highly erratic conversion factors for small diameter logs. Figure 6 shows the conversion factors for different log lengths and small-end diameters for the Scribner Decimal C log scale. The Scribner log scale provides an even more erratic pattern of conversion factors. Using the example metric conversion factor of 4.53 m3/mbf, the implied volume weighted average small-end diameter of the logs would range from under 12 inches to almost 17 inches, depending on the average log length in the sample For 12, 16 and 20 feet long logs m³/mbf Log Small-End Diameter (inches) Figure 5 Sensitivity of the Metric Conversion Factor for the International ¼-Inch Log Scale to Changes in Log Length 12

13 m³/mbf For 12, 16 and 20 feet long logs Log Small-End Diameter (inches) Figure 6 Sensitivity of the Metric Conversion Factor for the Scribner Decimal C Log Scale to Changes in Log Length Log Taper Figure 7 shows the metric conversion factor for the International ¼-Inch log scale for 16- foot logs for log tapers of 1, 2, 3 and 4 inches for every eight lineal feet of log. Now assume that the example metric conversion factor of 4.53 m3/mbf was applied to a sample of logs with tapers of 2, 3 or 4 inches per eight lineal feet. With these larger tapers the implied volume weighted average small-end diameter of the logs would increase from about 10½ inches under a 1 inch taper to diameters of 15, 19 and 26 inches respectively for the 2, 3 and 4 inch tapers. Figure 8 graphs the conversion factors for the Scribner Decimal C log scale under the same taper assumptions. Larger log tapers amplify the already erratic nature of the conversion factors for this log scale rule. The average small-end log diameters implied by the 4.53 m³/mbf conversion factor for the Scribner Decimal C log scale rule would increase from over 15 inches to 19 inches for a 2-inch taper, 23 inches for a 3-inch taper and 26 inches for a 4-inch taper. Once again the sensitivity of conversion factors to log length and taper discussed above assumes the logs are free of defect. The sensitivity would likely increase for logs containing defects. 13

14 m³/mbf Tapers of 1, 2, 3 and 4 inches per eight feet length Log Small-End Diameter (inches) Figure 7 Sensitivity of the Metric Conversion Factor for the International ¼-Inch Log Scale To Changes in Log Taper m³/mbf Tapers of 1, 2, 3 and 4 inches per eight feet length Log Small-End Diameter (inches) Figure 8 Sensitivity of the Metric Conversion Factor for the Scribner Decimal C Log Scale To Changes in Log Taper 14

15 Averaging Conversion Factors Derived from Different Timber Types These results presented above suggest that averaging conversion factors for logs derived from different timber types could produce a factor that is highly unrepresentative of either timber type. Thus, such a practices should be avoided if accuracy in conversion is required. 2.6 Other Elements of Scaling Practices Simply accounting for the techniques by which log scales calculate log volumes is insufficient for the correct determination of conversion factors. Other elements that will significantly affect an accurate measurement of a cross border conversion factor include: Differences in measurement and rounding conventions. Differences in defect deductions. Differences in utilization requirements. Measurement and Rounding Conventions Log scale rules differ in the way log measurements are taken and the way rounding is applied to both the log measurements and the estimated log volumes. The measurement rules can significantly affect volume estimates. For example, Hartman et al. (1976) in assessing conversion factors for the U.S. PNW state: An important factor which affects the accuracy of all log rules is the scaling procedure used to measure variables such as log diameter and length. Scaling procedures may cause greater variation in log volume estimates than the particular log rule used, particularly in cubic log scaling. (p. 6). Examples of differences in the way measurements are taken between the Scribner Decimal C log scale and the BC metric log scale include: Log lengths in Scribner are recorded as whole feet after allowing for a trim allowance. The allowance is 8 inches for logs 16 feet and shorter and 12 inches for logs longer than 16 feet. Thus a log 41 feet in length would, after trim allowance, be recorded as 40 feet long while a log scaled in BC metric log scale would be recorded as its actual log length measured to the nearest centimetre. Log lengths are measured in a straight line in the Scribner log scale but along the log contour in BC metric log scale. Thus, logs with crook or sweep will be longer in BC metric measurements. Scribner scale measurements of diameters are truncated to whole inches while metric measures are rounded to the nearest centimetre. On average this will mean that Scribner log diameters will be smaller than BC metric diameters. Bruce and Demars (1974) suggest that the Westside Scribner measurement conventions would cause a downward bias in diameter measurements of 0.70 inches for logs 15

16 10 inches in diameter and lower and a bias of 0.75 inches for logs greater than 10 inches. The downward bias for eastside measurement conventions would be 0.20 inches and 0.25 inches for logs 16 feet and under and logs over 16 feet respectively. 1 These are non-trivial biases as cubic volumes increase with the square of the log diameter. Scribner Decimal C log volume measurements are rounded to the nearest 10 board feet while BC metric log volumes are recorded to the nearest m³. Defect Deductions The discussion above has focussed on the measurement of the gross volume of the log. However, for most log scales it is the net volume that is of interest. For example, the objective of the BC metric log scale rule is to estimate the total firmwood content of the log with deduction only allowed for pathological defects, charred wood and cat face. Deductions for sweep, crook, shake, check and split are not allowed. On the other hand, the Scribner Decimal C scale allows for extensive deduction for log forms that would reduce the ability to cut lumber from the log. This is not surprising as the Scribner scale attempts to estimate the amount of lumber that can be cut from a log (albeit cut from the log using 1846 technology). Thus, cross-jurisdiction comparisons need to account for the differences in net volume adjustments made under the different log scales. Simply converting the board foot volume after deductions to metric units could significantly bias the results. Utilization Requirements Utilization requirements refer to both the portion of the trees in a stand that must be taken during the harvest and the portion of the tree trunks that will be included in the volume measurement. For example, in the interior of BC the close utilization standard requires the harvest of all conifer trees with a diameter at breast height (DBH) of 17.5 cm (7 inches) or greater and the harvest of all lodgepole pine trees with a DBH of 12.5 cm (5 inches) or greater. The portion of the trunk harvested is from a 0.3 metre (11.8 inch) stump height to a 10 cm (4 inch) top. Utilization standards in other provinces can be even more stringent. Utilization standards in the U.S. tend not to be as stringent as in Canadian provinces. A six-inch top diameter is a common U.S. harvest requirement. For example, that the mean log butt diameter reported by Quebec was 15.7 cm (6.18 inches) (Quebec, 2001). This is only slightly larger than the typical U.S. minimum top diameter. This means that for a given stand, one jurisdiction may harvest a greater volume of timber than would another jurisdiction. Thus, differences in utilization standards must be accounted for in determining an appropriate inter-jurisdictional conversion factor. 1 As logs do not have perfectly circular ends, the log diameter is taken as the average of the long and short axis diameters. On the Westside, the convention is to truncate both measures before the average is taken. If the average is not a whole number it is again truncated. On the eastside, the diameters are rounded to the nearest inch and the average is then truncated (Hartmann et al. 1976). 16

17 2.7 Effects of Changing Log Quality Over Time A final point to be made in this primer on scaling and conversion factors is the need to use a current conversion factor. As noted earlier the conversion factor is sensitive to the diameter, length and taper of the logs used to determine the conversion factor. If an old conversion factor were used, that was based on timber sizes different that the timber sizes found today, then inaccurate volume conversions would result. The need for current conversion factors would be clearly be required if there were some trend in timber size and timber characteristics. That there has been a trend towards smaller diameter timber over the last century would be difficult to dispute. For example, see the analysis of Constantino and Haley (1988) on trends in wood quality in coastal BC and the U.S. Pacific Northwest Westside, or the discussion by Waggener and Fight (1999). As the old-growth forests in timber producing regions have been harvested the forest industry has moved onto the smaller timber sizes available from new-growth forests. At the same time, as the biggest and best old-growth timber was harvested first; the remaining old-growth harvest has generally been of lower quality and size. 2.8 Summary This section has described some of the details of the more common board foot and cubic volume log scales used in North America. The difficulty in converting board foot measures to cubic volume measures arises because: The percentage of total log volume included in a board foot scale varies significantly by log size and by board foot log scale chosen. The conversion factors are sensitive to log length and log taper. When inter-jurisdictional volume comparisons are made the conversion factor must account for differences in log measurement and rounding practices plus the differences in the allowances made for log defect. Differences in utilization standards can also significantly affect conversion factors used in inter-jurisdictional comparisons. The discussion above has shown that it would be impossible to find a single conversion factor that could be used in all circumstances. Instead an accurate conversion factor must account for the all of the factors noted above and therefore must be tailored to the specific circumstances under which the conversion factor will be used. Anything else will potentially leave any given conversion factor open to serious inaccuracy and thus misuse. Finally, current conversion factors must be used in order to reflect the size distribution of the current log profile. Use of historical conversion factor is highly questionable and becomes more questionable the older the source of the conversion factor. 17

18 3.1 Introduction SECTION 3 THE CONVERSION FACTOR REQUIRED TO MEET THE DOC S INTENDED USE The DOC is undertaking a cross-border comparison of stumpage prices in selected U.S. states to stumpage prices in Canadian provinces. Note that the DOC is attempting to do a number of regional stumpage comparisons, not one national stumpage price comparison. Although there are a great number of analytic obstacles to making such comparisons, to do these comparisons with any accuracy at all, the DOC must first convert the average stumpage price for a given state measured in $/mbf as measured according to the scaling and utilization practices of that state into $/m³ as measured according to the scaling and utilization standards of the Canadian province being investigated. (Alternatively, the DOC could make the converse comparison, by converting Canadian provincial stumpage prices into the equivalent price in the relevant U.S. states.) 3.2 Criteria for Selecting Conversion Factors To achieve the goal set out by the DOC for itself, the conversions factor used for each state must have the following characteristics It must be a regional conversion factor not a national conversion factor. Given the abundance of different board foot log scale measures used in the U.S. and the differences in scaling practices employed in each state and Canadian province it would be impossible for one continental average to accurately translate stumpage prices measured in a given state into equivalent stumpage prices measured in the Canadian province being investigated. The conversion factor must be current. The conversion factor must represent the current scaling practices and utilization standards employed in the state and province being compared. It should also be based on the current size of timber being harvested. Basing the conversion factor on empirical studies conducted when scaling practices and utilization standards were different would bias the conversion factor. Similarly basing the conversion factor on log volume measurements of logs that are not representative of the current log profile would again bias the conversion factor. The conversion factor must account for difference in the scaling practices of the jurisdictions being compared. The board foot log scale measures employed by each state vary, as do the states procedures for taking measurements from the logs. Canadian scaling practices and utilization standards, while more uniform, also vary between jurisdictions. The conversion factor must account for difference in the utilization practices of the jurisdiction being compared. That is if one jurisdiction has more stringent timber utilization standards than does the other jurisdiction, then for the same stand one jurisdiction would bill stumpage on a greater volume of timber than would the other jurisdiction. 18

19 The calculation of the conversion factor must be empirically verifiable. That is the procedures used in calculating the conversion factor must be transparent and open to scrutiny. 3.3 Measuring the Ideal Conversion Factor The ideal conversion factor required for the DOC s purposes could in theory be estimated. This would be done in the following steps: A sample of timber sales that are representative of the sales used to calculate the state s average stumpage price would be selected. The timber on these sales would then be harvested according to the more stringent of the two utilization standards of the state and province to which the stumpage prices are being compared. The harvested timber would then be dual scaled according to the scaling practices of both the state and the respective Canadian province. The logs harvested according to the most stringent utilization standard of the state and province being compared would be pencil bucked to make them representative of the utilization standard of the less stringent jurisdiction. 2 To calculate the conversion factor the total volume of all the sample timber sales as measured by the provincial scaling and utilization practices would be divided by the total scale volume, as measured by the state s scaling and utilization practices. 3.4 A Practical Conversion Factor While this procedure is theoretically feasible, it is very different in practice. After all, what would motivate a harvester in one jurisdiction to harvest timber in that jurisdiction by the utilization standards of another jurisdiction and then dual scale it? For a government agency to do it is made more difficult by the time period allowed under the DOC s investigation deadlines. Given the difficulty of calculating an ideal conversion factor, the DOC must now select the factors that most closely approximate the five criteria described earlier. Three sets of conversion factors are available for the DOC. They are: The province-specific conversion factors provided to the DOC by Canadian provinces. The single conversion factor used by the DOC in its preliminary CVD determination. The single conversion factor proposed in the petitioner s study conducted by Professor Briggs (Briggs 2002). 2 Pencil bucking refers to the practice of considering a large log as consisting of two or more segments and measuring the log at points at which the log had been imaginarily bucked into shorter logs. 19

20 Each of these conversion factors is described below and assessed as to its ability to meet the criteria the DOC needs in order to convert stumpage prices measured in $/mbf to stumpage prices measured in $/m³. 20

21 SECTION 4 COMPARISON OF THE AVAILABLE CONVERSION FACTORS 4.1 Introduction This section provides a comparison of the three sets of conversion factors available to the DOC in conducting its regional comparison of stumpage price in provinces and bordering U.S. states. The section also evaluates the three sets according to the criteria identified earlier for the accurate conversion factor of U.S. stumpage rates measured in $/mbf to $/m3 measured in the comparison province s log scale. 4.2 Province Specific Conversion Factors As part of the CVD investigation the provinces of British Columbia, Alberta, and Saskatchewan have undertaken dual log scaling studies in order to derive accurate log scale conversion factors. These factors will allow accurate translation of the stumpage prices in bordering states into stumpage prices measured in the appropriate volume basis. Quebec estimated an appropriate conversion factor through analysis of log size profiles. In addition, Ontario has recommended the use of the log scale conversion factor employed in Minnesota, one of the states whose stumpage prices Ontario is being benchmarked against. The basis of these conversion factors is reviewed below. British Columbia-Washington Cross-Border Comparisons Different dual scaling studies were conducted by H&W Saunders Associates Ltd. and Wesley Rickard Inc. (2001) to provide conversion factors for comparing coastal British Columbia to Western Washington and the interior of British Columbia to Eastern Washington. The results and methods of these cross border studies are given below. Coastal BC to Western Washington Comparison Two firms provided dual log scale data on a business proprietary basis. One firm was a BC log company that dual scales in both British Columbia metric scale and in Scribner Decimal C scale prior to shipping. The other firm was a Washington State firm that provided summary data documenting its average mbf to m³ conversion factors by species and quality for its Western Washington timber operations during calendar year The report estimated species-specific conversion factors. However, two average conversion factors, based on the species harvest volume distribution in BC were presented for converting western Washington Scribner log scale to coastal BC log scale. The first 6.99 m 3 /mbf accounts for the log grade distribution of Washington State Department of Natural Resources bid volumes and the second, 6.89 m 3 /mbf, accounts for the log grade distribution of Washington State Department of Natural Resources cut volumes. 21

22 Interior BC to Eastern Washington Comparison Details of the Interior study include: Ministry of Forests staff selected mills in the Kamloops and Prince George areas that would approximate the species profile for the interior region of BC. The sample unit was one truckload and a total of 40 loads containing a total of 8,173 logs were included in the study. The loads were dual scaled in Scribner board feet and in m 3. The Scribner scaling was done according to Eastern Washington practices using Scribner Decimal C East Side Short Log Rule to a 5-inch top utilization. Metric scaling was done in accordance with BC metric scaling rules. Scalers from Pacific Rim Log Scaling Bureau Inc. conducted the Scribner scaling. Mill log scalers conducted the original metric scales with BC Ministry of Forests scaling staff check scaling the original metric log scale. Where actual log bucking was different from eastern Washington practices the original log was reassembled and pencil bucked to eastern Washington practices. This ensured that utilization and measurement practices in eastern Washington were taken into account. Sample loads were weighted by mill lumber production capacity as a proxy for mill lumber consumption. Species-specific conversion factors were estimated. A volume weighted average conversion factor based on the species composition of the BC interior harvest was then calculated. The estimated average conversion factor for converting eastern Washington Scribner log scale to interior BC log scale was 6.66 m 3 /mbf. As with the coastal BC conversion factors, this factor is an average of species specific conversion factors weighted by the BC Interior harvest by species. Alberta-Montana Cross-Border Comparison Details of the Alberta dual scaling study can be found in Appendix A to KPMG (2001b). Summary points include: A sample population was randomly selected from Alberta forest companies. These companies represented 85% of the lumber production capacity in the province and were located in all key forest regions of the province. Sampling intensity was one load per 50 mmbf of sawmill lumber production capacity. Loads were chosen from current delivered timber or randomly picked from the log storage deck. Loads sampled from the log storage deck were chosen to be representative of the mill s delivered log profile. Loads were selected to have a minimum of 135 trees. Over 7,500 trees were scaled. Sample loads were both Crown timber and green timber only. 22

23 The loads were dual scaled in board feet using Scribner Decimal C East Side Short Log Rule and in m 3 using Alberta log scaling rules. Under Alberta scaling rules cubic volumes are calculated using the Smalian formula with provincially developed rules for defect deduction. Scalers from the Pacific Rim Log Scaling Bureau Inc. of Tacoma, Washington conducted the Scribner scaling. The scaling conducted by the Alberta scaling rule was performed by independent provincial scaling contractors. The volume weighted average conversion factor estimated by the dual scaling study was 8.51 m 3 /mbf. The report notes that one of the major differences in the two scaling rules was the allowance made for tree defect. Under the Scribner rules 19% of the total timber volume would have been treated as cull while only 1.83% was recorded as cull under Alberta log scaling rules. This highlights the points made earlier in Section 2 about the need to account for different utilization standards when estimating cross-jurisdiction conversion factors. Saskatchewan-Montana Cross-Border Comparison The Saskatchewan study was conducted by KPMG (2001a). Details of their study include: A random sample of logs delivered to six Saskatchewan sawmills during the period September to October 2001 was chosen. The capacity of these six sawmills represented 90% of the total lumber production during the period of investigation. Sampling intensity was one load per 50 mmbf of sawmill lumber production capacity. An average load was defined as approximately 150 trees. Sample loads were Crown timber only and were green timber only. The loads were dual scaled in board feet using Scribner Decimal C East Side Short Log Rule and in m 3 using Saskatchewan log scaling rules. Under Saskatchewan scaling rules cubic volumes are calculated using the Smalian formula with provincially developed rules for defect deduction. Scalers from the Pacific Rim Log Scaling Bureau Inc. of Tacoma, Washington conducted the Scribner scaling. The scaling conducted by the Saskatchewan scaling rule was performed by both Saskatchewan government and sawmill scalers. Based on the results of the dual scaling exercise the study estimated a volume weighted average conversion factor of 8.62 m 3 /mbf. As in the Alberta study the report notes that one of the major differences in the two scaling rules was the allowance made for tree defect. Under the Scribner Rule 21.4% of the total timber volume would have been treated as cull while only 0.6% was recorded as cull under Saskatchewan s log scale rules. 23

24 Quebec Quebec analyzed the conversion factor problem by examining four log diameter class distributions (Del Degan, Massé et Associés Inc, 2001b). Details of the study include: The log diameter classes were 4, 5, 6, 7, 8, and 9 centimetres. The log volumes for each diameter class were determined assuming the logs were sound and defect free. Logs were assumed to be 16 feet 8 inches long with a 1 percent taper. The log volume was calculated using the Quebec metric log scale, the International ¼-Inch log scale and the Scribner Decimal C log scale rules. The four log diameter distribution scenarios used in the analysis are given in the table below. Scenario A skewed the log distribution to the lower log diameters while scenario D skewed the distribution towards the higher log diameters. Scenarios B and C distribution were between A and D with B closer to A and C closer to D. Summary results for the conversion factors are given in the table below. The report states that the actual Quebec log distribution would range from those of scenario B to C. Thus the authors conclude that a Scribner log scale conversion factor for Quebec should be in the range of 6.75 to 6.90 m 3 /mbf. A separate scenario analysis was also conducted by centimetre log class. The conversion factor range using this more accurate log diameter distribution was from 9.02 to 9.32 m³/mbf. This is close to the results reported by Alberta and Saskatchewan. Quebec Scenario Analysis Scenario Log Distribution (%) by Top End Diameter Class (in.) m 3 /mbf Int. 1/4 Scribner A B C D This exercise, while taking account of the methods of log volume calculation, would not account for differences in defect deductions. In the Alberta and Saskatchewan studies these were shown to have a major impact in increasing the metric conversion factor. Ontario Ontario did not undertake its own log scale conversion study. Instead it recommends the use of the conversion factor for the State of Minnesota, one of the states being used to benchmark Ontario stumpage prices. 24

25 Assessment of the Recommended Provincial Conversion Factors The scaling studies of British Columbia, Alberta and Saskatchewan provide conversion factor estimates that are regional, current and account for differences in scaling methods, rules, timber profiles and utilization requirements. The Quebec estimate is regional and accounts for differences in scaling methods and timber profile. Ontario s recommendation for the use of a Minnesota state conversion factor at least provides a regional conversion factor. 4.3 The Conversion Factor Used By the DOC in the Preliminary Determination The DOC conversion factor of 5.66 m 3 /mbf was taken from a U.S. International Trade Commission report (U.S. ITC, 1982). That report in turn considered an analysis of conversion factors for coastal British Columbia and Washington State conducted by Price Waterhouse in The DOC in its preliminary CVD determination uniformly applied this factor across Canada. While it was a regional estimate for coastal BC, its application across the rest of Canada is dubious. It is also not a current estimate; instead it is close to thirty years old. The ITC report identifies some additional limitations on this figure. Both the petitioner and respondents have criticized the conversion factor s lack of validity. 4.4 The Briggs Recommendation In a report prepared for the petitioner, Professor David Briggs criticizes the DOC s use of a 5.66 m 3 /mbf conversion factor in its preliminary CVD determination (Briggs, 2002). Instead he advocates the use of a 4.53 m 3 /mbf conversion factor. He does not empirically estimate this conversion factor; rather he promotes it because it is used by leading forest product analysts and institutions throughout the world as a continent-wide conversion factor (p. 13). This conversion factor Briggs claims will account for multiple local log rules, species mix and timber quality across North America. The main premise of Briggs recommendation is that the DOC, in its comparison of U.S. and Canadian stumpage prices, requires a continent-wide average conversion factor. This is a startling conclusion given that the DOC is undertaking a number of regional stumpage price comparisons and not a national comparison. As such, appropriate regional conversion factors are required, not a single national average. Even if we were to mistakenly accept the author s assertion that a continent-wide conversion factor is required, the report would fail to meet the aim set out by its author. The report states, The main issue in developing an appropriate, current national average conversion factor is to calculate a weighted average based on the percentage of the total U.S. timber harvest scaled by these systems (Briggs, 2002, p. 5, emphasis added). Yet nowhere in the study is the recommended conversion factor shown to be such a weighted national average and nowhere is it shown that the conversion factor is current. Indeed, as will be shown below, the conversion factor is incredibly dated. Thus, the author has failed to meet criteria he himself set out for developing an appropriate conversion factor. 25

26 Given the importance of an accurate conversion factor in the DOC s stumpage price comparisons the origin of the recommended 4.53 m 3 /mbf conversion factor was sought. The startling conclusion of this search, which is detailed later in this report, is that no empirical basis for the conversion factor can be found. Assessment of the Briggs Conversion Factor The conversion factor recommended by Briggs fails to meet any of the criteria necessary for the DOC to accurately convert stumpage prices from one U.S. state to the volume equivalent stumpage price of the Canadian province being studied. The conversion factor does not account for differences in utilization requirements in the jurisdictions being compared, it does not account for differences in scaling practices, it is not current, it is not a regional conversion factor, and its estimation cannot be empirically verified. 26

27 5.1 Introduction SECTION 5 FURTHER COMMENTS ON THE BRIGGS STUDY Some of the observations made in Briggs (2002) are open to question. A few of these observations are discussed below. 5.2 Specific Comments Biases in the Use of the Smalian Formula in the Calculation of Cubic Volumes The author s discussion of potential measurement biases when using the Smalian formula for cubic measurement is entirely moot. This is because the purpose of the conversion factor is to compare stumpage prices in one log scale to stumpage prices in another log scale. It is not to estimate the actual cubic volume. As long as each province s log scaling is consistently measured, which they are, then any over- or underestimate of actual cubic volume is totally immaterial. It is only the conversion to the log scale on which the provincial stumpage is billed that is important. Criticisms of the DOC Preliminary Determination Conversion Factor Briggs cites Haley s (1980) use of a 5.24 m 3 /mbf conversion factor in a study comparing stumpage prices in the PNW and the BC coast as further evidence that the DOC conversion factor is an overestimate of the needed conversion factor. However, Haley s 22 year-old paper simply assumes a conversion factor of a 5.24 m 3 /mbf; it does not estimate the conversion factor nor does it cite a source for the conversion factor. As such there is no basis for the acceptance of this factor as representative of a current conversion factor. Comments on Quebec s Findings In reviewing a Quebec study (Del Degan, Massé et Associés Inc, 2001a), Briggs incorrectly suggests that Quebec uses a conversion factor of 4.81 m³/mbf. In fact the Quebec study uses a conversion factor of m³/mbf for its estimates and states that this is a conservative (i.e. low) estimate. Only on page 44 in Tables 14 and 15 of the study does it use the Maine Forest Service conversion factor of 4.82 m³/mbf (not 4.81 m³/mbf) for showing Maine exports of timber and the volume of timber processed in Maine. Indeed the study cited by Briggs is not Quebec s analysis of conversion factors. Instead, the conversion factor is provided by Del Degan, Massé et Associés Inc. (2001b) as described in earlier in Section 4. 27