An Analysis of Auction Volume and Market Competition for the Coastal Forest Regions in British Columbia

Transcription

1 An Analyss of Aucton Volume and Market Competton for the Coastal Forest Regons n Brtsh Columba Susan Athey, Peter Cramton, and Allan Ingraham 1 Market Desgn Inc. and Crteron Auctons 0 September 00 The B.C. Mnstry of Forests s consderng the mplementaton of a package of complementary reforms to mprove market performance and competton n the Brtsh Columban tmber ndustry. The key feature of these reforms s that a porton of Crown owned tmber wll be sold at aucton, and those aucton prces shall be used to determne stumpage rates for tenured tmber. Ths process s known as the Transacton Evdence Prcng System (TEPS). The TEPS system wll be loosely based on the current Small Busness Forest Enterprses Program (SBFEP), where loggers compete for auctoned tmber comprsng approxmately 6.5 percent of the volume n Brtsh Columba. Brtsh Columba s dvded, geographcally, nto a coastal area and an nteror area by a seres of mountan ranges. Ths creates two dstnct tmber markets the Coast and the Interor. Steep slopes and hgh qualty tmber domnate the Coast, whle the Interor s characterzed by more shallow terran and tmber that vares substantally n qualty. Tmber extracton on the coast can be costly upfront because extracton on a mountansde requres cable yardng or even helcopter removal. But log transportaton n the Coast s often cheap, because logs can be barged f they are close enough to a major waterway. In the Interor, ground skdder extracton s frequent, and s much cheaper than cable or helcopter removal. Thus, upfront extracton n the Coast s, on average, more expensve than n the Interor. Almost all logs n the Interor, however, must be hauled ther entre travel dstance from the feld to the mll, ncreasng the transportaton costs n the Interor relatve to those n the Coast. Also, an actve log market exsts n the Coast, whereas almost all logs n the Interor move drectly from the feld to a lumber or pulp mll. Therefore, the market n the Coast s vastly dfferent from the market n the Interor. Because of the dfferences between the Coast and the Interor, careful attenton must be pad to how these dfferences wll affect the mplementaton of TEPS. In partcular, the volume of auctoned tmber that s requred to ensure a precse average stumpage rate n the one area may dffer from that whch s necessary n the other area. Also, competton n one area may dffer from competton n the other area. If competton n the Coast s much lower than competton n the Interor, then the regresson specfcaton used n the Coast could have dfferent effects on the ablty of certan frms to exercse market power than t would n the Interor. We addressed necessary aucton volume and dstrct level competton for the Interor n our paper, Aucton-Based Tmber Prcng and Complementary Market Reforms n Brtsh 1 Susan Athey s Assocate Professor of Economcs at Stanford Unversty and a Prncpal of Market Desgn Inc. Her research focuses on aucton theory and the statstcal analyss of aucton data. She has publshed on a wde range of topcs n ndustral organzaton, ncludng market domnance and colluson. Peter Cramton s Professor of Economcs at the Unversty of Maryland and Presdent of Market Desgn Inc. He has advsed numerous governments on market desgn n energy, telecommuncatons, forestry, and the envronment. Hs research focuses on auctons, barganng, and market exchange. He has publshed many artcles on aucton theory and aucton practce n major journals. Allan Ingraham s Vce Presdent at Crteron Auctons. Hs areas of expertse are aucton desgn and strategy, detecton of bd rggng, ndustral organzaton, and econometrcs

2 Columba. Here, we address those same ssues for the Coast. We begn by revewng the Coast regresson specfcaton as t exsts currently n the SBFEP system. We then analyze the aucton volume that s necessary to produce statstcally accurate average tmber prces on the Coast. An analyss of local competton and ts role n regresson specfcaton follows the aucton volume analyss, and we conclude wth a summary of our fndngs. 1 REGRESSION SPECIFICATION Currently, the Mnstry uses a three-step method to estmate the value of a tmber stand that s to be let at aucton. The frst step s to predct the market prce of tmber usng an ordnary least squares (OLS) regresson, but substtutng the average number of bdders n the regresson sample rather than the actual number of bdders n the aucton. Ths estmated market prce s then used to predct the ex-ante number of bdders that was expected to enter the aucton. In the thrd step, the expected number of bdders s used to predct the market prce usng the regresson equaton from the frst step. The Mnstry uses ths three-step process to correct a perceved under-predcton of the true stumpage rate at aucton that t found when usng a one-step OLS model. Ths s worthy of note, because n future trade negotatons wth the Unted States, the U.S. Industry s bggest justfable concern wth tmber prcng n Brtsh Columba s that a prcng system mght lead to stumpage rates that are based downward. However, the bas that the Mnstry found was more lkely the result of the regresson specfcaton choce and the representatveness of the aucton sample. A smpler one-step method may be less prone to bas when those problems are corrected. It wll be mportant to show that a tmber prcng system accurately predcts the average prce of future auctoned stands, so that the average prce of B.C. tmber exported to the Unted States reflects market prces. If the sample of auctoned tracts s representatve, then a one-step regresson cannot lead to bas n the average predcted prce. Of course, gven a partcular sample, the estmated regresson lne may be dfferent from the true regresson lne. The larger the sample, the more precse s the estmate of the true relatonshp between sale characterstcs and market prces. The Mnstry s current Coast specfcaton uses a sample of far fewer observatons than the Interor specfcaton. Smply ncreasng the sample sze (.e. ncreasng the aucton volume from 6.5 percent), and payng close attenton that the sample s representatve of the populaton of stands, mght mprove the predctve power of a smple one-step OLS regresson. Also, careful attenton should be pad to possble outler stands that exst n the current dataset. When expandng aucton volume, the extent that extreme tracts (say, hgh-volume tracts) are present n the aucton sample should reflect ther prevalence n the tracts that wll be extracted from longterm tenures. The current Coast specfcaton wth the current sample sze leads to nosy results. Increasng the regresson sample wth hstorcal data does not mprove upon those results. When one ncludes sales datng back to 199 (wthout changng the specfcaton), the standard devaton of the resduals ncreases. The move to the Market Prcng System n 1999 surely contrbutes to ths result, and n the future, outcomes are more lkely to be comparable across years. Nevertheless, because ncludng the hstorcal data does not mprove the estmaton, one can conclude that, at least ntally, larger aucton volume n a gven year n the Coast s requred. Before proceedng wth an analyss of how ncreasng the aucton volume can mprove precson, we frst llustrate how outlers and specfcaton choce can produce msleadng results n a gven sample. Under the current specfcaton, n both the stumpage equaton and the number of bdders equaton, volume enters, ether drectly or ndrectly, through the varables - -

3 volume 1000 and ( volume 1000), where volume s the total conferous cruse volume. The volume varable, however, contans one large outler relatve to the rest of the sample. The maxmum value of volume 1000 s 140.8, whle the second largest value s only If a researcher were to estmate a one-step regresson wth volume 1000 and rght-hand-sde, she would fnd that ths one outler drves the coeffcent on ( volume 1000) on the ( volume 1000). To see ths effect most clearly, recall that the effect of ( volume 1000) on bds, condtonal on other covarates, can be calculated n two ways. One way s to run a regresson of bds on ( volume 1000) and other covarates, and examne the estmated coeffcent on ( volume 1000). An equvalent way to evaluate ths effect, but one that s easer to depct graphcally, requres a seres of three regressons. Frst, bds are regressed on other covarates, and the resduals are obtaned. Second, ( volume 1000) s regressed on other covarates, and the resduals are obtaned. Thrd, we regress the resduals from the frst regresson on the resduals from the second regresson. The latter regresson tells us how the part of bds unexplaned by other covarates depends on the part of ( volume 1000) unexplaned by other covarates. Ths regresson s easer to depct graphcally, because t bols down to the relatonshp between two sets of resduals, rather than ncludng all other covarates. Fgure 1 llustrates exactly ths relatonshp usng an added varable plot that s, a scatter-plot of the two sets of resduals graphed wth the correspondng regresson lne. Wth ether of these two methods, we can then examne the costs and benefts of ncludng the addtonal varable n the regresson, as well as evaluate our chosen functonal form

4 Fgure 1. Added Varable Plot Bd Regresson Resduals y = x - 9E Volume Regresson Resduals Fgure 1 llustrates graphcally that a sngle data pont can drve the estmated relatonshp between two varables. Ths does not mean that the estmated coeffcent on ( volume 1000) s naccurate, but t does cause reason for concern. Large tmber stands should be n the regresson because those stands must be prced on tenured lots, and these stands convey valuable prcng nformaton. However, large stands should only affect the average tmber prce to the extent that the frequency wth whch they are sampled concdes wth ther exstence n the populaton. Furthermore, when there are large gaps n the dstrbuton of a varable lke volume, the chosen functonal form wll dramatcally affect predctons. As the fgure llustrates, fttng a sngle lne through these observatons wll affect predctons dramatcally for both the lowvolume and hgh-volume tracts. If the true relatonshp between ( volume 1000) and bds s lnear, then there s stll the problem that the estmated slope of the lne s hghly senstve to one datapont. (Antcpatng ths, frms could have an ncentve to manpulate bds n outler sales.) Perhaps an even more serous problem s that there s no reason to beleve that the relatonshp s lnear. The predcted bd for volumes n a mddle range (where there s no data) s determned entrely by extrapolaton. Fttng a parabola or a cubc to these ponts would yeld drastcally dfferent predctons for volumes n the mddle range. Thus, f predctons wll be requred n that range, functonal forms n such a case should be chosen based on some pror nformaton. Overall, t s much more desrable to select a sample that s representatve, so that there are observatons of auctoned sales throughout the range where predctons are needed. One must therefore ensure that the sample s representatve of the populaton, and that a small group of stands s nether over-represented nor under-represented n the sample. In ths scenaro, two - 4 -

5 solutons exst. Frst, f the regresson wll be used to prce but few stands wth characterstcs smlar to those of the outler, then the outler should be omtted. However, f many hgh-volume stands are to be prced, then more stands need to be auctoned n that range. The set of auctoned stands wll then be representatve. In the latter case, f there are two clusters of volume, low and hgh volume, one should not attempt to ft a sngle lne through both clusters. A more flexble functonal form would be superor. However, the mplcatons of that functonal form for out-ofsample predctons should be carefully examned. For example, f observatons are clustered nto groups, we should probably estmate a separate relatonshp for each cluster, mplemented by ncludng dummy varables for ranges of volume and nteractng the volume varable wth a dummy varable for the range. Wth ths approach, the analyst s forced to choose how to extrapolate n regons wth lttle data. Usng pror nformaton, the moderate volume sales must be grouped ether wth low or hgh-volume stands, and the functonal form should be examned to be sure those (rare) sales would be predcted n a sensble way. AUCTION VOLUME To determne the mnmum aucton volume that wll produce an accurate average tmber prce wth a reasonable level of statstcal confdence, we perform a Monte Carlo study of selecton from a populaton of tmber stands. We assume a true stumpage equaton, and then vary the sample volume to determne the ncremental beneft n statstcal precson that comes from more auctoned tmber. For varables that look as though they are normally dstrbuted, we use the jont dstrbuton of those varables n the Coast SBFEP dataset to generate our populaton. For varables such as helcopter extracton volume or cable yard volume, where an assumpton of normalty s not justfed, we apply a frequency table of the slope varable to dfferent categorcal values of the relevant extracton method. Fnally, we use a two-equaton model to depct the true workngs of the market. In partcular, we assume that stumpage rates are determned by relevant value and cost varables, but that the level of competton s also determned value specfc varables and a random cost of enterng the aucton. Thus, we post the followng model: (1) () log( Bdders ) = a + a changevlm + a HemlockBalsam + a Slope + a Hel a Cable + a Haul + ε 5 6 Bd = b + b Prce + b OperCost + b DevCost + b VolPerHect b log( Bdders ) + b Volume + u 5 6 A reduced form for the stumpage equaton can then be calculated by substtutng the number of bdders varable from equaton 1 nto equaton. We now descrbe the process by whch we generate the random dataset. For varables data that appear to be roughly normal (.e. mound shaped), or where transformatons of those varables appear normal, we generate data from a jont normal dstrbuton usng the approprate emprcal correlaton matx. Table 1 contans ths matrx. Prce Change VLM TABLE 1. CORRELATION MATRIX FOR NORMALLY DISTRIBUTED VARIABLES Prce 1.0 Change VLM Hem- Balsam Slope log(dev Cost) log(op Cost) Vol per Hectare log (Haul) log (Vol) - 5 -

6 Hem- Balsam Slope log(dev Cost) log(op Cost) Vol per Hectare log (Haul) log (Vol) After generatng a seres of jont-randomly dstrbuted varables wth the above correlaton matrx and zero mean and varance of one, we then adjust each varable for ts mean and varance n our dataset. We then generate the hel-extracton and cable-yard varables based on ther frequency dstrbutons wth varyng degrees of slope. We break the slope nto quadrants, and then plot the frequences wth whch cable-yardng accounts for 0 percent, 100 percent, or some ntermedate percent of total extracton. We do the same for hel-extracton. We then create 0/1 varables for hel and cable extracton based on the frequences seen n the regresson sample for the 0/1 extracton proportons. When our probablty rule tells us that one of the extracton methods should have an ntermedate value (between 0 and 100 extracton by that method), we sample from a truncated normal dstrbuton centered at 0.5. We perform ths procedure based on frequences over the four slope quadrants: 0 to 4 percent grade, 5 to 49 percent grade, 50 to 74 percent grade, and 75 to 100 percent grade. Ths process mantans the relatonshp between slope and extracton method (steeper slopes requre more specalzed means of extracton) whle takng nto consderaton the unque characterstcs of the hel and cable-extracton varables. To generate our populaton dataset, we assume approxmately 1000 stands per year, wth an average stand volume of about 14 thousand. We fnd an average bd of about $53, and an average log(bdders) of approxmately 1.5. We generate the error terms for equatons 1 and respectvely from predcted errors n regressons run on the coast regresson dataset. In partcular, we appled the specfcaton n equaton 1 to the coast data, and then obtaned the resduals. These dsturbances had mean of approxmately zero, and standard devaton of.634. We therefore assume that the ε errors are a random sample from a normal dstrbuton wth zero mean and standard devaton of.634. We then estmated the reduced form equaton found by substtutng equaton 1 nto equaton. Runnng ths specfcaton on the coast data yelds predcted dsturbances wth mean zero and standard devaton of Assumng that ε and u are statstcally ndependent, t s possble to solve for the standard devaton of u accordngly. Although ths helps us descrbe the data-. Denote the dsturbances n the reduced form equaton as υ (as n equaton 3). Gven our estmaton, the standard devaton of the υ dsturbances s Assumng statstcal ndependence between the - 6 -

7 generatng process ntutvely, t s unnecessary to assume ndependence or solve for the propertes of u, because we can randomly generate bds based on the propertes of the predcted dsturbances we found n the reduced form estmaton. Thus, we generate bds accordng to the reduced form equaton (equaton 3 below), assumng that υ are dstrbuted normally wth zero mean and a standard devaton of (3) Bd = c + c Prce + c OperCost + c DevCost + c VolPerHect c Volume + c changevlm + c HemlockBalsam + c Slope c Hel + c Cable + c Haul + υ We sample 00 tmes (n 5 percent ncrements from 10 percent to 50 percent) the representatve stands n our model, and then apply a one-equaton regresson to the reduced form equaton defned by equaton 3. We then compute the R for the regresson as well as the confdence ntervals around the estmated regresson lne. Thus, we can see how the ft of the regresson, and the sze of the confdence ntervals that contan the true regresson lne wth 95% probablty, are mproved by ncreasng the sample volume. Table below contans these results. Volume (%) TABLE. RESULTS FROM 00 MONTE CARLO SIMULATIONS Average Mean R Incremental 95% Conf. Improvement Int. Sze Incremental Improvement (%) Table ndcates that the statstcal precson of the estmaton ncreases wth addtonal volume. The sze of the 95 percent confdence nterval around the predcted bds decreases wth an ncrease n sample volume. Thus, the accuracy of the estmated regresson lne wth respect to the true regresson lne mproves as more tmber s auctoned off. The last two columns of Table show the ncremental mprovement n the precson of the estmated equaton wth each 5 percent ncrease n volume. The last column gves the mprovement as a percentage of the average bd. The largest ncrease n the precson of the estmate occurs when we move from a sample of 10 percent to a sample of 15 percent. Here, the 95 percent confdence nterval decreases by $.98, a sgnfcant mprovement n precson. Each further ncrease n volume results n a smaller mprovement of our estmated regressons lkely resemblance to the true stumpage equaton. For dsturbances n equaton 1 and equaton, we can wrte the followng: Var( υ ) = = b Var( ε ) + Var( u ). Above, we estmated Var( ε ) =.634 =.40. Estmatng 5 equaton usng OLS, we obtan as an unbased estmate of b 5. Solvng the above equaton yelds Var( u ) = *.40 = Thus, the standard devaton of the u dsturbances s

8 example, movng from 45 to 50 percent results n an mprovement of only $0.3, or about onetenth the mprovement from ncreasng volume from 10 to 15 percent. Results n Table ndcate that predcton errors, at the 95 percent level, wll not fall to below plus or mnus 50 cents untl the aucton volume exceeds 5 percent. The benefts n statstcal precson n movng beyond 35 percent volume are very small. In partcular precson at the 95 percent level ncreases to only plus or mnus 15 cents n movng from 35 percent to 50 percent volume. Thus, t appears that an aucton volume of between 5 and 35 percent would ensure suffcent statstcal accuracy, and ncreasng volume beyond 35 percent offers lttle ncremental beneft..1 Aucton volume over tme The above analyss focused on the ncremental mprovement n statstcal precson from auctonng a larger volume n a gven year. Tmber sales occur over tme, however, and eventually multple years of data wll be avalable for analyss. Therefore, t may be possble to decrease the aucton volume n future years, and stll mantan a reasonable level of accuracy. Below, we test ths hypothess by doublng the populaton sze (smulatng two years of data), and notng the changes n statstcal precson as we ncrease the sample sze. Table 3 contans these results. We then compare these results to our fndngs n Table above that assumed only one year s worth of data. TABLE 3. RESULTS FROM 00 MONTE CARLO SIMULATIONS WITH TWO YEARS OF DATA Average Volume Mean R Incremental 95% Conf. (%) Improvement Int. Sze In Table 3, we see that auctonng 0 percent volume over a two-year perod offers smlar statstcal precson to auctonng 35 percent volume n a one-year perod. In partcular the 95 percent confdence nterval for the predcted regresson lne s plus or mnus $3.68, on average, when 0 percent of the cumulatve two-year volume s auctoned. Auctonng 35 percent volume durng a one-year perod yelds an average 95 percent confdence nterval of plus or mnus $3.79, whch s very smlar to results obtaned when 0 percent volume over two years s auctoned. The mportance of ths result s that as observatons buld over tme, aucton volume n the subsequent year may be decreased. Cauton should be used n a decson to decrease aucton volume n a subsequent year, however. If the market s n a stage of rapd fluctuaton, then, over tme, stumpage rates on tenured tmber wll ether decrease or ncrease n response to the prces of auctoned tmber. But f fewer stands are auctoned n tme t relatve to those n the regresson sample for tme t-1, then the adjustment of tenure prces could be hndered. Ths problem s lkely mtgated by the smple ncluson of a tme trend n the regresson analyss. A dsadvantage to ths approach s that t - 8 -

9 mght be dffcult to mplement quckly certan specfcatons that would be necessary. Thus, the changes should be planned n advance. An alternatve soluton mght be to choose a tme frame (two years, three years, etc) over whch to sample data. The sample volume would be naturally hgher n the frst year n whch the reforms are mplemented, but would declne n the second year, and stay constant nto the future. The hgher volume n the frst year would be necessary to ensure statstcal accuracy n the only year when lttle aucton data s avalable. Alternatvely, the Mnstry could aucton the same volume n each year, and smply accept less accurate estmates n the frst year. 3 COMPETITION WITHIN DISTRICTS To analyze the current state of competton wthn loggng areas, we proceed along two lnes. Frst, we measure the level of concentraton n partcular combnatons of Coast Dstrcts where common loggers operate. Second, we measure the benefts, by dstrct, that mght be experenced through a coordnated effort to decrease stumpage on auctoned tmber. Together, these two analyses allow us to target dstrcts where local market power s mostly lkely to exst (f t exsts at all). Ths analyss s smlar to one we performed on the Interor. 3.1 Dstrct Area Concentraton We begn our analyss of competton n the Coast by determnng mll concentraton at the dstrct level. In our paper Aucton-Based Tmber Prcng and Complementary Market Reforms, we found that the Coast as a whole was moderately concentrated, as defned n the U.S. Department of Justce and Federal Trade Commsson Horzontal Merger Gudelnes. 3 The majorty of the mll capacty n the Coast s controlled by three frms, each wth between 15 and percent market share. Analyzng the concentraton of mll capacty wthn the Coast as a whole s reasonable, because the Coast has an actve log market. If prces of tmber n Squamsh exceed the prces n Chllwack, then, through purchases on the log market, mlls n Squamsh wll purchase tmber from Chllwack and the prces wll realgn. Therefore, the ablty of a group of mlls n a partcular dstrct to nfluence prces n that dstrct wll be effected by the overall level of competton between mlls n the Coast Regon. If the log market n the Coast were to dsappear (an unlkely scenaro) then mll competton would be determned by the ablty of loggers to move between dstrcts and bargan over prces. Thus, we also perform a mll concentraton analyss by dstrct groupngs that would lkely drve competton n the event that the Coast log market were to declne. Table 4 lsts those groupngs. Area 1 TABLE 4. LOGGER BIDDING AREAS IN THE COAST Dstrcts North Coast, Queen Charlotte, Md Coast, Port McNell, Campbell Rver Port McNell, Campbell Rver, South Island, Sunshne Coast, Squamsh 3 Chllwack, Squamsh To measure the effect of Coast concentraton f the Coast s log market were to declne n scale, we agan use the Herfndahl-Hrschman Index (HHI), whch sums the squared market 3. We determned that the HHI n the Vancouver Forest Regon s See, Susan Athey, Peter Cramton, & Allan Ingraham, Aucton-Based Tmber Prcng and Complementary Market Reforms n Brtsh Columba, 13 (BRITISH COLUMBIA MINISTRY OF FORESTS, Workng Paper 00)

10 shares of frms n the partcular area of queston. An HHI of zero ndcates perfect competton, and an HHI of 10,000 ndcates total monopoly power. Table 5 lsts HHIs for the Coast s bddng Areas. TABLE 5. DISTRICT LEVEL CONCENTRATION IN THE COAST Area HHI Concentraton Level 1 1,953 Hgh,447 Hgh 3 1,378 Moderate Above, we see that mll concentraton s hgh n two of the three bddng Areas. However, the concentraton levels n Table 5 would occur only n a worst-case scenaro namely, f the log market n the Coast were to dsappear. Therefore, the mportance of the log market on competton n the Coast s evdent. Changes n mll capacty n the Coast should be montored along wth the relatve mportance of the log market on tmber prces n the Coast. Table 6 lsts mll capacty n each of the Coast Areas. TABLE 6. MILL CAPACITY BY BIDDING AREA IN THE COAST Dstrct Annual Capacty (MBF) ,930 3,446 Total Capacty 4,831 The data n Table 6 shows that the combned mll capacty n Area 1 s only 9 percent of total mll capacty n the Coast. Mll capacty n Area s 40 percent of total mll capacty n the Coast. Thus, f the log market n the Coast were to dsappear, any changes n the level of Competton n the Coast would most lkely appear wthn the Coast Dstrcts that comprse Area. 3. Dstrct Competton To gauge the potental ablty of frms n the Coast to undermne the ntegrty of the aucton market, we perform an analyss smlar to our Interor analyss. We suppose that bdders n a sngle dstrct are able to decrease aucton prces by 10 percent, and then nvestgate how predcted prces for non-auctoned tmber would respond. We then consder the prce effect on Dstrct A s non-auctoned tmber f frms n another dstrct (chosen randomly) were able to force a 10 percent prce decrease. We present the results from ths analyss n Table 7 below

11 TABLE 7. TENURE PRICE EFFECTS FROM AUCTION PRICE REDUCTION Percent Reducton n Own Dstrct Predcted Average Percent Reducton n Dstrct Name Tenure Prce from 10 percent Decrease Tenure Prces as a Result of Reducton n own Aucton Prces n Aucton Prces n Other Dstrcts Campbell Rver Chllwack Duncan Md Coast North Coast Port McNell Queen Charlotte Squamsh Sunshne Coast The frst column n Table 6 shows the percent reducton n tenure prces f frms n that dstrct successfully decrease aucton prces by 10 percent. The largest effect occurs n Queen Charlotte, an effect that mght be compounded by the Isolated varable that ncludes the entre Queen Charlotte dstrct. Thus, t mght be prudent, gong forward, to consder the omsson of ths varable, partcularly consderng that t s not statstcally sgnfcant n the market prce equaton. The dstrcts of Chllwack, Port McNell, and Squamsh would also experence rather hgh prce decreases from a coordnated declne n auctoned stumpage. Other dstrcts have predcted declnes n tenured tmber rates of between 1 and 4 percent. These results are more problematc than those found n the Interor analyss, but there are fewer dstrcts n the Coast than n the Interor. Thus, any auctoned tmber n the Coast represents a larger porton of total the sample than t dd n the Interor. The actve Coast log market, however, wll lkely reduce the predcted effects n Table 5. In partcular, f frms n Port McNell successfully engage n tactcs that sgnfcantly reduce stumpage prces at aucton, then frms n, say, Cambell Rver wll lkely enter the Port McNell aucton market to purchase cheap tmber, and then float those logs to mlls they are accustomed to processng at n Cambell Rver. Of course, careful attenton must stll be pad to any frcton that mght nhbt the proper functonng of such market forces. For example, f certan areas may only be logged va helcopter, and an expensve upfront cost s necessary to develop such extracton n that area, then barrers to entry may preclude such competton for some tme nto the future. The second column n Table 6 ndcates average prce reducton on tenured tmber n a partcular dstrct that mght occur f another dstrct, chosen randomly, was able to sustan a 10 percent decrease n the prce of ts auctoned tmber. Contrary to results for the Interor, we fnd that certan dstrcts wll experence a prce rse on ther tenured tmber f another dstrct systematcally decreases ts prces on auctoned tmber by 10 percent. Only one dstrct, the Md- Coast, would experence a sgnfcant declne n tenured stumpage f another dstrct decreased ts aucton prces. These results reduce some of the worres that column one n Table 6 showed, although the ablty of one dstrct to affect s owned tenured stumpage prces by reducng prces on ts own auctoned tmber should stll be of concern gven the current specfcaton and data. 4 CONCLUSION We found that the aucton volume necessary to ensure statstcal accuracy usng TEPS s hgher n the Coast than t was n the nteror. An aucton volume of between 5 and 35 percent

12 would ensure accurate out of sample prcng n the Coast f only a sngle year s worth of data was used to estmate the TEPS equaton. However, f multple years of data are pooled to form the regresson sample, volume could be decreased to approxmately 0 percent. Tme trends, or further structural changes to the specfcaton could be used to account for major market fluctuatons between years. Such specfcaton changes would facltate the ncluson of multple years of data n the regresson sample, and would therefore lower the aucton volume that would be necessary to ensure statstcally accurate stumpage rates. Regardng local market power, we found that mll concentraton could be problematc only n the most remote areas of the Coast, whch represent a mnscule percent of the total market. We dd, however, fnd that, gven the current data and specfcaton, certan dstrcts would beneft sgnfcantly from a coordnated effort to lower aucton prces. Thus, careful attenton should be pad to reduce these ncentves as the Mnstry moves closer toward applyng the reforms