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W [$  (W ^$  -W g$  4W $  QW $  W A$ s W w$  FW $  W $  WW $  mW $  W $  W $  W $  W &$ W W <$ m W H$ y W $  bW V$  $W $ ) W $ : W M$  W $  W $ S W W$  &W $  _W $  W $  W $ E W =$ p W k$  :W $  qW $  xW $  }W $ $ W W$  %W $  W $  W $  W $ , W $ 6 W z$  GW $  pW $  zW $  W $ > W ,$ ] W >$ p W _$  .W i$  7W $  gW 5$ g W k$  8W $  hW J$ { W $ Y W $"$ U" !W W"$ " &"W "$ " k"W "$ " "W "$ # "W a#$ # 0#W #$ $ #W $$ 3$ #W 4$$ e$ $W ;$$ l$ $W h$$ $ 6$W $$ $ f$W %$ P% $W &$ & T&W '$ ' W'W ($ N( 'W e($ ( 4(W )$ ) M)W )$ ) c)-e O<Lh  b8A\r+=a p/7ih7.t _C 8w          # V  Wr  $~ L  }z G  x G  t B  j 8  \ * < L ;  l }  I F  x {  )  \ '  Y  2  c ?  2  c ?  `  3 -  u  0 C   $           (   ^   +   [   }       :  2  e   8  j   @  q  L  }   } P  x  t   t   q  q '  q ,  q /   o 6  9 j k   c X  c i  ^   ^   \ #  DT u  yP  H M  l} K  { H  z H  z H ) x F F w F O v 6D g t VA  %i 8 B h %5 W _ .  _ .  Y _'  .V $  sU "  Q  C M w  DJ  | H  ?z E [ x (E ^ x -E g x 4D  u QC  u > A sp = w n F;  n 5  g W5  g m4  g 4  g 4  g 4  g 2 & Wd 1 < mb 1 H yb /  b b+ V ] $(  )[ (  :[ & M X $  V "  ST ! W T &!  T _  Q   Q   EO  = pO  k O :  O q  O x  O }  $L  W L %  J   J   J   ,J   6J  z H G  H p  H z  H   >E  , ]E  > pE  _ E . i E 7  C g 5 gC  k C 8  @ h J {@   > Y  $" U"9 ! W" "7 &" " "7 k" " "7 " " #7 " a# #7 0# # $7 # $ 3$4 # 4$ e$4 $ ;$ l$4 $ h$ $4 6$ $ $4 f$ % P%2 $ & &2 T& ' '0 W' ( N(- ' e( (- 4( ) )+ M) ) )+ c)---'--- )d---'--- /+ ---'--- , ----'--- %\0 c2 U=Figure 1: The Common Line Formula of the Commission and NECA:TOOOOOO:OT:OYOYO:xx:OO---'--- , ----'--- V 2 Loops / ExchangelsssbCCCsnlslssl---'--- X4  y X4y  #Xj\  P6G;W XP#Federal Communications Commission  *xxX DA 972710  X4yxdddy#Xj\  P6G;W XP# Ãpp y#Xj\  PG;XP# k#X\  PG;P#Before the "Federal Communications Commission  yO'IWashington, D.C. 20554 #Xj\  PG;XP#у  Xb4In the Matter of hhCq)pp  *xxX (#(#` `  hhCq)  X44National Exchange CarrierhhCq)  X4Association, Inc. (NECA)hhCq)ppAAD 972xxX (#(# X4Proposed Modifications to the 1997hhCq)  X4Interstate Average Schedule Formulasq) ` `  hhCq  X 4and` `  hhCq ` `  hhCq)  X 4Proposed Further Modifications to the 199798)ppAAD 97109  X| 4Interstate Average Schedule Formulasq) Xe 4  XN4,V ORDER ON RECONSIDERATION  X74|R AND  X 4tORDER \  X4X` hp x (#%'0*,.8135@8: 'para. 5.4 (Millions) Sample Company Settlements using NECA's Proposed  X54Formula05B yO 'ԍNECA uses the simulated revenue requirements of the sample average schedule companies to develop  yO 'formulas that determine settlements for all average schedule companies. See supra, para. 5. (Millions) Overstatement of Costs     "u/^ "   |     Amount (Millions)  Percent  q   "_u/^ " "u19923 _$ 1653 _$U$ 113.73 _#$ 120.93 _$.2$ 7.23 _$ 6.3q q  "u1993 _$ 167 _$U$ 133.8 _#$ 140.4 _$.2$ 6.6 _$ 4.9q q 3 "u1994_$ 190_$U$ 122.7_#$ 129.1_$.2$ 6.4_$ 5.2q q  "u1995_$ 222_$U$ 138.8_#$ 150.9_$($ 12.1_$ 8.7q    "_u/^ " "u1996'$ 180'$U$ 103.0'#$ 108.6'$.2$ 5.6'$ 5.4    X4 e B20.` ` In addition to the bias inherent in the results of NECA's average schedule formulas  xduring the past five years, we have determined that NECA's linear spline model does not  X4 x+accurately reflect the sample data.1@$9 yO'ԍ A linear spline model consists of two lines of differing slopes meeting at an inflection point. There is a change in slope at the inflection point. First, these data do not demonstrate a sharp shift in slope  x that would support the selection of an abrupt inflection point characteristic of NECA's linear  x+spline model. Second, even if NECA's use of a linear spline model were reasonable, NECA's choice  X4 x9of an inflection point is not adequately supported by current data.{2X$9 yO 'ԍNECA's choice of inflection point, 385.55 lines per exchange, was selected based on a 1985 study. Thus, NECA has used this inflection point in its filings for 10 years. The Bureau, using NECA's current sample data, found that the linear spline that best fits the data would have an inflection point at 1103 lines per exchange.{ NECA's failure to  x+recalculate the inflection point based on more current data is likely to be a primary reason why NECA's linear spline model fails to accurately represent 1996 data. "X 20*&&JJI"Ԍ X4 e    21.` ` Impact on Small Companies.  We also affirm our decision to use a reciprocal model  xlto compute the Common Line formula. Upon examination of the data, we found several different  xmodels, including the reciprocal model, that fit the data more closely than NECA's proposal. At  xthe outset, we observe that any modification of the Common Line formula will change the  xamount of revenue received by individual companies. Such modifications are warranted,  xhowever, to ensure that the formulas used by NECA appropriately compensate average schedule  x8companies. Park Region argues that the Bureau did not adequately consider the effect that the  x0use of the reciprocal model would have on the settlements of individual average schedule  xAcompanies. The Bureau staff did, in fact, analyze the effect that the modified formula would  xhave on every average schedule company. We found that approximately half the 600 average  x schedule companies would have a higher settlement under the modification than they would  xusing NECA's proposal. In fact, 85 percent of the average schedule companies with fewer than  x1,000 lines per exchange (291 of 344 companies) would receive a higher settlement using the  xmodified formula than they would receive if NECA's proposed formula were used. Of the  xcompanies receiving higher settlements using the modified formula, a high proportion were the  xsmaller average schedule companies. The modified formula, therefore, has a positive impact on  X4these smaller incumbent LECs.  Xb4 e S22. ` ` Validity of the R2 statistic.  Table 2 shows a comparison of the R2 statistics, which  XK4 x measure goodness of fit, for various models. NECA's linear spline model had the lowest R2 value  xand therefore was the poorest fit among these alternative models. The reciprocal model, which  X4 xis the model selected by the Bureau, had the highest R value and therefore was the best fit.[3X$9 yO'ԍThe reciprocal model also performed better than NECA's model using another goodness of fit measure, the Mean Relative Absolute Deviation ("MRAD"). MRAD is based on the sum of the absolute deviations of the model from revenue requirements, while the R is based on the sum of squared deviations.[  X4 xNECA argues in its petition that the R statistic used by the Bureau as a measure of goodness  X4 x8of fit is not valid when the residuals4$9 yO'ԍResiduals are the differences between the dependent variable (in this case the simulated revenue requirements) and the model. do not conform to a normal distribution.)5X@$9 yO'ԍThe normal distribution is a symmetric, bellshaped distribution that is commonly encountered in  yO'statistical analysis. See Morris H. DeGroot, Probability and Statistics, AddisonWesley Publishing, 1986, pp. 263272.)  We reject that  xargument. The passage from the Kmenta text cited by NECA to support its challenge regarding  X4 xh R2 statistics does not discuss R2 analysis. 6` $9 {O!'ԍ #X\  P6G;gP#Petition at n. 10 citing Jan Kmenta, Elements of Econometrics, The MacMillan Company, New York,  yO"'1971, p. 252.#x6X@`7 pX@#  In fact, the Kmenta text supports the Bureau's use  xof linear regression analysis with least squares criterion, stating that such analyses produce the" 60*&&JJI"  X4 xmost reliable unbiased estimators in the presence of nonnormal residuals.7$9 yOy'ԍKmenta at p. 247 (Kmenta states that "...even without the assumption of normality the least squares estimators are unbiased and have the smallest variance among all linear unbiased estimators of the respective  yO 'parameters."). See also Irwin Miller and John E. Freund, Probability and Statistics for Engineers, Prentice Hall,  yO'p. 231; and George Judge, W. W. Griffiths, R. Carter Hill, Helmut Lutkepohl, and Tsoung Chao Lee, The Theory and  yO'Practice of Econometrics, John Wiley and Sons, 1985, p. 824. NECA also argues  xthat, according to the Scheffe text, mathematically correct statistical inferences rely on the  X4 xcondition that residuals are distributed normally around zero.8x$9 yO'ԍPetition at n. 10 citing Henry Scheffe, The Analysis of Variance, John Wiley & Sons, 1959, p. 197. We reject that argument as  X4 xAirrelevant because no statistical inferencesA9X$9 yOt 'ԍStatistical inference concerns generalizations about the population based on information provided by the sample. The R, or goodness of fit, is an operational criterion that does not depend on statistical inference.  yO 'See Kmenta at pp. 7, 234.A were involved in our choice of the R statistic as a measure of goodness of fit.   Xv4q Table 2 ă  X_4  Comparison of Common Line Settlement Models:_( $I yO8'ԍThe R statistic can vary from 0.0 to 1.0, with 1.0 representing that 100% of the variation in the dependent variables is explained by the model.փ ^ !ddx HVV ##  AddxH H H ^    u/   X4 Models  i Ѓ_ xP?$-ԍFor a complete description of these models see_փ zP?$-ԍFor a description of the models see National Exchange Carrier Association, Inc., Memorandum Opinion  zP %-and Order, AAD 972, DA 971114, released May 28, 1997, at Attachment 2. փ ԃ" R  2   aH Ru/   Xa 4 NECA's Linear Spline J R"Z0.16aa  X 4 Bureau's Estimated Spline  R"Z0.19aaJ   X# 4 Reciprocal  R"Z0.20a  Ryu/   X 4 Log Reciprocal y"Z0.17 y  X4 e  23. ` ` Variance in Settlements over Time. NECA argues that, over time, use of the  xBureau's modification will result in excessive variation or volatility in the interstate average  xschedule settlements for small average schedule companies. The basis for this volatility,  xqaccording to NECA, is that the reciprocal model is more sensitive to the variation for small  x~companies than the linear spline model. We find no basis for this argument. After careful  xanalysis of the changes in estimated settlements over the last five years using the reciprocal  X4 xmodel, we found no excessive variation for small average schedule companies.; < yO-#'ԍOf the companies below 100 lines per exchange, we found none that experienced variation in their annual common line settlements that exceeded $10,500. Changes in  xAtechnology and cost structure for average schedule companies, however, may require that we" ;0*&&JJ "  xNconsider other models over time. Our task is to ensure that, each year, the model used best  xsimulates cost companies based upon analysis of the cost company data. We do not believe that  xselecting the optimal model for a given year will inevitably lead to excessive variation or  x8volatility. For the current year, we found that a reciprocal model fits the sample data supplied  xby NECA better than the linear spline model filed by NECA. We do not expect significant volatility  xin the cost data that form the basis for the Common Line average schedule model, because these  xNdata are largely a function of embedded loop costs that do not typically increase or decrease significantly from year to year.  XH4  X14 e m24. ` ` Inclusion of Erroneous Data Points.  In addition to challenging which model more  xclosely represents the data, NECA also argues that, in determining that the average schedule  xJmodel should be modified, the Bureau used two data points that resulted from significant  xreporting errors. NECA argues that for one of the reported outliers it was unable to allocate  xcosts correctly to Common Line because the company had incorrectly included costs from other  xoperations. This reporting error should result in artificially inflated costs, implying that  xuinclusion of this data point would result in an average schedule that is too high. Exclusion of  xAthis data point, however, results in an increased average schedule. For the other data point,  xNECA claims that this point is not usable because the company operates in two states, but  xreported data for only one state. Elsewhere, however, NECA reveals that it has complete  XK4 xEcompany information for that carrier,M<K< yO'ԍSee Petition at p. 11.M thus establishing that it could have determined the costs  xof the company's operations in the second state. Furthermore, we agree with MCI's conclusion  X4 xhthat the faulty data points had only a marginal effect on the intercept slope and R2 values of  X4 xWthe Commission reciprocal model.H=X< yO'ԍMCI Opposition at p. 6.H Therefore, we conclude that both of these data points should be included in the sample set used to derive the formula.  X4 e 25.` ` Settlements and Cost Trends.  NECA argues that its formula would produce a 2.4  xupercent increase in perunit Common Line settlements, while the Bureau's modification would  xRcause perunit Common Line settlements to decline by 1.0 percent. According to NECA, this one  xpercent decline is inconsistent with universal service fund data, which show that Common Line  Xe4unit costs have increased each year from 1993 to 1996.>e< yO'ԍNECA referred to data provided by incumbent local exchange carriers, pursuant to Part 36, Subpart F, in the annual universal fund filings.  X74 e 26.` ` NECA's argument is misleading because it implies that the perunit common line  xlsettlements received by average schedule companies have accurately tracked the estimated per xunit common line unit costs computed using simulated cost data. That has not, however, been"  @>0*&&JJ "  xthe case. As Table 1 shows, over the past several years the average schedule formulas have  xRproduced results much higher than those derived using simulated cost data. This overstatement  xuwas particularly pronounced for last year's Common Line formula settlements, which exceeded  X4 xthe results from the sample by nearly nine percent.:?< yO4'ԍId.: NECA, in citing a one percent decline  xusing the Bureau's modification, compared last year's Common Line formula settlements and the  xlevel of settlements using the Bureau's modification. Given the significant overstatement of last  xyear's Common Line formula settlements, the alleged "one percent decline" does not demonstrate that the Bureau's modification is unwarranted.  X14 e r27.` ` Sensitivity of the Model. NECA argues that our statistical analysis is unduly  xsensitive to a few data points of the smallest companies. We disagree. In fact, as shown by the  xR statistic, our analysis accurately reflects the sample data provided to the Commission by  xlNECA. Nonetheless, we believe that NECA has identified a potential area of concern regarding the  xRvalidity of the sample data upon which NECA bases its average schedule models. Specifically, the  xsample data may not contain information for a sufficient number of very small companies, and  x therefore the sample may not be an accurate representation of the entire group of such  xcompanies. Accordingly, we hereby direct NECA to work with the Bureau staff to develop a  xmeans of assuring that the sample data produced for design of future average schedule models  xwill accurately reflect all sizes of average schedule companies, including those with very few  xlines. Should we determine that the use of sample data continues to be problematic, however,  xthe Bureau will consider requiring the use of expense and investment data from all average schedule companies.  X4   X4 e   28. ` ` Notice. NECA and many commenters argue that the Bureau violated section 205  xhof the Communication's Act and section 553 of the Administrative Procedures Act by failing to  X4 xprovide notice of the required modifications to NECA's proposed Common Line formula.\@X< yO'ԍSee supra, n.16 and n.20.\ These assertions are without merit.  X|4 e  29.` ` Section 553 of the Administrative Procedures Act is inapplicable because this  xproceeding to consider NECA's average schedule formulas is not a rulemaking. Consideration of  xAthe average schedule formulas is, instead, an intermediate step in the development of NECA's  xminterstate access tariff process. Under Section 69.606(a) of the Commission's rules, the  x4computation of average schedule payments is made in accordance with formulas approved or  X 4 xNmodified by the Commission.BA < yO#'X` hp x (#%'0*,.8135@8:41.` ` IT IS FURTHER ORDERED, pursuant to Section 4(i) of the Communications Act of  x1934, as Amended, 47 U.S.C.  154(i), and Sections 0.91 and 0.291 of the Commission's rules, 47 C.F.R.  0.91, 0.291, that THIS ORDER IS EFFECTIVE UPON ITS RELEASE.  X4 e 42.` ` IT IS FURTHER ORDERED, that the National Exchange Carrier Association, Inc.,  xSHALL FILE revised tariffed rates in accordance with this Order. For these purposes we will  xNwaiver Sections 61.58 and 61.59 of our rules, 47 C.F.R.  61.58, 61.59, to allow NECA to file its  xurevised rates on 2days notice, on a nonstreamlined basis, on December 30, 1997, to become  xEeffective January 1, 1998, if it chooses to do so. NECA shall cite the DA number of this Order for its permission. ` `  hhCq ` `  hhCqFEDERAL COMMUNICATIONS COMMISSION ` `  hhCqA. Richard Metzger, Jr. ` `  hhCqChief, Common Carrier Bureau  X74` `  hhCqpp  *  X 4` `  hhCqpp  *APPENDIX y!1(xF F9 0*dd xxy Xh$Q0*%%JJ" 3~9 $g!F XԌ