ࡱ; !O"  $#;:%&'()*+,-./0123456789~@<=>?ABCEDFHGIJKMLPNSgQRUTXVWYZ[\]_^a`fbcdehlijkmnopqrstuvwxy{z|}~Root Entry F@CompObjbWordDocumentObjectPoolzz 4@   !"#$%&'()*+,-/234569;<=>?@ABCDEFGHJMNQSTUVWXYZ[\]_beghijklmnpsvxyz{|}~ FMicrosoft Word 6.0 Document MSWordDocWord.Document.6; ࡱ; L,|ࡱ; O  .1  `& & MathType`PSymbol- 2 !ܥe3 ed`ҡҡҡ2.C`L 4HJJJ+uDD^Tcҡ4Iҡҡ`ҡҡHD*rD`rҡҡHh4. Proposed solutions (a) Introduce exogenous variables If exogenous variables are added (to a first-order autoregressive process), the bias in the OLS estimator is reduced in magnitude but remains positive. The coefficients on the exogenous variables are biased towards zero. (The direction of bias for a pth order AR process is difficult to identify a priori.) The LSDV estimator remains biased if exogenous variables are added to (2), for small T. (b) Instrumental variable methods (i) Anderson-Hsiao A normal technique for dealing with variables that are correlated with the error term is to instrument them. Taking first differences eliminates the  EMBED Equation.2 , which were the source of the bias in the OLS estimator. This gives:  EMBED Equation.2  (15) Now we need to instrument  EMBED Equation.2 , which is still clearly correlated with the error  EMBED Equation.2 . The second lag of the level,  EMBED Equation.2 , and the first difference of this second lag,  EMBED Equation.2 , are possible instruments, since they are both correlated with  EMBED Equation.2  but are uncorrelated with  EMBED Equation.2 , as long as the  EMBED Equation.2  themselves are not serially correlated. Both the resulting instrumental variables estimators (known as Anderson-Hsiao):  EMBED Equation.2  (16) and  EMBED Equation.2  (17) are consistent when N EMBED Equation.2  or T EMBED Equation.2  or both. Instrumenting with the second lag of the level, (17), has the advantage over instrumenting with the second lagged difference, (16), that only two time periods are required, rather than at least three. When  EMBED Equation.2 , the choice of instrument can be based on correlations between  EMBED Equation.2  and each of  EMBED Equation.2  and  EMBED Equation.2 . It has been found that the estimator resulting from instrumenting using differences  EMBED Equation.2  has a singularity point and very large variances over a significant range of parameter values. Instrumenting using levels does not lead to the singularity problem, and results in much smaller variances, and so is preferable. (ii) Arellano-Bond The Anderson-Hsiao instrumental variables estimator may be consistent, but it is not efficient because it does not take into account all the available moment restrictions. (Moment restrictions are restrictions on the covariances between regressors and the error term. Regressors may be orthogonal to the error term, in which case we are justified in imposing, or using, orthogonality restrictions that the covariance between regressor and error is zero.) Arellano and Bond (1991) argue that a more efficient estimator results from the use of additional instruments whose validity is based on orthogonality between lagged values of the dependent variable  EMBED Equation.2  and the errors  EMBED Equation.2 . The Arellano-Bond estimator is now widely used in short dynamic panels, not least due to the fact that they wrote a Gauss-based regression package, DPD, which gives the standard OLS, fixed effects (Within or differences), random effects estimators, plus their own. (See below for a schematic discussion of the estimators available in DPD.) Take (15) above, the first-differenced simple AR(1) model with no regressors. At t=3, the first period we observe the relationship in (15),  EMBED Equation.2  (18) [NB 3 is t, 2 is t-1, 1 is t-2]  EMBED Equation.2  is a valid instrument for  EMBED Equation.2 , since these are highly correlated, and  EMBED Equation.2  is not correlated with  EMBED Equation.2  unless the  EMBED Equation.2  are serially correlated. At t=4,  EMBED Equation.2  (19) Here  EMBED Equation.2  and  EMBED Equation.2  are both valid instruments: neither is correlated with  EMBED Equation.2  unless the  EMBED Equation.2  are serially correlated. Proceeding in this manner, we can see that at T, the valid instrument set is ( EMBED Equation.2 , EMBED Equation.2 ,..., EMBED Equation.2 ). The matrix of instruments is  EMBED Equation.2 , where  EMBED Equation.2  [NB The top row of this matrix refers to t=3, and the last to t=T: it is a square (T-2) matrix.] The moment conditions are given by  EMBED Equation.2  (20) or, in vector form,  EMBED Equation.2  (21) where  EMBED Equation.2  (22) There are m=(T-2)(T-1)/2 linear moment restrictions for  EMBED Equation.2 . Premultiplying (15) (here written in vector form) by  EMBED Equation.2  gives  EMBED Equation.2  (23) Performing generalised least squares (GLS) on (23) gives the Arellano-Bond (1991) preliminary one-step consistent estimator:  EMBED Equation.2  (24) where  EMBED Equation.2  and G is a (T-2) square matrix with twos in the main diagonal, minus ones in the first subdiagonals and zeros otherwise:  EMBED Equation.2  Arellano and Bond also put forward a consistent 2-step generalised method of moments (GMM) estimator:  EMBED Equation.2  (25) where  EMBED Equation.2 , and in practice the differenced residuals from the preliminary one-step consistent estimator  EMBED Equation.2  are used in place of  EMBED Equation.2 . Why should we use  EMBED Equation.2  rather than  EMBED Equation.2 ? Because  EMBED Equation.2  does not rely on knowledge about the distribution of the components of  EMBED Equation.2 ;  EMBED Equation.2  and  EMBED Equation.2  are asymptotically equivalent if the  EMBED Equation.2  are IID(0, EMBED Equation.2 ). (Nor does  EMBED Equation.2  require knowledge about initial conditions,  EMBED Equation.2 .) What happens if we have additional independent explanatory variables in our equation? Specifically, assume there are K additional independent explanatory variables, so we revert to equation (1):  EMBED Equation.2  (1) where  EMBED Equation.2  and b and  EMBED Equation.2  are  EMBED Equation.2 . The two-step estimators for b and g are given by:  EMBED Equation.2  (26) where X is the N(T-2) EMBED Equation.2 K matrix of observations on  EMBED Equation.2 . The one-step estimator is obtained if  EMBED Equation.2  is replaced by  EMBED Equation.2  (cf. (25) and (24) above). The instrument matrix W can be expanded to take advantage of the additional independent explanatory variables. The instrument matrix that is optimal (i.e. efficient) differs according to whether the additional explanatory variables are correlated with the fixed effects or not, and whether they are predetermined or strictly exogenous. If the  EMBED Equation.2  are all correlated with the fixed effects  EMBED Equation.2 : 1. If the  EMBED Equation.2  are predetermined, then future values of these regressors are correlated with the current error, i.e.  EMBED Equation.2  for s PSymbol- 2 <*p & "System-:4;;72 ࡱ; ࡱ; h =  a i*ࡱ; ObjInfo Equation Native <_917017824 FzzOle ry price, adjusted by average weekly hours worked in manufacturing industries), the log of an inflation-adjusted estimate of the companys capital stock (Gross fixed assets), and the log of industry output (value added), each company having been classified into one of 9 sub-sectors of manufacturing according to their main product by sales. The equation can be motivated along the lines of Layard and Nickells work. With zero adjustment costs, a price-setting firm facing a constant elasticity demand curve would choose to set employment according to a log-linear labour demand equation of the form:  EMBED Equation.2  (32) where  EMBED Equation.2 ,  EMBED Equation.2  and  EMBED Equation.2 .  EMBED Equation.2  is the log of the real product wage,  EMBED Equation.2  is the log of gross capital, and  EMBED Equation.2  is a measure of the expected demand for the firms product relative to potential output (industry output captures industry demand shocks in the estimated equation (31), and time dummies capture aggregate demand shocks). If it is costly to change employment, actual employment  EMBED Equation.2  will deviate from  EMBED Equation.2  in the short run, suggesting a lag structure as in (31). ABs Table 4 shows GMM estimates of equation (31) (based on first differences) [we will ignore column (d) since it is not relevant for our purposes]. Table 5 shows other estimates (the two Anderson-Hsiao estimators, OLS and Within-groups). Employment adjustment does appear to take 2 years, employment responds negatively to current wage rises, and positively to (industry) output shocks, and is higher, the higher is the capital stock. Column (c) is ABs preferred specification, and suggests a long-run wage elasticity of -0.24 (but s.e.=0.28), and a long-run elasticity w.r.t. capital of 0.7 (s.e.=0.14). Employment appears affected by changes in industry output (0.890 EMBED Equation.2 0.875), which accords with the Layard-Nickell interpretation that employment responds to movements in demand relative to potential output. Columns (a1) and (a2) instrument the lags of the dependent variable with the efficient levels of employment as in the Wi matrix on page 9 above. Despite assuming the other regressors are exogenous, AB dont exploit any additional restrictions (which would be as in 2. above if the regressors were correlated with the individual effect, and as in 5. if they were not). (a1) shows 1-step estimates and (a2) shows 2-step estimates. Increased efficiency resulting from the 2nd step might be shown in the roughly 30%-lower (asymptotic) standard errors, but AB also refer to simulation results in which they found 2-step standard errors to be biased downwards (in finite samples) by around 20% (see AB p.285). Column (b) omits insignificant dynamics from the 2-step model, with little change in the long-run properties. Column (c) allows for the fact that the real wage and capital stock may be endogenous. In principle, these would each be instrumented with own (t-2)-and-earlier lags. In practice, only (t-2) and (t-3) lags are used as instruments due to computational complexity and relatively small sample size, but additional instruments are used (lags of company sales and inventories). The instrument tests discussed above are reported under the coefficient estimates. None of the m2, the Sargan s, and the difference-Sargan ds tests reject the null of serially uncorrelated errors in the levels equations for the 2-step GMM estimator. The s and ds tests reject for the 1-step estimator, but ABs simulation suggested these tests reject too often in the presence of heteroskedasticity. The Hausman test rejects for both 1- and 2-step, but again, in simulations, AB found this test over-rejects. AB hypothesise that the rejections reflect the fact that some of the regressors that have been assumed exogenous are in fact endogenous. When these variables - wages and capital - are instrumented (column (c)), none of the tests reject the necessary null of no serial correlation in the levels disturbances. Column (e) of Table 5 reports the Anderson-Hsiao estimator with the differenced lagged dependent variable instrumented with the own differenced third lag. The number of observations falls as one further observation per individual is lost (estimation is over 1980-84). Column (f) reports the other Anderson-Hsiao estimator, using the third lag of the level as the instrument. In both cases, the estimates are poorly determined: there appears to be a large gain in efficiency through using the additional instruments in the AB GMM procedure. Column (f) reports OLS estimates (these are over 1978-84 as one observation is gained). The lagged dependent variable coefficient is biased upward, as we would expect in the presence of firm-specific effects (which we have of course been assuming). Column (g) reports Within-groups estimates (again, a year is gained). Surprisingly, the coefficient on the lagged dependent variable is greater than that using the GMM estimators (we would expect it to be biased downwards in the presence of fixed effects). AB point out that the endogeneity of some regressors could cloud the comparison between Within-groups and GMM. Using DPD The above relates directly to the estimators available in DPD. The package gives the options: State form of model - type 0 for levels 1 for first differences 2 for orthogonal deviations 3 for combined first differences and levels 4 for combined first differences and average level 5 for combined orthogonal deviations and levels 6 for combined orthogonal deviations and average level 7 for within groups 8 for error components generalised least squares Model 0 - levels is OLS. Use this if you have a static model and dont want to allow intercepts to vary across individuals. Model 1 - first differences is OLS on first differences, i.e. the fixed effects model transformed using first differencing to remove the fixed effects. Use this if you have a static model in which you think intercepts vary across individuals and are non-random. Arguments for fixed rather than random include: my regressors are correlated with the error term; I am content to make inferences conditional on the set of individuals in my dataset (e.g. I can talk happily about what matters for OECD countries, and I dont want to make inferences about all countries in the world); everyone else uses the fixed effects model too. Model 7 - within groups is OLS on data demeaned by the Within transformation, i.e. the fixed effects model transformed by subtracting time-means to eliminate the fixed effects. Use this if you have a static model in which you think intercepts vary across individuals and are non-random. Rationales for using this model are as for Model 1, plus additional efficiency since you dont lose a time period through differencing. Model 2 - orthogonal deviations is OLS on data demeaned by the orthogonal deviations transformation, i.e. the fixed effects model transformed by subtracting forward time-means to eliminate the fixed effects (see Note below for more detail on orthogonal deviations). Use this if you have a static model in which you think intercepts vary across individuals and are non-random. Rationales for using this model are as for Model 7. In addition, it has computational advantages: it reduces the size of the computational problem of calculating the instrumental variables estimators. [Arellano and Bover (1995), Another look at the instrumental variables estimation of error-component models, Journal of Econometrics, vol.68, 29-51, has more detail and motivation.] Model 8 - error components generalised least squares is GLS. Use this if you have a static model in which you think intercepts vary across individuals and are random. Model 8 is inconsistent unless all regressors are strictly exogenous. Arguments for random rather than fixed effects include: I want to draw implications for the whole population, rather than make inferences conditional on my sample. Model 3 - combined first differences and levels is a version of the Arellano-Bond estimator. Use this if you have a dynamic model in which you think intercepts vary across individuals and are non-random, and if your model includes other independent regressors which are not correlated with the fixed effects, but not all of which are strictly exogenous (i.e. some are predetermined). gmm() gives asymptotically efficient instruments for these regressors. Model 4 - combined first differences and average level is a version of the Arellano-Bond estimator. Use this if you have a dynamic model in which you think intercepts vary across individuals and are non-random, and if your model includes other independent regressors, and all of these regressors are not correlated with the fixed effects and are strictly exogenous. Model 5 - combined orthogonal deviations and levels is a version of the Arellano-Bond estimator. Model 6 - combined orthogonal deviations and average level is a version of the Arellano-Bond estimator. DPD then gives the option of various form of constant term: Select from choice of constants to be included - type 0 for none 1 for time dummies only 2 for time dummies interacted with industry dummies and if you chose model 0 or any of 3-8 you can also choose: 3 for constant only 4 for industry dummies only 5 for time dummies and industry dummies For models 0-2 and 7 you are given the choice of robust test statistics and 2-step estimates (a yes/no decision). 1-step estimates involve a known G matrix. Estimates using first differences use the G matrix defined above. Estimates using levels or orthogonal deviations use the identity matrix in place of this G matrix. If 1-step residuals are heteroskedastic, efficiency will be increased by using these residuals in a second step. Models 3-6 and 8 imply 2-step and robust estimates. Models 3-6 will automatically use the instrument matrix you define in the DPD command program. Note: Orthogonal deviations An orthogonal deviation  EMBED Equation.2  is given by:  EMBED Equation.2  An orthogonal deviation is the deviation of the observation from the average of future observations in the sample,  EMBED Equation.2 ; this deviation is then weighted to standardise the variance, by multiplying by  EMBED Equation.2 . If the original errors are IID, so will be the errors using orthogonal deviations. Note that an estimator that uses orthogonal deviations is, like that using deviations from the full-sample mean, sometimes known as a within-groups estimator. 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L+WTࡱ; +W;  .1   & & MathType`PSymbolE- 2 `>DTimes New Roman- 2 `(y Times New RomanPICObj LMETAfo CompObjNativeZObjInfo3F- 2 i> Times New Roman- 2 2p & "System-ࡱ;  FMicrosoft Equation 2.0 DS Equation Equation.2ࡱ; ࡱ; p E(C)C Dy i2;Equation Native1414&1p (24(24<_917174947F`G}`G}Ole PIC Lࡱ; LW,Tࡱ; W  .1   & & MathType`Times New Roman- 2 `Jy Times New Roman- 2 i> Times New METAbj CompObjZObjInfoNativeEquation Native F<Roman- 2 ,1p & "System-itServerAuto Tray Sࡱ;  FMicrosoft Equation 2.0 DS Equation Equation.2ࡱ; ࡱ; p EXCC y i12ࡱ; _917174984F`G}`G}Ole PIC LMETA LWTࡱ; W^& A .1   & & MathType`Times New Roman- 2 `.( 2 `S)Times New Roman- 2 `u 2 `u Times New Roman- 2 fi> 2 di> Times New Roman- 2 3p 2 2pPSymbol- 2 `- & "System-+D&Oࡱ FMicrosoft Equation 2.0 DS Equation Equation.2ࡱ; ࡱ; CompObjZObjInfoNativeEquation Native F\_917175002F`G}`G}     !"#$&)*-/0123457<>?@ABCDFKMNOPQRSTUVX[^`abcdeglnopqrstv{}~p@E((C)C (u i3 -u i2 )ࡱ; ࡱ; LWTࡱ; WK  .1   & & MathType`Times New Roman-Oleion Native1414&1p (24(24PIC70805 FLMETA CompObj Z 2 `0u Times New Roman- 2 it>> & "System-ࡱ; 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ࡱ; p EXCC y i1ࡱ; L4W@Tࡱ; 4W  .1   & & MathType`Times New Roman- 2 `Jy Times New Roman _917175532F`G}`G}@OleObj yPICocument zLMETAPool |@ - 2 i> Times New Roman- 2 >2p & "System-ࡱ;  FMicrosoft Equation 2.0 DS Equation Equation.2ࡱ; ࡱ; p E&C(C y i2CompObjZObjInfoNativeEquation Native F<_917175554;_F`G}`G}Olenfo2 F PICion Native)*+,-/ 569L@META4905GHJMN F(CompObjghijklmnpvxyZࡱ; LqWTࡱ; qW>  .1    & & MathType`Times New Roman- 2 `Jy Times New RomanP- 2 iT>| PSymbol- 2 -{ Times New RomanP- 2 _2p & "System-Plus90Minus90AnyNoFontsDownloadedࡱ FMicrosoft Equation 2.0 DS Equation Equation.2ࡱ; ࡱ; p@E&CX(C y iT-22ObjInfoNative1414&1p(24(24Equation Native F\_917175767tiveFx~x~H<Ole75380 Fp & ࡱ; ࡱ; Lp W|Tࡱ; p WU  .1   ` &  & MathType`Times New Roman - 2 `3W@ 2 `W@ 2 `MW@ PIC74381    FLMETA%&'()+0 5678(CompObjFGHIJKLOUVWXYZObjInfogijklmnopuTimes New Roman<- 2 tNPSymbol- 2 `= 2 d^ 2 d^ 2 d ^Times New Roman - 2 ` [| 2 `,` 2 `.` 2 `.` 2 `_.` 2 `,` 2 `A ]~ Times New Roman<- 2 1p & "System-ࡱ FMicrosoft Equation 2.0 DS Equation Equation.2ࡱ; ࡱ; Y`/HoGx oG W=[2W 1 ,...,2W N "]ࡱ; Lc Equation Native |_917175827tiveFx~x~<Ole75258tive FPIC71803 FLࡱ; c 64  .1   & & MathTypeTimes New Roman- 2 3W@ 2 oy 2 xy 2  y 2 /hy 2 /y Times New RomanR- 2 @_i> 2 Bi> 2 0 i> 2 d i> 2  i>METAbjNative1414&1p (24(24CompObj7FZObjInfoNativeEquation Native F 2 QiT>|PSymbol- 2 7= 2 q 2 q 2 q 2 q 2 q 2 pq 2  2  2  2  2  2 p PSymbol- 2 .-{Times New RomanSy- 2 o[| 2 o!]~ 2 [| 2  ,` 2 g ]~ 2 /[| 2 /,` 2 /x.` 2 /.` 2 /r.` 2 /,` 2 /k]~ Times New RomanR- 2 1p 2 p 1p 2  2p 2 `1p 2 2pTimes New RomanSy- 2 o}0 2 /0MT Extra- 2 O & "System-"D"Dࡱ FMicrosoft Equation 2.0 DS Equation Equation.2ࡱ; ࡱ; pB'W (W  W i =[y i1 ]0[y i1 ,y i2 ]O0[y i1 ,...,y iT-2 ][]y 2  yࡱ; ࡱ; L({ hࡱ; ({O  .1  @%&$ & MathTypepTimes New Roman - 2 `FE 2 `"y 2 `y 2 ` _917191611Fx~x~Ole PIC LMETA y 2 `%jk 2 `stk 2 `tk 2 `#T Times New Roman0- 2 it>> 2 Sit>> 2 R it>> 2  j>Times New Romans - 2 `,[(| 2 ` ) 2 ` ]~ 2 `,` 2 `j.` 2 `.` 2 `d.` 2 `,` 2 `8!,` 2 `!.` 2 `9".` 2 `".` 2 `5#,`PSymbol- 2 `8D 2 `D 2 `- 2 ` = 2 `= 2 `I- 2 `c= PSymbol- 2 -{ 2  -{PSymbol- 2 `g Times New Roman- 2 d 1pTimes New Roman0- 2 `0 2 `*2 2 `X1 2 ` 32 ` `````````` 2 ` ```` 2 `  ```` & "System- O@ࡱ FMicrosoft Equation 2.0 DS Equation Equation.2ࡱ; ࡱ; Y/H8&oG$oG E[(Dy itCompObj1   FZObjInfo&'()+05678Equation NativeIJKLO UVWXY_917175975gijklmnopFx~x~H -gDy it-1 )y it-j ]=0              j=2,...,t-1    t=3,...,T.` 2 `.` 2 `ࡱ; ࡱ; L; W<Tࡱ; ; WU S .Olenfo PICion Native LMETA5258tive FCompObj3FZ    !$&'()*+,.356789:?ABCDEFGHIJKLMNPSVXYZ[\]^_`abcdefghijklmnopqrsuxyz{|1   `&  & MathType`Times New RomanZ- 2 `FE 2 `W@ 2 `u Times New Roman - 2 i> 2 i>Times New RomanZ- 2 `;( 2 `C)PSymbol- 2 d(^ 2 `#= 2 `2DTimes New RomanZ- 2 `_0 & "System-s New Roman<-ࡱ;  FMicrosoft Equation 2.0 DS Equation Equation.2ࡱ; ࡱ; Y@/HoGloG E(2W i Du i )=0ࡱ; ObjInfoNative  F Equation Native)*+,-/ F\@_917176033GHJMN% Fx~x~jOleeghijklmnp vxyࡱ; LJW Tࡱ; JWV  .1   &@ & MathType`PSymbol- 2 `>D 2 d^ 2 `= 2 `3- 2 ` - PSymbol-PICnfo   LMETAon Native  CompObj8tive FZObjInfo3F 2 -{Times New Roman - 2 `(u 2 `Ru 2 `Pu 2 ` u 2 `1u Times New RomanZ- 2 i> 2 i> 2 i> 2  iT>| 2 iT>|Times New Roman - 2 `( 2 `,` 2 `[ .` 2 ` .` 2 `3 .` 2 ` ,` 2 `) Times New RomanZ- 2 W3p 2 X2p 2 H1p & "System-ࡱ;  FMicrosoft Equation 2.0 DS Equation Equation.2ࡱ; ࡱ; YΠ/HoGloG D2u i =(Equation Native _917191854tiveFx~x~Oleion Native F"PIC75554 F#Lu i3 -u i2 ,...,u iT -u iT-1 ) `&ࡱ; LDࡱ; >   .1  &`e & MathType0Times New Roman-METAbj %CompObjNative-ZObjInfoNativeF/Equation Native F0< 2 `4TPSymbol- 2 `Times New Roman- 2 `3 & "System-cࡱ;  FMicrosoft Equation 2.0 DS Equation Equation.2ࡱ; ࡱ; p E&/E(/E T3ࡱ; L{hࡱ; {.B  .1  @&v & MathType0PSymbol7- 2 d^Times New Roman-_917253694Fx~x~@OleObj 1PICocument 2LMETAPool 4@ 2 `3W@&,MathTypeUU  2WC;9%(#" & "System-ࡱࡱ; Y /H  2Wࡱ; LS4c @ࡱ; ObjInfo2F;Equation Native <<_917176256t Fx~x~zLOlePool =@ PICnfoNative "F>L METAon Native)*+,-/ F@@CompObj3GHJMN!#FOZObjInfoghijklmnp$vxyQS4   .1  &` & MathTypePPSymbol- 2 d^ 2 `= 2 dn^ 2 ` + PSymbol- 2 -{Times New Roman - 2 `3W@ 2 `y 2 `W@ 2 `Ky 2 ` W@ 2 `uPSymbol- 2 `D 2 `aD 2 `DTimes New RomanZ- 2 `( 2 ` ) 2 `'C Times New Roman - 2 o 1pPSymbol- 2 `j g & "System-New RomanZ-ࡱ FMicrosoft Equation 2.0 DS Equation Equation.2ࡱ; ࡱ; Y`/HoGoG 2WDy=2W(Dy -1 )g+WDuࡱ; L4|ࡱ; 4   .Equation Native R|_917176367tive,'Fx~x~Oleion Native FTPIC75554 &)FULMETAfoNative FW( CompObjNative)*+,-/(*FtZ@ObjInfo3GHJMN+FvEquation Nativeijklmnp vxyw\1  `0&/ & MathType`MT Extra- 2 sc$Times New Roman6M- 2 [(| 2 ) 2 ( 2 J ( 2 ) 2 ) 2 H( 2 q)]~ 2 ][(| 2 ) 2 I ( 2 "( 2 \') 2 =)) 2 ,( 2 .)]~PSymbol- 2 %g Times New Roman6M- 2 1p 2 *1p 2 1p 2 1p 2 1p 2 w1p 2 C*1pPSymbol- 2 = 2 8^ 2  ^ 2  ' 2 ^ 2 ^ 2 4"^ 2 $' 2 2,^ PSymbol- 2 -{ 2 {-{ 2 k-{ 2 m-{ 2 -{ 2 )-{PSymbol- 2 D 2 D 2 iD 2 %-DTimes New Roman6M- 2 y 2 W@ 2  W@ 2  I 2 G 2 W@ 2 W@ 2 y 2 Sy 2 W@ 2  W@ 2 2#I 2 <&G 2 'W@ 2 *W@ 2 .y Times New Roman- 2 u N 2 #N & "System-- 2 ࡱ FMicrosoft Equation 2.0 DS Equation Equation.2ࡱ; ࡱ; Y@/HD&oG'oG "g  1 =[(Dy -1 ")W(2W(I N G)W) -1 2W(Dy -1 )] -1 [(Dy -1 ")W(2W(I N G)W) -1 2W(Dy)]1p 2 *ࡱ; ࡱ; L] Dࡱ; _917176602   .Fx~x~ Ole$&'()*+,. 56789}PICDEFGHIJKLMNP -0VXY~L`METAdefghijklmnop uxy]B  .1  &W & MathTypePSymbol- 2 $^ 2 3' 2 = 2 $ ^ 2 9E  PSymbol- 2 B ={Times New Roman- 2 3W@ 2 I 2 G 2 ?W@ 2  W@ 2  GW@ Times New Roman- 2 'N 2  i> 2 i> 2 B0 i> 2 NTimes New Roman- 2 ( 2 ) Times New Roman- 2 B 1p & "System-ࡱ FMicrosoft Equation 2.0 DS EqCompObjNative /1FZ ObjInfoNative)*+,-/2F@Equation NativeJMN F_917177500ghijklmnp:5Fx~uation Equation.2ࡱ; ࡱ; Y΀/H)oG`+oG 2W(I N G)W=2W i GW ii=1N  ࡱ; ࡱ; LS pࡱ; OleObjNative1414&1p (24(24PICnfo7 47FLMETAon Native (CompObj068FZ     2 !#"&$%('*),+.-/0315O47698:;<=>A?@BCDFEHGJILKNMPTlQRSUVWXZY\[^]`_acbdefghijkmnopqsrutwvyx{z|}~S   .1   @&/ & MathType0Times New RomanSy- 2 5GPSymbol- 2 = 2 v|- 2 - 2 b - 2 |- 2 v - 2 - 2  2  2  2 R 2  2 8 2  2   2  2 L 2 L 2 L 2 RL 2 L 2 8L 2 L 2  L 2 LTimes New RomanSy- 2 v2 2 vO1 2 v 0 2 vJ0 2 v00 2 i1 2 2 2 5 1 2 J0 2 00 2 0 2 O1 2  2 2 J0 2 00 2 v 0 2 v 0 2 v 0 2 v I2 2 v 1 2 0 2 0 2 0 2 1 2 /2MT Extra- 2 v" L 2 " L 2 " L 2 6M 2 6M 2 6 M 2 6" O 2 6jM 2 6PM 2 v " L 2 " L & "System-ࡱ FMicrosoft Equation 2.0 DS Equation Equation.2ࡱ; ࡱ; pBW x W  G=2-10L00-12-1L000-12L00MMMOMM000L2-1000L-12ObjInfo49FEquation Native _917176715t V<F2LOlePool @ ()ࡱ; ࡱ; L#|ࡱ; #@  .1  `& & MathType`MT Extra- 2 sc$Times New Romani-PICnfo2 ;>FLMETAon Native CompObj6t=?FZObjInfol@@  2 4[(| 2 ) 2 A ( 2 j)]~ 2 V[(| 2 ) 2 c( 2 )]~PSymbol- 2 %g Times New Romani- 2 !2p 2 N1p 2 1p 2 1p 2 1p 2 p1p 2 /1pPSymbol- 2 = 2 \^ 2  ^ 2 ~^ 2 ^ PSymbol- 2 -{ 2 -{ 2 d-{ 2 f-{ 2 -{ 2 -{PSymbol- 2 @D 2  D 2 bD 2 DTimes New Romani- 2 *y 2 WV@ 2 x W@ 2 y 2 Ly 2 WV@ 2 W@ 2 y Times New Roman- 2  N 2 N & "System-? Vࡱ;  FMicrosoft Equation 2.0 DS Equation Equation.2ࡱ; ࡱ; Y/H8&oG'oG "g  2 =[(Equation Native _917176871tiveCFOleion Native FPIC75554 BEFLDy -1 ")WV N  -1 2W(Dy -1 )] -1 [(Dy -1 ")WV N  -1 2W(Dy)]1p ࡱ; ࡱ; L Dࡱ; X  .METAbjNative F CompObjNative)*+,-/DFFZ@ObjInfoNativeJMNGFEquation Nativeijklmnp F1  &@W & MathTypeTimes New Roman,- 2 0V 2 W@ 2 u 2 N u 2  W@ Times New Roman- 2 N 2 i> 2 i> 2  i> 2 i> 2 Bi> 2 NPSymbol- 2 T= 2 $_^ 2 $6 ^ 2 9 PSymbol- 2 B={Times New Roman,- 2 ( 2 T )( 2  )PSymbol- 2 D 2 d D Times New Roman,- 2 BS1p & "System-ࡱ;  FMicrosoft Equation 2.0 DS Equation Equation.2ࡱ; ࡱ; sΠGWFx WF V N =2W i (Du i )(Du i ")W ii=1N ࡱ; LWT_917176984tive AOJF OleObjNative)*+,-/ F@PICnfoNativeJMN ILFLMETAon Nativeijklmnp Fࡱ; WvC  .1   & & MathTypePMT Extra- 2 Sc$PSymbol- 2 %g Times New Roman- 2 %1p & "System-6L      $&'()*+,.356789:;=BDEFGHIJKLMNPSVXYZ[\]^`eghijklmotvwxyz{}ࡱ;  FMicrosoft Equation 2.0 DS Equation Equation.2ࡱ; ࡱ; p E(C/C "g  1ࡱ; LWTࡱ; CompObj2KMFZObjInfoNativeNEquation Native F<_917177015QF=@ Oleion Native PIC75827tive PSFLMETA5258tive FCompObj3RTFZWW  .1   &h & MathType0PSymbolE- 2 `>DTimes New RomanX- 2 `(u & "System-4E FEz ࡱ; 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L WTࡱ;  Wf  I .1    & & MathType`PSymbolH- 2 `/e 2 `a Times New Roman- 2 it>> 2 i>Times New Roman- 2 `]uTimes New Roman- 2 `,` 2 `m `2 `s and `` Times New Roman- 2 .it>> & "System-ࡱ;  FMicrosoft Equation 2.0 DS Equation Equation.2ࡱ; ࡱ; Y`/H&oGX(oG e it , a i  and u it `ࡱ; LW,Tࡱ; WV  .ObjInfoNativeqQEquation Native FR|_917177257tivedtFOle75554 FTPICObjNative svFUL METAfoNative)*+,-/ FW@CompObjNativeJMNuwF_ZObjInfo0ghijklmnpxFa1   & & MathTypePMT Extra- 2 Sc$PSymbol- 2 %g Times New Roman- 2 !2p & "System-ࡱ;  FMicrosoft Equation 2.0 DS Equation Equation.2ࡱ; ࡱ; p E )C)C "g  2ࡱ; LWTࡱ; WvC  .1   & &Equation Native Fb< _917177266tive)*+,-/{F@OlenfoNativeJMN FcPICon Nativeijklmnp z}FdLMETAfo2 FfCompObjNative|~nZObjInfo5tFpEquation Native q<@ MathTypePMT Extra- 2 Sc$PSymbol- 2 %g Times New Roman- 2 %1p & "System-6L ࡱ;  FMicrosoft Equation 2.0 DS Equation Equation.2ࡱ; ࡱ; p E(C/C "g  1ࡱ; LWTࡱ; WT  .1   & & MathType`Times New RomanZ -_917177296yFڀfOleObjNative rPICnfo5t FsLMETAon Native u@ 2 `0u Times New Roman- 2 it>> & "System-WOn itP_ETRࡱ; 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ࡱ; CompObjNative FZ ObjInfoNative)*+,-/F@Equation NativeJMN F_917195499ghijklmnpFڀڀY/H'oG(oG y it =gy it-1 +"bx it +e it               i=1,...,N   t=1,...,T=ࡱ; LWTࡱ; WN  .OlenfoNative F PICion Native)*+,-/ FL@META6033GHJMN FhCompObjghijklmnpvxyZ1    & & MathType`PSymbolH- 2 `/e 2 `La Times New Roman6- 2 it>> 2 i> 2 Qit>>Times New Roman- 2 `uPSymbol- 2 `1= 2 `[+ & "System-ࡱ FMicrosoft Equation 2.0 DS Equation Equation.2ࡱ; ࡱ; Y`/H&oGt(oG e it =a i +u it    &ࡱ; L4@ObjInfo1FEquation Native |_917192833FڀڀLOle PICObjNative FL METAfoNative)*+,-/ F@CompObjNativeJMNFZObjInfo0ghijklmnpFࡱ; 4:  .1  & & MathTypePTimes New Roman- 2 `Lx Times New Roman- 2 it>> & "System-ࡱ;  FMicrosoft Equation 2.0 DS Equation Equation.2ࡱ; ࡱ; ) WF&D(D x itࡱ; LDࡱ; L  .Equation Native <_917192768tiveFڀڀOleion Native FPIC75554 FLMETA2770 FCompObjZObjInfoEquation Native <1  &`E & MathType Times New Roman- 2 `EKPSymbol- 2 `Times New Roman- 2 `1 & "System-ࡱ;  FMicrosoft Equation 2.0 DS Equation Equation.2ࡱ; ࡱ; Y /Hp'oG)oG K1 ࡱ; L+ࡱ; +" F .1  '&'E &_917203028yFڀ Ole PIC LMETA       #%&'(*/12345679>@ABCDEFGHJMPRSTUVWXYZ[\]_beghijklnsuvwxyz| MathTypeMT Extra- 2 }$$ 2 `$$Times New Roman- 2 [(| 2  ) 2 ( 2 )]~ 2 [(| 2 ) 2 $( 2 &)]~PSymbol- 2 g 2 bPSymbol- 2 1 2 1 2 1 2  2  2  2 = 2 ] ^ 2 ?^ 2 =^ 2 $^ PSymbol- 2 -{ 2  -{ 2 -{ 2 -{ 2 -{ 2 !-{PSymbol- 2 D 2 D 2 2D 2 D 2 D 2 D 2 %DTimes New Roman- 2 y 2 X 2  WV@ 2 W@ 2 y 2 X 2 y 2 X 2 WV@ 2 "W@ 2 %y Times New Roman- 2  N 2  N Times New Roman- 2 D1p 2 >1p 2 X1p 2 e1p 2 $1p 2 "1p & "System-Tiࡱ FMicrosoft Equation 2.0 DS Equation Equation.2ࡱ; ࡱ;  W^]x ] "g "b ()=[(Dy -1 DX")WV N  -1 2W(Dy -1 DX)] -1 [(Dy -1 DX")WVCompObj2FZObjInfoNativeEquation Native F<_917203470F  @  N  -1 2W(Dy)]ࡱ; Lࡱ;   .1  ``& E & MathType PSymbolB- 2 : & "SystemOleObjNative F! PICnfoNative)*+,-/ F"L@METAon NativeJMN F$(CompObj0ghijklmnpF)Z-ࡱ FMicrosoft Equation 2.0 DS Equation Equation.2ࡱ; ࡱ; p B*W x1W   ࡱ; LWTࡱ; ObjInfo1F+Equation Native ,<_917203528rF  LOle -PICnfo1 F.LMETAon Native 0CompObj3F8ZObjInfo:WN_  .1   & & MathType`PSymbolB- 2 `>DTimes New Roman- 2 `(x Times New Roman- 2 it>> & "System-90XCG ࡱ;  FMicrosoft Equation 2.0 DS Equation Equation.2ࡱ; ࡱ; p B*W 1W  Dx itࡱ; L{hࡱ; {X " .Equation Native ;<_917203627tiveF  Oleion Native F<PIC75554 F=LMETA3694 F?hCompObjIZObjInfoentKEquation Native L\@ 1  @& & MathType`Times New Roman- 2 3WV@ 2 W@ Times New Romans - 2 GN PSymbol- 2 -{PSymbol- 2 M^ Times New Roman- 2 |1p & "System-[(| 2 ^)ࡱ FMicrosoft Equation 2.0 DS Equation Equation.2ࡱ; ࡱ; s@GWFWF WV N  -1 2Wࡱ; ࡱ; Lg |_917203675F  ZOlenfo NPICion Native OLMETA1803 FQ(ࡱ; g X } .1  `@ &  & MathType`Times New Roman- 2 .( 2 ( 2 ) 2 | )PSymbol- 2 /^ 2 ' PSymbol- 2  -{Times New Roman(- 2 W@ 2 -I 2 {G 2 W@ Times New Roman- 2 N Times New Roman(- 2 1p & "System-2 >1 2 1ࡱ FMicrosoft Equation 2.0 DS Equation Equation.2ࡱ; CompObjNative F^Z ObjInfoNative)*+,-/F`@Equation NativeJMN Fa|_917193327ghijklmnpF  ࡱ; s`GWFlWF (2W(I N G)W) -1" ࡱ; L4@ࡱ; 4:  .1  & &OleObjNative Fc PICnfoNative)*+,-/ FdL@METAon NativeJMN FfCompObj0ghijklmnpFmZ MathTypePTimes New Roman- 2 `Lx Times New Roman- 2 it>> & "System-ࡱ;  FMicrosoft Equation 2.0 DS Equation Equation.2ࡱ; ࡱ; ObjInfoNativeoEquation Native Fp<_917193340tiveF  "Ole75554 Fq) WF&D(D x itࡱ; LW,Tࡱ; W64  .1   & & MathType`PSymbolB- 2 `@m Times New Roman-PICnfo1 FrLMETAon Native tCompObj3F{ZObjInfo} 2 Oi> & "System-ࡱ;  FMicrosoft Equation 2.0 DS Equation Equation.2ࡱ; ࡱ; p B`&W *W  m, iࡱ; Equation Native ~<_917193422tiveF  Oleion Native FPIC75554 FLL4@ࡱ; 4:  .1  & & MathTypePTimes New Roman- 2 `Lx Times New Roman- 2 it>> & "System-METAfo1 FCompObjNativeZObjInfo8FEquation Native <ࡱ;  FMicrosoft Equation 2.0 DS Equation Equation.2ࡱ; ࡱ; ) WF&D(D x itࡱ; LWTࡱ; _917614180F  OleObjNative PICnfo8 FLMETAon Native WL C .1   & & MathType`Times New RomanD- 2 `FE 2 `x 2 `?u Times New Roman- 2 it>> 2  is>WTimes New RomanD- 2 `;( 2 `)PSymbol- 2 `Times New RomanD- 2 `0 & "System-ࡱ FMicrosoft Equation 2.0 DS Equation Equation.2ࡱ; ࡱ; Y@/H'oGP)oG E(x it u is )0ࡱ; CompObjNativeZObjInfo4tiveFEquation Native F\_917614161 FA=A=#LOlenfo1 FPICion Native LMETA2833 FCompObjZࡱ; LW,Tࡱ; WL  .1   & & MathType`Times New Roman- 2 `Kx Times New Roman- 2 it>> & "System- 2 it>> &ࡱ;  FMicrosoft Equation 2.0 DS Equation Equation.2ࡱ; ࡱ; s G'WFH)WF x itࡱ; L*WTObjInfo8FEquation Native <_917193524<FA=A=LOle PIC03028 FLMETA CompObjZObjInfoࡱ; *W; ] .1   &@ & MathType`Times New Roman- 2 `Kx 2 `x Times New Roman- 2 i> 2 is>W Times New Roman- 2 81p 2 1pTimes New Roman- 2 `,` 2 `).` 2 `.` 2 `.` 2 `o,` PSymbol- 2 b-{ & "System-ࡱ FMicrosoft Equation 2.0 DS Equation Equation.2ࡱ; ࡱ; Equation Native |_917614351tiveFA=A=p<Ole93340tive FPIC75554  FLp`B,)W *W  x i1 ,...,x is-1- 2 `ࡱ; L+WTࡱ; +WO  .1   & & MathType`Times New RomanC-META3028 F(CompObj ZObjInfo Equation Native \ 2 `Kx Times New Roman- 2 is>W PSymbol- 2 -{ Times New Roman- 2 11p & "System-- 2 `0u ࡱ FMicrosoft Equation 2.0 DS Equation Equation.2ࡱ; ࡱ; s@G&WF'WF x is-1.1ࡱ; ࡱ; LWTࡱ; W  #+ .1   &Q &_917614340vFA=A=Oleion Native PIC76715t  FLMETAPool h@ MathType`Times New Romanܪ- 2 `0u Times New Roman- 2 is>W PSymbol- 2 -{ Times New Roman- 2 1p+&LMathTypeUU@ u is-1 & "System-ࡱObjInfoNativeEquation Native F\_917193847tiveFA=A=<Ole75554 Fࡱ; s@G  u is-1ࡱ; ࡱ; L> #ࡱ; > > A .1   9&8 &PICnfo1 FLMETAon Native  CompObj8FZObjInfo      "#$%&').0123456789:;<>ADFGHIJKMRTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~ MathTypeTimes New RomanV- 2 3W@ 2 w,y 2 whx 2 w x 2  y 2  y 2 kx 2 x 2 x 2 7y 2 7"y 2 7%x 2 7)x 2 v5tk 2 5tk 2 65tk 2 67T Times New Roman- 2 @ai> 2 i> 2 -i> 2 t i> 2 i> 2 i> 2 0i> 2 wi> 2 i> 2 i> 2 "iT>| 2 ]&i> 2 *iT>| PSymbol- 2 4+{ 2 #-{ 2 +-{PSymbol- 2 = 2 {B^ 2 { ^ 2 E^ 2 ^ 2 ^ 2 ;r&^ 2 ;*^ 2  2  2  2  2  2 h 2 - 2 - 2 - 2 - 2 - 2 h- 2 v6= 2 6= 2 66=Times New RomanV- 2 w[| 2 w,` 2 w ,` 2 wy ]~ 2 6 [| 2 `,` 2 ,` 2 ,` 2 q,` 2 ]~ 2 7A[| 2 7k,` 2 7.` 2 7r .` 2 7 .` 2 7t!,` 2 7$,` 2 73',` 2 7'.` 2 7:(.` 2 7(.` 2 7<),` 2 7,]~ Times New Roman- 2 &1p 2 m1p 2  2p 2 1p 2 2p 2 p1p 2 2p 2 13p 2 1p 2 D$2p 2 &1p 2 ,1pTimes New RomanV- 2 70 2 v73 2 74 2 w$0 2 vM. `` 2 vQ/-2 v0 refers to`~`k 2 ve5 ` 2 ?. `` 2 C/-2 0 refers to`~`k 2 W5 ` 2 6- ``` 2 6^/-2 6 0 refers to`~`k 2 6r5 `MT Extra- 2 O 2  3M & "System- 2 x 2 ࡱ FMicrosoft Equation 2.0 DS Equation Equation.2ࡱ; ࡱ; `W^X]] W i+ =[y i1 ,2x i1 ,2x i2 ]0[y i1 ,y i2 ,2x i1 ,2x i2 Equation Native |_917194263tive'5FA=A=p<Ole93340tive FPIC75554 FL,2x i3 ]O0[y i1 ,...,y iT-2 ,2x i1 ,...,2x iT-1 ][]  - refers to t=3  - refers to t=4M   - refers to t=Tࡱ; L4@ࡱ; 4:  .1  & & MathTypePTimes New Roman- 2 `Lx Times New Roman- 2 it>> & "System-ࡱ; METAfo8 F!CompObjNative(ZObjInfo4F*Equation Native +< FMicrosoft Equation 2.0 DS Equation Equation.2ࡱ; ࡱ; ) WF&D(D x itࡱ; Lp W|Tࡱ; p W   ._917194262"FnnnnZOlenfoNative ,PICion Native !$F-LMETA5554 F/h1   ` &  & MathType`Times New Roman- 2 `FE 2 `x 2 `?u 2 `u Times New Roman- 2 it>> 2  is>W 2 is>WTimes New Roman- 2 `;( 2 `Q) PSymbol- 2 6-{PSymbol- 2 `&= Times New Roman- 2 1pTimes New Roman- 2 `W 0 & "System-ࡱ FMicrosoft Equation 2.0 DS Equation Equation.2ࡱ; ࡱ; CompObj1#%F=ZObjInfoNative&?Equation Native F@|_917194261 )Fnnnn-s`G%WFp'WF E(x it u is u is-1 )=0 ࡱ; LWTࡱ; W6K  .1   &` & MathType`Times New Roman-Olenfo1 FBPICion Native (+CLMETA2833 FECompObj*,LZ 2 `Kx Times New Roman- 2 i> & "System- 2 i> & ࡱ; 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ࡱ; p B  x 1itࡱ; L4@ࡱ; 4d  .1  & & MathTypePTimes New Roman- 2 `Lx Times New RomanOle03028 F)PIC *LMETA ,CompObj3Z- 2 it>> & "System-F ࡱ;  FMicrosoft Equation 2.0 DS Equation Equation.2ࡱ; ࡱ;  W^|)] +] x itࡱ; ObjInfo0F5Equation Native 6<_917636115FLOleon Native 7PIC14180 F8LMETAbjNative :CompObj8FBZObjInfoNativeDL{h,ࡱ; {   .1  @& & MathTypePTimes New Romanw - 2 @Jx Times New Roman- 2 6i> Times New Romanw - 2 1p 2 3p & "System-ࡱ FMicrosoft Equation 2.0 DS Equation Equation.2ࡱ; ࡱ;  W^D)]*] x 1i3ࡱ; L{4h@Equation Native E<_917636038tiveFO<Ole35818tive FFPIC75554 FGLࡱ; {4d  .1  @& & MathTypePTimes New Roman- 2 `Lx Times New Roman- 2 Ui> Times New Roman- 2 1p 2 1p & "System-META4340 FICompObjNativeQZObjInfo5tFSEquation Native T<@ d8MPLB<ࡱ FMicrosoft Equation 2.0 DS Equation Equation.2ࡱ; ࡱ;  W^)]-] x 1i1ࡱ; L4|@ࡱ; _917636046FІІOleion Native UPIC93524 FVLMETA X4^   .1  `&  & MathTypePTimes New Roman- 2 `Lx Times New Roman- 2 Wi> Times New Roman- 2 1p 2 2p & "System-ࡱCompObj2F`ZObjInfoNativebEquation Native Fc<_917255033FІІ@  FMicrosoft Equation 2.0 DS Equation Equation.2ࡱ; ࡱ;  W^)]@*] x 1i2ࡱ; L 4d@ࡱ;  4N   .Ole94513 FdPICnfoNative eLMETAon Native FgHCompObj4FuZ1  &` & MathTypePTimes New Roman- 2 `LE 2 `x Times New RomanĻ- 2 i> 2 i>Times New Roman- 2 `Z( 2 `)Symbol- 2 `e Times New Roman- 2 2p 2 M1p 2 1pTimes New RomanĻ- 2 `0Symbol- 2 `t= & "System-ࡱ;  FMicrosoft Equation 2.0 DS Equation Equation.2ࡱ; ࡱ; ObjInfoNativewEquation Native Fx|_917255032tiveFІІ\Ole14161 Fz`W^)]t*] E(e i2 x 1i1 )=0ࡱ; L; W<Tࡱ; ; W6;  .1   `&  & MathType`Times New Roman-PICObjNative {LMETAfo4tive F}(CompObjNativeFZObjInfo1F 2 `FE 2 `ax Times New Roman- 2 it>> 2 it>>Times New Roman- 2 `;( 2 `I)PSymbol- 2 `e Times New Roman- 2 1pTimes New Roman- 2 `O0PSymbol- 2 `= & "System-0tXCG90 ࡱ FMicrosoft Equation 2.0 DS Equation Equation.2ࡱ; ࡱ; p`Bt*W `1W  E(e it x 1it )=0 2 `eࡱ; Equation Native |_917202331tiveFІІOleion Native FPIC75554 FLL> #Xࡱ; > P   .1   9&8o & MathTypeTimes New RomanV- 2 @3W@ 2 8W@ 2 'h x 2 ' x 2 g*x 2 ix 2 5&tk 2 ~+T 2 #&tk 2 6&&tk 2 &METAfo1 FH CompObjNativeZObjInfo8FEquation Native tk Times New Romanv- 2 ai> 2 fi> 2  i> 2 0 i> 2 Mi> 2 G iT>| PSymbol- 2 +{ 2 K+{ 2 +{PSymbol- 2 @g= 2 +B ^ 2 + ^ 2 k^ 2 C^ 2  2 K  2 % 2  2  2 x 2  2 Z  2  2 K  2 % 2  2  2 x 2  2 Z Times New RomanV- 2 0 2 0 2 5(3 Times New Romanv- 2  1p 2  1p 2  1p 2  2p 2 1p 2 3p 2 G 1pTimes New RomanV- 2 '[| 2 'a ,` 2 'A]~MT Extra- 2 O 2 v)MTimes New RomanV-2 } ``````````2 = `````` 2 -2  refers to`~`k 2 % ` 2 '= 2 (,` 2 g).` 2 ).` 2 g*.` 2 *,`2 S, differenc`k~~2 2 e equation`kk 2 L8s2  - refers t`~`k 2 %o ` 2 &=2 (( 2 levels e`kk`2 -quationkk2 6 - refers t`~`k 2 6%o ` 2 6&=2 6&( 3 levels e`kk`2 6-quationkk 2 vC( ````2  - refers t`~`k 2 $o ` 2 &=2 ( T levels e`kk`2 -quationkk & "System-rgeCapacity$*ࡱ; 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