Estimating Efficiency Spillovers with State Level Evidence for Manufacturing in the U.S.

Transcription

1 Estmatng Effcency Spllovers wh State Level Evdence for Manufacturng n the U.S. Anthony Glass a,, Karlgash Kenjegaleva a, Robn C. Sckles b a School of Busness and Economcs, Loughborough Unversy, Lecs, LE11 3TU, UK b Department of Economcs, Rce Unversy, Houston, U.S., and School of Busness and Economcs, Loughborough Unversy, Lecs, LE11 3TU, UK Abstract Un specfc effects are often used to estmate non-spatal effcency. We extend ths effcency estmator to the case where there s spatal autoregressve dependence and dstngush between own effcency and spllover effcency. We apply our estmator to a cost fronter model for state manufacturng n the U.S. JEL Classfcaton: C23; C51; D24 Keywords: Spatal Autoregresson, Fronter Modelng, Panel Data, Effcency Spllovers Correspondng author. E-mal: A.J.Glass@lboro.ac.uk. Tel.: Fax.: Preprnt submted to Economcs Letters June 4, 2013

2 Introducton The classc Schmdt & Sckles (1984) (SS from hereon) tme-nvarant effcency estmator benchmarks the relatve performance of the cross-sectonal uns usng the fxed or random effects. The SS estmator was extended to the case of tme-varant effcency by Cornwell et al. (1990) (CSS from hereon). We extend the non-spatal CSS effcency estmator to the case where there s spatal autoregressve dependence. Ths nvolves estmatng drect effcency (own effcency accountng for feedback effects), ndrect effcency (spllover effcency) and total (drect plus ndrect) effcency. We apply our spatal tme-varant effcency estmator to a cost fronter model for manufacturng n the U.S. The model s estmated usng annual data for the contguous states from The Determnstc Spatal Autoregressve Cost Fronter Model We develop a spatal CSS type effcency estmator for determnstc fronter models. The estmator s appled to the determnstc spatal autoregressve cost fronter model n equaton (1). We do not dscuss spatal panel data models n detal here but for a comprehensve and up-to-date survey see Baltag (2011). C =κ + α + τ t + TL (h, q, t) + λ = 1,..., N ; t = 1,..., T. N w j C jt + z φ + ε, (1) j= N s a cross-secton of uns; T s the fxed tme dmenson; C s the cost of the h un; α s a un specfc fxed effect; τ t s a tme perod effect; T L (h, q, t) represents the technology as the translog approxmaton of the log of the cost functon where h s a vector of normalzed nput prces and q s a vector of outputs; 1 λ s the spatal autoregressve parameter; w j s an element of the spatal weghts matrx, W ; z s a vector of exogenous 1 In the applcaton, h s a vector of three nput prces, prce of producton labor, prce of non-producton labor and prce of energy, all of whch are normalzed by a fourth nput prce, the prce of capal. Furthermore, n the applcaton q s a sngle output and not a vector of outputs. 2

3 61 40 characterstcs and φ s the assocated vector of parameters; ε s an..d. 41 dsturbance for and t wh zero mean and varance σ W s a (N N) matrx of known posve constants whch descrbes the 43 spatal arrangement of the cross-sectonal uns and also the strength of the 44 spatal nteracton between the uns. All the elements on the man dagonal 45 of W are set to zero. λ s assumed to le n the nterval (1/r mn, 1), where 46 r mn s the most negatve real characterstc root of W and because W s 47 row-normalzed n the applcaton, 1 s the largest real characterstc root 48 of W. 2 We model the effects of tme n equaton (1) by, frstly, ncludng a 49 tme trend, t, and the assocated quadratc and cross terms n the translog 50 functon and secondly, va tme perod effects to account for common shocks 51 to manufacturng costs across the cross-sectonal uns. 52 Equaton (1) s estmated usng maxmum lkelhood and we ensure that 53 λ les n s parameter space, account for the endogeney of the spatal au- 54 toregressve varable and also the fact that ε t s not observed by ncludng 55 the scaled logged determnant of the Jacoban transformaton of ε t to C t 56 (.e. T log I λw ) as a term n the log-lkelhood functon. Detals of 57 the estmaton of equaton (1) by demeanng n the space dmenson can be 58 found n Elhorst (2009) wh the followng caveat. Lee & Yu (2010) show 59 that demeanng n the space dmenson to estmate a model such as that n 60 equaton (1) results n a based estmate of σ 2 when N s large and T s fxed, whch we denote σb 2. Followng Lee & Yu (2010) we correct for ths bas by 62 replacng σb 2, σbc 2 = T σ2 B /(T 1), whch changes the t-values. 64 We do not also demean n the tme dmenson even though we nclude 65 tme perod dummes. Ths s because ths would elmnate the tme trend 66 and the assocated quadratc term whch are sgnfcant n the applcaton. 67 Moreover, by retanng n equaton (1) the tme trend and the assocated 68 cross and quadratc terms, the fted model could be used to conduct a spa- 69 tal TFP growth decomposon wh, among other thngs, drect and nd- 70 rect techncal change components. Glass et al. (2013) propose such a spatal 71 TFP growth decomposon but nclude, among other thngs, own effcency 72 change rather than drect and ndrect effcency changes. Ther spatal TFP 2 Furthermore, (I N λw ) s taken to be nonsngular for all values of λ n the parameter space. It s also assumed that the row and column sums of W and (I N λw ) are bounded unformly n absolute value. Ths lms the spatal correlaton to a manageable degree. 3

4 growth ecomposon could be extended to nclude drect and ndrect effcency changes by followng the approach whch we set out here to calculate drect and ndrect effcences Margnal Effects and ect, Indrect and Total Effcences A key recent development n appled spatal econometrcs s the demonstraton by LeSage & Pace (2009) that the coeffcents on the explanatory varables n a model wh spatal autoregressve dependence such as that n equaton (1), cannot be nterpreted as elastces. Ths s because the margnal effect of an explanatory varable s a functon of the spatal autoregressve varable. In lght of ths, LeSage & Pace (2009) propose the followng approach to calculate drect, ndrect and total margnal effects for the explanatory varables. Stackng successve cross-sectons we can rewre equaton (1) as: C t = (I λw ) 1 κι + (I λw ) 1 α + (I λw ) 1 τ t ι+ (I λw ) 1 Γ t β + (I λw ) 1 z t φ + (I λw ) 1 ε t, (2) where ι s an (N 1) vector of ones; α s an (N 1) vector of fxed effects; Γ t s an (N K) matrx of stacked observatons for T L (h.q, t) t ; and β s a vector of translog parameters. Dfferentatng equaton (2) wh respect to the k th varable n T L (h, q, t) t, Γ k,t, yelds the followng vector of partal dervatves: [ C Γ k,1 ] C Γ k,n t = C 1 Γ k,1 C 1 Γ k,n C N Γ k,1 C N Γ k,n t β k 0 0 = (I λw ) 1 0 β k, (3) 0 0 β k where the product of the matrces on the far rght of equaton (3) s ndependent of tme. The man dagonal of ths product conssts of drect margnal 3 Not demeanng n the tme dmenson does not create an ncdental parameter problem n the applcaton as the sample only spans twelve years. In the applcaton, when estmatng the non-spatal model usng standard software, a small number of tme perod dummes are dropped by the software for reasons of collneary. We drop the same tme perod dummes when ftng the spatal fronter models. 4

5 effects and all the non-dagonal elements of ths product are ndrect margnal effects. Equaton (3) yelds dfferent drect and ndrect margnal effects on each un so to faclate nterpretaton LeSage & Pace (2009) advse reportng a mean drect effect (average of the dagonal elements of the product of matrces on the far rght of equaton (3)) and a mean ndrect effect (average column sum or row sum of the non-dagonal elements from the same product as the magnude of these calculatons s the same). The mean drect effect whch ncludes feedback effects (.e. effects whch pass through other uns va the spatal multpler matrx and back to the un whch nated the change) s the mean effect on a un s dependent varable followng a change n one of s ndependent varables. The mean ndrect effect can be nterpreted n two ways: () the mean effect followng a change n an ndependent varable for one un on the dependent varables of all the other uns (average column sum of the non-dagonal elements); () the mean change n the dependent varable for one partcular un followng a change n an ndependent varable for all the other uns (average row sum of the non-dagonal elements). The mean total effect s the sum of the mean drect and ndrect effects. We calculate the t-statstcs for the mean effects by obtanng the standard errors usng the delta method. The un specfc effects from a spatal model can be used to calculate effcences by drectly applyng the non-spatal CSS modfyng estmaton procedure, where the effcences are drectly comparable to those from a nonspatal determnstc fronter model usng the same procedure. Ths approach has been appled usng a spatal error cost fronter model wh random effects (Druska & Horrace (2004)). The steps nvolved are as follows. Frstly, solve for the partal dervatves of the followng log-lkelhood functon assocated wh equatons (1) and (2) wh respect to α for α (see equaton (5)). 1 2σ 2 N =1 log L = NT 2 log (2πσ2 ) + T log I λw ( 2 T N C λ w j C jt κ α τ t T L (h, q, t) z φ), (4) t=1 j=1 α = 1 T ( ) T N C λ w j C jt κ α τ t T L (h, q, t) z φ. (5) t=1 j=1 5

6 Secondly, the fxed effects can be used to estmate cost effcency, CE, as follows, where n each perod s assumed that the most effcenct un les on the fronter. [ ] CE = exp mn(δ ) δ, (6) where δ = α +θ t+ρ t 2 so α s the tme-nvarant component of tme-varant cost effcency and the estmates of the parameters θ and ρ are obtaned by usng the resduals from equaton (1), ε, to estmate ε = θ t + ρ t 2 + e, where e s an..d. dsturbance. We extend the CSS methodology and set out a spatal modfyng estmaton procedure by recognzng that n equaton (2), (I λw ) 1 α = α T ot, where α T ot s a (N 1) vector of total fxed effects. Equvalently usng column vector notaton: α 1 α 2 (I λw ) 1 = α N 11 + α12 Ind + + α1n Ind 21 + α α2n Ind = αn1 Ind + αn2 Ind + + αnn α α Ind α1 T ot α T ot 2 α T ot N, (7) where αj (.e. where = j) and αj Ind (.e. where j) are drect and ndrect fxed effects, respectvely. In the same way as we obtan drect and ndrect fxed effects as ndcated n equaton (7), we obtan drect and ndrect resduals from (I λw ) 1 ε t n equaton (2), ε jt and ε Ind jt. ect cost effcency, CE and total cost effcency, CE T ot where: δ δ AggInd CE T ot = α j CE CE AggInd, aggegate ndrect cost effcency, CE AggInd,, are calculated as follows. [ ( ) ] = exp mn δ δ, (8) [ ( = exp mn [ ( = exp mn δ + θ t + ρ t 2 ; = N j=1 αind j δ AggInd + δ AggInd ) + θ AggInd t + ρ AggInd t 2. ) ] δ AggInd, (9) δ ] δ AggInd, (10) 6

7 The θ, ρ and CE AggInd, θ AggInd and ρ AggInd can be obtaned by regressng n turn ε jt parameters needed to estmate CE and N j=1 εind jt on t and t 2 for each un. The correspondng parameters to estmate CE T ot are obtaned by summng θ and θ AggInd, and ρ and ρ AggInd. Interestngly, the aggregate ndrect cost effcency from equaton (9) refers to the effcency of cost spllovers to the h un from all the jth uns, whch s how ndrect effcency should be nterpreted when ncorporatng change n effcency spllovers nto a spatal TFP growth decomposon for the h un. It s also vald to nterpret aggregate ndrect cost effcency as the effcency of cost spllovers to all the h uns from a partcular jth un. Snce αj Ind αj Ind and ε Ind jt ε Ind j, the effcency of cost spllovers to the h un from all the jth uns wll not be equal to the effcency of cost spllovers to all the h uns from a partcular jth un. We only consder effcency spllovers to the h un here and leave examnaton of the asymmetry between effcency spllovers for future research. To calculate drect and aggregate ndrect cost neffcences, CIE and CIE AggInd, as shares of total cost neffcency, CIE T ot, SCIE and SCIE AggInd, CIE, CIE AggInd and CIE T ot must be calculated relatve to the same un where ths un s the best perfomng un n the calculaton of CIE T ot. 4 Formally, we recognze that CE T ot can be dsaggregated nto s drect and aggregate ndrect effcency components: CE T ot [ = exp mn CE T ot ( δ ) ] [ δ exp ( mn CE T ot δ AggInd Takng logs of equaton (11) yelds an expresson for CIE T ot : ) ] δ AggInd. (11) [ CIE T ot = mn CE T ot ( δ ) ] [ δ + mn CE T ot ( δ AggInd ) ] δ AggInd, (12) 162 from whch SCIE s: SCIE = [ mn CE T ot ( δ ) ] δ /CIE T ot. (13) 4 We report SCIE and SCIE AggInd but these shares are equal to the drect and aggregate ndrect cost effcency shares of CE T ot 7.

8 SCIE AggInd can be calculated n a smlar manner Applcaton: Cost Fronter for Manufacturng n U.S. States 4.1. Data The startng pont for the constructon of our data set s the data used n the key study by Morrson & Schwartz (1996) (MS from hereon) to estmate a non-spatal cost functon for state level manufacturng n the U.S. We focus, however, on estmaton of effceny spllovers whereas MS focus on the effect of nvestment n publc capal. Summarzng, our data s for the perod for the contguous states. We obtaned all data from the Annual Survey of Manufactures (ASM) conducted by the U.S. Census Bureau unless otherwse stated and all monetary varables are expressed n 1997 prces usng the CPI. The measure of output s value added (q), and the three nput prces are average annual wages of a producton worker (h 1 ) and a non-producton worker (h 2 ), and the prce of energy (h 3 ), where all three nput prces are normalzed by the prce of capal. Followng MS, we assume a harmonzed capal market and the prce of capal s approxmated by T X t Pt I (r t + γ). T X t s the corporate tax rate whch we obtan for the U.S. from the OECD tax database, Pt I s the prce deflator or more specfcally, PPI for fnshed capal equpment, r t s the longterm lendng rate for the manufacturng sector approxmated by Moody s Baa corporate bond yeld and γ s the deprecaton rate, whch followng Hall (2005) we assume s 10%. The data for h 3 s from the U.S. Energy Admnstraton and s the prce pad by the ndustral sector per mllon Btu. The data for total cost (C) s calculated by summng the wage blls for nonproducton and producton workers, expendure on new and used capal and expendure on fuels and electrcy. The ASM only contans manufacturng expendure on fuels and electrcy for the U.S. so ths expendure was 5 We could proceed to estmate dsaggregated ndrect cost effcences for a gven. Ths would nvolve usng the ndrect resduals from equaton (2), ε Ind jt, to successvely estmate ε Ind jt = θ j t + ρ j t 2 + e jt for each. The resultng dsaggregated cost effcences refer to the effcency of cost spllovers across the jth uns to a gven h un. The other vald estmator of dsaggregated ndrect cost effcences, whch wll yeld a dfferent estmate for the reasons gven above, refers to the effcency of cost spllovers across the h uns from a gven jth un. We leave the estmaton of asymmetrc dsaggregate effcency spllovers for future research. 8

9 allocated to the states usng annual shares of U.S. energy expendures by the ndustral sector, where the state shares were calculated usng data from the U.S. Energy Admnstraton. We extend the data set whch MS use by ncludng a number of z-varables whch shft the cost fronter technology. To capture the effect of dfferences n tax condons across states we nclude the rato of personal current tax payments to personal ncome (z 1 ). Snce the densy of economc actvy n a state s not meanngful because a lot of land s not productve, we follow Cccone & Hall (1996) and control for agglomeraton effects by ncludng average county employment densy whn a state (z 2 ). 6 We take account of urban roadway congeston effects by ncludng the share of a state s sampled urban natonal hghway length wh a volume-servce flow (VSF) rato: < 0.21; ; ; ; > 0.95 (z 3 -z 7, respectvely, where we om the share). A VSF rato > 0.80 ndcates that congeston has set n. 7 Two states wh small manufacturng sectors are hghly effcent outlers (Rhode Island and Delaware) and were therefore omted, whch s n lne wh the hgh effcency scores whch we report for other small states n the North East regon or just outsde. Furthermore, we use two row-normalzed specfcatons of W, a contguy matrx, W 1, and a matrx weghted by average state real GDP for the manufacturng sector over the study perod for contguous states, W 2, whch serves as a proxy for economc dstance. Wh the excepton of the data for z 1 and z 3 -z 7, all the data s logged and normalzed around the relevant sample mean so that the frst order tme trend, output and nput prces can be nterpreted as elastctes Estmaton Results To faclate comparson, n Table 1 we present the non-spatal Whn model as well as the models fted usng W 1 and W 2, where the tme perod effects are not reported for reasons of brevy. We get an ndcaton of whether 6 The tax and ncome data to calculate z 1 and county employment data to calculate z 2 were obtaned from the Bureau of Economc Analys Regonal Economc Accounts. 7 z 3 -z 7 were calculated usng data from Hghway Statstcs publshed by the Federal Hghway Admnstraton. The avalably of ths data restrcted the study perod to Descrptve statstcs for the raw data are avalable from the correspondng author on request. 9

10 the z-varables are endogenous both ndvdually and collectvely from four Hausman-Wu tests by usng the non-spatal Whn and Hausman-Taylor estmators, where n the latter model z 1, z 2 and/or z 3 -z 7 are assumed to be endogenous. All four tests fal to reject the null of no endogeney bas at the 0.1% level. Moreover, at the 0.1% level an LR test rejects the null that the fxed effects are not jontly sgnfcant for both spatal models. λ cannot be nterpreted as an elastcy but can be used to ndcate how the spatal dependence of C a affected by the specfcaton of W. The estmates of λ are 0.21 from the W 1 model and 0.28 from the W 2 model, both of whch are sgnfcant at the 0.1% level. Ths suggests that state manufacturng cost s about 33% more spatally dependent across our measure of economc dstance than s across state borders. In both models the drect q, h 1, h 2 and h 3 parameters are sgnfcant at the 5% level or lower. Also, n both models these four parameters are posve whch suggests the monotoncy of the cost functon s satsfed at the sample means. The ndrect h 3 parameter from the W 2 model s only sgnfcant at the 10% level, whereas all the other ndrect nput prce and output parameters n the two models are sgnfcant at the 5% level or lower. The largest ndrect nput prce or output parameter n both models s by some margn for h 1. Ths ndcates that there are larger producton wage spllovers than there are output, energy prce or non-producton wage spllovers. As expected we fnd evdence of technologcal progress from one year to the next because n both models the drect tme trend parameters (β 15 ) are negatve and sgnfcant at the 5% level or lower. The parameter estmates for the z-varables are partcularly nterestng. To llustrate, we fnd that the drect z 2, z 6 and z 7 parameters are posve and sgnfcant at the 1% level or lower n both models. The mplcaton s that state manufacturng cost wll be hgher n more urbanzed states where employment densy and urban roadway congeston are hgher. The drect z 3 parameter s also posve and sgnfcant at the 5% level n both models. Ths suggests that state manufacturng cost s hgher for the least urbanzed states where low traffc levels on the state s urban hghways s a more frequently observed phenomenon ect, Aggregate Indrect and Total Effcences Effcences from the spatal models whch are calculated usng equatons (8)-(10) are denoted by CE A n Table 2. To calculate the drect and aggregate ndrect neffcency shares, whch are denoted by SCIE n Table 2, we 10

11 Table 1: Results for selected determnstc cost fronter models No SD Wh SD: W 1 Wh SD: W 2 Varable Coef. ect Indrect Total ect Indrect Total Coef. Coef. Coef. Coef. Coef. Coef. ln h 1 β *** 0.815*** 0.173*** 0.988*** 0.753*** 0.246*** 0.999*** (9.00) (9.08) (3.58) (8.35) (8.34) (4.58) (7.93) ln h 2 β *** 0.284*** 0.060** 0.344*** 0.259*** 0.084** 0.344*** (3.90) (4.19) (2.84) (4.10) (3.78) (3.10) (3.75) ln h 3 β ** 0.079* 0.017* 0.096* (2.61) (2.39) (2.07) (2.40) (1.76) (1.68) (1.76) ln q β *** 0.233*** 0.050*** 0.283*** 0.223*** 0.073*** 0.296*** (10.10) (10.30) (3.68) (9.30) (9.84) (4.75) (9.12) (ln h 1) 2 β (1.57) (1.89) (1.65) (1.88) (1.89) (1.78) (1.89) (ln h 2) 2 β ** 1.079*** 0.231* 1.310** 1.046*** 0.342** 1.388** (2.81) (3.34) (2.45) (3.27) (3.32) (2.78) (3.27) (ln h 3) 2 β ** ** * ** ** * ** (-2.59) (-2.78) (-2.19) (-2.75) (-2.94) (-2.56) (-2.92) (ln q) 2 β * 0.019* 0.004* 0.023* (2.32) (2.47) (1.97) (2.43) (1.91) (1.79) (1.91) (ln h 1) β * * * * * * (ln h 2) (-2.00) (-2.28) (-1.93) (-2.27) (-2.25) (-2.09) (-2.25) (ln h 1) β (ln h 3) (1.57) (1.18) (1.10) (1.18) (1.09) (1.05) (1.09) (ln h 2) β (ln h 3) (-0.65) (-0.49) (-0.46) (-0.48) (-0.31) (-0.31) (-0.31) (ln h 1) β * 0.110* 0.023* 0.133* 0.113* 0.037* 0.150* (ln q) (2.54) (2.33) (2.04) (2.34) (2.48) (2.25) (2.47) (ln h 2) β (ln q) (-1.38) (-1.69) (-1.49) (-1.68) (-1.79) (-1.63) (-1.77) (ln h 3) β * * * (ln q) (-1.51) (-1.62) (-1.46) (-1.61) (-2.21) (-2.00) (-2.19) t β *** *** ** *** * * * (-5.25) (-3.65) (-3.14) (-3.78) (-2.46) (-2.51) (-2.53) t 2 β *** 0.003*** 0.001** 0.004*** 0.003*** 0.001*** 0.004*** (5.19) (5.25) (3.12) (5.10) (4.91) (3.58) (4.80) ln h 1t β ** 0.046*** 0.010* 0.056*** 0.041** 0.014* 0.055** (2.83) (3.41) (2.43) (3.32) (3.06) (2.56) (3.01) ln h 2t β (-0.60) (-0.46) (-0.45) (-0.46) (0.15) (0.15) (0.15) ln h 3t β * * * (-0.85) (-0.87) (-0.82) (-0.87) (-2.29) (-2.04) (-2.25) ln qt β *** *** ** *** *** ** *** (-3.45) (-3.34) (-2.58) (-3.33) (-3.53) (-2.97) (-3.50) z 1 φ * 1.361* 0.286* 1.648* 1.428* 0.466* 1.893* (2.19) (2.28) (1.98) (2.28) (2.40) (2.19) (2.39) ln z 2 φ *** 0.286** 0.060* 0.346** 0.350*** 0.127** 0.478*** (3.42) (2.65) (2.30) (2.67) (3.34) (2.89) (3.31) z 3 φ * * 0.111* 0.036* 0.147* (1.88) (2.09) (1.80) (2.08) (2.24) (2.07) (2.24) z 4 φ (0.37) (0.34) (0.34) (0.34) (0.20) (0.18) (0.20) z 5 φ (1.09) (1.23) (1.15) (1.23) (1.52) (1.42) (1.51) z 6 φ ** 0.358** 0.076* 0.434** 0.348** 0.113** 0.461** (2.97) (3.16) (2.45) (3.13) (3.15) (2.74) (3.13) z 7 φ ** 0.214** 0.045* 0.260** 0.214** 0.069* 0.283** (2.78) (2.69) (2.20) (2.68) (2.65) (2.41) (2.65) W 1 W 2 N j=1 wj Cjt λ 0.180*** 0.258*** (4.52) (6.80) Log-lkelhood Note: *, **, *** denote statstcal sgnfcance at the 5%, 1% and 0.1% levels, respectvely. SD refers to spatal dependence. t statstcs are n parentheses. 11

12 calculate drect, aggregate ndrect and total effcences usng equaton (11) whch are denoted by CE B n Table 2. The sample average own/drect CE A from the non-spatal model and the W 2 model s 0.40, whch rses to 0.45 from the W 1 model. The sample average ndrect (total) CE A s 0.87 (0.44) from the W 1 model and 0.74 (0.38) from the W 2 model. Ths suggests, frstly, that geographcal contguy (W 1 ) s a source of larger aggregate effcency spllovers than economc contguy (W 2 ) and, secondly, that drect effcency s the prncpal component of total effcency. Among other thngs, we can see from Fgure 1 that average annual ndrect CE A s greater than average annual drect CE A over the entre sample for both spatal models. We also observe that average annual ndrect CE A from the W 1 model s always greater than that from the W 2 model. Table 2 ndcates that from both spatal models, average drect and/or ndrect CE A s relatvely hgh for several small states n the North East regon or just outsde (Maryland; Connectcut; New Jersey; Mane; Massachusetts; New Hampshre; Vermont). Interestngly, the two states wh the largest average real GDP and average state manufacturng real GDP over the study perod (Calforna and Texas) have the lowest average drect CE A for both spatal models. The state wh the thrd largest average real GDP and average state manufacturng real GDP (New York), however, has a respectable average drect CE A of the order 0.60 (14) and 0.63 (9), where the correspondng rankngs are n parentheses. In terms of average ndrect CE A, Calfona and Texas far much better and are much closer to New York (0.96 (5) and 0.86 (6)). A comparson of average drect, ndrect and total CE A for Calforna and Texas ndcate that average drect CE A s the reason for ther low average total CE A. Some of the estmates of average drect (aggregate ndrect) CE B are greater than 1 and when ths s the case average drect (aggregate ndrect) SCIE s negatve. Ths s because Connectcut s the best performng state n each perod for the calculaton of total cost effcency but ths s not the case for the calculaton of drect and ndrect cost effcences. To llustrate, consder the one of the more complex cases- the estmates of average drect and ndrect SCIE of 5.30 and 6.30 for Maryland from the W 1 model. These estmates ndcate that, on average, Maryland operates beyond the drect reference level but below the ndrect reference level. The net ndrect SCIE s 1, ndcatng that Maryland s relatve total neffcency s all due to s relatve ndrect neffcency. 12

13 Table 2: Selected average cost effcences and effcency shares State No SD Wh SD: W1 Wh SD: W2 ect Agg Indrect Total ect Agg Indrect Total Maryland CE A 1.00(1) 1.00(1) 0.90(16) 0.98(2) 0.99(1) 0.77(16) 0.95(2) CE B 1.05(1) 0.93(15) 0.98(2) 1.18(1) 0.81(16) 0.95(2) SCIE Connectcut CE A 0.86(2) 0.95(2) 0.96(5) 1.00(1) 0.84(4) 0.96(4) 1.00(1) CE B 1.00(2) 1.00(5) 1.00(1) 1.00(4) 1.00(4) 1.00(1) SCIE N/A N/A N/A N/A New Jersey CE A 0.84(3) 0.91(4) 0.88(19) 0.88(3) 0.86(3) 0.81(10) 0.86(4) CE B 0.96(3) 0.91(19) 0.88(3) 1.02(3) 0.85(9) 0.86(4) SCIE Illnos CE A 0.18(44) 0.21(44) 0.82(35) 0.19(44) 0.17(44) 0.71(24) 0.15(44) CE B 0.23(44) 0.85(35) 0.19(44) 0.21(44) 0.74(26) 0.15(44) SCIE Calforna CE A 0.17(45) 0.15(45) 0.91(11) 0.15(45) 0.12(45) 0.86(6) 0.12(45) CE B 0.16(45) 0.94(11) 0.15(45) 0.14(45) 0.90(6) 0.12(45) SCIE Texas CE A 0.08(46) 0.09(46) 0.88(18) 0.09(46) 0.06(46) 0.80(11) 0.06(46) CE B 0.09(46) 0.92(17) 0.09(46) 0.08(46) 0.83(12) 0.06(46) SCIE Mane CE A 0.63(10) 0.63(12) 1.00(1) 0.68(9) 0.44(15) 1.00(1) 0.54(10) CE B 0.66(12) 1.04(1) 0.68(9) 0.52(15) 1.05(1) 0.54(10) SCIE Massachusetts CE A 0.81(4) 0.68(9) 0.99(2) 0.74(8) 0.73(5) 0.96(4) 0.87(3) CE B 0.72(9) 1.03(2) 0.74(8) 0.87(5) 1.00(4) 0.87(3) SCIE New Hampshre CE A 0.75(5) 0.77(7) 0.98(3) 0.82(7) 0.70(7) 0.98(2) 0.85(5) CE B 0.81(7) 1.01(3) 0.82(7) 0.83(7) 1.02(2) 0.85(5) SCIE Vermont CE A 0.63(9) 0.80(6) 0.98(4) 0.85(5) 0.69(8) 0.97(3) 0.82(6) CE B 0.84(6) 1.01(3) 0.85(5) 0.82(8) 1.01(3) 0.82(6) SCIE Note: The correspondng rankng s gven n parenthess where the rankngs are all n descendng order. 13

14 Fgure 1: Average effcency scores Concluson We have extended the CSS estmator of non-spatal tme-varant effcency to the case where there s spatal autoregressve dependence. Ths nvolved dervng estmators of drect effcency (own effcency accountng for feedback effects), ndrect (spllover) effcency and total (drect plus ndrect) effcency. We then estmated a state level cost fronter model for U.S. manufacturng to apply our spatal effcency estmators. There are a number of possbles for further analyss of the estmators some of whch we have alluded to here such as asymmetrc ndrect effcences. Acknowledgments The applcaton to state manufacturng was nspred by the partcpants n the specal sesson dedcated to the memory of Catherne Morrson Paul at the 2012 North Amercan Productvy Workshop. Baltag, B. H. (2011). Spatal panels. In A. Ullah, & D. E. A. Gles (Eds.), Handbook of Emprcal Economcs and Fnance. Boca Raton, Florda: Chapman and Hall, Taylor and Francs Group. Cccone, A., & Hall, R. E. (1996). Productvy and the densy of economc actvy. Amercan Economc Revew, 86, Cornwell, C., Schmdt, P., & Sckles, R. C. (1990). Producton fronters wh cross-sectonal and tme-seres varaton. Journal of Econometrcs, 46, Druska, V., & Horrace, W. (2004). Generalzed moments estmator for spatal panel data: Indonesan rce farmng. Amercan Journal of Agrcultural Economcs, 86,

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