Agricultural & Applied Economics Association

Convergence of Productivity: An Analysis of the Catch-up Hypothesis within a Panel of States Author(s): V. Eldon Ball, Charles Hallahan, Richard Nehring Source: American Journal of Agricultural Economics, Vol. 86, No. 5, Proceedings Issue (Dec., 2004), pp. 1315-1321 Published by: Oxford University Press on behalf of the Agricultural & Applied Economics Association Stable URL: http://www.jstor.org/stable/3697947 . Accessed: 26/09/2011 07:55
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CONVERGENCE PRODUC11VITY: ANALYSIS OF AN OFTHECATCH HYPOTHESIS UP WITHIN A PANEL STATES OF
V. ELDON BALL,CHARLES HALLAHAN, RICHARD AND NEHRING

A consensus appears to have emerged in the literature that per capita income levels and/or levels of productivity in the industrialized market economies have converged significantlyover the last century,and especially since the end of the second world war (see, e.g., Abramovitz,Baumol, Baumol and Wolff, De Long, Dollar and Wolff, Dowrick and Nguyen). The resultsof Abramovitzand Baumol, in particular, highlightthese trends. They found an almost perfect inverse relation between laborproductivity levels in 1870 and the rate of labor productivitygrowthbetween 1870 and 1979 among sixteen OECD countries. Abramovitz also investigated subperiods andfoundthatlaborproductivity convergence was much slower in the period before World War II than after. Indeed, even in the postwarperiod,thereis evidencefromAbramovitz and from Baumol and Wolffthat productivity convergenceslowed duringthe 1970s,though this is disputedby Dowrickand Nguyen,who findparameter stability theircatch-up in model betweenpre- andpost-1973periodswhencontrollingfor growthof factorintensities. Results of De Long show little evidence of productivity convergenceover the last centurywhen the sampleis no longerrestrictedto OECD countries. However, Baumol and Wolff, using the Summersand Heston's sample,which covers countriesat alllevelsof development,findconvergence in real GDP per capita among the top thirdor so of the countriesover the 195> 81 period, though it was weaker than among OECD countriesalone. More recently,Dollar and Wolfffind evidence of convergenceof toV. Eldon Ball and RichardNehringare economistsand Charles Hallahan mathematician, is EconomicResearch Service, S. DeU partment Agriculture. of The authorsthankCarlosArnadeandDavidSchimmelpfennig for helpfulcomments an earlierversionof thismanuscript. on This articlewas presentedin a principalpapersession at the AAEA annualmeeting(Denver,Colorado, August2004).Thearticlesin these sessionsare not subjected the journal's to standard rerereelng process. r tal factor productivity(TFP) levels both in the aggregateand within industriesbetween 1963 and 1985. However,the disparityin levels of TFP was greater at the industrylevel, suggestingthat countriesspecializedin different industries.Finally,Ball et al. (2001) find convergence of levels of TFP in agriculture amongten OECD countriesbetween1973and 1993. Various explanationshave been proposed to account for the observed tendency for income and productivity levels to converge. Abramovitz and Baumol suggest that technologicaladvances,particularly those embodied in capital equipment, flow from leaders to followers,allowingmore rapid growth in economies that start-off technologically backward.In addition to technologicalcatch up, Dowrick and Nguyen hypothesize that convergence may result from differences in the growth rates of factor intensities among countries. The objective of this article is to determine whether there has been a tendency for TFP levels in agricultureto converge across the United States since 1960, and if so to investigate whether such convergence can be explained by differences in the rates of growthof factorintensitiesor by productivity catchup. Data and Methods The U.S. Department of Agriculture'sEconomic Research Service (ERS) has recently constructedstate productionaccountsfor the farm sector. The salient features of the state accounts are well documented in Ball et al. (1999).Consequently, focus in this section our will be on constructing transitivemultilateral comparisons output,inputs,and TFP. of An index of real outputbetween two states is obtained by dividing the nominal output valueratiofor two statesby the corresponding

Amer. J. Agr. Econ. 86 (Number 5, 2004): 1315-1321 Copyright 2004 American Agricultural Economics Association

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Amer. J. Agr. Econ.

output price index. We constructmultilateral price indexes using a method proposed independentlyby Elteto andKoves andSzulc.The "EKS" index is based on the idea that the mostappropriate indexto use whencomparing two statesis the binaryFisherindex.However, when the numberI of statesin a comparison is greaterthan two, the applicationof the Fisher indexnumberprocedureto the I(I - 1)/2 possible pairs of states gives results that do not satisfy Fisher'scircularitytest. The problem, therefore,is to obtainresultsthat satisfytransitivity,and that deviate the least from the bilateralFisherindexes. Let PFkdenotethe bilateral Fisher price index for state j relative to state k. If PikKs denotes the multilateral price index, then the EKS method suggests that PEKSshould deviate the least from the bilateralprice index PF. Thus PEKSshould minimizethe distance criterion: l l

Differences in the relative efficiencies of land across states prevent the direct comparison of observedprices.Our estimatesof the relative price of land in each state are based on hedonic regressions.For our cross-section of states, we estimate the following equation by least squares: c (3)

ln

(Pii) =

E i=l bi Di + E c=l cXiJc

+ £ii,

i = 1, . . . , I whereP} is the priceof landin countyj in state i, X' is a vector of land characteristics,2 is a Di dummyvariableequal to unity for the correspondingstate and zero otherwise,and £ij is a stochasticerror term.3When the log of price is related to linear state dummyvariablesas in (3), a hedonicprice index can be calculated fromthe antilogsof the bicoefficients.4 In constructing indexes of relativelaborinput, we assume that the relative efficiency of an hour worked is the same for a given type of labor in all forty-eightstates. Hours workedand averagehourlycompensationare cross-classified sex, age,education,andemby ployment class (employee vs. self-employed and unpaid family workers). Since average compensationdata are not availablefor selfemployed and unpaid family workers, each self-employed worker is imputed the mean wage of hired workerswith the same demographiccharacteristics. indexesof relative Our labor input are constructedusing the demographically cross-classified hoursandcompensation data. Fertilizersand pesticides are importantintermediateinputs.We construct relativeprices
2 The land characteristics are derived from climatic and geographic data contained in State Soil Geographic (STATSGO) Data Base (USDA). In addition to environmental attributes, we include 'population accessibility" indexes for each county. The indexes are derived from a gravity model of urban development, which provides measures of accessibility to population concentrations (Shi, Phipps, and Colyer). A gravity index accounts for both population size and distance of the parcel from that population. The index increases as population increases and/or distance from the population center decreases. Our construction of the population accessibility index is calculated on the basis of population within a 50-mile radius of each parcel. 3 The observations on P consist of average prices. When averages are used rather than actual observations, the disturbance term will likely be heteroskedastic. To obtain efficient parameter estimates, we apply weighted least squares, using the land area in each county as weights. 4 For the semilogarithmic specification used here, Halverson and Palmquist have shown that a consistent estimate of is given by exp(t ) - 1.

(1)

E

j=l k=l

E

( lnPi KS-ln P} )

Using the first-orderconditions for a minimum, it can be shown that the multilateral priceindexwiththe minimum distanceis given by (Rao and Banerjee):
I

(2)

P1KS

= rl i=l \ 1/1

pJi

p,k)

j, k = 1, . . . , I. The EKS price index may therefore be expressedas the geometricmeanof the I indirect comparisons j and k throughother states. of Using (2), we constructindexes of relative outputpricesforallforty-eight statesin a single base year.The corresponding outputquantity indexes are formedimplicitly.1 Measuresof real inputacrossstates require dataon relativeinputprices.Relativepricesof capital inputs are obtained based on relative investmentgoods prices, taking into account the flow of capitalservicesper unit of capital stock in each state (see Ball et al. 2001).

l The data are available at the USDA/ERS web site http:l/ www.ers.usda.gov/datalagproductvity/ and can be downloaded as LOTUS or EXCEL spreadsheets.

Ball, Hallahan, and Nehring

Convergence Productivity 1317 of

of fertilizers and pesticides among states from hedonic regression results. A price index for fertilizeris formed by regressingthe prices of single nutrient and multigradefertilizers on the proportion of nutrients contained in the fertilizer materials.Prices for pesticides are regressedon levels of physical characteristics such as toxicity,persistencein the environment,and leachingpotential.The quantityindexes for fertilizersand pesticides are formedimplicitlyby dividingthe nominal inputcost ratiosby the corresponding hedonic prlce lncex. Finally,all our calculationsare base-state invariant,but they are not base-year invariant. We use 1996 as the base year for all our time series indexes.The reason for this is that the EKS price indexes are constructedonly for 1996, which means that we constructindexes for earlierand later years in the sample by chain linkingthem to 1996.The result is a "true"panel with both temporal and spatial comparability.
. .

to second. The largest relative gains in TFP were made by North Carolinaand Arkansas. North Carolina improved from sixteenth to fifth among the forty-eightstates; Arkansas rose from twenty-fourthto sixth. This relatively rapid TFP growth was, in part, a consequence of the "industrialization" agriculof ture,characterized the expandingpresence by of large,verticallyintegratedfirms.The industrializationphenomenon has been especially apparentin the SoutheasternUnited States, with accompanyingabsolute and relative increasesin productivity. Arizona was second among the forty-eight states in 1960, but slipped to seventh in 1999. Oklahoma fell from fourth to thirtysixth. And Kansas fell from fifth to tenth in terms of relative levels of productivity. West Virginiawas last throughoutthe period. Moreover,its productivityrelative to Florida fell from one-half in 1960 to one-third in
1999.

Comparisons TotalFactorProductivity of The data described in the previous section are used to constructindexes of TFP (defined as the ratio of output to an index of capital, labor, and materialsinputs) for the fortyeight contiguous states for the 1960-99 period. These indexes, normalizedso that the level of TFP for Alabamain 1996is unity,are available from the UDA/ERS web site (see footnote 1). In table 1 the states are ranked by their level of TFP in 1999. Also included in table 1 is their rank in 1960 and the average annual percentage growth from 1960 to 1999. One remarkablesimilarityexists across all states for the full 1960-99 period. Every state exhibitsa positiveandgenerallysubstantial averageannualrateof TFPgrowth.Thereis considerablevariancehowever.The medianTFP growth rate is 1.71% year. One-thirdof per the states have growth rates averagingmore than 2% per year. Two states Oklahoma andWyoming have averageannualratesless than 1%. The reported average annual rates of growthrangefrom 0.73°/O Oklahomato for 2.59% Michigan. for The wide disparityof growthrates over the 1960-99 periodresultedin substantial changes in the rankorderof the states.Forexample,between 1960 and 1999 Florida rose from third to first, while Georgia rose from thirteenth

Figure1 providesdetailsfor the intervening years.It plots for each year the coefficientof variation(the ratio of the standarddeviation to the mean)of productivity levels for all fortyeight states.We use these coefficientsto show that there was some narrowing the rangeof of levels of productivity over the 196>99 period, although the pattern of convergencewas far fromuniform. Thisis a remarkable resultgiven the widevariation productivity in growthrates. The fact that some states grew more rapidly than others and yet the cross-sectiondispersion decreasedimpliesthatthe statesthatgrew most rapidlywere those with lower initiallevels of productivity,a finding consistent with technologicalcatchup. EconometricTestsof TFP Convergence In the previoussection,we saw that there has been some narrowing the rangeof levels of of productivityamong states. We now turn to a regressionframeworkto test two hypotheses concerningtechnologyconvergence.The first is the catch-uphypothesis, whichstates simply that those states that lag furthestbehind the technologyleaders benefit the most from the diffusion of technicalknowledge and, hence, shouldexhibitthe most rapidrates of productivity growth.Takingeach state as an observation, this hypothesisimpliesthat the rate of growthof TFP is inverselycorrelatedwith the level of productivityat the beginning of the period.

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Table 1. States Rankedby 1999Level of Agricultural Productivity
Average Annual Growth of Productivity 196>99 Level 0 7291 0.6176 0.7674 0.5322 0.5845 0.5468 0.7298 0.5695 0.6568 0.7056 0.6244 0.4567 0.6823 0.6538 0.5644 0.5734 0.4362 0.5655 0.6037 0.5808 0.5958 0.4328 0.4479 0.5137 0.6211 0.6368 0.4993 0.5320 0.4287 0.5148 0.5667 0.5620 0.4581 0.4463 0.5218 0.7244 0.4572 0.3386 0.6635 0.4737 0.4559 0.4601 0.5405 0.3893 0.4954 0.4019 0.3804 0.3317 Rank
12 7 35 3
10

1999 State
FL GA CA WA NC AR AZ ID IA KS NE MS
CO

1960 Level 1.5938 1.4611 1.3795 1.3536 1.3333 1.3103 1.2929 1.2828 1.2575 1.1989 1.1799
1.1595

Rank

Rank
3

Growth 0.0201 0.0221
0.0150

2

13
1

3 4 s 6 7 8
9 10 11

26 16 24 2
19

6 36
11

8 s 11

SD ND MN CT DE NY IL WI OR LA IN TX NV
SC

12 13 14
15

1.1534
1.1511

37 6
9

26 41 29 4 42 37
19

16 17 18
19

1.1416 1.1227
1.1100

MD MA AL VT MO PA OH NM OK KY MI
WY

UT ME VA NJ RI MT NH TN
WV

20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48

1.0986 1.0981 1.0771 1.0740 1.0496 1.0484 1.0462 1.0370 1.0318 1.0129 1.0077 0.9981 0.9782 0.9762 0.9760 0.9726 0.9697 0.9680 0.9623 0.9473 0.9310 0.9149 0.9084 0.9042 0.8900 0.8684 0.8262 0.8139 0.7543 0.7507 0.5799

22 18 41 21 14 17
15

22 2 23 33 32 34 s 0.0239 0.0211 0.0224 0.0147 0.0208 0.0167 0.0136 0.0163 0.0239 0.0135 0.0145 0.0181 0.0172 0.0240 0.0170 0.0153 0.0158
0.0151

42 39 30 12
10

31 27 43 29 20 23 35 40 28 4 36 47 7 33 38 34 25 45 32 44 46 48

8 17 43 45 18 28
9

27 40 39 14 13 31 48 16
1

0.0227 0.0218 0.0182 0.0131 0.0124 0.0181 0.0164 0.0217 0.0165 0.0139 0.0142 0.0193
0.0199

47 25 20 24 46
15

44 30 21 38

0.0158 0.0073 0.0187 0.0259 0.0082 0.0167 0.0176 0.0169 0.0122 0.0193 0.0127 0.0161 0.0174 0.0143

The second hypothesisis that technological information embodiedin the factorsof prois duction.If the input measuresdo not correct for inputquality,then this hypothesissuggests

that the rate of TFP growthwill be positively correlatedwithgrowthof capitaland intermediate inputs.Again, we treat each state as an observationto test this hypothesis.

Ball, Hallahan, and Nehring

Convergence Productivity 1319 of

0.2500

Table 2. PanelData Unit Root TestStatistics

0.2000 -

0.1500 -

^/sArov*
1965 1970 1975
1980

Variable TFP growthrateb TFP levelC Capital/labor growthrated Material/labor growthrated

Levinand Im, Pesaran, Lin'sTest and Shin'sTest Statisticsa Statisticsa _11.55 -14.78 -3 .34 -9 .40 -16.14 -15.13 -4.33 -1 3.44

0.1000 -

0.0500 -

0.0000

1960

1985

1990

1995

Figure1. Coefficients of variation of state productivity

aAysmptotic standard normal, 5% critical value-1.65. bCalculated with a time trend based on preliminary observations. Other variables were calculated without a time trend based on preliminary observations. CAnnual observations in natural logarithms. dCalculated without a time trend based on preliminary observations.

To investigateboth hypotheses,we employ the basicspecification: from the cross-section,the inference about the existence of unit roots can be made more straightforward precise, especially when and (4) TFPt= 2 + 1 ln TF?t + 2 ( L ) the time series dimension of the data is not very long and similardata may be obtained zM\i from a cross-sectionof units such as countries + 3 t L J + git or industries. second advantagewhen using A t panel unit root tests is that the estimatorsare where TFPis the productivity level relativeto normallydistributed. Alabamaat the beginningof each period and In this article, we employ tests proposed ( KL and ( ML are relativefactorintensities. ) ) The by Im, Pesaran, and Shin and Levin and circumflexes denote time derivatives (A) orrel- Lin (2003). These tests are described in deative rates of change.Five-yearaverages are tail in Levin, Lin, and Chu. The null hyused for the ratesof changeto reducerandom pothesis in both panel unit root tests is that noise. Alabama is excluded from the estima- each series in the panel contains a unit root tion since the value of the dependentvariable and is, thus, difference stationary.Based on is alwaysunity. the test statisticsreported in table 2, we reIn order to minimize the potential for ject the null hypothesis of a unit root. We spuriousregressionresults, we first examine proceed by estimatingequation (4) assuming whether the behavior of the economic vari- stationarity. ables in equation (4) is consistentwith a unit The Baltagi and Li's test for seriallycorreroot. Typically,this analysis has been car- lated residualsyields a p-value of 0.0001.This ried out using tests such as the Augmented leads us to rejectthe null hypothesisof no seDickey and Fuller's test or semiparametric rial correlation. tests, such as the Phillips and Perron's test. Next, we estimatea two-way(stateandyear) The main problem is that, in a finite sample, fixed effects model with state-specificautoany unit root process can be approximated correlation coefficientsandstate-specific error by a trend-stationary process. For example, variances.An F-test of the joint significance the simple difference stationaryprocess Yt= of the state-specific fixed effects yielded a fixed effects oyt-l + tt with 0 = 1 can be arbitrarily well p-value of 0.18. The state-specific approximated a stationaryprocess with 0 arethendroppedanda one-way(byyear)fixed by less than but close to 1. The result is that effects model is estimated, again with stateunit root tests have limitedpower againstthe specificautocorrelation coefficientsand statealternative. specificerrorvariances. The Akaike InformaRecently,startingfromthe seminalworksof tion Criterion(AIC) for the two-way model Levin and Lin (2002, 2003), many tests have is-9467 and -9528 for the one-way model. been proposed for unit roots in panel data. Hence, our final model specificationis the Levin and Lin (2002,2003) show that by com- one-wayfixedeffectsmodel with state-specific bining the time series informationwith that autocorrelation coefficientsand state-specific

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Amer. J. Agr. Econ.

Table 3. Regression of Relative Productiv- Summary Conclusions and ity Growthon RelativeProductivity Leveland Growthin FactorIntensities In this article, we estimate the growth and relative levels of agricultural productivityfor Regressions the forty-eight contiguousstatesfor the period Without WithSlope 196s99. For the full 196s99 period, every Dummy Dummy state exhibitsa positiveand generallysubstanln TEP - 0.1631 - 0.1635 tial averageannualrate of TFP growth.There variancehowever.The median (-25.82)*** (-25.80)*** is considerable rate of TFP growthwas 1.71%per year,while ( L) 0.1230 0 0950 for (5.27)*** (3.71)*** average growthrates ranged from 0.73°/O Oklahomato 2.59% Michigan. for ( L) - 0.0326 - 0.3277 The wide disparityin growthrates resulted (-1.49) (-1.48) in substantialchanges in the rank order of D6080( L ) * 0.0656 states. For each year, we compute the coef(2.76)*** ficient of variationof productivitylevels for X2value 1136.82 1145.80 all forty-eightstates.We use these coefficients ***Means significance at the 1% level (t = 2.576). to show that the range of levels of TFP has Notes: Regressions use five-year moving averages for rates of change to reduce narrowedsomewhatover time. The fact that random noise. All regressions use year fixed effects and correct for autocorsome states grew faster than others and yet relation and heteroskedasiticity. D6080 is a period dummy variable defined as unity on or before 1980 and zero afterwards. The x2 value reported is assothe cross-sectiondispersiondecreasedimplies ciated with the null model likelihood ratio test. All test statistics are highly that the states that grew most rapidly were significant. those with lower initial levels of productivity, a finding consistent with technologicalcatch up. Those states that were particularly befar hind the technology leaders had the most to errorvariances.PROC MIXED in SAS 8.2 is gain from the diffusionof technicalinformaused in estimation. tion and proceeded to grow most rapidly.FiThe results,shown in table 3, confirmthe nally,we observea positiveandstatistically sigcatch-uphypothesis,showinga highly signifi- nificantrelationbetween productivity growth cant inverserelationbetween the rate of pro- and growthof the capital-labor ratio,implying ductivitygrowth by state and its initial level embodimentof technologyin capital. relative to Alabama (column 1). The results for the embodiment hypothesisaremixed.The variable(KL) has a positive and significant coefficient (column 1). This result suggeststhat References embodimentof technology in capital was an M. Up, important source of productivitygrowth in Abramovitz, "Catching ForgingAhead, and FallingBehind."Journal of Economic History agriculture. 46(1986):385X06. Net investmentin fixed capitalwas positive Ball, V.E., J.-C. Bureau, J.-P. Butault, and R. for most statesthrough1980,but was negative Nehring."Levelsof FarmSectorProductivity: thereafter.In a second regression,we include An International Comparison."JournalofProa dummyvariable,D6080, defined as unity on ductivity Analysis 15(2001):5-29. or before 1980 and zero thereafter,which interactswith ( KL to control for this period ef- Ball, V.E., F.M. Gollop, A. Kelly-Hawke, and ) G. Swinand. "Patternsof State Productivity fect. The coefficient on the interactionterm Growthin the U.S.FarmSector:LinkingState D6080 ( KL iS alsopositiveandsignificant * ) (coland AggregateModels."American Journal of umn2). We concludethat the embodimentefAgricultural Economics 81(1999):16$79. fect was more importantduringthe 1960-80 Baltagi, B.H., and Q. Li. "TestingAR(1) Against periodwhen net investmentwas positivethan MA(1) Disturbances an ErrorComponents in duringthe 1981-99 subperiod. Model" Journal of Econometrics 68(1995): Finally, coefficientfor ( ML was negative, the ) 133-51. butstatistically insignificant. arguethatthis Baumol,W.J."Productivity We Growth,Convergence, result reflects our efforts to adjust the input andWelfare: Whatthe Long-Run DataShow?" indexes to reflect the improvementsin their American Economic Review 76(1986):1072quality. 85.

Ball, Hallahan, and Nehring

of Convergence Productivity 1321 Department of Applied Economics, University of Cambridge, 1997. Levin, A., and C.F. Lin. "Unit Root Tests in Panel Data: Asymptotic and Finite Sample Properties." Discussion Paper Series 92-23, Dept. Econ., University of San Diego, San Diego, CA, 1992. . "Unit Root Tests in Panel Data: New Results." Discussion Paper Series 93-56, Dept. Econ., University of San Diego, San Diego, CA,1993. Levin, A., C.F. Lin, and C. Chu. "Unit Root Tests in Panel Data: Asymptotic and FiniteSample Properties." Journal of Econometrics 108(2002):1-24. Phillips, P.C.B., and P. Perron. "Testing for a Unit Root in Time Series Regression." Biometrika 75(1988):335-46. Rao, D.S.P., and K.S. Banerjee. "A Multilateral Index Number System Based on the Factorial Approach." Statistische Hefte 27(1984):297-313. Szulc, B. "Indices for Multiregional Comparisons." Przeglad Statystyczny 3(1964):239-54. Shi, U.J., T.T. Phipps, and D. Colyer. "Agricultural Land Values under Urbanizing Influences." Land Economics 73(1997):9W100. Summers, R., and A. Heston. "A New Set of International Comparisons of Real Product and Prices: Estimates for 130 Countries, 195>85." Review of Income and Wealth34(1988):1-26.

Baumol, W.J., and E.N. Wolff. "Productivity Growth, Convergence,and Welfare:Reply." EconomicReview78(1988):1155-59. American Growth,Convergence, De Long, B. "Productivity AmericanEconomic Comment." and Welfare: Review78(1988):1138-54. Dickey, D.A., and W.A. Fuller. "LikehoodRatio Time Series with Statisticsfor Autoregressive 49(1981):1057-72. a Unit Root."Econometrica Dollar, D., and E.N. Wolff. "CapitalIntensityand TFP Convergenceby Industryin Manufacturing, 1963-1985."In W. Baumol, R. Nelson, of andE. Wolff,eds. Convergence Productivity: Evidence. ies CrossNationalStud andHistorical New York: Oxford University Press, 1994, pp. 197-224. Dowrick, S., and D. Nguyen. "OECD Comparative Economicgrowth1950-85:Catch-upand Convergence."American Economic Review 79(1989):101(}31. Elteto, O., and P. Koves. "On an Index Computation Problemin InternationalComparisons." Szelme42(1964):507-18. Statisztikai Halverson,R., and R. Palmquist."The Interpretation of Dummy Variablesin SemilogarithAmericanEconomic Review mic Equations." 70(1980):47>75. for and Im,K.S.,M.H.Pesaran, Y.Shin.Testing Unit Roots in HeterogeneousPanels. Cambridge: