Economic Policy - World Bank Group

1 September 2000nnuummbbeerr 4422 Economic Policy Gains in total factor productivity (TFP),reflecting more efficient use of inputs, havelong been recognized as an importantsource of improvements in income andwelfare. Cross-country differences in incomelevels and growth rates are mostly due todifferences in productivity (Klenow andRodriguez-Clare 1997; Easterly and Levine2000).Measuring TFP is therefore important inassessing countries past and potentialeconomic performance. But it is alsodifficult, for two reasons. Fairly innocuousdifferences in assumptions can lead to verydifferent estimates of TFP growth. And theinterpretation of measured TFP growth canbe problematic when such growth reflectsfactors other than purely technical change such as increasing returns to scale, markupsdue to imperfect competition, or gains fromsectoral reallocations. This note discusses some of these diffi-culties using data for the Republic of Koreain 1960 97 for illustration.

2 An Excel work-sheet is available to readers who wish to repro-duce the exercises described here for othercountries; see PREM notes or the GrowthThematic Group Web site under starting point for estimating TFPis a production function that representshow inputs are combined to produceoutput. For example, suppose that GDP (Y)is produced using two factors , physicalcapital(K)and human-capital-adjustedlabor input (H), using a Cobb-Douglasproduction function:(1)Y= A(K H 1 ) ,where Ais TFP, measures the extent ofreturns to scale, and measures theimportance of physical capital in = 1 ( > 1) ( < 1), there are constant(increasing) (decreasing) returns to expressing equation 1 in growth ratesand rearranging the variables, TFP growthcan be written as growth in output less aweighted average of growth in inputs:(2)gA=gY [ gK+ (1 ) gH ],where gXis the growth rate of variable data on the growth rates of Y, K,andHand information on the parameters ofthe production function, we can obtainestimates of productivity growth as thedifference between output growth and aweighted average of growth in inputs.

3 Thisnote considers these two ingredients andinterprets the data matterWhile real GDP growth rates are easy toobtain, measuring the growth rates of KandHis more difficult. In most cases physicalcapital is measured using the perpetualinventory method, which uses an estimateof the capital stock in a base year,assumptions on depreciation, and the flowof new investment. But measured growthrates of capital stock and thus estimatesof TFP growth can be very sensitive toassumptions about initial stocks andGains in total factor productivitydrive gains inincome and growthMeasuring growth in total factorproductivityEstimating growth in total factor productivity is difficult, but it is essential forassessing countries past and potential Economic World Bankfrom the development economics vice presidency and poverty reduction and Economic management networkSmall differences in assumptions can lead to big differences inestimates of TFP growthdepreciation rates, and it is important tocheck the robustness of conclusions on TFPgrowth against small changes in theseassumptions (see Pritchett 1996).

4 The production function also dependson human-capital-adjusted labor input (H),which is a way of summarizing thecontribution of brains (education) and brawn (the size of the labor force) to laborinput. One way to do this is to adjust thenumber of workers for their years ofschooling (S) by assuming that eachadditional year raises workers productivityby a given percentage. Various estimatessuggest that, defined in this way, the returnsto education are about 10 percent. Thenumber of workers is the product of theworking-age population (L) and theparticipation rate (P). Thus we can express:(3)H= L P e How important is it to measure laborinput in this way rather than simply aspopulation? In many countries it can be veryimportant. In Korea the combined effect ofgrowth in the working-age population, inparticipation rates, and in average educationlevels increased the human-capital-adjustedlabor force by about 5 percent a yearbetween 1960 and 1997 almost three timesas fast as the growth in population of a year.

5 Such differences can havesubstantial effects on estimated production function mattersWith data on Y, K,and H,we now requireonly information on the parameters of theproduction function to estimate productivitygrowth. Because these parameters are notdirectly observable, it is common to makesome a constant returns to scaleproduction function ( = 1), it is commonto assume values of between and on the observed growth ratesof physical and human capital, the valuechosen can matter a lot for estimates of TFPgrowth. The top panel of table 1 reportsaverage annual growth rates of Y, K, and Hin Korea in 1960 97. The first row in themiddle panel shows how TFP growth rateschange as the value of is increased (resulting in TFP growth of percenta year) to (resulting in TFP growth ofjust percent a year). By increasing , weare increasing the weight on the fastest-growing factor of production in equation2, physical capital, resulting in lowerestimated TFP growth.

6 Estimates of TFP growth are also verysensitive to assumptions about the degreeof scale economies. The remaining rows ofthe middle panel fall with increasing returnsto scale, because some of the increase inoutput previously attributed to productivityimprovements is instead attributed to scaleeconomies. In some cases the distinctionbetween the two may be relevant. If, forexample, there are increasing returns toscale at low levels of development, anddecreasing returns to scale at high levels ofdevelopment, the distinction would beimportant in identifying how much ofmeasured TFP growth is likely to besustained over the long run. So far we have assumed that theparameters of the production function donot change over time. But they might. If,for example, the production function is ofthe constant elasticity of substitution (CES)type with an elasticity different from 1, theweight on capital in equation 1 can changePREM note 42 September 2000 Table 1 Estimates of TFP growthare sensitive to assumptions aboutthe production function (percent)Input and output growthAverage annual growth in Korea, 1960 of TFPgrowth estimates 1 Average annual TFP growth in Korea, 1960 97 = = = = = = of TFPgrowth estimates 2 Average annual TFP growth in Korea, 1960 97 = = = = time, depending on the size of theelasticity of substitution and the rate atwhich Kgrows relative to H.

7 This effect isshown in the bottom panel of table 1 forsome plausible values of the elasticity ofsubstitution between physical and humancapital ( ).Finally, it is worth noting that estimatesof TFP growth constructed in this way cantrack output growth closely and so maynot be very informative because theysubtract growth of measured physical andhuman capital (which by construction arequite smooth) from output growth (whichtypically is not). Thus estimates of thevariation in TFP growth over time can bequite sensitive to the period for which theyare calculated, and the robustness of theresults to the sample period should bechecked interpretation mattersWhat do these estimates of TFP growthactually measure? At the firm level it is fairlystraightforward to equate gAwith technicalprogress. At the aggregate level it is less resources shift from less productive tomore productive firms, perhaps as a resultof Economic reforms or if more productivefirms simply grow faster, aggregate TFPgrowth may be observed even in the absenceof technical progress at the firm we may also be interested inthese other effects,gAmeasures more thanjust the fundamental improvements intechnology that underpin growth in thelong run.

8 Distinguishing between thesedifferent sources of TFP growth is importantbecause there are likely to be natural limitsto the gains from structural change onceresources have been reallocated to the mostefficient can be said of TFP growth relativeto output growth? It is often asserted thatTFP growth accounts for a certain fractionof growth. For example, given outputgrowth of percent in Korea in 1960 97,and estimated TFP growth of percent,one might think that TFP growth accountedfor just 18 percent of output growth ( divided by percent). But thisconclusion is misguided, because it ignoresthe fact that decisions to invest in physicaland human capital are themselves likely todepend on TFP growth. A simple ratioignores the portion of growth in inputsinduced by productivity growth, whichshould also be attributed to TFP better way of assessing the importanceof TFP growth is to ask the followingquestion: if output growth is above average,how much of this additional growth canbe attributed to TFP growth?

9 One way toanswer this question is to consider thecovariance between productivity growth andoutput growth divided by the variance ofoutput growth (see Klenow and Rodriguez-Clare 1997). Because this calculation reflectsTFP-induced increases in inputs, rather thanassuming inputs to be exogenous, it givesa more accurate picture of the role of TFPgrowth in the growth process. In Korea theshare of growth attributable to productivitygrowth jumps from the naive estimate of 18percent to more than 80 percent. While thesecond figure may be high, it illustrates theimportance of taking into account theendogeneity of factor inputs when assessingthe importance of TFP do we go from here?Estimated TFP growth is very sensitive toassumptions about the underlyingparameters in the production a natural step is to try to estimate theproduction function directly. There are twoways to do so.

10 One is to assume that theeconomy in question is characterized byconstant returns to scale ( = 1) and perfectcompetition. Then it is possible to view theparameter as 1 minus the share of wagesin value added (see Young 1995 and Hsieh1999). But in many developing countriesit seems implausible to assume constantreturns to scale and perfect competition and we have already seen how sensitiveestimates of productivity growth are toassumptions on constant returns to , reliable data on wages are oftennot available for the economy as a second approach is to try to estimatethe production function econometrically The endogeneity offactor inputs shouldbe considered whenassessing the importance of TFP growthPREM note 42 September 2000for example, by regressing output growthon input growth (see Basu and Fernald1995). While this approach does not requireassumptions of constant returns and perfectcompetition, the problem of inputsresponding endogenously to TFP growthreturns to the fore.