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Improving capital measurement using micro data Abdul Azeez Erumban 24-02-2009 CBS, the Hague

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Structure of the presentation Issues in the Measurement of aggregate capital Standard practice and its problems Measurement of depreciation and problems Asset lifetime estimation Estimation of lifetime using Dutch micro data Standard methodology Our alternative approach Data Results Comparison: standard approach vs. new approach Comparison: Earlier CBS estimates vs. new estimates Comparison: Estimates for other countries vs. Estimates for the Netherlands Conclusions

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3 Issues in the measurement of Aggregate capital Co-existence of multiple vintages =Different vintages have different marginal productivities =Each generation of capital assets will embody different levels of technology, and are therefore not homogenous And Heterogeneity of Capital Assets =Aggregating computers, machines, trucks and many more! =Cambridge Controversy (aggregating money value vs. impossibility of aggregation)

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4 Standard Practice & its problems Perpetual Inventory Method Aggregate money value of different assets (value of computers + value of trucks) Problems Aggregation of vintages: Use efficiency weights (under the assumption that newer vintage embody newer technology). Takes account of differences in vintages to some extent, given that depreciation and asset prices are properly measured Aggregation across assets: Aggregate money value of different assets. Takes no account of asset heterogeneity Measures of Capital services (Capital assets, weighted by their marginal productivities.)

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Depreciation and lifetimes: Major ingredients in capital measurement Whether it is aggregation across vintages, or across assets, an important factor is loss of value due to ageing

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Measurement of depreciation But Scarce empirical evidence on depreciation Common Depreciation across countries & over time =Same age-price profile across countries & over time Empirical Measurement of Depreciation-two prominent methods Used -asset price model (Hulten and Wykoff 1981) depreciation can be isolated by comparing prices of same asset at various ages Asset lifetime based Declining balance rate (straight line, double declining, sum of year digit) Hulten and Wykoff, 1981; Fraumeni, 1997 6

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Problems in Empirical Measurement of Depreciation Used-price approach Lack of data Lifetime based approach Availability of reliable estimates of life time Rely on expert advice, tax information, company records- all have potential bias An important deviation - Estimation of asset lifetime from actual data Meinen et al 1998; Meinen, 1998; van den Bergen et al, 2005; Nomura, 2005) This presentation Lifetime estimation using actual data for Dutch manufacturing (improving on earlier Dutch studies) 7

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Estimating lifetimes using Dutch unit level data Methodology: The Weibull function Lifetime estimation using survival function (the probability that the asset survives until a given age) Survival function with a longer tail-The Weibull Weibull is a flexible distribution According to Weibull, the survival function S at a given age x can be written as for x 0, where =shape parameter, =scale parameter = 1 => Exponential distribution And from the Weibull properties, the mean lifetime can be derived as 8

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Remaining question: Measuring survival function from actual data Survival function is the cumulative distribution of survival rate (s), which is the rate at which an asset scurvies until any given age x, i.e. And the survival function (S) is calculated as the cumulative distribution of survival rates, i.e. This is exactly what the CBS followed before A crucial assumption (standard, but very strong) is Sj(x)=s(x) 9

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Why this assumption No information on K& D in ‘all’ vintages over a ‘long’ span of time Therefore, for all vintages the survival rate at any given age is assumed to be the same! An Example Suppose there exists 3 vintages, 1979, 1980 & 1981, of an asset in year 1990. The survival rate of these 3 vintages at age 10 can be calculated if we have information about their discard in 1989, 1990 & 1991. In practice this may not be available Suppose, we have this information since 1991, then we can calculate the survival rate of only vintage 1981 at age 10, as Then the above approach assumes for all vintages But, the discard pattern could be different for each vintage, threatening the assumption sj(x)=s(x). Is it possible to account for vintage heterogeneity completely? Not with the limited data available 10

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11 Alternative approach: Our approach Suppose we have information on discards in more years, so that we can calculate discard rate for these years more for all these vintages…!

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Alternative Approach Average of more than one discard rate for each vintage (within our data availability, 3 different vintages); more formally where Assumes absence of second hand investment Advantages: the assumption sj(x)=s(x) becomes more reliable as s(x) now carries information on more than vintage j, and helps make generalization more accurate 12

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13 Data Estimate equation using a non-linear regression Dutch micro data Extensive use of Dutch firm level data on capital stock & discards Lifetime estimates for three assets- Machinery, transport & computer 15 2-digit manufacturing industries

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14 Results: Lifetime estimates for Dutch manufacturing Shorter lifetime in capital asset (?) lease effect and second-hand sale Single-year survival rate vs. 3 year approach

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15 Single year vs. 3 year discard approaches Difference in life times (3 year –Single year)

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16 Single year vs. 3-year approach Comparing new estimates with earlier Dutch studies Methodological differences: Less discard information vs. more discard information Other differences: Treatment of data

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17 Obviously there are differences: But are the new results better? More industries (with reliable estimates) Better Fit And More realistic Estimates

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18 Average life time in Manufacturing, comparing with other countries Usual assumption of a common lifetime across countries (e.g. Caselli, 2005) doesn’t seem to be true

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19 Does it matter which lifetime one uses? Capital stock in Netherlands under various lifetime Assumptions New Estimates Source: EU-KLEMS

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20 Conclusions Choice of lifetime does matter for the estimation of capital stock Using survival information of more vintages in the lifetime calculation improves the fit of the model improves the estimates of lifetime helps estimate lifetime for more industries Current adjustments followed by the CBS in order to account for second-hand and lease effect may be followed.

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21 Are lifetimes endogenous? Determinants of Discard: Marginal coefficients from probit regression Dependent variable = 1, if discard rate>0, and 0 otherwise

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22 Differences in discard probabilities Innovative firms have higher discard probabilities for machinery, High-tech firms are more prone to discard computers at average age

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