Building the capital stock

Building the capital stock Ralf Martin 28 November 2002 1 Introduction The ARD1 does not contain information on capital stocks. If we still wish to use it for applications such as calculating TFP we have to calculate capital stocks with a perpetual inventory method (PIM). There various ways to do this. This document describes the method we used and discusses various alternatives. 2 Building the capital stock 2.1 Perpetual inventory We use the following perpetual inventory formula: kt = kt −1 (1 − δ ) + it where k represents the capital stock , δ the geometric depreciation rate and i is investment. 2.2 Investment series The basic ingredient to the perpetual inventory method is the investment information provided in the ARD. The ARD distinguishes between 3 types of investment: 1. Plant and Machinery 2. Buildings 3. Vehicles We do a perpetual inventory calculation for each one of these asset types. Our measure of total capital stock is then obtained by summing across the 3 asset types. Table 1 shows in detail which variables we used to calculate investment series. We use what in ARD terminology is net capital expenditure: This is capital expenditure minus proceeds from disposal of capital; i.e. this is not net of depreciation which the ARD does not have any information about. 1 For a detailed description of the ARD see Barnes and Martin [1] 1/ 10 Table 1: Variables used as investment information Variable 1980 1981-1992 1993-1995 1996-1997 1998 1999-2000 total net capital (q154- (q154- q154-q155 q817-q818 q523 wq522+wq521 q155)/1000 q155)/1000 (q517- (q517- q517-q518 q853-q854 q527-q530 wq527-wq530 q518)/1000 q518)/1000 net capital buildings (q501+q502- (q501+q502- q501+q502- q849+q848- q524+q525- wq524+wq525 q503)/1000 q503)/1000 q503 q850 q528 -wq528 net capital (q513+q515- (q504- q504-q505 q851-q852 q526-q529 wq526-wq529 q514- q505)/1000 expenditure net capital expenditure for plant and machinery expenditure for q516)/1000 vehicles Notes: The cell entries refer to the ARD question numbers; i.e. total net capital expenditure in 1980 is obtained by subtracting question 155 from question 154 and dividing by 1000 to account for the unit change after 1992. 2.2.1 Gaps The ARD surveys smaller units only on a random basis. If we want to calculate capital stocks for these we cannot just include only those years in the perpetual inventory method where the units were sampled. Because they are investing in the other years as well we would vastly underestimate their true capital stock. To avoid this we apply 3 types of interpolations: 1. We linearly interpolate the investment series in years where we have an observation both before and after the missing period, 2. set missing values at the birth of a unit equal to the first observed value and 3. set missing values at the death of a unit equal to the last observed. Figure 1 shows this graphically. Figure 1: Inter- and extrapolation of investment series investment interpolated missing non missing time 2/ 10 2.2.2 Other Problems In 1994 and 1998 investment information by 3 asset types was missing from our data. For these years we interpolated the numbers as described in the last section. Attanasio et al. [2] report about a structural break in investment reporting in 1988. According to them there has been a change in the treatment of leased assets in this year. Figure 2 shows average investment levels by sector as found in our dataset. As there is no apparent structural break in 1988 we assumed that the problem described by Attanasio et al. is not present in our release of the data. Figure 2: Average investment by sector (Aggregated from figures by 3 asset types) 25 20 15 10 5 0 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 Food and tobacco Wood Rubber Machinery nec nec 2.3 Textile Paper and Publishing Minerals electrical and optical equipment Leather Chemicals Basic metals Transport equipment Initial values There are two problems with initial values. First, as our panel ranges from 1980 to 2000 units which are born before 1980 suffer from left censoring. Because they have accumulated capital before 1980 we would grossly underestimate their capital stock if we only considered their post 1980 investment. Secondly, even units which are born after 1980 will have undertaken some initial investment before they first report to the ONS. To take account of both issues we allocate initial capital 3/ 10 stock values from sectoral aggregates at the 2 digit level. The sectoral aggregates are based on historical investment series by various asset types stretching back to 1948 provided by the ONS. To derive these stocks a perpetual inventory method with geometric depreciation has been applied on the sectoral level. We use real and nominal values of the same series to get implied deflators. Figure 3 Allocating initial capital stock Aggregated non Selected capital stock Selected Estab. 1 Estab. 2 Estab. 3 …. Estab N To get initial values we have to estimate how much of the aggregate capital stock in a given year is due to the individual establishments in our selected2 sample (see Figure 3). To do this we proceed in 2 steps: First, we have to estimate the share of aggregate sectoral capital stock which corresponds to the selected units in our sample. We estimate this as the investment share of a sectors selected units: γ Sector = I Selected , SectorI I SectorI . Secondly, we distribute this selected units capital stock among the selected new born or left censored units on a pro rata basis according to the average material usage over the live time of a unit, that is establishment i gets a share γ i of the capital stock where 1 Ti ∑ M t ,i T i t =1 γi = 1 Ti ∑ ∑ M t ,i i∈Sector T i t =1 2.4 Investment deflators We use investment deflators with base year 1995. For years pre 1995 these are implicitly derived from nominal and real sectoral ONS historical investment series (see also previous section). From 1995 on we use the publicly available MM17 series. 2 to the selected units we count in this context also the who were not selected in a year but whose investment series have been interpolated as described in 2.2.1. 4/ 10 2.5 Depreciation rates Depreciation rates have to be assumed we make the following assumption: Asset Type Deprecation rate Plant and machinery 0.06 Building 0.02 Vehicles 0.2 Composite asset invesstment average of above=0.11 These numbers are equal to the average depreciation rates used in PIM calculations for sectoral aggregates by the ONS. 3 Alternative ways to calculate the capital stock 3.1 Treatment of initial values We experimented with allocating initial capital stocks only to units which were born before 1980. We thought that such an underestimation of capital stock might be preferable to the crude allocation of initial values from some aggregate value. It turned out however that it is crucial to get plausible results. Table 2 and Table 3 show annual transition matrices of TFP calculated once with a capital stock series with and once without initial values post 1980. The transition matrix for the series without initial values (Table 2) has implausible concentration of entries with very high productivity and an exit rate from the top quintile as high as for the bottom. This is most likely a consequence of the capital stock underestimation post 1980: Newly entering establishments which are more likely to exit have an overestimated TFP. Table 2: Annual TFP Transitions without initial values post 1980 20 40 60 80 100 exit 20 0.57 0.21 0.08 0.03 0.01 40 0.23 0.38 0.21 0.08 0.02 60 0.09 0.24 0.35 0.20 0.05 80 0.04 0.10 0.24 0.39 0.15 100 0.02 0.03 0.08 0.24 0.53 entry 0.13 0.11 0.13 0.18 0.44 5/ 10 0.10 0.07 0.07 0.08 0.10 Table 3: Annual TFP Transitions with initial values in all years 20 40 60 80 100 exit 20 0.52 0.22 0.09 0.04 0.02 0.11 40 0.22 0.35 0.22 0.10 0.03 0.08 60 0.09 0.22 0.32 0.22 0.07 0.07 80 0.05 0.10 0.23 0.36 0.19 0.08 100 0.03 0.04 0.09 0.22 0.52 0.09 0.24 0.19 0.18 0.18 0.21 entry Further we experimented with allocating initial values on the basis of an establishments average share in aggregate investment (instead of material). It turned out that taking material shares is again crucial to get plausible results when calculating TFP. Table 4 shows a TFP transition matrix using a capital stock measure calculated on the basis of investment shares. Again there is a problem with entry and exit rates. Table 4: Transition Probabilities for ln_TFP_go_mean_sep02_yearly 20 40 60 80 100 entry 20 0.62 0.21 0.06 0.02 0.01 0.19 40 0.21 0.41 0.24 0.07 0.02 0.12 60 0.06 0.23 0.38 0.24 0.06 0.14 80 0.02 0.07 0.21 0.43 0.22 0.18 100 exit 0.01 0.08 0.02 0.07 0.04 0.07 0.15 0.08 0.59 0.11 0.37 Source: Authors' calculations based on ARD Notes: Row 1 column 2 shows for example the probability that a firm whose TFP in t falls into the bottom quintile moves on to the 2nd quintile in t+1. Things get even worse when using both: investment shares and no initial values post 1980 (Table 5). 6/ 10 Table 5: Annual transition matrix for TFP (TFP relative to 4 digit sector mean, based on gross output) 20 40 60 80 100 entry 20 0.65 0.21 0.06 0.02 0.01 0.13 40 0.20 0.42 0.24 0.08 0.02 0.11 60 0.05 0.21 0.38 0.25 0.07 0.13 80 0.02 0.07 0.20 0.41 0.24 0.19 100 exit 0.01 0.08 0.02 0.07 0.04 0.07 0.15 0.08 0.55 0.11 0.45 Source: Authors' calculations based on ARD Notes: Row 1 column 2 shows for example the probability that a firm whose TFP in t falls into the bottom quintile moves on to the 2nd quintile in t+1. The entry row shows the fraction of entrants that have entered to the various quintiles. 3.2 Accounting for plant closures Richard Harris (Harris and Drinkwater 2000) in particular has pointed out that for multiplant establishments plant closures could lead to an overestimation of the capital stock with the perpetual inventory method. With the perpetual inventory method we assume a constant depreciation rate which does not account for the discrete drop in an establishments capital stock in connection with a plant closure. We have not accounted for plant closures in our calculations for 3 reasons: 1. To be able to account for plant closures we need to have an estimate of the size of the capital stock at individual plants. To do this strong assumptions are needed which we eschewed to make. The problem is that for multi-plant establishments the only data available at the plant level is a an unreliable estimate of a plants employment. So one has to distribute establishment level capital stocks and/ or the investment according to this employment figure. 2. The additional work required to make to account for plant closures is considerable 3. It is not clear if accounting for plant closures would make a great difference to our results. As a matter of fact about 30% of all selected plants belong to single plant establishments (about 50% of all plants are in establishments with less than 4 plants). About 50% of the employment in selected firms is in single plant establishments. Harris (2000) uses an ARD local unit dataset which takes account of plant closures when calculating the capitals stock. Harris finds that his results differ from a similar study by Griffith (1999) who worked on the establishment level. Inspecting his Table A2 suggests however that the differences were 7/ 10 mainly driven by using weighted regressions rather than local unit data. showed that working with local units. 4 Looking at the capital stock For most purposes we will only need a composite capital stock measure. When building the capital stock however, we run perpetual inventory calculations on 3 asset types: Plant and Machinery, buildings and vehicles. The composite capital stock is found in turn by aggregating these series. Figure 4 shows an index constructed from the so found sectoral aggregates of the capital stock measure. Figure 4: Index of real capital stock series by sector (Permament inventory calculations based on microdata from ARD) 4 3.5 3 2.5 2 1.5 1 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 Food and tobacco Leather Paper and Publishing Rubber Basic metals electrical and optical equipment nec 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 Textile Wood Chemicals Minerals Machinery nec Transport equipment To get an idea if our capital stock makes sense I compare it with the sectoral aggregate capital stock series based on the ONS historical investment series. An index of this capital stock measure is displayed in Figure 5. The basic qualitative features of the two sets of series seem to be in line with each other. The measure based on ARD microdata seems more volatile which is natural given that there we also capture entry and exit which affect the aggregate stock in a very lumpy way. 8/ 10 Figure 5: Index of real capital stock series by sector (Permament inventory calculations based ONS historical aggregate investment series) 4 3.5 3 2.5 2 1.5 1 y1980 y1981 y1982 y1983 y1984 y1985 y1986 y1987 y1988 y1989 y1990 y1991 y1992 y1993 y1994 y1995 y1996 y1997 y1998 y1999 y2000 Food and tobacco Textile Leather Wood Paper and Publishing Chemicals Rubber Minerals Basic metals Machinery nec electrical and optical equipment Transport equipment nec To further compare the two measures Figure 6 shows the ratios between our two sets of capital stocks. Note that we did not apply any weighting to the ARD series so it only represents the capital stock of selected units. It is therefore not surprising that the ratio is usually smaller than one. 9/ 10 Figure 6: ARD capital stock over Aggregate capital stock 1.4 1.3 1.2 1.1 1 0.9 0.8 0.7 y1980 y1981 y1982 y1983 y1984 y1985 y1986 y1987 y1988 y1989 y1990 y1991 y1992 y1993 y1994 y1995 y1996 y1997 y1998 y1999 y2000 Food and tobacco Textile Leather Wood Paper and Publishing Chemicals Rubber Minerals Basic metals Machinery nec electrical and optical equipment Transport equipment nec References Attanasio, Orazio, Lia Pacelli and Isabel Reduto dos Reis, Aggregate implications of plant level investment behaviour: Evidence form the UK ARD. 2000. Barnes, Matthew and Ralf Martin (2002), “ Business Data Linking: An Introduction” . Economic Trends Harris, R (2000), “ Foreign Ownership and Productivity in the United Kingdom - Some Issues When Using the ARD Establishment Level Data” , mimeo, http:/ / www.dur.ac.uk/ richard.harris/ griffith.pdf Harris, R. I. D. and S. Drinkwater (2000), “ UK Plant and Machinery Capital Stocks and Plant Closures” , Oxford Bulletin of Economics and Statistics, 62, 239-261. 10/ 10