Is investment time irreversible? Some empirical evidence for disaggregated UK manufacturing data

Abstract

It has long been suggested that investment may be time irreversible, and consideration of the option value of waiting to invest has aroused renewed interest in this issue. This study tests for time irreversibility in UK investment according to disaggregation by type of investment expenditure and across manufacturing sector groupings. The test results reported indicate that the irreversibility of investment patterns varies not only from industry to industry but also according to the type of capital being purchased, with significant time irreversibility detected in gross fixed capital formation and aggregate vehicles expenditure, and industrial sector groupings comprising fuels and oil refining, engineering and vehicles, and textiles and leather. However, only in the first and last of these series is time irreversibility attributable to non-linearities in the underlying data generating process, and consistent with threshold effects which may be associated with (S,s) type models of investment dynamics.

Notes

¹ Notable exceptions to this remark are provided by the work of Price (1995, 1996), who examines the consequences of aggregate uncertainty for capacity utilization and investment, and demonstrates in particular the existence of asymmetric adjustment dynamics governing UK manufacturing sector investment in the context of a non-linear time series model exhibiting threshold effects. Relatedly, Sensier (2003) investigates the asymmetric properties and time-series behaviour of UK manufacturing inventories and production over the business cycle in the context of a model of asymmetric adjustment, as well as providing test statistics for the asymmetric properties of that data.

² Lucas (1967), Gould (1968) and Mussa (1977) also provide important contributions to the subject of capital adjustment costs, particularly the separation of costs associated with capital good supply (external) and disruption costs to the firm (internal). It should also be noted that Eisner and Strotz recognized the potential inadequacy of symmetric costs, and appreciated that adjustment costs may indeed be asymmetric in practice.

³ See, for example, Dixit and Pindyck (1994) for a review of this earlier literature, and Caballero and Pindyck (1996) for an examination of the effects of irreversible investment on total investment and firm entry in a competitive industry subject to both industry-wide and idiosyncratic uncertainty. Relatedly, Gale (1996) has demonstrated that where the profitability of investment is dependent on the level of economic activity, the resulting incentive to delay investment in a recession may deepen the recession and lengthen the period of economic recovery. Abel and Eberly (1997) have shown that irreversible investment in the presence of convex costs leads to regions of behaviour in which investment in a homogeneous good is not responsive to Tobin's q, and other regions where it is. For extensions and empirical studies of the nonlinear relationship of investment to q, including regions of insensitivity, see for example Barnett and Sakellaris (1998) and Corrado et al . (2001). On the consequences of irreversible investment and idiosyncratic uncertainty for differences in firms’ capital stocks and the aggregate capital stock in a dynamic general equilibrium setting model, see Jamet (2004). For a recent application of the real options methodology in the context of the valuation of agricultural investment decisions, see Tzouramani and Mattas (2004).

⁴ In particular, Bertola and Caballero (1994) and Caballero et al . (1995) show that under certain distributional assumptions, and in the presence of a large amount of idiosyncratic microeconomic uncertainty in particular, there is likely to be little synchronization at the aggregate level but the history of accumulated past shocks can nevertheless greatly affect the elasticity of investment response to future shocks.

⁵ For an interesting recent applied analysis of the within-industry coordination problem and strategic behaviour implications that may arise as the result of such lumpy investment patterns in the context of the British brick industry, see Wood (2005).

⁶ More specifically, and in some parallel with option value of waiting approach, Caballero and Engel (1999) explain investment delays as the strategic response of firms’ to heterogeneous adjustment hazards which have the capacity to either magnify or dampen the response of investment to an aggregate shock, depending on the shock size. The presence of such adjustment hazards implies asymmetry due to nonlinearity in aggregate investment, consistent with threshold effects, in that there are occasional sharp responses of investment to current or cumulative shocks.

⁷ In the pursuit of evidence for such behaviour, Doms and Dunne (1998), for example, examine plant level investments in US manufacturing over the period 1973–1988 and find the distribution of investment rates to be symptomatic of irreversible investment, in that very few firms exhibit negative gross investment rates, whilst many firms group the majority of their investment in just three years of the sample period covered. The same study also found there to be a correlation between the number of investment spikes and the aggregate investment rate. In an interesting cliometric application of the Doms and Dunne methodology, Süssmuth (2003) similarly reports evidence of lumpiness and asymmetry as defining characteristics of German firm level capital adjustment patterns for the period 1880–1913.

⁸ For further discussion of threshold models see Tong (1990).

⁹ Ramsey and Rothman (1996) offer the time path of a round projectile in (windless) flight as an intuitive example of a time reversible process, and the dispersal of ink in water as an intuitive example of a time irreversible process. Investment aside, the diffusion of technology provides an obvious further example of a time irreversible economic process.

¹⁰ In relation to the extensive empirical literature concerned with testing for asymmetries in economic time series, time irreversibility therefore captures those measures of asymmetry that are ‘longitudinal’, whilst purely ‘transversal’ asymmetries are time reversible; in particular, longitudinal ‘steepness’ asymmetry is time irreversible, while transversal ‘deepness’ asymmetry is time reversible. These alternative definitions refer to differing speeds of adjustment in expansions and contractions; for example, the business cycle has long been thought to be characterized by steeper recessions and longer more gentle expansions. A particular advantage following from the representation of asymmetries in terms of time irreversibility, as noted in Section I, is that the formulation in terms of time irreversibility lends itself to a discriminating test between circumstances where the process innovations are asymmetric but the impulse transmission mechanism is linear, and circumstances where innovations are symmetric and the impulse transmission mechanism is nonlinear. In contrast, the representation of asymmetries in terms of ‘steepness’ associated with the properties of the third moment of a series distribution does not permit such discrimination. See Mittnik and Niu (1994) and Psaradakis (2000) for further discussion of a number of commonly employed tests of asymmetry.

¹¹ Ramsey and Rothman (1996) suggest that the appropriate values for m and K that should be selected in practice are m = 3 and K = 5. The choice of order 3, and similarly degree 5, arguably provides the best compromise value for identifying time reversibility given the degrees of freedom typically available for economic time series.

¹² For further details, see Theorem 2 of Ramsey and Rothman (1996), and for a frequency domain variant of the TR-test statistic based upon the bispectrum, see Hinich and Rothman (1998).

¹³ Under this latter approach an estimate of the variance of the variance of is calculated by fitting a linear autoregressive (AR) model to the data, obtaining an estimate of the innovations variance, and then simulating a series using the estimated AR coefficients and generating a Gaussian error process with zero mean and variance equal to that estimated in the preceding stage. Values of are calculated for each such replication for N replications, where N = 100, permitting straightforward computation of the estimated variance using the replicated values for . If the process is truly linear Gaussian, and time reversible, this is an exact simulation procedure. If the series is truly nonlinear (Type I time irreversible), the linear model constitutes a local approximation to the unknown nonlinear model, but the procedure should nonetheless provide asymptotically unbiased estimates of the variance of in the presence of uncorrelated innovations.

¹⁴ Note that it is a requirement of the TR-test statistic that the data possess a finite sixth moment. Chen et al . (2000) have proposed an alternative to the TR-test statistic which does not have any moment restrictions. However, as Chen et al . note, their test is not directly applicable to model residuals because it is a test of unconditional symmetry, and cannot therefore be used in order to discriminate between Type I and Type II time irreversibility.

¹⁵ Note that whilst Type I time irreversibility implies nonlinearity, the converse is not necessarily true, since there exist stationary nonlinear processes that are time reversible (e.g. Lewis et al ., 1989). The TR-test cannot therefore be considered as equivalent to a test for nonlinearity of unknown form.

¹⁶ For more detailed discussion of this test procedure and its rationale, see Ramsey and Rothman (1996). On the uses and possible limitations of the TR-test statistic as a guide to model specification tool in application to nonlinear conditional mean and conditional variance model residuals, see Rothman (1999) and Belaire-Franch and Contreras (2002, 2003, 2004).

¹⁷ Note that whilst Type I time irreversibility implies nonlinearity, the converse is not necessarily true, since there exist stationary nonlinear processes that are time reversible (e.g. Lewis et al ., 1989). The TR test cannot therefore be considered as equivalent to a test for nonlinearity of unknown form.

¹⁸ Whilst the first four of these investment series are net of disposals of capital, gross fixed capital expenditure refers only to acquisitions.

¹⁹ ONS series codes (http://www.statistics.gov.uk): New Building Work (IMKQ); Vehicle Expenditure (IMWB); Other Capital Expenditure (INHM); Total Business Investment (INLN); Gross Fixed Capital Formation (INLN).

²⁰ ONS series codes (http://www.statistics.gov.uk): Solid and Nuclear Fuels, Oil Refining (INKZ) ; Metals and Metal Goods (INLC); Chemicals and Man Made Fibres (INLA); Engineering and Vehicles (INKQ); Food, Drink and Tobacco (INKV); Textiles Clothing, Leather and Footware (INKW); Other Manufacturing (JZKM).

²¹ Whilst not reported here in full, the appropriateness of this transformation is confirmed by the results of Phillips-Perron test statistics which are unable to reject the presence of a unit root in the logarithmically transformed data but are able reject a unit root in the first difference of logarithms, for all the investment series considered. These inferences are also robust to variation in the test equation specification concerning inclusion or exclusion of a trend, constant or both, for the logarithmic data and the differenced logarithmic data. Full details of these unit root test results are available on request from the authors.

²² Recall from the discussion in Section II that an appropriate linear specification is necessary in order for the significance of the standardized test statistic results to be calculated and the alternative hypothesis of time irreversibility to be tested against the null of time reversibility, as well as in discriminating between Type I and Type II time-irreversibility. In particular, the results reported employ an estimate of the variance of calculated by Monte Carlo simulation using a a linear autoregressive AR(p) model fitted to the data of order p determined by reference to the Akaike Information Criterion (AIC). Alternative results based on application of the Schwarz (Bayesian) Information Criterion (BIC) which provide qualitatively equivalent results are omitted here in the interest of conserving space, but are available from the authors on request.

²³ Indeed, along with other industries based in the primary sector such as mining (Brennan and Schwartz, 1985) and forestry (Morck et al ., 1989), where natural resources lend themselves easily to the explanation of the option value of an investment, the oil industry provides one of the ‘benchmark’ examples of irreversible investment.