We test a q investment model for Belgium using a multivariate cointegration approach. The introduccion of the degree of capacity utilization duc, in addition to investment and average q, is necessary to determine the cointegration space. This support the idea that marginal q differs from average q by a factor which is a function of duc, as suggested by Licandro(1992)

Croix, David de la

Licandro, Omar

English

De la Croix, David

Licandro, O.

DI-fusion

The q theory of investment under unit root tests

Name not available

The Q theory of investment under unit root tests

Universidad Carlos III de Madrid e-Archivo

Working Paper 92-07 [ February 1992 División de Econom~a Universidad Carlos IJI de Madrid Calle Madrid, 126 28903 Getafe (Spain) THE q THEORY OF INVESTMENT UNDER UNIT ROOT TESTS [ David de la Croix and Ornar Licandro· [1 Abstract _ We test a q investment model for Belgium using a multivariate cointegration approach. The introduction of the degree oí capacity utilization duc, in addition to investment and average q, is necessary to determine the cointegration space. This supports the idea that marginal q differs from average q by a factor which is a function of duc, as suggested by Licandro (1992). Key Words Cointegration Tests; Degree of Capacity Utilization; Monopolistic Competition; q Invest-[ ment Theory; Quantity Rationing Model • David de la Croix, Catholic University of Louvain. Ornar Licandro, Universidad Carlos III de Madrid. We are grateful to Frédéric Aprahamian and to Luc Bauwens for their useful comments. Paul Olbretchts kindly provided the statistical material '~[l .-.J fJ [ Average q and marginal q According to the q theory of investment, in the presence of convex adjustment costs for capital input, investment depends upon the ratio between the discounted value of ali expected future profits generated by the instaliation of an additonal unit of capital and the purchase price of investment goods. This ratio, called marginal q, is equal to the average q under the conditions derived by Hayashi (1982). In that case, the discounted value of future profits is equal to the average stock market value of capital. The main interest oí this approach is that expectations about future profits are contained in the q termo Various authors have tried to test empiricaliy the infiuence of stock market value on firms' investment (cf. Abel and Blanchard (1986)). Average q turns out to be highly significant in explaining investment, although it is unsatisíactory for various reasons: Lagged values oí q also have significant coefficients (while the theory 8Ugg~ts that current q ineludes aH available information about future profits); moreover, the residuals are autocorrelated. These elements Buggest that marginal q differs from average q and that this difference is a function oí missing variables (see Galeotti and Schiantarelli (1991)). FoHowing an idea initially proposed by Malinvaud (1987), Licandro (1992) has shown that the difference between marginal q and average q could be explained by the ratio of production to capacities, called the degree of capacity utilization and denoted duc. The idea is that ií firms íace demand uncertainty at the time oí their input (and possibly aIso price) decision, the predetermined capacity can be underutilized. Together with average profitability, the intensity oí this underutilization determines the marginal value of the firm. In this case, average q differs from marginal q by a factor which depends on the sequence of all expected íuture duc. In the long run, investment depends on average q and duc. This framework can be compared to another recent contribution by Schiantarelli and Georgoutsos (1990) who stress the role of imperfect competition: Contrary to Licandro's (1992) model, their firm can always adjust employment in order to fully utilize its capacity. However, monopolistic competition allows them to include output per unit oí capital as an additional explanatory variable in investment equation. In order to investigate the relevance oí Licandro's (1992) contribution, we test the existence oí two different cointegration relations. The first relation is derived from the usual elassical q investment model, with"'the simplifying assumption that the adjustment cost íunction is exponential. In this case, the investment rate o is simply a function of the logarithm of q, which is the average value oí the firm (measured by the stock market index) divided by the price of investment. This equation assumes the equality between average q and marginal q: 0= bo+ b1 In q (1) The second specification we want to test is taken from Licandro (1992). It is direelty comparable to the elassical model and takes the following long-ron form: o = bo+ b1 In q + b2 In duc (2) where b2 is positive: the closer the firm is to the full utilization of capacity, the more it invests. Tbe data The Belgian data we use are quarlerly and extend from 1971:3 to 1990:2 (76observations). The investment rate a is defined as it/kt- 1 where i is real investment according to VAT declarations. The capital stock k has been built using the investment series with an annual depreciation rate oí 10%. Average q is measured by the stock market index oí industrial values divided by an index of the wholesale price of the investment goods sector. The duc comes from the business surveys oí the Belgian National Bank. Beíore doing any multivariate analysis, we have to test the order oí integration oí the variables a, In q and lJ In duc. Note that the classical theory suggests that these variables are stationary since the endogenous response oí investment should ensure that duc is driven to its "normal" level and q to unity in the long runo To test the level oí integration oí any variable y, we use a standard ADF test selecting carefully the number of lags p in the following regression: P l1Yt = J.L + aYt-1 +L l1Yt-i + ft i=1 The role oí these lags is to cope with remaining autocorrelation in the residuals. However, if their number is too large the power oí the test is weakened. Thereíore, careful inspection oí whether the residuals are white noise and whether the lags are significant, as we11 es the use oí some iníormation criterion, can give important guidance. The estimations are - I [J I presented in Table 1. Together with the number of lags and the value of the ADF test (Ta ) we give the Akaike information criterion (Ale), the LM test íor the autocorrelation of residuals up to order 4 (whose critical value at 95% is a X~ =9.49) and an LM test of neteroscedasticity regressing the squared residuals on the squared levels of the estimated dependent variable (whose critical valt:.e at 95% is a X~ = 3.84). The best model with respect to these criteria is given in italles. From MacKinnon (1990), the critical value below which stationarity is rejected is -2.90 íor Ta , implying that our three variables are not. stationary in levels. The optimal lag length is 4 íor a and In duc while the best representation for In q is apure random walk. Table 1 ADF Unit Root Tests Q lnq lnduc To AlC AR4 HET To AlC AR4 HET TG AlC AR4 HET DF -2.69 -11.24 6.85 0.06 -0.14 -4.97 5.13 1.8~ -1.72 -7.92 19.53 0.09 ADF1 -2.32 -11.20 10.4 0.49 -0.43 -4.95 3.5 4.81 -2.54 -8.07 7.21 4.08 ADF2 -1.15 -11.32 10.8 2.25 -0.77 -4.92 3.06 0.38 -2.74 -8.03 7.26 5.92 ADF3 -0.68 -11.32 7.07 3.42 -1.01 -4.88 2.65 0.13 -2.65 -7.98 7.05 5.56 ADF4 -1.~5 -11.34 6.3~ 0.01 -0.92 -4.82 1.04 0.17 -1.96 -8.00 1.77 1.81 ADF5 -1.45 -11.31 6.78 0.01 -1.2 -4.79 3.52 0.79 -2.08 -7.95 5.53 2.21 ADF6 -1.16 -11.31 5.01 0.03 -1.13 -4.73 3.19 0.76 -2.42 -7.96 2.3 2.94 ADF7 -1.08 -11.25 6.3 0.03 -1.12 -4.67 15.5 0.91 -2.4 -7.90 4.94 2.86 ADF8 -1.58 -11.27 3 0.11 -0.68 -4.64 6.03 0.9 -2.32 -7.83 5.31 2.68 r~, An argument against this result could be that there is very slow mean reversion in a11 three variables, which is not adequately captured by the ADF test. It would be too optimistic to hope that twenty years of data would reveal such slow mean reversion. To cope with this argument we have computed the non-parametric test due to Phillips and Perron (1988) which should allow for alarger cless of error term distributions. Their [j [J [J [J statistic Z(Ta ) are presented in Table 2 for different values ofthe truncation lag parameter l (cf. the artiele of Phillips and Perron for details). The critica! value is the same as in the parametric ADF test. This test raises some doubts about the robustness of the conelusion concerning investment rate, since for l = 1 the unit root hypothesis is rejected. However, since we have no good reason for selecting any particular value oí l, we are not able to draw a definitive conelusion. Since for all other values of l the test does not reject the unit root hypothesis, we treat the investment rate as an integrated variable. Non-reported tests on the first differences of the variables show that the three variables are 1(0) in variations. We now try to find some cointegration relationship between these variables. Table 2 Non-Parametric Unit Root Tests DF 1=1 1=4 1=7 1=10 a -2.69 -3.11 -2.54 -2.57 -2.41 lnq -0.14 -0.13 -0.12 -0.11 -0.11 lnduc -1.72 -1.29 -1.39 -2.76 -2.17 Tbe cointegration space Using the methodology of Johansen (1988), we estimate a system composed of three au-toregressive error correction equations. The determination oí the dimension of the cointe-gration space can be found by a procedure which is a kind ofmultivariate generalization of the augmented Dickey-Fuller test. Once this rank is determined, standard asymptotic theory can be used for testing on the cointegrating vectors and ana!yzing the shape of the error correction terms. We are interested in identifying thecointegration space, if any, and testing whether ln duc is important in this identification. In order to avoid mispecifi-cation problems due to the omission oí important lags, we have chosen a reasonably large number oí lags (7) in the VAR with respect to the number oí observations. The following' model is tested: 6 AXt = J.L +L '"YiAXt-i + el3'Xt-1 + ft i=l where Xt = [at lnqt lnduCt]', p, is a 3 x 1 vector oí constants, 'Yi are a 3 x 3 matrices, eand 13 are 3 x r matrices, r being the dimension of the cointegration space. Table 3 presents the cointegration tests used to determine r, the number of cointegration vectors. Two statistics are provided: the first is based on the maximal eigenvalue oí Johansen's stochastic matrix; the second uses the trace of this matrix. The last column gives the threshold aboye which the null hypothesis is rejected. Table 3 Dimension 01 the cointegration space null alternative statistics 95% threshold (eigenvalue) r = O r = 1 22.93 22.00 r :s 1 r = 2 10.68 15.67 (trace) r = O r ~ 1 35.45 34.91 r < 1 r = 2 12.52 19.96 The two statistics unanimously allow us to conc1ude that there is onIy one cointegation relationship in the model. This unique cointegration vector, normalized to have a unit weight íor a, implies the íollowing long-run relationShip: a =0.049 +O.OUln q + 0.083 In duc The signs are compatible with the theoretical model. This can be compared to what we would have obtained using the Engle and Granger (1987) estimates: a = 0.052 + 0.007 In q + 0.082 In duc [J Johansen's procedure also allows to test the presence oí cointegrating vectors in each equation oí the system, using a likelihood ratio test whose criticaI value is distributed as a X~. This aims at anaIyzing whether the variations oí the variables adjust to the long run oí the model. This test in presented in Table 4: OnIy the investment rate and the degree oí utilization of capacity adjust in order to satisfy the long run reIationship. Table 4 Absence 01 cointegrating vectors equation Aa A In q A In duc test 11.48 0.00 4.90 We now turn to our main question, and test whether duc is important in the determi-nation oí the cointegration space. If duc is oí no importance in the long run, its weight in the cointegration relation should be zero. We thereíore test the exc1usion of duc from -the cointegration space using a likelihood ratio test whose critica! value is distributed as a X~. The result is presented in Table 5 together with the exclusion tests íor the other variables. From this, it is clear that duc helps significantIy to determine the cointegration space. Table 5 Exclusion from the cointegration space [J variable a In q In duc test 10.29 8.86 10.07 Moreover, ií we try to specify the system without In duc by considering only two equations (for a and lnq), Johansen's test implies that the dimension ofthe cointegration space is zero (Table 6). Table 6 Dimension 01 the cointegration space without ln duc null aIternative statistics 95% treshold (eigenvalue) r = O r = 1 13.51 15.67 (trace) r = O r = 1 15.96 19.96 This leacls to the conc1usion that In duc not only improves significantly the determi-nation of the cointegration space, but moreover seems necessary to locate some Iong-run relationship involving investment and average profitability. These results give some sup-port to the idea that, in the long run, average q diverges from marginal q and that this difference can be explained by the ratio oí efi'ective output to total capacity. References [1] ABEL A. and O. BLANCHARD (1986), "The Present Value of Profits and Cyclical Movements in Investment" , Econometioo, 54, 249-273. [2] ENGLE R. and C. GRANGER (1987), "C~integration and Error Correction: Rep-resentation, Estimation and Testing", Econometrioo, 55, 251-276. [3] GALEOTTI M. and F. SClllANTARELLI (1991), "Generalized Q Models for In-vestment", Joumal 01 Economics and Statistics, 3, 383-392. [4] HAYASHI F. (1982), "Tobin's Marginal q and Average q: A Neoclassical Interpre-tation." Econometrica, 50, 213-224. [5] JOHANSEN S. (1988), "Statistical Analysis of Cointegration Vectors", Joumal 01 Economic Dynamic and Control. [6] LICANDRO O. (1992), "Investment Dynamics and Capacity Utilization in Monop-olistic Competition", Annales d'Economie et de Statistique, forthcoming. [7] MacKINNON J. (1990), "Critical Values for Cointegration Tests", UCSD Discussion Paper 90-4. [8] MALINVAUD Edmond (1987), "Capital Productif, Incertitudes et Pro fitabilité."," [J Annales d'Economie et de Statistique, 5, 1-36. [9] PHILLIPS P.C.B. and P. PERRON (1988), "Testing for a Unit Root in Time Series Regression", Biometrika, 75, 335-346. [10] SCHIANTARELLI F. and D. GEORGOUTSOS (1990), "Monopolistic Competition and the Q Theory of Investment", European Economic Review, 34, 1061- 1078. 

C~integration and Error Correction: Representation, Estimation and Testing&quot;,

Capital Productif, Incertitudes et Pro fitabilité.&quot;, &quot;

Critical Values for Cointegration Tests&quot;,

Generalized Q Models for Investment&quot;,

Investment Dynamics and Capacity Utilization in Monopolistic Competition&quot;, Annales d'Economie et de Statistique,

The Q theory of investment under unit root tests

Abstract

Similar works

Full text

Available Versions

DI-fusion

Name not available

Universidad Carlos III de Madrid e-Archivo

DIAL UCLouvain

Name not available