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Evidence on the relationship between uncertainty and irreversible investment
The Quarterly Review of Economics and finance, Vol. 35, No. 1, Spring, 1995, pages 41-52 Cop+@ 0 1995 Trustees of the University of Illinois All rights of reproduction in any form reserved. ISSN 00335797
Evidence on the Relationship between Uncertainty and Irreversible Investment ATHANASIOS EPISCOPOS Clarkson University
Recent theoretical literature on irreversible investment has suggested that increased uncertainty about (i.e., volatility of) exogenousfactors
depresses investment. However, empirical
confirmation of the theory has been minimal. This paper considers five major uncertainty
real interest rate, personal consumption, composite
variables, namely, the growth rates of
index of leading indicators, index of stock prices and GDP deflator. Their conditional variance is estimated using ARCH methodology and is related to growth infixed private investment. The latter type of investment is assumed to be largely irreversible. The results show a signt$cant
negative relationship between uncertainty and investment,
thereby
confirming the received theory.
I.
INTRODUCTION
Recent
papers have shown that uncertainty
has a negative effect on irreversible
investment. Pindyck (1991)) Dixit (1992)) and Dixit and Pindyck (1994)) summarize a growing literature, with connections
to option pricing, that examines such prob
lems as investment timing, optimal capacity entry-exit, and project valuation. The basic idea involves optimal stopping rules, where firms tend to wait before sinking capital when business conditions are uncertain. Such reluctance to act manifests itself in lower rates of investment during periods of increased uncertainty. Despite the growing theoretical has been little econometric
literature on uncertainty and investment, there
testing. One possible reason for the lack of econometric
analysis is the diffkulty in defining irreversibility and uncertainty. This paper attempts to partially fill that void by employing a methodology which takes into account the changing nature of uncertainty over time. Five variables are used to capture the major sources of uncertainty in an economy. The volatility of these variables is found to be negatively related attempt
to growth in fixed investment.
to discriminate
between
alternative 41
Although
theories
the paper does not
of investment,
the results
42
QUARTERLY REVIEW OF ECONOMICS AND FINANCE
constitute much needed empirical evidence supporting
the underlying
theory of
irreversible investment. The following section presents a brief review of the basic theory and the related econometric
literature. Subsequent sections describe the methodology, data, results,
and problems associated with the technique involved, and present conclusions.
II.
BACKGROUND
ON THEORY AND EMPIRICAL LITERATURE
Investment is irreversible when it cannot be recovered after being installed. For instance, capital which is firm-specific or industry-specific is generally irreversible, which suggests that firm has to “think twice” before committing to such investments. Analysis of this kind of behavior by firms appears in the early work of Arrow (1968). The modern extension is in the direction of dynamic uncertainty, the latter being specified by the variance of the shocks that drive a model. It turns out that the greater the uncertainty, the more reluctant firms are to make irreversible investments, This result is independent of attitudes towards risk, and instead is traced to the potential of conditions to change in the future. It is commonly assumed that a random shock (or vector of shocks), S, occurs in the system. Typically, S obeys the stochastic differential equation:’ dS, = l@,t)dt
+ o(S, t)dW( t)
(1)
where l.t and G are the drift and standard deviation functions, respectively, and dW is the increment of a Weiner process. S usually follows a geometric diffusion with lt and (Tproportional to the shock. This shock can take several forms. It can be the interest rate as in Ingersoll and Ross (1992)) project cost as in Pindyck (1993)) unit price of capital as in Bertola (1989), project value as in McDonald and Siegel (1986), or a multiplicative demand shock as in Dixit (1991) and Episcopos (1994). A typical formulation is where the firm maximizes expected profits by choosing optimal times for investing. The profit maximization assumption allows for the determination of the critical shock level necessary to induce investment. This critical shock is always different than the one derived under certainty. For instance, suppose that S is positively related to the profit function. Suppose further that the value of S that triggers investment, in a deterministic world, is &. In other words, S, is such that the marginal revenue from the investment equals marginal cost. However, if S is stochastic, the trigger shock is higher than &,. The “adjusted” marginal cost must include the opportunity cost of sinking the capital now versus later; the intuition is that investing irreversibly entails the destruction of options to invest in the future. These options have higher value when the variability of the shock is higher, in the same way stock options have higher value when the stock price volatility is higher. It follows that, for larger levels of shock variability, there is a correspondingly wider divergence* of the trigger shock from So. In general, as S evolves over time, there are
UNCERTAINTY AND IRREVERSIBLEINVESTMENT
43
periods when the firm does not invest at all and simply “waits” until S reaches the trigger level. The upshot is that such inaction by firms implies lower investment rates each period. Therefore,
the central hypothesis tested is whether increases in instan-
taneous uncertainty imply decreases in irreversible investment. There are two ways to approach the problem. The first is to focus on the trigger shock, L$,,and see whether it changes in the predicted direction as volatility changes. This approach
is pursued by Caballero and Pindyck (1992).
However, the trigger
shock is not directly observable and must be estimated from data. The second method is to directly test the connection
between the volatility of S
and actual investment. A notable attempt is made in Pindyck (1992)) who considers the effect of stock market volatility on investment. In contrast, the present paper explores a wider range of uncertainty sources to strengthen the results. Because many macroeconomic time series can be estimated by conditional heteroskedastic3 models (Weiss, 1984), the ARCH methodology is chosen in this paper. Five different shocks are considered: (1) The growth rates of the real interest rate; (2) the index of stock prices; (3) the composite index of 11 leading indicators; (4) the aggregate personal consumption
expenditure;
sources of uncertainty.
and (5) the price level. These shocks cover considerable
Conditional
variance estimates are extracted
from simple
autoregressive models with ARCH specifications in the disturbances. These variance estimates enter as regressors in AR(l)
models of fixed investment. The main result
is a negative relationship between the variance and fixed investment, which confirms the theory that irreversible investment and uncertainty are inversely related.
III.
DISCUSSION
OF METHODOLOGY,
DATA AND RESULTS
Several important issues are associated with testing the main proposition. First, testing irreversibility in capital formation is difficult due to lack of firm and industry level data. However, casual observation suggests that there are various degrees of irreversibility. It is more difficult to resell industry-specific capital than capital that has alternative uses. For instance, it is more difficult to resell a nuclear reactor or a steel mill than office furniture. Even in the latter case, the price of a used item is much less than that of a new item, even when one accounts for physical depreciation. It seems reasonable, however, to assume that irreversibility is likely to exist in fixed investments rather than in inventories, for instance. Thus, fixed investment is used as a proxy for irreversible investment. Choosing the random shock and measuring uncertainty are also important issues in empirical tests. In Pindyck (1992)) stock returns are used as proxies for profitability. The idea is that profit variability naturally translates to variability in stock returns. However, the uncertainty measure used in that paper-computing the sample variance from smaller periods within a quarter-does not make efficient use of the data in general (Bollerslev, Chou and Kroner 1992, p. 18).
44
QUARTERLY REVIEW OF ECONOMICS AND FINANCE
A desirable feature of the chosen shocks is that they have to be pervasive enough to have an impact on all firms, and be readily and frequently observable within the measurement
period. The shocks used here share these features. The growth rate of
the composite index of 11 leading indicators comprises several aspects of economic activity and can be thought of as the net sum of a variety of shocks. The growth rate of the New York Stock Exchange composite index, which reflects profit shocks, can be estimated almost continuously. All producers sense changes in the growth rate of aggregate personal consumption
expenditure.
The reason is that actual changes in
the final quantities demanded are transmitted backwards to other stages of production in the form of canceled
or rush orders for raw materials. Similarly, firms are
sensitive to changes or growth rates of real interest rates. Finally, businesses and individuals readily detect price level changes. estimated below as tests of the corresponding test of the relationship
One can think of the equations
published models. For instance, the
between interest rate uncertainty
and investment
can be
viewed as a test of the model by Ingersoll and Ross (1992). The test of the relationship between stock index uncertainty and investment can be viewed as a test of Bertola (1989) or Pindyck (1988). The empirical model is given by: GFIX =f(S, DRIFT, VAR; GGDP, RI)
(2)
where, GFIX is growth of fixed investment, S is the shock level, DRIFT is a proxy for the drift, VAR is a proxy for the instantaneous
variance. The function J which can
include lags of all variables, contains also RI, the average growth rate of real interest rates, and GGDP, the growth rate of gross domestic product. The data4 used for each shock is: 1.
Monthly and seasonally adjusted observations of the composite index of 11 leading indicators from 1948:Ol to 1993:03 are used. A series of annual growth rates of the index,
2.
GLED
is created
by using the formula
GLED,
=
I2log(%/%l). The same process is used for monthly observations of the New York Stock Exchange
Composite price index from 1947:Ol to 1993:03 to create growth
rates, GSTK 3.
Quarterly and seasonally adjusted observations of real personal consumption expenditures in billions of constant 1987 dollars from 1947:l to 1993:l
are taken. A series of growth rates is computed
by the formula
GCON, = 41og( xJ+i). 4.
Monthly figures for Moody’s AAA and BAA annual yield series from 1947:Ol to 1993:03 are summed for each month and divided by two. Then the growth rate in the GDP implicit price deflator (1987=100) is subtracted to arrive at a proxy for the long term real interest (see Santoni and Stone, 1982), GINT.
Due to the lack of monthly data for inflation, I subtracted the quarterly figures 5.
from the corresponding monthly yield entries. The implicit price deflator (1987=100) for GDP is used to create an inflation series, GPRI, by using the formula GPRI, = 4log(x,/x,i).
The series of investment
growth rates are computed
seasonally adjusted real expenditures
dollars. The data cover the period from 1947:l nonresidential
by using quarterly and
on fixed private investment in billions of 1987 to 1993:l.
(Fixed investment is 66%
and 34% residential investment; nonresidential
is 19% investment in
structures and 81% investment in producers’ durable equipment.) The investment growth series is computed by the formula GFIX, = 4log(x, / +r). GGDP is defined in the same manner. RI is defined as RI, = (GINT, + GINT,r)/ 2. Estimated conditional variances from models with ARCH errors are desirable candidates for volatility. The common equations can be written succinctly as:
i=l
where E is the error term and h is the variance. ARCH captures
the changing
conditional variance of each shock. From Equation 4, it is obvious that past errors magnify the current variance. A description of the diagnostic and identification steps taken for the case of the index of leading indicators follows. (The same procedure was adopted for the rest of the series.) GLED series: Inspection of the Ljung-Box Qstatistics for 12,24 and 36 lags, which are 421.5, 626.7 and 632.8, respectively, and are shown in Table 1, imply significant serial correlation. After some searching, the AR model shown in the top section of Table 2 is fitted. The residuals from this model are checked for serial correlation in the first and second moments. The 12,24 and 36 lag Qstatistics on the residuals are 5.53, 28.72 and 43.78 as shown in the top section of Table 2. The corresponding critical points of chi-square with 8,20, and 32 degrees of freedom at 5% significance are, respectively, 15.51, 31.41, and 43.77. Therefore, most of the serial correlation has been removed. The Qstatistics of the squared residuals for 12,24 and 36 lags are 115.09, 136.75, and 187.04, respectively, and they are shown in brackets in Table 2. This means that non-linearities are present and an ARCH model appears suitable. The top section of Table 3 shows the estimated model. The maximum likelihood estimation uses the Berndt-Hall-Hall-Hausman (BHHH) iterative procedure. The Q statistics for the standardized residuals, E, /a, for 12,24 and 36 lags are 9.04,23.25 and 36.27, respectively, and are shown in Table 3. The Qstatistics for the same lags of the squared residuals, I$?/&,were 18.54,26.28 and 41.95. Similar results are found
46
QUARTERLY REVIEW OF ECONOMICS AND FINANCE Table1. Q STATISTICS FOR SHOCKS & INVESTMENT GROWTH RATE Variable
Q(12)
Q(24)
Q(36) 632.8
GLED
421.5
626.7
GSTK
48.6
71.0
78.9
GCON*
18.4
27.5
36.3
GIhT
168.9
174.9
182.5
GFXI
398.3
572.0
613.9
GFm
83.0
100.8
115.9
Nota:
* Exhibits correlation mostly in shorterlags at 5% significance: = 12.6. QJ4) = 19.0. 0J5) = 13.0, Q(6) = 14.0.
Q(Z) = 11.6. Q(3)
for the rest of the series.5 The variable GCON is unique in that it exhibits serial correlation for shorter lag (see Table 1 and Table 2 for details). After the AR-ARCH models are estimated, replacing errors with residuals in Equation 4 produces the variance, VAR, which now enters as a regressor in the investment models.6 The estimated variances were averaged over the respective
Table2. ESTIMATED AR MODELS* GLEDt= 0.019 + 0.380 GLED&l t 0.237 GLEDb2 - 0.200 GLEDc12 + q (4.152) (9.190)
(5.774)
(-5.810)
R* = 0.407
D= 2.004
SEE = 0.097
Q(12) =5.53 [115.09]**
Q(24) = 28.72 [ 136.751
Q(36) = 43.78 [ 187.041
GSI& = 0.058 + 0.276 GST&_l - 0.089 GSTKg2 + et (3.374) (6.522)
(-2.095)
R = 0.099
D = 2.000
SEE = 0.398
Q( 12) = 13.32 [29.47]
Q(24) = 29.94 [35.11]
Q(36) = 35.19 [43.31]
GCONl = 0.024 t 0.235 GCONc2 t et (7.569) (3.257) R* = 0.540
D = 1.881
SEE = 0.030
Q(12) = 10.62 [14.70]***
Q(24) = 25.21 [ 18.851
Q(36) = 35.92 [25.01]
GINTt = 0.561 GINTbl - 0.154 GINTh2 + et (13.28)
(-3.63)
R2 = 0.254
D = 1.993
SEE = 0.053
Q(12) = 14.34 [93.73]
Q(24) = 20.99 [122.12]
Q(36) = 28.29 [137.05]
GPRIt = 0.011 + 0.450 GPRIt-1 t 0.285 GPRIb2 + et (3.551) (6.268)
(3.969)
R* = 0.804
D = 1.953
SEE = 0.023
Q( 12) = 12.85 [87.52]
Q(24) = 26.18 [109.54]
Q(36) = 38.23
No&s:
* Dam for GCON and GPRI: Quarterly, 1947:1-1993:l. CLED: Monthly, Monthly, 1947+1993:3. ** Qstatistics for rhe squared residual series are in brackets.
*** This squared
residuals
series exhibits
conelation
1948:1-1993:3.
[ 110.20]
GSTK: Monthly,
mainly in short lags: Q(Z)=1 1.58, Q(4)=13.17,
1947:1-19932.
Q(6)=13.54.
GINT:
UNCERTAINTY AND IRREvERsIBLELNvEsTMENT
Tabb 3. ESTIMATES AND TESTS FOR FlVE MAJOR INDICATORS UNCERTAINTY St = GLEDl
Monthly 194&l-93:3
S1= 0.020 + 0.338 SF1 + 0.284 Stp - 0.176 $12 (0.044) (0.0037) (0.04) (0.029)
Q(24) = 23.3 [26.3]
Q(36) = 36.3 [42.0] LL = 239.80
S1= 0.068 + 0.245 S&l - 0.077 SC2 + Ed; (0.0168)(0.051) (0.0426) ht= 0.137 f 0.127 E~,I ; (0.0089) (0.044) Q(12) = 15.3 [16.3]
St = GCONt
LL = gg1.52
(0.055) (0.039)
(0.052)
Q( 12) = 9.0 [18.5]**
Monthly 1947:1-93:3
OF
h,=4.87x10-3+0.145~~~+0.190&~~+0.160~~~ (5.34 x 10-3
St = GST&
+ Ed;
47
Q(24) = 30.5 [24.3]
Q(36) = 35.6 [31.8]
LL = 547.48
St = 0.024 + 0.246 St_2 f &t; (2.9 x 10-3)(0.063)
Quarterly 1947:1-93:l
ht= 7.7 x 10”’
+
0.118 $1 (0.063)
(9.7 x 10-5, Q(12) = 13.4 [7.0] S1= GINTI
Monthly 194?4-93:3
Q(24) = 31.8 [13.8]
ht= 1.3 x lO-3 + 0.049 &:I+ 0.233 $2 + 0.173$3 (0.077)
(1.6 x 104) (0.057) Q(12) = 14.2 [9.3] St = GPW
St = 0.011
+
(1.8 x lo-‘) Quarterly 1947:1-93:l
ht= 1.1 x lo4 (3.8 x 10-5)
+ 0.305 S,q +
(0.064) +
0.830& (0.215)
Q(12) = 14.2 [11.36]
**Qtests for standardized residuals. leadine indicators. GSIX is ercwtb rate o~real interest rate (a&age of log-likelihood function. h is variance. 4).
(0.054)
Q(24) = 19.9 [21.8]
0.452 $1
Q(36) = 43.9 [23.6]
LL = 1357.96
S1= 0.582 Se1 - 0.116 St2 + Ed; (0.043) (0.044)
+ 0.107 E’M (0.039) Q(36) = 32.7 [31.5] LL
Et
=
625.45
(0.056) + 0.203 $2 (0.105) Q(24) = 30.2 [23.4]
Q(36) = 45.6 [30.1]
In brackets are Qtests for the squared standardized residuals. GIXD is growth rate of index of rate of stock mice index. GCON is mowh rate of real ~enonal consummion. GINT is erowth AA4 and 6 yields minus inflat&). GPRI is growth r&e of implicit GdP price deflator. LL is e is error term. The estimated models are used to compute conditional variances (‘JAR in Table
originalseries arefromcitibase.
quarters where monthly data is involved. Equation appropriateffunction.
2 is investigated to find an
An AK(l) model appears to fit the data best and is estimated
by the Hildreth-Lu procedure. Table 4 summarizes the estimates of the five models. The GSTK column is similar to Pindyck (1992) but quantitative comparisons are not possible because the variables used are different. A distinct feature of these regressions is that they include the current variance of the shocks, where significant. (Variance lags higher than two were not significant,
48
QUARTERLY
REVIEW OF
ECONOMICS AND FINANCE
Table 4. AR(l) ESTIMATES FOR FIXED INVESTMENT GROWTH IN THE U.S.; QUARTERLY DATA FROM 1948:3 TO 1993:l Dependent Variable = GFIXI lndep. Var.
(S, = GLEDJ
Gm5tant
0.023 (1.565)*
St
0.199 (2.474) 0.335 (3.702) 0.213 (2.552)
St1
SC‘2
(S, = GSTKJ
(S, = GCON,)
0.175 (2.346)
2.326 (7.253)
-0.438 (-1.465)
V‘w-1
MC1
0.355 (1.890) -0.367
=
GINTt2)/2
GINTt1+
P
SEE
0.080
QW) ~(24) Q(36) No&x
(-1.593) 0.132 (1.454) 0.483
(Rho) R2
0.046 (2.752)
0.022 (1.939)
-0.546 (-3.840)
1.644 (8.661) -2.736 (-2.209)
C=DPcl
(S, = GPlUJ
-0.673 (-4.730)
DRIFT= St- St1 V&
(S, + GINTJ
-9.452 (-2.285)
-11.924 (-1.855)
0.715 (4.147)
a.551 (-1.967)
-57.048 (-4.648)
0.552 (3.131) -1.187 (-5.025) 0.343 (4.143) 0.412
0.357 (2.084) -0.799 (-4.250) 0.259 (3.220) 0.574
0.588 (3.365)
0.074
0.087
0.087
16.80
13.86
25.80 34.24
-1.286 (-5.956) 0.303 (3.487)
0.306 (3.360)
0.415
0.409 0.087
8.97
12.33
12.03
22.21
17.44
23.10
20.32
37.45
28.78
35.32
31.47
*t-statistics in parentheses. For GL.ED, GSTK. GOON, GINT, and GPIU see Table 3. Where the original variables were monthly annualized rates, the average of the three observations was used. The same notation as in Table 3 is used for simplicity. Similarly for variances, V! which are the conditional variances of each shock from Table 3. DRIkTis a proxy for the instantaneous mean )1. GFIXis growth rate of fixed private investment. GGDPis growth rate of GDP. RIis the average growth of the real interest rate. Fixed investment is negatively related to the variances of the shocks.
albeit they had a negative cance
of the current
conditions
change,
sign).
variance.
A time-to-build
argument
can explain
Firms usually have several outstanding
firms exercise
their options
to accelerate
the signifi-
projects. As
or decelerate
the
installment process (Majd and Pindyck 1987). These decisions are not difficult to make in the course ofa quarter, as the firm continually adapts to the shocks it receives. Given that the shocks are frequently observed, it follows that the data may show an aggregation of these continual adjustments of expenditures. Thus, the current variance can be statistically significant. Figure 1 plots the quarterly conditional variance of one of the shocks, namely, the growth in interest rates, multiplied by a factor of a hundred, on investment growth. Notice, first, the clustering of volatility, which is a unique property of ARCH
UNCERTAINTY AND IRREVERSIBLE INVESTMENT 1.75
49
I
1.50
I.25
1.00
0.75
0.50
0.25
0.00
-0.25
-0.50
Figure 1.
Conditional Variance and Investment
No&x VAR denotes conditional variance of growth rates of real interest rate (x 100). The latter is found as the average of AAA and BAA yields minus inflation. CFIX denotes growth rates of fixed private invesmxnt. High or increasing variances in a quarter are followed by low and decreasing growth rates of investment.
models. Also, a high or increasing variance is associated with negative or declining investment relationship recoveries.
growth rates for several quarters. Careful examination is independent This is expected
of the state of the economy,
shows that this
namely, recessions
or
because the GDP growth variable takes into account
recessions or recoveries. To confirm this, a business cycle dummy variable, taking the value of 1 in recoveries (cycle trough plus one quarter to cycle peak) and 0 in recessions, was added. As expected, with the GGDP variable included, the dummy variable had very low significance
IV.
and it was omitted.
CONCLUSIONS
This paper demonstrates
that fixed investment is inversely related to the uncertainty
of price, interest rate, consumption, prices. The results are consistent
index of leading indicators and index of stock with the theoretical
literature
on irreversible
50
QUARTERLY REVIEW OF ECONOMICS AND FINANCE
investment under uncertainty’ does not discriminate uncertainty
The reader, however, should be aware that the model
among alternative
relationship.
hypotheses
explaining
the investment-
For instance, Greenwald and Stiglitz (1989, 1993) argue
that risk aversion would make firms invest less (as well as reduce output, labor and other inputs).
However, Dixit and Pindyck (1994)
emphasize
that the theory of
irreversible investment does not rest on investors’ or managers’ risk preferences. another
strand of literature-(Bernake
(1983),
Baldwin (1982)-firms
investing due to the benefits from the arrival of new information.
In
postpone
In other words,
waiting makes the future less uncertain. In short, there is a variety of explanations
of
the same phenomenon. Clearly, more empirical work is needed. The testing procedure presented can be extended by using other proxies for the driving shock such as the implicit
price deflators
for each type of fixed
investment. The main problem is to find a model describing such a series at the first stage, in order to get conditional variance estimates with low standard errors. If the data is quarterly, ARCH effects may not be as strong, since this behavior is usually observed in higher frequency financial series. Another possible extension regards alternative types of irreversible investment, such as advertising or promotion expenditures. Acknowledgment:
I thank Andreas Pericli, Fred Menz, Jon Vilasuso, Bob Mulligan,
Phil Baird, Jeff Zimmerman and two anonymous referees for comments and suggestions. Editorial assistance by Jim Hallas is acknowledged. Any remaining errors are my responsibility.
NOTES *Athanasios Episcopos, Clarkson University, Department of Economics, Potsdam, NY 13676. 1. For an introduction to Weiner processes and stochastic calculus with economics and finance applications see Malliaris and Brock (1982). 2. The trigger shock under uncertainty can be lower than the one in a deterministic environment depending on how the model is set up. In Ingersoll and Ross (1992) the exogenous shock is the interest rate. For higher interest rate variances lower trigger interest rates are required to entice the firm to commit to irreversible investment, ceterisparibus.The same is true for Pindyck’s (1993) uncertain cost model. 3.
The Autoregressive Conditional Heteroskedasticity methodology, presented in Engle
(1982), takes into account the time-varying nature of the conditional variance. 4.
The source of data was CITIBASE, and, in particular, its series GCQ, GIFQ GINQ,
GIPDQ GIRQ GDPD, FSPCOM, DLEAD, FYAAAC, and FYBAAC. 5. A Lagrange Multiplier test statistic (LM) was constructed for the hypothesis of no !, on an intercept and appropriate heteroskedasticity. A regression of the squared residuals, &2
UNCERTAINTY AND -IBLEINvEsTMENT
51
lagged values of ETwas estimated. LM equals TR* where Tis the number of observations and is distributed as a chi-square with 5 degrees offreedom. LM was 138.1, 132.1,41.5,141.4, and 43.53 in the cases of GLED, GSTK, GCON, GINT, and GPRI, respectively. These results confirm the computed Qstatistics. 6. The method is in the spirit of Pozo (1992) who investigated the relationship exchange rate variability on imports in a paper not related to irreversible investment.
of
7. Very similar results were found for the various categories of fixed investment.
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: 707-727.
Pagan, Adrian and Schwert, William. 1990. “Alternative Models for Conditional Stock Volatility.”Journal of Econometrics, 45: 267-290. Pindyck, Robert. 1988. “Irreversible Investment, Capacity Choice, and the Value of the Firm.” -. -.
American Economic Reviezu, 78( 5) : 969-985. 1991. “Irreversibility, Uncertainty and Investment.” Journal of Economic Literature, 29 1110-1148. 1992. Pp. 129-141 in Stochastic Models and Option klues, edited by Diderik Lund and
Bernt Oksendal. New York: North Holland.
52
QUARTERLY
REVIEW OF ECONOMICS
AND FINANCE
1993. “Investments of Uncertain Cost.” Journal of Financial Economics, 334:53-76. Pozo, Susan. 1992. “Conditional Exchange-Rate Volatility and the Volume of International Trade: Evidence from the Early 1900s.” ReviewofEconomics andStatistics, 72(2): 325-329. Santoni, G. and Courtenay Stone. 1982. “The Fed and the Real Rate of Interest.” Federal Reserve Bank of Saint Louis ReuzaU,(December): 8-18. Weiss, Andrew. 1984. “ARMA Models with ARCH Errors.” Journal of Time Series Analysis, 5: 129-143.
-.
Evidence on the Relationship between Uncertainty and Irreversible Investment ATHANASIOS EPISCOPOS Clarkson University
Recent theoretical literature on irreversible investment has suggested that increased uncertainty about (i.e., volatility of) exogenousfactors
depresses investment. However, empirical
confirmation of the theory has been minimal. This paper considers five major uncertainty
real interest rate, personal consumption, composite
variables, namely, the growth rates of
index of leading indicators, index of stock prices and GDP deflator. Their conditional variance is estimated using ARCH methodology and is related to growth infixed private investment. The latter type of investment is assumed to be largely irreversible. The results show a signt$cant
negative relationship between uncertainty and investment,
thereby
confirming the received theory.
I.
INTRODUCTION
Recent
papers have shown that uncertainty
has a negative effect on irreversible
investment. Pindyck (1991)) Dixit (1992)) and Dixit and Pindyck (1994)) summarize a growing literature, with connections
to option pricing, that examines such prob
lems as investment timing, optimal capacity entry-exit, and project valuation. The basic idea involves optimal stopping rules, where firms tend to wait before sinking capital when business conditions are uncertain. Such reluctance to act manifests itself in lower rates of investment during periods of increased uncertainty. Despite the growing theoretical has been little econometric
literature on uncertainty and investment, there
testing. One possible reason for the lack of econometric
analysis is the diffkulty in defining irreversibility and uncertainty. This paper attempts to partially fill that void by employing a methodology which takes into account the changing nature of uncertainty over time. Five variables are used to capture the major sources of uncertainty in an economy. The volatility of these variables is found to be negatively related attempt
to growth in fixed investment.
to discriminate
between
alternative 41
Although
theories
the paper does not
of investment,
the results
42
QUARTERLY REVIEW OF ECONOMICS AND FINANCE
constitute much needed empirical evidence supporting
the underlying
theory of
irreversible investment. The following section presents a brief review of the basic theory and the related econometric
literature. Subsequent sections describe the methodology, data, results,
and problems associated with the technique involved, and present conclusions.
II.
BACKGROUND
ON THEORY AND EMPIRICAL LITERATURE
Investment is irreversible when it cannot be recovered after being installed. For instance, capital which is firm-specific or industry-specific is generally irreversible, which suggests that firm has to “think twice” before committing to such investments. Analysis of this kind of behavior by firms appears in the early work of Arrow (1968). The modern extension is in the direction of dynamic uncertainty, the latter being specified by the variance of the shocks that drive a model. It turns out that the greater the uncertainty, the more reluctant firms are to make irreversible investments, This result is independent of attitudes towards risk, and instead is traced to the potential of conditions to change in the future. It is commonly assumed that a random shock (or vector of shocks), S, occurs in the system. Typically, S obeys the stochastic differential equation:’ dS, = l@,t)dt
+ o(S, t)dW( t)
(1)
where l.t and G are the drift and standard deviation functions, respectively, and dW is the increment of a Weiner process. S usually follows a geometric diffusion with lt and (Tproportional to the shock. This shock can take several forms. It can be the interest rate as in Ingersoll and Ross (1992)) project cost as in Pindyck (1993)) unit price of capital as in Bertola (1989), project value as in McDonald and Siegel (1986), or a multiplicative demand shock as in Dixit (1991) and Episcopos (1994). A typical formulation is where the firm maximizes expected profits by choosing optimal times for investing. The profit maximization assumption allows for the determination of the critical shock level necessary to induce investment. This critical shock is always different than the one derived under certainty. For instance, suppose that S is positively related to the profit function. Suppose further that the value of S that triggers investment, in a deterministic world, is &. In other words, S, is such that the marginal revenue from the investment equals marginal cost. However, if S is stochastic, the trigger shock is higher than &,. The “adjusted” marginal cost must include the opportunity cost of sinking the capital now versus later; the intuition is that investing irreversibly entails the destruction of options to invest in the future. These options have higher value when the variability of the shock is higher, in the same way stock options have higher value when the stock price volatility is higher. It follows that, for larger levels of shock variability, there is a correspondingly wider divergence* of the trigger shock from So. In general, as S evolves over time, there are
UNCERTAINTY AND IRREVERSIBLEINVESTMENT
43
periods when the firm does not invest at all and simply “waits” until S reaches the trigger level. The upshot is that such inaction by firms implies lower investment rates each period. Therefore,
the central hypothesis tested is whether increases in instan-
taneous uncertainty imply decreases in irreversible investment. There are two ways to approach the problem. The first is to focus on the trigger shock, L$,,and see whether it changes in the predicted direction as volatility changes. This approach
is pursued by Caballero and Pindyck (1992).
However, the trigger
shock is not directly observable and must be estimated from data. The second method is to directly test the connection
between the volatility of S
and actual investment. A notable attempt is made in Pindyck (1992)) who considers the effect of stock market volatility on investment. In contrast, the present paper explores a wider range of uncertainty sources to strengthen the results. Because many macroeconomic time series can be estimated by conditional heteroskedastic3 models (Weiss, 1984), the ARCH methodology is chosen in this paper. Five different shocks are considered: (1) The growth rates of the real interest rate; (2) the index of stock prices; (3) the composite index of 11 leading indicators; (4) the aggregate personal consumption
expenditure;
sources of uncertainty.
and (5) the price level. These shocks cover considerable
Conditional
variance estimates are extracted
from simple
autoregressive models with ARCH specifications in the disturbances. These variance estimates enter as regressors in AR(l)
models of fixed investment. The main result
is a negative relationship between the variance and fixed investment, which confirms the theory that irreversible investment and uncertainty are inversely related.
III.
DISCUSSION
OF METHODOLOGY,
DATA AND RESULTS
Several important issues are associated with testing the main proposition. First, testing irreversibility in capital formation is difficult due to lack of firm and industry level data. However, casual observation suggests that there are various degrees of irreversibility. It is more difficult to resell industry-specific capital than capital that has alternative uses. For instance, it is more difficult to resell a nuclear reactor or a steel mill than office furniture. Even in the latter case, the price of a used item is much less than that of a new item, even when one accounts for physical depreciation. It seems reasonable, however, to assume that irreversibility is likely to exist in fixed investments rather than in inventories, for instance. Thus, fixed investment is used as a proxy for irreversible investment. Choosing the random shock and measuring uncertainty are also important issues in empirical tests. In Pindyck (1992)) stock returns are used as proxies for profitability. The idea is that profit variability naturally translates to variability in stock returns. However, the uncertainty measure used in that paper-computing the sample variance from smaller periods within a quarter-does not make efficient use of the data in general (Bollerslev, Chou and Kroner 1992, p. 18).
44
QUARTERLY REVIEW OF ECONOMICS AND FINANCE
A desirable feature of the chosen shocks is that they have to be pervasive enough to have an impact on all firms, and be readily and frequently observable within the measurement
period. The shocks used here share these features. The growth rate of
the composite index of 11 leading indicators comprises several aspects of economic activity and can be thought of as the net sum of a variety of shocks. The growth rate of the New York Stock Exchange composite index, which reflects profit shocks, can be estimated almost continuously. All producers sense changes in the growth rate of aggregate personal consumption
expenditure.
The reason is that actual changes in
the final quantities demanded are transmitted backwards to other stages of production in the form of canceled
or rush orders for raw materials. Similarly, firms are
sensitive to changes or growth rates of real interest rates. Finally, businesses and individuals readily detect price level changes. estimated below as tests of the corresponding test of the relationship
One can think of the equations
published models. For instance, the
between interest rate uncertainty
and investment
can be
viewed as a test of the model by Ingersoll and Ross (1992). The test of the relationship between stock index uncertainty and investment can be viewed as a test of Bertola (1989) or Pindyck (1988). The empirical model is given by: GFIX =f(S, DRIFT, VAR; GGDP, RI)
(2)
where, GFIX is growth of fixed investment, S is the shock level, DRIFT is a proxy for the drift, VAR is a proxy for the instantaneous
variance. The function J which can
include lags of all variables, contains also RI, the average growth rate of real interest rates, and GGDP, the growth rate of gross domestic product. The data4 used for each shock is: 1.
Monthly and seasonally adjusted observations of the composite index of 11 leading indicators from 1948:Ol to 1993:03 are used. A series of annual growth rates of the index,
2.
GLED
is created
by using the formula
GLED,
=
I2log(%/%l). The same process is used for monthly observations of the New York Stock Exchange
Composite price index from 1947:Ol to 1993:03 to create growth
rates, GSTK 3.
Quarterly and seasonally adjusted observations of real personal consumption expenditures in billions of constant 1987 dollars from 1947:l to 1993:l
are taken. A series of growth rates is computed
by the formula
GCON, = 41og( xJ+i). 4.
Monthly figures for Moody’s AAA and BAA annual yield series from 1947:Ol to 1993:03 are summed for each month and divided by two. Then the growth rate in the GDP implicit price deflator (1987=100) is subtracted to arrive at a proxy for the long term real interest (see Santoni and Stone, 1982), GINT.
Due to the lack of monthly data for inflation, I subtracted the quarterly figures 5.
from the corresponding monthly yield entries. The implicit price deflator (1987=100) for GDP is used to create an inflation series, GPRI, by using the formula GPRI, = 4log(x,/x,i).
The series of investment
growth rates are computed
seasonally adjusted real expenditures
dollars. The data cover the period from 1947:l nonresidential
by using quarterly and
on fixed private investment in billions of 1987 to 1993:l.
(Fixed investment is 66%
and 34% residential investment; nonresidential
is 19% investment in
structures and 81% investment in producers’ durable equipment.) The investment growth series is computed by the formula GFIX, = 4log(x, / +r). GGDP is defined in the same manner. RI is defined as RI, = (GINT, + GINT,r)/ 2. Estimated conditional variances from models with ARCH errors are desirable candidates for volatility. The common equations can be written succinctly as:
i=l
where E is the error term and h is the variance. ARCH captures
the changing
conditional variance of each shock. From Equation 4, it is obvious that past errors magnify the current variance. A description of the diagnostic and identification steps taken for the case of the index of leading indicators follows. (The same procedure was adopted for the rest of the series.) GLED series: Inspection of the Ljung-Box Qstatistics for 12,24 and 36 lags, which are 421.5, 626.7 and 632.8, respectively, and are shown in Table 1, imply significant serial correlation. After some searching, the AR model shown in the top section of Table 2 is fitted. The residuals from this model are checked for serial correlation in the first and second moments. The 12,24 and 36 lag Qstatistics on the residuals are 5.53, 28.72 and 43.78 as shown in the top section of Table 2. The corresponding critical points of chi-square with 8,20, and 32 degrees of freedom at 5% significance are, respectively, 15.51, 31.41, and 43.77. Therefore, most of the serial correlation has been removed. The Qstatistics of the squared residuals for 12,24 and 36 lags are 115.09, 136.75, and 187.04, respectively, and they are shown in brackets in Table 2. This means that non-linearities are present and an ARCH model appears suitable. The top section of Table 3 shows the estimated model. The maximum likelihood estimation uses the Berndt-Hall-Hall-Hausman (BHHH) iterative procedure. The Q statistics for the standardized residuals, E, /a, for 12,24 and 36 lags are 9.04,23.25 and 36.27, respectively, and are shown in Table 3. The Qstatistics for the same lags of the squared residuals, I$?/&,were 18.54,26.28 and 41.95. Similar results are found
46
QUARTERLY REVIEW OF ECONOMICS AND FINANCE Table1. Q STATISTICS FOR SHOCKS & INVESTMENT GROWTH RATE Variable
Q(12)
Q(24)
Q(36) 632.8
GLED
421.5
626.7
GSTK
48.6
71.0
78.9
GCON*
18.4
27.5
36.3
GIhT
168.9
174.9
182.5
GFXI
398.3
572.0
613.9
GFm
83.0
100.8
115.9
Nota:
* Exhibits correlation mostly in shorterlags at 5% significance: = 12.6. QJ4) = 19.0. 0J5) = 13.0, Q(6) = 14.0.
Q(Z) = 11.6. Q(3)
for the rest of the series.5 The variable GCON is unique in that it exhibits serial correlation for shorter lag (see Table 1 and Table 2 for details). After the AR-ARCH models are estimated, replacing errors with residuals in Equation 4 produces the variance, VAR, which now enters as a regressor in the investment models.6 The estimated variances were averaged over the respective
Table2. ESTIMATED AR MODELS* GLEDt= 0.019 + 0.380 GLED&l t 0.237 GLEDb2 - 0.200 GLEDc12 + q (4.152) (9.190)
(5.774)
(-5.810)
R* = 0.407
D= 2.004
SEE = 0.097
Q(12) =5.53 [115.09]**
Q(24) = 28.72 [ 136.751
Q(36) = 43.78 [ 187.041
GSI& = 0.058 + 0.276 GST&_l - 0.089 GSTKg2 + et (3.374) (6.522)
(-2.095)
R = 0.099
D = 2.000
SEE = 0.398
Q( 12) = 13.32 [29.47]
Q(24) = 29.94 [35.11]
Q(36) = 35.19 [43.31]
GCONl = 0.024 t 0.235 GCONc2 t et (7.569) (3.257) R* = 0.540
D = 1.881
SEE = 0.030
Q(12) = 10.62 [14.70]***
Q(24) = 25.21 [ 18.851
Q(36) = 35.92 [25.01]
GINTt = 0.561 GINTbl - 0.154 GINTh2 + et (13.28)
(-3.63)
R2 = 0.254
D = 1.993
SEE = 0.053
Q(12) = 14.34 [93.73]
Q(24) = 20.99 [122.12]
Q(36) = 28.29 [137.05]
GPRIt = 0.011 + 0.450 GPRIt-1 t 0.285 GPRIb2 + et (3.551) (6.268)
(3.969)
R* = 0.804
D = 1.953
SEE = 0.023
Q( 12) = 12.85 [87.52]
Q(24) = 26.18 [109.54]
Q(36) = 38.23
No&s:
* Dam for GCON and GPRI: Quarterly, 1947:1-1993:l. CLED: Monthly, Monthly, 1947+1993:3. ** Qstatistics for rhe squared residual series are in brackets.
*** This squared
residuals
series exhibits
conelation
1948:1-1993:3.
[ 110.20]
GSTK: Monthly,
mainly in short lags: Q(Z)=1 1.58, Q(4)=13.17,
1947:1-19932.
Q(6)=13.54.
GINT:
UNCERTAINTY AND IRREvERsIBLELNvEsTMENT
Tabb 3. ESTIMATES AND TESTS FOR FlVE MAJOR INDICATORS UNCERTAINTY St = GLEDl
Monthly 194&l-93:3
S1= 0.020 + 0.338 SF1 + 0.284 Stp - 0.176 $12 (0.044) (0.0037) (0.04) (0.029)
Q(24) = 23.3 [26.3]
Q(36) = 36.3 [42.0] LL = 239.80
S1= 0.068 + 0.245 S&l - 0.077 SC2 + Ed; (0.0168)(0.051) (0.0426) ht= 0.137 f 0.127 E~,I ; (0.0089) (0.044) Q(12) = 15.3 [16.3]
St = GCONt
LL = gg1.52
(0.055) (0.039)
(0.052)
Q( 12) = 9.0 [18.5]**
Monthly 1947:1-93:3
OF
h,=4.87x10-3+0.145~~~+0.190&~~+0.160~~~ (5.34 x 10-3
St = GST&
+ Ed;
47
Q(24) = 30.5 [24.3]
Q(36) = 35.6 [31.8]
LL = 547.48
St = 0.024 + 0.246 St_2 f &t; (2.9 x 10-3)(0.063)
Quarterly 1947:1-93:l
ht= 7.7 x 10”’
+
0.118 $1 (0.063)
(9.7 x 10-5, Q(12) = 13.4 [7.0] S1= GINTI
Monthly 194?4-93:3
Q(24) = 31.8 [13.8]
ht= 1.3 x lO-3 + 0.049 &:I+ 0.233 $2 + 0.173$3 (0.077)
(1.6 x 104) (0.057) Q(12) = 14.2 [9.3] St = GPW
St = 0.011
+
(1.8 x lo-‘) Quarterly 1947:1-93:l
ht= 1.1 x lo4 (3.8 x 10-5)
+ 0.305 S,q +
(0.064) +
0.830& (0.215)
Q(12) = 14.2 [11.36]
**Qtests for standardized residuals. leadine indicators. GSIX is ercwtb rate o~real interest rate (a&age of log-likelihood function. h is variance. 4).
(0.054)
Q(24) = 19.9 [21.8]
0.452 $1
Q(36) = 43.9 [23.6]
LL = 1357.96
S1= 0.582 Se1 - 0.116 St2 + Ed; (0.043) (0.044)
+ 0.107 E’M (0.039) Q(36) = 32.7 [31.5] LL
Et
=
625.45
(0.056) + 0.203 $2 (0.105) Q(24) = 30.2 [23.4]
Q(36) = 45.6 [30.1]
In brackets are Qtests for the squared standardized residuals. GIXD is growth rate of index of rate of stock mice index. GCON is mowh rate of real ~enonal consummion. GINT is erowth AA4 and 6 yields minus inflat&). GPRI is growth r&e of implicit GdP price deflator. LL is e is error term. The estimated models are used to compute conditional variances (‘JAR in Table
originalseries arefromcitibase.
quarters where monthly data is involved. Equation appropriateffunction.
2 is investigated to find an
An AK(l) model appears to fit the data best and is estimated
by the Hildreth-Lu procedure. Table 4 summarizes the estimates of the five models. The GSTK column is similar to Pindyck (1992) but quantitative comparisons are not possible because the variables used are different. A distinct feature of these regressions is that they include the current variance of the shocks, where significant. (Variance lags higher than two were not significant,
48
QUARTERLY
REVIEW OF
ECONOMICS AND FINANCE
Table 4. AR(l) ESTIMATES FOR FIXED INVESTMENT GROWTH IN THE U.S.; QUARTERLY DATA FROM 1948:3 TO 1993:l Dependent Variable = GFIXI lndep. Var.
(S, = GLEDJ
Gm5tant
0.023 (1.565)*
St
0.199 (2.474) 0.335 (3.702) 0.213 (2.552)
St1
SC‘2
(S, = GSTKJ
(S, = GCON,)
0.175 (2.346)
2.326 (7.253)
-0.438 (-1.465)
V‘w-1
MC1
0.355 (1.890) -0.367
=
GINTt2)/2
GINTt1+
P
SEE
0.080
QW) ~(24) Q(36) No&x
(-1.593) 0.132 (1.454) 0.483
(Rho) R2
0.046 (2.752)
0.022 (1.939)
-0.546 (-3.840)
1.644 (8.661) -2.736 (-2.209)
C=DPcl
(S, = GPlUJ
-0.673 (-4.730)
DRIFT= St- St1 V&
(S, + GINTJ
-9.452 (-2.285)
-11.924 (-1.855)
0.715 (4.147)
a.551 (-1.967)
-57.048 (-4.648)
0.552 (3.131) -1.187 (-5.025) 0.343 (4.143) 0.412
0.357 (2.084) -0.799 (-4.250) 0.259 (3.220) 0.574
0.588 (3.365)
0.074
0.087
0.087
16.80
13.86
25.80 34.24
-1.286 (-5.956) 0.303 (3.487)
0.306 (3.360)
0.415
0.409 0.087
8.97
12.33
12.03
22.21
17.44
23.10
20.32
37.45
28.78
35.32
31.47
*t-statistics in parentheses. For GL.ED, GSTK. GOON, GINT, and GPIU see Table 3. Where the original variables were monthly annualized rates, the average of the three observations was used. The same notation as in Table 3 is used for simplicity. Similarly for variances, V! which are the conditional variances of each shock from Table 3. DRIkTis a proxy for the instantaneous mean )1. GFIXis growth rate of fixed private investment. GGDPis growth rate of GDP. RIis the average growth of the real interest rate. Fixed investment is negatively related to the variances of the shocks.
albeit they had a negative cance
of the current
conditions
change,
sign).
variance.
A time-to-build
argument
can explain
Firms usually have several outstanding
firms exercise
their options
to accelerate
the signifi-
projects. As
or decelerate
the
installment process (Majd and Pindyck 1987). These decisions are not difficult to make in the course ofa quarter, as the firm continually adapts to the shocks it receives. Given that the shocks are frequently observed, it follows that the data may show an aggregation of these continual adjustments of expenditures. Thus, the current variance can be statistically significant. Figure 1 plots the quarterly conditional variance of one of the shocks, namely, the growth in interest rates, multiplied by a factor of a hundred, on investment growth. Notice, first, the clustering of volatility, which is a unique property of ARCH
UNCERTAINTY AND IRREVERSIBLE INVESTMENT 1.75
49
I
1.50
I.25
1.00
0.75
0.50
0.25
0.00
-0.25
-0.50
Figure 1.
Conditional Variance and Investment
No&x VAR denotes conditional variance of growth rates of real interest rate (x 100). The latter is found as the average of AAA and BAA yields minus inflation. CFIX denotes growth rates of fixed private invesmxnt. High or increasing variances in a quarter are followed by low and decreasing growth rates of investment.
models. Also, a high or increasing variance is associated with negative or declining investment relationship recoveries.
growth rates for several quarters. Careful examination is independent This is expected
of the state of the economy,
shows that this
namely, recessions
or
because the GDP growth variable takes into account
recessions or recoveries. To confirm this, a business cycle dummy variable, taking the value of 1 in recoveries (cycle trough plus one quarter to cycle peak) and 0 in recessions, was added. As expected, with the GGDP variable included, the dummy variable had very low significance
IV.
and it was omitted.
CONCLUSIONS
This paper demonstrates
that fixed investment is inversely related to the uncertainty
of price, interest rate, consumption, prices. The results are consistent
index of leading indicators and index of stock with the theoretical
literature
on irreversible
50
QUARTERLY REVIEW OF ECONOMICS AND FINANCE
investment under uncertainty’ does not discriminate uncertainty
The reader, however, should be aware that the model
among alternative
relationship.
hypotheses
explaining
the investment-
For instance, Greenwald and Stiglitz (1989, 1993) argue
that risk aversion would make firms invest less (as well as reduce output, labor and other inputs).
However, Dixit and Pindyck (1994)
emphasize
that the theory of
irreversible investment does not rest on investors’ or managers’ risk preferences. another
strand of literature-(Bernake
(1983),
Baldwin (1982)-firms
investing due to the benefits from the arrival of new information.
In
postpone
In other words,
waiting makes the future less uncertain. In short, there is a variety of explanations
of
the same phenomenon. Clearly, more empirical work is needed. The testing procedure presented can be extended by using other proxies for the driving shock such as the implicit
price deflators
for each type of fixed
investment. The main problem is to find a model describing such a series at the first stage, in order to get conditional variance estimates with low standard errors. If the data is quarterly, ARCH effects may not be as strong, since this behavior is usually observed in higher frequency financial series. Another possible extension regards alternative types of irreversible investment, such as advertising or promotion expenditures. Acknowledgment:
I thank Andreas Pericli, Fred Menz, Jon Vilasuso, Bob Mulligan,
Phil Baird, Jeff Zimmerman and two anonymous referees for comments and suggestions. Editorial assistance by Jim Hallas is acknowledged. Any remaining errors are my responsibility.
NOTES *Athanasios Episcopos, Clarkson University, Department of Economics, Potsdam, NY 13676. 1. For an introduction to Weiner processes and stochastic calculus with economics and finance applications see Malliaris and Brock (1982). 2. The trigger shock under uncertainty can be lower than the one in a deterministic environment depending on how the model is set up. In Ingersoll and Ross (1992) the exogenous shock is the interest rate. For higher interest rate variances lower trigger interest rates are required to entice the firm to commit to irreversible investment, ceterisparibus.The same is true for Pindyck’s (1993) uncertain cost model. 3.
The Autoregressive Conditional Heteroskedasticity methodology, presented in Engle
(1982), takes into account the time-varying nature of the conditional variance. 4.
The source of data was CITIBASE, and, in particular, its series GCQ, GIFQ GINQ,
GIPDQ GIRQ GDPD, FSPCOM, DLEAD, FYAAAC, and FYBAAC. 5. A Lagrange Multiplier test statistic (LM) was constructed for the hypothesis of no !, on an intercept and appropriate heteroskedasticity. A regression of the squared residuals, &2
UNCERTAINTY AND -IBLEINvEsTMENT
51
lagged values of ETwas estimated. LM equals TR* where Tis the number of observations and is distributed as a chi-square with 5 degrees offreedom. LM was 138.1, 132.1,41.5,141.4, and 43.53 in the cases of GLED, GSTK, GCON, GINT, and GPRI, respectively. These results confirm the computed Qstatistics. 6. The method is in the spirit of Pozo (1992) who investigated the relationship exchange rate variability on imports in a paper not related to irreversible investment.
of
7. Very similar results were found for the various categories of fixed investment.
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1992. “Investment and Hysteresis.” Journal ofEconomic Perspectives 6( 1): 107-132. Dixit, Avinash and Robert Pindyck. 1994. Investment Under Uncertainty. Princeton: Princeton University Press. Engle, Robert. 1982. “Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of United Kingdom Inflation.” Econometrica, 50(4): 987-1007. Episcopos, Athanasios. 1994. “Investment Under Uncertainty and the Value of the Firm.”
-.
Econaics
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