industries—the Chemicals industry—and is available from 1974Q1–1987Q4.
13
Data on total sales Q and domestic sales Q
d
is available from various issues of British Business; foreign sales Q
f
was calculated as the difference between the two. The expected price series, P
d
, P
f
was calculated as a four-quarterly moving average of the chemical industry’s domestic and foreign price indexes, and a moving standard deviation of P
d
, P
f
was used to generate s
d
and s
f
. A price index of materials and fuel purchased by the chemicals industry was used as the input price index w.
The notion that British firms in the chemicals industry face domestic and foreign price uncertainty needs to be elaborated. Domestic price risk arises from random domestic
demand, whereas foreign price risk arises from random exchange rates.
14
Available data indicate that over the period 1979 –1987, at least 47 by value of the chemical
industry’s export contracts were denominated in foreign currency and, thus, exposed to currency risk. Of these, only 11 were covered by forward contracts. Thus, by and large,
British firms were exposed to foreign price uncertainty.
Before conducting empirical tests, it was necessary to determine the stationarity properties of the data. The results of a Dickey-Fuller unit root test indicated the following
Dickey-Fuller test statistic values: P
f
5 22.52; P
d
5 23.60; s
f
5 23.74; s
d
5 22.05; w 5 22.91. The applicable MacKinnon critical value 5 level is 21.95. Clearly, the
hypothesis of a unit root was rejected for all variables; these are therefore stationary variables.
VII. Empirical Results
Equations 13 and 14 were estimated for the Chemicals industry of the United Kingdom for the period 1974Q1–1987Q4, using a Seemingly Unrelated Regression Estimation
SURE procedure. The results of this estimation are reported in Table 2, and constitute the parameter estimates of the Unrestricted Model. The log of the likelihood function of
the Unrestricted Model is 2629.79.
A useful check on the appropriateness of the model specification is to test if the empirical form of the indirect utility function satisfies concavity or convexity conditions.
The indirect utility function, V, is quasi-convex in prices. This convexity requirement was satisfied at the point of approximation using the estimates of the Unrestricted Model in
Table 2. The satisfaction of this requirement provides reassuring evidence that the utility function is well-behaved and there are no model specification errors.
The first hypothesis to be tested was the symmetry restrictions implied by both CARA and separability. The empirical restrictions implied by this, equations 15 and 16, were
imposed on equations 13 and 14, and the resulting parameter estimates are reported as Restricted Model 1 in Table 2. The log likelihood function of this constrained model was
2632.30. The calculated test statistic was 5.02,
15
and as this is less than the critical x
2
value of 5.99, the hypothesis that CARA and separability hold could not be rejected. Consequently, Model 1 was a maintained hypothesis for all subsequent tests.
13
Data is not available beyond this point because of rebased indexes. Later data is therefore not comparable with earlier data.
14
The data indicate that the coefficient of variation is 33 for the domestic price index and 31 for the foreign price index over the period covered by the study. This is, by any measure, a high level of volatility.
15
The test statistic is given by 22 ln l, where l is the ratio of the likelihood functions for the restricted and unrestricted models. Under the null, this is distributed as x
2
with degrees of freedom equal to the number of independent restrictions.
322 S. Satyanarayan
The next hypothesis to be tested was the hypothesis that the direct utility function is separable but does not display CARA. Imposition of the additional restrictions required by
separability equations 18, 19 and 20, led to Restricted Model 2 see Table 2. The log likelihood was 2634.50, and the calculated test statistic was 4.40 calculated by
treating Model 1 as the maintained hypothesis. As the critical x
2
value with four degrees of freedom at the 5 level is 9.49, the hypothesis that the direct utility function is
separable could not be rejected. The empirical results imply that the data is best described by a direct utility function
that is separable. We, therefore, turn to an analysis of this form and the implications for comparative statics results. The estimated form for the separable function Restricted
Model 2 in Table 2 implies that the signs of the parameters are as follows: V
P
f
P
f
. 0,
Table 2. Parameter Estimates
Parameter Unrestricted
Model Restricted
Model 1 Restricted
Model 2 V
P
f
[V
1
] 1389.77
1395.52 1369.64
29.25 32.21
27.86 V
P
f
P
f
[V
11
] 4.60
18.67 6.24
4.63 V
P
f
s
f
[V
12
] 18.87
224.70 214.28
49.49 60.96
9.43 V
P
f
P
d
[V
13
] 222.33
214.23 23.04
7.64 9.48
4.72 V
P
f
s
d
[V
14
] 298.70
217.10 22.14
66.13 87.34
15.38 V
P
f
w
[V
15
] 20.24
11.38 25.35
10.94 13.71
1.81 V
HP
f
[V
61
] 2.01
.0039 V
Hs
f
[V
62
] .02
2.0075 .0333
.0395 V
HP
d
[V
63
] 2.0064
2.0085 .0040
.0042 V
Hs
d
[V
64
] 2.0680
2.0184 .0419
.0548 V
Hw
[V
65
] .0135
.0074 .0063
.0080 V
P
d
[V
3
] 2131.09
2179.84 2143.87
30.03 22.94
27.90 V
P
d
s
f
[V
32
] 50.53
25.75 7.20
72.21 85.66
7.93 V
P
d
P
d
[V
33
] 215.92
219.16 1.78
6.72 7.80
4.92 V
P
d
s
d
[V
34
] 2163.01
272.49 222.51
88.75 115.18
13.91 V
P
d
w
[V
35
] 26.71
15.90 13.40
16.63 Log likelihood
2629.79 2632.30
2634.50 Restrictions
2 4
Calculated x
2
— 5.02
4.40 Critical x
2
5 —
5.99 9.49
Notes: Asymptotic standard errors are in parentheses. See text for appropriate restrictions.
Econometric Tests of Decision Making 323
V
P
f
s
f
, 0, V
P
f
P
d
5 V
P
d
P
f
, 0, V
P
f
s
d
. 0, V
P
f
w
, 0, V
P
d
s
f
. 0, V
P
d
P
d
. 0, V
P
d
s
d
, 0, and V
P
d
w
, 0.
16
All these signs are unambiguously implied by theory see Table 1, column 4, and all estimated parameters are in agreement with theoretical predictions for a separable
utility function. The result that the utility function under uncertainty is best described by a separable function is in broad conformity with previous results by Antonovitz and Roe
1986 and Park and Antonovitz 1992a.
The empirical results imply that an increase in the expected price in any market leads to a supply increase in that market [V
P
f
P
f
. 0, V
P
d
P
d
. 0]. Thus, supply curves are upward sloping even under dual sources of risk. The sign of the cross-price derivative is negative
[V
P
f
P
d
5 V
P
d
P
f
, 0], implying that an increase in the expected price in one market leads to a supply decrease in the other market. Thus, domestic and foreign output are net
substitutes. An increase in risk in any market leads to a supply decrease in that market [V
P
f
s
f
, 0, V
P
d
s
d
, 0], but as domestic and foreign output are substitutes, supply increases in the other market [V
P
f
s
d
. 0, V
P
d
s
f
. 0]. An increase in input prices leads to a supply decrease in both domestic and foreign markets [V
P
f
w
, 0, V
P
d
w
, 0]. These results have important implications for the empirical literature on exchange rate
uncertainty. The focus in this literature is on the macro effects of exchange rate risk, but there is no consensus on the effects of exchange rate risk on the volume of foreign trade
[Pozo 1992]. This paper has examined the effect of uncertainty at the microeconomic level and concludes that an increase in uncertainty in the foreign market does reduce
exports. However, it is possible that for a different risk preference function an increase in foreign market uncertainty need not necessarily reduce exports. If the utility function is
consistent with CARA, for instance, an unambiguous conclusion regarding the effect of an increase in risk on output cannot be inferred i.e., [Q
f
s
f
: 0; Q
d
s
d
: 0]. The effect of risk preferences on output decisions under uncertainty, which are typically ignored in
studies on the macro effects of exchange rate risk, may explain why these studies are unable to make a clear finding regarding the effect of uncertainty on the volume of trade.
VIII. Concluding Remarks
