Data Description and Stationarity Properties of the Data

which is imposable in equations 13 and 14. Next, note that Q 5 V P f 1 V P d V H . The parameter restriction implied by the second symmetry condition see Table 1, evaluated at the approximation point, is given by: V 11 5 ~V 13 1 V 33 2 V 63 ~V 1 1 V 3 ~V 15 2 V 65 V 1 ~V 35 2 V 65 V 3 1 F V 63 V 1 V 3 ~V 1 1 V 3 2 V 13 G , 16 where the prior restriction equation 15 is imposed in equation 16. If the restrictions given by equations 15 and 16 are rejected, then both CARA and separability must be rejected. The comparative statics of the model provide one source of empirically refutable symmetry restrictions. Additional symmetry restrictions can be easily derived by using the derivatives of the indirect expected utility function [Dalal 1994]. The indirect function V corresponding to the separable utility function is given by: V~P f , s f , P d , s d , w, H 5 P f Q f 1 P d Q d 2 C~w, Q 1 H 2 b~Q f 2 s f 2 1 Q d 2 s d 2 , 17 where s f 2 and s d 2 are the variance of the domestic and foreign price distributions. The envelope theorem applied to equation 17 immediately implies that V P f 5 Q f , V P d 5 Q d , V s f 5 22bQ f 2 s f , V s d 5 22bQ d 2 s d , V w 5 2­C­w 5 2C w , V H 5 1, and Young’s theorem implies that: ~V P f s f V P d s f 5 ~V s f P f V s f P d f S ­ Q f ­ s f Y ­ Q d ­ s f D 5 S ­ Q f ­ P f Y ­ Q f ­ P d D ; 18 ~V P f s d V P d s d 5 ~V s d P f V s d P d f S ­ Q f ­ s d Y ­ Q d ­ s d D 5 S ­ Q d ­ P f Y ­ Q d ­ P d D ; 19 V Hu 5 V u H 5 0 where u 5 ~P f , P d , s f , s d , w, H. 20 Now, equations 15 and 16 are valid restrictions for both CARA and the separable utility function. If these restrictions are rejected, then both CARA and separability must be rejected. However, if these restrictions cannot be rejected, then CARA or separability are possible forms for the utility function. To distinguish separabilty from CARA, impose the additional restrictions for separability given by equations 18, 19 and 20. If these restrictions are rejected, 11 the utility function is consistent with CARA but is not separable. However, if these restrictions cannot be rejected, then the utility function is separable and does not display CARA. 12

VI. Data Description and Stationarity Properties of the Data

All required data for this study were drawn from the Monthly Abstract of Statistics and British Business. The data pertain to one of the United Kingdom’s most important 11 These restrictions can be established thus. Now equations 18–19 imply that at the expansion point: V 33 5 [V 11 V 32 V 34 ][V 12 V 14 ], and equation 16 implies that V 11 5 {[V 13 1 V 33 V 15 ][V 35 ]} 2 V 13 as V 63 5 V 65 5 0 by equation 20. Substituting V 33 into V 11 above yields the restriction V 35 5 [V 13 1 {V 11 V 32 V 34 V 12 V 14 }][V 15 ][V 11 1 V 13 ], which with equation 20 can be imposed on equations 13 and 14 to test for separability. 12 See Dalal 1994, who comments on an error on this point in Park and Antonovitz’s paper 1992a. Econometric Tests of Decision Making 321 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