Wildcat activity. Wildcats are wells drilled to find and produce oil and/or gas in an improved area or to find a new reservoir in a field previously found to be productive of oil or gas or to extend the limit of a known oil or gas reservoir. The following gives data on these variables:

Y = the number of wildcats drilled
X₂ = price at the wellhead in the previous period (in constant dollars, 1972 = 100)
X₃ = domestic output
X₄ = GNP constant dollars (1972 = 100)
X₅ = trend variable, 1948 = 1, 1949 = 2, . . . , 1978 = 31

See if the following model fits the data:

Y_t = β₁ + β₂X_2t + β₃ ln X_3t + β₄X_4t + β₅X_5t + u_tY_t = β₁ + β₂X_2t + β₃ ln X_3t + β₄X_4t + β₅X_5t + u_t

a. Can you offer an a priori rationale to this model?
b. Assuming the model is acceptable, estimate the parameters of the model and their standard errors, and obtain R₂ and RÌ…².
c. Comment on your results in view of your prior expectations.
d. What other specification would you suggest to explain wildcat activity? Why?

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Domestic Output (millions of Per Barrel GNP, Thousands barrels Price, Constant $ (X2) Constant $ Billions (X4) per day) (X3) of Wildcats, (Y) Time (Xs) 8.01 9.06 5.52 4.89 487.67 1948 = 1 4.83 5.05 490.59 1949 = 2 4.68 4.42 10.31 5.41 533.55 1950 = 3 11.76 6.16 576.57 1951 = 4 598.62 12.43 4.36 4.55 6.26 1952 = 5 6.34 13.31 621.77 1953 = 6 6.81 13.10 4.66 613.67 1954 = 7 7.15 7.17 14.94 4.54 654.80 1955 = 8 1956 = 9 16.17 4.44 668.84 6.71 14.71 4.75 681.02 1957 = 10 13.20 4.56 7.05 679.53 1958 = 11 4.29 13.19 7.04 720.53 1959 = 12 7.18 11.70 4.19 736.86 1960 = 13 1961 = 14 755.34 10.99 4.17 7.33 10.80 799.15 4.11 7.54 1962 = 15 10.66 4.04 7.61 830.70 1963 = 16 10.75 3.96 7.80 874.29 1964 = 17 9.47 3.85 8.30 925.86 1965 = 18 10.31 3.75 8.81 8.66 980.98 1966 = 19 8.88 8.88 3.69 1,007.72 1,051.83 1,078.76 1,075.31 1,107.48 1,171.10 1,234.97 1,217.81 1,202.36 1,271.01 1,332.67 1,385.10 1967 = 20 8.78 1968 = 21 3.56 9.70 9.18 3.56 1969 = 22 7.69 3.48 9.03 1970 = 23 6.92 3.53 3.39 9.00 8.78 1971 = 24 7.54 1972 = 25 7.47 3.68 8.38 1973 = 26 8.63 5.92 8.01 1974 = 27 9.21 6.03 7.78 1975 = 28 6.12 7.88 7.88 9.23 1976 = 29 = 30 1977 = 9.96 6.05 10.78 5.89 8.67 1978 = = 31