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In this paper we represent this type of matrix by Zi = diag (yil, .Yis), (s = 1 ... i T-2).
An alternative choice of AN is (N-1 ZfAlZi)-l withA = N-1 S The resulting estimator does not depend on the data fourth-order moments and is asymptotically equivalent to '2 provided the vi, are serially independent. Note that in this case E(Z!ti3ivZi) = E(Z!fliZi) and limN o0 N-1 , E[Z!(fli -fN)Zi] = O (see White (1982), p. 492).
A dataset of 25 metrics collected from the 10-Ks of 20 oil and gas operators was segregated into two panels: One with operators with a diversified business strategy (conventional group), and a second with operators focused on shale plays (unconventional group). Under the assumption that through exploration expenses (EXPEX) the cost of geoscientific information can be measured, fixed effects panel regressions with robust standard errors were constructed using proven reserves (P90), and the price per flowing barrel (PFB) as dependent variables, EXPEX as the variable of interest, and a series of controls accounting for other line items expensed in this account. Using the regression coefficients of these regressions the ceteris paribus effect of investments in geoscientific information on P90 and PFB is quantified. According to results, a million dollars invested in the geosciences increases P90 by 304 mboe after four years for operators in the conventional group. For operators in the un-conventionals group, results indicate an increment of 935 mboe also after four years. Under an efficient market hypothesis the stock price of an operator should reflect all current available information. Therefore, these increments in proven reserves attributed to investments in geoscience should have a positive impact on the market capitalization of an operator. However, results from PFB models indicate that investments in exploration, even though having an impact on the amount of proven reserves, have a minimal impact on how the market values a barrel of crude from each operator regardless its business strategy.
In this paper we derive the asymptotic properties of within groups (WG), GMM, and LIML estimators for an autoregressive model with random effects when both T and N tend to infinity. GMM and LIML are consistent and asymptotically equivalent to the WG estimator. When T /N → 0 the fixed T results for GMM and LIML remain valid, but WG, although consistent, has an asymptotic bias in its asymptotic distribution. When T /N tends to a positive constant, the WG, GMM, and LIML estimators exhibit negative asymptotic biases of order 1/T , 1/N , and 1/ 2N − T , respectively. In addition, the crude GMM estimator that neglects the autocorrelation in first differenced errors is inconsistent as T /N → c > 0, despite being consistent for fixed T . Finally, we discuss the properties of a random effects pseudo MLE with unrestricted initial conditions when both T and N tend to infinity.
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