Identification in Linear Simultaneous Equations Models with Covariance Restrictions: An Instrumental Variables Interpretation

Campaign Spending and Incumbency: An Alternative Simultaneous Equations Approach

“…4-5;Goldberger I 991, 361-62;Johnston 1963, 248-49;Maddala 1977, 226-28;Malinvaud 1966, 528-38; see also Heise 1975, 181-82;Hanushek and Jackson 1977, 271-76. ) For a general discussion, see Hausman and Taylor (1983) and Hausman,Newey,and Taylor (I 987). For a political science application, see Erikson I 982. Meanwhile, unmeasured variables that might affect spending directly are not likely to affect the vote directly.…”

Opium for the Masses? Conflict-Induced Narcotics Production in Afghanistan

“…Although this is a strong assumption, the fact that we use two-way fixed effects reduces the problem considerably. Under this restriction, Hausman and Taylor (1983) have shown that a valid instrument for C it in equation (5b) is the estimated residuals ε 1 it obtained from a 2SLS regression on equation (5a) with W it as instruments for opium. Due to the restriction on the covariance matrix of the errors, ε 1 it will be correlated with C it (from equation (5a)), but will be uncorrelated with ε 2 it , i.e.…”

“…We see that bothb andβ are positive and highly significant. In columns (3) and (4) we control for the simultaneity bias by estimating the parameters using the Hausman and Taylor (1983) approach. We here see that the effect of conflict on opium (β) is still highly significant, and in numerical value almost equal to the ones presented in Table 3.…”

“…Instruments for casualties in column (4) are the residuals from the estimations in column (3), cf. Hausman and Taylor (1983). First stage F is is the F-value on excluded instruments in the first stage regressions.…”

Efficient Estimation and Identification of Simultaneous Equation Models with Covariance Restrictions

“…To analyze the limiting distribution of the A3SLS estimator in the general case, it will be helpful to rewrite the FIML estimator from equations (3-13) in an instrumental variables form, following the derivation in Hausman (1975) for the unrestricted^case. Since we have one equation in equation (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13) for each unknown 6, we take each equation from the first block of the gradient (3' 13) corresponding to the system of equations (3*1 …”