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#### Simultaneous Linear Equation

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Journal Article
Demography (1976) 13 (2): 287–290.
Published: 01 May 1976
...Andrel Rogers; Jacques Ledent 26 1 2011 © Population Association of America 1976 1976 Life Table Apply System Analysis Simultaneous Linear Equation Life Table State Life Table Cohort References Rogers Andrei ( 1975 ). Introduction to Multiregional Mathematical...
Journal Article
Demography (2013) 50 (1): 237–260.
Published: 27 October 2012
... and forecast utility are improved by introducing randomness and uncertainty into the standard differential equations governing population processes. Our approach is to add time-series stochasticity to linearized versions of each process. We derive both Monte Carlo and analytic methods for estimating forecast...
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Journal Article
Demography (1989) 26 (4): 717–726.
Published: 01 November 1989
... linear equations is set up as follows: RE + AE + BE + ABE = CRD, RE + BE + ABE = RD(A), RE + AE + ABE = RD(B), RE = RD(AB), (7) (8) (9) (10) where RE stands for rate effect, AE for A effect, BE for B effect, and ABE for AB joint effect, as previously defined. CRD denotes the crude rate difference. RD...
Journal Article
Demography (1965) 2 (1): 276–288.
Published: 01 March 1965
...-homogene de nais- sance et de mort a deux variables aleatoires," Bull. classe sci. (Acad. royale Belg., 1957), Series 5, XLIII, 711-19. They will be presented in a sequel to this article. The resulting pair of simultaneous linear equations (4) happen to be soluble by a simple device which...
Journal Article
Demography (1970) 7 (2): 155–167.
Published: 01 May 1970
... approximation for r(k) to obtain linear equations in r(I), r(2), .. " r (k - 1) and solve for them using any of the familiar procedures for solv- ing simultaneous linear equations. Sub- stituting those solutions in the remaining equation gives one equation in one un- known, r(k), and the solution obtained from...
Journal Article
Demography (1975) 12 (2): 313–324.
Published: 01 May 1975
... At the same time, k2+2k simul- taneous linear equations are available, k from equation (1), k2 from equation (2), and k from equation (3). When the equations are too complex for direct algebraic solution, they can be dealt with in any particular case by a recursive procedure which converges to the correct...
Journal Article
Demography (1995) 32 (1): 63–80.
Published: 01 February 1995
... the predicted probabilities from the multinomial logit model as instruments. 4) Form (linear) predicted probabilities from the WLS coefficient estimates. 5) Estimate the two equations of the two-part model for work hours as a function of the structural regressors and the linear predicted probabilities. 6...
Journal Article
Demography (1979) 16 (4): 575–601.
Published: 01 November 1979
... required in the origi- nal or natural variables (Goldberger, 1964, pp. 213- 277) and a non-linear system can often be approxi- mated by a linear system (Chow, 1975, p. 131). Theoretical considerations indicate that a num- ber of restrictions must be imposed on a simultane- ous equation model. Thus...
Journal Article
Demography (1973) 10 (4): 507–515.
Published: 01 November 1973
... fertility and mortality rates 507 508 DEMOGRAPHY, volume 10, number 4, November 1973 is nonlinear, suggesting, therefore, a non- linear regression equation.) 15-64 log w- = ao + at log GRR GRR_to I U+ a2 log E + aa log GRR + og , (1) where log U is a disturbance term with mean zero and constant variance c...
Journal Article
Demography (1986) 23 (2): 283–284.
Published: 01 May 1986
...-components regression can capture only the linear decline in the CBR. Thus, to the extent that changes in population density better correspond to changes in the CBR than does a linear time trend, the effect of outside-of-model changes in the CBR will be reflected in the coefficient of density. In other words...
Journal Article
Demography (1996) 33 (3): 313–327.
Published: 01 August 1996
... form hazard equations Inh7( t) = 1tmO + 1t:'dT( t) + 1t:"2X;(t) + Em + 1tm,E h Inh;(t) = 1t.,o + 1t:,T(t) + 1t:2X(t) + E, + 1t"Eh InhJ(t)=1tdo+1t:,T(t)+1t;'2X(t)+EJ +1t J JE h , where the 1t"" 1t., ' and 1t tl values are linear combinations of ~s and ns, ys and ns, and as and l1S, respectively...
Journal Article
Demography (1982) 19 (3): 291–299.
Published: 01 August 1982
... order optimality conditions using simultaneous equation methods. The authors adopted the approach of direct maximization us- ing NAG subroutine C04UAF for non- linear optimization (NAG, 1978). This routine uses an augmented Lagrangian quasi-Newton procedure. The numerical integration was performed using...
Journal Article
Demography (2020) 57 (2): 779–797.
Published: 24 March 2020
... movements, the last two equations in (21) specify the occurrence/exposure transfer rates under the linear assumption, and the third equation in (21) is the cross-product ratio in the N = 2 linear model. Thus, (21) shows five equations with eight unknowns ( x 10 , x 11 , x 20 , x 21 , d 12 , d...
Includes: Supplementary data
Journal Article
Demography (1989) 26 (4): 711–716.
Published: 01 November 1989
... of vital rates: A review . International Statistical Review , 55 , 119 – 152 . 10.2307/1403190 Santi , L. L. ( 1989 ). Partialling and purging: Equivalencies among log-linear analysis, logit analysis, and partial CG purging . Sociological Methods and Research , 17 , 376 – 397 . 10.1177...
Journal Article
Demography (2013) 50 (6): 1945–1967.
Published: 26 September 2013
... is that these linear trends must satisfy Eq. ( 17 ). If, in fact, the true age, period, and cohort trends do not satisfy this equation, then the implicit LC imposed by IE is incorrect. Because the constraint that IE implicitly imposes is b  ⋅  b 0  = 0, by Eqs. ( 8 ), ( 10 ), and ( 16 ), the specific form...
FIGURES
Includes: Supplementary data
Journal Article
Demography (1970) 7 (1): 93–120.
Published: 01 February 1970
... that satisfies f / e-rmc/J(a)da = 1. If B(t - a) were linear, then f / B(t - a)f(a)da wouldequal B(t whereä= f,/ af(a)da. Then, if f(a) did not vary with time, the integral in Equation (2) would reduce to B(t) = R(t) ·B(t - which in log- arithmic form becomes a non-homo- geneous linear difference equation. How...
Journal Article
Demography (1970) 7 (2): 175–183.
Published: 01 May 1970
... migrants to destination areal units within the city, using a normative linear programming framework based on behavioral considerations. Measures of place utilities for each areal unit and of comparative place utilities for each pair-wise permutation of areal units are provided by the shadow prices...
Journal Article
Demography (1978) 15 (2): 139–159.
Published: 01 May 1978
... ( 1972 ). Econometric Methods . 2d ed. New York : McGraw-Hill Book Company . Jöreskog , Karl, G. ( 1973 ). A General Method for Estimating a Linear Structure Equation System . In Arthur S. Goldberger , &amp; O. D. Duncan (Eds.), Structural Equation Models in the Social...
Journal Article
Demography (1993) 30 (4): 653–681.
Published: 01 November 1993
... coefficients to be recovered from the reduced form coefficients. The residual terms reflecting heterogeneity in the dissolution and the conception hazard equations retain normal distribution (being the linear combination of normal variates). That is, Marital Childbearing and Marital Disruption 661 (4...
Journal Article
Demography (2005) 42 (1): 91–108.
Published: 01 February 2005
... that the unobservable differences among people affect only their levels of Y through the linear, additive error term and not 9. The method of instrumental variables was developed within economics in its most well-known form in the simultaneous equations model about 60 years ago. It was translated into the Rubin causal...