The OLS results are examined in order to compare them with the simultaneous equations
estimates and to illustrate the potential benefits of the latter methodology in the presence of interdependent relationships.
The information in the first two rows can now be written as the pair of simultaneous equations
, and labelled as equations (1) and (2) respectively.
The Statistical Implications of a System of Simultaneous Equations
This paper extends the existing MCMC simulation methods to a system of simultaneous equations
with hidden Markov chains.
Therefore, including capital as an explanatory variable in a short-run cost equation would result in simultaneous equations
bias (Grannemann, Brown, and Pauly 1986).
In addition, several simultaneous equations
studies supported the deterrence hypothesis using the three equation model, but they did not report their production function equation results, suggesting that the equation did not perform well [19; 32; 40]--see Cameron  for additional references.
The general behavioral or structural system with (m) simultaneous equations
can be formatted as follows:
Using data on the sources of revenue and characteristics of aid recipients, the model characterizes three simultaneous equations
Today, cost accounting textbooks describe the reciprocal method with simple examples that involve repeated iterations or simultaneous equations
(or both) to model the cost of each department.
The values of the PWM frequency and duty cycle to obtain the desired average current and constant dither amplitude can be calculated by solving the two simultaneous equations
, (10) and (11).
One way to model a situation like the one described in the previous paragraph is to build a system of simultaneous equations
like the following:
somehow, magically, morphed into cricketers' batting averages; xerophytes and pteridophytes in the botany class miraculously gave root to the simple curry leaf tree and its aromatic leaves that, when added to thinned, slightly chilled butter milk, made the most refreshing drink on a hot day of cricket under the summer sun.
When designing this piezoelectric converter, specific application-adequate simultaneous equations
should be defined and solved.
With k = 1 and k = 2 there are two simultaneous equations
for A and B, namely:
The solution [chi] in the two simultaneous equations
of (4) is assumed in the PV theory to represent a relativistic vacuum wave propagating within the PV state.