We  find  very  useful  to  begin  the  introduction  by  taking  a  look  at  the beginnings of simultaneous equations system. As it is known in the literature  of  econometrics,  when  we  use  the  simultaneous  equations  system,  we  decide  to  deal  with  several  linear  or  dynamic  regressions  basing  to  the  macro-economic  theory.  Thus,  a  simultaneous  equation  model (SEM) will be available provided they has been chosen in the light of the economic theory allowing a correct diagnosis of the system and reflecting the real interactions between variables which their use helps in prediction and in proper planning. For this the importance of looking to the interactions between the variables, on the one hand, to realize a correct estimate of the equations, and on the other hand, to have for the ability to interpret them. The proposed equations, which are known as structural  equations,  must  comport  with  the  economic  theory.  

This  paper  has  carried  out  an  in-depth  study  based  on  the  simultaneous  equations  model  by  estimating  three  structural  equations  associated  to  the  three  components  of  the  Real  Gross  Domestic  Product  per  Capita  (gdp)  in  Singapore over the period (1991-2017), that is, the Real Gross Domestic Saving per Capita (gds), the Household Final Consumption  Expenditure  per  Capita  (hfce),  the  Government  Final  Consumption  Expenditure  per  Capita  (gfce).  The  primary nominal data were divided by the product of the consumer price index and the annual population for leading to real data per capita taking into account both inflation and population. The fourth equation represented the income identity expressed by equality (gdpt=gdst+hfcet+gfcet). Seven instruments variables are used to accomplish the study: a constant, three predetermined variables characterized by gdst-1, hfcdt-1 and gfcet-1, three exogenous variables as real interest  rate  (rirt),  the  real  foreign  direct  investment  per  capita  (fdit)  and  the  real  money  supply  per  capita  (m1t).  The  study shows that the three structural equations are over-identified and by consequence; each equation is estimated using  the  following  methods:  Two-Stage  Least  Square  estimator  (2SLS),  HeteroscedasticTwo-Stage  Least  Squares  (H2SLS), Limited Information Maximum Likelihood (LIML) and the Three-Stage Least Squares (3SLS) which is often more efficient than other methods and promoted by Hausman test. Finally, the performance of the estimated equations is measured comparing the fitted values with the observed values by the Mean Relative Error (MRE). The findings have shown that the MRE values are 2.46%, 1.37%, 4.9% and 1.37% for the variables gdst, hfcet gfcet and gdpt respectively.

Finally,  to  measure  the  performance  of  the  estimated  equations,  the  fitted  values  are  calculated  and  a  comparison  with  the  observed  values  is  performed.  This  is  measured  by  the  Mean  Relative  Error  (MRE) expressed as a percent recalling that the (MRE) expresses how large the absolute errors are compared with the observed values we are measuring. The findings in Appendix 3 shown the MRE values 2.46%, 1.37%,  4.9%  and  1.37%  for  the  variables  gdst,  hfcet,  gfcet and  gdpt respectively.

With Reagrds,

Alina Smith
Journal of Business & Financial Affairs
ISSN: 2167-0234
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E-mail: finance@businessjournals.org