1. Econometrics
"...Experience has shown that each of these three viewpoints, that of statistics, economic
theory, and mathematics, is a necessary, but not by itself a sufficient, condition for a real
understanding of the quantitative relations in modern economic life. It is the unification of all
three that is powerful. And it is this unification that constitutes econometrics..."
economic theories are usually sharp and unambiguous
o models of demand, production, labor supply etc. specify
deterministic relationships
but, the model (any) is a simplifcation of reality
o it includes salient features of the relationship of interest
but leaves unaccounted for influences that are present but
regarded as unimportant
ultimate goal of the econometricmodel is to uncover the deeper causal connections between
dependent and independent variable
Regression analysis
is a statistical technique that attempts to explain movements in one variable, the dependent
variable, as a function of movements in a set of other variables, the independent variables.
regression analysis is concerned with statistical relationships between variables
deterministic vs. stochastic relationship
statistical relationships between variables assumes working with random/stochastic
variables that have probability distribution
Finally, regression analysis is concerned with investigating the dependence between
dependent variable and one or more independent variables
E(Y I Xi ) = _0 + _1Xi LINEAR REGRESION FUNCTION
were _0 i _1 are unknown, but fixed parameters which are called regression parameters
(coefficients).
Stohastic
U
representseveryvariablesthatare leftoutof the model,buthave andimpacton Y.
1 shortcomingsintheory
2 availabilityof the data
2. 3 variablesof differentimportance
4 idiosyncrasiesinthe humanbehavior
5 measurementerrors
6 simplicity
7 wrongfunctional form
Primary goal of the regressionanalysisis
Ordinaryleastsquares(OLS)
(TSS) isequal to the explainedsumof squares(ESS) andresidual sumof squares(RSS)
FindingminRSS
ingeneral,whatwe needtodo inorderto findthe minimumvalue of some function
1) firstderivationof the function
2) equalize the obtainedexpressionfromthe firststepwith0
3) obtainthe value of x
b1 andb0 are called estimators,but the numberthatyou obtainafter regresscommandinStata are
estimates
so, estimatorhasa distributionand estimate thatyouobtainisjustone scalarthat is "takenout"of the
bunchof otherestimatesfrom particulardistribution
The Classical Assumptions
1)the regressionmodel islinear,iscorrectlyspecified,andhasan additive errorterm
2) the error term hasa zeropopulationmean
3) all explanatoryvariablesare uncorrelatedwiththe errorterm
4) observationsof the errortermare uncorrelatedwitheachother
5) the error term hasa constantvariance (homoscedasticity)
6) no explanatoryvariable isaperfectlinearfunctionof anyotherexplanatoryvariable
7 the error termisnormallydistributed(optional assumption)
