![The estimation of the /coefficients of the variable/ the model can be computed using any one of the above
stated econometrics techniques. Some techniques which are theoretically applicable may not be used for
estimation purpose due to non-availability of data or defaults of the statistical results obtained from the
technique.
Having selected the econometric method that will be applicable for estimation of the model one should
take in to consideration whether the model is linear in variable & in parameters.
a) If the model is non - linear in parameters it is beyond to this level of Econometric analysis
Ex.
Y =α+β1
2
X1 +β1
3
X2+Ui -------------------------1.16
Since the coefficient β1 is the power of 2 & β2 is the power of 3 then we call these kinds of model
non-linear in the coefficients.
b) If the model is non-linear in variables then before estimation the model has to be transformed in
to linear model.
To know whether the model is linear or non-linear in variable we can take the first derivatives & if the
first derivative of the model gives us a constant number then the model is linear in variables but if it
doesn't give us a constant number the model is non-linear in variable.
Example (1)
Yi=α+β1 X1+Ui−−−−−−−−−−−−(1.17)
If you take the first derivation of Yi w.r.t. X.
i.e
α yi
α xi
=β1
[Which is the coefficient of Xi] is a constant number then the equation is
linear in variable.
Example (2)
Yi=α+ βXi2+Ui−−−−−−−−−−−(1.18)
α yi
α xi
=2 βXi
Then we can say that the model is non-linear in variable because the first
derivation w.r.t.x does not give us a constant number.
(Example 3)
Y i=β1+β2(
1
X2
)+Ui−−−−−−−−−−−(1 .19 )
α yi
α xi
=−2 β2 X
i
−3
or
−β2(
1
X3
)
then since the first derivation is not equal to a
constant number then again the model is non-linear in the variable.
To estimate the model which is non-linear in variable we should first transform the model in to linear
model.
Equation (1.18)
Yi=α+βxi¿+Ui−−−−−−−−−−−−−−−−1.20
Where
Xi
¿=x
2
Equation (3)
Yi=β1+β2 Xi¿ +Ui−−−−−−−−−−−−−−−1.21
Where
Xi ¿=
1
xi
Again if you have the following models first transform as follows
Yt=
αx
i
− β e
u
transform in to lnyt= ln-β ,ln Xi +Ui](https://image.slidesharecdn.com/chapter1-240918132603-4bb402c7/85/Chapter-1-docxt5t5y6uyjujyujoodkdjmvkkff-8-320.jpg)
Chapter 1.docxt5t5y6uyjujyujoodkdjmvkkff
- 1. Chapter 1: Definition, Scope, & Division of Econometrics Definition of Econometrics: - Econometrics deals with measurement of economic relationships between economic variables (dependent & independent variables). The term econometrics is derived from two Greek words. i.e. economy & measure. Different economists give different definition for Econometrics, but all of them are arriving at the same conclusions and we can boils down the whole definition in to the following. “Econometrics is the positive interaction between data & ideas about the way the economy works.”The central role of Econometrics was often regarded as one of estimating the parameters of the model as efficient way as possible, given a particular set of data with which to apply statistical & mathematical techniques. To test the validity of Economic theory Econometrics provides us numerical values for the parameters of economic relationships & using these numerical values we can verify the economic theories. To arrive at these numerical values of economic relationships we use economic theory, mathematics & statistics. Though econometrics uses all these it is different from each one of them due to its distinctive nature. One of the most distinctive natures of Econometrics is that it contains the random term which is not reflected in mathematical economics & economic theory. 1.1 Econometrics & Other Disciplines of Economics Econometrics is an integration of economic theory, Economic statistics, mathematical statistics & mathematical Economics. A) Economic theory states a qualitative relationship between the explanatory & explained variable using Cetrus Peribus assumptions. Ex.1. Consumption depends up on current income (Yt) & previous income (Yt-1) of an individual other things being constant. This theory does not give any insight how current income & previous income will affect consumption by giving numerical values. B) Mathematical Economics: It explains the economic theory in the equation or mathematical forms. Or mathematical economics explain the theory of economics in to mathematical relationship between variables. /we can explain the above theoretical relationship in mathematical form /example 1/ as follows Ex. 2. Ct=α+β1 Yt+ β2 Yt−1−−−−−−−−−(1.1) Where Ct.: consumption expenditure Yt: current income Yt-1: previous income Again this mathematical relation does not capture other factors that affect consumption expenditure. Then mathematical economics explain the exact relation ship between the dependent variable (Ct) & the independent variables (Yt &Yt-1) by ignoring other variables that affects consumption expenditure. C) Economic Statistics:- It is a descriptive aspects of economic theory. i.e. by collecting, processing and presenting economic data in the form of table & charts. Though Economic statistics provides numerical data like mean, median - standard deviation etc. but it does not make reliable the relationship between the economic variables. D) Mathematical statistics:- This is based up on the probability theory, which are developed on the basis of controlled experiments. This statistical method can be applied in economic relationships because such experiment can not be designed for economic phenomena. This probability theory applied for very few cases in economics such as Agricultural or industrial experimentations.
- 2. In all of the above methods they completely ignore the other factors that will affect the economic relationship but econometrics by developing a method for dealing with the random term that will affect the economic relation ships differentiate itself from the remaining. Ct=α+β1 Yt+ β2 Yt−1+ut :−−−−−−−−−−(1.2) All variables have the same meaning as equation (1.1) Ut: means the random term which represents all other factors that will affect consumption expenditure. These factors may be many such as, invention of new product, wealth, wind fall gain & loss, migration, tradition, etc. are affecting consumption expenditure. All these factors will have their own influences on the consumption expenditure. Then econometrics by considering other factors (represented by Ui) will find numerical values for coefficients of the variable that will explain the relationship to verifying economic theories. 1.2 Goals of Econometrics There are three main goals of Econometrics. These are: 1. Testing of Economic theories /Analysis/ 2. Estimation of the coefficients of Economic relationship /Policy making/ 3. Forecasting the future values of economic magnitudes. /Forecasting/ Successful econometric application should include some combination of all the three goals. 1.2.1 Analysis: Testing of Economic Theories In the early stages of the development of economic theory, so called armchair economist, were formulating basic economic principles using verbal explanation and applying deductive procedure (from general to particular). During this period of time economists by pure logical reasoning derive some general conclusions /laws/ concerning the working process of economic system. In this period no attempt were made to examine whether the theories explained adequately the actual economic behavior or not. Now a day any economic theory is subject to the empirical test of econometrics. i.e. the explanation power of economic theory to explain the economic behavior is tested by econometrics. Then Econometrics aims primarily at the verification of Economic theories & there by to know & decide how well they explain the observed behavior of the economic units. 1.2.1 Policy Makings This means by applying different methods of econometrics techniques we can obtain individual numerical values for the coefficients of economic relationship. Using these numerical values a decision can be undertaken by different economic agents. Econometrics can supply MPC, elastic ties, MC, MR etc. Using these magnitudes (numerical values) decision will be undertaken. Ex. D=α+β1 I+ β2 Ex+β3 PI+β4 PEx +Ui---------- - - - -1.3 Where D= devaluation, I is volume of import, PE volume of export; PI is price of import, PE x is Price of export. Then devaluation will depend on all these explanatory variable coefficients. From these coefficients we can have B1 = Marginal propensity to import, B2 = Marginal propnsity to export B3 & B4 import & export propensities respectively
- 3. Then on the basis of these coefficients of numerical values the government will decide whether devaluation will eliminate the countries deficit or not. 1.2.3 Forecasting It means using the numerical values of the coefficients of economic relation ships we can judge whether to take any policy measure in order to influence the future value of economic variables or not Assuming that the estimated result from the Ethiopian economy for the year 1985-1995. ^ Y=−261.09+0.2453Xi−−−−−−−−−−−−−−−−−−−−(1.4) Where Yi = Ethiopian expenditure on imposed goods Xti = Personal disposable income. Then on the basis of the above result the government can able to know his expenditure in any year after 1995 using the above equation. If disposable income (Xt) will be 1 million in 1999 his expenditure on imported goods will be ^ Yi=-261.09 + 0.2453 (1,000, 000) = 245,038.91 by the year 1999. Then since the government knows the future values of expenditure on imported goods & services he can take any measure to increase or cut down imports using these numerical values.Forecasting is used for both developed & developing countries in different ways. i.e. developed countries used it for regulation of their economics where as developing countries used it for planning purpose. 1.3 Division of Econometrics Just like any subjects Econometrics also decomposed in to two branches:- Theoretical & Applied econometrics. 1.3.1 Theoretical Econometrics: - It is the development of appropriate econometric methods for measuring economic relationship between variables in theoretical Econometrics. i. the data used for measurement purpose are observations from the real world but are not derived from controlled experiments ii. Econometric relation ships are not exact. The econometrics method that will be used in theoretical Econometrics may be classified in to two a) Single - equation techniques i.e. one side relationship between variables at a time. Ex. Qd=α+ β1 Pi+ui−−−−−−−−−−−−−(1.5) Means quantity demanded depends up on the price of the commodity but not price depends up on quantity. Then we have only one side causations. Then we can apply Econometrics techniques only for this equation. b) Simultaneous equation model :- When there is two sided causation Ex. Equation (1.5) explains that quantity demand depends on the price of the commodity but if the price of the commodity is in turn depends on the quantity of commodity supplied. Then we will have two side causations Pi=α+βQs.+Ui−−−(1.6) Econometrics techniques will applied for three equations Qd = α +βpi+Ui−−−−−dd−equation−−−−−−−−−−−−(1.6) Pi = α +αqs i +ui−−−−−price−equation−−−−−−−−−−−(1 .7) Qd = Qs --------------------- Identity ---------------------------- - - - - (1.8) Then in this case we applied Econometrics techniques simultaneously for all equations at a time. 1.3.2 Applied Econometrics:- This is the application of theoretical Econometrics methods to the specific branch of economic theory i.e.application of theoretical Econometrics for verification & forecasting of demand, cost, supply, production, investment, consumption & other related field of economic theory.
- 4. 1.4 Methodology of Econometric Research In any econometrics research we may distinguish the following steps. Economic theory Mathematical model of the theory Econometric model of the theory Collecting data Estimation of Econometric model Evaluation of Estimates (Hypothesis testing) Application (forecasting) Stage 1. The first step in Econometrics is to formulate the economic theory that will be tested against reality using Econometrics. Ex, The theory may hypothesize that "Aggregate saving in the economy is affected by the average interest rate and the one year lag of income (Previous year income). Or if you take Keynes psychological law of consumption it hypothesize consumption is a function of income to be precise. "Aggregate consumption in terms of wage units (Cw) & aggregate income (Yw) in terms of wage units are called this relation ship propensity to consume. Or consumption of an individual at any period of time depends upon income of an individual at period t & future rate of interest. Stage 2. Specification of the Model:-This is transformation of econometric theory in to mathematical model that explain the relationship between economic variables. Under this stage we will have the followings. A) Selecting variables:- it involves the determination of dependent (endogenous or explained) variable and independent (exogenous or explanatory) variables of the theory. From the above example we can identify that Ex.1. Aggregate saving is the dependent variable & the remaining variables (interest rate & previous year income) are the independent variable. E.x.2 Aggregate consumption in terms of wage units is the dependent variable & aggregate income in terms of wage units is the independent variable
- 5. Ex. 3. Consumption of an individual at time t is dependent variable and future rate interest & income are independent variables. B) Determine the theoretical values: a prior expectation of the sign & magnitude of the parameters. This needs only a theoretical background to determine the relationship between the dependent & independent variables i.e. negative or positive relationship between variables. From our example we can have the following sign or direction of relationship between variables Ex.1. i. Interest rate & saving have positive relationship and also there is a positive relationship between income and saving. Then we can say that the sign of the parameters that will explain the relationship between aggregate saving & interest rate & income have to be positive. ii. Aggregate consumption in terms of wage & Aggregate income in terms of wage are positively related & the sign of the parameter has to be positive iii. The relationship between consumption at time t & income at time t has positive relationship & consumption at time t & future rate of return have negative relationship (if future rate of interest is high an individual will cut down his consumption at time t & post pone his consumption for other period & increase his savings). C) Specification of the model: In this stage we specify the relationships between the dependent & independent variables on the basis of economic theories. In this stage we also determine the number of equations (single equation or simultaneous equation model) & the type of equation i.e. whether the relationship between economic variables explained using linear or non- linear equations. Let’s specify our previous theoretical relationships. Ex. 1. St=α+β1Yt−1+β2r−−−−−−−−−−−−−−−(1.9) Where St = aggregate savings, Yt-1 is previous income r is rate of interest. Ex- 2 Ct=α+β1Y w−−−−−−−−−−−−−−−−−(1.10) Where Ct = aggregate consumption in terms of wage Yw is aggregate income in terms of wage. Ex. 3. Ct=αYi β1 ri β2 −−−−−−−−−−−−−−−−−−(1.11) Where Ct is consumption at time t, Y is income at time t re is future rate of interest. All the above equation is single equation model but equation 1.9 & 1.10 are linear equations & equation 1.11 is non linear equation. Magnitude of the coefficients of the variables ( α ,β1∧β2), what will be the likely magnitudes of these coefficients? The magnitude or the size of the numerical values of the coefficients of the variables ( α ,β1∧β2) are determined by the economic theory & empirical observation of the real world. In equation 1.9 & 1.10the coefficient β1 represents marginal propensity to consume and the magnitude of β1 is 0<β<1 it is determined by the economic theory. The explanation of the magnitude of equation 1.9 &1.10 are different from equation 1.11. In equation 1.9 &1.10 which is a linear equation the coefficients of the variable explains the marginal magnitudes but equation 1.11 explains the elastic ties. Ex. In equation 1.9 & 1.10 if income increases by 1 birr on the average consumption will increase by β amount. The same thing is true in the interpretation of β2 in equation 1.10 i.e. if rate of interest is
- 6. increasing by one birr on the average saving will increased by β2 amount. But in equation 1.11 β1 & β2 explains elastic ties i.e. if income increases by 1% consumption will increase on the average by β1% & for β2 if rate of interest is increasing by 1% consumption will be cut down on the average by β2 %. Possible errors committed at this stage are i. Wrongly specifying the model (i.e. relationships that will be explained using non-linear r elationship may be specifying in linear form & the reverse.) - Mis-specification of the model. ii. Relevant explanatory variables may not be included (Omission of relevant explanatory variables) iii. Irrelevant explanatory variables may be included. Step - 3. Specification of the econometric model The above equation (1.9 to 1.11) explains the mathematical relationship between the explained & explanatory variables is inexact form or deterministic form. i.e. all the dependent variable will be affected only by those independent variables alone & any other variables can not affect the dependent variable. But in reality different factors will affect the economic relationships that will not be captured by our example. Ex. In equation 1.9 states that saving will depend up on previous income & rate of interest alone. But in reality many variables will affect savings such as wealth; consumption, windfall gain & loss, health of the individual, etc. There are many factors that will affect the saving capacity of individuals. Then those factors which are not incorporated in our model will make the relationship between the dependent & the independent variables inexact. Then these factors make the Economic relationship between the dependent & the independent variable is inexact & it can be specified in the following model. St=α+βYt−1+β2r+Ui−−−−−−−−−−- - - - - - 1.12 Cw=α+β Yw+Ui−−−−−−−−−−−−−−− ------1.13 Ct=αYi β1 r−e β2 eui −−−−−−−−−−−−−−− -------1.14 In all the above equations Ui represents all factors that affects the dependent variable but not explained or taken in to account explicitly in the model. Then Ui is called the disturbance term or error term or random term or stochastic variables. The inclusion of Ui in the mathematical economics (exact relationship between variables) will transform the model in to Econometric model (inexact relationship between variables or the unexplained variable in the model will capture or explained by Ui.) Step - 4 Obtaining Data The data used in the estimation of econometric model may be of various types. Time series data: a data related to a sequence of observations over time on an individual or group of individuals etc. Ex. 1996 E.C. represent by Ct where t indicates time from 1980 - 1996 E.C. Cross-sectional data: data collected on one or more variables collected at particular period of time. Ex. Number of children registered for schooling in all K.G. Schools of Bahir Dar in 1999 E.C. by sex, age, religion etc. Panel data:- These are the results of repeated survey of a single (cross sectional data) sample in different periods of time. Ex. If consumption expenditure of a sample of population from Bahir Dar city on Teff, Coffee, cloth is taken in 1985, in 1990 & 1996. Polled data:- These are data of both time series & cross sectional data. Dummy Variable: These are data constructed by econometricians when they are faced with qualitative data. These qualitative data may not be measurable in any one of the above methods ex. sex, religion, race, profession etc. The value of these data can be approximated using dummy variables ex. if religion is appearing in the independent side of the equation since we do not have qualitative data we can assign 1 for Christian & 0 Otherwise. Accuracy of data:- Though plenty of data are available for research purpose but the quality of data matters in arriving at a good results. The quality of data may not be good for different reasons.
- 7. i. Most social science data are not - experimental in nature i.e. there will be omission, errors etc. ii. Approximation & round off the numbers will have errors of measurement. iii. In questioner type of survey non-response and not giving an answer for all questions may lead to selectivity bias. /rejecting non-response & excluding those questions which is not answered by the respondent/ iv. The data obtained using one sample may be varying with the data obtained in another sample & it is difficult to compare the results of these two samples. v. Economic data are available at aggregated level & errors may be committed in aggregation. vi. Due to confidentiality of some data’s it is impossible to get the data or may be published in aggregated form. Because of the above reasons one can deduce that the results obtained by any researchers are highly depending up on the quality of the data. Then if you get unsatisfactory results the reason may be the quality of the data if you correctly specifying the model. Step 5. Estimation of the Econometric Model We can estimate the coefficients of the independent variables which explain the relationship between economic variables in two different ways. Single or simultaneous equation methods. Single equation method:- This techniques of estimation is applicable only for one equation at a time Ex. Qd=+ βPi+Ui-- - - - - - - - ---1.15 Where Qd= quantity demanded P is price. For this & any this kinds of equation we can apply different methods of estimation. These are OLS (Ordinary least squares,) In direct least square or reduced form techniques, two stages least squares (2SLS), Limited Information (LI), Maximum likelihood (MLI) & Mixed estimation method may be used. Simultaneous equation techniques!- When we have more than one equation & if the numerical values of the coefficients are determined simultaneously at a time then we use any one of the following methods of estimation, Three stage least squares (3SLS), & the Full information Maximum Likelihood (FIML) method. The selection of the techniques of estimation will depends upon many factors. a) Nature of the relationship between economic variables and its identification. Under this condition if we studied the economic relationship using a single equation method then the best method is OLS. But if the relationships between economic variables are in a function of simultaneous equation we may use any techniques from the above stated. b) On the properties of the estimated coefficients obtained from each method agood estimate should give the properties of unbiased ness, consistency, efficiency & sufficiency or a combination of such properties.If one method gives an estimate which passes more of these desirable characteristics than any other estimates from other methods, then that techniques which possess more of the desirable characteristics will be selected. c) On the purpose of Econometric research:- If the purpose of the model is forecasting the property of minimum variance is very important i.e. the techniques which will give the minimum variance of the coefficients of the variables will be selected. But if the purpose of the research is for policy making (analysis) that techniques which gives unbiased ness of the variables will be selected. d) On the simplicity of the techniques: If our interest is simple computation we can select that technique which involves simple computation & less data requirement. e) Time & cost required for computation of the coefficients of the variables may determine the selection of the Econometric techniques.
- 8. The estimation of the /coefficients of the variable/ the model can be computed using any one of the above stated econometrics techniques. Some techniques which are theoretically applicable may not be used for estimation purpose due to non-availability of data or defaults of the statistical results obtained from the technique. Having selected the econometric method that will be applicable for estimation of the model one should take in to consideration whether the model is linear in variable & in parameters. a) If the model is non - linear in parameters it is beyond to this level of Econometric analysis Ex. Y =α+β1 2 X1 +β1 3 X2+Ui -------------------------1.16 Since the coefficient β1 is the power of 2 & β2 is the power of 3 then we call these kinds of model non-linear in the coefficients. b) If the model is non-linear in variables then before estimation the model has to be transformed in to linear model. To know whether the model is linear or non-linear in variable we can take the first derivatives & if the first derivative of the model gives us a constant number then the model is linear in variables but if it doesn't give us a constant number the model is non-linear in variable. Example (1) Yi=α+β1 X1+Ui−−−−−−−−−−−−(1.17) If you take the first derivation of Yi w.r.t. X. i.e α yi α xi =β1 [Which is the coefficient of Xi] is a constant number then the equation is linear in variable. Example (2) Yi=α+ βXi2+Ui−−−−−−−−−−−(1.18) α yi α xi =2 βXi Then we can say that the model is non-linear in variable because the first derivation w.r.t.x does not give us a constant number. (Example 3) Y i=β1+β2( 1 X2 )+Ui−−−−−−−−−−−(1 .19 ) α yi α xi =−2 β2 X i −3 or −β2( 1 X3 ) then since the first derivation is not equal to a constant number then again the model is non-linear in the variable. To estimate the model which is non-linear in variable we should first transform the model in to linear model. Equation (1.18) Yi=α+βxi¿+Ui−−−−−−−−−−−−−−−−1.20 Where Xi ¿=x 2 Equation (3) Yi=β1+β2 Xi¿ +Ui−−−−−−−−−−−−−−−1.21 Where Xi ¿= 1 xi Again if you have the following models first transform as follows Yt= αx i − β e u transform in to lnyt= ln-β ,ln Xi +Ui
- 9. Yt=eα+β xtu Transform in to lnyt =+βXi + Ui e − y =α +x β tui Transform in to y=+β log ex + Ui Y=e α+ β /xtui Transform in to y=+β ( 1 x ) + Ui Having transformed the model from non-linearity in variable to linearity in variable then we can estimate the model using the appropriate (selected) method of econometrics methods. Step - 6 Evaluations of Estimates: After estimating & obtaining the coefficients of the variables one has to precede to the evaluation of the results obtained using econometric methods. At this stage we are evaluating the reliability of the results whether they are theoretically meaningful & statistically satisfactory results. To evaluate the reliability of the estimates we apply /follow/ the following steps i. Economic interpretation of the results - Economic a priori criterion. ii. Statistical interpretation of the results - statistical analysis on the basis of R2 ,t, test, F- test, s.d. iii. iv. Test of Econometric criterion. Step A. Economic a prior criterion: at this stage we should confirm that whether the estimated values explain the economic theory or not i.e. it refers to the sign & magnitudes of the coefficients of the variables. Ex. 1. If we have the following consumption function Ct= +β1Yt + Ut -------------------------------------------1.22 Where Ct: consumption expenditure, Yt is income From the economic theory (economic relationship between consumption and income) it is known that β represents MPC (Marginal Propensity to consume). Then on the basis of a priori-economic criterion it is determined that the sign of β has to be positive & the magnitude (size) β again is in between zero & one (0< β<1). If the estimated results of the above consumption function gives ^ Ci=−3.32+0.2033Yt ----------------------------1.23 From the economic relationship explained by economic theory states that if your income increase by 1 birr your consumption will increase on the average by less than one birr i.e .203 cents. Then the value of β1 is less than one & greater than zero in its magnitude (size) again the sign of β1 is positive. Therefore, the estimated models explains the economic theory (economic relationship between consumption & income) or satisfies the a priori - economic criterion. If another estimation of the model using other data gives the following estimated results ^ Ct=24.45−5.091Yt -----------------------------1.24 Where Ct is consumption expenditure Yt is income. From Economic theory it is known that β1 has to be positive & its magnitude is greater than zero & less than one. But the estimated model results that the sign of β1 is negative & its magnitude is greater than one then we reject the model because the results are contradictory or do not confirm the economic theory. In the evaluation of the estimates of the model we should take in to consideration the sign & magnitudes of the estimated coefficients. If the sign & magnitudes of the parameter do not confirm the economic relationship between variables explained by the economic theory then the model will be rejected. But if there is a good reason to accept the model then the reason should be clearly stated. In general if the apriori theoretical criterions are not satisfied, the estimates should be considered as unsatisfactory.In most of the cases the de
- 10. ficiencies of empirical data utilized for the estimation of the model are responsible for the occurrence of wrong sign or size of the estimated parameters. The deficiency of the empirical data means either the sample observation may not represents the population (due to sampling procedure problem or collecting inadequate data or some assumption of the method employed are violated). In general if a prioriy criterion is not satisfied, the estimates should be considered as unsatisfactory. Step-B- First order test or statistical criterion: If the model passes a prior-economic criterion the reliability of the estimates of the parameters will be evaluated using statistical criterion. The most widely used statistical criterions are: The correlation coefficient - R2 /r2 / The standard error /deviation/ S.E of the estimate t- ratio or t-test of the estimates. Since the estimated value is obtained from a sample of observations taken from the population, the statistical test of the estimated values will help to find out how accurate these estimates are (how they accurately explain the population?). R2 will explain that the percentage of the total variation of the dependent variable explained by the change of the explanatory variables (how much % of the dependent variable is explained by the explanatory variables). S.E. (Standard error or deviation) - measures the dispersion of the sample estimates around the true population parameters. The lower the S.E. the higher the reliability (the sample estimates are closer to the population parameters) of the estimates & vice -versa. Step -C- Second order test /Economic Criterion/: after testing a prior test & statistical test the investigator should check the reliability of the estimates whether the econometric assumptions are holds true or not. If any one of the assumption of Econometric assumptions are violated. The estimates of the parameters cease to posses some of the desirable properties (un biased ness, consistency, sufficiency etc) Or the statistical criterion loses their validity & became unreliable. If the assumptions of econometric techniques are violated then the researcher has to re –specifying the already utilizing model. To do so the researcher introduce additional variable in to the model or omit some variables from the model or transform the original variables etc. By re-specify the model the investigator proceeds with re- estimation & re-application of all the tests (a priori, statistical & econometric) until the estimates satisfies all the tests. Step 7. Forecasting or Prediction Forecasting is one of the prime aim of econometric research the estimated model may economically meaningful, statistically & econometrically correct for the sample period. But given all these it may not have a good power of forecasting due to the inaccuracy of the explanatory variables & deficiency of the data used in obtaining the estimated values. If this happens the estimated value (i.e. forecasted) should be compared with the actual realized value magnitude of the relevant dependent variable. The difference between the actual & forecasted value is tested statistically. If the difference is significant we concluded that the forecasting power of the model is poor. If it is statistically insignificant the forecasting power of the model is good. Exercise for chapter one 1) Define Econometrics? How does it differs from Mathematical Economics & Mathematical statistics? 2) What are the goles of econometrics & explain it using example? 3) What is the difference between theoretical & applied econometrics?
- 11. 4) What is the differencebetween the model which is linear in variable & & non linear in variable? & how would you interperate the parameters? 5) What are the steps apply to evaluate the reliability of the estimates? 6) Explain the difference between economic theory & econometrics? 7) Given the following theory which is given by the well known monetary economist Milton Fridman “ the theory of demand for money have a strong positive relation ship with price & income but has no relation ship with rate of interest” Write the mathematical relation ship Formulate the econometric relation ship What will be the size & magnitude of the relation ship between the dependant & independent variables? 8) Explain the stages in the methodology of econometrics?