The demand for chicken refers to the quantity of chicken demanded by households (in lbs) in the identified areas (one rural and one urban), at the available prices within the specified areas. It must be noted at this point, that the true population in any given situation is never really known. As such samples are usually collected and estimated using econometric methods.
The results are then used to infer or make judgments about the true population.Basically, econometrics is based on economic theory, mathematical economics and statistics. Where the relationships among variables are measured using numerical values and estimates are then interpreted.
This assignment has been embarked on to apply the theoretical knowledge learnt in the classroom to real world situations using actual data. I. e. the quantity of chicken demanded (dependent variable), subject to constraints such as the selling price of chicken, available substitutes, etc. In doing an econometric research, there are four stages.
These stages are 1.Specification of the model. 2. Estimation of the model. 3.
Evaluation of the estimates. 4. Evaluation of the model. These steps will be further explained in the proposal. REVIEW OF LITERATURE This comprises of two parts; 1. The general theory of demand 2. Previous models done and comparisons.
Theory of Demand A fundamental characteristic of demand is…. ”All else equal, as price falls, the quantity demanded rises, and as price rises, the quantity demanded falls. ” What this implies is that there is a negative or inverse relationship between price and quantity demanded.However, price is not the only factor that affects or determines the quantity of a product demanded. Other factors such as the taste and preferences of consumers, the prices of related goods, number of buyers in the market, changing expectations (of price, availability, income) etc. The prices of related goods can increase or decrease the demand for a good depending on whether the related good is a substitute (can be used in place of another) or complement (used together with another). Example, assuming that good (A) is a complement of good (B), as the price of good B rises; the demand for good A will decrease, I.
. , a negative relationship exist. On the other hand, if the goods are substitutes of each other, as the price of one good rises, the quantity demanded of the other good will also increase because the consumers will substitute the more expensive good with a cheaper substitute. A change in consumers’ taste and preferences also affects demand. For instance, if the good becomes more desirable to consumers, the quantity demanded will increase and vice versa. In the same way, if the number of buyers in the market increases, the quantity demanded will also increase and vice versa.
Should consumers expect the future price of a commodity to increase, the present demand will more than likely increase because persons will purchase more in anticipation of the price increase and the opposite will apply for an expected decrease in prices. Additionally, if consumers expect the availability of the product to change, they will also change their demand. E. g. , should consumers expect a shortage of chicken in February; they are likely to increase their demand in January to stock up in expectation of the shortage.Changes in the income status of consumers may also prompt consumers to change their current spending pattern. Whereby, they may increase or decrease the amount purchased, depending on if there is an increase or decrease in their income levels. So in essence, the quantity of a product demanded depends on the price of the product, prices of related goods, changes in consumers’ taste and preferences, changing expectations in prices, availability of the product and income etc.
PREVIOUS MODELS DONE AND COMPARISONS In preparing this model, the researcher looked at other persons work on the demand for chicken.It was realized that others also choose the same three dependent variables in constructing a demand function for chicken. One researcher even went through the process of identifying the variables and going through the process of justifying their selection in the model based on the t statistic. A copy of this researcher’s process will be included in the appendix of the final paper SPECIFICATION OF THE MODEL Specification deals with expressing the economic theory (relationship between variables) in a mathematical form.It is the specification of the model with which the economic phenomenon will be explored empirically. In this proposal, it is the relationship between the quantity of chicken demanded and the factors that influence or determine the quantity demanded that are being examined. Specification of the model entails 1. The dependent and explanatory variables which will be include in the model.
2. The apriori theoretical expectations about the size and sign of the parameters of the function. 3. The mathematical form of the model 4.The econometric form of the model.
In this proposal, the quantity of chicken demanded (Dc) is the dependent variable. The independent variables are the price of chicken (Pc), the price of substitutes (Ps) because chicken is usually substituted with other products such as fish, beef etc and the income of households (Yd) and other unspecified variables. This is shown in the following equation; Dc = ((Pc, Ps, Yd,………….
) Where: Dc ( quantity of chicken demanded. Pc ( Price of chicken. This price will be the price each household pays for a lb of chicken.Ps ( Price of substitute. The reason the price of a substitute is used in the model instead of the price of a complement is because chicken is a good that is usually substituted by other goods such as beef, fish etc.
Yd ( This represents the net income of households. It is known from theory that changing expectations in income affects demand. So the affect of income on demand cannot be truly represented by a straight line, a curve is more realistic.
To represent this ln Yd is going to be used in the function.Even though there are other factors which affect demand, only the three independent variables stated above will be used in the model because theory and previous models done suggest that these are the core (most important ) variables for a demand function, particularly the demand for a consumer product such as chicken. There are usually coefficients for the explanatory variables. These coefficients are known as the (s’.
So the mathematical form of the model is: Dc = ((0 + (1Pc + (2Ps + (3LnYd ) Another term used to describe the mathematical form of the model is the deterministic model.The econometric form of the model is formed when the stochastic or random term is added to the mathematical form of the model. Therefore the econometric form of the model is; Dc = ? 0 + ? 1Pc + ? 2Ps + ? 3LnYd + µ. Where µ the stochastic term,? represents all other less significant independent variables and it collects all errors of the model. Additional, the expected sign of the parameters (? s’) are as follows; ? 0 > this is the constant. The expected sign of this is +.
The reason being, this represents the autonomous consumption of chicken/ it represents the demand for chicken hen the value of the dependent variables are 0. ?1 > -ve. The reason being, there is an inverse relationship between the price of chicken and the quantity demanded of chicken. ?2 > +ve. The reason being, if the price of chicken increases, the quantity demanded of the substitute for chicken will increase. ?3 > +ve. The reason being chicken is considered to be a normal good. Therefore if income increases, quantity demanded will increase and vice versa.
The sizes of the elasticities are dependent on the nature of the commodity and the existence of substitutes.For example if the good is a necessity, price and income elasticity’s are expected to be small. On the other hand, if the product is a luxury, the elasticity’s are expected to be high.
Therefore for this proposal the elasticity’s (income and price) are expected to be small. Additionally, if the commodities are close substitutes, the cross elasticity will be high. ESTIMATION OF THE MODEL. Estimation is concerned with obtaining numerical values for the variables used in the model and estimates for the parameters.This step involves • Gathering of statistical observations (data) on the variables included in the model. • Choice of the appropriate econometric technique. The researcher proposes to use cross-sectional data.
This type of data gives information on the variables concerning individual agents (households) at a given period of time. I. e. using the demand function stated previously (econometric form) and inserting values for a number of households in order to compute an estimate of the demand function. i. e.
Dc = ? 0 +? 1Pc +? 2Ps + ? 3LnYd + ?.The proposed econometric technique is the OLS/ Classical least squares. What this does is select values for the coefficients that minimize the sum of the squared errors.
(? ei? ) The assumptions of this econometric technique are: 1. Linearity. This refers to linearity in coefficients; the model must be correctly specified and has the additive error term. 2. The mean of the error term is 0 3. Observations of the error term are uncorrelated with each other, i. e.
there is no autocorrelation. 4. The explanatory or independent variables are uncorrelated with the error term so that E (Xe) = 0 5.The error term has a constant variance, i. e. there is no heteroscidastiscity. 6.
No explanatory variable is a perfect linear function of other variables, i. e. there is no multicollinearity. 7. The error term is normally distributed. EVALUATION OF THE ESTIMATES. In a nutshell, this is the interpretation of the reliability of the coefficients estimated.
That is, if the results are theoretically meaningful and statistically satisfactory. There are basically three criteria’s for evaluating the estimates. • The economic apriori criteria. This is determined by economic theory.
• The statistical criteria.This is determined by statistical theory. • The econometric criteria. Determined by econometric theory. • The selection of the confidence interval. Economic apriori is determined by the principles of economic theory and refers to the sign and size of the parameters. In this case, the reliability of the estimated coefficients will be determined based on economic theory. For instance, the expected sign of ? 1 is expected to be negative because theory states that demand and price are inversely related.
The statistical or first order conditions are determined by statistical theory.At this point in the assignment, the researcher will look at the basic statistics such as the mean, median, mode, correlation coefficient etc to examine the data. Additionally the R2 and adjusted R2 values, the F statistics and t statistics will be used to also examine the coefficients.
The relevance of all these test will also be further explained, for instance the R2 and adjusted R2 speaks about the fit of the model. The next stage is the second order tests or econometric criteria. These tests determine the reliability of the statistical tests.They help to establish whether or not the estimates have the desirable properties of OLS.
These properties are linearity, unbiased estimator ie E (? ) = ? , minimum variance (the distribution of the estimates around the true line fits tightly) and consistency (as the sample size gets larger, the variance gets smaller). Simply, the econometric criterion is aimed at detecting violations of the assumptions of OLS. To this end a number of tests are proposed. 1.
The Durbin – Watson (d) statistic) to test for autocorrelation. 2. The Spearman Rank Test.Performed to test whether or not the assumption of homoscedastiscity is violated. 3. The experimental technique based on Frisch’ confidence analysis.
That is testing for the level of multicollenearity. 4. The Ramsey – Reset Test. This test is done to determine whether or not the model is properly specified. Selection of the confidence interval.
In order to carry out any statistical test, the null and alternative hypothesis will have to be correctly specified. Additionally the confidence interval will have to be determined, i. e.
the level of significance of the hypothesis test.This is especially critical in minimizing errors’1 and errors’ 2. For instance, at the 95% confidence level, only 5% of the time error 1 occurs. This means that only 5% of the time a true null is rejected.
However at the 99% confidence level, the possibility of error 2 occurring increases, i. e. the possibility of not rejecting a true null. For this paper, the 95% confidence interval is proposed.
EVALUATION OF THE MODEL Before using a model to forecast, it is first important to ensure that the model satisfies the economic, statistical and econometric criteria’s’.After which the stability of the model has to be examined. The Chow Test will be done to examine the stability of the model. After which the final results will be reported. These results include discussing the R2, adjusted R2, the resulting F and t statistics, the elastic ties etc. The conclusion follows.
Then there will be an appendix, consisting of the data sets, a sample of the questionnaire used, statistical graphs etc. The final page will be a bibliography of all books and websites used in the assignment.