ECN 322long Paper

8/8/2019 ECN 322long Paper

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ECN 322: APPLIED ECONOMETRICS

May, 2006


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PART 1

Topic: The monthly demand for chicken, in a rural and urban area ofGuyana.

Introduction

As was stated in the proposal, the assignment was proposed using two data sets; one urban and

the other rural. In particular, the rural data was to be drawn from a rivering area. However, the

researcher encountered problems in accessing the rural data and as such had to drop that data set.

The monthly demand for chicken refers to the quantity of chicken demanded by households (in

lbs) per month, at the available prices within the specified area. Demand varies from period to

period depending on such factors as religious customs, holidays, seasonality etc. In terms of

religious customs, and using the month of Ramadan as an example, Muslims fast during this

month as such the demand for chicken reduces significantly. On the other hand, during the

Christmas season there is a significant increase in the demand for chicken. The reason being, in

Guyana, Christians, Muslims and Hindus are the three main religious denominations.

Seasonality affects demand in various ways, for instance during slow months, income is low and

demand reduces. Like- wise seasonality affects the availability of cheap substitutes for chicken

such as fish (banga mary). For these reasons, the researcher has chosen to estimate the demand

for chicken during the month of April.

Note Had this research focus on the month of November, which is usually the month of

Ramadan (subject to changes, based on the moon sighting etc) the researcher would have used adummy variable to represent religion.

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.


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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 to apply the theoretical knowledge

learnt in the classroom to real world situations using actual data. More specifically, the

following will be looked at;

To determine what are peoples preferred preference as a substitute for chicken.

To determine various elasticity,( income, cross price and same price) this measures the

responsiveness of the dependent variable to the various independent variables.

To determine if there may be other factors not stated in the model, that affects the

demand for chicken.

In doing 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.1

Note. These steps will be further explained in the model.

1 Koutsoyannis pg 11.


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REVIEW OF LITERATURE

The review of literature consists of two parts;

1. The general Theory of demand.

2. Previous models done and comparisons.

THEORY OF DEMAND

Demand is that quantity of a good that consumers are not only willing to purchase but also

have the capacity to buy at the given price. For example, a consumer may be willing to purchase

2 lb of potatoes if the price is $0.75 per lb. However, the same consumer may be willing to

purchase only 1 lb if the price is $1.00 per lb.2 Wikedia went on to explain that, "Demand" is

the relationship between the price that is charged and the amount that will be bought at that price

and, that Quantity demanded" is the amount that will be bought at a particular given price.

However, price is not the only factor that affects of determines the quantity of a product

demanded. Other factors such as the taste and preferences of consumers, the price of relatedgoods, the 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 good is a substitute (can be used in place of another) or a 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. IE, a negative relationship exists. 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.

2 Wikepedia the free encyclopedia.


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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.

The number of persons or consumers in the market will also affect demand. As the market

increases, demand is likely to increase and as the market decreases the demand will likely fall.

This is so because people must consume to survive, especially if the good under consideration is

a consumer good and, the good is a necessity such as food.

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 works done on demand for consumer

goods, because, only one previous model was found specifically, on the demand for chicken.

The model was basically a checklist to follow in constructing a multiple regression model for the

demand for chicken, including possible variables to use and steps that should be taken in an

econometric research. A copy of this model will be placed in the appendix.


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The other model looked at was a demand for eggs in Australia. IN both models, income and

price were used as independent variables and, for this assignment the researcher has included

those variables (price and income in the model). Additionally theory tells us that the price of

related goods (substitutes or complement) also affects the demand for a product along with the

size of the market. As such, the dependent variables used in this model are;

1. Price of chicken.

2. Price of substitute.

3. Income.

4. The number of persons in the household.

The dependent variable is the quantity of chicken demanded. The model studied were developed

using time series data but because this paper is based on the monthly demand for chicken cross

sectional data is used in this research.

TIME SERIESE DATA. Time series data give information about the numerical values of

variables from period to period. For example the data on gross national income in the period

1950-65 forms a time series on the variable income3

CROSS-SECTIONAL DATA. These data give information on the variables concerning

individual agents (consumers or Producers) at a given point in time. For example a cross section

sample of consumers is a sample of family budgets showing expenditures on various

commodities by each family, as well as information on family income, composition etc.4

In acquiring data for this model, the researcher will be using a questionnaire to gather the data.

Questions will be asked to determine the monthly demand in house-holds, income in the house-

holds, the number of persons that make up the house hold etc.

3 KOutsoyannis pg 17.4 Koutsoyannis pg 17.


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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 (Q) is the dependent variable. The

independent variables are the price of chicken (P), the price of substitutes (Ss) because chicken

is usually substituted with other products such as fish, beef etc ,the income of households (Yd),

The number of persons in the house-holds(N), and other unspecified variables. This is shown in

the following equation;

Q = (P, S, Yd, N .)Where:

Q quantity of chicken demanded.

P Price of chicken. This price will be the price each household pays for a lb of chicken.

S 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.Y 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 Y is going to be used

in the function and its the average income of households will be used.

N => This represents the number of persons in the house-hold. Because is know from theory


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that, market size affects demand.

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 + 1P + 2S + 3LnY+ 4N)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;

Q = 0 + 1P+ 2S + 3LnY + 4N + .

Where 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 theautonomous consumption of chicken/ it represents the demand for chicken when 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.

4 +ve. The reason being, if market the market size increases, the demand is likely to


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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 elasticitys are expected to

be small. On the other hand, if the product is a luxury, the elasticitys are expected to be high.

Therefore for this proposal the elasticitys (income and price) are expected to be small.

Additionally, if the commodities are close substitutes, the cross elasticity will be high.


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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.

Q = 0 +1P +2S + 3LnY + 4 + .

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. (e)

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.


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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 criterias 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 of1 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 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 i.e. E () = ,

minimum variance (the distribution of the estimates around the true line fits tightly) andconsistency (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. Testing for Heteroscedasticity, The Whites Test.


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2. The Ramsey Reset Test. This test is done to determine whether or not the model is

properly specified.

3. Testing for the level of multicollenearity. The VIF Test.

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 errors1

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.


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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 criterias. 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 statistics, the elastic ties etc.

The conclusion follows.


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BIBLIOGRAPHY

BOOKS:

Economics Cambell R. McConnell McGraw-Hill

Principles problems and Policies Stanley L. Brue USA 2002

Theory of Econometrics A. Koutsoyannis Macmillan

London 1977

The World Wide Web:

Wikipedia the free encyclopedia


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B. Hypothesis tests on the overall goodness of fit for the model, evaluating thefollowing hypotheses:

H0: b1 = b2 = ... = bk = 0

Ha: at least one coefficient is not equal to zero.

1. Use an F-test to evaluate the joint significance of all independent variables.

Global Test

bCPIchicken bCPImeats bDPIStep 1: Set uphypotheses to test

H0: bCPIchicken 0Ha: bCPIchicken< 0

H0: bCPImeats 0Ha: bCPImeats> 0

H0: bDPI 0Ha: bDPI> 0

Step 2: Select a

level of significance

= .01

= .01

= .01Step 3: Formulatethe decision rule

Reject H0 if t.01,48/40 2.423

Reject H0 if t.01,48/402.423

Step 4: Calculate thetest statistic

t = -0.661 t = 1.801 t = 5.979

Step 5: Make adecision Since t=-0.661 is not less

than the critical t-value,we cannot reject H0.Thus we are at least 99%confident that bCPIchicken isgreater than or equal tozero.

Since t=1.801 is notgreater than the criticalt-value, we cannot rejectH0. Thus we are at least99% confident thatbCPImeats is less than orequal to zero.

Since t=5.979 greater than thcritical t-value, we careject H0. Thus we arat least 99% confidenthat bDPI is greater thazero.

Step 6: Evaluate thep-value

The 2-tail p-value = .5118indicates that we areonly 74.41% confident

that bCPIchicken is less thanzero.

The 2-tail p-value =0.0780 indicates that weare 96.10% confident

that bCPImeats is greaterthan zero.

The 2-tail p-value 2.70E-07 indicates thawe are virtual

100.00% confident thabDPI is greater thazero.


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Step 1: Set up hypotheses totest

H0: bCPIchicken = bCPImeats = bDPI = 0Ha: at least one coefficient is not equal to zero

Step 2: Select a level ofsignificance

= .01

Step 3: Formulate thedecision rule

Reject H0 if F.01,3, 48/40 > 4.31

Step 4: Calculate the teststatistic

F = 618.15

Step 5: Make a decision Since F=618.15 is greater than the critical t-value, we can rejecH0. Thus we are at least 99% confident that at least onestimated b is not equal to zero.

Step 6: Evaluate the p-value The p-value = 2.46E-38 indicates that we are virtually 100.00confident that at least one estimated coefficient is not equal t

zero.

2. Rejection of H0 implies that at least one of the independent variables addsexplanatory power to the model. Further testing is needed to determine whichone(s).

C. Hypothesis tests on the correlation between the dependent variable and any one of

the independent variables. Perform these tests after the overall goodness of fit Ftest.

1. Remember that each one of these tests is evaluating if the independent variable

in question adds significant explanatory power to the model.

2. The appropriate test statistic to use in this case is a two-tail t-test associatedwith each coefficient.

NOTE: Given the similarity in the tests run for parts A and C, you may want to run boththe one-tail test to evaluate the theoretical relationship and the two-tail test to evaluate theexplanatory power of each independent variable, simultaneously.

bCPIchicken bCPImeats bDPIStep 1: Set uphypotheses to test

H0: bCPIchicken = 0Ha: bCPIchicken 0

H0: bCPImeats= 0Ha: bCPImeats 0

H0: bDPI= 0Ha: bDPI 0

Step 2: Select alevel of significance

= .01 = .01 = .01


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Step 3: Formulatethe decision rule

Reject H0 if |t.01,48/40|>2.704

Reject H0 if |t.01,48/40|>2.704

Reject H0 if |t.01,48/402.704

Step 4: Calculatethe test statistic

t = -0.661 t = 1.801 t = 5.979

Step 5: Make adecision

Since t=-0.661 is notgreater than the criticalt-value, we cannot rejectH0. Thus we are at least99% confident thatbCPIchicken is equal to zero.

Since t=1.801 is notgreater than the criticalt-value, we cannot rejectH0. Thus we are at least99% confident thatbCPImeats is equal to zero.

Since t=5.979 is greatethan the critical t-valuwe can reject H0. Thuwe are at least 99confident that bDPInot equal to zero.

Step 6: Evaluatethe p-value

The 2-tail p-value = .5118indicates that we are only48.82% confident that

bCPIchicken is not equal tozero.

The 2-tail p-value =0.0780 indicates that weare 92.20% confident

that bCPImeats is not equalto zero.

The 2-tail p-value 2.70E-07 indicates thawe are virtually 100.00

confident that bDPIgreater than zero.

Collect the necessary data. If you find there is not an adequate data series for some of theindependent variables, you may now need to respecify the model to include only theestimable variables. Adjust the hypotheses tests in part III as necessary.

V. Perform a regression analysis of the above-specified model.

Per capita consumption of chicken = a + bCPIP*CPIpoultry + bCPIM*CPImeats + bDPI*DPI

1-{ESS/TSS} = R 0.975

1-{[ESS/(n-k-1)]/[TSS/(n-1)]}= AdjustedR 0.973

R 0.987

Std. Error 2.759

52 observations

3 predictor variables

Per capita Consumption of Chicken(pounds) is the dependent variable

ANOVA

Source SS df MS F p-value


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Regression 14,117.8384 3 4,705.95 618.15 2.46E-38

Residual 365.4188 48 7.6129

Total 14,483.2572 51

Regression output

variables coefficients std. error t (df=48) p-value 1-(p-value/2)

intercept 1.5190 3.5288 0.430 .6688 66.56%

CPI Chicken 1982-84=100, changed to1996 base -0.0496 0.0751 -0.661 .5118 74.41%

CPI Meat 1982-84=100, changed to1996 base 0.1901 0.1056 1.801 .0780 96.10%

Per capita DisposablePersonal Income,Chained (1996) dollars 0.0024 0.00040749 5.979 2.70E-07 100.00%

Interpret the results.

A. Determine what each regression coefficient says about the relationship between thedependent variable and the corresponding independent variable.

B. Remember how to interpret the regression coefficients. For a linear model, a one-

unit change in the Xi variable corresponds to a bi unit effect on y, holding the effectsof all of the other independent variables constant.

If CPI of chicken increases by 1%, the per capita consumption ofchicken will decrease by 0.05 pounds. In other words, if the CPI ofchicken increases by 10%, the per capita consumption of chickendecreases by 0.5 pounds, ceteris paribus.

If the CPI of Meat increases by 1%, the per capita consumption ofchicken will increase by 0.19 pounds. In other words, if the CPI ofmeat increases by 10%, the per capita consumption of chicken

increases by 1.9 pounds, ceteris paribus.

If the Per capita Disposable Personal Income increases by 1%, the percapita consumption of chicken will increase by 0.0024 pounds. In otherwords, if the Per capita Disposable Personal Income increases by$1000, the per capita consumption of chicken increases by 2.4 pounds,ceteris paribus.


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C. Interpret the adjusted-R2 regarding the degree to which the model explains thevariation in the dependent variable.

The adjusted R2 is .973, which is very close to 1, explains 97.3% ofthe variation in the dependent variable.

VII. Evaluate the statistical significance of the results.

A. For the individual regression coefficients:

1. Determine if the hypothesized sign was obtained.


t = -0.661 t = 1.801 t = 5.979

Expected sign, givenunderlying economictheory?

Yes Yes Yes

2. Conduct the hypothesis tests and determine, at the appropriate level of significance,whether to reject or not reject the null hypothesis.

Step 5: Make adecision aboutthe postulatedhypotheses

Since t=-0.661 is not lessthan the critical t-value,we cannot reject H0. Thuswe are at least 99%confident that bCPIchicken is

greater than or equal tozero.

Since t=1.801 is notgreater than the critical t-value, we cannot reject H0.Thus we are at least 99%confident that bCPImeats is

less than or equal tozero.

Since t=5.979 is greatethan the critical t-valuwe can reject H0. Thuwe are at least 99confident that bDPI

greater than zero.

Step 5.5:Good economicresults?

No No Yes

3. Evaluate the p-value obtained.

bCPIchicken bCPImeats bDPIStep 6:Evaluatethe p-value

The 2-tail p-value of .5118 indicates that weare only 74.41% confidentthat bCPIchicken is less thanzero.

The 2-tail p-value of0.0780 indicates that weare 96.10% confident thatbCPImeats is greater thanzero.

The 2-tail p-value of 2.70E-0indicates that we are virtual100.00% confident that bDPIgreater than zero.


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B. Evaluate the F-stat and determine the overall significance of the model.


F = 618.15

Step 5: Make a decision Since F=618.15 is greater than the critical t-value, we ca

reject H0. Thus we are at least 99% confident that at least onestimated b is not equal to zero.

Step 6: Evaluate the p-value The p-value = 2.46E-38 indicates that we are virtually 100.00confident that at least one estimated coefficient is not equal tzero.

C. After using the F-test to reject H0, assess which of the independent variablescontribute significantly to the models ability to explain the variation in the dependentvariable.

Step 4:Calculatethe teststatistic

t = -0.661 t = 1.801 t = 5.979

Step 5:Make adecision

Since |t|=0.661 is notgreater than the critical t-value, we cannot reject H0.Thus we are at least 99%confident that bCPIchicken is

equal to zero.

Since t=1.801 is notgreater than the critical t-value, we cannot reject H0.Thus we are at least 99%confident that bCPImeats is

equal to zero.

Since t=5.979 is greater thathe critical t-value, we careject H0. Thus we are at leas99% confident that bDPI is noequal to zero.

Step 6:Evaluatethe p-value

The 2-tail p-value = .5118indicates that we are only48.82% confident thatbCPIchicken is not equal tozero.

The 2-tail p-value = 0.0780indicates that we are92.20% confident thatbCPImeats is not equal to zero.

The 2-tail p-value = 2.70E-0indicates that we are virtual100.00% confident that bDPIgreater than zero.

STEPS?

Several options may now be pursued.

Rerun the existing regression equation after omitting the least statistically-significantindependent variable. This process may be continued until all regression coefficientshave the expected sign and are statistically significant.

Re-specify the models underlying functional form, and rerun the regression. You maywant to use non-linear transformation of your model, especially since many economic


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relationships are better specified by a non-linear form. Perhaps the most frequently-usedtransformation is the double-log transformation.

Test the regression results for statistical problems, such as multicollinearity andmisbehaved residual patterns.

Which is the best model?

Determining the answer to this question is truly more of an art than a science. Given the natureof econometric analysis, the first priority should be the signs obtained on the regressioncoefficients.

If they correspond to what is predicted by the underlying economic theory, thecoefficients then should be tested for statistical significance.

finally, compare the adjusted R2 values across the functionally-identical models. Thebest model is the one with the highest adjusted R2 assuming that you have obtained similarlygood results on the regression coefficients.

.

An Econometric Analysis of the Demand for Eggs in Australia*

Edward Oczkowski - School of Management,Charles Sturt University Riverina, PO Box 588, Wagga Wagga, NSW, 2678, Australia.Phone: +61 2 69332521 Fax: +61 2 69332125 E-mail: [email protected]
mailto:[email protected]:[email protected]


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and Tom Murphy - Director, Western Research Institute,c/o Charles Sturt University, Panorama Ave, Bathurst, NSW, 2795, Australia.Phone: + 61 2 63384435 Fax: +61 2 63384699 Email: [email protected]

* Funding for this study was provided by the Rural Industries Research and Development

Corporation (Australia). The assistance of Hugh McMaster is gratefully acknowledged for thecollation egg industry data. Comments from a referee and the editors are also gratefullyacknowledged

Abstract

This paper provides the first comprehensive econometric analysis of Australian State eggdemand behavior. Explicit diagnostic testing of models is employed to help gain robust demandelasticities. Demand is found to be own price and income inelastic, with price elasticity being

effectively zero for the majority of states. Prices of related products tend to have only a minoroverall influence. The proportion of paid working females is statistically important for themajority of states. A worldwide cholesterol information index appears to capture the healthconcerns held about egg consumption. Interestingly, results for advertising expenditure aremixed with both significant and insignificant effects identified.

Keywords: egg demand, econometric modeling, demand elasticities, cholesterol healthconcerns, advertising expenditure.
mailto:[email protected]:[email protected]


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QUESTIONNAIRE

This questionnaire is being done for an assignment determining, the demand for

chicken. You do not need to place your name on it.

1. What area do you reside in? Rural Urban

2. As a substitute for chicken, what is your preference?Beef Fish Other

3. How many lbs of the substitute do you consume per month?.........

4. What price do you pay per lb for the substitute?.............................

5. How many pounds of chicken do you consume in an averagemonth? Not the amount you consume during the holiday.

6 How much does a pound of chicken cost you?.................................

7. What is your monthly take home salary?Zero - $10,000 $11,000 - $20,000 $21,000 - $30,000$31,000 - $40,000 $41,000 - $50,000 $51,000 - $100,000Over $100,000

8. How many persons make up your household?..................................


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PART 2

DATA COLLECTION AND TREATMENT OF DATAAs was stated in the proposal, for this research, a questionnaire was used to gatherinformation for this assignment. The following is the data set.

AREA SUBSTITUTE PRICE OFSUBSTITUTE

QUANTITYOF

CHICKENDEMANDED

PRICE

OFCHICKEN INCOMERANGE

NUMBEROFPERSONSIN

HOUSE-HOLD AVERAGEINCOME

Urban Fish 180 6 200 41 -50 1 41 50 45.5

Urban Fish 125 30 260 100 and over 4 100 150 125


Urban beef 190 70 200 100and over 12 100 150 125

Urban beef 280 15 220 50 - 100 2 50 100 75

Urban Fish 100 10 200 31 -40 1 31 40 35.5


Urban Fish 100 20 200 50 - 100 2 50 100 75

Urban Fish 180 20 180 50 - 100 5 50 100 75

Urban Fish 100 60 180 50 - 100 4 50 100 75

Urban other/mutton 400 50 200 100 and over 7 100 150 125

Urban other/chunks 348 2 200 31 - 40 1 31 40 35.5

Urban Fish 100 16 240 41 - 50 3 41 50 45.5

Urban Fish 100 20 240 41 -0 50 3 41 50 45.5

Urban Fish 100 20 200 41 - 50 5 41 50 45.5

Urban beef 220 24 240 100 and over 8 100 150 125


Urban other/mix 300 20 200 41 - 50 4 41 50 45.5

Urban beef 240 40 200 31 -40 4 31 40 35.5

Urban Fish 300 60 240 50 - 100 6 50 100 75

Urban Fish 180 8 260 41 - 50 3 41 50 45.5

Urban Fish 100 30 220 41 - 50 3 41 50 45.5

Urban Fish 100 4 240 21 - 30 4 21 30 25.5Urban Fish 100 28 240 31 - 40 1 31 40 35.5

Urban Fish 190 8 260 31 - 40 4 31 40 35.5

Urban beef 240 30 200 100 and over 4 100 150 125

Urban Fish 180 20 200 41 - 50 4 41 50 45.5

Urban other/pork 300 30 220 50 - 100 6 50 100 75

Urban Fish 180 10 240 under 20 2 11 20 15.5

Urban other/mix 200 40 200 31 - 40 4 31 40 35.5



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Urban Fish 180 15 220 50 - 100 3 50 100 75


Urban Fish 200 16 220 50 - 100 3 50 100 75

From the data above, it can be seen that most persons prefer fish as a substitute for chicken. Ofcourse there are reasons for this. The main reasons are religious persuasions and persons arebecoming more health conscious and are using more white meat as against red meat.

UNRESTRICTED DATA SET AS TAKEN FROM SAMPLE (QUESTIONNAIRE)

obs Q P PS Y N

1 6 200 180 45.5 12 30 260 125 125 43 40 220 180 125 34 70 200 190 125 125 15 220 280 75 26 10 200 100 35.5 17 25 220 300 125 18 20 200 100 75 29 20 180 180 75 510 60 180 100 75 411 50 200 400 125 712 2 200 348 35.5 113 16 240 100 45.5 3

14 20 240 100 45.5 315 20 200 100 45.5 516 24 240 220 125 817 40 200 100 125 418 20 200 300 45.5 419 40 200 240 35.5 420 60 240 300 75 621 8 260 180 45.5 322 30 220 100 45.5 323 4 240 100 25.5 424 28 240 100 35.5 125 8 260 190 35.5 426 30 200 240 125 427 20 200 180 45.5 428 30 220 300 75 629 10 240 180 15.5 230 40 200 200 35.5 431 40 200 100 125 432 25 220 360 125 433 15 220 180 75 334 40 200 200 125 735 16 220 200 75 3


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EQUATION

Dependent Variable: QMethod: Least SquaresDate: 05/15/06 Time: 14:29Sample: 1 35Included observations: 35

Variable Coefficient Std. Error t-Statistic Prob.

P -0.164856 0.095774 -1.721296 0.0955PS -0.016965 0.024841 -0.682929 0.4999Y 0.129550 0.062503 2.072687 0.0469N 3.605258 1.043634 3.454522 0.0017C 41.99815 22.49397 1.867084 0.0717

R-squared 0.531303 Mean dependent var 26.62857

Adjusted R-squared 0.468810 S.D. dependent var 16.57263S.E. of regression 12.07859 Akaike info criterion 7.952310Sum squared resid 4376.773 Schwarz criterion 8.174503Log likelihood -134.1654 F-statistic 8.501810Durbin-Watson stat 2.024073 Prob(F-statistic) 0.000104

GRAPHING THE DEPENDENT AND INDEPENDENT VARIABLES

0

20

40

60

80

0

100

200

300

400

500

5 10 15 20 25 30 35

Q

P

PS

Y

N

LOGGING THE VARIABLE INCOME/ DATA SET


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Q P PS Y N1 6.000000 200.0000 180.0000 3.817712 1.0000002 30.00000 260.0000 125.0000 4.828314 4.0000003 40.00000 220.0000 180.0000 4.828314 3.000000

4 70.00000 200.0000 190.0000 4.828314 12.000005 15.00000 220.0000 280.0000 4.317488 2.0000006 10.00000 200.0000 100.0000 3.569533 1.0000007 25.00000 220.0000 300.0000 4.828314 1.0000008 20.00000 200.0000 100.0000 4.317488 2.0000009 20.00000 180.0000 180.0000 4.317488 5.00000010 60.00000 180.0000 100.0000 4.317488 4.00000011 50.00000 200.0000 400.0000 4.828314 7.00000012 2.000000 200.0000 348.0000 3.569533 1.00000013 16.00000 240.0000 100.0000 3.817712 3.00000014 20.00000 240.0000 100.0000 3.817712 3.00000015 20.00000 200.0000 100.0000 3.817712 5.00000016 24.00000 240.0000 220.0000 4.828314 8.000000

17 40.00000 200.0000 100.0000 4.828314 4.00000018 20.00000 200.0000 300.0000 3.817712 4.00000019 40.00000 200.0000 240.0000 3.569533 4.00000020 60.00000 240.0000 300.0000 4.317488 6.00000021 8.000000 260.0000 180.0000 3.817712 3.00000022 30.00000 220.0000 100.0000 3.817712 3.00000023 4.000000 240.0000 100.0000 3.238678 4.00000024 28.00000 240.0000 100.0000 3.569533 1.00000025 8.000000 260.0000 190.0000 3.569533 4.00000026 30.00000 200.0000 240.0000 4.828314 4.00000027 20.00000 200.0000 180.0000 3.817712 4.00000028 30.00000 220.0000 300.0000 4.317488 6.00000029 10.00000 240.0000 180.0000 2.740840 2.00000030 40.00000 200.0000 200.0000 3.569533 4.00000031 40.00000 200.0000 100.0000 4.828314 4.00000032 25.00000 220.0000 360.0000 4.828314 4.00000033 15.00000 220.0000 180.0000 4.317488 3.00000034 40.00000 200.0000 200.0000 4.828314 7.00000035 16.00000 220.0000 200.0000 4.317488 3.000000

EQUATION


Variable Coefficient

Std. Error t-Statistic Prob.


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P -0.153404

0.096642 -1.587351 0.1229

PS -0.016409

0.024825 -0.661002 0.5137

Y 8.636488 4.201619 2.055514 0.0486N 3.655260 1.035864 3.528707 0.0014C 12.88895 28.78815 0.447717 0.6576

R-squared 0.530332 Mean dependentvar

26.62857

Adjusted R-squared

0.467710 S.D. dependentvar

16.57263

S.E. of regression

12.09110 Akaike infocriterion

7.954379

Sum squared

resid

4385.839 Schwarz criterion 8.17657

2Log likelihood -

134.2016F-statistic 8.46873

3Durbin-Watsonstat

1.988351 Prob(F-statistic) 0.000107

ADJUSTED DATA SET/ FISH PREFERENCE ONLY

1 6.000000 200.0000 180.0000 45.50000 1.0000002 30.00000 260.0000 125.0000 125.0000 4.0000003 40.00000 220.0000 180.0000 125.0000 3.0000004 10.00000 200.0000 100.0000 35.50000 1.0000005 25.00000 220.0000 300.0000 125.0000 1.0000006 20.00000 200.0000 100.0000 75.00000 2.0000007 20.00000 180.0000 180.0000 75.00000 5.0000008 60.00000 180.0000 100.0000 75.00000 4.0000009 16.00000 240.0000 100.0000 45.50000 3.00000010 20.00000 240.0000 100.0000 45.50000 3.00000011 20.00000 200.0000 100.0000 45.50000 5.00000012 40.00000 200.0000 100.0000 125.0000 4.00000013 60.00000 240.0000 300.0000 75.00000 6.00000014 8.000000 260.0000 180.0000 45.50000 3.00000015 30.00000 220.0000 100.0000 45.50000 3.00000016 4.000000 240.0000 100.0000 25.50000 4.00000017 28.00000 240.0000 100.0000 35.50000 1.00000018 8.000000 260.0000 190.0000 35.50000 4.00000019 20.00000 200.0000 180.0000 45.50000 4.00000020 10.00000 240.0000 180.0000 15.50000 2.00000021 40.00000 200.0000 100.0000 125.0000 4.00000022 25.00000 220.0000 360.0000 125.0000 4.000000


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23 15.00000 220.0000 180.0000 75.00000 3.00000024 40.00000 200.0000 200.0000 125.0000 7.00000025 16.00000 220.0000 200.0000 75.00000 3.000000

EQUATION



P -0.0765356203786

0.113656254095

-0.673395590837

0.508403390493

PS -0.0227819282428

0.0385093702983

-0.591594411083

0.560750392138

Y 0.195867254046

0.0785747016531

2.49275211901

0.0215645483618

N 3.17316112491

1.76410368176

1.79873845155

0.0871703849646

C 20.2610882421

26.7465309028

0.757522099436

0.457570139867

R-squared 0.445719264445

Mean dependent var 24.44

Adjusted R-squared 0.334863117334

S.D. dependent var 15.3

S.E. of regression 12.478056

4538

Akaike info criterion 8.062676

68457Sum squared resid 3114.0378

5727Schwarz criterion 8.306451

84954Log likelihood -

95.7834585571

F-statistic 4.02069958284

Durbin-Watson stat 2.63027529716

Prob(F-statistic) 0.0149371289881

LOG VARIABLE INCOME/DATA SET

obs Q P PS Y N1 6.000000 200.0000 180.0000 3.817712 1.0000002 30.00000 260.0000 125.0000 4.828314 4.0000003 40.00000 220.0000 180.0000 4.828314 3.0000004 10.00000 200.0000 100.0000 3.569533 1.0000005 25.00000 220.0000 300.0000 4.828314 1.0000006 20.00000 200.0000 100.0000 4.317488 2.000000


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7 20.00000 180.0000 180.0000 4.317488 5.0000008 60.00000 180.0000 100.0000 4.317488 4.0000009 16.00000 240.0000 100.0000 3.817712 3.00000010 20.00000 240.0000 100.0000 3.817712 3.00000011 20.00000 200.0000 100.0000 3.817712 5.00000012 40.00000 200.0000 100.0000 4.828314 4.00000013 60.00000 240.0000 300.0000 4.317488 6.00000014 8.000000 260.0000 180.0000 3.817712 3.00000015 30.00000 220.0000 100.0000 3.817712 3.00000016 4.000000 240.0000 100.0000 3.238678 4.00000017 28.00000 240.0000 100.0000 3.569533 1.00000018 8.000000 260.0000 190.0000 3.569533 4.00000019 20.00000 200.0000 180.0000 3.817712 4.00000020 10.00000 240.0000 180.0000 2.740840 2.00000021 40.00000 200.0000 100.0000 4.828314 4.00000022 25.00000 220.0000 360.0000 4.828314 4.00000023 15.00000 220.0000 180.0000 4.317488 3.00000024 40.00000 200.0000 200.0000 4.828314 7.00000025 16.00000 220.0000 200.0000 4.317488 3.000000

EQUATION

Dependent Variable: QMethod: Least Squares

Date: 05/15/06 Time: 15:27Sample: 1 25Included observations: 25


P -0.054258 0.115587 -0.469411 0.6439PS -0.021425 0.037998 -0.563846 0.5791Y 13.28684 5.200185 2.555072 0.0189N 3.032419 1.765897 1.717212 0.1014C -25.15723 36.54847 -0.688325 0.4992

R-squared 0.452292 Mean dependent var 24.44000Adjusted R-squared 0.342750 S.D. dependent var 15.30000S.E. of regression 12.40385 Akaike info criterion 8.050748Sum squared resid 3077.111 Schwarz criterion 8.294523

Log likelihood -95.63435 F-statistic 4.128952Durbin-Watson stat 2.605193 Prob(F-statistic) 0.013417

PART 3


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REPORTING AND COMMENTING ON FINDINGS.

The results from the unrestricted data set, i.e. the sample of 35 give the best results. Therefore

the researcher will be using this model to further explain the work done in this assignment.

The results from the unrestricted data set (sample size 35) with income log is as follows

SIGNS OF COEFFICIENTS

The expected signs of the coefficients according to the theory of demand are;

.price -ve

Price of substitute +ve

Income +ve

Number in household (market size) +ve.

In running the regression, all signs other than the price of the substitute confer to theory. I.e.

The price of substitute is negative and, theory states that this is suppose to be positive.

STATISTICAL SIGNIFICANCE OF INDEPENDENT VARIABLES.

This is based on the t test. The level of significance is 5%.

Should the t statistics fall below 1.96, the variable is not statistically significant to the model.

It therefore means that only income and number of persons in the house-hold are significant to

this model. This is a problem based on theory because; the theory states that price and price of

substitutes are suppose to be significant to this model.

R2 and Adjusted R2

The results from the regression are .530332 and .467710 respectively. This shows that the

independent variables only explained 53% and $6% respectively of the total variations in Q , the

dependent variables. This is not a very good model according to theory.


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Time: 04:58Sample: 1 35

Q P S Y N

Mean 26.62857 216.5714 192.9429 4.159708 3.885714

Median 24.00000 220.0000 180.0000 4.317488 4.000000Maximum 70.00000 260.0000 400.0000 4.828314 12.00000Minimum 2.000000 180.0000 100.0000 2.740840 1.000000Std. Dev. 16.57263 21.95488 86.49820 0.568888 2.246192Skewness 0.776432 0.479311 0.641109 -0.303403 1.424182Kurtosis 3.125987 2.279217 2.504464 2.258522 6.234528

Jarque-Bera 3.539757 2.097787 2.755726 1.338757 27.08905Probability 0.170354 0.350325 0.252117 0.512027 0.000001

Observations 35 35 35 35 35

The basic stat essentially measures the quality of the data. It suggests whether or not it is good

for research purposes. In analyzing this, the researcher is looking for low standard deviation

which would indicate minimal spread around the mean. In addition measures of central

tendency are also crucial in determining the overall variation of the data. The minimum and

maximum value also gives some idea of the spread of the data, in terms of if there are outliers

within the data set.

STANDARD DEVIATION

The standard deviation of the variables income(y) and number of persons in the house-holds (N)

shows that these variables have minimal spread around their mean. However the price of

chicken and even more so the prices of substitutes are widely dispersed around their individual

means. In terms of the price of substitute, this may be because this sample represents a

collection of prices for various substitutes and not a single substitute. Additionally the prices for

the same substitute also vary depending on the consumer taste and preference.


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The range as calculated by the difference between the minimum and maximum values has large

variations according to the results. This also will reflect dispersions in the data around its mean.

Because of the problems in the above model, the researcher will have to run a number of tests.

The first being, the Ramsey-Reset Test.

The Ramsey Reset Test

Ramsey RESET Test:

F-statistic 0.818963 Probability 0.524830Log likelihood ratio 4.153329 Probability 0.385653

Test Equation:Dependent Variable: QMethod: Least SquaresDate: 05/18/06 Time: 12:32Sample: 1 35Included observations: 35


P 0.665434 1.511622 0.440212 0.6634S 0.071455 0.161910 0.441327 0.6626Y -35.42880 84.65438 -0.418511 0.6790

N -15.65992 36.36638 -0.430615 0.6703C -33.86363 96.67147 -0.350296 0.7289FITTED^2 0.265799 0.886523 0.299822 0.7667FITTED^3 -0.003599 0.034651 -0.103876 0.9181FITTED^4 -3.28E-05 0.000603 -0.054386 0.9570FITTED^5 6.65E-07 3.80E-06 0.175259 0.8622

R-squared 0.582886 Mean dependent var 26.62857Adjusted R-squared 0.454543 S.D. dependent var 16.57263S.E. of regression 12.23972 Akaike info criterion 8.064284Sum squared resid 3895.080 Schwarz criterion 8.464231Log likelihood -132.1250 F-statistic 4.541638Durbin-Watson stat 1.971681 Prob(F-statistic) 0.001499

Since the F statistics (5% confidence level) is less than theoretical value, it can be seen that there

is no specification error in this model.


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Heteroskedasticity

White Heteroskedasticity Test:

F-statistic 0.847804 Probability 0.617563Obs*R-squared 13.03526 Probability 0.523749

Test Equation:Dependent Variable: RESID^2Method: Least SquaresDate: 05/18/06 Time: 12:45Sample: 1 35Included observations: 35


C 9032.560 6567.031 1.375440 0.1842P -60.22565 39.42761 -1.527499 0.1423P^2 0.084956 0.078409 1.083492 0.2915P*S 0.060580 0.030420 1.991476 0.0603P*Y 2.603498 4.067264 0.640111 0.5294P*N 0.344501 1.374225 0.250688 0.8046S -14.49305 7.780961 -1.862629 0.0773S^2 0.000858 0.005335 0.160888 0.8738S*Y 0.201023 1.058469 0.189919 0.8513S*N 0.139012 0.297058 0.467962 0.6449Y -334.2285 1531.484 -0.218238 0.8295Y^2 -49.49193 129.2641 -0.382875 0.7059

Y*N 10.64195 65.69186 0.161998 0.8729N -111.3905 325.3656 -0.342355 0.7357N^2 -1.711451 7.358404 -0.232585 0.8184

R-squared 0.372436 Mean dependent var 125.3097Adjusted R-squared -0.066859 S.D. dependent var 187.8544S.E. of regression 194.0327 Akaike info criterion 13.67146Sum squared resid 752973.6 Schwarz criterion 14.33803Log likelihood -224.2505 F-statistic 0.847804Durbin-Watson stat 2.136863 Prob(F-statistic) 0.617563

At the 5% confidence level, the calculated value is less than the table value. As such we

conclude that, there is no heteroskedasticity

.


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Multicollinearity

(a) Regressing P on S Y and N, the following is the regression.

Dependent Variable: PMethod: Least SquaresDate: 05/18/06 Time: 13:11Sample: 1 35Included observations: 35


S -0.012764 0.046528 -0.274336 0.7856Y -0.069893 0.116538 -0.599749 0.5530N -0.490213 1.955140 -0.250730 0.8037C 226.1172 11.40480 19.82649 0.0000


From this it can be seen that there is not a problem with multicollinearity because the VIF, which

is measured by 1/ (1-R2) is less than 5. I.e. the actual figure is 1.03.

(b) Regressing S on P Y and N, the following is the regression,

Dependent Variable: SMethod: Least SquaresDate: 05/18/06 Time: 13:20Sample: 1 35Included observations: 35


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P -0.189737 0.691623 -0.274336 0.7856Y 0.461762 0.444231 1.039462 0.3066N 3.198235 7.523715 0.425087 0.6737C 187.3971 159.1135 1.177757 0.2479


As such it can be seen that there is no problem with multi i.e. 1/ (1 r2) = 1.07. This value is

less than 5.

Regressing Y on P S and N, the following is the regression

Dependent Variable: YMethod: Least SquaresDate: 05/18/06 Time: 13:26Sample: 1 35Included observations: 35


P -0.164108 0.273628 -0.599749 0.5530S 0.072939 0.070170 1.039462 0.3066N 7.158324 2.709346 2.642085 0.0128C 67.73865 63.48190 1.067054 0.2942


As such it can be seen there is no problem with multi. The reason being the VIF is lees than 5.

1/ (1 R2) = 1.33.


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(d) Regressing N on P S and Y

Dependent Variable: NMethod: Least SquaresDate: 05/18/06 Time: 13:32

Sample: 1 35Included observations: 35


P -0.004128 0.016466 -0.250730 0.8037S 0.001812 0.004263 0.425087 0.6737Y 0.025676 0.009718 2.642085 0.0128C 2.528011 3.844404 0.657582 0.5157


From this regression, it can be seen that there is not a problem with multicollinearity. The reason

being, the VIF is under 5. 1/ (1-R2) = 1.2.


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CONCLUSION

After running all the above test and reporting on the results, the only possible reason for low a

low R2 and un-satisfactory ts for Price of chicken and the price of substitute (S) has to be omitted

variables. It is known from theory that, here are many factors that affects the demand for

products. Some of them are not even quantifiable as such cannot be properly represented in a

mathematical model. Omitted variables will cause biasness and as such reduce the t values. In

concluding, this model represents the major determinants for the demand for chicken in urban

areas of Guyana. But there are also other factors, such as religion, etc that are not reflected in

this model.


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