# Introductory econometrics.

Essay by iamdon79University, Bachelor'sC+, November 2003

introductory econometrics

(Textile and textile industry)

Q1:

Present your data in a table giving precise definitions and sources for each variable plus brief footnote

QDD

(ÃÂ£m)POPN

(k)P-PRICE R-PRICE GDP

(ÃÂ£m)QTYPCTA RELPRICE INCPCPA DUMMY

514056,330100.066.8229,5830.911.497061.01320

491856,357104.574.8252,2440.841.463959.83720

506856,298110.481.2275,8510.821.453260.34280

543956,328116.484.9301,5240.831.465363.05071

614056,432123.189.2323,0980.881.480964.18651

664856,567129.694.6354,2290.911.473666.19571

678856,699135.497.8380,5970.881.486768.63591

757156,850141.8101.9418,2210.941.481872.19401

793056,970149.3106.9466,5200.931.476176.60311

794257,248156.2115.2511,8890.891.428077.61811

764857,436164.0126.1554,4860.811.380776.55811

738457,472174.5133.5582,9460.741.374575.97851

754457,593180.2138.5606,5820.731.371176.04491

Annual demand for textile and textile industry 1980-1992

QDD: Annual Demand for Good Y (textile and textile industry)

POPN: Population

P-PRICE: Producer Price for textile and textile industry; all Converted to base 1980 price as 100

R-PRICE: Retail price for all Goods; all Converted to base Jan 1987 price as 100

GDP: GDP at current price

QTYPCTA: Per Capita Consumption of Good Y

(Total Demand for Goods in money term/ Producer Price / Population)

RELPRICE: Relative Price (producer price/ retail price)

INCPCPA: Real Income per Capita (GDP at current price/retail price/population)

DUMMY: Dummy Variable (1 for last ten years; 0 for the rests)

This is the annual demand table for textile and tixtile industry from 1980 to 1992, as relative figures after 1992 could not be found in Annual Abstracts of Statistics of the U.K.

(I got he agreement from Dr Sam Cameron that I can reduce my year)

P.S. 1. The data for annual demand for Good Y in annual abstract is described in money term, so it

is divided by the producer price to get the unit term data.

2. Relative Price is the price of Good Y as ratio of Price of other Goods, so it is calculated as

producer price /retail price.

3. GDP (at current price) is divided by retail price to eliminate the effect of inflation.

Q2.1

The estimated equation goes as followed:

Y=b0+b1X1t+b2X2t-b3X3t+Ut

qtypcta = 0.08619 + 0.642relprice - 0.00236incpcta+ 0.05781dummy + Ut

Q2.2

Present your results in a table, which shows the coefficients with standard errors

in brackets, sample size and R squared.

CoefficientSample sizeR squared

constant

Relprice

Incpcta

dummy0.08619(0.424)

0.642 (0.257)

0.00236(0.003)

0.05781(0.059)

13(1980-1992)

0.429

Q2.3

State the expectations for the signs of b0, b1, b2, b3 that economic theory would predict

b0+-It is depends on the best fit line, it may be negative or positive

b1-In line with demand theory, the higher the price of the good in relation to other goods, the lower the consumption of that good. It is negative.

b2+In line with demand theory, the higher the income, the higher and the consumption. It is positive.

b3+-It is the coefficient of dummy variable; the dummy represents a structural break into the economic behavioural relationship. There is no enough information to expect it. It may be positive, neutral or negative.

Q2.4

Using your results from (i) test separately each of the following hypotheses at the 5% level on

(a) H0:b0=0

(b) HO:b2=0

(c) HO: b3=0

(d) HO: b1=0

a) Compare the significance that SPSS provide to the significance level of 5%.significanceb0 =84.4%

84.4% > 5%, hence accept H0, reject H1, b0 is not different from zero.

b) Compare the significance that SPSS provide to the significance level of 5%. b1 =3.4%

3.4 %< 5%, so accept H1, reject H0, b1 is different from zero.

c) Compare the significance that SPSS provide to the significance level of 5%. b2 =51.5%

51.5%>5% hence accept H0, reject H1, b2 is not different from zero.

d) Compare the significance that SPSS provide to the significance level of 5%. b3 =31.5%

35.1%>5%, so accept H1, reject H0, b3 is not different from zero.

Q2.5

Test the hypothesis

H0: b1=b2=b3=0

at the 1 % level

Significance of whole equation is 15.1%>1%, so there is no evidence to reject H0

Q3.1

The equation is followed as below:

Log(Y) = logb0-b1 (logX1t) + b2 (logX2t) +b3X3t+Ut

Log(Y) = log0.294-1.088 (logX1t) -0.202(logX2t) +0.06838X3t+Ut

Q3.2

Present your results in a table which shows the coefficients with standard errors

in brackets, sample size and R squared.

CoefficientSample sizeR squared

constant

Relprice

Incpcta

dummy0.294(1.175)

1.088 (0.424)

-2.02(0.283)

0.06838 (0.07)

13(1980-1992)

0.444

Q3.3

State the expectations for the sign of b0, b1, b2, b3 that economic theory would predict

b0+Bo could be positive or negative as there is no economics theory to support it.

(The constant could be negative, because it is the logarithm of b0. it will happen if the b0 is less than the logarithm base.)

b1-In line with demand theory, the higher the price of the good in relation to other goods, the lower the consumption of that good. It is negative.

b2+In line with demand theory, the higher the income, the higher and the consumption. It is positive.

b3+-It is the coefficient of dummy variable; the dummy represents a structural break into the economic behavioural relationship. There is no enough information to expect it. It may be positive, neutral or negative.

Q3.4

Using your results from (i) test separately each of the following hypotheses at the 10% level

(a)H0: b1=1

H1: b1 not equal to 1

(b)H0: b2=1

H1: b2 <1

(c) H0: b3=0

H0: b3>0

a). H0. b1=1. h1: b1Ã¢Â 1

t b1= (1.088-1)/0.424=0.208

Critical value=1.83.

Because 0.208 is between -1.83 and 1.83, so accept H0

b). H0. b2=1. h1 b2<1

t b2= -0.202-1/0.283= -3.513

Critical value=1.38

-3.513<-1.38, so reject H0

c). H0: b3=0 h1: b3 >0

Get from spss, t b3=0.978

Critical value=1.38

0.978<1.38, so accept H0

Q3.5

Test the hypothesis

H0: b1=b2=b3=0

at the 1 % level

Significance of whole equation is 13.6%>1%, so there is no evidence to reject H0

Q4.

Summary

All of the data were chosen from Annual Abstract of Statistics, it shows textile Industries from 1980 to 1992. The data table and the analysis result from the computer had been attached in appendix. In this assessment, it uses linear equation and non-linear equation to estimate the relationship between explanatory variable and independent variable.

In question 2, the equation is estimated in linear form. Through the computer analysis and t test, I found the line described by the equation does not fit very well. Except the significance of b 1, the significances of all the other three variables are greater than 5% significance level. I use F-test to test the whole equation, in this test, I accept H1, reject H0, it means that there is a relationship between the explanatory variable and independent variable.

I also calculated the elasticity of relative price, real income (per capita) and quantity of the good (per capita). The way of calculation is explained as below:

The formula of elasticity is: b*x/y, x and y are the mean of variable, b is the coefficient of the variable. If the elasticity of relative price is greater than 1, it will be elasticity. If the elasticity of real income is greater than 1, it will be elasticity.

Question 3 is a non-linear equation, in order to convert it into linear equation, I took the nature log on both side of this equation. I used two tail test to test b1, I accept H0, b1 is possible to be1, while I used one tailed test to test b2, and I accept H1, reject H0, b2 is less than 1.The one tailed test to test b3 tell us that H0 is accepted, b3 is not different from zero. I use the F test to test the whole equation, I accept H1, reject H0. It means that there is a strong relationship between the explanatory variable and independent variable.

In this log equation, the coefficient also means the elasticity. In the other words, the elasticity of relative price is 1.088, it is greater than 1, it is elastic; the elasticity of real income is -0.202 less than 1, it is inelastic.

The sample size is 13, it is not very big, and will affect the accuracy of the estimation. The more data will improve the accuracy. In addition, a large spread of values of explanatory variable improves accuracy of estimation.

Regression

Regression