Factors affecting quantity of new cars sold foreign trade university students

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1. FOREIGN TRADE UNIVERSITY INTERNATIONAL ECONOMICS FACULTY o0o ECONOMETRICS FINAL EXAM TOPIC: FACTORS AFFECTING QUANTITY OF NEW CARS SOLD FOREIGN TRADE UNIVERSITY STUDENTS Class : K57 JIB Lecturer : Ms. Tu Thuy Anh Ms. Chu Mai Phuong Group : 16 Members : Dao Thi Kim Linh - 1815520187 Mai Thanh My Linh - 1815520189 Nguyen Thi Ha Vy - 1815520239 HaNoi – 10/2019
2. Introduction The market of car in US remains fiercely competitive from the beginning in the late 1890s until now. Beginning in the 1970s, a combination of high oil prices and increased competition from foreign auto manufacturers severely affected the car companies in US. Therefore, it is necessary to investigate the car industry in the period of time in 1970s to understand not only the car market but also the market operation as a whole. In this research we want to investigate the six variables which seem to have impact on the number of car in US from 1975 to 1990. This result can contribute to the judgement on the car industry in US. Moreover, it helps to strength the theory of the relationship between macroeconomic and microeconomic factors and the quality of product sold. The research has use the quantitative method and has the following structure: Part 1: Data description Part 2: Econometrics model Part 3: Robustness check Part 4: Result table
3. TABLE OF CONTENT I. Abstract 1 II. Literature Review 2 III. Methodology 5 IV. Theoretical background 6 V. Data description 10 1. Variables table 10 2. Data description 10 3. Correlation matrix 11 VI. Econometrics model 13 1. Population regression function (PRE) 13 2. Sample of regression function (SRF) 13 3. Result 13 4. Meaning of coefficient 14 5. Testing a hypothesis relating to a regression coefficient 15 6. Adjusted regression model 18 VII. Robustness check 20 1. Multi-collinearity 20 2. Heteroskedasticity 22 3. Normality 23 4. Autocorrelation 24 VIII. Result table 26 IX. Conclusion 28 X. References 29 XI. Appendix 30
4. I. Abstract This research investigates the relationship between microeconomic, macroeconomic variables and number of cars sold in US. The main objective is to determine the factors that affecting the number of car sold in US. This research covers the time period from 1975 to 1990. The analysis methods that have been applied in this study include descriptive statistics, linear regression and correlation analysis. The findings show that price, income have positive relationship with the number of car sales in US, while the prime interest rate and population have negative relationship with the number of car sales in US. The income has the most influence on the quantity of car sold while the population has unreliable effect on it. However, the gap in impact on number of cars sold among four factors is not huge. The findings were consistent with the previous findings done by other researcher. 1
5. II.Literature Review There are many researches that investigated the relationship between quantity of car sold and its determined factors all around the world. Our research focuses on the relation between number of car sold in US and six variables including Price index, Prime interest rate, Income, Unemployment rate, Stock, Population. In the research process, there are some studies which share the same common with objects to our studies’. We present them here below. In 2010, Faculty of Mechanical Engineering, Industrial Engineering and Computer Sciences in School of Engineering and Natural Sciences University of Iceland performed a study called The Effects of Changes in Prices and Income on Car and Fuel Demand in Iceland. It examined the elasticities of demand for fuel and cars in Iceland will be examined, both with a common classical reversible demand model and also with an irreversible model, in order to examine asymmetric effects from variables influencing the demands. It constructed both reversible and reversible models for the demand of new cars and then used regression analysis on these models. The econometrics results showed that income has a great impact on the demand for new cars in Iceland. Increase in income has much more effect on the purchase of new cars than the size of the car fleet, which means that more new cars come into the fleet and more old ones go out when income increases. So that the car fleet changes with increasing income and consists more of newer and better cars that use less energy and are better for the environment. In 2012, Education University of Sultan Idris Malaysia did a research on Automobile Sales and Macroeconomic Variables: A Pooled Mean Group Analysis for Asean Countries. This paper analysed the impact of economic variables on automobile sales in five ASEAN countries involving Malaysia, Singapore, Thailand, Philippines and Thailand collecting annual data from 1996 to 2010. The long term and short term correlation between these variables are implemented using the panel error-correction model. Two methods are implemented specifically the Mean Group (MG) and Pooled Mean Group (PMG). These two methods were introduced by 2
6. Pesaran dan Smith (1995) and Pesaran et al. (1999). Result from the test shows that gross domestic product (GDP), inflation (CPI), unemployment rate (UNEMP) and loan rate (LR) have significant long term correlation with automobile sales in these ASEAN countries. The GDP variable is found to have positive relationship with car sales. This proves that national income level is an important determinant for the automotive industry. In contrast, spikes of inflation, unemployment rate and interest rate are found to inflict negative impact on car sales. Besides, each country is influenced by different variables in the short term period. In 2013 Joseph Chisasa and Winnie Dlamini from University of South Africa, South Africa did a research on An Empirical Analysis Of The Interest Rate-Vehicle Purchase Decision Nexus In South Africa. This paper empirically examines the link between interest rates and the borrowers’ decision to purchase a passenger vehicle in South Africa. They used monthly time series data of passenger vehicles purchased, household income, fuel prices, prime interest rates and producer price index for manufacturers from January 1995 to December 2011. With passenger vehicle unit purchases as the dependent variable, they obtained OLS estimates of the passenger vehicle purchase function. Results show that there is a negative, but insignificant, relationship between interest rates and passenger vehicle purchases in South Africa. Holding other factors constant, a 1% increase in interest rate results in a 0.9% decrease in passenger vehicle purchases. Household income, fuel price and producer price index are observed to have a positive and insignificant impact on the decision to purchase a passenger vehicle. In 2014, Vaal University of Technology University of KwaZulu did a research on The Impact of Inflation on the Automobile Sales in South Africa. This paper analysed the relationship between inflation (INF) and Automobile sales in South Africa by using the co-integration and causality tests. The analysis has been conducted using monthly data over the period 1960:1 through 2013:9. The 3
7. empirical results show that there is a long-run relationship between new vehicle sales and inflation over the sample period of 1969 to 2013. Other factors that have been analysed were income level, interest rate, financial aggregate and unemployment rate. These include in the research by Shahabudin (2009) on domestic and foreign cars sales. In this research, it was discovered that all variables could significantly influence car sales. However, this regression model suffered from heteroscedasticity that affected the efficiency to gauge domestic and foreign car sales. In this research, it is proven that all variables could significantly influence car sales. However, the problem of heteroscedasticity had impaired the efficiency of the model as a whole. Dargay (2001) using Family Expenditure Survey from 1970 t0 1995, it was found out that the statistics of vehicle ownership recorded a positive upward trend with income increase. However, there is a negative correlation when there is an income reduction. This is associated with the personal habit of individual consumers as vehicle is seen as an important necessity in the present context of everyday life. All the researches we mentioned above just focused on the effect of one or some factors of the 6 factors we chose and none of them described the effect of all the 6 factors on the quantity of new cars sold, especially in the US market. Considering that there is no specific research conducted to analyse the relationship between these economic variables in the context of US thus far, we decided to conduct a study on “Factors affecting quantity of new cars sold in the US”. We will examine the effect of 6 factors (Price index, Prime interest rate, Income, Unemployment rate, Stock, Population) on quantity of new cars sold with the help of regression analysis, and then draw some conclusions through the result. Our research will focus on the US market. 4
8. III. Methodology We carry out this research by using 15 years’ time periods from 1975 till 1990 as the sample of analysis. Consequently, time series analyses were used in the study of car sales in US and each factor throughout 15 years. To analyze the relationship between dependent variables and independent variables in this study, linear regression will be used. The software that chosen for analyze and work with these data is the software Gretl. The data we use in the research is taken from Gretl as well: It is the data 9.7 in Ramathan category in Gretl. 5
9. IV. Theoretical background In many countries car is one of the most expensive goods and is considered as a luxury good. However, in this research we want to examine the number of cars sold in US generally, which means that car is considered as a normal good. The theory we based on is the theory of principle of microeconomics and macroeconomics formulated by N. Gregory Mankiw. The detail application of this theory will be presented in order of the relationship between the dependent variable and four independent variables in our research. Price index A price index (also known as "price indices" or "price indexes") is a normalized average (typically a weighted average) of price relatives for a given class of goods or services in a given region, during a given interval of time. It is a statistic designed to help to compare how these price relatives, taken as a whole, differ between time periods or geographical locations. In the research, we will analyze the effect of consumer price index (CPI) on the quantity of goods sold. The CPI is the measure of overall cost of the goods and services bought by a typical consumer. It is also a helpful means to measure the inflation rate. Because the CPI indicates prices changes—both up and down—for the average consumer, the index is used as a way to adjust income payments for certain groups of people. For instance, more than 2 million U.S. workers are covered by collective bargaining agreements, which tie wages to the CPI. If the CPI goes up, so do their wages. The CPI also affects many of those on Social Security—47.8 million Social Security beneficiaries receive adjusted increases in income tied to the CPI. And when their incomes increase, the demand for goods and services also increases, which raises the quantity of goods sold, in our case is quantity of new cars sold. 6
10. Income According to the theory of market forces of supply and demand in microeconomics of Mankiw, income is one of the main factors that shifts the demand curve, which contributes to the change in the number of product sold. When being considered as a normal good, the income and the price goes in the same direction, which means an increase in income leads to an increase in demand. In the model, the demand curve shifts to the right. As a result, when the demand rises, it raises the quantity of car sold. Prime interest rate The prime rate is the interest rate that commercial banks charge their most creditworthy corporate customers. ese are the businesses and individuals with the highest credit ratings. They received this rate because they are the least likely to default. Banks have little risk with these loans The prime interest rate, or prime lending rate, is largely determined by the federal funds rate, which is the overnight rate that banks use to lend to one another. Prime forms the basis of or starting point for most other interest rates—including rates for mortgages, small business loans, or personal loans—even though prime might not be specifically cited as a component of the rate ultimately charged. Banks base most interest rates on prime. That includes adjustable-rate loans, interest-only mortgages, and credit card rates. Their rates are a little higher than prime to cover banks' bigger risk of default. They've got to cover their losses for the loans that never get repaid. The riskiest loans are credit cards. That's why those rates are so much higher than prime. The prime rate affects household when it rises. When that happens, the monthly payments increase along with the prime rate. The prime rate also affects liquidity in the financial markets. A low rate increases liquidity by making loans less expensive and easier to get. When prime lending rates are low, businesses expand and so does the economy. Similarly, when rates are high, liquidity dries up, and the economy slows down. In sum, the prime rate considered as a factor affecting the quantity of product sold has the same role and effect as interest rate. It influences the quantity 7
11. in two sides: the household which affects the consumption and the firms which affects the investment or production. According to the theory of aggregate demand of Mankiw, the interest rate has the power to shift the aggregate demand curve. Changes in interest rates can affect several components of the AD equation. The most immediate effect is usually on capital investment. When interest rates rise, the increased cost of borrowing tends to reduce capital investment, and as a result, total aggregate demand decreases. Conversely, lower rates tend to stimulate capital investment and increase aggregate demand. On the household side, lower interest rate encourages them to hold money in hands. Consumer confidence about the economy and future income prospects also affect how much consumers are willing to extend themselves in spending and financing obligations. As a result, it increases the consumption. An increase in interest rates may lead consumers to increase savings since they can receive higher rates of return. A corresponding increase in inflation often accompanies a decrease in interest rates, so consumers may be influenced to spend less if they believe the purchasing power of their dollars will be eroded by inflation. Unemployment rate The unemployment rate is defined as the percentage of unemployed workers in the total labor force. One of the main factors influencing demand for consumer goods is the level of unemployment, which is measured by the unemployment rate. The more people there are receiving a steady income and expecting to continue receiving one, the more people there are to make discretionary spending purchases. That also means when the unemployment rate increases, the demand for a good decreases, which leads to the decrease in the quantity sold of a product. Therefore, the monthly unemployment rate report is one economic leading indicator that gives clues to demand for consumer goods. 8
12. Stock The stock represents for the number of cars on the road. This number of cars in the time series data shows the trend in consumption of cars. In other words, it tells the demand direction of people. If the number increase time after time, the demand increases, therefore, the quantity of car sold and the stock go the same direction. In contrast, when the demand for car decreases, the stock has a negative impact on number of car sold. Population According to Microeconomics knowledge developed by Mankiw, the change in population will shift the demand curve. As the population increases, the demand for goods increase because each member of the population has needs to be filled. That leads to the increase in the quantity of goods sold. However, these needs changes overtime as the segments of the population age and their needs and wants change. So that there is nothing sure about the increase in the quantity of a specific goods sold if the population increase in real- life situation. 9
13. V. Data description 1. Variables table Table 5.1: Variables table Variables Abbreviation Meaning Unit Quantity of new cars sold New car sales Y 1000 units quarterly Average real price index of Price $ a new car Per capita disposable Income personal income 1000$ Prime Prime interest rate % Unemployment Unemployment rate % Stock X5 Number of cars on road 1000 units Population X6 Population 1000 people 2. Data description Table 5.2: Summary statistic table ( Source: Gretl) QNC Price Income Prime Unemp Stock Pop (Y) (X1) (X2) (X3) (X4) (X5) (X6) Mean 2488.6 95.213 10.521 10.687 7.0109 109.77 233.77 Median 2495.5 98.250 10.166 10.000 7.1000 107.77 234.04 Minimum 1754.0 60.200 8.9850 6.2500 5.1000 93.145 215.97 Maximum 3337.0 121.40 11.930 20.320 10.500 123.30 251.97 10
14. Std.Dev 332.92 18.947 0.84566 3.3994 1.3626 8.9283 10.489 C.V. 0.13378 0.19900 0.080376 0.31809 0.19435 0.081334 0.044870 Skewness 0.18571 -0.31097 0.24957 1.0855 0.60303 0.018833 -0.024827 Ex.kurtosis -0.22879 -1.1880 -1.0855 0.51036 -0.20593 -1.1244 -1.1555 Description: • Y QNC Mean: The average quantity of new cars sold from data surveyed is 2488.6 x103 units quarterly. • Y QNC Median: Fitted value of dependent variable Y QNC is 2495.5x103 units quarterly. • Y QNC Minimum: The minimum quantity of new cars sold among 64 quarters surveyed is 1754.0x103 units. • Y QNC Maximum: The maximum quantity of new cars sold among 64 quarters surveyed is 3337.0x103 units. • Std. Dev. (Standard Deviation): is a measure of how spread the numbers are, equals to the square root of sample variance. The Std. Dev. of Y QNC here is 332.92. • C.V. (Coefficient of Variation): is simply the standard deviation divided by the sample mean. Large values of the C.V. indicate that the mean is not very precisely measured. The C.V. of Y QNC here is 0.13378. ⇒ From the summary statistic table, we can see that it might be the representative sample for Quantity of new cars sold quarterly(Y) (QNC) depends on the 6 variables which are Price (X1), Income (X2), Prime(X3), Unemployment (X4), Stock(X5), Population (X6). 3. Correlation matrix Correlation Coefficients, using the observations 1975:1 - 1990:4 5% critical value (two-tailed) = 0.2461 for n = 64 11
15. Table 5.3: Correlation of variables table (Source:Gretl) QNC Price Income Prime Unemp Stock Pop (Y) (X1) (X2) (X3) (X4) (X5) (X6) QNC 1.000 0.0164 0.1994 -0.4588 -0.4533 0.1363 0.0441 (Y) Price 1.0000 0.9386 0.1285 -0.3553 0.9732 0.9918 (X1) Income 1.0000 -0.0485 -0.6137 0.9849 0.9642 (X2) Prime 1.0000 0.1779 0.0050 0.0560 (X3) Unemp 1.0000 -0.5354 -0.4206 (X4) Stock 1.0000 0.9864 (X5) Pop 1.0000 (X6) Look at the table of correlation, we draw some comments: Generally, correlation of the independent variables with each others are very different: There are correlations that are significantly high: • r(X5;X1)= 0.9732⇒ the relation of Stock and Price is high. • r(X6;X1)=0.9918 ⇒ the relation of Population and Price is high. • r(X5;X2)=0.9849 ⇒ the relation of Stock and Income is high. • r(X6;X2)=0.9642⇒ the relation of Population and Income is high. 12
16. • r(X6;X5)=0.9864⇒ the relation of Population and Stock is high. There are some correlations are moderate that fluctuate around 0.35 to 0.6. The others are very low: smaller than 0.2. There are 5 correlations that gain the negative relation: r < 0 : • r(X3;X2)= -0.0485 ⇒ the relation of Prime and Income is negative. • r(X4;X1)=-0.3553⇒ the relation of Unemployment and Price is negative. • r(X4;X2)=-0.6137⇒ the relation of Unemployment and Income is negative. • r(X5;X4)=-0.6137⇒ the relation of Stock and Unemployment is negative. • r(X6;X4)=-0.4206⇒ the relation of Population and Unemployment is negative. VI. Econometrics model 1. Population regression function (PRE) 2. Sample of regression function (SRF) ( is error). 3. Result: Figure 6.1: The estimate OLS regression (Source: Gretl) 13
17. So we have the temporary regression function for “quantity of new cars sold quarterly”: 50.1164X1+ 630.491X2 - 44.3828X3-41.8123X4+ 14.0646X5 - 150.679X6+ 25531.7 + e. R2= 0,493523 : It means that the 6 regressors explain 49,35% of the variance of Quantity of new cars sold quarterly. SER = 249.0894: It estimates standard deviation of error ui. A relatively high spread of scatter plot means that prediction of Quantity of new cars sold quarterly basing on these variables might be not much reliable. 4. Meaning of coefficient Bo: If all these other factors equal to zero, quantity of new cars sold quarterly equals to 25531.7x103 units . But this situation can not occur due to the theory because the quantity of good sold in the market always depends on other factors that affect to demand and supply. B1: If the real price index of a new car increases 1$ , the quantity of new cars sold quarterly will increase 50.1164x103 units. ⇒ It follows the law of macroeconomics mentioned in theory background above. B2: If the capita disposable personal income increase 1$, the quantity of new cars sold quarterly will increase 630.491 units. ⇒ It follows the law of microeconomics mentioned in theory background above . B3: If the prime rate increases 1%, the quantity of new cars sold quarterly will decrease 44.3828x103 units. ⇒ It follows the law of macroeconomics mentioned in theory background above . B4: If the unemployment rate increases 1%, the quantity of new cars sold quarterly will decrease 41.8123x103 units. ⇒ It follows the law of macroeconomics mentioned in theory background above . 14
18. B5: If the number of cars on road increases 1 units, the quantity of new cars sold quarterly will increase 14.0646 units. ⇒ It doesn’t follow the law of economics. But, in the fact that, it is easy to understandable and which is explained in the theory background above. B6: If the population increase 1 people, the quantity of new cars sold quarterly will decrease 150.679 units. ⇒ It doesn`t follow the law of economics. But, now, there is no theory to explain about that. 5. Testing a hypothesis relating to a regression coefficient 2-tail testing : H0 : j= j* H1 : j≠ j Our data has : • The number of observations : n = 64 • The number of variables : k = 7 • Degree of freedom = n - k = 57 • Level of significance : / 2 = 0.025 Searching in the Significance level table of t-student distribution, we have: tob 2.00 Basing on the result of t-ratio ( t statistic) and p-value on the Figure 6.1 above calculated thanks to Gretl, we come to test hypothesis relating to regression a coefficient. 5.1. Intercept β0 Null hypothesis: : β0=0 Alternative hypothesis: H2: β0≠0 From the chart above, we see: 15
19. We have: , And p-value = 0.0003 Moreover , means that the statistical significance of const equals to 1%  At 5% level of significance, we have enough evidence to reject H0: β0=0 β0 has meaning in model 5.2. Coefficient β1 Null hypothesis: : β1=0 Alternative hypothesis: H1: β1 ≠ 0 From the chart above, we see: We have: , And p-value = Moreover , means that the statistical significance of const equals to 5%  At 5% level of significance, we have enough evidence to reject : β1=0 β1 has meaning in model 5.3 Coefficient β2 Null hypothesis: : β2=0 Alternative hypothesis: H1: β2 ≠0 From the chart above, we see: We have: , And p-value = Moreover , means that the statistical significance of const equals to 5%  At 5% level of significance, we have enough evidence to reject : β2=0 β2 has meaning in model 5.4 Coefficient β3 Null hypothesis: : β3=0 Alternative hypothesis: H1: β3 ≠0 From the chart above, we see: We have: , And p-value = 0.0025 Moreover , means that the statistical significance of const equals to 1%  At 5% level of significance, we have enough evidence to reject : β3=0 16
20. β3 has meaning in model 5.5 Coefficient β4 Null hypothesis: : β4 = 0 Alternative hypothesis: H1: β4 ≠0 From the chart above, we see: We have: /ts/<tob , And p-value = 0.5730  At 5% level of significance, we have enough evidence to accept : β4=0 β4 has not meaning in model 5.6: Coefficient β5 Null hypothesis: : β5 = 0 Alternative hypothesis: H1: β5 ≠0 From the chart above, we see: We have: /ts/<tob , And p-value = 0.7684  At 5% level of significance, we have enough evidence to accept : β5=0 β5 has not meaning in model 5.7: Coefficient β6 Null hypothesis: : β6=0 Alternative hypothesis: H1: β6 ≠0 From the chart above, we see: We have: , And p-value = 0.0003  At 5% level of significance, we have enough evidence to reject : β6=0 β6 has meaning in model 5.8. Hypothesis testing of Hypothesis From the chart above, we see: p-value (F) = 4.47e-07 < 0.05 17
21.  At 5% level of significance, we have enough evidence to reject We have suitable model. 6. Adjusted regression model: From the beginning, our model has 6 independent variables which are Price(X1), Income(X2), Prime(X3), Unemployment(X4), Stock(X5), Population(X6). However, after finishing test hypothesis relating to regression a coefficient, we decide to reject 2 independent variables: Unemployment(X4) and Stock(X5) that have no meaning in the model and keep 4 others. Conclusion: We have the adjusted OLS regression: Figure 6.2: The estimate OLS regression (Source: Gretl) The estimated OLS regression is: = 24761.6 + 47.6529Price + 903.472Income - 41.6461Prime - 153.443Pop. With: QNC : Quantity of new cars sold quarterly (1000 units) Price: Average real price index of a new car ( $) Income: Per capita disposable personal income (1000$) 18
22. Prime: Prime interest rate (%) Pop: Population (1000 people) It can be shown from the figure 6.2 that: Meaning of coefficient: - Intercept= 24761.6 : If all these other factors equal to zero, quantity of new cars sold quarterly equals to 24761.6 x103 units . But this situation cannot occur due to the theory because the quantity of good sold in the market always depends other factors that affect to demand and supply. - Coefficient of Price = 47.6529. If the real price index of a new car increases 1$ , the quantity of new cars sold quarterly will increase 47.6529x103 units. ⇒ It follows the law of macroeconomics mentioned in theory background above. - Coefficient of Income= 903.472. If the capita disposable personal income increases 1$, the quantity of new cars quarterly sold will increase 903.472 units. ⇒ It follows the law of microeconomics mentioned in theory background above . - Coefficient of Prime= - 41.6461. If the prime rate increases 1%, the quantity of new cars sold quarterly will decrease 41.6461x103 units. ⇒ It follows the law of macroeconomics mentioned in theory background above . - Coefficient of Population= -153.443. If the population increases 1 people, the quantity of new cars sold quarterly will decrease 153.443 units. ⇒ It doesn`t follow the law of economics. And, now, there is no theory to explain about that. R 2 = 0.483821. It means that the 4 regressors explain 48.38% of the variance of Quantity of new cars sold quarterly. It is quite similar to model 1. SER = 247.1650. It estimates standard deviation of error ui. A relatively high spread of scatter plot means that prediction of Quantity of new cars sold quarterly base on these variables might be not much reliable. It is quite similar to model 1. All the independent variables show with the statistical significance of 1%. P-value(F)= 5.15e-08 < 0.05 Model 2 has the statistical significance 19
23. VII. Robustness check 1. Multi-collinearity 1.1: Symptom 1 - VIF To detect the presence of multicollinearity, multicollinearity was conducted. The easiest method to detect multicollinearity is through VIF. Through multicollinearity test, we can check whether the explanatory variables in our model are highly linearly correlated. An optimum value of VIF is between 1 and 10. If the value greater than 10, it mean that the independent variables have high correlations and lead to a multicollinearity problems. Figure 7.1:Collinearity table (Source: Gretl) From the figure 7.1 , only one value of vif of prime variable from test by gretl smaller than 2 and 3 other variables have the values of vif more than 10. Besides, mean VIF approximately equals 72.5 ⇒ The multicollinearity is found in the model. 1.2 Symptom2 - Correlation 20
24. Figure 7.2: Correlation matrix (Source: Gretl) There are some correlations are more than 80% (>0.8): • r(income;price)=0.9386 • r(population;price)=0.9918 • r(population;income)=0.9642 Conclusion: Our model has the multicollinearity. However, our model has statistical significances (because p-value(F) of model 2 - the model after rejecting 2 non-meaning variables mentioned above) is 5.15.e- 08<0.05) , we can ignore the multicollinearity. Analysis: The high correlation between these four variables is reasonable. Because, in the economic field, the price index implies the inflation which influences the increase or decrease in the interest rate and the income. Besides, the interest rate determines the investment and consumption which has impact on the wage and income of people. The behaviour of households and firms also has influence of the interest rate. These changes in the economic also affect the expectation of people and somehow affects their decision of birth or population. These four variables have the mutual effects. 21
25. 2. Heteroskedasticity 2.1 Qualitative analysis Figure 7.3: Residual plot against QNC (Source: Gretl) Heteroscedasticity means unequal scatter, the residuals therefore, should have a constant variance. As seen from the figure 7.3, the scattered points spread out quite equally. ⇒ Errors might not happen. 3.2. Quantitative analysis The residuals are called heteroscedastic if the residual variables have different variances and homoscedastic if constant. White test is a statistical test that establishes whether the residual variance of a variable in a regression model is constant. The null hypothesis in White test is that the residuals are homoscedastic. 22
26. Figure 7.4: White test (squares only)(Source: Gretl) Null Hypothesis: Ho : var ( ui) = σ2 for all i Alternative Hypothesis: H1: var (ui)# σ2 for all i The data table above shows that p-value = 0.635525 > = 0.05 • For the common = 5% for the 2-tail test, we are able to give the conclusion not to reject hypothesis Ho : var (ui ) = σ2 for all i. Conclusion: No heteroscedasticity is found. Analysis: While heteroscedasticity does not cause bias in the coefficient estimates, it does make them less precise. Lower precision increases the likelihood that the coefficient estimates are further from the correct population value. Our model is not heteroscedastic, which means the preciseness of the coefficient is high. 3. Normality The hypotheses used are: : The sample data are not significantly different than normal. 23
27. : The sample data are significantly different than normal. Figure 7.5: Normality test (Source: Gretl) It can be seen from the figure 7.5 that: p-value=0.6038>0.05 ⇒With the common = 5% for the 2-tail test, we are able to give the conclusion to accept the assumption H0 Conclusion: ui follows the normal distribution. Analysis: The normal distribution is a probability function that describes how the values of a variable are distributed. The result of our test showed that the model has a normal distribution, which means that the parameters of our model is significant. 4. Autocorrelation: Autocorrelation occur when there are correlation between the values of the same variables is based on related objects. The Breusch-Godfrey serial correlation 24
28. LM can be used to test for the presence of autocorrelation in time series data test. A LM-test was carried out to estimate if there were autocorrelation in the residuals. Hypothesis for the LM test are shown as below: H0 :No autocorrelation H1 : Autocorrelation exits. If the null hypothesis is rejected, the data is correlated, and if the null hypothesis is not rejected, there are no autocorrelation. Figure 7.6: Autocorrelation test (Source: Gretl) The data of figure 7.6 shows that p-value = 0.257 > = 0.05 => We have enough evidence to accept Ho Conclusion: There is no autocorrelation to be found. Analysis: Autocorrelation occurs when adjacent residuals are correlated, one residual can predict the next residual. This correlation represents explanatory information that the independent variables do not describe. Models that use time-series data are 25
29. susceptible to this problem. However, our model does not have autocorrelation, which means the independent variables explained well the dependent variable. VIII. Result table: Variables Model 1 Model 2 25531.7 24761.6 Constant (3.865) (3.991) 50.1164 47.6529 Price (2.182) (2.790) 630.491 903.472 Income (2.032) (5.500) -44.3828 -41.6461 Prime (-3.163) (-3.695) -41.8123 Unemployment Rejected (-0.5669) 14.0646 Stock Rejected (0.2959) -150.679 -153.443 Population (-3.834) (-4.081) N 64 64 R2 0.493523 0.483821 p-value= 0.6038> 0.05 Normality ⇒ ui follows the normal distribution p-value=0.635525>0.05 Heteroscedasticity ⇒ No heteroscedasticity is found 26
30. LMF: 1.313169 Autocorrelation p-value: 0.257 >0.05 ⇒ No autocorrelation is found Multi-collinearity VIF Price 107.974>10 Income 19.898>10 Prime 1.514 10 Population 72.5>10 MeanVIF ⇒ The multicollinearity is found in the model. But it is not necessary to cure because of the statistical significances of model. Note: The figures in ( ) are t-statistic. 27
31. IX. Conclusion The research has shown the relationship between the six economic variables and the quantity of car sold in US in the period of 1975 to 1990. From the analysis results, it can see that only four variables including prime interest rate, income, population and price has relationship with number of new cars sold. The unemployment and number of cars on the road do not hold effect. The income has the most impact on the number of car sold in a positive way. Together with the price, income variable has the positive relationship with the dependent variable. In contrast, the prime interest rate and the population has a negative relationship with the number of car sold. However, when applying the result into reality, we found that population variable does has impact on the number of new cars sold but the scale impact did not as much as the result numbers told. This could come from the drawback of our observations. The number of observations is small, the time is restricted in fifteen years, the origin of the observations is not clear enough. All these things could lead to some imprecise in our research result. According to the result, the research has reached the main purpose of its. The research has determined the significant factors to the number of car sold in US ( 1957-1990) and measured the impact of them on the dependent variable. However, its drawback affected the judgement of us. Based on the result of our research, we would like to have some suggestions on the fiscal policy to the government. The research has shown the relationship between the macroeconomic variables to the number of new cars sold, these three variables could be affected by the decision of government. The government can use their fiscal tool to adjust the prime interest rate, the price to get the best profit for car firms in the national economy. Besides, the government can intervene into the wages to adjust the income as well. We would like to express our deep gratitude to our beloved teachers for your guidance and support to help us finish our research and for all the time and enthusiasm we received during the econometrics course. 28
32. X. References 1. “Principles of Macroeconomics” (2016), Eight Edition, N. Gregory Mankiw, Cengage Learning, Inc, United States. 2. “Principles of Microeconomics” (2014), Seventh Edition, N. Gregory Mankiw, Cengage Learning, Inc, United States. 3. “Basic Econometrics”, Fourth Edition, Damodar N. Gujarati. 4. “Introduction to Econometrics”, Brief Edition , James H. Stock and Mark W. Watson. 5. _on_the_Automobile_Sales_in_South_Africa 6. Macroeconomic_Variables_A_Pooled_Mean_Group_Analysis_for_Asean_Co untries 7. 99.pdf?fbclid=IwAR1e4pyD_O0R3PGCC9YS9B6xp47hg9LC8Ymlz4NoQ0A n-K7VBNT4Vh_iCf4 8. 29
33. XI. Appendix QNC Price Income Prime Unemp Stock Pop 1975:1 1923 60.2 8.985 8.98 8.7 93.145 215.973 1975:2 2165 62.9 9.176 7.32 8.6 93.845 216.489 1975:3 2198 62.8 9.167 7.56 8.3 95.241 217.004 1975:4 2328 63.9 9.307 7.58 8.3 95.846 217.52 1976:1 2381 65.4 9.376 6.83 7.5 96.456 218.035 1976:2 2788 66.2 9.439 6.9 7.5 97.19 218.586 1976:3 2416 66.6 9.474 7.09 7.8 97.818 219.137 1976:4 2513 68.6 9.454 6.54 7.9 98.294 219.688 1977:1 2617 68.8 9.561 6.25 7.3 98.791 220.239 1977:2 3195 69.3 9.586 6.47 7.1 98.397 220.826 1977:3 2668 70.2 9.716 6.9 6.9 99.904 221.412 1977:4 2688 72 9.793 7.67 6.3 100.631 221.999 1978:1 2540 74.2 9.813 7.98 6.2 101.319 222.585 1978:2 3337 74.6 10.037 8.3 5.8 102.222 223.203 1978:3 2713 75.6 10.047 9.14 5.9 102.957 223.82 1978:4 2710 77.2 10.139 10.81 5.9 103.896 224.438 1979:1 2739 78.9 10.176 11.75 5.7 104.845 225.055 1979:2 2942 81.1 10.159 11.72 5.7 105.864 225.723 1979:3 2571 82.3 10.155 12.12 5.8 106.755 226.391 1979:4 2396 83.1 10.094 15.08 5.9 107.585 227.058 30
34. 1980:1 2511 85.1 10.172 16.4 6.3 106.59 227.726 2139 87.3 9.955 16.32 7.3 105.595 228.286 .01980:2 1980:3 2130 88.4 9.977 11.61 7.6 104.6 228.846 1980:4 2189 90.2 10.051 16.73 7.5 104.9 229.406 1981:1 2373 90.8 10.104 19.21 7.4 105.2 229.966 1981:2 2207 91.8 10.053 18.93 7.4 105.5 230.522 1981:3 2192 95 10.115 20.32 7.4 105.8 231.077 1981:4 1754 95.5 10.109 17.01 8.1 106.075 231.633 1982:1 1944 96.8 9.976 16.27 8.7 106.35 232.188 1982:2 2094 96.7 10.099 16.5 9.3 106.625 232.718 1982:3 1910 98 10.047 14.72 9.8 106.9 233.248 1982:4 2032 97.9 10.008 11.96 10.5 107.425 233.77 1983:1 2045 98.5 10.086 10.67 10.2 107.95 234.307 1983:2 2505 99.2 10.143 10.5 10 108.475 234.817 1983:3 2237 99.8 10.269 10.67 9.2 109 235.328 1983:4 2394 100.9 10.381 11 8.4 109.75 235.838 1984:1 2584 101.6 10.609 11 7.8 110.5 236.348 1984:2 2895 102.3 10.706 12 7.4 111.25 236.878 1984:3 2448 102.9 10.758 12.92 7.3 112 237.407 1984:4 2463 103.5 10.773 11.33 7.2 112.675 237.937 1985:1 2644 104.5 10.922 10.5 7.2 113.35 238.466 1985:2 2988 105.5 11.038 10 7.2 114.025 239.012 31
35. 1985:3 2968 106.1 10.926 9.5 7.1 114.7 239.559 1985:4 2442 106.9 10.96 9.5 7 115.35 240.105 1986:1 2600 107.8 11.09 9.33 6.9 116 240.651 1986:2 3046 108.9 11.381 8.5 7.1 116.65 241.189 1986:3 3124 111.2 11.252 7.67 6.9 117.3 241.728 1986:4 2689 112.3 11.227 7.5 6.8 117.925 242.266 1987:1 2341 114.1 11.271 7.5 6.5 118.55 242.804 1987:2 2767 113.5 10.877 7.83 6.2 119.175 243.358 1987:3 2785 115.1 11.263 8.25 5.9 119.8 243.913 1987:4 2382 115.6 11.441 8.75 5.8 120.225 244.467 1988:1 2636 115.1 11.52 8.58 5.6 120.65 245.021 1988:2 2864 115.7 11.586 8.67 5.4 121.075 245.601 1988:3 2556 117 11.794 9.5 5.4 121.5 246.182 1988:4 2486 118.5 11.875 10.17 5.2 121.825 246.762 1989:1 2337 118.4 11.82 10.83 5.1 122.15 247.342 1989:2 2757 119.2 11.829 11.33 5.2 122.475 247.985 1989:3 2631 119.2 11.905 10.5 5.2 122.8 248.628 1989:4 2053 119.5 11.866 10.5 5.3 122.925 249.27 1990:1 2310 121.2 11.921 10 5.2 123.05 249.913 1990:2 2532 120.4 11.925 10 5.2 123.175 250.597 1990:3 2358 120.4 11.93 10 5.5 123.3 251.282 1990:4 2100 121.4 11.703 10 5.9 123.3 251.966 32