Factors affecting quantity of new cars sold foreign trade university students

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. 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. 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. 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 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. 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. V. Data description 1. Variables table Table 5.1: Variables table Variables Abbreviation Meaning Unit New car sales Y Quantity of new cars sold quarterly 1000 units Price Average real price index of a new car $ Income Per capita disposable 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 (Y) Price (X1) Income (X2) Prime (X3) Unemp (X4) Stock (X5) Pop (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 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 Table 5.3: Correlation of variables table (Source:Gretl) QNC (Y) Price (X1) Income (X2) Prime (X3) Unemp (X4) Stock (X5) Pop (X6) 1.000 0.0164 0.1994 -0.4588 -0.4533 0.1363 0.0441 QNC (Y) 1.0000 0.9386 0.1285 -0.3553 0.9732 0.9918 Price (X1) 1.0000 -0.0485 -0.6137 0.9849 0.9642 Income (X2) 1.0000 0.1779 0.0050 0.0560 Prime (X3) 1.0000 -0.5354 -0.4206 Unemp (X4) 1.0000 0.9864 Stock (X5) 1.0000 Pop (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. 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) 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 . 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: 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 è 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 è 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 è 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 è 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 è 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 èβ5 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 èβ6 has meaning in model 5.8. Hypothesis testing of Hypothesis From the chart above, we see: p-value (F) = 4.47e-07 < 0.05 At 5% level of significance, we have enough evidence to reject è 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 ( $) Income: Per capita disposable personal income (1000$) 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. R2 = 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 è Model 2 has the statistical significance 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  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.  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. 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. : 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. Autocorrelation: Autocorrelation occur when there are correlation between the values of the same variables is based on related objects. The Breusch-Godfrey serial correlation 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 susceptible to this pr