- Level: AS and A Level
- Subject: Maths
- Word count: 4377
Estimate a consumption function for the UK economy explaining the economic theory and statistical techniques you have used.
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Introduction
Estimate a consumption function for the UK economy explaining the economic theory and statistical techniques you have used.
Consumption has been considered as the most important single element in aggregate demand, accounting for almost 66% of GDP in 1989. Therefore, it is essential that the level of consumption be predicted accurately, for even a small percentage error may lead to a large absolute error. Another reason why consumption such important is that the marginal propensity of consume is one of the factor which is used to determine the size of the multiplier. This will influence the changes of investment and government spending. Moreover, as saving ratio, another factor that used to predict the behavior of consumers, has fluctuated rapidly during these years, so the consumption become more important. Thus, many economists attempt to develop many theories and equations to predict consumers’ expenditure. Therefore, in this project, there are two main theories and their equations will be given. Some data from Economic Trends Annual Supplement and graphs will be used to estimate the performance of the model on the basis of some econometric tests.
Keynes, John Maynard introduced consumption function in 1936. In The General Theory of Employment Interest and Money, Keynes pointed out that
“ We should therefore define what shall call the propensity to consume as the functional relationship, between Y, a given level of income and C the expenditure on consumption out of that level of income…The amount that the community sends on consumption depends (i) partly on the amount of its income, (ii) partly on other objective attendant circumstances, and (iii) pa rtly on the subjective needs and the psychological
Middle
ct=c0+c1yt+c2ct-1+c3πt
where πis the inflation rate. Use the same data as the previous equation to gain the equatipon.we can gain new equation as below:
LC=+1.001*LY_1-0.002921*p
According to the tests which display in the Table 6, we can see that the coefficients of both parameters are significant as the value of t-test are quit high. But DW just 0.14, below than 2, which means not good. Figure 6(a) and (b) shows the same conclusion as DW.
Thus, another factor which called error correction should be added to the consumption. As in the short run consumption will not equal the desired proportion of income. Thus, assume that consumption towards their consumption to their long-term goal. Then, consumption function in this case is:
Δct=c0+c1Δyt+c2st-1+c3πt
Use the same ways to gain the test result to estimate the consumption function. The following consumption function can be generate from the data is:
DLC=+0.01119+0.6508*DLY+0.1092*LS_1-0.001078*p
In Table 6, the result of the tests shows that all the absolute value of the t-test are bigger than 2, which are good. The highest value in this test is DLY, which is 7.23. It is means that the coefficient of DLY is significant in this equation. The same conclusion can be gained from the other tests. Such as the p-test, the higher the value of t-test the lower the value of p-test. Thus, the consumption function which incorporating inflation and error correction is successful. The predictions from this equation are shown in Figure 7(a). The equation performs very well from 1950 to 1982. This can be shown in the Figure 7(b) as well. In the same period, the graph is random.
Conclusion
(SE) (0.128) (0.0101)
Figure3
Table 4
EQ (4) Modelling LC by OLS (using project12min.xls)
The estimation sample is: 1950 to 2002
Coefficient Std.Error t-value t-prob Part.R^2
LC_1 0.632198 0.1034 6.11 0.000 0.4278
Constant 0.206148 0.1075 1.92 0.061 0.0685
LY 0.351899 0.09701 3.63 0.001 0.2083
sigma 0.0182645 RSS 0.0166796213
R^2 0.998055 F(2,50) = 1.283e+004 [0.000]**
log-likelihood 138.489 DW 0.858
no. of observations 53 no. of parameters 3
mean(LC) 12.6755 var(LC) 0.161805
LC = + 0.6322*LC_1 + 0.2061 + 0.3519*LY
(SE) (0.103) (0.108) (0.097)
Figure 4
Table 5
EQ( 5) Modelling LC by OLS (using project12min.xls)
The estimation sample is: 1950 to 2002
Coefficient Std.Error t-value t-prob Part.R^2
LY_1 0.999415 0.0004450 2246. 0.000 1.0000
sigma 0.0411118 RSS 0.0878894078
log-likelihood 94.4484 DW 0.46
no. of observations 53 no. of parameters 1
mean(LC) 12.6755 var(LC) 0.161805
LC = + 0.9994*LY_1
(SE) (0.000445)
Figure 5
Table 6
EQ( 6) Modelling LC by OLS (using project12min.xls)
The estimation sample is: 1950 to 2002
Coefficient Std.Error t-value t-prob Part.R^2
LY_1 1.00082 0.0006735 1486. 0.000 1.0000
P -0.00292117 0.001097 -2.66 0.010 0.1221
sigma 0.0388953 RSS 0.0771549661
log-likelihood 97.9004 DW 0.41
no. of observations 53 no. of parameters 2
mean(LC) 12.6755 var(LC) 0.161805
LC = + 1.001*LY_1 - 0.002921*P
(SE) (0.000674) (0.0011)
Figure 6
Table 7
EQ( 7) Modelling DLC by OLS (using project12min.xls)
The estimation sample is: 1950 to 2002
Coefficient Std.Error t-value t-prob Part.R^2
Constant 0.0111950 0.004826 2.32 0.025 0.0990
DLY 0.650824 0.09000 7.23 0.000 0.5163
LS_1 0.109243 0.05125 2.13 0.038 0.0849
P -0.00107845 0.0003864 -2.79 0.007 0.1372
sigma 0.0126726 RSS 0.00786908294
R^2 0.632806 F(3,49) = 28.15 [0.000]**
log-likelihood 158.397 DW 1.27
no. of observations 53 no. of parameters 4
mean(DLC) 0.0265864 var(DLC) 0.000404345
DLC = + 0.01119 + 0.6508*DLY + 0.1092*LS_1 - 0.001078*P
(SE) (0.00483) (0.09) (0.0512) (0.000386)
Figure 7
Table 8
EQ(8) Modelling DLC by OLS (using project12min.xls)
The estimation sample is: 1950 to 2002
Coefficient Std.Error t-value t-prob Part.R^2
Constant 0.0152043 0.004323 3.52 0.001 0.2049
DLY 0.429792 0.09556 4.50 0.000 0.2965
LS_1 0.0650428 0.04600 1.41 0.164 0.0400
P -0.00178033 0.0003788 -4.70 0.000 0.3152
HP 0.000917289 0.0002263 4.05 0.000 0.2550
sigma 0.0110511 RSS 0.00586207711
R^2 0.726458 F(4,48) = 31.87 [0.000]**
log-likelihood 166.199 DW 1.55
no. of observations 53 no. of parameters 5
mean(DLC) 0.0265864 var(DLC) 0.000404345
DLC = + 0.0152 + 0.4298*DLY + 0.06504*LS_1 - 0.00178*P + 0.0009173*HP
(SE) (0.00432) (0.0956) (0.046) (0.000379) (0.000226)
Figure 8
Table 9
EQ(9) Modelling DLC by OLS (using project12min.xls)
The estimation sample is: 1952 to 2002
Coefficient Std.Error t-value t-prob Part.R^2
Constant 0.0176739 0.005014 3.52 0.001 0.2164
DLY 0.393545 0.1146 3.43 0.001 0.2075
LS_1 0.0426819 0.05511 0.774 0.443 0.0132
P -0.00166234 0.0005008 -3.32 0.002 0.1967
HP 0.00100082 0.0002372 4.22 0.000 0.2835
U -0.101787 0.1912 -0.532 0.597 0.0063
sigma 0.0111487 RSS 0.00559323806
R^2 0.717132 F(5,45) = 22.82 [0.000]**
log-likelihood 160.144 DW 1.57
no. of observations 51 no. of parameters 6
mean(DLC) 0.0273824 var(DLC) 0.000387711
DLC = + 0.01767 + 0.3935*DLY + 0.04268*LS_1 - 0.001662*P + 0.001001*HP- 0.1018*U
(SE) (0.00501) (0.115) (0.0551) (0.000501) (0.000237) (0.191)
Figure 9
REFERENCE
All handouts from EQ1162
http://www.gmu.edu/departments/writingcenter/handouts/abstract.html
http://www.usfca.edu/economics/veitch/ECON621/Assignments/621Assign1%20F01.doc
http://www.iupui.edu/~econ/courses/whcin.pdf^{[1]}
[1]
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Here's what a teacher thought of this essay
The author recognises the importance of consumption to the UK economy and models it well. However, explanation of statistics is poor, even though the conclusions are generally accurate. The application of theory and comparison of models based on theory is a good approach for this essay.
The conclusion doesn't seem to discuss which models were good and which were bad, which was the point of the essay. It does however talk about which other factors could be considered.
3 stars.
Marked by teacher Nick Simmons 28/02/2012