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

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.

(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]