Project: Estimate a consumption function for the UK economy explaining the economic theory and statistical techniques you have used.

Introduction:

Being able to model the behaviour of consumption is an immensely important economic tool, as consumption accounts for between half and two-thirds of the UK’s GDP each year and so is critical in evaluating the performance of the economy and predicting future economic forecasts. During this project I will layout the theory of the consumption function and then work through the process of estimating a suitable equation.

Theory:

The consumption function is an expression of the relationship between consumption and income, the general rule being that as national income increases so does consumption as people have more money to spend. This theory was first put forward by John Maynard Keynes in 1936 in his TheGeneral Theory of Employment, Wages and Money.  He argued that ‘The fundamental psychological law…is that men are disposed as a rule and on the average, to increase their consumption as their income increases, but not by as much as the increase in their income.’^[1] From this he derived the simplest of consumption functions:

Where consumption, C, is equal to autonomous consumption, c0, plus disposable income, Y, multiplied by the marginal propensity to consume, c1. The marginal propensity to consume is ‘the proportion of a rise in national income that goes on consumption’^[2] which as Keynes stated earlier is positive and yet below unity. When this equation is fitted to the data we get the equation:

Ct = 13530 + 0.9224Yt

This fits with Keynes statement that m.p.c. must be between 0 and 1 and shows that nearly all additional income is consumed.

Fig.  4.

 The main reason, it was argued, was that a combination of rapidly rising house prices and increased availability of credit meant that people had more wealth and so increased their consumption. The argument was based on the fact that because the price of people’s houses went up and being available to secure loans and equity against your property became easier people started to borrow more money and so increase their consumption accordingly. Because of this, to accurately predict consumption house prices needed to come into consideration. If we include them in our equation we obtain the following equation where HP stands for house prices:

Δct = 0.01342 + 0.4657Δyt + 0.07634st-1 - 0.001617πt + 0.0007924HPt

As you can see from comparing figures 4 (above) and 5 (below), by adding the HP variable the difference between the derived and the actual consumptions during the late 80’s and early nineties is much closer:

Fig. 5.

However there is still an unaccounted for gap during this period, another reason that was argued about why the original model fell apart was because uncertainty about future wage raises was falling. Throughout the 1980’s income levels had increased much more steadily than during the 1970’s and so people saved less for precautionary reasons, which meant that they had more disposable income and so increased their consumption accordingly. Uncertainty is not an easy variable to measure but for this project, uncertainty was taken as the ‘standard deviation over the previous four years of the growth of real personal income.’^[4] This meant that our equation looks as follows:

Δct = c0+c1Δyt+c2st-1+c3πt+c4HPt+c5Ut

This left the derived consumption function as:

Δct = 0.02213 + 0.3729Δyt + 0.07338st-1  - 0.00179πt + 0.

 DLC              1.0000

 Constant        0.00000     0.00000

 DLY             0.74022     0.00000      1.0000

 Inf            -0.47105     0.00000    -0.36329      1.0000

 S_1         -0.00049433     0.00000    -0.22889     0.16807      1.0000

EQ( 1) Modelling DLC by OLS  (using es1162proj.in7)

The present sample is:  1949 to 2003

Descriptive statistics

         DLC =  +0.01062              +0.6556 DLY        -0.001038 Inf        

(SE)          ( 0.004535)          (  0.08744)          (0.0003759)        

                  +0.1089 S_1        

              (  0.04746)        

R^2 = 0.632903  F(3,51) = 29.309 [0.0000]  \sigma = 0.0124386  DW = 1.29

RSS = 0.007890707309 for 4 variables and 55 observations

Seasonal means of differences are

     0.00013

R^2 relative to difference+seasonals =    0.69974

AR 1- 2 F( 2, 49) =     4.9335 [0.0112] *

ARCH 1  F( 1, 49) =     4.7432 [0.0343] *

Normality Chi^2(2)=     5.0768 [0.0790]  

Xi^2    F( 6, 44) =    0.72456 [0.6321]  

Xi*Xj   F( 9, 41) =    0.58121 [0.8046]  

RESET   F( 1, 50) =   0.089081 [0.7666]  

Descriptive statistics

Means

          DLC    Constant         DLY         Inf         S_1      HP_Inf

     0.026250      1.0000    0.027993      5.9691    0.031910      8.8491

Standard Deviations

          DLC    Constant         DLY         Inf         S_1      HP_Inf

     0.019951     0.00000    0.021134      4.8543    0.036799      8.6500

Correlation matrix

                     DLC    Constant         DLY         Inf         S_1

 DLC              1.0000

 Constant        0.00000     0.00000

 DLY             0.74022     0.00000      1.0000

 Inf            -0.47105     0.00000    -0.36329      1.0000

 S_1         -0.00049433     0.00000    -0.22889     0.16807      1.0000

 HP_Inf          0.46519     0.00000     0.39641     0.22712     0.10990

                  HP_Inf

 HP_Inf           1.0000

EQ( 2) Modelling DLC by OLS  (using es1162proj.in7)

The present sample is:  1949 to 2003

         DLC =  +0.01342              +0.4657 DLY        -0.001617 Inf        

(SE)          ( 0.004141)          (  0.09411)          (0.0003727)        

                 +0.07634 S_1        +0.0007924 HP_Inf    

              (  0.04351)          (0.0002169)        

R^2 = 0.710259  F(4,50) = 30.642 [0.0000]  \sigma = 0.0111606  DW = 1.49

RSS = 0.006227953112 for 5 variables and 55 observations

Seasonal means of differences are

     0.00013

R^2 relative to difference+seasonals =    0.76301

AR 1- 2 F( 2, 48) =     2.5038 [0.0924]  

ARCH 1  F( 1, 48) =     0.1878 [0.6667]  

Normality Chi^2(2)=    0.39869 [0.8193]  

Xi^2    F( 8, 41) =    0.54099 [0.8186]  

Xi*Xj   F(14, 35) =    0.53082 [0.8976]  

RESET   F( 1, 49) =    0.14221 [0.7077]  

---- PcGive 9.10 session started at 19:53:05 on Sunday 24 April 2005 ----

Descriptive statistics

Means

DLC    Constant         S_1         DLY      HP_Inf           U

0.026440      1.0000    0.034970    0.028037      8.9811      16790.

Inf

6.0830

Standard Deviations

DLC    Constant         S_1         DLY      HP_Inf           U

0.020282     0.00000    0.033813    0.021528      8.7545      21894.

Inf

4.9098

Correlation matrix

DLC    Constant         S_1         DLY      HP_Inf

DLC              1.0000

Constant        0.00000     0.00000

S_1           -0.025510     0.00000      1.0000

DLY             0.74051     0.00000    -0.25974      1.0000

HP_Inf          0.46981     0.00000    0.086457     0.40063      1.0000

U              -0.30424     0.00000    -0.15604    -0.29136    0.063056

Inf            -0.48217     0.00000     0.12881    -0.36765     0.22112

U         Inf

U                1.0000

Inf            0.081866      1.0000

EQ( 3) Modelling DLC by OLS  (using es1162proj.in7)

The present sample is:  1953 to 2003

DLC =  +0.02213             +0.07338 S_1          +0.3729 DLY

(SE)          ( 0.005464)          (    0.059)          (   0.1046)

+0.0009742 HP_Inf      -0.00179 Inf        -4.439e-007 U

(0.0002279)          (0.0003766)          (1.89e-007)

R^2 = 0.720782  F(5,45) = 23.233 [0.0000]  \sigma = 0.0108564  DW = 1.59

RSS = 0.005303797832 for 6 variables and 51 observations

Seasonal means of differences are

-0.00039

R^2 relative to difference+seasonals =    0.76502

AR 1- 2 F( 2, 43) =     1.5488 [0.2241]

ARCH 1  F( 1, 43) =   0.025411 [0.8741]

Normality Chi^2(2)=    0.13477 [0.9348]

Xi^2    F(10, 34) =    0.71796 [0.7019]

Xi*Xj   F(20, 24) =    0.73126 [0.7595]

RESET   F( 1, 44) =    0.20253 [0.6549]