There are many factors affecting the demand for money. This chapter chooses some major factors and tries to find their long term stable relationships. It also shows the graph of variables and their descriptive statistics. There are twenty years of quarterly data from 1988 to 2008. The base data are GDP, consumer price index (CPI), short and long run interest rate, broad money-M4, real money, money growth rate (Î”m), inflation rate (Î”CPI). All data and graph are in logs for easy to show their change. For instance: LGDP=LOG (GDP), LCPI= LOG (CPI), LRM=LOG (RM), LM4=LOG (M4), LRS=LOG (RS), LRL=LOG (RL); Î”m= logmt-logmt-1, Î”CPI = logCPIt-logCPIt-1.

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In the figure1, it is shows the data of GDP, broad money-M4, CPI and real money in United Kingdom from 1988 to 2008. The variables have same trend, it has been a reasonably close relationship between these variables.

Figure 1

## .

## The dependent variable -Real money

According to monetary theory, demand for money means demand for real money balance. In the money stock, almost all data are measured in nominal terms. It is necessary to divided by a price index to measure of real money. Also, it is generally accepted that a broadly base index. (Laidler, 1985, p.85). Therefore, the real money is equal to broad money divided by consumer price index: RM=M4/CPI. The M4 has a definition that the broad money to measure of the quantity of UK money supplies from Bank of England. The M4 includes holdings of sterling notes and coin; deposits; commercial paper, bonds, Floating ration notes (FRNs) and other instruments of up to and including five years’ original maturity issued by UK MFIs; claims on UK MFIs arising from repos (from December 1995);estimated holdings of sterling bank bills; and from end-1986, 95% of the domestic sterling interbank difference. (Bank of England). The dissertation adopts the broad money for the index because it could reflect the real demand for money.

In the figure 1, LRM shows an upward trend similar to LGDP. In these 20 years, the LRM has a great advance from 8.53928 to 9.77667. The actual level of real money shows growth from 5111.75 to 17617.90. It means the demand for money was increasing during 20 years.

## The scale variables

The scale variables include the income or wealth variables. It always measure by the GDP and CPI. GDP stands for the gross domestic production. It is an important index to measure income generated by the United Kingdom economy situation. The data of GDP is constant price which means it is real GDP. In the LGDP of figure 1: During 1988 Q1 to 1990 Q2, the UK joined the European Union that shows an increase from 12.26939 to 12.32066. However, the growth does not keep a long time. From 1990 Q3 to 1992 Q4, the GDP decrease from 12.30871 to 12.30528. The reason is the UK quit the European Exchange rate Mechanism and UK pounded crisis. After 1992, the UK adopted the fixed inflation rate that brought the long time stability to the economy. It can be seen in the data increase to 12.73899 from 1993Q1 to 2008Q3.

CPI is the consumer prices index. The UK government adopted CPI to the measure the inflation target. In addition, The Bank of England’s Monetary Policy Committee is required to achieve a target of 2 per cent. (ONS, 2010). In the LCPI of Figure 1, the data of CPI shows an increase from 4.12786 to 4.698661 in these 20years. The actual value of CPI shows an increase from 62.1 to 109.8 CPI did not behave the same as GDP ,the 2 years pound crisis does not effect the growth of CPI, on the contrary stimulates the upward CPI from 4.12786 to 4.393214.

Figure 2

Figure 3

## The opportunity cost variables

The dissertation has five opportunity cost variables which are short and long interest rate, money growth rate, inflation rate and stock exchange index. For the short run interest rate I choose the three month Treasury bill. For the long run interest rate I choose the yield from British Government securities for ten years. The money growth is calculated using the difference operator: log (M4t)-log (M4t-1). The same as for inflation rate which is equal: log (CPIt )-log (CPIt-1). The stock exchange price index chooses the FTSE 100 from 1990 Q1 to 2008 Q4.

In figure 2 there are three variables which are CPI annual inflation (LCPII), short run (LRS) and long run interest rate (LRL). All these series in the figure 2 have followed a broadly similar pattern over the economic cycle. The actual level of CPI annual inflation shows that a speed growth rate reached 8.3 percent in July 1991. After the 1992 to 2007, the actual level of inflation keeps a lower number, around 2 per cent and CPI shows stable increasing due to the monetary policy. It is nonetheless evident that, during the late 2007s and for the most of the 2008s, the actual level of CPI annual inflation increased to 3.9% due to the financial crisis.

The short and long run interest rate have similar pattern with CPI annual inflation. The short run interest rate shows more sensitivity and is more unstable than the long run interest rate. There are two periods during which the short run interest rate shows the different pattern from CPI annual inflation. The first period is 1999Q4 to 2000Q2, the actual level of short run interest rate increase from 5.31% to 5.98%, but the CPI annual inflation decrease from 1.1% to 0.6%. The second period is 2007Q1 to 2007Q3, when the actual level of short run interest rate increase from 5.32% to 5.76%, but the CPI annual inflation decrease from 2.9% to 1.8%. In the last period from 2008 Q3 to 2008Q4, the CPI annual inflation and short run rate both more downward rapidly. Moreover, the short run rate decreased from 4.94% to 2.34 % which is even lower than the CPI annual inflation which decreased by 3.9%.

Figure 3, also shows the money growth rate and inflation rate (Î”LM4, Î”LCPI). The money growth rate is DLM4 that is calculated suing the difference operator: DLM4= LM4-LM4 (-1). The same applies to the inflation rate (DLCPI) which is equal: LCPI-LCPI (-1). These series move relatively closely overall. There are three notable periods: Before the Pound crisis, 1991Q1 to Q4, when inflation is about 4.3% with money growth of 1.7%. The second period: during 1997 to 1998, when money growth decreased from 3.5% to -2.4%, the inflation rate increased from 0% to 0.3%. The third period: during 2007 to 2008, when the money growth movers upward from 1.3% to 5.7%, while the inflation rate downward from 1% to 0.09%. During other periods, the money growth rate is higher than the inflation rate.

Figure 4.

Figure 4 shows the stock exchange price index -FTSE 100 from 1990 Q1 to 2008 Q4. (DataStream only cores time from 1990 Q1 to 2008 Q4). It is the opportunity costs of demand for money- LOP. The opportunity cost is the major variable for the real money balance. When people were holding the money, they would lose a chance to earn a profit in the stock market. In the figure 4 shows two periods: The first period was 1990 Q1 to 2003 Q1 that displays a huge wave. The index increases from actual value of 2050.1 to 6401.67, then decreases to 3678.72. The second period was 2003 Q2 to 2008 Q4 that displays a huge wave too. It increases from 3952.59 to 6603.66, then decreases to 4530.73.

Descriptive statistics

Table 1.

LGDP

LCPI

LM4

LRS

LRM

LRL

LOP

Mean

12.52765

4.521687

13.66187

1.691005

9.140180

1.786344

8.390568

Median

12.54594

4.529368

13.61985

1.667705

9.091563

1.660086

8.445456

Maximum

12.75075

4.698661

14.47533

2.508786

9.776670

2.341806

8.795379

Minimum

12.29493

4.301359

13.09007

0.850151

8.762499

1.425515

7.697121

Std. Dev.

0.150488

0.092737

0.393164

0.291080

0.302950

0.278089

0.314014

Skewness

-0.124661

-0.183575

0.315784

0.492721

0.419514

0.516705

-0.494531

Kurtosis

1.673850

2.394824

2.027517

4.107995

2.023742

1.805762

1.993441

Jarque-Bera

5.462508

1.503113

4.033808

6.596243

4.971145

7.482420

5.974214

Probability

0.065138

0.471632

0.133067

0.036953

0.083278

0.023725

0.050433

Sum

901.9908

325.5614

983.6544

121.7524

658.0929

128.6168

604.1209

Sum Sq. Dev.

1.607907

0.610612

10.97506

6.015646

6.516300

5.490674

7.000951

Observations

72

72

72

72

72

72

72

Table 1 shows the descriptive statistics of seven variables. All the variables of table are in log. It has only 72 observations due to the limited times on data of opportunity cost. All the variables in terms of mean, median, maximum and minimum show data meaning: mean, max, mini and median are close to each other. In terms of the standard derivation, all the variables have it smaller than 0.5. The broad money has the highest standard derivation among the variables. It means broad money has more volatility than others in these years.

## Test the data by ADF

Table 2

## ã€€

## ã€€

level

1st

2st

5% c-value

## ã€€

## ã€€

t-statistic

t-statistic

t-statistic

## ã€€

Lrm

t&i

0.86

-6.77

## ã€€

-3.47

## ã€€

intercept

2.57

-3.80

## ã€€

-2.90

## ã€€

none

3.34

-1.95

## ã€€

-1.94

## ã€€

## ã€€

## ã€€

## ã€€

## ã€€

## ã€€

Lgdp

t&i

-1.23

-2.56

-11.19

-3.47

## ã€€

intercept

-1.07

-2.67

-11.15

-2.90

## ã€€

none

1.63

-2.18

-11.13

-1.94

## ã€€

## ã€€

## ã€€

## ã€€

## ã€€

## ã€€

Lm4

t&i

-0.60

-4.23

-9.64

-3.47

## ã€€

intercept

0.89

-4.22

-9.48

-2.90

## ã€€

none

3.86

-0.77

-9.55

-1.94

## ã€€

## ã€€

## ã€€

## ã€€

## ã€€

## ã€€

Lrs

t&i

-2.72

-3.46

-8.13

-3.47

## ã€€

intercept

-0.60

-3.48

-8.14

-2.90

## ã€€

none

-1.09

-3.41

-8.15

-1.94

## ã€€

## ã€€

## ã€€

## ã€€

## ã€€

## ã€€

Lrl

t&i

-3.15

-6.64

## ã€€

-3.47

## ã€€

intercept

-0.85

-6.69

## ã€€

-2.90

## ã€€

none

-1.76

-6.42

## ã€€

-1.94

## ã€€

## ã€€

## ã€€

## ã€€

## ã€€

## ã€€

Î”cpi

t&i

-4.40

## ã€€

## ã€€

-3.47

## ã€€

intercept

-3.92

## ã€€

## ã€€

-2.90

## ã€€

none

-2.46

## ã€€

## ã€€

-1.94

It is important by using the ADF statistic to test whether the time series data are stationary or not. The non-stationary data will strongly influence the model’s results and properties. The use of non-stationary data will lead to spurious regression in the model. (Chris, 2008, p.319). Therefore, one needs to use the ADF statistic to test the stationery or not. If it has the non -stationery data, the model will not be co-integration. The null hypothesis of the test is that a variable has a unit roots process. Table 2 records the ADF statistic over the sample 1988- 2008 for six variables. Every ADF statistic is reported for the automatic selection of lags where the maximum leg is 2. The unit root must be tested sequentially. In addition, it depends on the 5% critical values. There are three results in the table 2. The first result is the LRM t- statistic |6.77| > the critical value | 3.47|, so reject the null of nonstationarity. It means the variable d (LRM) = Î”LRM is a stationary series. It follows that the since RM has to be differenced once to obtain stationary, it is integrated of order 1. The same result applies to the long run interest rate. The second result is LGDP t- statistic | 11.19|>the critical value |3.47| in the 2nd difference. So reject the null of non stationary in the 2nd difference. It means LGDP is integrated of order 2. The same result as LM4 and LRS, but LRS is t- statistic | -3.46 ||3.70| in the level differences. So reject the null of non stationary, it means inflation rate is integrated of order 0. As the result, the LRM~I(1), LRL~I(1); LGDP~I(2),LM4~I(2),LRS~I(1) ; Î”LCPI~I(0).

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Above unit root test yield that variables have difference results. According to Chris (2008, p335)” if two variables that are I (1) are linearly combined, then the combination will also be I (1). More generally, if variables with differing orders of integration are combined, the combination will have an order of integration equal to the largest.” It means the variables of LGDP, LRL, LM4, Î”CPI and LRS did not change their order to the same order of integration. However, the variables have three different orders, so it only can used Dynamic OLS to co-integrate which allows for the different order of integration.