11. Hypothesis Testing on Model 2
Now we examine the second model. The model is similar to the model conducted above with the exception that it uses LR5 instead of R1, it is a log model (all the explanatory variables are logged) and that a lagged term has been added LRM4 (-1). This is to correct for the autocorrelation and heteroscedasticity found in the previous model.
The model runs from the 1st quarter of 1969 due to the lagged variable and missing data, to the 2nd quarter of 2001, because of missing data for the variables in the 3rd quarter of 2001. The same tests will be run as in the first model to compare and see whether any improvements to the model have been made.
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All variables appear statistically significant at the 95% level. They have their expected signs. The R bar square value is very high (.99806), as well as the F-stat (22135.4).

Normal Distribution

T-Test – Confidence Intervals

P-Value | Similar to the previous model, the P-values for all 3 variables are 0.000. Since the value is less than 0.005, we reject the null hypothesis Ho and accept H1. The results are also statistically significant. There is 0% chance the null hypothesis is true. | Goodness of fit | Based on the R-bar squared figure of .99806. As the R-bar squared is above > 0.50, it also conforms to the third Gauss Markov assumption whereEUtVt-1=0, t≠t-1. | T-Ratio | From the results, * A: Serial Correlation*CHSQ ( 4) = 15.2797. This is not as bad as the value of 117.9066 obtained in the first model. | Normality | As can be seen from the results, C: Normality *CHSQ ( 2) = 289.8492. This exceeds the chi square critical value of 5.99 or 6 so we have to reject the normality of the model. |

F-Distribution
The F statistics can also be seen from the results above and have been compiled in the table below:

Test Statistic | Degrees of Freedom | Chi Square Critical Value | F statistic | Accepted / Rejected | Serial Correlation | 4 | 9.49 | 4.0623 | Accepted | Functional Form | 1 | 3.34 | 8.9386 | Rejected | Heteroscedasticity | 1 | 3.34 | .047190 | Accepted |

Based on the F distribution test, hence there is autocorrelation and heteroscedasticity present in the model and results. The functional form of the model is not acceptable. These do not adhere to the Gauss Markov assumptions.

12. Heteroscedasticity in 2nd Model
This second model attempts to correct for the heteroscedasticity of the first model with the introduction of a lagged variable (LRM4 (-1)).
Informal Tests
Plot of Residuals and Two Standards
Error Bands
Quarters
-0.02
-0.04
-0.06
-0.08
-0.10
0.00
0.02
0.04
0.06
0.08
1969Q1
1974Q1
1979Q1
1984Q1
1989Q1
1994Q1
1999Q1
2001Q2

Formal Tests X² (chi squares) Test | * D: Heteroscedasticity *CHSQ ( 1) = .047910[.827]*F ( 1, 128) = .047190[.828]The obtained value is .047910which is smaller than the critical value of 3.34 or 4. Therefore, at a glance, there may not be heteroscedasticity. However, the value may also be too small to be accurate as it is less than 1. | F-Distribution Test | * D:Heteroscedasticity *CHSQ ( 1) = .047910[.827]*F ( 1, 128) = .047190[.828]Like the above result, the value is too small and is cause for worry as it may not be accurate. |

13. Autocorrelation for 2nd model
This second model is run in a log form instead of the previous linear model to attempt to correct for autocorrelation. Autocorrelation function of residuals, from 1969Q1 to 2001Q2 Order of lags
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
0
2
4
6
8
10
12
14
16
18
20
22
22
Formal Tests Durbin h test (dh stat) | The Durbin h statistic is 3.7260 and larger than 2, we reject the null hypothesis of no serial correlation. Therefore, there is autocorrelation present. | F-Distribution Test | * A: Serial Correlation* F (4, 122) = 4.0623[.004]. The computed value of F is 4.0623 which is smaller than 9.49 (critical value). Therefore, we can conclude that there is no autocorrelation. | X² (chi squares) Test | A: Serial Correlation*CHSQ ( 4) = 15.2797[.004]. The computed value is 15.2797 which is larger than 9.49 (critical value). Therefore, we can conclude that there is autocorrelation present in the model. |

14. Empirical Results
The existence of a well-specified demand for money is important for the conduct of monetary policy, whether the central banks’ major policy variable is the stock of money or the official interest rate or inflation. This project examines the short run and long run determinants for money demand in Australia from 1969Q1 to 2001Q2. The microfit software and hand calculations are used to model the long run and short run demand for broad money. For consistency, the data have been obtained from one single source (CD-ROM). The choice of the variables in this project was contingent upon the availability of consistent time series data on them. It should be noted that according to de Brouwer (1993), a broader measure of money is more appropriate for modeling purposes because it: a) is less distorted by financial deregulation and innovations; and b) has a more reliable relationship with income. M4 is the broadest monetary aggregate for which data are available for the period under consideration. It should be noted that the choice of interest rates depends on the measure of money being modeled.

Ericsson (1998) suggests that long-run rates should not be included in the demand equation for M1. However, if a broader definition of money (such as M4) is modeled, it is essential to incorporate longer-term interest rates in the demand for money function so as to capture financial asset substitutions.

According to the results set out in Section 11, 02, 13 and consistent with theoretical assumptions discussed in Section 2, the demand for broad money in the long run is positively related to real income and negatively to the interest rate spread.

Furthermore the estimated coefficients of the short run model have been sensibly signed, with the interest rate spread having negative coefficient of -0.017683, respectively. As expected, changes in real income exert a positive impact (+0.10954) on money demand. This model has performed well in terms of goodness of fit (R bar square = .998). Although the P-value and the R bar square for the model is acceptable, there still appears to be some autocorrelation and heteroscedasticity present in the model. These may be corrected by adding in different explanatory variables to improve the model.

There does appear to be a stable long run broad money demand relationship using recent
Australian data. This analysis reveals some qualified support linking broad money, real GDP, the interest rate spread. Real GDP increase the demand for Broad money while interest rate reduces it. Further broad money is characterised by these results as a luxury good because the income elasticity of demand for it exceeds the value one. Money demand relationships have a reputation for being structurally unstable. This raises serious doubts.

Therefore, the RBA should pursue a forward looking policy in relation to changes in the cash rate; otherwise the policy may not have a timely and desirable effect. The long- and short-run models estimated for money demand support the view that BM is a predictable monetary aggregate. The RBA’s major policy instrument, changing the official cash rate, is effective in affecting BM, a fundamentally important macroeconomic variable. The models developed by Abbas Valadkhanit (2008) can provide useful policy guides for the RBA in its quest for price stability by measuring the impact of a change in the official cash rate on money demand and hence inflation.

The more responsive money demand is to the interest rate, the more elastic is the LM curve. The LM curve holds constant price-level, expectations, and Money Supply.
When interest rates are very low, people have no special reason to avoid holding idle cash, and will hold considerable amounts. If they hold lots of cash idle, the fixed amount of money cannot support very much spending. Lots of idle cash means that the representative dollar is not being spent very frequently.