Applied Econometrics

The paper aims to analyze the money demand function both in the short run and in the long run. The static money demand function has been estimated taking inflation rate, real GDP and interest rate. In order to analyze robustness of the model autocorrelation test has been performed for examining presence of serial correlation in the model. Condition in the short run however is different from that in the long run. In the long run, it is assumed that money demand function is not directly observable and difference between observed money supply tends to adjust towards the expected difference in money supply having certain speed of adjustment. In the long run inclusion of lagged dependent variables may result in the problem of endogeneity where independent variables are found to be related with the error term. In order to eliminate the problem of endogeneity the technique of instrumental variables is used through the estimation method of two stage least square. Each of the series has been tested for unit root by employing the Augmenyed Dicky Fuller test. Finally, Engel Granger test has been performed to examine cointegration among the variables. The money demand function and its associate determinants provide useful implication for policy formulation.

Running head: APPLIED ECONOMETRICS
Applied Econometrics
Name of the Student
Name of the University
Course ID

1APPLIED ECONOMETRICS
Executive Summary
The paper aims to analyze the money demand function both in the short run and in the long run.
The static money demand function has been estimated taking inflation rate, real GDP and interest
rate. In order to analyze robustness of the model autocorrelation test has been performed for
examining presence of serial correlation in the model. Condition in the short run however is
different from that in the long run. In the long run, it is assumed that money demand function is
not directly observable and difference between observed money supply tends to adjust towards
the expected difference in money supply having certain speed of adjustment. In the long run
inclusion of lagged dependent variables may result in the problem of endogeneity where
independent variables are found to be related with the error term. In order to eliminate the
problem of endogeneity the technique of instrumental variables is used through the estimation
method of two stage least square. Each of the series has been tested for unit root by employing
the Augmenyed Dicky Fuller test. Finally, Engel Granger test has been performed to examine co-
integration among the variables. The money demand function and its associate determinants
provide useful implication for policy formulation.

2APPLIED ECONOMETRICS
Table of Contents
Question 1........................................................................................................................................4
Question 2........................................................................................................................................6
Question a....................................................................................................................................6
Question b....................................................................................................................................7
Question c....................................................................................................................................8
Question 3........................................................................................................................................8
Question a....................................................................................................................................8
Question b....................................................................................................................................9
Question 4......................................................................................................................................10
Question a..................................................................................................................................10
Question b..................................................................................................................................12
Question c..................................................................................................................................12
Question 5......................................................................................................................................13
Question a..................................................................................................................................13
Question b..................................................................................................................................13
Question c..................................................................................................................................13
Question d..................................................................................................................................13
Question 6......................................................................................................................................14
Question 7......................................................................................................................................15

3APPLIED ECONOMETRICS
Question a..................................................................................................................................15
Question b..................................................................................................................................15
Question c..................................................................................................................................15
Question 8......................................................................................................................................15
Question a..................................................................................................................................15
Question b..................................................................................................................................16
Question c..................................................................................................................................16
Question 9......................................................................................................................................16
Question a..................................................................................................................................16
Question b..................................................................................................................................18
Question c..................................................................................................................................18
Question 10....................................................................................................................................18
References and Bibliography.........................................................................................................20
Appendix........................................................................................................................................22

4APPLIED ECONOMETRICS
Question 1
Figure 1: Dynamic trend of inflation rate
The inflation series is highly volatile. The series initially increases, reaches peak and then
again declines. Most of the times, inflation rate varies between 0.01 to 0.02 percent.

5APPLIED ECONOMETRICS
Figure 2: Dynamic trend in interest rate
Like inflation series, the series of interest rate also shows dynamic fluctuating trend.
Figure 3: Dynamic trend in real GDP

6APPLIED ECONOMETRICS
The real GDP trend shows a continuous increasing trend overtime.
Figure 4: Dynamic trend in real money supply
Unlike inflation and interest rate, the series of money supply is relatively less volatile.
Initially money supply decreases at a continuous pace. Since 1980s, the series shows a
continuous rising trend similar to the series of real GDP.
Question 2
The model to be estimated is given as
lmt =β0 +β1 inf t +β2 lyt +β3 irt +ut
Question a
From the regression result (appendix, Table 1), the estimated static demand for money
equation is obtained as

7APPLIED ECONOMETRICS
lmt =1.423214+0.079303inf t +0.0413525 lyt −0.361611 irt
Question b
From the estimated static demand equation, the constant is obtained as 1.423214. The
constant implies slope of the money demand curve. That is all other variables influencing money
demand and such as inflation, real GDP and interest rate are zero, then money demand in the
economy is 1.423214. The coefficient associated with inflation rate is 0.0799303. The positive
value of inflation coefficient means that inflation has a positive relation with money demand
(Johnson 2017, pp. 121-128). That is higher the inflation, higher is the money demand and vice-
versa. More precisely, for 10 percent increase in inflation rate, log of real money balance
increases by 0.7 percent. This is consistent with expectation because during high inflation people
require more money to purchase goods and services increasing demand for money. For real
GDP, the estimated coefficient is 0.0413525. This implies real GDP is again positively
associated with money supply. From the coefficient estimate, it can be said that 10 percent
increase in log real GDP increases money demand by 0.04 percent. Increase in GDP thus
increase money supply and vice versa. A higher GDP implies a higher average income for
people. With increases in income people demand more money. The finding thus is consistent
with expectation. In case of interest rate, the associated coefficient is - -0.361611. The negative
coefficient suggests an inverse association with money demand and interest rate. That is money
demand increase with a decrease in interest rate. This is expected as interest rate is the cost of
holding money and hence is inversely associated with demand for money (Gan 2019).

8APPLIED ECONOMETRICS
Question c
Computed ‘t’ value for inflation rate 0.8764. The critical t value at 5% level of
significance and 101 degrees of freedom is 1.9837. As the absolute value of computed t is less
than the critical t, null hypothesis for no significant relation between inflation and money
demand is accepted. The independent variable, inflation thus is not statistically significant.
Associated p value for the coefficient is 0.3829. The p value exceeds the value of 5%
significance level again implying acceptance of null hypothesis of no significant relation
between dependent and independent variable. The proposed association between inflation and
money demand thus is not statistically significant. The proposed association between real GDP
and money demand thus is statistically significant as the computed t exceeds the critical t and p
value is smaller than the significance level. In case of interest rate a statistically significant but
negative association is obtained between money demand and interest rate.
Question 3
Question a
The joint significance test for the regression model can be performed using the F test. The
null and alternative hypotheses for the test are given as follows.
Null hypothesis: β1 = β2= β3 = 0
Alternative hypothesis: At least any of the β’s is not equal to zero.
The computed F value of the model is 75.07595. The critical F value at 5 percent level of
significance and (3, 101) degrees of freedom is 2.6946. The computed F value exceeds the
critical F value at 5 percent level of significance implying rejection of null hypothesis stating all

9APPLIED ECONOMETRICS
coefficients are zero. This can therefore be said that at least one of the coefficient is significantly
different from zero and hence, the model is jointly significant. The result is again supported by
the p value test. Associated p value for the F statistics is 0.0000. As the p value is less than
significance value of 0.05, the null hypothesis stating that the overall model is insignificant is
rejected. The independent variables in the model thus are jointly significant.
Question b
In multiple regression model adjusted R square is used as a measure of goodness of fit.
The obtained value of adjusted R square is 0.6812. The value indicates that inflation, real GDP
and interest rate can together explain 68 percent variation of the dependent variables. As the
independent variables account a considerably higher variability of the dependent variable, the
model is a good fit model.

10APPLIED ECONOMETRICS
Question 4
Question a
Correlogram of residual squares
Date: 04/27/19 Time: 16:12
Sample: 1963Q1 1989Q2
Included observations: 104
Autocorrelation Partial Correlation AC PAC Q-Stat Prob
1 0.676 0.676 48.862 0.000
2 0.419 -0.06... 67.879 0.000
3 0.217 -0.07... 73.019 0.000
4 0.005 -0.17... 73.023 0.000
5 -0.06... 0.068 73.440 0.000
6 -0.11... -0.07... 74.985 0.000
7 -0.07... 0.106 75.614 0.000
8 -0.04... -0.05... 75.871 0.000
9 -0.02... 0.016 75.951 0.000
1... -0.02... -0.07... 76.034 0.000
1... -0.02... 0.039 76.110 0.000
1... -0.02... -0.02... 76.174 0.000
1... 0.020 0.110 76.222 0.000
1... 0.098 0.076 77.389 0.000
1... 0.098 -0.04... 78.571 0.000
1... 0.054 -0.09... 78.935 0.000
1... 0.000 -0.02... 78.935 0.000
1... -0.04... 0.010 79.152 0.000
1... -0.04... 0.053 79.411 0.000
2... -0.03... 0.005 79.609 0.000
2... -0.01... 0.009 79.628 0.000
2... 0.038 0.033 79.825 0.000
2... 0.059 -0.00... 80.303 0.000
2... 0.047 -0.02... 80.603 0.000
2... 0.025 0.003 80.691 0.000
2... -0.02... -0.03... 80.755 0.000
2... -0.12... -0.16... 83.063 0.000
2... -0.20... -0.09... 89.146 0.000
2... -0.20... 0.034 95.063 0.000
3... -0.18... 0.007 99.892 0.000
3... -0.14... -0.01... 103.03 0.000
3... -0.11... -0.04... 104.88 0.000
3... -0.05... 0.017 105.33 0.000
3... -0.03... -0.05... 105.49 0.000
3... -0.00... 0.037 105.49 0.000
3... 0.002 -0.04... 105.49 0.000
Correlogram- Q statistics

11APPLIED ECONOMETRICS
Date: 04/27/19 Time: 16:09
Sample: 1963Q1 1989Q2
Included observations: 104
Autocorrelation Partial Correlation AC PAC Q-Stat Prob
1 0.836 0.836 74.858 0.000
2 0.670 -0.09... 123.41 0.000
3 0.499 -0.11... 150.61 0.000
4 0.346 -0.05... 163.81 0.000
5 0.206 -0.07... 168.52 0.000
6 0.097 -0.01... 169.58 0.000
7 -0.00... -0.08... 169.58 0.000
8 -0.08... -0.03... 170.36 0.000
9 -0.17... -0.15... 174.01 0.000
1... -0.21... 0.088 179.30 0.000
1... -0.20... 0.062 184.41 0.000
1... -0.20... -0.05... 189.19 0.000
1... -0.21... -0.11... 194.63 0.000
1... -0.23... -0.09... 201.22 0.000
1... -0.24... -0.02... 208.87 0.000
1... -0.21... 0.140 214.41 0.000
1... -0.16... 0.012 217.88 0.000
1... -0.12... -0.09... 220.00 0.000
1... -0.05... 0.128 220.38 0.000
2... -0.00... -0.02... 220.39 0.000
2... 0.041 0.049 220.61 0.000
2... 0.083 0.007 221.54 0.000
2... 0.109 -0.06... 223.14 0.000
2... 0.134 0.014 225.62 0.000
2... 0.129 -0.02... 227.93 0.000
2... 0.097 -0.01... 229.26 0.000
2... 0.082 0.026 230.22 0.000
2... 0.071 0.026 230.96 0.000
2... 0.068 0.018 231.64 0.000
3... 0.098 0.134 233.07 0.000
3... 0.095 -0.07... 234.43 0.000
3... 0.085 -0.02... 235.54 0.000
3... 0.111 0.164 237.45 0.000
3... 0.115 -0.01... 239.53 0.000
3... 0.083 -0.14... 240.64 0.000
3... 0.033 -0.08... 240.82 0.000
The correlogram has spikes up to lags 5. The Q statistics corresponding to all the lags are
statistically significant implying presence of significant serial autocorrelation in the residuals.

12APPLIED ECONOMETRICS
Question b
Consequences of autocorrelation on OLS estimator
Presence of autocorrelation affects the OLS estimator in the following ways.
 When the error terms suffer from autocorrelation, then OLS estimators though give an
unbiased result but fail to satisfy the minimum variance property.
 In the presence of autocorrelation among the disturbance term, variance computed by
OLS method is larger than variance computed by other method. As a result, the
significance of t and f under OLS no longer give a valid result (Giles and Beattie 2018,
pp. 99-116).
 The autocorrelation among the error terms seriously underestimate the variance of
disturbances.
 OLS estimators are no longer asymptotic if the random error terms suffer from
autocorrelation.
Question c
In order to test presence of serial autocorrelation in the error terms, LM test is used. The
null and alternative hypotheses of the test are as follows
Null hypothesis: There is no serial autocorrelation in the residuals
Alternative hypothesis: Serial autocorrelation presents in the residuals
The result of LM test is given in appendix (Table 2). The p value associated with LM
statistics is 0.0000. As the p value is less than significance level of 0.05, the null hypothesis of no
serial autocorrelation in the residual terms is rejected. The LM test thus indicates presence of

13APPLIED ECONOMETRICS
serial autocorrelation in the residuals supporting the result obtained from correlogram and Q
statistics.
Question 5
Question a
The model in equation (1) uses independent variables such as rate of inflation, real GDP
and interest rate to predict the desired level of money supply in the economy. Under the new
specification, money supply depends on expected level of money supply and the money supply
in the previous period.
Question b
The model for long run money demand is given as
lnMt −lnMt −1=δ (lnMt
¿−lnMt −1)
The regression result with new specification is given in appendix (Table 3). The
estimated long run money demand equation as obtained from the regression is
lnMt −lnMt −1=0.9999(lnM t
¿−lnM t−1)
The output shows that the difference between expected money supply and that of
previous period money supply has a positive influence on the different between actual money
supply and money supply in the previous period. The associated p value of the coefficient is
0.0000. This shows the independent variable in the model is statistically insignificant.
Question c
The speed of adjustment to the long run level is 0.99.

14APPLIED ECONOMETRICS
Question d
The static money demand model in the long run can be specified as
lnMt −lnMt −1=β0 + β1 (inf t−inf t−1 ) + β2 (ly¿¿ t−lyt−1 )+ β3 (irt −irt −1)+ut ¿
The estimated static money demand equation in the long run is obtained as (Table 4)
lnMt −lnMt −1=−0.999679−0.065064 ( inf t−inf t−1 ) +0.286499(ly ¿¿ t−lyt −1)−0.047124 (irt−irt−1 )¿
The new model of long run money demand equation includes lagged values for all of the
independent variables. For inflation the sign of coefficient now become negative. That means in
the long run association the difference between current and previous period inflation is inversely
associated with the difference between current period money supply and that of the previous
period money supply That is higher the difference between inflation in the two period lower is
the difference between money supply. Like equation (1), real GDP is positively associated with
money supply in long run while interest rate has a negative association with money supply. All
the independent variables in the long have become statistically significant unlike in model (1)
where inflation turned out to be statistically insignificant.
Question 6
In order to perform autocorrelation test for the new model LM test is used. The obtained
result from the LM test is produced in appendix (Table 5). P value of the LM statistics is 0.0003.
The significant p value is less than the statistical significance level of 0.05. This implies rejection
of null hypothesis of no serial autocorrelation in the residuals. The error terms in the long run
money demand model thus also suffers from the problem of serial autocorrelation.

15APPLIED ECONOMETRICS

16APPLIED ECONOMETRICS
Question 7
Question a
In a statistical model endogeneity problem refers to the correlation between the
independent variable and that of the error term. Error term in the model accounts for all the
variation that are not explained by the independent variables of the model (Sande and Ghosh
2018, pp.185-204). The inclusion of lagged dependent variables and GDP, inflation and interest
rate may lead to endogeneity problem because of interconnectedness among the variables.
Question b
Presence of endogeneity distorts OLS estimation of a model. Endogeneity has serious
implications for OLS estimates. In a model that suffers from endogeneity problem, the OLS
estimation gives biased and inconsistent estimates for the parameters (Gordon 2015, pp. 99-116).
With a biased estimation, the hypotheses tests are unable to provide a statistically valid result.
Question c
In order to deal with endogeneity problem either Ad Hoc solution or instrumental
variable methods are used.
Question 8
Question a
The selected instrument include one period lagged values of money supply, inflation, real
GDP and interest rate. The lagged values are chosen as instruments as these are independent of
error terms (Amsler, Prokhorov and Schmidt 2016, pp.280-288).

17APPLIED ECONOMETRICS
Question b
The estimated result with two stage least square is given in appendix (Table 6). The value
of coefficient though is almost same as that obtained by using OLS in Q5, running two stage
least square correct for bias present due to endogenety problem and therefore gives a preferable
result.
Question c
When the TSLS estimation of long run static money demand function (Table 7) is
compared to the static model of equation 1, a contractionary result is obtained. All the variables
in TSLS are statistically insignificant. The result of equation 1, however showed a statically
significant relation between money supply and that of real GDP and interest.
The comparison of TSLS with the obtained result for static long run money demand
equation again reveals a contradictory result. Unlike the OLS estimation, all the independent
variables are statistically insignificant. The coefficient values are smaller under TSLS than that
under OLS in equation 1.
Question 9
Question a
The Augmented Dicky-Fuller test or ADF test is used test stationarity of a particular time
series model (Paparoditis and Politis 2018, pp.955-973). In order to test the stationary of lm, inf,
ly and ir, ADF test is performed for the individual series. The null and alternative hypotheses for
ADF tests are given as follows
Null hypothesis: The series has a unit root

18APPLIED ECONOMETRICS
Alternative hypothesis: The series does not have a unit root
The ADF tests for each of series are given in Appendix (Table 8 – Table 15). The test include
maximum lag of 12 based of Schwarz Info Criterion (SIC).
For the money supply series, the ADF test performed at levels show that the absolute
value of computed t (1.0075) is less than critical t value (3.4963, 2.8903 and 2.5821) at 1%, 5%
and 10% level of significance. The null hypothesis that the series has a unit root is thus accepted.
The result is further supported by the obtained p value. The associated p value is 0.7484. As the
p value is larger than the significance value, this again implies acceptance of null hypothesis
indicating the series has unit root.
In case of inflation series, the ADF test performed at levels show that the absolute value
of computed t (16.5080) is greater than critical t value (3.4963, 2.8903 and 2.5821) at 1%, 5%
and 10% level of significance. The null hypothesis that the series has a unit root is thus rejected.
The result is further supported by the obtained p value. The associated p value is 0.0000. As the
p value is less than the significance value, this again implies rejection of null hypothesis
indicating the series is stationary at level.
For real GDP series, the ADF test performed at levels show that the absolute value of
computed t (0.130075) is less than critical t value (3.4963, 2.8903 and 2.5821) at 1%, 5% and
10% level of significance. The null hypothesis that the series has a unit root is thus accepted. The
result is further supported by the obtained p value. The associated p value is 0.9424. As the p
value is larger than the significance value, this again implies acceptance of null hypothesis
indicating the series has unit root.

19APPLIED ECONOMETRICS
For the interest rate series, the ADF test performed at levels show that the absolute value
of computed t (2.304109) is less than critical t value (3.4963, 2.8903 and 2.5821) at 1%, 5% and
10% level of significance. The null hypothesis that the series has a unit root is thus accepted. The
result is further supported by the obtained p value. The associated p value is 0.1726. As the p
value is larger than the significance value, this again implies acceptance of null hypothesis
indicating the series has unit root.
Question b
The order of integration depends on the level at which the concerned series becomes
stationary. For Money supply (lm), the series is stationary at second difference. It can therefore
be said that the series is integrated with order 2, I(2). In case of inflation series, it is stationary at
level and thus is integrated of order 0 or I (0). Both real GDP (ly) and interest rate (ir) are
stationary at first difference and therefore are integrated of order 1 or I(1).
Question c
In order to be co-integrated the two variables need to be stationary at same level. Not all
the four variables are stationary at same level and therefore, all of them are not co-integrated
(Lee and Lee 2015, pp.3154-3171). The seroes ly and ir both are integrated of order 1 and
therefore, might be co-integrated. Co-integration test performed for the two variables and the
result is given in appendix (Table 16). The co-integration equation includes maximum lag of 12
as selected by SIC. The associated p values for IR and LY are respectively 0.3302 and 0.9897.
As both the values are greater than significance level of 0.05, the null hypothesis that the series
are not co-integrated are accepted. The variables thus are not co-integrated.
Question 10

20APPLIED ECONOMETRICS
Demand for money refers to the amount of money that people I the economy willing to
hold at a certain point of time. The theory of liquidity preference suggests that money demand
depends on income and interest rate. Income is positively associated with money demand while
interest rate is inversely associated with money demand (Mele and Stefanski 2019, pp.393-410).
The analysis of the paper include an additional variable inflation for estimating money demand
function. The discussion provides useful insights related to money demand in the short run and
that in the long run. Monetary policy deals with money supply in the economy. Depending on
state of the economy, central bank takes the decision regarding expansionary or tight monetary
policy. In the short run, money demand has a positive significance association with real GDP.
That means policies to stimulate GDP and economic growth increase money demand as well. In
order to reduce money demand and controls inflationary pressure government should take a tight
monetary policy by increasing interest rate . Interest rate, which is the reward of saving, is
negatively associated with money demand (Palley 2015, pp.1-23). Therefore, government
policies of lowering interest rate (part of expansionary monetary policy) to encourage investment
has a positive impact on money demand. Higher money demand in turn brings a higher inflation
through demand-pull inflation. Policymakers therefore should take a policy that can balance
between macroeconomic variables such as inflation, real GDP and interest and that of real
money balances. In the long run however money supply quickly adjusts to the expected money
supply.

21APPLIED ECONOMETRICS
References and Bibliography
Amsler, C., Prokhorov, A. and Schmidt, P., 2016. Endogeneity in stochastic frontier
models. Journal of Econometrics, 190(2), pp.280-288.
Becu, J.M., Grandvalet, Y., Ambroise, C. and Dalmasso, C., 2017. Beyond support in two-stage
variable selection. Statistics and Computing, 27(1), pp.169-179.
Carrera, C. and Flores, J., 2017. Modelling and forecasting money demand: divide and
conquer (No. 2017-91).
Chatterjee, S. and Hadi, A.S., 2015. Regression analysis by example. John Wiley & Sons.
Darlington, R.B. and Hayes, A.F., 2016. Regression analysis and linear models: Concepts,
applications, and implementation. Guilford Publications.
Fox, J., 2015. Applied regression analysis and generalized linear models. Sage Publications.
Gan, P.T., 2019. Economic uncertainty, precautionary motive and the augmented form of money
demand function. Evolutionary and Institutional Economics Review, pp.1-27.
Giles, D.E. and Beattie, M., 2018. Autocorrelation pre-test estimation in models with a lagged
dependent variable. In Specification analysis in the linear model (pp. 99-116). Routledge.
Goodwin, N., Harris, J.M., Nelson, J.A., Roach, B. and Torras, M., 2015. Macroeconomics in
context. Routledge.
Gordon, D.V., 2015. The endogeneity problem in applied fisheries econometrics: A critical
review. Environmental and Resource Economics, 61(1), pp.115-125.

22APPLIED ECONOMETRICS
Johnson, H.G., 2017. The Demand for Money: Estimation of Structural Equations.
In Macroeconomics and Monetary Theory (pp. 121-128). Routledge.
Jonung, L., 2017. Demand for money: an analysis of the long-run behavior of the velocity of
circulation. Routledge.
Lee, H. and Lee, J., 2015. More powerful Engle–Granger cointegration tests. Journal of
Statistical Computation and Simulation, 85(15), pp.3154-3171.
Mele, A. and Stefanski, R., 2019. Velocity in the long run: Money and structural
transformation. Review of Economic Dynamics, 31, pp.393-410.
Palley, T.I., 2015. Money, fiscal policy, and interest rates: A critique of Modern Monetary
Theory. Review of Political Economy, 27(1), pp.1-23.
Paparoditis, E. and Politis, D.N., 2018. The asymptotic size and power of the augmented
Dickey–Fuller test for a unit root. Econometric Reviews, 37(9), pp.955-973.
Petit-Bois, M., Baek, E.K., Van den Noortgate, W., Beretvas, S.N. and Ferron, J.M., 2016. The
consequences of modeling autocorrelation when synthesizing single-case studies using a three-
level model. Behavior research methods, 48(2), pp.803-812.
Sande, J.B. and Ghosh, M., 2018. Endogeneity in survey research. International Journal of
Research in Marketing, 35(2), pp.185-204.
Schumacker, R.E., 2017. Interaction and nonlinear effects in structural equation modeling.
Routledge.
Uribe, M. and Schmitt-Grohé, S., 2017. Open economy macroeconomics. Princeton University
Press.

23APPLIED ECONOMETRICS
Appendix
Table 1: Static money demand equation
Dependent Variable: LM
Method: Least Squares
Date: 04/26/19 Time: 16:11
Sample (adjusted): 1963Q2 1989Q2
Included observations: 105 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
C 1.423214 0.139993 10.16634 0.0000
INF 0.079303 0.090484 0.876427 0.3829
LY 0.413525 0.057020 7.252307 0.0000
IR -0.361611 0.033889 -10.67046 0.0000
R-squared 0.690400 Mean dependent var 2.409453
Adjusted R-squared 0.681204 S.D. dependent var 0.017106
S.E. of regression 0.009658 Akaike info criterion -6.404633
Sum squared resid 0.009422 Schwarz criterion -6.303529
Log likelihood 340.2432 Hannan-Quinn criter. -6.363664
F-statistic 75.07595 Durbin-Watson stat 0.230013
Prob(F-statistic) 0.000000
Table 2: Serial correlation LM test
Breusch-Godfrey Serial Correlation LM Test:
F-statistic 65.66106 Prob. F(5,95) 0.0000
Obs*R-squared 80.45876 Prob. Chi-Square(5) 0.0000
Test Equation:
Dependent Variable: RESID
Method: Least Squares
Date: 04/27/19 Time: 13:34
Sample (adjusted): 1963Q3 1989Q2
Included observations: 104 after adjustments
Presample missing value lagged residuals set to zero.
Variable Coefficient Std. Error t-Statistic Prob.
C -0.047874 0.072364 -0.661569 0.5098
INF -0.034081 0.054793 -0.621994 0.5354
LY 0.019927 0.029469 0.676216 0.5005
IR -0.007997 0.012564 -0.636536 0.5260

24APPLIED ECONOMETRICS
RESID(-1) 1.038066 0.106109 9.783014 0.0000
RESID(-2) -0.066647 0.146891 -0.453719 0.6511
RESID(-3) -0.141486 0.145558 -0.972022 0.3335
RESID(-4) 0.151278 0.149153 1.014244 0.3130
RESID(-5) -0.126483 0.109919 -1.150697 0.2527
R-squared 0.773642 Mean dependent var 0.001623
Adjusted R-squared 0.754580 S.D. dependent var 0.009523
S.E. of regression 0.004718 Akaike info criterion -7.792394
Sum squared resid 0.002114 Schwarz criterion -7.563552
Log likelihood 414.2045 Hannan-Quinn criter. -7.699683
F-statistic 40.58612 Durbin-Watson stat 1.955545
Prob(F-statistic) 0.000000
Table 3: Long run money demand
Dependent Variable: Y
Method: Least Squares
Date: 04/27/19 Time: 10:12
Sample (adjusted): 1963Q2 1989Q2
Included observations: 105 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
X 0.999904 0.000929 1076.067 0.0000
R-squared -13.326306 Mean dependent var -0.999513
Adjusted R-squared -13.326306 S.D. dependent var 0.002515
S.E. of regression 0.009518 Akaike info criterion -6.461879
Sum squared resid 0.009421 Schwarz criterion -6.436603
Log likelihood 340.2486 Hannan-Quinn criter. -6.451636
Durbin-Watson stat 0.229991

25APPLIED ECONOMETRICS
Table 4: Long run static money demand model
Dependent Variable: Y
Method: Least Squares
Date: 04/27/19 Time: 13:39
Sample (adjusted): 1963Q3 1989Q2
Included observations: 104 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
C -0.999679 0.000244 -4096.008 0.0000
INF_NEW -0.065064 0.027094 -2.401423 0.0182
LY_NEW 0.286499 0.140946 2.032692 0.0447
IR_NEW -0.047124 0.018244 -2.582917 0.0112
R-squared 0.173547 Mean dependent var -0.999514
Adjusted R-squared 0.148754 S.D. dependent var 0.002527
S.E. of regression 0.002331 Akaike info criterion -9.247174
Sum squared resid 0.000543 Schwarz criterion -9.145467
Log likelihood 484.8530 Hannan-Quinn criter. -9.205969
F-statistic 6.999694 Durbin-Watson stat 1.283716
Prob(F-statistic) 0.000254
Table 5: LM test of serial autocorrelation for long run static money demand model
Breusch-Godfrey Serial Correlation LM Test:
F-statistic 8.866617 Prob. F(2,98) 0.0003
Obs*R-squared 15.93541 Prob. Chi-Square(2) 0.0003
Test Equation:
Dependent Variable: RESID
Method: Least Squares
Date: 04/27/19 Time: 13:39
Sample: 1963Q3 1989Q2
Included observations: 104
Presample missing value lagged residuals set to zero.
Variable Coefficient Std. Error t-Statistic Prob.
C 8.34E-05 0.000229 0.363926 0.7167
INF_NEW -0.011353 0.025364 -0.447607 0.6554
LY_NEW -0.103922 0.138165 -0.752159 0.4538
IR_NEW -0.013629 0.017275 -0.788953 0.4320
RESID(-1) 0.331367 0.101641 3.260180 0.0015
RESID(-2) 0.162657 0.106414 1.528533 0.1296
R-squared 0.153225 Mean dependent var 1.08E-17

26APPLIED ECONOMETRICS
Adjusted R-squared 0.110022 S.D. dependent var 0.002297
S.E. of regression 0.002167 Akaike info criterion -9.375033
Sum squared resid 0.000460 Schwarz criterion -9.222472
Log likelihood 493.5017 Hannan-Quinn criter. -9.313226
F-statistic 3.546647 Durbin-Watson stat 2.059277
Prob(F-statistic) 0.005451
Table 6: Two stage least square for long run money demand
Dependent Variable: Y
Method: Two-Stage Least Squares
Date: 04/27/19 Time: 14:55
Sample (adjusted): 1963Q4 1989Q2
Included observations: 103 after adjustments
Instrument specification: LM_T INF_T LY_T IR_T
Constant added to instrument list
Variable Coefficient Std. Error t-Statistic Prob.
X 0.999908 0.000947 1055.564 0.0000
R-squared -13.328140 Mean dependent var -0.999518
Adjusted R-squared -13.328140 S.D. dependent var 0.002539
S.E. of regression 0.009610 Sum squared resid 0.009419
Durbin-Watson stat 0.229882 Second-Stage SSR 0.008087
J-statistic 83.72996 Instrument rank 5
Prob(J-statistic) 0.000000
Table 7: TSLS for long run static money demand
Dependent Variable: Y
Method: Two-Stage Least Squares
Date: 04/27/19 Time: 15:07
Sample (adjusted): 1963Q4 1989Q2
Included observations: 103 after adjustments
Instrument specification: LM_T INF_T LY_T IR_T
Constant added to instrument list
Variable Coefficient Std. Error t-Statistic Prob.
C -1.002580 0.002175 -460.9890 0.0000
INF_NEW -0.178078 0.237465 -0.749913 0.4551
LY_NEW 5.066604 3.299247 1.535685 0.1278
IR_NEW -0.336989 0.419101 -0.804075 0.4233
R-squared -11.434900 Mean dependent var -0.999518
Adjusted R-squared -11.811715 S.D. dependent var 0.002539

27APPLIED ECONOMETRICS
S.E. of regression 0.009087 Sum squared resid 0.008175
F-statistic 0.867052 Durbin-Watson stat 2.653666
Prob(F-statistic) 0.460926 Second-Stage SSR 0.000443
J-statistic 1.061957 Instrument rank 5
Prob(J-statistic) 0.302769
Table 8: ADF test of LM at level
Null Hypothesis: LM has a unit root
Exogenous: Constant
Lag Length: 4 (Automatic - based on SIC, maxlag=12)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -1.007529 0.7484
Test critical values: 1% level -3.496346
5% level -2.890327
10% level -2.582196
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(LM)
Method: Least Squares
Date: 04/27/19 Time: 13:43
Sample (adjusted): 1964Q2 1989Q2
Included observations: 101 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
LM(-1) -0.016727 0.016602 -1.007529 0.3162
D(LM(-1)) 0.279979 0.095587 2.929047 0.0043
D(LM(-2)) 0.191625 0.097829 1.958775 0.0531
D(LM(-3)) -0.110389 0.101650 -1.085963 0.2802
D(LM(-4)) 0.448964 0.101753 4.412296 0.0000
C 0.040400 0.039950 1.011282 0.3145
R-squared 0.327827 Mean dependent var 0.000472
Adjusted R-squared 0.292450 S.D. dependent var 0.002561
S.E. of regression 0.002154 Akaike info criterion -9.385310
Sum squared resid 0.000441 Schwarz criterion -9.229957
Log likelihood 479.9582 Hannan-Quinn criter. -9.322419
F-statistic 9.266547 Durbin-Watson stat 1.981630
Prob(F-statistic) 0.000000

28APPLIED ECONOMETRICS
Table 9: ADF test of LM at first difference
Null Hypothesis: D(LM) has a unit root
Exogenous: Constant
Lag Length: 3 (Automatic - based on SIC, maxlag=12)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -2.358420 0.1562
Test critical values: 1% level -3.496346
5% level -2.890327
10% level -2.582196
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(LM,2)
Method: Least Squares
Date: 04/27/19 Time: 13:44
Sample (adjusted): 1964Q2 1989Q2
Included observations: 101 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
D(LM(-1)) -0.286537 0.121496 -2.358420 0.0204
D(LM(-1),2) -0.453739 0.122487 -3.704376 0.0004
D(LM(-2),2) -0.274649 0.118490 -2.317908 0.0226
D(LM(-3),2) -0.412258 0.095015 -4.338885 0.0000
C 0.000151 0.000221 0.680228 0.4980
R-squared 0.490343 Mean dependent var 1.74E-05
Adjusted R-squared 0.469108 S.D. dependent var 0.002957
S.E. of regression 0.002154 Akaike info criterion -9.394483
Sum squared resid 0.000446 Schwarz criterion -9.265022
Log likelihood 479.4214 Hannan-Quinn criter. -9.342074
F-statistic 23.09052 Durbin-Watson stat 1.955680
Prob(F-statistic) 0.000000
Table 10: ADF test of LM at second difference
Null Hypothesis: D(LM,2) has a unit root
Exogenous: Constant
Lag Length: 2 (Automatic - based on SIC, maxlag=12)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -11.74276 0.0001
Test critical values: 1% level -3.496346
5% level -2.890327

29APPLIED ECONOMETRICS
10% level -2.582196
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(LM,3)
Method: Least Squares
Date: 04/27/19 Time: 13:45
Sample (adjusted): 1964Q2 1989Q2
Included observations: 101 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
D(LM(-1),2) -2.571710 0.219004 -11.74276 0.0000
D(LM(-1),3) 0.913857 0.168977 5.408166 0.0000
D(LM(-2),3) 0.495915 0.090194 5.498310 0.0000
C 2.07E-05 0.000219 0.094499 0.9249
R-squared 0.823805 Mean dependent var -2.59E-06
Adjusted R-squared 0.818356 S.D. dependent var 0.005172
S.E. of regression 0.002204 Akaike info criterion -9.357963
Sum squared resid 0.000471 Schwarz criterion -9.254394
Log likelihood 476.5771 Hannan-Quinn criter. -9.316035
F-statistic 151.1757 Durbin-Watson stat 2.005811
Prob(F-statistic) 0.000000
Table 11: ADF test of inf at level
Null Hypothesis: INF has a unit root
Exogenous: Constant
Lag Length: 0 (Automatic - based on SIC, maxlag=12)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -16.50802 0.0000
Test critical values: 1% level -3.495021
5% level -2.889753
10% level -2.581890
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(INF)
Method: Least Squares
Date: 04/27/19 Time: 13:46
Sample (adjusted): 1963Q4 1989Q2
Included observations: 103 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.

30APPLIED ECONOMETRICS
INF(-1) -1.444896 0.087527 -16.50802 0.0000
C 0.000212 0.000777 0.273144 0.7853
R-squared 0.729596 Mean dependent var 0.000198
Adjusted R-squared 0.726918 S.D. dependent var 0.015092
S.E. of regression 0.007886 Akaike info criterion -6.828128
Sum squared resid 0.006282 Schwarz criterion -6.776968
Log likelihood 353.6486 Hannan-Quinn criter. -6.807407
F-statistic 272.5147 Durbin-Watson stat 1.903154
Prob(F-statistic) 0.000000
Table 12: ADF test of ly at level
Null Hypothesis: LY has a unit root
Exogenous: Constant
Lag Length: 1 (Automatic - based on SIC, maxlag=12)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -0.130075 0.9424
Test critical values: 1% level -3.494378
5% level -2.889474
10% level -2.581741
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(LY)
Method: Least Squares
Date: 04/27/19 Time: 13:47
Sample (adjusted): 1963Q3 1989Q2
Included observations: 104 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
LY(-1) -0.001199 0.009218 -0.130075 0.8968
D(LY(-1)) -0.346078 0.090536 -3.822535 0.0002
C 0.003783 0.022645 0.167075 0.8676
R-squared 0.127042 Mean dependent var 0.000608
Adjusted R-squared 0.109755 S.D. dependent var 0.001635
S.E. of regression 0.001543 Akaike info criterion -10.08225
Sum squared resid 0.000240 Schwarz criterion -10.00597
Log likelihood 527.2769 Hannan-Quinn criter. -10.05135
F-statistic 7.349258 Durbin-Watson stat 1.933410
Prob(F-statistic) 0.001048

31APPLIED ECONOMETRICS
Table 13: ADF test of ly at first difference
Null Hypothesis: D(LY) has a unit root
Exogenous: Constant
Lag Length: 0 (Automatic - based on SIC, maxlag=12)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -14.95941 0.0000
Test critical values: 1% level -3.494378
5% level -2.889474
10% level -2.581741
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(LY,2)
Method: Least Squares
Date: 04/27/19 Time: 13:48
Sample (adjusted): 1963Q3 1989Q2
Included observations: 104 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
D(LY(-1)) -1.346584 0.090016 -14.95941 0.0000
C 0.000838 0.000162 5.172540 0.0000
R-squared 0.686909 Mean dependent var -5.73E-05
Adjusted R-squared 0.683840 S.D. dependent var 0.002730
S.E. of regression 0.001535 Akaike info criterion -10.10131
Sum squared resid 0.000240 Schwarz criterion -10.05046
Log likelihood 527.2682 Hannan-Quinn criter. -10.08071
F-statistic 223.7840 Durbin-Watson stat 1.934387
Prob(F-statistic) 0.000000
Table 14: ADF test of ir at level
Null Hypothesis: IR has a unit root
Exogenous: Constant
Lag Length: 1 (Automatic - based on SIC, maxlag=12)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -2.304109 0.1726
Test critical values: 1% level -3.494378
5% level -2.889474
10% level -2.581741
*MacKinnon (1996) one-sided p-values.

32APPLIED ECONOMETRICS
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(IR)
Method: Least Squares
Date: 04/27/19 Time: 13:49
Sample (adjusted): 1963Q3 1989Q2
Included observations: 104 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
IR(-1) -0.078762 0.034183 -2.304109 0.0233
D(IR(-1)) 0.222175 0.097156 2.286776 0.0243
C 0.006976 0.003235 2.156135 0.0334
R-squared 0.081672 Mean dependent var 0.000112
Adjusted R-squared 0.063487 S.D. dependent var 0.013242
S.E. of regression 0.012815 Akaike info criterion -5.847966
Sum squared resid 0.016587 Schwarz criterion -5.771686
Log likelihood 307.0943 Hannan-Quinn criter. -5.817063
F-statistic 4.491234 Durbin-Watson stat 2.039309
Prob(F-statistic) 0.013533
Table 15: ADF test of ir at first difference
Null Hypothesis: D(IR) has a unit root
Exogenous: Constant
Lag Length: 0 (Automatic - based on SIC, maxlag=12)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -8.359246 0.0000
Test critical values: 1% level -3.494378
5% level -2.889474
10% level -2.581741
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(IR,2)
Method: Least Squares
Date: 04/27/19 Time: 13:50
Sample (adjusted): 1963Q3 1989Q2
Included observations: 104 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
D(IR(-1)) -0.816600 0.097688 -8.359246 0.0000
C 0.000107 0.001283 0.083055 0.9340
R-squared 0.406552 Mean dependent var 8.15E-05
Adjusted R-squared 0.400734 S.D. dependent var 0.016900

33APPLIED ECONOMETRICS
S.E. of regression 0.013083 Akaike info criterion -5.815969
Sum squared resid 0.017459 Schwarz criterion -5.765115
Log likelihood 304.4304 Hannan-Quinn criter. -5.795366
F-statistic 69.87700 Durbin-Watson stat 2.008875
Prob(F-statistic) 0.000000
Table 16: Engel-granger test
Date: 04/27/19 Time: 14:01
Series: IR LY
Sample: 1963Q1 1989Q2
Included observations: 106
Null hypothesis: Series are not cointegrated
Cointegrating equation deterministics: C
Automatic lags specification based on Schwarz criterion (maxlag=12)
Dependent tau-statistic Prob.* z-statistic Prob.*
IR -2.246474 0.4045 -10.26665 0.3302
LY 0.061290 0.9895 0.145733 0.9897
*MacKinnon (1996) p-values.
Intermediate Results:
IR LY
Rho - 1 -0.076838 0.000644
Rho S.E. 0.034204 0.010505
Residual variance 0.000163 2.45E-06
Long-run residual variance 0.000269 1.28E-05
Number of lags 1 6
Number of observations 104 99
Number of stochastic trends** 2 2
**Number of stochastic trends in asymptotic distribution