Example 15.2: Money Demand Model

The PDLREG Procedure

Example 15.2: Money Demand Model

This example estimates the demand for money using the following dynamic specification:

$m_{t} = a_{0} + b_{0} m_{t-1} + \sum_{i=0}^5{c_{i} y_{t-i}} + \sum_{i=0}^2{d_{i} r_{t-i}} + \sum_{i=0}^3{f_{i} p_{t-i}} + u_{t}$

where

: m_t = log of real money stock (M1)
: y_t = log of real GNP
: r_t = interest rate (commercial paper rate)
: p_t = inflation rate
: c_i, d_i, and f_i (i>0) are coefficients for the lagged variables

The following DATA step reads the data and transforms the real money and real GNP variables using the natural logarithm. Refer to Balke and Gordon (1986) for a description of the data.

   data a;
      input m1 gnp gdf r @@;
      m    = log( 100 * m1 / gdf );
      lagm = lag( m );
      y    = log( gnp );
      p    = log( gdf / lag( gdf ) );
      date = intnx( 'qtr', '1jan1968'd, _n_-1 );
      format date yyqc6.;
      label m    = 'Real Money Stock (M1)'
            lagm = 'Lagged Real Money Stock'
            y    = 'Real GNP'
            r    = 'Commercial Paper Rate'
            p    = 'Inflation Rate';
   cards;
      ... data lines are omitted ...
   ;
   
   proc print data=a(obs=5);
      var date m lagm y r p;
   run;

Output 15.2.1 shows a partial list of the data set.

Output 15.2.1: Partial List of the Data Set A

Obs	date	m	lagm	y	r	p
1	1968:1	5.44041	.	6.94333	5.58	.
2	1968:2	5.44732	5.44041	6.96226	6.08	0.011513
3	1968:3	5.45815	5.44732	6.97422	5.96	0.008246
4	1968:4	5.46492	5.45815	6.97661	5.96	0.014865
5	1969:1	5.46980	5.46492	6.98855	6.66	0.011005

The regression model is written for the PDLREG procedure with a MODEL statement. The LAGDEP= option is specified to test for the serial correlation in disturbances since regressors contain the lagged dependent variable LAGM.

   title 'Money Demand Estimation using Distributed Lag Model';
   title2 'Quarterly Data - 1968Q2 to 1983Q4';
   
   proc pdlreg data=a;
      model m = lagm y(5,3) r(2, , ,first) p(3,2) / lagdep=lagm;
   run;

The estimated model is shown in Output 15.2.2 and Output 15.2.3.

Output 15.2.2: Parameter Estimates

Money Demand Estimation using Distributed Lag Model

Quarterly Data - 1968Q2 to 1983Q4

The PDLREG Procedure

Dependent Variable	m
	Real Money Stock (M1)

Ordinary Least Squares Estimates
SSE	0.00169815	DFE	48
MSE	0.0000354	Root MSE	0.00595
SBC	-404.60169	AIC	-427.4546
Regress R-Square	0.9712	Total R-Square	0.9712
Durbin h	-0.7533	Pr < h	0.2256

Variable	DF	Estimate	Standard Error	t Value	Approx Pr > \|t\|
Intercept	1	-0.1407	0.2625	-0.54	0.5943
lagm	1	0.9875	0.0425	23.21	<.0001
y0**	1	0.0132	0.004531	2.91	0.0055
y1**	1	-0.0704	0.0528	-1.33	0.1891
y2**	1	0.1261	0.0786	1.60	0.1154
y3**	1	-0.4089	0.1265	-3.23	0.0022
r0**	1	-0.000186	0.000336	-0.55	0.5816
r1**	1	0.002200	0.000774	2.84	0.0065
r2**	1	0.000788	0.000249	3.16	0.0027
p0**	1	-0.6602	0.1132	-5.83	<.0001
p1**	1	0.4036	0.2321	1.74	0.0885
p2**	1	-1.0064	0.2288	-4.40	<.0001

Restriction	DF	L Value	Standard Error	t Value	Approx Pr > \|t\|
r(-1)	-1	0.0164	0.007275	2.26	0.0223

Output 15.2.3: Estimates for Lagged Variables

Money Demand Estimation using Distributed Lag Model

Quarterly Data - 1968Q2 to 1983Q4

The PDLREG Procedure

Estimate of Lag Distribution
Variable	Estimate	Standard Error	t Value	Approx Pr > \|t\|	-0.196 0 0.2686
y(0)	0.268619	0.0910	2.95	0.0049	\| \|************************\|
y(1)	-0.196484	0.0612	-3.21	0.0024	\|****************\| \|
y(2)	-0.163148	0.0537	-3.04	0.0038	\| *************\| \|
y(3)	0.063850	0.0451	1.42	0.1632	\| \|****** \|
y(4)	0.179733	0.0588	3.06	0.0036	\| \|**************** \|
y(5)	-0.120276	0.0679	-1.77	0.0827	\| *********\| \|

Money Demand Estimation using Distributed Lag Model

Quarterly Data - 1968Q2 to 1983Q4

The PDLREG Procedure

Estimate of Lag Distribution
Variable	Estimate	Standard Error	t Value	Approx Pr > \|t\|	-0.001 0 0.0018
r(0)	-0.001341	0.000388	-3.45	0.0012	\|*****************\| \|
r(1)	-0.000751	0.000234	-3.22	0.0023	\| *********\| \|
r(2)	0.001770	0.000754	2.35	0.0230	\| \|***********************\|

Estimate of Lag Distribution
Variable	Estimate	Standard Error	t Value	Approx Pr > \|t\|	-1.104 0 0.2634
p(0)	-1.104051	0.2027	-5.45	<.0001	\|********************************\| \|
p(1)	0.082892	0.1257	0.66	0.5128	\| \|*** \|
p(2)	0.263391	0.1381	1.91	0.0624	\| \|********\|
p(3)	-0.562556	0.2076	-2.71	0.0093	\| ****************\| \|

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