The PDLREG Procedure

Example 28.2 Money Demand Model

This example estimates the demand for money by 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';
datalines;
187.15  1036.22    81.18     5.58

   ... more lines ...

Output 28.2.1 shows a partial list of the data set.

Output 28.2.1: Partial List of the Data Set A

National Industrial Conference Board Data

Quarterly Series - 1952Q1 to 1967Q4

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 28.2.2 and Output 28.2.3.

Output 28.2.2: 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
MAE	0.00383648	AICC	-421.83758
MAPE	0.07051345	HQC	-418.53375
		Total R-Square	0.9712

Parameter Estimates
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
y**0	1	0.0132	0.004531	2.91	0.0055
y**1	1	-0.0704	0.0528	-1.33	0.1891
y**2	1	0.1261	0.0786	1.60	0.1154
y**3	1	-0.4089	0.1265	-3.23	0.0022
r**0	1	-0.000186	0.000336	-0.55	0.5816
r**1	1	0.002200	0.000774	2.84	0.0065
r**2	1	0.000788	0.000249	3.16	0.0027
p**0	1	-0.6602	0.1132	-5.83	<.0001
p**1	1	0.4036	0.2321	1.74	0.0885
p**2	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 28.2.3: Estimates for Lagged Variables

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	\| *********\| \|

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	\| ****************\| \|