# The PDLREG Procedure

### Example 21.2 Money Demand Model

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

where

log of real money stock (M1)

log of real GNP

interest rate (commercial paper rate)

inflation rate

and 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 21.2.1 shows a partial list of the data set.

Output 21.2.1: 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 21.2.2 and Output 21.2.3.

Output 21.2.2: 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
Regress R-Square 0.9712
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 21.2.3: 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 |                ****************|        |