PDL Procedure

@PDL computes a polynomial distributed lag, with or without end-point constraints. Note that PDL's are rarely used nowadays.

@PDL( options ) depvar start end

# xseries startlag endlag PDLdegree (default is 3)

Parameters

depvar	dependent variable
start, end	range to estimate, defaults to maximum range permitted by all variables involved in the regression.

Supplementary Card

xseries	Explanatory variable
startlag	First (lowest numbered) lag in the polynomial. Leads, if you use them, are negative lags.
endlag	Last lag in the polynomial
PDLDegree	Degree of the polynomial

Options

CONSTRAIN=NEAR/FAR/BOTH/[NONE]

The NEAR constraint makes the polynomial zero at startlag-1. The FAR constraint makes the polynomial zero at endlag+1. Note that these do not affect directly any of the included lags; they just control the shape. BOTH does both.

AR1/[NOAR1]

Compute using Cochrane-Orcutt

SPREAD=Residual variance series [unused]

See SPREAD option

SMPL=Standard SMPL option [not used]

CODEDREG/[NOCODEDREG]

Show regression of coded model

LAGCOEFFS=(output) SERIES of lag coefficients

GRAPH/[NOGRAPH]

[PRINT]/NOPRINT

VCV/[NOVCV]

These are the standard controls for printing the regression table and the covariance/correlation matrix of coefficients, respectively.

Example

This estimates a consumption function as a distributed lag with lags 0 to 5 of on log income. The first is an unrestricted OLS. The second does a 2nd order PDL with a near endpoint constraint. (3rd order PDL's are more commonly used, particularly with longer lags).

open data consump.dat

calendar 1950

data(format=prn,org=columns) 1950:1 1993:1 year y c

set logc = log(c)

set logy = log(y)

linreg logc

# constant logy{0 to 5}

@pdl(constrain=near,graph) logc

# logy 0 5 2

Sample Output

This is the output from the example. Note that the degrees of freedom have been adjusted to show that there are only two free parameters in the lag polynomial (a quadratic naturally has three, but then the near constraint takes one). The third lost degree of freedom is for the CONSTANT. Note also that the t-statistics on the coefficients can be quite high. This is due to the fact that these are all conditional on the lag polynomial following the quadratic with the near constraint. It may be very hard to put that through zero at any lag (particularly in the middle), thus a (misleadingly) high t-statistic.

Linear Regression - Estimation by Polynomial Distributed Lag

Dependent Variable LOGC

Annual Data From 1955:01 To 1993:01

Usable Observations 39

Degrees of Freedom 36

Centered R^2 0.9960120

R-Bar^2 0.9957905

Uncentered R^2 0.9999972

Mean of Dependent Variable 9.1481439980

Std Error of Dependent Variable 0.2469788136

Standard Error of Estimate 0.0160242069

Sum of Squared Residuals 0.0092439074

Regression F(2,36) 4495.5672

Significance Level of F 0.0000000

Log Likelihood 107.4348

Durbin-Watson Statistic 0.6372

Variable Coeff Std Error T-Stat Signif

************************************************************************************

1. Constant -0.015867627 0.100753974 -0.15749 0.87573962

2. LOGY 0.502077057 0.063607495 7.89336 0.00000000

3. LOGY{1} 0.309164950 0.021724669 14.23105 0.00000000

4. LOGY{2} 0.159945883 0.008070301 19.81907 0.00000000

5. LOGY{3} 0.054419854 0.024731896 2.20039 0.03428002

6. LOGY{4} -0.007413136 0.029021062 -0.25544 0.79983721

7. LOGY{5} -0.025553088 0.020780959 -1.22964 0.22680815