Example 3LC3. Poisson model: patents and R&D expenditure over time (336 firms in 20 industrial classes)

The data (patents.dat) we use in this example are from Hall, Griliches and Hausman (1986), and refer to the number of patents awarded to 346 firms each year from 1975 to 1979. Hall et al (1986) were particularly interested in the effect of current and lagged research and development (R&D) expenditures on the number of awarded patents. The data were made available on the web page http://cameron.econ.ucdavis.edu/racd/racddata.html to accompany Cameron and Trivedi (1988).  Our analysis differs from that of Cameron and Trivedi (1988) as we allow for clustering by SIC (level 3) as well as by firm (level 2) over time. Our rationale for this is that there are 20 Industrial Classifications (IC) in these data, too many for dummy variables without amalgamating some of them, and more importantly we expect that firms in the same IC exhibit more similar patent and R&D behaviours to each other than to firms in different ICs.

References

Bronwyn Hall, Zvi Griliches, and Jerry Hausman (1986),  "Patents and R&D: Is There a Lag?", International Economic Review, 27, 265-283.

A.C. Cameron and P.K. Trivedi (1998), Regression Analysis of Count Data, Econometric Society Monograph No.30, Cambridge University Press.

Data description

Number of observations = 1681

Number of level-2 cases (‘cusip’ = identifier for firms) = 336

Number of level-3 cases (‘ardsic’ = identifier for R&D industrial classifications) = 20

The variables  are:

obsno= observation number (1-1681)

cusip =  Compustat's identifying number for the firm (Committee on Uniform Security Identification Procedures number).

ardssic  =  a two-digit code for the applied R&D industrial classification

scisect  =  dummy equal to 1 for firms in the scientific sector, 0 otherwise

logk =   the logarithm of the book value of capital in 1972

sumpat = the sum of patents applied for between 1972-1979.

pat  =  the number of patents applied for during the year that were eventually granted.

pat1 = the 1 (year) lagged number of patents applied for that were eventually granted.

pat2 = the 2 (years) lagged number of patents applied for that were eventually granted.

pat3 = the 3 (years) lagged number of patents applied for that were eventually granted.

pat4 = the 4 (years) lagged number of patents applied for that were eventually granted.

logr  =  the logarithm of R&D spending during the year (in 1972 dollars)

logr1 = the 1 (year) lagged logarithm of R&D spending during the year (in 1972 dollars)

logr2 = the 2 (years) lagged logarithm of R&D spending during the year (in 1972 dollars)

logr3 = the 3 (years) lagged logarithm of R&D spending during the year (in 1972 dollars)

logr4 = the 4 (years) lagged logarithm of R&D spending during the year (in 1972 dollars)

logr5 = the 5 (years) lagged logarithm of R&D spending during the year (in 1972 dollars)

The first few lines of patents.dat look like:

Sabre commands

out patents.log

data obsno year cusip ardssic scisect logk sumpat pat pat1 pat2 pat3 pat4 &

logr logr1 logr2 logr3 logr4 logr5

case first=cusip second=ardssic

yvar pat

family p

constant cons

factor year fyear

mass first=96 second=96

ari a

fit logr logr1 logr2 logr3 logr4 logr5 fyear logk cons

dis m

dis e

stop

Sabre log file

<S> data obsno year cusip ardssic scisect logk sumpat pat pat1 pat2 pat3 pat4 &

<S>      logr logr1 logr2 logr3 logr4 logr5

1680 observations in dataset

<S> case first=cusip second=ardssic

<S> yvar pat

<S> family p

<S> constant cons

<S> factor year fyear

<S> mass first=96 second=96

<S> ari a

<S> fit logr logr1 logr2 logr3 logr4 logr5 fyear logk cons

Initial Homogeneous Fit:

Iteration       Log. lik.       Difference

__________________________________________

1          -21734.475

2          -18762.081        2972.

3          -18671.031        91.05

4          -18670.851       0.1793

5          -18670.851       0.9293E-06

Iteration       Log. lik.         Step      End-points     Orthogonality

length    0          1      criterion

________________________________________________________________________

1          -5304.2733        1.0000    fixed  fixed       163.13

2          -5295.6553        0.1250    fixed  fixed       47.596

3          -5285.3719        0.1250    fixed  fixed       183.49

4          -5267.5198        0.2500    fixed  fixed       98.797

5          -5262.3811        0.1250    fixed  fixed       41.092

6          -5250.0271        0.1250    fixed  fixed       131.98

7          -5242.3925        0.5000    fixed  fixed       83.603

8          -5239.5246        0.2500    fixed  fixed       117.25

9          -5237.0838        0.2500    fixed  fixed       126.27

10          -5231.7553        0.1250    fixed  fixed       205.75

11          -5228.1188        0.1250    fixed  fixed       422.83

12          -5217.5973        0.5000    fixed  fixed       2372.4

13          -5140.6265        1.0000    fixed  fixed       28.298

14          -5140.1334        0.0625    fixed  fixed       69.417

15          -5139.7696        0.1250    fixed  fixed       72.977

16          -5139.7344        0.0625    fixed  fixed       22.144

17          -5135.6159        0.0625    fixed  fixed       42.629

18          -5135.5317        0.0625    fixed  fixed       26.594

19          -5134.6396        0.0313    fixed  fixed       1121.2

20          -5120.4806        1.0000    fixed  fixed       25.493

21          -5119.6906        0.0313    fixed  fixed       402.63

22          -5117.0621        1.0000    fixed  fixed       85.167

23          -5116.8356        0.0313    fixed  fixed       33.358

24          -5116.7245        0.0156    fixed  fixed       10.637

25          -5116.7083        0.0039    fixed  fixed       60.915

26          -5116.6335        0.0156    fixed  fixed       7.8819

27          -5116.6126        0.0020    fixed  fixed       52.222

28          -5116.5142        0.0313    fixed  fixed       6.2128

29          -5116.4997        0.0020    fixed  fixed       35.055

30          -5116.4745        0.0078    fixed  fixed       17.366

31          -5116.4626        0.0039    fixed  fixed       60.681

32          -5116.4378        0.0156    fixed  fixed       8.8708

33          -5116.4209        0.0020    fixed  fixed       86.564

34          -5116.3791        0.0313    fixed  fixed       7.4576

35          -5116.3561        0.0020    fixed  fixed       43.747

36          -5116.3456        0.0156    fixed  fixed       9.9933

37          -5116.3251        0.0020    fixed  fixed       79.304

38          -5116.3017        0.1250    fixed  fixed       8.3197

39          -5116.1818        0.0039    fixed  fixed       25.815

40          -5116.1496        0.0078    fixed  fixed       137.16

41          -5116.0310        0.1250    fixed  fixed       6.6260

42          -5115.9642        0.0078    fixed  fixed       34.590

43          -5115.9462        0.0313    fixed  fixed       8.4507

44          -5115.9257        0.0039    fixed  fixed       70.921

45          -5115.9079        0.0313    fixed  fixed       32.974

46          -5115.8982        0.0078    fixed  fixed       112.65

47          -5115.8908        0.5000    fixed  fixed       599.82

48          -5115.3268        1.0000    fixed  fixed       707.69

49          -5115.3255        1.0000    fixed  fixed       428.38

50          -5115.3255        1.0000    fixed  fixed

<S> dis m

X-vars            Y-var             Case-var

________________________________________________

cons              pat               cusip

logr                                ardssic

logr1

logr2

logr3

logr4

logr5

fyear

logk

Univariate model

Standard Poisson

Gaussian random effects

Number of observations             =    1680

Number of level 2 cases            =     336

Number of level 3 cases            =      20

X-var df           =    12

Scale df           =     2

Log likelihood =     -5115.3255     on    1666 residual degrees of freedom

<S> dis e

Parameter              Estimate         Std. Err.

___________________________________________________

cons                  -0.17569          0.62216E-01

logr                   0.39203          0.38717E-01

logr1                 -0.40336E-01      0.48160E-01

logr2                  0.11930          0.45000E-01

logr3                  0.41324E-01      0.40867E-01

logr4                  0.13509E-01      0.38088E-01

logr5                  0.59821E-01      0.30853E-01

fyear       ( 1)        0.0000          ALIASED [I]

fyear       ( 2)      -0.44875E-01      0.13270E-01

fyear       ( 3)      -0.46142E-01      0.13457E-01

fyear       ( 4)      -0.17366          0.13785E-01

fyear       ( 5)      -0.22427          0.13901E-01

logk                   0.28345          0.62823E-02

sclev2                 0.89170          0.18744E-01

sclev3                 0.69836          0.18762E-01

<S> stop