1
Supplemental Material
The data used in our analysis are in the form of a panel covering a number of periods (T) and
individuals (N – the states). Such data may not be stationary as found in McCarl, Villavicencio
and Wu (2008). Thus we first test for a unit root (See section 1 below) and find that the
hypothesis of stationarity is rejected (see testing results in Table S1).
Given we found nonstationarity we must address it. The concept of co-integration provides a
powerful tool for coping with nonstationarity in regressions (Hamilton, 1994). Co-integration
refers to the phenomenon that the error term of a regression over nonstationary variables can
itself be stationary allowing inference of meaningful causal relationship from regressions over
nonstationary time series.
Thus next we test the hypothesis of co-integration. In particular, we test whether a linear
combination of the variables given in the our models is stationary, or co-integrated meaning we
need to use an error-correction model. (see a Section 2 or Engle, R.F. and C.W.J. Granger (1987)
and Greene (2003) for details). Our tests fail to reject co-integration within our proposed model
thus indicating we can do statistical inference over regression results and that we need to use an
error correction model.
We then use an error correction model to fit the proposed model. An error correction
model is a dynamical system with the characteristics that the deviation of the current state from
its long-run relationship will be fed into its short-run dynamics (Engle and Granger, 1987). This
family of models is useful for estimating both short term and long term effects of one time series
on another, especially when dealing with integrated data.
Lastly, we examined the sensitivity of our results using alternative specifications. Since one focus
of this paper is to examine the impact of research investment on agricultural productivity, we reestimate our models with simplified parameterization of research funding by excluding research
and funding shares. We also experimented with alternative specification of regions by dividing
the Mountain region into Mountain-North and Mountain-South, and the Pacific region into
Pacific-North and Pacific-South. The results reported in the text are found to be quantitatively
similar to these alternative estimates.
2
1
Panel Unit Root and Cointegration Tests
Unit root tests could be applied to the data for each individual state. However, we assume that
the data for all states exhibit similar structural and inter-temporal relationships, and thus conduct
the test taking into account the panel structure of our data explicitly.
We use three unit root tests:
Levin, Lin and Chu (LLC) Test
The Levin, Lin and Chu (2002) test examines the null hypothesis that a family of time series
contains a unit root versus the alternative that the time series are stationary. The test is similar to
an Augmented Dickey-Fuller (ADF) test but is applied in a panel framework. This test assumes
independence across cross sections, which does not necessarily hold; and that all cross sections
have or do not have a unit root, which is very restrictive.
Im, Pesaran and Shin (IPS) Test
Im, Pesaran and Shin (2003) propose an alternative testing procedure that averages the individual
unit root test statistics. The null hypothesis is that each series in the panel has a unit root,
H 0 :  i    0 and the alternative hypothesis states that some individual series have unit roots
while others are stationary.
Breitung Test
Breitung (2000) suggests a test statistic with greater power. The test involves performing a pooled
regression on the error terms and then testing using the t-statistic for H 0 :   0 .
The results from the application of the unit root tests are presented in Table S1. There the results
indicate that the hypothesis of stationarity is rejected.
2
Addressing Panel Cointegration
Next we provide the technical details of the panel cointegration tests used. Through this section,
the regressor X includes all variables specified in formula (5) in the text; for instance, it includes
temperature and its square.
Following Greene (2003), suppose that a simplified model in which two nonstationary variables
yt and z t are cointegrated, with a cointegrating vector [1,   ] . Then yt , z t , and ( yt   z t )
are stationary, where ∆ represents first difference. Therefore, the error correction model (ECM)
3
yt   zt   ( yt 1   zt 1 )   t
(1)
describes the variation in yt around its long-run trend in terms of the variation in z t around its
long-run trend, and the error correction ( yt   z t ) , which is the equilibrium error in the model
of cointegration. This model is stable because the implied variables are stationary. The same
assumption that we make to establish cointegration implies (and is implied by) the existence of an
ECM as shown by the Granger representation theorem (see Hamilton, 1994).
In the more general framework of a multivariate and heterogeneous panel model, the error
correction equation can be expressed as:
(2)
p 1
q 1
j 1
j 0
yit  i ( yit 1  iX it )   ijyit  j    ij X it  j  i   it
where the parameter  i is the error-correcting speed of adjustment term. It is expected that
i  0 , in which case there is evidence of cointegration. The vector i captures the long-run
relationship between the variables, and the other estimated parameters (ij ,  ij ) characterize the
short-run dynamics of the implied variables.
Pesaran, Shin and Smith (1999) proposed a pooled-mean-group (PMG) estimator that combines
both pooling and averaging: the estimator allows the intercept, short-run coefficients, and error
variances to differ across individuals but constrains the long-run coefficients to be equal across
individuals. Since model (2) is nonlinear in the parameters, they developed a maximum
likelihood method to estimate the parameters. The log likelihood function takes the form
(3)
lT ( ,  ,  )  
T N
1 N 1
ln(2 i2 )   2 {yi  i i ( )}H i {yi  i i ( )}

2 i 1
2 i 1  i
where  i ( )  yit 1  X i i , H i  I T  Wi (WiWi )Wi , I T is an identity matrix of order T , and
Wi  (y it 1 ,, y it  p 1 , X i , X it 1 ,, X it  q 1 ) . The estimators can be computed using the
usual Newton-Raphson algorithm, which needs first and second derivatives of the likelihood
function, or an iterative “back substitution” algorithm which requires only first derivative
computations. More details are given in Pesaran, Shin and Smith (1999).
Three different cointegration tests were used the Kao, Pedroni and Westerlund tests as desciberd
below.
4
Kao Tests
This is a residual-based Dickey-Fuller (DF) kind of test. It is based on testing whether the
residuals of the panel estimation are stationary or not. Kao (1999) proposed DF and ADF tests of
unit root for the residuals eit as a test for the null of no cointegration. The DF test is applied to
the fixed effect residuals.
Pedroni Tests
Pedroni (1999) proposed several tests and critical values for the null hypothesis of panel
cointegration, which allow not only the dynamics and fixed effects to differ across members of
the panel, but also that they allow the cointegrating vector to differ across members. These tests
are applied over the regression residuals from the hypothesized cointegrating regression.
Westerlund Tests
Westerlund (2007) proposes four panel tests of the null hypothesis of no cointegration that are
based on structural rather than residual dynamics. These structural kind of test does not impose
any common factor restriction,1 which is a main reason associated to loss of power for residualbased cointegration tests. However, Westerlund tests are more restrictive than Pedroni’s residualbased tests in the sense that the former do not allow endogenous regressors in the model.
Test results
The results of our co-integration tests are given in Table S.2 below. The panel co-integration
hypothesis is not rejected, lending support to our use of the panel error correction models in our
estimations.
3
Elasticities for research investments
This model is expressed in a double-logarithmic form such that the estimated coefficient  i
represents the elasticity of TFP with respect to variables of interest (RPUBSPILL, EXT, RPRI).
The funding shares (SFF and GR) are multiplied with the public agricultural research capital
(RPUB) such that the elasticity of TFP with respect to RPUB depends on the funding
composition:
1
Kremers, Ericsson and Dolado (1992) define common factor restriction to the fact that residual-based tests
require the long-run cointegrating vector for the variables in their levels being equal to the short-run
adjustment process for the variables in their differences.
5
 ln(TFP) /  ln( RPUB)   2  3 SFF   4 ( SFF ) 2  5GR   6 (GR) 2 .
(4)
Similarly, the effect on TFP of a one percent change in SFF (or GR) is not constant and it can
include nonlinear impacts of funding composition:
 ln(TFP) /  ln( SFF )  ( 3  2 4 SFF ) ln RPUB
(5)
(6)
4
 ln(TFP) /  ln(GR)  ( 5  26GR) ln RPUB .
Alternative specifications
To investigate the stability of our results we estimated the model using alternative
construction of regions. To assess the sensitivity of our results to the construction of
research funding variables and region specifications, we remove the funding and grant
shares and further divide the mountain and pacific regions into a north sub-region and a
south sub-region. The estimation results are reported in Table S3. It is seen that the
overall results are similar to those reported in the text.
References
Engle, R.F. and C.W.J. Granger, “Co-Integration and Error Correction: Representation,
Estimation, and Testing”, Econometrica, Vol. 55, No. 2 (Mar., 1987), pp. 251-276.
6
Table S1. Panel Unit Root Test: Summary
Sample: 1970 1999
Cross Sections: 48
Individual effects
Level
LTFP
Statistic
P-value
Null: Unit root (assumes common unit root process)
Levin, Lin & Chu t*
1.34
0.909
Breitung t-stat
2.70
0.997
Obs.
Individual effects & linear trends
Level
Statistic
P-value Obs.
1329
1281
-11.87
-1.28
0.000
0.100
1367
1319
Null: Unit root (assumes individual unit root process)
Im, Pesaran and Shin W-stat 7.52
1.000
1329
-12.62
0.000
1367
LRPUB
Levin, Lin & Chu t*
-8.34
Breitung t-stat
1.57
Im, Pesaran and Shin W-stat 0.10
0.000
0.941
0.542
1257
1209
1257
0.94
-8.01
-7.39
0.827
0.000
0.000
1265
1217
1265
LRPUB  SF
Levin, Lin & Chu t*
-1.40
Breitung t-stat
-1.06
Im, Pesaran and Shin W-stat -2.45
0.080
0.145
0.007
1353
1305
1353
-3.94
-3.86
-5.43
0.000
0.000
0.000
1350
1302
1350
LRPUB  SF2
Levin, Lin & Chu t*
-1.45
Breitung t-stat
-1.58
Im, Pesaran and Shin W-stat -2.85
0.073
0.057
0.002
1354
1306
1354
-4.57
-3.73
-5.89
0.000
0.000
0.000
1356
1308
1356
LRPUB  GR
Levin, Lin & Chu t*
-0.63
Breitung t-stat
-2.25
Im, Pesaran and Shin W-stat -0.45
0.265
0.012
0.326
1371
1323
1371
-2.38
1.50
-2.38
0.009
0.933
0.009
1361
1313
1361
LRPUB  GR2
Levin, Lin & Chu t*
-1.13
Breitung t-stat
-1.97
Im, Pesaran and Shin W-stat 0.78
0.130
0.025
0.783
1357
1309
1357
-2.60
0.41
-1.99
0.005
0.658
0.024
1352
1304
1352
LEXT
Levin, Lin & Chu t*
-8.57
Breitung t-stat
-2.17
Im, Pesaran and Shin W-stat -4.62
0.000
0.015
0.000
1369
1321
1369
-7.52
-0.55
-8.37
0.000
0.292
0.000
1365
1317
1365
LRPUBSPILL
Levin, Lin & Chu t*
-6.87
Breitung t-stat
3.96
Im, Pesaran and Shin W-stat 3.03
0.000
1.000
0.999
1288
1240
1288
11.88
-10.45
0.26
1.000
0.000
0.601
1281
1233
1281
7
Table S1 continued
Individual effects
Level
Statistic
P-value
Obs.
Individual effects & linear trends
Level
Statistic
P-value Obs.
0.000
0.000
0.000
1338
1290
1338
-24.92
0.45
-25.92
0.000
0.675
0.000
1344
1296
1344
LTEMP
Levin, Lin & Chu t*
-24.45
Breitung t-stat
-22.90
Im, Pesaran and Shin W-stat -21.21
0.000
0.000
0.000
1373
1325
1373
-23.78
2.65
-20.56
0.000
0.996
0.000
1356
1308
1356
LPREC
Levin, Lin & Chu t*
-30.46
Breitung t-stat
-18.68
Im, Pesaran and Shin W-stat -28.49
0.000
0.000
0.000
1372
1324
1372
-26.37
-3.56
-24.58
0.000
0.000
0.000
1366
1318
1366
LINTENS
Levin, Lin & Chu t*
-28.00
Breitung t-stat
-19.79
Im, Pesaran and Shin W-stat -28.65
0.000
0.000
0.000
1385
1337
1385
-24.51
-7.43
-26.71
0.000
0.000
0.000
1377
1329
1377
LPRI
Levin, Lin & Chu t*
-27.50
Breitung t-stat
-26.01
Im, Pesaran and Shin W-stat -26.05
** Probabilities for Fisher tests are computed using an asymptotic Chi-square distribution. All other tests
assume asymptotic normality.
8
Table S2. Cointegration Test: Summary
Sample: 1970 1999
Cross Sections: 48
Pedroni cointegration tests
panel v-stat
panel rho-stat
panel pp-stat
panel adf-stat
Constant
Statistic
-0.82
-4.60
-20.10
-9.88
P-value
0.205
0.000
0.000
0.000
Constant & Trend
Statistic P-value
-3.76
0.000
-2.45
0.007
-23.80
0.000
-9.69
0.000
group rho-stat
-2.22
0.013
-0.03
0.489
group pp-stat
-22.28 0.000
-26.89
0.000
group adf-stat
-8.24
0.000
-9.12
0.000
**All reported values are distributed N(0,1) under null of unit root or no cointegration.
**Panel stats are unweighted by long run variances.
Kao cointegration tests
Constant
Statistic P-value
DFrho
-31.88 0.000
DFt
-17.59 0.000
**Stats are distributed N(0,1) under null of no cointegration.
Constant & Trend
Statistic P-value
-33.94
0.000
-18.64
0.000
Westerlund cointegration tests
Lags: 1 – 2
Leads: 0 – 1
Average AIC selected lag length: 1.98
Average AIC selected lead length: .96
Constant
Constant & Trend
Statistic
Value
Z-value P-value Value
Z-value
Gt
-4.06
-11.71 0.000
-4.23
-10.39
Ga
-0.24
11.50
1.000
-0.13
13.81
Pt
-22.25 -6.80
0.000
-25.95
-7.75
Pa
-2.56
6.16
1.000
-1.99
9.57
**Z-values are distributed N(0,1) under null of no cointegration.
P-value
0.000
1.000
0.000
1.000
9
Table S3. Regression results under alternative region specifications
Dependent Variable
ln (Ag. TFP)
ln (Public Ag. Research
Capital)
ln (Public Extension
Capital)
ln (Public Ag. Research
Capital Spilling)
ln (Private Ag. Research
Capital)
Trend
Model A
Coef.
P>|z|
Model B
Coef.
P>|z|
0.0941
0.002
0.002
-0.0235
0.168
0.0929
0.0243
0.4937
0.000
0.000
-0.1358
0.0029
0.004
0.348
ln (Temperature) × D1
-0.2497
0.027
ln (Temperature) × D2
-0.0536
0.807
ln (Temperature) × D3
-0.0200
0.877
ln (Temperature) × D4
-0.0320
0.843
ln (Temperature) × D5
ln (Temperature) × D6
ln (Temperature) × D7
ln (Temperature) ×
D6_1
ln (Temperature) ×
D6_2
ln (Temperature) ×
D7_1
ln (Temperature) ×
D7_2
ln Total Precipitation
ln Precipitation
Intensity
Intercept
-0.4812
-0.1129
0.0161
0.065
0.497
0.966
0.4953
0.1347
0.0029
0.2498
0.0543
0.0192
0.0312
0.4811
0.0288
0.2587
0.1891
0.904
1.1413
0.0352
0.0255
0.283
0.019
0.0349
0.020
-0.0246
0.080
0.154
0.004
0.345
0.027
0.805
0.881
0.847
0.065
0.272
0.628
0.070
Notes: Model A: estimation with alternative funding parameterization. Model B: estimation with alternative funding
parameterization and alternative region definition. In Model A, D6 and D7 are dummy variables for the Mountain and
Pacific regions, in Model B, D6_1 and D6_2 refer to the Mountain-North and Mountain-South regions and D7_1 and
D7_2 refer to the Pacific-North and Pacific-South regions.