1

Econometric Modeling of Technical Change (Supplement)

by

Hui Jin and Dale W. Jorgenson

August 13, 2008

2

Supplementary Figures

Figure 1: 1KKT vv −

Figure 2: 1LLT vv −

Figure 3: 1EET vv −

Figure 4: 1MMT vv −

Figure 5: )lnlnlnln()lnlnlnln(

)lnlnln()lnlnln(

1111

1

1

1

1

1

1

MKMEKELKLKKKMTKMETKELTKLKTKK

M

EKE

M

LKL

M

KKK

MT

ETKE

MT

LTKL

MT

KTKK

PPPPPPPPPP

PP

PP

PP

PP

PP

ββββββββ

ββββββ

+++−+++=

++−++

Figure 6: )lnlnln()lnlnln(1

1

1

1

1

1

M

ELE

M

LLL

M

KKL

MT

ETLE

MT

LTLL

MT

KTKL P

PPP

PP

PP

PP

PP ββββββ ++−++

Figure 7: )lnlnln()lnlnln(1

1

1

1

1

1

M

EEE

M

LLE

M

KKE

MT

ETEE

MT

LTLE

MT

KTKE P

PPP

PP

PP

PP

PP ββββββ ++−++

Figure 8: )lnlnlnln()lnlnlnln( 1111 MMMEEMLLMKKMMTMMETEMLTLMLMKM PPPPPPPP ββββββββ +++−+++=

Figure 9: 1KKT ff −

Figure 10: 1LLT ff −

Figure 11: 1EET ff −

Figure 12: 1MMT ff −

3

Figure 13: )ln(ln1

1

M

Q

MT

QT

PP

PP

−−

Figure 14:

[ ]

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪

⎭

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪

⎬

⎫

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪

⎩

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪

⎨

⎧

−+−+−

+

⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

−

⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

−

−

−

−

−

= −

−∑ )ln(ln)ln(ln)ln(ln

)

lnln

lnln

lnln

)(ln

)(ln

)(ln

ln

ln

ln

lnln

lnln

lnln

)(ln

)(ln

)(ln

ln

ln

ln

(

1

1

1

1

2 1

1

1

1

1

1

1

1

1

1

1

1

1

1

2

1

121

2

1

121

2

1

121

1

1

1

1

1

1

221

221

221

Mt

Et

Mt

EtKt

Mt

Lt

Mt

LtLt

T

t Mt

Kt

Mt

KtKt

M

E

M

L

M

E

M

K

M

L

M

K

M

E

M

L

M

K

M

E

M

L

M

K

MT

ET

MT

LT

MT

ET

MT

KT

MT

LT

MT

KT

MT

ET

MT

LT

MT

KT

MT

ET

MT

LT

MT

KT

LEKEKLEELLKKELK

PP

PPf

PP

PPf

PP

PPf

PP

PP

PP

PP

PP

PP

PPPPPPPPPPPP

PP

PP

PP

PP

PP

PP

PPPPPPPPPPPP

ββββββααα

Figure 15: ])(ln)(ln)(ln)(ln[

)](ln)(ln)(ln[

21111

112

1

∑

∑

=−−−−

−−=

−

−+−+−+−−=

−+−+−−

T

tMtMtMtEtEtEtLtLtLtKtKtKt

EtEtMt

EtLtLt

Mt

LtT

tKtKt

Mt

Kt

ffPffPffPffP

ffPPff

PPff

PP

4

Figure 16: )( 1ppT ff −−

Figure 17: 19601980 EE ff −

Figure 18: 19802005 EE ff −

Figure 19: 20062030 EE ff −

Figure 20: 20062030 KK ff −

Figure 21: 20062030 LL ff −

Figure 22: 20062030 MM ff −

5

Figure S1.

Latent biases of technical change for capital, 1960-2005, and projections for 2006-2030

6

Figure S2. Latent biases of technical change for labor, 1960-2005, and projections for 2006-2030

7

Figure S3. Latent biases of technical change for energy, 1960-2005, and projections for 2006-2030

8

Figure S4. Latent biases of technical change for material, 1960-2005, and projections for 2006-2030

9

Figure S5. Latent levels of technology, 1960-2005, and projections for 2006-2030

10

Supplementary Estimates

In Table S1 we present estimates of the unknown parameters for each of the 35

sectors in Table 1. These parameters are the coefficients of the explanatory variables in

the state equations (4’) and (5’) and coefficients of lagged values of the latent variables

in the transition equation (12). We have used the parameters of the transition equation

to extrapolate the endogenous rates and biases of technical change given in the

Appendix.

We have constructed constrained two-step maximum likelihood estimates of the

parameters of the observation equation (14). These estimates are presented in Table S1

and correspond to the parameters in the matrix 'A in the definition of the Kalman filter.

The parameters ikβ are the share elasticities and represent the responses of the shares of

the four inputs – capital, labor, energy, and materials – to changes in the input prices in

Equation (5) for a given state of technology. Note that the matrix 'H in the definition of

the Kalman filter involves no unknown parameters and consists of known constants and

functions of the data.

11

Table S1. Parameter Estimates

Note: For other parameter estimates, see Table S2 below.

12

Table S1. Parameter Estimates (Continued)

13

Table S1. Parameter Estimates (Continued)

14

Table S1. Parameter Estimates (Continued)

15

Table S1. Parameter Estimates (Concluded)

16

In Table S2 we present estimates of the parameters of the covariance matrices, defined as follows:

.

00000000000000000000000000

,')(

,000000

,')(

44434241

333231

2221

11

44434241

333231

2221

11

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

===

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

===

qqqqqqq

qqq

LLLvVarQ

rrrrrrr

rrr

LLLwVarR

qqqt

rrrt

The r’s and q’s are unknown parameters; the matrices R and Q are symmetric and positive semi-definite, as required for a covariance matrix.

In Table S2 we also present estimates of the mean and covariance matrix of the

initial state of technology 1ξ , with 0pf normalized to constant 0. These are defined as

follows:

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

=′=

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

=

0000000ˆˆˆˆ000ˆˆˆ0000ˆˆ00000ˆ0000000

,;

0

ˆˆ

ˆ1

ˆ

44434241

333231

2221

11

0|1

0|1

0|1

0|1

0|1

0|1

ppppppp

ppp

LLLP

ffff

PPP

p

E

L

K

ξ

17

.Table S2. Parameter Estimates

18

Table S2. Parameter Estimates (Continued)

19

Table S2. Parameter Estimates (Continued)

20

Table S2. Parameter Estimates (Continued)

21

Table S2. Parameter Estimates (Concluded)