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ee

Figure 1: Shares of Nominal Investment

1950 1960 1970 1980 1990 20000

0.5

1

1.5

2

2.5

Agricultural machinery,except tractors

Time

Log

of P

rice

Inde

xes

(194

7=0)

1983

NIPA Q−adj (Gordon) Q−adj (Forecast)± 2 S.E.

1950 1960 1970 1980 1990 2000−3

−2

−1

0

1

2

3Aircraft

Time

Log

of P

rice

Inde

xes

(194

7=0)

1983

NIPA Q−adj (Gordon) Q−adj (Forecast)± 2 S.E.

1950 1960 1970 1980 1990 2000−0.5

0

0.5

1

1.5Autos

Time

Log

of P

rice

Inde

xes

(194

7=0)

1983

NIPA Q−adj (Gordon) Q−adj (Forecast)± 2 S.E.

1950 1960 1970 1980 1990 2000−3

−2.5

−2

−1.5

−1

−0.5

0

0.5

1Communication equipment

Time

Log

of P

rice

Inde

xes

(194

7=0)

1983

NIPA Q−adj (Gordon) Q−adj (Forecast)± 2 S.E.

Figure 2: Price Forecasts

1950 1960 1970 1980 1990 20000

0.5

1

1.5

2

2.5

Construction machinery,except tractors

Time

Log

of P

rice

Inde

xes

(194

7=0)

1983

NIPA Q−adj (Gordon) Q−adj (Forecast)± 2 S.E.

1950 1960 1970 1980 1990 2000−0.5

0

0.5

1

1.5Electrical equipment

Time

Log

of P

rice

Inde

xes

(194

7=0)

1983

NIPA Q−adj (Gordon) Q−adj (Forecast)± 2 S.E.

1950 1960 1970 1980 1990 2000−1

−0.5

0

0.5

1

1.5

2

2.5

3Engines and turbines

Time

Log

of P

rice

Inde

xes

(194

7=0)

1983

NIPA Q−adj (Gordon) Q−adj (Forecast)± 2 S.E.

1950 1960 1970 1980 1990 2000−0.5

0

0.5

1

1.5

2

Electrical transmission, distributionand industrial apparatus

Time

Log

of P

rice

Inde

xes

(194

7=0)

1983

NIPA Q−adj (Gordon) Q−adj (Forecast)± 2 S.E.

Figure 3: Price Forecasts

1950 1960 1970 1980 1990 2000−0.5

0

0.5

1

1.5

2Fabricated metal products

Time

Log

of P

rice

Inde

xes

(194

7=0)

1983

NIPA Q−adj (Gordon) Q−adj (Forecast)± 2 S.E.

1950 1960 1970 1980 1990 2000−0.5

0

0.5

1

1.5

2Furniture and fixtures

Time

Log

of P

rice

Inde

xes

(194

7=0)

1983

NIPA Q−adj (Gordon) Q−adj (Forecast)± 2 S.E.

1950 1960 1970 1980 1990 2000−1

−0.5

0

0.5

1

1.5

2

2.5

3General industrial equipment

Time

Log

of P

rice

Inde

xes

(194

7=0)

1983

NIPA Q−adj (Gordon) Q−adj (Forecast)± 2 S.E.

1950 1960 1970 1980 1990 2000−2

−1.5

−1

−0.5

0

0.5

1

1.5

2Instruments and photocopies

Time

Log

of P

rice

Inde

xes

(194

7=0)

1983

NIPA Q−adj (Gordon) Q−adj (Forecast)± 2 S.E.

Figure 4: Price Forecasts

1950 1960 1970 1980 1990 20000

0.5

1

1.5

2

2.5Mining and oilfield machinery

Time

Log

of P

rice

Inde

xes

(194

7=0)

1983

NIPA Q−adj (Gordon) Q−adj (Forecast)± 2 S.E.

1950 1960 1970 1980 1990 2000−1

−0.5

0

0.5

1

1.5

2

2.5

3Metalworking machinery

Time

Log

of P

rice

Inde

xes

(194

7=0)

1983

NIPA Q−adj (Gordon) Q−adj (Forecast)± 2 S.E.

1950 1960 1970 1980 1990 2000−0.5

0

0.5

1

1.5Other

Time

Log

of P

rice

Inde

xes

(194

7=0)

1983

NIPA Q−adj (Gordon) Q−adj (Forecast)± 2 S.E.

1950 1960 1970 1980 1990 20000

0.5

1

1.5

2

2.5Railroad equipment

Time

Log

of P

rice

Inde

xes

(194

7=0)

1983

NIPA Q−adj (Gordon) Q−adj (Forecast)± 2 S.E.

Figure 5: Price Forecasts

1950 1960 1970 1980 1990 2000−1

−0.5

0

0.5

1

1.5Service industry machinery

Time

Log

of P

rice

Inde

xes

(194

7=0)

1983

NIPA Q−adj (Gordon) Q−adj (Forecast)± 2 S.E.

1950 1960 1970 1980 1990 2000−1

−0.5

0

0.5

1

1.5

2

2.5

3Ships and boats

Time

Log

of P

rice

Inde

xes

(194

7=0)

1983

NIPA Q−adj (Gordon) Q−adj (Forecast)± 2 S.E.

1950 1960 1970 1980 1990 2000−1

−0.5

0

0.5

1

1.5

2

2.5

3Special industry machinery

Time

Log

of P

rice

Inde

xes

(194

7=0)

1983

NIPA Q−adj (Gordon) Q−adj (Forecast)± 2 S.E.

1950 1960 1970 1980 1990 20000

0.5

1

1.5

2

2.5Tractors

Time

Log

of P

rice

Inde

xes

(194

7=0)

1983

NIPA Q−adj (Gordon) Q−adj (Forecast)± 2 S.E.

Figure 6: Price Forecasts

1950 1960 1970 1980 1990 2000−0.5

0

0.5

1

1.5

2Trucks, buses, and truck trailers

Time

Log

of P

rice

Inde

xes

(194

7=0)

1983

NIPA Q−adj (Gordon) Q−adj (Forecast)± 2 S.E.

Figure 7: Price Forecasts

Figure 8:Official NIPA prices for computers and software

Figure 9:Quality bias in the NIPA official price index for E&S

Figure 10: Rate of quality improvement embodied in E&S

Figure 11: Real Investment in E&S: NIPA official series and quality-adjustedestimate

Figure 12:Official economic depreciation and physical decay for E&S

Figure 13:Official economic depreciation and physical decay for IPES

Figure 14:Hulten’s index for E&S and IPES

0.0

0.1

0.2

0.3

0.4

0.5

0.07

0.08

0.09

0.10

0.11

0.12

0.13

0.14

50 55 60 65 70 75 80 85 90 95 00

Hulten’s Index Returns to Education

Hul

ten’

s In

dex

Returns to E

ducation

Figure 15: Technological Gap and the Returns to Education

Figure 16: “Equilibrium” growth accounting estimates of technical changeembodied in capital, in labor and disembodied

Figure 17:Distribution of rate of quality improvement by industry

Figure 18:Distribution of Hulten’s Index by industry

TABLE 1 (part 1 of 3) - Regression Results for the 21 Quality-adjusted Price Indexes

Explanatory Variables (1) Agric (2) Aircrafts (3) Auto (4) Comm (5) Constr (6) Electr (7) Engines (8) ETDIA

NIPA Official Price (∗) 1.71 2.37 0.84 1.68 0.95 1.23 1.48 1.40

(14.16) (8.40) (4.99) (10.33) (25.56) (7.65) (9.86) (13.39)

NIPA Official Price−1 (∗) - - - - - - - -

- - - - - - - -

NIPA Official Price−2 (∗) -0.69 - - - - -0.49 - -

(-5.18) - - - - (-2.53) - -

NIPA Official Price−3 (∗) - - 0.42 - - - - -

- - (2.16) - - - - -

GDP Growth - - - - - - - -

- - - - - - - -

GDP Growth−1 - - - 0.01 -0.01 - - -

- - - (1.57) (-2.82) - - -

GDP Growth−2 - - - - - - - -

- - - - - - - -

Constant -3.40 -3.89 -4.70 -5.47 -2.55 -2.71 -3.26 -4.23

(-62.78) (-5.84) (-8.51) (-9.19) (-30.97) (-16.00) (-9.77) (-13.62)

Time Trend*100 - -14.97 -0.85 -6.65 -1.91 - -6.06 -3.30

- (-11.91) (-3.39) (-15.82) (-9.86) - (-7.83) (-9.42)

Adjusted R2 0.99 0.89 0.79 0.91 0.99 0.95 0.77 0.87

Note: t-statistics are in parethesis, (∗) denotes logs, there are 37 observations for each estimated

equation and all price indexes are in logs.

TABLE 1 (part 2 of 3) - Regression Results for the 21 Quality-adjusted Price Indexes

Explanatory Variables (9) FMP (10) Furniture (11) GIE (12) Ins-Pho (13) Mine (14) MWM (15) Other Eq (16) Rail

NIPA Official Price (∗) 1.23 0.60 0.76 -0.57 0.73 0.72 1.10 0.86

(15.07) (3.02) (13.60) (-1.14) (18.74) (3.14) (10.28) (29.33)

NIPA Official Price−1 (∗) - 0.42 - - - 0.72 - -

- (2.07) - - - (1.76) - -

NIPA Official Price−2 (∗) - - - 1.36 - -0.74 - -

- - - (2.43) - (-3.13) - -

NIPA Official Price−3 (∗) - - - - - - - -

- - - - - - - -

GDP Growth - -0.01 -0.01 - - - - -

- (-2.91) (-2.00) - - - - -

GDP Growth−1 -0.01 - -0.01 - -0.01 - - -

(-1.81) - (-3.65) - (-2.12) - - -

GDP Growth−2 - - - - - -0.01 - -

- - - - - (-3.44) - -

Constant -3.40 -3.25 -2.22 -1.70 -2.10 -2.27 -3.67 -2.57

(-15.55) (-25.20) (-16.25) (-1.24) (-23.70) (-45.13) (-11.06) (-36.65)

Time Trend*100 -3.13 -0.91 -1.08 -4.57 -0.85 - -1.37 -0.82

(-8.84) (-5.16) (-4.00) (-3.42) (-4.07) - (-4.47) (-5.65)

Adjusted R2 0.93 0.99 0.98 0.77 0.98 0.99 0.86 0.99

TABLE 1 (part 3 of 3) - Regression Results for the 21 Quality-adjusted Price Indexes

Explanatory Variables (17) Serv (18) Ships (19) Spec (20) Tract (21) Trucks

NIPA Official Price (∗) 1.22 1.51 0.99 1.25 1.15

(22.30) (8.48) (18.45) (6.86) (18.21)

NIPA Official Price−1 (∗) - 0.55 - - -

- (1.83) - - -

NIPA Official Price−2 (∗) - -0.88 - -0.55 -

- (-4.26) - (-2.70) -

NIPA Official Price−3 (∗) - 0.01 - - -

- (2.97) - - -

GDP Growth - - - - -

- - - - -

GDP Growth−1 - - - 0.01 -

- - - (2.66) -

GDP Growth−2 - - - - -

- - - - -

Constant -3.16 -3.24 -2.01 -2.29 -2.99

(-18.96) (-34.54) (-17.83) (-28.89) (-17.82)

Time Trend*100 -4.64 -3.16 -4.58 - -3.65

(-29.06) (-18.63) (-16.52) - (-14.75)

Adjusted R2 0.96 0.99 0.91 0.98 0.91

Note: t-statistics are in parethesis, (∗) denotes logs, there are 37 observations for each estimated equation

and all price indexes are in logs.

Table 2 – Constant-Quality Capital Growth (1948-2000)

48-00 47-60 61-70 71-80 81-90 91-00

∆k∗e 0.088 0.091 0.089 0.087 0.075 0.100

∆ke 0.058 0.056 0.059 0.061 0.046 0.068

∆k∗ipes 0.163 0.137 0.165 0.179 0.172 0.163

∆kipes 0.123 0.086 0.132 0.137 0.132 0.133

Table 3– Annual Rates of Embodied Technical Change by Asset Type

48-00 48-60 61-70 71-80 81-90 91-00

Equipment and Software .040 .023 .036 .036 .046 .063

Information Processing Equipment and Software .074 .043 .063 .065 .082 .078

Computers and Peripheral equipment .235(∗) - .266 .265 .182 .225

Prepackaged Software .153(∗) - .157 .181 .158 .099

Custom Software .038(∗) - .040 .044 .036 .026

Own Account Software .002(∗) - .005 .003 .001 .003

Communication equipment .087 .096 .051 .073 .085 .129

Instruments and Photocopies .056 .017 .034 .135 .050 .054

Office and Accounting equipment .024 .000 .021 .053 .031 .024

Industrial Equipment .030 .031 .017 .028 .039 .033

Fabricated Metal Products .027 .028 .031 .012 .044 .047

Engines and Turbines .032 .044 .037 .017 .034 .059

Metalworking Machinery .009 .005 .011 .009 .008 .016

Special Industry Machinery, n.e.c. .038 .032 .042 .027 .036 .052

General Industrial equipment .016 .004 .018 .022 .013 .026

Electrical Transm., Distr. and Industr. .026 .018 .041 .025 .007 .044

Transportation Equipment .030 .044 .020 .022 .035 .026

Trucks, Buses, and Truck Trailers .033 .030 .045 .015 .033 .040

Autos .025 .029 .032 .030 .006 .026

Aircraft .079 .081 .084 .035 .091 .106

Ships and Boats .021 .015 .026 .003 .030 .034

Railroad Equipment .010 .013 .023 .006 .031 .023

Other Equipment .019 .018 .005 .022 .028 .023

Furniture and Fixtures .011 .009 .014 .006 .008 .020

Tractors .003 .022 .009 .001 .020 .018

Agricultural Machinery .001 .005 .007 .030 .016 .009

Construction Machinery .013 .005 .016 .005 .016 .026

Mining and Oilfield Machinery .014 .005 .016 .005 .024 .021

Service Industry Machinery .049 .053 .060 .036 .046 .051

Electrical Equipment, n.e.c. .020 .014 .027 .011 .024 .030

Other Equipment .024 .034 .020 .021 .019 .023

Note: (∗) denotes the period 1960-2000. Each entry is the average over the period. Rates of technical

change embodied in asset j is computed as the inverse of the growth rate of the quality-adjusted price of

asset j relative to the price of consumption.

Table 4: Statistical growth accounting (1948-1999)

Output unadjusted for quality Output adjusted for quality

48-99 48-60 61-70 71-80 81-90 91-99 48-99 48-60 61-70 71-80 81-90 91-99

GDP growth 3.718 3.675 4.338 3.639 3.394 3.532 4.014 3.687 4.821 3.893 3.599 4.148

Contribution of Capital (k) .536 .411 .487 .597 .602 .642 .497 .410 .438 .558 .568 .547

Quantity of Capital (k) .325 .229 .306 .428 .361 .332 .301 .228 .275 .400 .341 .283

Quantity of IT Capital (kipes) .055 .026 .039 .049 .060 .049 .051 .026 .035 .046 .057 .042

Quantity of Other Capital (kother) .270 .203 .267 .379 .301 .283 .250 .202 .240 .354 .284 .241

Quality of Capital (Q) .211 .182 .181 .169 .241 .310 .196 .181 .163 .158 .227 .294

Quality of IT Capital (Qipes) .060 .014 .027 .062 .090 .124 .056 .014 .024 .058 .085 .118

Quality of Other Capital (Qother) .151 .168 .154 .107 .151 .186 .140 .167 .139 .10 .142 .176

Contribution of Labor (l) .323 .200 .290 .342 .413 .419 .299 .200 .261 .320 .389 .397

Quantity of Labor (n) .219 .029 .158 .186 .351 .345 .203 .029 .142 .174 .331 .327

Quality of Labor (h) .104 .171 .132 .156 .062 .074 .096 .170 .119 .146 .058 .070

Aggregate TFP (z) .141 .389 .224 .061 -.015 -.061 .204 .390 .301 .122 0.04 .056

Note: The contribution of each component is defined as the ratio between the share-weighted real growth rate of that component and real GDP growth.

The aggregate share of labor (capital) is constant at .64 (.36) over the sample period. To compute the contribution of IT goods we used the Tornquist

decomposition in equation (??).

Table 5: Cycle and Trend in the Recent Productivity Surge

Total Cycle Trend

λ=6.25 λ=100 λ=6.25 λ=100Total 1.00 .315 .889 .685 .111

Capital Deepening .423 .170 .433 .253 -.100

Quantity of Capital -.238 .077 .125 -.315 -.363

IT Capital -.040 .051 .136 -.090 -.175

Other Capital -.199 .026 -.009 -.225 -.188

Quality of Capital .661 .093 .308 .568 .353

IT Capital .286 .058 .204 .228 .082

Other Capital .375 .035 .104 .340 .271

Labor Quality -.297 -.124 -.294 -.173 -.003

Aggregate TFP .875 .270 .750 .605 .125

Note: The labor productivity acceleration is .087, computed comparing average annual productivity

growth in 1995-1999 to 1973-1995. The cyclical component is extracted from each series through the

Hodrick-Prescott filter. The data have annual frequency, so both a value of λ=100 and a value of λ=6.25are used (see the main text for an explanation). The contribution of the various components reported

in each row is defined as the ratio between the share-weighted real growth rate of that component and

real GDP growth (quality-adjusted). The aggregate share of labor (capital) is constant at .64 (.36) over the

sample period. To compute the contribution of IT goods we used the Tornquist decomposition in equation

(10).

Table 6 - Embodied Technical Change by Industry

Industry 48-99 48-60 61-70 71-80 81-90 91-99

ETC Share ETC Share ETC Share ETC Share ETC Share ETC Share

1 Agriculture 0.011 0.080 0.008 0.124 0.011 0.087 -0.008 0.084 0.023 0.044 0.024 0.043

2 Extractive 0.024 0.033 0.009 0.030 0.024 0.032 0.015 0.039 0.035 0.040 0.044 0.022

3 Construction 0.022 0.037 0.011 0.052 0.024 0.047 0.010 0.037 0.027 0.020 0.045 0.024

4 Durable Manufacturing 0.035 0.139 0.013 0.148 0.032 0.155 0.039 0.145 0.041 0.129 0.057 0.115

5 Nondurable Manufacturing 0.039 0.119 0.024 0.129 0.039 0.127 0.040 0.121 0.041 0.107 0.056 0.108

6 Transport and Utilities 0.040 0.156 0.023 0.184 0.049 0.162 0.022 0.155 0.046 0.143 0.067 0.123

7 Communications 0.077 0.079 0.076 0.062 0.052 0.086 0.073 0.086 0.081 0.082 0.109 0.085

8 Wholesale Trade 0.055 0.058 0.026 0.035 0.048 0.045 0.060 0.054 0.064 0.080 0.088 0.086

9 Retail Trade 0.043 0.057 0.033 0.067 0.043 0.056 0.038 0.050 0.049 0.056 0.059 0.054

10 FIRE 0.056 0.131 0.034 0.088 0.048 0.097 0.070 0.117 0.058 0.177 0.080 0.195

11 Other Services 0.050 0.111 0.029 0.081 0.046 0.106 0.053 0.111 0.062 0.121 0.068 0.145

Table 7 - Hulten’s Technological Gap by Industry

Industry 48-99 48-60 61-70 71-80 81-90 91-99

ETC ETC ETC ETC ETC ETC

1 Agriculture 0.051 0.015 0.067 -0.008 0.064 0.134

2 Extractive 0.118 0.027 0.097 0.075 0.142 0.295

3 Construction 0.094 0.031 0.098 0.064 0.103 0.203

4 Durable Manufacturing 0.177 0.042 0.129 0.173 0.245 0.355

5 Nondurable Manufacturing 0.228 0.088 0.219 0.240 0.272 0.379

6 Transport and Utilities 0.283 0.056 0.320 0.280 0.301 0.556

7 Communications 0.410 0.240 0.319 0.274 0.568 0.734

8 Wholesale Trade 0.183 0.069 0.154 0.188 0.230 0.320

9 Retail Trade 0.185 0.092 0.206 0.177 0.213 0.273

10 FIRE 0.200 0.084 0.179 0.242 0.233 0.309

11 Other Services 0.182 0.059 0.161 0.211 0.247 0.280

TABLE 8: Sources of Growth at the Industry Level (1977-99)

Annual average share-weighted growth rate (%) 1977-99 1977-89 1990-99

Source

Industry: Durable Goods Manufacturing

Value-Added 2.544 2.602 2.639

Labor -0.127 -0.105 0.029

Capital

Quantity of Capital 0.656 0.703 0.546

Quality of Capital 0.949 0.780 1.070

TFP 1.066 1.224 0.994

Industry: Non-Durable Goods Manufacturing

Value-Added -0.308 -0.267 0.043

Labor -0.183 -0.027 -0.362

Capital

Quantity of Capital 0.976 0.972 0.858

Quality of Capital 1.395 1.159 1.535

TFP -2.496 -2.370 -1.989

Industry: Transportation and Utilities

Value-Added 2.088 1.207 3.101

Labor 0.834 0.795 0.821

Capital

Quantity of Capital 1.131 1.294 0.865

Quality of Capital 1.566 1.301 1.760

TFP -1.444 -2.183 -0.345

Industry: Communications

Value-Added 4.837 4.355 4.855

Labor 0.448 0.171 0.649

Capital

Quantity of Capital 2.480 2.643 2.063

Quality of Capital 3.641 3.013 4.101

TFP -1.732 -1.472 -1.958

Annual average share-weighted growth rate (%) 1977-99 1977-89 1990-99

Source

Industry: Wholesale Trade

Value-Added 5.269 4.775 6.027

Labor 0.951 1.229 0.639

Capital

Quantity of Capital 2.366 2.883 1.593

Quality of Capital 2.451 2.144 2.651

TFP -0.498 -1.481 1.144

Industry: Retail Trade

Value-Added 3.688 3.310 4.237

Labor 1.412 1.683 1.030

Capital

Quantity of Capital 1.421 1.517 1.164

Quality of Capital 1.455 1.383 1.397

TFP -0.601 -1.274 0.646

Industry: FIRE

Value-Added 1.344 -2.550 5.307

Labor 0.519 0.719 0.234

Capital

Quantity of Capital 3.471 4.205 2.166

Quality of Capital 3.420 3.402 3.114

TFP -6.067 -10.876 -0.207

Industry: Other Services

Value-Added 3.322 4.115 2.082

Labor 2.944 3.120 2.421

Capital

Quantity of Capital 1.235 1.210 1.165

Quality of Capital 1.511 1.347 1.568

TFP -2.368 -1.562 -3.074