5.1Is IT Capital a Productive Input?

In this section, I present the empirical results related to the measurement of the productive capacity of IT capital. Derived from equations 4.14 and 4.13, the two following equations are estimated:

ln(Y)its = ln(A) + α1ln(KIT)its + α2ln(KNIT)its + βln(L)its(5.1)

Using fixed effects for industries, states and years

ln(Y)its = ln(A) + Σi-1Di + Σs-1Ds + Σt-1Dt + α1ln(KIT)its + α2ln(KNIT)its + βln(L)its(5.2)

Coefficients α1, α2, and β represent the output elasticities to various inputs, which are also the percent change in output for a 1% change in the quantity of input. An input is a productive resource if its output elasticity is significantly positive. These parameters can also be considered as the marginal products of each input, which represent the amount of additional output provided for an additional dollar invested in the input. Table 5.1 reports estimates of elasticities for equation 5.1. Results indicate a positive and significant elasticity (or marginal product) of IT capital input at all levels of study (with a value between 0.115 and 0.211), except for the estimation of equation 5.2 at the level of detailed industries nationally.

First, equations 5.1 and 5.2 were estimated at the detailed industries level, by state and year, representing 55,692 observations (one observation for each industry, in each state, for each year). Without the use of fixed effects (equation 5.1), results indicate output elasticities of 0.196 for IT capital, 0.162 for traditional capital, and 0.638 for hours worked. These coefficients are close to their expected values in the presence of constant returns to scale (0.66 for labor and 0.33 for total capital). The R-squared and Durbin Watson (0.95 and 1.83, respectively) indicate a high degree of explanatory power of the model and the absence of serial correlation in the error term. However, the elasticity of IT capital drops from 0.196 to 0.021 when industry, state and time fixed effects are accounted for (equation 5.2). This result indicates that roughly 90% of the elasticity of IT capital may be attributable to industry, state and time effects. Thus, there are industry and state differences, across years, regarding the productive capacity of IT capital, and these differences may increase the estimates of the marginal product of IT capital by 90%. Still, this elasticity is significantly positive, and IT capital can be considered as a productive input.

Table 5.1Estimates of Elasticities for Equations 5.1 and 5.2 for Detailed Industries by State, for Aggregated Industries by State and for Detailed Industries at the National Level

Equation Estimated	(5.1)	(5.2)	(5.1)	(5.2)	(5.1)	(5.2)
Level of study	Detailed Industries by State	Detailed Industries by State	Aggregated Industries by state	Aggregated Industries by state	Detailed Industries at the National level	Detailed Industries at the National level
Fixed Effects	No	Yes: Di, Ds, Dt	No	Yes: Dt, Ds	No	Yes: Di, Dt
Constant	2.936	1.470	2.684	3.414	4.298	14.591
IT capital	0.196	0.021	0.211	0.092	0.210	(-0.007)
Non-IT capital	0.162	0.337	0.125	0.216	0.130	(-0.000)
Labor	0.638	0.632	0.671	0.650	0.597	0.386
R2	0.95	-	0.99	-	0.95	0.98
Durbin Watson	1.83	-	1.56	-	-	-
Time periods	21	21	21	21	21	21
Industries	52	52	-	-	52	52
States	51	51	51	51	-	-
N	55,692	55,692	1,071	1,071	1,092	1,092
Note: All coefficients are significant at the 0.01 level, except those in parentheses.

Equation 5.1 is also estimated at the state level (aggregated industries, by state and by year). Results are similar, but vary when fixed state and time effects are introduced (equation 5.2). The estimated elasticity drops from 0.211 to 0.092 because of state and time effects. Equation 5.1 is finally estimated at the detailed industries national level. Results show that the output elasticities are similar to the ones at the detailed industries level by state. However, regression using fixed effects (equation 5.2) produces estimates of output elasticities of capital not significantly different from zero.

To understand better how input elasticity estimates vary at the different levels of analysis, I estimated equations 5.1 (or 5.2 when fixed effects were needed) by selected industry sector, by year and by state. Results appear in Tables 5.2, 5.3 and 5.4, respectively.

Results of regression 5.2 vary across industry sectors as reported in Table 5.2. The output elasticity of IT capital is positive and significant for all sectors except Finance, Insurance and Real Estate (F.I.R.E.). This is probably due to mismeasurement errors resulting from the difficulty of measuring inputs and outputs in this sector.

Table 5.2Estimates of Elasticities from Equation 5.2 for Selected Industry Sectors across States

Sector	Constant	IT capital	Non-IT capital	Labor
All6	3.719	0.247	0.126	0.600
Manufacturing:	4.209	0.191	0.247	0.470
Durable goods	3.149	0.113	0.194	0.664
Nondurable Goods	5.333	0.317	0.124	0.435
Service Sector:	3.301	0.219	0.127	0.657
Transportation	3.120	0.213	0.250	0.500
Trade7	1.944	0.016	0.920	(-0.01)
F.I.R.E.8	5.069	-0.556	0.970	0.335
Service Industry	4.210	0.171	-0.030	0.835
Note: Separate regressions for each sector, with time and state dummies. All coefficients are significant at the 0.01 level, except those in parentheses. The number of observation for each regression is 1,071 (1 observation for each state, each year: 51*21 = 1,071)

For all sectors aggregated, the output elasticity of IT capital is 0.247, and it is greater than the output elasticity of traditional capital (0.126). The sum of output elasticities is not significantly different from one for all regressions, which support the constant returns to scale hypothesis. The service sector has a greater output elasticity of IT capital than the manufacturing sector (0.219 and 0.191 respectively), but the difference is small. The nondurable goods manufacturing sector has the highest elasticity of IT capital (0.317). IT capital has a greater output elasticity than traditional capital in the service sector, while the reverse is true in the manufacturing sector. The coefficients for Finance, Insurance and Real Estate (F.I.R.E.) sector is negative for IT capital. Once again, this may be due to the difficulty of measuring output in that industry (mismeasurement hypothesis).

The output elasticities of inputs vary also across time during the last two decades. Table 5.3 reports estimates of equation 5.1 for each year between 1977 and 1997. These output elasticities are all positive and significant. The aggregate output elasticity of IT capital ranges from 0.13 in 1977 to more than 0.27 in 1982. Figure 5.1 clearly shows the gap between output elasticities of IT capital and traditional capital. The difference between the output elasticities of the two types of capital was highest during the 1980s.

Table 5.4 presents elasticities estimates from equation 5.2 for each of the 51 states at two levels: (1) at the detailed industries level (controlling for industry fixed effects) and (2) at the aggregated industry level. At the detailed industries level, all coefficients are significant and the output elasticity of IT capital (α1) averages 8.48% across states, with a standard deviation of 1.22.

Table 5.3Estimates of Equation 5.1 Over Time

YEAR	Constant	IT capital	Non-IT capital	Labor
1977	3.13	0.13	0.21	0.65
1978	3.26	0.17	0.15	0.67
1979	3.36	0.21	0.12	0.65
1980	3.28	0.24	0.07	0.68
1981	3.25	0.26	0.07	0.67
1982	3.28	0.27	0.05	0.67
1983	3.17	0.27	0.07	0.66
1984	3.06	0.25	0.09	0.66
1985	3.06	0.25	0.10	0.65
1986	3.02	0.23	0.12	0.64
1987	3.08	0.24	0.13	0.62
1988	3.00	0.23	0.15	0.62
1989	3.06	0.24	0.13	0.63
1990	2.97	0.23	0.13	0.63
1991	2.79	0.22	0.17	0.62
1992	2.73	0.21	0.17	0.62
1993	2.78	0.22	0.17	0.61
1994	2.78	0.22	0.18	0.60
1995	2.83	0.23	0.18	0.59
1996	2.77	0.24	0.19	0.56
1997	2.83	0.25	0.19	0.55
Note: No fixed effects included. All coefficients significant at the 0.01 level

Figure 5.1Trends in Aggregate Output Elasticities of IT and Traditional Capital, 1977-1997

Table 5.4Estimates of Elasticities from Equation 5.1 for Detailed and Aggregated Industries by State

Level of Analysis	Detailed Industries				Aggregated Industries
State	Constant	IT capital	Non-IT capital	Labor	Constant	IT capital	Non-IT capital	Labor
Alabama	2.61	9.2	27.6	55.2	(-3.96)	(11)	(21)	98
Alaska	0.68	7.9	36.0	60.0	9.88	17	14	33
Arizona	3.06	11.0	33.6	45.6	2.31	21	(9)	72
Arkansas	4.95	10.2	23.6	42.4	(-0.27)	11	20	81
California	2.17	8.6	28.0	60.2	(-0.71)	13	30	68
Colorado	3.86	10.5	30.7	43.7	6.44	20	(-5)	70
Connecticut	4.02	8.7	15.4	61.6	(-0.77)	13	31	69
Delaware	2.11	7.8	28.3	61.3	-7.90	(-6)	77	73
Dist. Of Col.	2.18	6.3	29.9	59.6	1.62	8	19	78
Florida	3.02	8.9	22.8	60.7	1.58	9	24	70
Georgia	3.13	8.6	21.7	57.0	-5.40	(2)	44	82
Hawaii	3.08	6.5	21.3	71.6	1.86	7	15	82
Idaho	2.09	9.1	30.9	56.2	3.42	21	(-199)	88
Illinois	4.69	8.3	19.0	51.7	-6.06	14	57	60
Indiana	3.10	7.6	27.9	59.9	-7.69	8	57	75
Iowa	5.16	8.1	29.5	47.5	(-0.14)	15	34	61
Kansas	4.05	8.2	32.5	48.3	13.90	19	(-11)	42
Kentucky	4.23	8.3	24.0	58.4	9.76	18	-57	1.19
Louisiana	1.61	8.0	33.6	57.2	11.62	16	(-6)	52
Maine	4.23	9.9	20.9	49.4	-7.62	(5)	53	87
Maryland	3.04	8.9	30.5	50.7	-1.84	9	46	61
Massachusetts	2.65	7.9	25.3	57.7	-1.55	13	42	60
Michigan	3.78	8.9	25.8	52.7	-8.31	7	66	68
Minnesota	4.72	9.6	24.7	48.5	(2.27)	18	(-5)	92
Mississippi	3.93	7.4	26.2	58.2	(-0.45)	15	20	79
Missouri	4.54	9.2	27.7	44.0	-8.50	(2)	71	69
Montana	1.86	9.2	37.2	49.1	10.34	20	-26	76
Nebraska	2.32	6.9	30.5	58.7	(-0.31)	10	29	73
Nevada	2.59	9.7	31.7	51.9	(0.28)	(-1)	15	97
New Hampshire	2.64	7.3	28.7	63.3	(0.21)	20	18	73
New Jersey	3.05	7.5	20.6	62.9	-4.01	10	18	66
New Mexico	1.91	9.7	37.6	47.8	7.55	20	-45	1.13
New York	6.74	6.6	10.3	52.5	(0.85)	20	16	71

Table 5.4(Continued)

Level of Analysis	Detailed Industries				Aggregated Industries
State	Constant	IT capital	Non-IT capital	Labor	Constant	IT capital	Non-IT capital	Labor
North Carolina	2.36	6.7	21.9	71.0	6.91	20	-61	1.34
North Dakota	2.62	7.8	36.1	52.4	6.88	13	-4	37
Ohio	3.78	8.2	23.5	48.1	(-0.70)	20	(12)	82
Oklahoma	4.12	9.1	28.0	41.9	11.70	16	-10	55
Oregon	2.36	9.3	33.0	49.5	1.68)	19	(1)	87
Pennsylvania	2.94	7.4	23.5	58.5	(-0.47)	18	40	51
Rhode Island	4.49	7.2	17.8	66.5	-7.38	6	47	92
South Carolina	1.49	5.7	26.6	72.2	-3.95	15	27	86
South Dakota	1.67	8.2	31.7	58.7	4.76	14	21	53
Tennessee	5.21	11.4	16.6	51.6	-4.04	7	41	79
Texas	1.74	8.7	32.1	57.1	16.45	37	-44	56
Utah	1.96	9.7	37.4	47.9	11.27	33	-43	79
Vermont	4.92	8.9	20.9	58.9	(0.44)	14	26	69
Virginia	3.09	9.7	27.5	50.7	5.34	14	(-2)	79
Washington	2.07	10.1	37.0	46.7	2.09	11	42	45
West Virginia	4.22	6.9	21.1	55.0	12.93	41	-55	76
Wisconsin	3.09	8.8	27.6	52.4	(2.82)	20	(-8)	91
Wyoming	2.33	8.5	38.9	43.9	21.35	44	-79	60
Note: Elasticities are expressed in percentage. All coefficients are significant at the 0.01 level except those in parentheses. For detailed industries regressions (using industry dummy variables), there are 52 industries * 21 years = 1,092 observations for each state. For aggregated industry there are 21 observations for each state.

Tennessee and Arizona present the highest returns to IT capital stock (greater than 11%), and South Carolina and Hawaii the lowest. This means that some states seem to use IT capital more efficiently than others, even though the differences do not seem to be very important. Eight of the “most IT” states (Figure 2.9) present an output elasticity of IT capital less than or equal to the overall states’ average of 8.48%. Hence, the returns to IT capital do not seem to be the greatest for states that own the highest share of IT capital. At the aggregated industry level by state, many coefficients are not significant, and regression results vary significantly from the results at the detailed industries level. This is certainly due to the fact that, at the aggregated industry level, only 21 observations are available for each state (one for each year), as opposed to 1,092 observations per state at the detailed industries level (one for each industry each year). The average output elasticity of IT capital at the aggregated industries level is higher than at the detailed industries level (14.82% and 8.48%, respectively), and the standard deviation is 10 times greater. Furthermore, at this aggregated industries level, output elasticities of IT capital for the most IT states are greater than or equal to average elasticity, except for California, which owns the highest share of the nation’s IT capital stock.

Hence, several conclusions can be drawn from the estimates of equations 5.1 and 5.2. First of all, IT capital is a productive input, that has an output elasticity estimated at roughly 0.20 at the detailed industry level by state, but industry and state fixed effects may account for most of this value. At the sectoral level, there are no major differences between manufacturing and the service sector regarding output elasticities of IT capital (also estimated at around 0.20), but there are some differences at a more disaggregated level. Indeed, the elasticity IT capital is highest for the nondurable goods sector (0.32) and lowest for the trade sector (0.02), not including the negative elasticity for the F.I.R.E. sector, which may be due to measurement difficulties in that sector. The returns to IT capital are relatively stable at the national level over time (between 0.15 and 0.25), with an increase until 1983, a plateau for the rest of the 1980s, and a slight increase since the early 1990s. Finally, the average returns to IT capital across states is around 0.08 at the detailed industries level across states, and is around 0.14 at the aggregated industries level across states. However, results from the aggregated industries level must be interpreted carefully since only 21 observations were available for each state. From the detailed industries regression results, the returns to IT capital appear lower than average in states that own the highest share of the nation’s IT capital stock.

Hence, based on all these findings, IT capital stock seems to be a productive input with an output elasticity that varies between 10% and 20%, and between 2% and 10% when fixed effects are introduced. In order to further investigate the productive capacity of IT capital, the next section discusses the “excess” returns hypothesis.