Pure Technology Gaps and Production Predictability

Pure Technology Gaps and Production PredictabilityI

Ziemowit Bednarek

California Polytechnic State University, Orfalea College of Business, 1 Grand Ave, San Luis Obispo, CA 93407

Abstract

An average machine lags in terms of productivity and technological advancement behind acutting-edge machine. This lag was first defined by Cummins and Violante (2002) as thetechnology gap. Using the vector error correction model, I show that the technology gap iscointegrated with human capital factors, and then decompose it into a long-run trend and atransitory mean-reverting component, which I term as the pure technology gap. I show thatthe pure technology gap has a predictive power for the aggregate production. Intuitively, a highpure technology gap acts as an economic shock that increases production in the long term dueto a higher future productivity level.

Keywords: Technology gap, productivity, price index, log utility, vector error correctionmodel, predictability

IFinancial support from the Dean Witter Foundation and the Fisher Center for Real Estate and UrbanEconomics is gratefully acknowledged. I would like to thank Nigel Barradale, Greg Duffee, Dmitry Livdan,Christine Parlour, Adam Szeidl, Johan Walden, Nancy Wallace, Amir Yaron, and UC Berkeley’s Haas Schoolof Business lunch seminar participants for helpful discussions and suggestions. I thank Gianluca Violante forproviding me with the data. Special thanks go to Boyan Jovanovic, Martin Lettau, and my adviser RichardStanton, who contributed greatly to my understanding of the issues raised in this article. All errors are my own.

Email address: [email protected] (Ziemowit Bednarek)

Preprint submitted to The Quarterly Review of Economics and Finance June 12, 2014

1. Introduction

The most technologically advanced machines are on the productivity frontier of an industry.An average machine in use in a given industry will lag behind the ones on the frontier in termsof its productivity and the level of the technological advancement. Following Cummins andViolante (2002), I call the difference in productivity between the cutting-edge and the averagemachine for a given group of machines “the aggregate technology gap”. With time, throughindustry and geographic spillover effects, the average machine catches up to the frontier machinethrough the process of efficiency change. Efficiency change may be due to human capital factors(workers learning to better operate the machinery) or physical capital factors (machine partsare upgraded).

In this article I demonstrate that the aggregate technology gap can be decomposed intotwo parts: a long-term trend component and a transitory mean-reverting component. Thedecomposition of the technological progress across different vintages of installed capital in orderto derive the mean-reverting component of the technological growth (what I will refer to as the“pure technology gap”) enables me to use it as a leading indicator of the economic growth.

I demonstrate empirically in the vector error correction model (VECM) setting that thepure technology gap has a predictive power for the future aggregate production levels. I focuson the aggregate technology gaps estimated from two groups of machines: 1) equipment andsoftware; 2) information processing equipment and software. The rationale for investigatingthe effect of these two groups of machines on the aggregate economy is in their widespread useacross different industry sectors.

Intuitively, the closing of the technology gap by industry followers catching up with theleader should increase the productivity of the whole industry or perhaps even economy if themachines from a given industry are prevalent. The closing of the technology gap occurs becauseof the efficiency change process and can be related to both human and physical capital relatedfactors. It is also intuitive to expect that if the technology gap closes or is at least reduced,production and subsequently consumption stream generated by that machine will be higher perunit of time.

The empirical strategy developed in this article is based on the estimation of the technicalchange using durable goods price indices as in Gordon (1990), and Cummins and Violante(2002). I measure the technical change from quality-adjusted price indices of durable investmentgoods. Comparing a constant quality price index with an index unadjusted for quality allowsme to obtain the estimate of the productivity frontier growth. I measure the productivity of anaverage machine by dividing the accumulated capital in efficiency units by the installed capitalin natural units. The aggregate technology gap is equal to the relative difference between theproductivity of the latest vintage and the productivity of an average machine. The aggregatetechnology gap, a human capital factor, consumption and production levels are then jointlymodeled in the VECM. The pure technology gap is a cointegrating vector from the VECM, ithas a mean-reverting nature and is stationary by construction. In the baseline specification, Iuse the return to education as the human capital factor.

The VECM setting comfortably accommodates testing for the predictability of the pro-duction levels with the pure technology gap through the short-run adjustment coefficients. Ifind those coefficients to be significant in most model specifications, which suggests that thepure technology gap predicts future aggregate production. I further confirm this effect by in-vestigating the impulse response functions of the aggregate levels of production and find thatthe technology gaps have first a transitory negative effect in the short-run and then a perma-nent positive effect on the levels of production in the long-run. These results are robust to

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several other model specification, including different human capital factors: share of workerswith college education, share of young workers, share of women, and others, as well as includingadditional variables in the VECM specification.

The findings of this article are significant for two reasons. First, I present a new predictorof the aggregate production: the pure technology gap. The long-run risk literature in assetpricing (e.g. Bansal and Yaron, 2004) which links asset returns to moments of consumptionand production growth imposes predictability exogenously and it seems that having a predictorwith an economic meaning is a step forward. Second, the technology gaps have possible policyimplications, e.g. tax credits for shortening the life of capital and research and developmentexpenditures, and therefore might be useful in the economic policy literature.

2. Empirical methodology

In this section I show the empirical methodology employed in this article. I begin withpresenting how to measure the technical change and installed capital productivity. This allowsme to next define the aggregate technology gap. I then demonstrate the vector error correctionmodel (VECM) used in the estimation of the production response to the technology gaps.

2.1. Measure of technical change

I use the method of Hulten (1992), and Cummins and Violante (2002)1 to measure thetechnical change from investment goods’ prices. Hulten (1992) first shows that quality-adjustedprice indices can be used to measure the technology gap between the productivity of newvintages and the average practice in the economy.

I will introduce a very simple framework that will help understand the estimation of thetechnical change from price indices. There is an economy producing final goods kt that can beaccounted for in natural units or in efficiency units ht, with technology

ht = qtkt, (1)

where qt is the Hicks-neutral index of the technology. An example of a natural unit would be aprocessor. An example of an efficiency unit would be the number of operations per second of acomputer processor. Measure qt is the estimate of the productivity of the last available vintageof capital goods. I have the price of investment goods in efficiency units given by pht and theprice of consumption goods in natural units equal to pct . The value of production is the same,irrespective of measurement units2:

pht ht = pctkt, (2)

which yields

qt =pctpht. (3)

The estimate of the technical change qt is further calculated using official NIPA consump-tion chain-weighted deflator of nondurable and services personal consumption expenditures for

1Many thanks to Gianluca Violante for providing me with the data necessary to estimate the technology gaps.2As in Hulten (1992), change of measurement units will change the price per unit but not the total price. If

for example a maximum potential productivity of a $1000 processor is three times higher than that of a processorfrom last year, then either one processor was purchased or three processors worth $333 each were purchased forthe same dollar amount. Actual productivity of the newer processor may be only slightly higher or even initiallylower than that of the previous processor.

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pct and the quality-adjusted durable investment goods deflator calculated as in Gordon (1990),Cummins and Violante (2002) and Fisher (2006) for pht .

2.2. Measure of installed capital productivity

In order to measure the technology gap, I need a measure of the productivity of average(installed) capital. Since capital in place is a combination of several past vintages with differentcharacteristics, to obtain one average measure of productivity I will weigh subsequent vintageswith their value. Using the notation as in Cummins and Violante (2002), the amount of physicalcapital available at any time t can be expressed in constant-quality units as:

kt = (1 − det )kt−1 + it, (4)

where det is the economic depreciation rate at time t. Weights det, given by depreciation rates,convert each vintage of investment into new-machine equivalents. Capital stock kt is theninterpreted as the number of new-machine equivalents implied by the stream of past investments,following Hulten (1992).

Each new vintage of capital embodies differences in technical design. For example, acomputer manufactured in 2000 will be more productive than a computer made in 1995, evenif their accounting values are the same. Because of that, using the regular capital accumulationequation (4) understates the true value of successive vintages of productive capital. Vintage ofcapital introduced at time t is recorded as in equation (1). Then I have the capital accumulationequation in efficiency units as:

k∗t = (1 − δet )k∗t−1 + i∗t , (5)

where δet is the time-varying physical depreciation rate and i∗t is the quality-adjusted investmentseries. I use the physical depreciation rate for the quality-adjusted capital stock as investment ismeasured in efficiency units, following Oliner (1993), Gort and Wall (1998), and Whelan (2001).As in Cummins and Violante (2002), the measure of the productivity of an average machinecomes from comparing the two quantities of capital from (4) and (5) and can be expressed as:

Qt =k∗t

kt. (6)

Equation (6) states that the productivity of an average machine at time t is a weighted averageof past vintages’ productivities with weights given by the fraction of surviving (depreciated)vintage kt in the capital kt.

The importance of using the economic and physical depreciation rates for capital measuredin natural and efficiency units respectively should be underlined. Bureau of Economic Analysisdefines and measures the economic depreciation as the change in the asset value stemming fromthe aging process, consisting of an age effect and a time effect. The age effect measures thephysical decay and the time effect measures the degree of obsolescence due to the change in therelative prices, qjt /q

jt−1 for asset j. The economic and physical depreciation rates are related to

each other as

djt = 1 − (1 − δjt )qjt−1

qjt. (7)

When there is no technical change and qjt = qjt−1, economic and physical depreciation are equal.

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2.3. Aggregate technology gap

Using equations (3) and (6), I now define the aggregate technology gap following Cumminsand Violante (2002) as

Γt =qt −Qt

Qt. (8)

Γt is the aggregate technology gap, stemming from both human capital and physical capitalfactors. In the next section I will specify the VECM and define the pure technology gap. I willdemonstrate that in the data, aggregate technology gaps are non-stationary and cointegratedwith human capital related factors, e.g. return to education. Pure technology gap on the otherhand, the main predictive variable used in this article, is stationary by construction as shownin subsequent sections.

Properties of the aggregate technology gaps depend on the specification of the depreciationrates when calculating the capital stock in constant-quality and efficiency units. For example,if the capital was fully depreciated within one period, the aggregate technology gap wouldalways be closed. The divergence between time-varying physical and economic depreciationrates is partially responsible for the non-stationary nature of the aggregate technology gapspresented in this article. Furthermore, as pointed out in the previous section, when the economicdepreciation rate equals to the physical depreciation rate, then there is no technical change andthe aggregate technology gap is closed faster.

2.4. VECM and pure technology gap

I lay out the empirical framework used in the estimation of the pure technology gap andits effect on the aggregate variables. In particular, since I suspect there is a cointegratingrelationship between the level of the aggregate technology gap and human capital factors (e.g.return to education, college education, share of young workers and women in the workforce), Iwill rely on the VECM. Following Johansen (1988, 1991, 1995); Park and Philips (1988, 1989);Sims, Stock, and Watson (1990); Stock (1987); and Stock and Watson (1988), I can present thegeneral multivariate VECM as:

∆yt = αβ′yt−1 +

p−1∑i=1

Λi∆yt−i + ν + δt+ εt, (9)

where in the baseline specification

yt =

Γt

HCt

Ct

Yt

, (10)

and Γt is the aggregate technology gap, HCt is a human capital related factor, Ct is the aggregateconsumption, and Yt is the aggregate production (GDP). The deterministic components in (9)can be further defined as:

ν = αµ+ γ (11)

δ = αρ+ τ, (12)

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which then allows me to transform (9) into:

∆yt = α(β′yt−1 + µ+ ρt) +

p−1∑i=1

Λi∆yt−i + γ + τt+ εt, (13)

where the cointegrating vector is defined as:

β′yt−1 + µ+ ρt = εt. (14)

From now on, I will refer to the cointegrating vector in (14) as the pure technology gap. In allthe estimations I will assume a linear time trend in the levels of all the variables, implying thatτ = 0 and ρ = 0.

I verify that the specification of the VECM is correct by performing a series of diagnostics.I show that the pure technology gap is mean-reverting and stationary using the Dickey-Fullertest. I select the optimal number of lags based on the methods developed in Tsay (1984),Paulsen (1984) and Nielsen (2006). The number of lags is calculated using the Hannan-Quinninformation criterion method, Schwarz Bayesian information criterion method, Akaike informa-tion criterion method, and the sequential likelihood ratio test. However, I also incorporate theresults of Gonzalo (1994) which indicate that underspecifying the number of lags can substan-tially raise the finite-sample bias in the estimates and in consequence cause serial correlation.I formally test for the cointegration using methods described in Engel and Granger (1987).

3. Empirical results

3.1. Time-series properties of the aggregate technology gaps

The upper panel of figure (1) presents the technical change measure based on Gordon(1990), Cummins and Violante (2002), and Fisher (2006) quality-adjusted price indices. Thefigure also presents the aggregate technology gap based on equipment and software (ES) prices,and information processing equipment and software (IPES) prices.

I use data on quality-adjusted price indices from Gordon (1990), and Cummins and Violante(2002). Gordon (1990) estimates quality-adjusted prices of 25,650 goods selected to the sample,covering 1947 to 1983, and meeting the criteria of sufficient information on good’s characteristicsand on transaction, rather than list prices. Sources of data on the good’s characteristics includemail-order catalogs, Consumer Reports, Current Industrial Reports, Department of Energydata on equipment costs and characteristics of electric utility generating plants, Departmentof Transportation data on aircraft characteristics and others. Individual goods’ price deflatorswere weighted into 26 major categories and then into an aggregate durable goods deflator.Weights within the 26 categories are using implicit deflator method of National Income andProduct Accounts (NIPA), but across the 26 categories, they were calculated using Tornqvistindices. Cummins and Violante (2002) extended the original Gordon (1990) dataset (1947 to1983) through 2000.

I use the technology gap estimates obtained from equation(8) for equipment and software(ES), including information processing equipment and software (IPES), industrial equipment,transportation equipment and other equipment. I also present a separate estimate for only theIPES subcategory, which includes computers, communication equipment and software.

The technology gap is typically high just prior to the recession and it decreases during therecession. Because of that, I expect the technology gap to be a predictor of positive production

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growth in the long run. After retooling the existing physical capital, expected productiongrowth in the long-run will be high as the economy recovers.

The most striking feature of the data is a highly positive trend of the aggregate technologygap based on both ES and IPES. The ES gap increased around four times between 1947 and2000. The growth in the IPES gap is smaller but clearly visible as well. A possible explanationof this strong trend lies in the well-known evidence on wage inequality. In the postwar data,the technical change and returns to education move together at low frequencies (bottom panel),which might suggest that the strong positive trend is caused by the wage inequality. The onlytime period after World War II when the skills premium falls is the 1970s, when the ES technicalchange levels off.

The IPES technology gap was consistently higher than the ES, with the largest differencebetween 1975 and 1985. Later the IPES technical change leveled off. Cummins and Violante(2002) attribute this pattern to technological progress in IPES from 1975 to 1985 when this typeof equipment was not widespread. When firms began to substitute other equipment for IPESand heavily invest in new technology, the technical change started slowing down and leveledin the 1990s. Cummins and Violante (2002) present the distribution of the annual technicalchange across 62 industries. The general increasing pattern is preserved for all the industries,but there is a significant dispersion. For example, the technical change in communications from1990 to 2000 was 73% compared with 13.4% of agriculture, forestry and fishing. In terms ofthe average gaps from 1947 to 2000, communications and transportation recorded the highestlevel, and agriculture and construction the lowest level. This result is intuitive. Industries moreheavily dependent on technology experience higher productivity growth of new vintages andreport higher depreciation rates of its equipment. The technology abandonment rate in suchindustries is also likely to be higher, resulting in more incompatibilities of new technology andexisting capital.

3.2. VECM estimation in the baseline case

I will now show the results of the baseline and then alternative VECM specifications,with the optimal number of lags, cointegrating equations, and testing for the stability of thesystem. My baseline specification was laid out in equations (9) and (10). I use the returnto education as the human factor variable in equation (10) and the aggregate technology gapfor equipment and software (ES). In the subsequent section I present results for alternativespecifications of vector yt, as well as information processing equipment and software (IPES)gap. In all the predictability regressions, consumption data is a real nondurable and servicesNIPA consumption per capita from 1947 to 2000. Aggregate production data is real GDP andcomes from the Bureau of Economic Analysis (BEA).

VECM is a natural setting for the analysis in this article, as I find the cointegrationbetween the aggregate technology gaps, return to education and other human capital factorsdescribed before. For example, a brief examination of figure (1) indicates that the aggregatetechnology gaps and return to education move together at low frequencies suggesting a possiblecointegration between the two series. I perform Engle and Granger (1987) test for cointegrationand find the two series to be cointegrated.

In the baseline specification I am able to comfortably reject the null hypothesis of nocointegration, and find there to be evidence of one cointegrating equation. The results of thebaseline VECM estimation with two lags can be summarized as:

α = (−0.36, 0.02,−0.05,−1.00) (15)7

β = (1,−8.58,−0.62, 0.13) (16)

ν = (−0.03, 0.01, 0.01, 0.01) (17)

Λ =

0.21 11.45 0.37 0.06−0.02 0.86 −0.00 0.00−0.05 3.95 0.56 −0.020.68 22.87 4.41 −0.13

, (18)

where α is the vector of the adjustment coefficients, β is the vector of the parameters in thecointegrating equation, ν is the vector of the time trend coefficients, and Λ is the array of theshort-run coefficients, all defined formally in equation (9).

The coefficient on the lagged error term from the cointegrating regression (short termadjustment α) for the aggregate technology gap is significant at 1% level and equal to -0.36.If in period t − 1 the error term εt−1 was to be positive, which is equivalent to Γt−1 (laggedaggregate technology gap) being too high compared to the equilibrium relationship with returnto education, it will then fall toward the equilibrium. The speed of the adjustment is the higherthe closer the coefficient is to -1. If the coefficient was -1, then the entire error εt−1 would becorrected in the next period.

3.2.1. Pure technology gap

The cointegrating equation from the VECM is defined as:

Γt−1 − 8.58ret−1 − 0.62Ct−1 + 0.13Yt−1 + 0.73 = εt, (19)

where ret−1 stands for return to education. I will refer to εt as the pure technology gap. Theterm “pure” technology gap stems from the decomposition of εt into the human capital relatedfactors (i.e. return to education) responsible for the long-run trend in the level of the aggregatetechnology gap, and the mean-reverting component of the technology growth, which may furtherbe interpreted as coming from factors other than HCt.

Whether the inference on the parameters of the VECM is correct or not depends on thestationarity of the cointegrating equation. In order to formally test for stationarity of (19), Iuse the augmented Dickey-Fuller unit-root test on εt. Test statistic is -3.703 and I reject thenull hypothesis of a unit-root with the p-value of 0.0041.

Companion matrixI verify that VECM has the correct number of cointegrating equations using the companionmatrix. Following Lutkepohl (2005), the companion matrix of the VECM with four endogenousvariables and one cointegrating equation will have three unit eigenvalues. The moduli of theother eigenvalues must be strictly less than one for the process to be stable. I present the rootsof the companion matrix in figure (2). The modulus closest to one is equal to 0.79, whichimplies a reasonable stability of the process.

Serial correlation in residualsNext, I check whether the residuals are serially correlated, using a Lagrange-multiplier (LM)test for autocorrelation in residuals of VECMs. The maximum order of autocorrelation in theLM test is set at four. The p-values for lags one-four are respectively: 0.28, 0.80, 0.21 and 0.86,and I fail to reject the null of no autocorrelation.

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3.3. Technology gaps and predictability

This section presents the main results of the article about the predictability of the pro-duction growth process with the pure technology gap. Figure (3) demonstrates the impulseresponse functions from the system defined in equation (9). All the panels show the responseof GDP to the orthogonalized shock to the level of the aggregate technology gap for differentmodel specification. The system is estimated using two lags in (9).A cursory look at the figure indicates the predictive effect that the aggregate technology gaphas on the level of GDP. A one standard deviation shock to the aggregate technology gap firstcauses a drop in GDP. This is consistent with for example a new technology introduced, notfully compatible with the existing skills of the workers, and in effect a slump in the productioncapacity due to this friction. As the workers learn how to operate the new technology, thelevel of production gradually recovers until it reaches a new higher permanent level. Thisdemonstrates how the technology gap has a predictive power for the level of GDP .

Furthermore, I present more evidence supporting the hypothesis of the predictive power ofthe pure technology gap in column (1) of table (1). The table shows the adjustment coefficients,corresponding to α in equation (9). The coefficients on both ∆C and ∆Y are negative, andthe coefficient on change in GDP is significant at 10% level. When the pure technology gap(cointegrating error εt−1) in the previous year is low, which is equivalent to the aggregatetechnology gap being too low compared to the equilibrium relationship with the return toeducation, GDP next year will be high.

3.4. Results for alternative specifications

I now show results for alternative specifications with several possible human capital factorspecifications in (10). The human capital variables used in the estimation are demographiccharacteristics of the workforce having a potential effect on the aggregate technology gap:college education (share of college graduates in the workforce lagged two years), gender (shareof women in the workforce), and age (share of workers 16-24 years old). I also use the Hoand Jorgenson (1999) labor quality index. Ho and Jorgenson (1999) construct an index of thequality of the labor force in this the United States in the postwar period based on most ofthe characteristics included in the regression. All data are annual 1947-2000. Some of theregressors, like labor quality index, or college education, cover a shorter period (1948-1995),and so the specifications using these variables have fewer observations. To test whether thepure technology gap has a predictive power, I will also introduce into the VECM the logarithmof P-D ratio. Including P-D ratio when testing for predictability is standard in the literatureand can be found in e.g. Bansal, Kiku and Yaron (2009). Finally, I will present results for theIPES aggregate technology gap, constructed based on only information processing portion ofthe equipment and software group.

Results of the VECM estimation are summarized in table (1) for the ES aggregate tech-nology gap, and in table (2) for the IPES aggregate technology gap. The tables demonstratethe short-term adjustment coefficients α. I present a total of six model specifications, withthe baseline specification denoted as (1). In both tables and for most model specifications, thecoefficients on the lagged error term are statistically significant and negative, indicating thespeed of adjustment. Just like in the baseline specification, a positive εt−1, equivalent to thelagged aggregate technology gap being too high compared to the equilibrium relationship witha human capital factor, means that it will fall towards equilibrium next period. The speed ofthis error correction is the higher the closer the coefficient is to negative one. For the ES gap,the fastest error correction occurs when college education is the human capital factor in model

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(3), with the error almost entirely corrected within one period. For the IPES gap, the fastesterror correction occurs for model (1).

Next, short-term adjustment coefficients on the lagged production are negative and sta-tistically significant for most model specifications, indicating the predictive power of the puretechnology gap for the level of production. For example, the short-term adjustment coefficientα on ∆Y in model (3) in table (1) is equal to -3.66 and highly statistically significant at 1%level. Results are stronger for the ES gap, and less pronounced for the IPES gap. One possibleexplanation for this is visible in figure (1). IPES gap, while also indicating a strong positivetrend, is not cointegrated with the return to education, and presumably other human capitalfactors, to the same extent as the ES gap.

These results are confirmed in figure (3), showing impulse responses of the productionlevel to orthogonalized shocks to the aggregate level of the ES gap. Just like in the baselinespecification, the shock first causes the GDP level to decline, and then recover. There is apronounced transitory short-term negative effect on the production level, and a permanentlong-term positive effect for all ES specifications except (6), and these results carry over to theIPES gaps.

Stationarity of the pure technology gaps is of crucial importance to the statistical inferencein this article, therefore I present results of the Dickey-Fuller test for unit root of the cointe-grating vectors (pure technology gaps) in table (5). The pure technology gaps are analyticallydefined in tables (3) and (4), and presented graphically in figure (4). A cursory look at figure(4) suggests a mean-reverting and stationary nature of the gaps. This is confirmed with formaltests. Table (5) demonstrates the test statistic Z(t) from Dickey-Fuller test with the approxi-mate MacKinnon p-value for Z(t), for both the ES and IPES based pure technology gaps. I amable to comfortably reject the null hypothesis of unit root in the pure technology gaps for allmodels except specification (6) for the ES gap. Based on these results, I conclude that the puretechnology gaps are stationary, and the inference about production predictability is correct.This is further confirmed in the results on the stability of the system based on the companionmatrix in figure (2). None of the specifications cause instability of the system, and results forthe IPES gaps are similar (not presented here).

4. Concluding remarks

I demonstrate a new production growth predictor, which unlike those in the existing lit-erature, has an economic meaning, and is linked to the macroeconomic fundamentals. I findevidence that the pure technology gaps predict economic troughs in the short run, and strongeconomic recovery in the longer run.

Future extensions of the work presented in this article may include studying the cross-sectional distribution of the technology gaps across industries or firms, and linking it to theknown asset pricing puzzles.

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Figure 1: This figure presents technical change and technology gaps calculated on an annual basis between 1947and 2000, based on the methodology developed in Hulten (1992), and Cummins, and Violante (2002). The upperfigure shows technical change. The lower figure shows the technology gaps for equipment and software (ES), andinformation processing equipment and software (IPES), as well as the return to education based on Goldin andKatz (1999).

1950 1960 1970 1980 1990−0.1

−0.05

0

0.05

0.1

0.15

0.2

0.25Technical change from prices of durable goods

qt

ES

IPES

1950 1960 1970 1980 19900

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5Aggregate technology gaps versus return to college education

Γt

1950 1960 1970 1980 19900

0.1

0.2R

etu

rn to e

ducation

ES

IPES

red

t

12

Figure 2: This figure presents the roots of the companion matrix of the VECM in equation (9). Presented resultsare for the ES gap and model specifications (1) - (6). The remaining specifications are qualitatively similar andwere not included for expositional purposes.

-1-.5

0.5

1Im

agin

ary

-1 -.5 0 .5 1Real

The VECM specification imposes 3 unit moduli

(1)

-1-.5

0.5

1Im

agin

ary

-1 -.5 0 .5 1Real

The VECM specification imposes 4 unit moduli

(2)

-1-.5

0.5

1Im

agin

ary

-1 -.5 0 .5 1Real

The VECM specification imposes 3 unit moduli

(3)

-1-.5

0.5

1Im

agin

ary

-1 -.5 0 .5 1Real

The VECM specification imposes 2 unit moduli

(6)

-1-.5

0.5

1Im

agin

ary

-1 -.5 0 .5 1Real

The VECM specification imposes 3 unit moduli

(7)

-1-.5

0.5

1Im

agin

ary

-1 -.5 0 .5 1Real

The VECM specification imposes 4 unit moduli

(8)

13

Figure 3: This figure presents the orthogonalized impulse response function from the VECM defined in equation(9) with the number of lags optimally selected using the criteria described in Tsay (1984), Paulsen (1984) andNielsen (2001). The graphs show the response function of the level of GDP to a one standard deviation orthogonalshock to the level of the aggregate technology gap. Presented results are for the ES gap and model specifications(1) - (6). The remaining specifications are qualitatively similar and were not included for expositional purposes.

-.04

-.02

0

.02

0 10 20 30 40

(1)

step

-.04

-.02

0

.02

0 10 20 30 40

(2)

step

-.1

-.05

0

.05

0 10 20 30 40

(3)

step

.024

.026

.028

.03

0 10 20 30 40

(4)

step

-.03

-.02

-.01

0

.01

0 10 20 30 40

(5)

step

-.03

-.02

-.01

0

.01

0 10 20 30 40

(6)

step

14

Figure 4: This figure presents the predicted cointegrated vectors (pure technology gaps) for all model specifica-tions and the ES aggregate technology gap. The pure technology gap is formally defined in equation (14). Theremaining specifications are qualitatively similar and were not included for expositional purposes.

-.15

-.1-.05

0.05

1947 19871967 2007

(1)

-.1-.05

0.05

1947 1967 1987 2007

(2)

-.08

-.06

-.04

-.02

0.02

1947 1967 1987 2007

(3)

-.15

-.1-.05

0.05

1947 1967 1987 2007

(4)

-.15

-.1-.05

0.05

1947 1967 1987 2007

(5)

-.4-.3

-.2-.1

0

1947 1967 1987 2007

(6)

15

Table 1: This table presents results of the estimation of the VECM in equation (9). The aggregate technologygap (Γt) is based on equipment and software (ES) prices. Each column shows short-adjustment coefficients α

in equation (9), where ∆yt =

∆Γt

∆HCt

∆Ct

∆Yt

, and HCt is return to education (ret ), labor quality index (LQIt),

share of college educated workers (Collt), share of young workers (16-24) (Y oungt), or share of women in theworkforce (Woment). Aggregate consumption is Ct and aggregate production is denoted as Yt. Data are annualfrom 1947 to 2000, depending on the specification of the model. AIC is the Akaike Information Criterion.

Short-term adjustment coefficients – ES gaps

(1) (2) (3) (4) (5) (6)

∆Γt -0.36∗∗∗ -0.60∗∗∗ -0.87∗∗∗ -0.08∗ -0.55∗∗∗ -0.04(-2.61) (-2.85) (-2.70) (-1.84) (-3.73) (-0.96)

∆ret 0.02∗∗∗ 0.02∗∗ 0.05∗∗∗ 0.02∗∗∗ 0.00∗∗∗

(4.12) (2.38) (4.42) (3.78) (4.34)∆LQIt 0.12∗∗

(2.45)∆Collt -0.19∗∗

(-2.18)∆Y oungt -0.04

(-1.44)∆Woment 0.00

(0.75)∆Ct -0.05 -0.10 0.00

(-0.51) (-0.74) (0.14)∆Yt -1.00∗ -1.53∗ -3.66∗∗∗ 0.52∗∗∗ -1.31∗ -0.25∗

(-1.66) (-1.70) (-2.70) (2.67) (-1.89) (-1.73)Observations 46 45 30 51 47 47AIC -1137.93 -1454.54 -748.30 -326.68 -1239.86 -1587.23

t statistics in parentheses∗ p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01

16

Table 2: This table presents results of the estimation of the VECM in equation (9) for IPES aggregate technologygap (Γt). The notation is just like in previous table.

Short-term adjustment coefficients – IPES gaps

(1) (2) (3) (4) (5) (6)

∆Γt -0.90∗∗∗ -0.98∗∗∗ -0.23∗ -0.12∗ -0.78∗∗∗ -0.56∗∗∗

(-5.00) (-3.68) (-1.92) (-1.69) (-4.81) (-3.02)∆ret 0.00 -0.01 0.01∗∗∗ 0.00 -0.01∗∗

(0.57) (-1.13) (3.32) (0.88) (-2.10)∆LQIt 0.10∗∗

(2.54)∆Collt -0.01

(-0.33)∆Y oungt 0.02

(0.71)∆Woment 0.02

(1.48)∆Ct 0.01 -0.11 -0.07

(0.09) (-1.01) (-0.95)∆Yt -0.08 0.37 -0.69∗ -0.69∗∗∗ -0.38 0.05

(-0.13) (0.49) (-1.82) (-3.61) (-0.71) (0.11)

N 46 45 30 51 47 47AIC -1095.84 -1415.75 -753.48 -285.35 -1200.43 -1545.85

t statistics in parentheses∗ p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01

17

Table 3: This table presents coefficients β in the cointegrating equation defined in (9) for the ES aggregatetechnology gaps. The cointegrating vector is defined as the pure technology gap in this article. For example, formodel specification (3), the pure technology gap is given by: Γt−1−5.61ret−1−0.45Collt−1 +0.03Yt−1 +0.29 = εt.

Pure technology gaps – ES

(1) (2) (3) (4) (5) (6)

ES gap 1.00 1.00 1.00 1.00 1.00 1.00(.) (.) (.) (.) (.) (.)

Return to education -8.58∗∗∗ -4.72∗∗∗ -5.61∗∗∗ -7.81∗∗∗ -14.00∗∗∗

(-6.41) (-6.59) (-8.32) (-7.18) (-3.23)Labor Quality -0.51∗∗∗

(-3.27)College education -0.45

(-1.28)Young -0.86∗∗∗

(-3.56)Gender 8.72∗∗∗

(2.71)Consumption -0.62 0.03 -4.39∗∗∗

(-1.55) (0.14) (-2.82)GDP 0.13 -0.01 0.03 -0.00 0.02∗ 0.65∗∗∗

(1.56) (-0.23) (1.17) (-0.37) (1.71) (2.45)Constant 0.73 0.70 0.29 0.02 0.59 0.03

(.) (.) (.) (.) (.) (.)

Observations 46 45 30 51 47 47

z statistics in parentheses∗ p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01

18

Table 4: This table presents coefficients β in the cointegrating equation (pure technology gap) defined in (9) forthe IPES aggregate technology gaps.

Pure technology gaps – IPES

(1) (2) (3) (4) (5) (6)

IPES gap 1.00 1.00 1.00 1.00 1.00 1.00(.) (.) (.) (.) (.) (.)

Return to education 2.33∗ 5.57∗∗∗ -4.07 4.28∗∗∗ 4.39∗∗∗

(1.83) (7.42) (-1.52) (2.94) (4.01)Labor Quality -1.12∗∗∗

(-6.81)College education -3.14∗∗

(-2.03)Young -0.47

(-1.46)Gender -3.56∗∗∗

(-4.39)Consumption -0.57 0.22 1.28∗∗∗

(-1.52) (0.82) (3.27)GDP 0.05 -0.10∗ 0.20∗ -0.08∗∗∗ -0.08∗∗∗ -0.23∗∗∗

(0.56) (-1.79) (1.88) (-7.64) (-6.55) (-3.50)Constant -0.06 0.38 -0.05 -0.15 -0.36 0.07

(.) (.) (.) (.) (.) (.)

Observations 46 45 30 51 47 47

z statistics in parentheses∗ p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01

Table 5: This table presents test statistics Z(t) and MacKinnon approximate p-values for Z(t) from the Dickey-Fuller test for unit root of the pure technology gaps for all model specifications and pure technology gaps basedon both ES and IPES.

Model ES IPES

Z(t) p Z(t) p

(1) -3.70 0.00 -3.63 0.01(2) -3.30 0.02 -4.55 0.00(3) -3.66 0.00 -3.02 0.03(4) -2.55 0.10 -3.20 0.02(5) -3.37 0.01 -3.73 0.00(6) -2.39 0.15 -3.48 0.01

19