Download To "Journal of Policy Modeling" Subject: Response to Editorial

To "Journal of Policy Modeling"
Subject: Response to Editorial Board's comments
Dear Editor-in-Chief,
We open by thanking the referees for the insightful comments on our earlier submission, which
provided clear guidance on how we might improve the paper, as well as some positive critiques. We
have implemented most of the reviewer suggestions (text highlighted in grey), and we were pleased
to have the opportunity to expand and improve the paper in line with these suggestions. We detail
below the changes that have been made in line with the reviewer’s comments.
Response to comment # 1:
1) Recast the paper with greater policy discussion and make sure that the hypothesis testing is
policy guided.
R: Again we thank the referees for this thoughtful suggestion, which forced us to develop a further
discussion on the policy implications of our analysis.
Based on this comment, we have re-written the paper in line with recent papers published in the
Journal of Policy Modeling (e.g. Konstantakopoulou and Tsionas, 2014)
In practice, we have added a Section devoted to policy implications. In addition, some policy
guidelines have been reported in the abstract as well as in the Conclusion section.
Response to comment # 2:
2) As we have published in JPM quite a number of papers on related subjects, please cite them in
your bibliography.
R: As suggested, some relevant JPM papers have been cited.
We thank again the referees for the thoughtful suggestions and insights, which have enriched the
manuscript and produced a more balanced and better account of the research. We hope the revised
manuscript is now suitable for publication in The Journal of Policy Modeling.
Needless to say, we are available to make any further changes.
We look forward to your reply.
The authors.
Marcella Lucchetta, Michael Donadelli, Antonio Paradiso
Reference
Konstantakopoulou, I., Tsionas, E. G. (2014) Half a century of empirical evidence of business
cycles in OECD countries, Journal of Policy Modeling, 36, 389-409.
1
Explaining the US-Canada productivity gap: the role of spillover effects and human capital*
Michael Donadelli
Research Center SAFE
Marcella Lucchetta
Ca’Foscari University
Antonio Paradiso
Ca’Foscari University
Abstract
This paper investigates the sources of the US-Canada productivity gap. We rely on a standard
production function in which disembodied technology is assumed to be driven by spillover effects
and human capital, and apply a general-to-specific-approach to identify those variables that best
explain the level of productivity in the two countries. We find that the absence of investment
spillover effects, low innovation rate, and non-recognition of high-skilled workers’ credentials in
Canada represent the main sources of the gap. Overall, our empirical findings suggest that Canada
may close its productivity gap with the US by adopting policies that (i) support the development of
new patents (i.e. R&D investments); (ii) stimulate the diffusion of “high-tech projects”; and (iii)
improve intra-country market competition.
Keywords: Productivity; Solow growth model; spillover effects; human capital
JEL: O4; O51; C22.
_________________________________
* We thank Monica Billio, Guglielmo Maria Caporale, Fulvio Corsi, Gianni De Nicolò, Alessandro Gioffrè, Patrick
Grüning and Lorenzo Prosperi for their helpful suggestions. We also thank the seminar participants at the Brunel
University and Ca’Foscari University of Venice. Authors’ e-mails: [email protected]; [email protected];
[email protected]. All remaining errors are our own responsibility.
2
“Yet Canada does underperform. We are not as productive as we could be. Our potential growth is
slowing. Moreover, this is occurring as the very nature of the global economy, in which we
previously thrived, is under threat. This debate can no longer be avoided."
[Mark J. Carney, Governor of Bank of Canada, 2010]
1. Introduction
It is widely accepted that productivity improves standards of living within a country. Over the longrun, wages, wealth, and per capita GDP are strictly linked to countries’ productivity performance
(Salvatore, 2008). Because of the increasing gap in the level of productivity between the United
States (US) and Canada (CAN) (see Figure 1), both academics and policymakers have raised
concerns about long-term growth prospects in Canada.
Our ultimate goal is to identify a range of possible causal factors of this productivity gap. To
accomplish this, we estimate a standard growth model for both the US and CAN. This approach is
very useful for those economists who are interested in understanding the determinants of growth
and/or productivity in a specific country.1 Of course, this allows them to compare countries’
standard of livings as well as design “alternative” or “ad hoc” policies (Greiner et al., 2005; Cooray
et al., 2013).
Figure 1: Productivity (1950-2011): United States vs. Canada. Notes: Productivity is measured as real GDP at constant
2005 US$ divided by number of employed persons. Red arrows indicate the distance between productivity in the US
and Canada. Source: Penn World Table 8.0.
1
For a detailed analysis on the sources of economic growth in the G7, G20 and World Economy see Jorgenson and Vu
(2013).
3
In the spirit of Greiner (2003), Rao (2010), and Kumar and Pacheco (2012), among others, we
estimate a Solow growth model where the TFP depends on the structure of the “stock of
knowledge”. The literature that focuses on factors explaining the evolution of technology across
countries is relatively large. Alternative structures embody variables associated to research activity,
productivity spillovers, market structure, trade competition, physical infrastructures, level of human
capital, institutions quality.2 An important strand of the endogenous growth literature has
emphasized the importance of spillover effects in TFP growth (Romer, 1986; Lucas, 1988;
Grossman and Helpman, 1991; Greiner, 2003; López-Pueyo and Mancebón, 2010; Roper et al.,
2013). Knowledge spillovers may have a strong impact on productivity as the stock of knowledge
developed by one independent firm (or organization) spreads to, and is used by, other firms.
Consistently with an increasingly globalized world where technology increases continuously, we
assume that trade openness (open) and investment-GDP-ratio (irat) represent adequate factors to
capture the knowledge spillover effect, and thus, to explain the technology progress. In addition, as
suggested by existing studies (Romer, 1990; Aghion and Howitt, 1998), we assume that the human
capital is crucial in understanding the technological progress. Therefore, an “ad hoc” human capital
index (hci) is employed.
Since open and hci may have non-linear effects on growth (Edwards, 1998; Kalaitzidakis et al.,
2001), in addition to a standard linear effect, a non-linear (i.e. quadratic) term for both open and hci
in the specification of the stock of knowledge is included.
All the variables embodied in our Solow growth model (i.e., productivity, physical capital per
worker, openness, human capital index, investment ratio) are non-stationary.3 In practice, we look
for a long-run relationship using an Autoregressive Distributed Lag (ADL) approach. We start the
analysis by specifying a general model where the growth rate of the stock of knowledge is a
function of irat, open, open2, hci and hci2. Both for the US and CAN, the explanatory variables
included in the model (i.e. lagged values of dependent variable and current and lagged values of
independent variables) are then selected according to a general-to-specific approach via the
Autometrics algorithm implemented in PcGive package.
We find that in the US both irat and hci are statistically significant, and hci enters linearly.
Differently, in CAN there is no role for irat. In addition, hci enters nonlinearly. Specifically, an
inverted U-shaped relationship is observed. These findings imply that there is no spillover effect on
physical investment in CAN and that hci has a positive impact on productivity up to a certain level.
We argue that these empirical regularities might be caused by (i) weak investments in applied
innovation as sustained by Rao et al. (2008); (ii) a relatively low degree of market competition in
CAN (Conference Board of Canada (CBC), 2004; Schwab and Sala-i-Martin, 2013); (iii) a low
correlation between the technological progress and the employment of high-skilled workers (Lee,
1999).
The rest of the paper is organized as follows. Section 2 presents the empirical strategy. Section 3
describes data and reports summary statistics. Section 4 reports the main empirical findings. Section
5 discusses policy implications. Section 6 concludes.
2
3
See Isaksson (2007) for a literature review.
Results are available upon request.
4
2. Model and estimation specification
We start from a standard Cobb-Douglas production function with constant returns expressed in per
worker terms. Formally,
𝑦𝑡 = 𝐴𝑡 𝑘𝑡𝛼 ,
(1)
where y is the output per worker, A is the stock of knowledge, k is the per worker capital stock. We
assume that A evolves as follows:
𝐴𝑡 = 𝐴0 𝑒 𝜏𝑡+𝛾∙𝑡 ,
(2)
where A0 is the initial stock of knowledge, t is a time trend, and 𝜏𝑡 takes the following form:
𝜏𝑡 = 𝜙 𝑖𝑟𝑎𝑡𝑡 + 𝜃1 𝑜𝑝𝑒𝑛𝑡 + 𝜃2 𝑜𝑝𝑒𝑛𝑡2 + 𝛿1 ℎ𝑐𝑖𝑡 + 𝛿2 ℎ𝑐𝑖𝑡2 ,
(3)
where irat represents the investment-GDP-ratio, open is the trade openness (i.e. import plus export
divided by GDP), hci is the human capital index based on years of schooling and returns in
education. By combining Eqs. (2) and (3), Eq. (1) can be re-written as follows:
2
2
𝑦𝑡 = 𝐴0 𝑒 [𝜙 𝑖𝑟𝑎𝑡𝑡 +𝜃1 𝑜𝑝𝑒𝑛𝑡 +𝜃2 𝑜𝑝𝑒𝑛𝑡 +𝛿1 ℎ𝑐𝑖𝑡 +𝛿2 ℎ𝑐𝑖𝑡 +𝛾∙𝑡] ∙ 𝑘𝑡𝛼
(4)
𝑙𝑛𝑦𝑡 = 𝑙𝑛𝐴0 + 𝜙 𝑖𝑟𝑎𝑡𝑡 + 𝜃1 𝑜𝑝𝑒𝑛𝑡 + 𝜃2 𝑜𝑝𝑒𝑛𝑡2 + 𝛿1 ℎ𝑐𝑖𝑡 + 𝛿2 ℎ𝑐𝑖𝑡2 + 𝛾 ∙ 𝑡 + 𝛼 𝑙𝑛𝑘𝑡 .
(5)
Eq. (5) can be written in an ADL form adding lags of dependent and independent variables on the
right-hand side: 4
𝑙𝑛𝑦𝑡 = 𝑙𝑛𝐴0 + ∑𝑠𝑙=1 𝜑𝑙 𝐷𝑈𝑙 + 𝜁 ∙ 𝑡 + ∑𝑛𝑗=1 𝜌𝑗 𝑙𝑛𝑦𝑡−𝑗 + ∑𝑛𝑗=0 𝑏𝑗 𝑖𝑟𝑎𝑡𝑡−𝑗 + ∑𝑛𝑗=0 𝑐𝑗 𝑜𝑝𝑒𝑛𝑡−𝑗 +
2
2
+ ∑𝑛𝑗=0 𝑑𝑗 𝑜𝑝𝑒𝑛𝑡−𝑗
+ ∑𝑛𝑗=0 𝑓𝑗 ℎ𝑐𝑖𝑡−𝑗 + ∑𝑛𝑗=0 𝑔𝑗 ℎ𝑐𝑖𝑡−𝑗
+ 𝜖𝑡 ,
(6)
where n-max = 35 and 𝐷𝑈𝑙 (for 𝑙 = 1, … , 𝑠) indicates dummies for picking up eventually large
outliers in residuals. Eq. (6) represents the General Unrestricted Model (GUM), which may contain
irrelevant variables that could generate biased coefficients. Autometrics algorithm is used to reduce
the GUM to a so-called specific model, which is supposed to pass all diagnostic tests and capture
the leading features of the dependent variable in both countries. From the specific model, the longrun solution is obtained by setting 𝑥 = 𝑥𝑡−1 = ⋯ = 𝑥𝑡−𝑛 for each variable (i.e. it is assumed that
all variables converge to a steady-state value).
3. Data statistics and sources
4
The ADL has several desirable statistical properties, such as the precise estimates of long-run parameters and valid tstatistics, even in presence of endogenous explanatory variables. Inder (1993) demonstrates that endogeneity bias
problem is minimal and negligible in ADL.
5
The max number of lags is selected via the BIC criteria.
5
We use annual data for the period 1950-2011. Descriptive statistics of all the variables (for US and
CAN) involved in the estimation are reported in Table 1. All series have been retrieved from the
Penn World Table 8.0. An exception is the investment ratio (i.e. irat), which is taken from “United
Nations Statistics Division – National Accounts Database”.
Table 1: Descriptive statistics: United States and Canada (1950-2011)
Code
𝑙𝑛𝑦
𝑙𝑛𝑘
𝑖𝑟𝑎𝑡
𝑜𝑝𝑒𝑛
𝑜𝑝𝑒𝑛2
ℎ𝑐𝑖
ℎ𝑐𝑖 2
Description
Log of real GDP per
worker
Log of real capital stock
per worker
Gross fixed capital
formation divided by
GDP
Imports plus exports
divided by GDP (trade
openness)
Square of trade openness
Mean
10.96 (US)
10.86 (CAN)
12.12 (US)
11.52 (CAN)
0.21 (US)
0.22 (CAN)
Std. Dev.
0.30 (US)
0.24 (CAN)
0.28 (US)
0.42 (CAN)
0.02 (US)
0.02 (CAN)
Min
10.37 (US)
10.31 (CAN)
11.53 (US)
10.71 (CAN)
0.17 (US)
0.18 (CAN)
Max
11.44 (US)
11.18 (CAN)
12.57 (US)
12.55 (CAN)
0.24 (US)
0.26 (CAN)
0.17 (US)
0.52 (CAN)
0.07 (US)
0.15 (CAN)
0.082 (US)
0.34 (CAN)
0.31 (US)
0.85 (CAN)
0.03 (US)
0.30 (CAN)
0.02 (US)
0.17 (CAN)
0.01 (US)
0.12 (CAN)
0.09 (US)
0.73 (CAN)
Human capital index per
person based on years of
schooling and returns to
education
Square of human capital
index
3.22 (US)
2.92 (CAN)
0.32 (US)
0.27 (CAN)
2.63 (US)
2.46 (CAN)
3.62 (US)
3.39 (CAN)
10.50 (US)
8.60 (CAN)
2.02 (US)
1.60 (CAN)
6.93 (US)
6.05 (CAN)
13.1 (US)
11.49 (CAN)
Notes: Real GDP and capital stock are calculated at constant 2005 US$.
4. Estimation results
OLS estimates of the specific models (for US and CAN) proposed by Autometrics are reported in
Table 2. Notice that our diagnostic tests confirm that both models are correctly specified. BanerjeeDolado-Mestre cointegrating test confirms the existence of the long-run relations; the factor
loadings are negative and statistically significant. Trade openness enters with both a linear and a
quadratic term in the US and CAN, producing a turnaround value of 0.30 (=|3.73⁄(2 ∙ (−6.28))|) and
0.64 (=|1.73⁄(2 ∙ (−1.36))|), respectively; hci enters linearly in the US, and with a quadratic
relationship in CAN with a turnaround value of 3.18 (=|−3.39⁄(2 ∙ (0.53))|). Figures 2 and 3 report
these nonlinear patterns for the US (see Panel (e)) and CAN (see Panels (e) and (f)), respectively,
along with additional estimations results.
Table 2: Estimation results: United States vs. Canada (1950-2011)
Panel (A): US
ln yt   0.733 ln yt 1  0.266 ln yt  2  0.348 ln yt 3  2.379  0.005 t  0.308 ln kt
 SE 
 0.109 
 0.128 
 0.107 
 0.568 
 0.001
 0.127 
 0.890 ln kt 1  0.450 ln kt  2  0.296 iratt  1.449 opent  2.440 opent2
 0.164 
 0.129 
 0.117 
 0.359 
 0.768 
 0.073 hcit  0.022 DU 80 s
 0.047 
 0.006 
ECT : 0.389  ln y  6.119  0.013 t  0.338ln k  0.761irat  3.727 open  6.276 open2  0.187 hci 
 0.079
6
R 2 = 0.999 ŝ = 0.0086 LJB = 1.120éë0.57ùû
LM (1) = 0.000éë0.99ùû LM ( 2) = 0.069éë0.93ùû LM ( 4) = 0.074 éë0.99ùû
BPG = 1.012éë0.45ùû RESET = 0.096éë0.76ùû BDM = -4.93**
Panel (B): CAN
ln yt   0.955 ln yt 1  0.241 ln yt  2  0.344  0.121 ln kt 1  1.165 hcit 1  0.194 hcit  2
 SE 
 0.088
 0.085
 0.308
 0.027 
 0.355
 0.112 
 0.153 hcit21  0.494 opent 1  0.388 opent21  0.050 DU 54  0.051 DU 55
 0.047 
 0.167 
 0.127 
 0.011
 0.012 
 0.045 DU 56  0.081 DU 60
 0.011
 0.010 
ECT : 0.286  ln y 1.202  0.422ln k  1.727 open 1.357 open2  3.394 hci  0.533 hci 2 
 0.063
R = 0.998 ŝ = 0.0095 LJB = 1.453éë0.48ùû
2
LM (1) = 0.866éë0.36ùû LM ( 2) = 0.833éë0.44ùû LM ( 4) = 0.702 éë0.59ùû
BPG = 0.601éë0.83ùû RESET = 0.781éë0.38ùû BDM = -4.50 **
Notes: Estimation method: OLS. ECT stands for Error Correction Term. LJB = Lomnicki-Jarque-Bera test of normality
of the errors; LM(i) = Breusch-Godfrey serial correlation LM test at lag order i; BPG = Breusch-Pagan-Godfrey
heteroskedasticity test; RESET = Ramsey RESET test of functional misspecification; BDM = Banerjee-Dolado-Mestre
test of the long-run relation conducted on the significance of the coefficient y in the ECM. P-values for diagnostic tests
are reported in square brackets. ** denotes statistical significance at 5% in the cointegration test.
Figure 2: Additional estimation results for US productivity. Panel (a) = Fitted versus historical US labour productivity
(lny US); Panel (b) = ECM residuals; Panel (c) = 1-step Chow breakpoint test; Panel (d) = 1-step ahead residuals with
95% confidence interval; Panel (e) =lny US as a quadratic function of open.
7
Figure 3: Additional estimation results for CAN productivity. Panel (a) = Fitted versus historical CAN labour
productivity (lny CAN); Panel (b) = ECM residuals; Panel (c) = 1-step Chow breakpoint test; Panel (d) = 1-step ahead
residuals with 95% confidence interval; Panel (e) = lny CAN as a quadratic function of open; Panel (f) = lny CAN as a
quadratic function of hci.
5. Policy implications
The ADL estimation results of our Solow growth model reveal that the US-Canada productivity gap
relies on investment spillover effects and human capital. In CAN, spillover effects in physical
investments are absent and human capital enters nonlinearly (see Table 2, Panel (B)). The absence
of spillover effects in investments is probably caused by: (i) weak investments in applied innovation
(Rao et al., 2008) as captured by the low share of ICT investment in total non-residential investment
respect to US and the average of G7 countries (see Figure 4);6 (ii) a low degree in market
competition (Conference Board of Canada (CBC), 2004; Schwab and Sala-i-Martin, 2013) that
might reduce firms’ incentive to self-innovate and adopt new technologies by other domestic firms.
A mild innovation rate affects also the employment level of high-skilled workers in CAN, which is
lower than in the US (Lee, 1999). We argue that this gives rise to non-recognition of high-skilled
workers’ credentials. As a result, high-skilled workers in CAN tend to be forced to accept a “nonsophisticated job”. Naturally, the inability of absorb qualified workers might depress both short6
Two additional statistics on the level of R&D investments and expenditures in the US and Canada are noteworthy
(Source: Science and Technology Indicators - OECD). First, the rate of growth of the Gross Domestic Expenditure in
R&D (as percentage of GDP) and Business Enterprise Investment in R&D (as percentage of GDP) in Canada over the
last decade is negative (i.e. -0.24% and -1.08%, respectively). Differently, the United States display positive growth
rates (i.e. 0.76% and 0.33%, respectively). Second, the rate of growth of the percentage of GDP used by the government
to finance investment in R&D in Canada is much lower than in the US (i.e. 0.53 vs. 1.47).
8
and long-run productivity growth. This could explain why hci has an adverse effect on productivity
in CAN after a certain level (see Figure 3, Panel (f)). To close the observed productivity gap, both
fiscal and monetary authorities should focus on policies that (i) support the development of new
patents; (ii) promote the diffusion of high-tech projects; and (iii) improve domestic market
competition. These interventions should also stimulate the investment spillover effect within firms
as well as increase the supply of high-skilled workers. In doing so, CAN might remove part of those
frictions that increase the productivity gap with the US.
Figure 4: Share of ICT investment in total non-residential fixed capital formation. Source: OECD, Factbook 2013.
6. Conclusions
We estimate a standard Solow growth model - where disembodied technology is driven by spillover
and human capital - to identify, via a general-to-specific-approach, the variables explaining the
productivity in CAN and in the US over the last 60 years. We find that in the US both investment
and human capital are statistically significant and exhibit a linear relationship with productivity.
Differently, in CAN investment has no role in explaining productivity and human capital enters
nonlinearly (i.e. inverted U-shaped relationship).
These results imply that there are no spillover effects in physical investment across firms in CAN
and that human capital has a positive impact on productivity up to a certain level. We argue that
these findings might be caused by (i) a lack of investments in applied innovation, as sustained by
Rao et al. (2008); (ii) a weak intra-country market competition (Conference Board of Canada
(CBC), 2004; Schwab and Sala-i-Martin, 2013); (iii) a low correlation between changes in
technology and employment of high-skilled workers (Lee, 1999). Accordingly, CAN should adopt
policies that (i) support the development of new patents; (ii) encourage the diffusion of high-tech
projects; and (iii) improve internal market competition.
9
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