2. The Data
- Purely applied (PA) papers: the title refers to an application, with no reference to an econometric method, technique or issue. We have found such papers.
- Mainly applied (MA) papers: the title refers both to an econometric method, technique or issue and an application, and the focus seems to be on the latter (e.g., “Does exchange-rate volatility affect import flows in G-7 countries? Evidence from cointegration models”). We have found such papers.
- Purely methodological (PM) papers: the title refers to an econometric method, technique or issue, with no reference at all to an application. We have found such papers.
- Mainly methodological (MM) papers: the title refers both to an econometric method, technique or issue and an application, and the focus seems on the first (e.g., “Robust cointegration testing in the presence of weak trends, with an application to the human origin of global warming”). We have found such papers.
3. The Bass Diffusion Model
3.1. Bass Discrete Time Model
3.2. Boswijk and Franses Model
- The assumption that is uncorrelated is at odds with the empirical evidence that deviations of the observed adoption path with respect to the ideal equilibrium path are persistent.
- The assumption that is homoskedastic is disputable since, at the beginning and at the end of the diffusion process, when is expected to be close to zero, the variance of is likely to be much smaller than around the peak; related to this, simulating (13) with an homoskedastic and Gaussian error is likely to produce negative values of in the initial and final phases of the diffusion.
3.3. Boswijk et al. Multivariate Model
4.1. Analysis of the Reduced Form—Comparing Bass, BF, BFF
4.2. Analysis of the Structural Form
5. Conclusions and Suggestions for Further Research
Data Availability Statement
Conflicts of Interest
Appendix A. Bass vs. Autoregressive Models
- If , , and , then and the model collapses into a standard stationary AR(1) with unconditional expectation m.
- If , and , then so that initially the system behaves like an explosive AR(1) with a positive drift . When , then so that the system locally behaves like a random walk with drift. When , then so that the system starts adjusting. An illustrative example, based on the estimated parameters for the methodological index, is given in Figure A1.
Appendix B. Sensitivity to ω
Many thanks for the provision of the initial Web of Science data to Evi Sachini, Antonis Kardasis and Penny Nikolaidou of the National Documentation Centre/N.H.R.F. based in Athens, Greece.
Around the same time Google Scholar (GS) reported more than 50,000 citations for the same 10 papers. We opted for WoS instead of GS because, to avoid double counting, the analysis carried on in this paper is based on the citing papers instead of the citations, and working out the citing papers from GS is not easy. Admittedly, one drawback with using WoS instead of GS is that books cannot be considered; we think however that this would not substantially change the picture. In fact, according to GS, the book Johansen (1995) would rank 4th in terms of citations, the book Juselius (2006) would rank 6th, and adding both books the total citations count would be about 15% higher; however, since many papers citing one of the books will cite also some of the older papers, the impact of the books on the citing papers is likely to be way less than 10%.
Among the “super-citing” papers, there are also 14 papers with six citations and 53 papers with five citations. We remark that 40 of the 6457 papers (i.e., 0.62%) are authored or coauthored by SJ and/or KJ: given the small share we did not correct for self-citations.
An alternative way of measuring the influence of a paper could be based on counting the authors instead of the papers. We could then consider the number of authors citing KJ or SJ in each quarter, or preferably the number of “new authors”, i.e., the number of authors citing KJ or SJ for the first time in each quarter, who never cited them before (this would avoid double counting, and would be a more precise measure of “contagion”). We do not explore this alternative in the present paper, leaving it for future research.
Classifying an econometric paper as “methodological” or “applied” is clearly arbitrary to some extent. A general discussion, although related to the ‘delineation of scientific areas’ may be found in Zitt (2006); he states that fields may be defined at various levels (e.g., institutional setting of academic actors; shared topics and possibly shared journals; shared terminology; close connections of collaboration or citation, etc.) and concludes that “… natural borders, generally speaking, are an illusion” (Zitt 2006, p. 6). In fact, a more scientific-bibliometric related methodological approach could be the analysis based on networks, as for instance in Vieira and Teixeira (2010), although this is outside the scope of the present paper.
When unsure regarding the screening, we proceeded following Katsaliaki and Mustafee (2011, p. 1434): “The two authors independently and critically reviewed all the abstracts of the (…) papers and read the full text when necessary.” Notice that an alternative classification scheme could be based on the publishing journal since some journals are more oriented toward applications, while others are more methodological. As discussed below, we believe that our approach provides a more accurate measure.
The title of the MA paper by Baillie and Bollerslev is "Common stochastic trends in a system of exchange rates", while the title of the PM paper by Gilbert is "Economic theory and econometric models"
Actually, at the individual level, the term “innovator” associated to a constant hazard is somewhat misleading, and not exactly a synonym of “early adopter”. In fact, an individual with constant hazard rate might well be a laggard, especially if his/her individual hazard rate is low. The parameter p is hardly interpretable in epidemiology, where the notion of “innovator” is essentially limited to the “patient zero”.
We remark that that the solution is not unique. The formulae in (15) are the ones giving positive values of m, p and q with our estimated ’s.
Maintaining the assumption that is i.i.d. normal, an alternative estimation strategy could be based on Non Linear Least Squares (NLLS). Estimates of m, p and q would be based on the following:
The advantage of NLLS is that it provides directly the estimates of the parameters of interest (m, p and q) and the corresponding standard error, without having to resort to the delta method. The disadvantage is that convergence of the numerical optimization routines is sometimes not easy: this is partly due to the strong collinearity, and partly to the fact that the optimization problem has two solutions. In the following, we opt for OLS and the delta method.
We decided to adopt slightly different symbols with respect to BF. In particular our has opposite sign with respect to theirs.
A diagonal corresponds to . As already observed, in this case ML would not correspond to equation by equation OLS, due to the correlation of the error terms. One might maximize the likelihood either by iterated SUR as illustrated in Section 3.2, or equivalently using the algorithm illustrated here.
Minor modifications are needed if instead we assume heteroskedasticity of the type postulated in Boswijk et al. (2009), where , with ( is assumed to be known) and . Notice that, premultiplying (30), left and right, by , using the properties of the operator, one obtains either the following:
The first equation allows to estimate by GLS when and are known, while the second allows to estimate by GLS when and are known. A "switching" iterative algorithm similar to Hansen (2003) is therefore possible also in this case. Of course, linear restrictions on or are easily dealt with also in this case.
We also considered different values of k, from 4 to 20, and the results remain essentially unchanged. Regarding the number of degrees of freedom, as illustrated in Appendix A, the standard Bass model can be seen as an AR(1) with state dependent parameters, while the BF and BFF models can be seen as AR(2): therefore we considered heuristically degrees of freedom in the Q test, with for the standard Bass model and for BF and BFF models.
Actually, the slope in the auxiliary regression is negative in some cases, which is exactly the opposite of BF intuition. We think that the result might reflect the neglected autocorrelation rather than heteroskedasticity: the ample swings in the residuals clearly visible in Figure 3 are misinterpreted by the test as heteroskedasticity.
Alternative initializations are possible: this point is further discussed in footnote 25.
For simplicity, we do not “orthogonalize” the shocks by assuming some direction for the simultaneous relationship: we believe that this is justified in this case, given the modest correlation between the residuals (16.1%). As a robustness check we also tried to orthogonalize in either direction, and to apply the “ordering invariant” method proposed in Pesaran and Shin (1998) but, as expected given the low correlation, the results are essentially unchanged. For a discussion of the simultaneous correlation, see also Appendix B.
It is important to remark that, given the nonlinear dynamics implied by (29), the impulse responses will change according to the initial conditions. We also considered alternative initializations, starting in different points of the diffusion path: we observed that when the impulse is given further ahead along the diffusion path, the shape of the responses changes in a rather intuitive way: the peak of the cumulative IRs occurs earlier, and the intensity becomes weaker. This can be explained in the light of the discussion presented in Appendix A: in the initial stages of the process, when both and are close to zero and much lower than and , respectively, the processes behave as explosive AR(2), and therefore, the shocks are initially amplified; however, as and grow, the processes become less and less explosive, until eventually they start adjusting and the cumulative impact of the shock is driven down to zero. However, some characteristics of the cumulative IRs do not change, even when the initial conditions are modified: the cumulative cross impact seems to be relatively stronger from the methodological to the applied literature than vice versa.
The variance-covariance matrix for is then obtained as the following:
Similarly, when , the 92 MM papers are entirely treated as methodological, whereas, when , only half of them (46) are treated as methodological, while the other half is treated as applied. Given the small number of MM papers, their influence on the indices is negligible, and that is why in our discussion we emphasize the role of the MA papers.
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|Order (Time)||Paper||Citations (WoS)||New Citations (WoS)|
|2||Johansen and Juselius (1990)||2567||1060|
|5||Johansen and Juselius (1992)||477||90|
|8||Johansen and Juselius (1994)||196||32|
|9||Johansen et al. (2000)||167||60|
|10||Hendry and Juselius (2001)||112||56|
|2||APPLIED ECONOMICS LETTERS||254||89.2%||10.8%|
|6||JOURNAL OF ECONOMETRICS||154||2.9%||97.1%|
|7||J. OF INTERNATIONAL MONEY & FINANCE||135||95.7%||4.3%|
|8||JOURNAL OF POLICY MODELING||121||96.4%||3.7%|
|10||JOURNAL OF MACROECONOMICS||96||92.0%||8.0%|
|11||OXFORD BULLETIN OF ECON. & STAT.||92||46.5%||53.5%|
|14||JOURNAL OF FUTURES MARKETS||70||96.1%||3.9%|
|15||JOURNAL OF APPLIED ECONOMETRICS||68||54.7%||45.3%|
|18||JOURNAL OF BANKING & FINANCE||58||94.8%||5.2%|
|19||JOURNAL OF BUSINESS & ECON. STAT.||55||38.4%||61.6%|
|20||JOURNAL OF FORECASTING||52||51.4%||48.6%|
|Model (18)||Model (27)||Model (29)|
|Model (18)||Model (27)||Model (29)|
|Model (12)||Model (19)||Model (28)|
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