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Empirical Economics

Erschienen in:

01.08.2015

A stochastic frontier model with structural breaks in efficiency and technology

verfasst von: Guangjie Li

Erschienen in: Empirical Economics | Ausgabe 1/2015

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Abstract

We have developed a stochastic frontier model with appropriate priors to estimate the locations and number of structural breaks for both production efficiency and technology, which experience different regime changes. We assume different units could have unknown common break dates. Although panel data with large cross-sectional size can help identify the break locations, it could render posterior simulation very inefficient. Hence, care must be taken to avoid such problems. We apply our method to study the world production over the period of 1960–2007 and find that the data support structural breaks in technology rather than in efficiency. For most countries under study, the most important source of growth is capital accumulation. The technology adopted by different countries shows signs of convergence. Changes of technology usually happen after economic crises to compensate for negative capital growth. Alternative modelling approach and priors are used for robustness check.

Vorheriger Artikel A matrix exponential spatial specification approach to panel data models

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We assume both the intercept and slopes could be time varying.

Note that the mode of \(\exp (\gamma )\) is \(\exp (\mu -\exp (\phi ))\), which can approach 0 when \(\mu \) and \(\phi \) are adjusted appropriately. Hence, log normal density can mimic the downward-sloping shape of half normal and exponential densities. However, log normal density does not have to be downward sloping with the peak close to 0.

That is, the posterior probabilities of the true number of regimes and the true break point locations will tend to one asymptotically with the increase of cross-sectional sample size. We rely on artificial data simulations to check our model. It appears that both the number of in-sample break points and their locations can be well identified with fairly large \(N\) (above 100). Such results are available upon request from the author.

If the change point takes place at period \(T\), it implies there is only one regime with no breaks inside the sample.

Note that \(Pr(S_T=1,S_{T-1}=1,\dots ,S_1=1)=\frac{1}{T}\ne 0\).

If the parameter values could change at every period, the choice of prior implies \(Pr(S_{1}=1,\dots ,S_{t}=t)=\frac{1}{T^{t-1}}\).

See Fig. 3. When \(D=16\), the number of sample periods in our application such effect is very obvious. However, when \(D=64\), the prior accumulation becomes very small.

It is gamma distribution for their case.

Inefficiency factor is the inverse of the relative numerical efficiency measure of Geweke (1992). It implies how many simulated draws are required to obtain one effective draw for posterior inference. The closer the IF is to 1, the more the efficient is the posterior simulation.

These numbers are from prior simulation.

The results are available upon request from the author.

Note that in general the posterior point estimates are between the prior and the maximum likelihood estimates.

See Table 4.

We have collected the data of 109 countries with all the variables available over 1960–2007 from Penn World Table, based on which the per capita income ranking is calculated.

Note that we average our data every 3 years. It is possible to convert the growth numbers into annual terms. For example, the overall average growth of the two groups is 13 %. The annual average growth would be 4.16 % (i.e. \(\root 3 \of {1.13}-1\)).

The break point location is estimated similarly by the frequency of a particular point being a break in the simulation.

Note that the efficiency estimates are relative to different production frontiers for the two groups of economies.

Cyprus is the only exception in our sample with technical progress higher than capital growth.

We would like to thank an anonymous referee for suggesting us estimate this model.

The exact estimation results are available upon request from the author.

We have also found that technology regimes in both models are not sensitive to \(D_\mathrm{max}\).

For example, if both period 1 and 2 belong to regime 1, i.e.\(S^a_1=S^a_2=1\), then \(\zeta _{i1}=(x_{i1},x_{i2})'.\)

Since the posterior estimate of \(\sigma ^2_\epsilon \) is consistent with the data separated into two regimes, replacing the posterior draw of \(\sigma ^2_\epsilon \) with its true value does not affect asymptotic analysis.

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Titel: A stochastic frontier model with structural breaks in efficiency and technology
verfasst von: Guangjie Li
Publikationsdatum: 01.08.2015
Verlag: Springer Berlin Heidelberg
Erschienen in: Empirical Economics / Ausgabe 1/2015
Print ISSN: 0377-7332
Elektronische ISSN: 1435-8921
DOI: https://doi.org/10.1007/s00181-014-0852-4

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