# Something structural break dating happens. sorry, does

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Here, a fully functional. This theory illuminates a. As described before, when the direction. In addition, the assumptions required for the fully.

The relaxation obtained here may be particularly useful for applications to. The paper is organized as follows. The estimator for the break date is introduced in Section 2, along with. The asymptotic properties developed in this section are inv estigated.

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Section 5 concludes. Proofs of the main results. In this paper, a simple functional data model allowing for a mean function break is considered.

It is assumed. Assumption 2. It is assumed that. Processes satisfying Assumption 2. Howev er, in many examples S is itself a function space, and the e valuation of. The main task when dealing with model 2. The proposed estimator is. Noting that 2. Details are given next. Theorem 2. If model 2. An interesting consequence of Theorems 2.

For example, if, under the condi. The proofs of Theorems 2.

The New Econometrics of Structural Change: Dating Breaks in U.S. Labor Productivity Bruce E. Hansen A pplied time series analysis and forecasting is based on the assumption of stationarity-the constancy of parameters like the mean, variance and trend over time. But what happens if the parameters change? A particularly.

The proof of Theorem 2. Observe that the limiting distribution in Theo. Computing the norm as required for the. Truncation of the sum under the square-root on the right-hand side giv es then approximations to the theoretical.

For practical purposes population eigenvalues have to be estimated from data. In the remainder of this section, the fully functional results put forward in this paper are compared to.

This procedure utilizes the. In the presence of a mean break as. K t, t 0 is the empirical counterpart of the population covariance kernel. In particular, eigen.

K t, t 0 conver ge to those of K t, t 0 under suitable assumptions that include the.

For - archotelzeeland.com case, the counterparts of Theorem. Remark 4. Let b 1 and b 2 be two orthogonal B -spline functions see the upper. This gives.

time. We say that a structural break has occurred if at least one of these parameters has changed at some date-the breakdate-in the sample period. While it may seem unlikely that a structural break could be immediate and might seem more reason-able to allow a structural change to take a period of time to take effect, we most. Structural break tests A single break in mean with a known breakpoint. For linear regression models, the Chow test is often used to test for a single break in mean at a known time period K for K ? [1,T]. This test assesses whether the coefficients in a regression model are the same for periods [1,2, ,K] and [K + 1, ,T]. Other forms of structural breaks. We extend the before?during?and?after method with an empirical cartel dating procedure, which infers structural breaks of unknown number and dates that mark the actual begin and end dates of the collusive effects. Empirical findings in the European Sodium Chlorate cartel corroborate our theoretical results.

Suppose simulations are run. Hence, the fPCA based method is expected to have. The use of the fully functional approach to dating break points is therefore especially advantageous in. The next section follo ws up on these.

Following the set-up in Aue et al.

# Structural break dating

Without loss of generality, the initial mean curv e. Independent curves were then generated according to. The fast setting describes functional data for which the eigenv alues of the covariance operator decay quickly.

T o explore the effect of temporal dependence on the break point estimators, second-order functional au. To ensure stationarity of the time. The positive constant c can be used to adjust the break impact. The prominent break case should be more. Both the fully functional procedure and its fPCA counterpart were applied.

The fPCA based method was. All results are based on runs. These processes are then. The results for the prominent break case are summarized in T able 3.

Combining the prominent break. The table shows that here. Measures of. Both methods struggle to identify breaks away from the. Results are similar.

Here, the situation becomes more advantageous for the proposed method.

easily illustrated in the context of detecting and dating structural breaks in the mean function: if the function representing the mean break is orthogonal to the basis used for dimension reduction, there cannot be a con-sistent test or estimator for the break date in that basis. This point will be further illustrated by theoreticalFile Size: KB. The New Econometrics of Structural Change: Dating Breaks in U.S. Labour Productivity by Bruce E. Hansen. Published in volume 15, issue 4, pages of Journal of Economic Perspectives, Fall , Abstract: We have seen the emergence of three major innovations in the econometrics of structural ch. Jul 26, In this article, a new empirical screen for detecting cartels is developed. It can also be used to date the beginning of known conspiracies, which is often difficult in practice. Structural breaks that are induced by cartels in the data-generating process of industry prices are detected by testing reduced-form price equations for structural archotelzeeland.com: Carsten J. Crede.

Overall, it can be seen that the fully functional method. The results for the moderate break case are summarized in T able 3. Here differences in performance. In general, the fully functional procedure is associated with smaller variation as evidenced in the. Overall, the proposed method performs better than the fPCA counterpart in.

Figure 3. It is nicely seen that there is less. Here the proposed procedure is. While the latter situation is by design preferable for the fully. T able 3. The case with slower decay of the eigen values. Results in T able 3.

The proposed method looks in general more favorable in the heavy-tail case than in the time series case of the. The performance is. The proposed method is seen to work for. In this section, the proposed methodology is applied to one-minute log-returns of Microsoft stock and con. During each day, stock price values were recorded in one-minute intervals. Rescaling intra-day time to the interval [01] by a linear transformation, let. The scaled cumulative. The results. The resulting curves are plotted in Figure 4.

An application of fPCA to. This date. Figure 4. A natural follow-up question is if the eigenfunctions associated with smaller sample eigenv alues suffer. These deviations might be interpreted as the risk incurred when trusting the log. Risk was assessed in the following way.

First the. Howeverthe break date selection is highly variable for the fPCA methodology. The results for d varying be. T able 4. The plot clearly shows. The situation is. The plot of the estimated break curve also reveals that the different risk. In this paper, a fully functional methodology was introduced to date mean curve breaks for functional data.

The assumptions are notably weaker. In a comprehensive simulation study it is shown that the. It is shown in an application to intra-day log-return data of Microsoft stock that such a. The Microsoft example is by no means a special case, as other stocks such. These results are not reported here, but are available upon request. It is hoped. More generally, this work provides an.

The latter difference is a. The proofs will be carried out via a sequence of lemmas that rely on the following observations. Notice that. Lemma 6. If the assumptions of Theorem 2. In the following, it will be shown that the deterministic component whose asymptotics is established in 6.

Therefore, an application of the Cauchy-Schwarz inequality yields that. T aking the maximum on right- and left-hand side leads to.

### Structural Change using a test for restrictions - in Stata (part 2/5)

By Lemma A. Similar arguments also imply that. Combining 6. It may be proven analogously using D 3. One may obtain similarly that. This establishes the limits of the drift terms. For the second term on the right-hand side of 6. T aken together, 6. It remains to be show that the other four terms on the concluding lines of 6. T o this end, by the Cauchy-Schwarz inequality. Ergodic Theorem in Hilbert spaces. Furthermore, again by the triangle inequality. Equations 6.

Additionally, in a similar f ashion to 6. Proof of Theor em 2. It follows that. Using similar arguments as those used to establish 6. The preceding two equations imply the lemma. It follows similarly that. An applica. In the following it is shown that.

According 6. It follows from the Cauchy-Schwarz inequality that. This combined with 6. A parallel argument shows that. It follows. The same argu. Therefore, 6. To see that the other terms. The same argument. Additionally, by the Cauch y-Schwarz and triangle inequalities. The remaining terms coming from 6.

The proof of the theorem follows from the lemmas in this subsection as the proof of. The proof is obtained from an application of the Continuous Mapping Theorem and. A T echnical Lemmas. Lemma A. Corrollary 1 to Proposition 4 of Berkes et al. According to Theorem 1. It then follows from the. Furthermore, again using Theorem 1.

This and A. Antoniadis, A. Sapatinas A functional wavelet-kernel approach for time series.

W avelet methods for continuous time prediction using Hilbert-v alued. Journal of Multivariate Analysis 87- Aston, J. Kirch a. Detecting and estimating changes in dependent functional data.

Kirch b. Evaluating stationarity via change-point alternati ves with applications to. FMRI data. The Annals of Applied Statistics 6- Aue, A. On the prediction of stationary functional time series. Journal of the American Statistical Association- Kokoszka Estimation of a change-point in the mean function of.

Journal of Multivariate Analysis- Dependent functional linear models with applica. Statistica Sinica 24- Structural breaks in time series. Journal of Time Series Analysis 341- Berkes, I. Detecting changes in the mean of functional. Schauer Split invariance principles for stationary processes. The Annals. On the asymptotic normality of kernel estimators of the long run. Technical Report. Besse, P. Stephenson Autoregressi ve forecasting of some functional climatic varia. Scandinavian Journal of Statistics 27- Bosq, D.

Linear Processes in Function Spaces. Springer-V erlag, New Y ork. Ferraty, F. Weakly dependent functional data. The Annals of Statistics 38. Kokoszka, P. Reeder Estimation of the mean of of functional time series and a two. Rice Testing stationarity of functional time series.

Journal of Econo. Extensions of some classical methods in change point analysis. Test 23. Jirak, M. On weak invariance principles for sums of dependent random functionals. Probability Letters 83- Figure 2. Middle: the functional observations. The proposed method is in blue, the fPCA method in red. The x -axis. Cartel detection in procurement markets. Managerial and Decision Economics, 35 6- International Pasta Organisation. Annual report Italian Competition Authority.

Kim, J. Comparison of structural change tests in linear regression models. Korean Journal of Applied Statistics, 24 6- Kuan, C. The generalized fluctuation test: A unifying view. Econometric Reviews, 14 2- Leisch, F. Monitoring structural changes with the generalized fluctuation test.

Econometric Theory, 16 6- Mueller, W. The bakers of Washington cartel: Twenty-five years later. Review of Industrial Organization, 7 1 Nieberding, J. Estimating overcharges in antitrust cases using a reduced-form approach: Methods and issues. Journal of Applied Economics, 9 2- Notaro, G. Methods for quantifying cartel damages: The pasta cartel in Italy. Journal of Competition Law and Economics, 10 1 Nyblom, J.

Testing for the constancy of parameters over time. Journal of the American Statistical Association, 84- Price hysteresis after antitrust enforcement: Evidence from Spanish food markets. Journal of Competition Law and Economics, 10 1- Perron, P. Dealing with structural breaks. Patterson Eds. Ploberger, W. Econometrica, 60 2- A new test for structural stability in the linear regression model. Journal of Econometrics, 40 2- Porter, R. A study of cartel stability: The joint executive committee, - The Bell Journal of Economics, 14 2- Detecting collusion.

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Nov 12, illustrated in the context of detecting and dating structural breaks in the mean function: if the function repre- senting the mean break is orthogonal to the basis used for dimension reduction. structural changes but is otherwise (trend) stationary within regimes speci ?ed by the break dates. Also, most tests trying to assess whether structural change is present will reject the null hypothesis of no structural change when the process has a unit root component but with constant model parameters. estat sbknown, break(tm(m1)) Wald test for a structural break: Known break date Number of obs = Sample: m1 - m12 Break date: m1 Ho: No structural break chi2(2) = Prob > chi2 = Exogenous variables: anopheles Coefficients included in test: anopheles _cons.

Journal of Applied Econometrics, 20 1 Zivot, E. Further evidence on the great crash, the oil-price shock, and the unit-root hypothesis. Download references. The views expressed in this article represent the personal opinion of the author, and do not represent positions of the Bundeskartellamt.

Any remaining errors are my own. Correspondence to Carsten J. Reprints and Permissions. Rev Ind Organ 54, - Download citation. Published : 26 July Issue Date : 15 May Search SpringerLink Search. Abstract In this article, a new empirical screen for detecting cartels is developed.

## A Structural Break Cartel Screen for Dating and Detecting Collusion

Immediate online access to all issues from Subscription will auto renew annually. Taxes to be calculated in checkout. Notes 1. The following results are robust to reasonable alternative specifications of the tested periods. References Abrantes-Metz, R. Google Scholar Abrantes-Metz, R. Article Google Scholar Andreou, E. Google Scholar Andrews, D.

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