Samira Demaria
email: demaria@gredeg.cnrs.fr

Dominique Dufour

Moïse Louisy-Louis
email: mlouisylouis@monaco.edu

Philippe Luu
email: luu@unice.fr

AN EXPLORATORY STUDY OF THE EXPOSURE DRAFT OF IAS 19 DUE PROCESS

Keywords: IAS 19, Due process, net interest approach Second Draft

In July 2006, the IASB launched a comprehensive review of IAS 19, the main pronouncement relating to the accounting for defined pension obligations. As part of its systematic due process, the Board called for accounting practitioners to express their views on IAS 19. As such, the Discussion Paper (or DP) released in March 2008 generated 150 comment letters and the Exposure Draft (or ED) published in April 2010 produced 227 comment letters in response.

Adopting a method of content analysis, this paper concentrates on the comment letters relating to the ED stage and seeks to pinpoint at issues which are of great concern to practitioners. This study has permitted to i) identify the most controversial questions for respondents, ii) highlight relationships between respondents' characteristics and comments, and iii) focus on issues and elements for further research. Because pensions are a sensitive issue, the results of this study could be of interest to the accounting profession and the public at large.

INTRODUCTION

For the past 40 years, pension accounting has been a major construction site. Most recently, the International Accounting Standard Board (IASB) has focused on reformatting IAS 19, Employee Benefits, the main pronouncement relating to the accounting for defined pension obligations. In April 2010, the global standard-setter released an Exposure Draft (ED) which clearly indicated the upcoming predominance of the fair value approach at the expense of the controversial corridor method.

The due process procedure was initiated in July 2006 when the Board added the project to its agenda and ended in June 2011 when the revised standard was released. The procedure lasted about five years and generated a sizeable number of comment letters from various interest groups as pension accounting represents a strategic issue for both private and public entities.

In response to the ED published in April 2010, the IASB received 227 comment letters, whose worldwide signatories are representatives of corporations, national standard-setters, academics, or interest groups. The document invited respondents to present their viewpoint in relation to 17 questions that could be grouped according to three main themes: recognition (especially immediate vs. deferred recognition), presentation (in particular in relation to gains and losses) and disclosure. In this paper, rather than addressing all questions raised by the standard-setter, we decided to focus on 5 strategic questions which deal with important accounting issues. In particular, the recognition of defined benefit cost components and the newly introduced notion of net interest approach.

We identified questions 1, 2, 3, 4, and 5 as being the most interesting ones as they addressed important conceptual and technical issues 1 . Furthermore, a statistical analysis isolated question 5 as the question for which answers had exhibited the greatest amount of dispersion.

Question 5, which indeed was a series of three questions, asked respondents to approve a common discount rate to be applied to both the defined benefit obligation 2 and plan assets as a means to determine a net finance cost component (disclosed in the face of the income statement). In contrast to other questions, a majority of respondents disagreed with the Board on this issue (only 22% of respondents were explicitly in favour of the net interest approach).

1 Please refer to section 2.2, "Content analysis" for further details 2 Please refer to section 1.1 "IAS 19 and Pension Accounting" for further details

The financial implications linked to the choice of the discount rate are tremendous for reporting entities since it impacts the amount of finance cost reported in current earnings and the net defined liability (asset) position disclosed on the statement of financial position. This has potential repercussions on EPS (and thus on the share price performance of public firms) and on leverage (and thus on the cost of debt financing). Consequently, question 5 provided the foundations for an ambitious debate between accounting practitioners, both in terms of quantity and quality.

In such a context, the paper aims at describing the key issues presented in the exposure draft and at analyzing feedback received by the Board from members of the financial community.

Moreover, the paper builds on an exploratory study of respondents' viewpoint(s) with the underlying ambition of identifying i) some correlation between respondents' characteristics and opinion(s) expressed and ii) to which extent these opinions have influenced or been taken into account in the revised version of IAS 19. The contributions of this paper are twofold.

First, the study enhances prior literature on pension accounting by analyzing IAS 19 due process, a topic which has so far attracted little interest from the research community. Second, this paper adds to the professional knowledge, by underlining the viewpoint of various stakeholders on a strategic issue that represents the accounting for defined benefit obligations. Indeed, the accounting for defined benefit obligations impacts both earnings and financial position; reporting entities (esp. large public firms) are therefore very sensitive to accounting changes that can affect their ability to raise equity or debt financing. In addition to reporting entities, standard-setters, accounting professionals or the public at large also represent an audience that is likely to be interested or concerned about the evolution of IAS 19.

The paper is structured into five sections described as follows: section 1 sets the research context, section 2 details the research design, section 3 reports the study's findings, section 4 discusses the results, and lastly section 5 draws concluding remarks and provides direction for further research.

RESEARCH CONTEXT

The IASB develops international standards through a public consultative process which seeks the involvement of members of the financial community, both individuals and organizations, from around the world. All standard or amendment to existing standard must go through this procedure. The standard-setting due process is detailed in the "IASB Due Process Handbook" [START_REF] Iasb | Due Process Handbook IASB[END_REF]. For the purpose of this paper, we have focused on the due process implemented in relation to the revision of IAS 19, Employee Benefits, which started in 2006 andended in 2011. In this section, we first examine IAS 19 and the issues raised by the accounting for pensions (1.1), second we discuss the 2006-2011 IAS 19 due process, and we consider the ED published by the Board (1.2), and finally we review the literature (1.3)

IAS 19 AND PENSION ACCOUNTING

IAS 19 deals with the methods of recognition and measurement of employee benefits. These are defined by the IASB as "all forms of consideration given by an entity for services rendered by employees" (IAS 19 § 7). These forms of consideration include short-term employee benefits (which need to be settled within twelve months), post-employment benefits (which are payable after the completion of employment), and post-employment benefit plans (which are formal or informal arrangements designed to provide benefits to one or more employees). Such plans include obviously i) defined contribution plans under which an employer "pays fixed contribution into a separate entity (a fund) and will have no legal or constructive obligation to pay further contributions if the fund does not hold sufficient assets to pay all employee benefits," and ii) defined benefit plans which are succinctly viewed as "plans other than defined contributions" (IASB, 2010). As a result, the accounting for defined contribution plans is rather straightforward. In contrast, the accounting for defined benefit plans requires more sophisticated methodologies and the formulation of a complex set of long-term estimations and/or assumptions. The main reason for this has to do with the fact that an employer promises to make pension payments (according to a specific contractual arrangement or formula) to employees after their retirement. In consequence, the employer retains both the investment and actuarial risks in managing its pension obligations (investment risk arises when return on plan assets may not be sufficient to meet expected benefits and actuarial risk surfaces when benefits fall short of expected needs).

The main conceptual changes to IAS 19 envisioned by the IASB since 2006 include three crucial elements. These are the elimination of the corridor method (which would be replaced by the immediate recognition of actuarial gains and losses in earnings), the disaggregation of the defined benefit cost into three components (i.e. service cost, finance cost and remeasurement), and improved disclosure requirements.

IAS 19'S DUE PROCESS

IAS 19, Employee Benefits, prescribes the accounting and disclosure for the treatment of employee benefits. The first version of the standard dates back to 1983 and since has been amended on several occasions. Its most recent version has been released in June 2011. The last update constitutes an ambitious reengineering of the standard. The revised standard significantly modified the recognition, presentation and disclosure requirements. This new standard must "ensure that financial statement provide investors and other users a clear picture of an entity's commitments resulting from defined benefit plans" [START_REF] Iasb | Due Process Handbook IASB[END_REF]. One of the main issues that the standard-setter has sought to address has to do with the fact that IAS 19 suffers from a lack of comparability and transparency (esp. because of the multiplication of recognition options). The objective of the 2006-2011 due process was to provide more transparency and to simplify the accounting for employee benefits.

The FASB, the IASB's counterpart responsible for the design of US GAAP, was invited to contribute to the design of IAS 19 (as part of the Memorandum of understanding (or MoU) between the two Boards). This agreement is a major step toward the convergence of the world's two major accounting frameworks, US GAAP and IFRS.

The below timeline illustrates the various successive events that the IASB has implemented since 2006 and until the revised standard becomes effective in January 2013.

Exhibit 1: IAS 19 calendar (IASB)

Source: IASB, Project Summary and Feedback Statement, 2011 The Exposure Draft (ED/2010/3) was published in April 2010 and participants were invited to submit comments for a period of five months. The April 2010 ED contained 17 questions structured around the following themes: recognition, disaggregation, presentation, settlements and curtailments, disclosures and other issues. In response, the board received 227 comment letters from a wide variety of individuals and organizations. At last, a revised version of IAS 19 was published in June 2011, which officialised the elimination of deferred recognition (the so-called corridor method) and the advent of the fair value approach (with immediate recognition of service cost and finance cost in earnings, though remeasurement items are accounted for in the other comprehensive income section of the balance sheet). In addition to these important conceptual topics, IAS 19 has significantly improved disclosure requirements and the standard has earned, at the European level, the support of the European Financial Reporting Advisory Group (or EFRAG), a prominent organization which influences the accounting landscape in Europe, on the grounds that the standard meets the technical criteria stipulated by 1606/2002 rules.

LITERATURE REVIEW

To our knowledge there is no research paper specifically devoted to the study of the due process of IAS 19. Therefore, to precisely establish the scope and aim of this paper, we have relied on a selective set of research which addresses i) the due process procedure and ii) pension accounting.

As noted by [START_REF] Georgiou | The IASB standard-setting process: participation and perceptions of financial statement users[END_REF] there is a dearth of research into users' participation and influence, into the standard setting process. In order to identify the key issues raised by the due process, we consider the work of Seamann and Cortese et Irvine. [START_REF] Seamann | Positions taken in the FASB and IASB due process on accounting for employee stock options[END_REF] examines and contrasts over time the due process model implemented by the Financial Accounting Standard Board (FASB) (in 1993) andIASB (in 2001) in the context of the accounting for employee stock options. The author shows that though participants in these processes are different, the arguments advanced are very similar (measurement reliability, decision usefulness, conceptual foundation and economic and public policy consequences).

Cortese et Irvine ( 2010) study the standard-setting process in relation to IFRS 6, Exploration for and evaluation of mineral resources. For the authors, the IASB presents an ambitious project to modernize the recognition of mineral resources (especially by eliminating the option of full cost and promoting the mandatory of successful effort method) but in fact, the revised standard changed nothing. To Cortese and Irvine, the Board preferred to maintain the status quo mainly because of the influence exercised by powerful industrial entities and interest groups. [START_REF] Larson | An examination of comment letters to the IASC: special purpose entities Research in Accounting Regulation[END_REF] analyses the content of 29 comment letters on the issue of accounting rules for Special Purpose Entities (SPE). Larson conducts a descriptive analysis of letters, by analysing answers functions to native country and national GAAP. He shows that supporters came from countries with similar rules as respondents against came from countries without rules for consolidation of SPE. Otherwise majority of public accounting firms, standard-setters and professional accountancy body support the effort to create a better standard. [START_REF] Yen | A content analysis of the comprehensive income exposure draft comment letters[END_REF] analyses the content of comment letters written in response to the Comprehensive Income ED published by the FASB. They show that the standard-setter seems to have modified the norm between the ED and the final standard. Indeed arguments advanced by respondents may have influenced the procedure.

The study of [START_REF] Georgiou | The IASB standard-setting process: participation and perceptions of financial statement users[END_REF], based on questionnaire survey on the perceptions and the participation in the IASB standard-setting process, shows that answering to an ED is a lobby action. The sample is constituted by UK investment management firms. Findings put in light that the participation to the due process is not as low as suggested by the IASB and as a consequence many firms give up participation on their own, choosing to participate through a representative body such as an association. [START_REF] Koh | What drives firms' decisions to lobby and determinants of their lobbying positions: Evidence from firms' comment letter submissions during the FASB's stock option expensing proposal in 2004[END_REF] examines what drives firms to lobby during the FASB due process dealing with the accounting for stock option programs. The study of the determinants to lobby is based on the positive accounting theory approach. The author finds that political visibility, composition and independence of the board and mimicry influence the decision to lobby during the due process.

While there is a lot of research that addresses the accounting of defined benefit obligation, we retained research and study that precisely describe the main conceptual and technical issues and which assess the evolution of the accounting treatment through time. [START_REF] Amen | Simulation-based comparison of existent IAS 19 accounting options[END_REF] compares the equity approach and the corridor approach. The author designs a simulation to detect systematic differences in long-term pure accounting effects. The study of a sample of German firms shows principally that the cumulated actuarial gains and losses related to the DBO are non-symmetrical. These results lead the author to conclude that this phenomenon represents "a stochastic process of several actuarial losses that stops randomly with one actuarial gain." [START_REF] Glaum | Pension accounting and research: a review[END_REF] provides an empirical review of the research on pension accounting. His work reveals the issues raised from the fact that the standard gives preparers a certain degree of discretion in electing methods and assumptions, which weakens transparency and comparability between reporting entities. In particular, Glaum discusses the corridor method and the disclosure requirements imposed by IAS 19 (especially whether or not certain pension items bypass current earnings). [START_REF] Beechy | The many challenges of pension accounting[END_REF] discusses most of the major issues that standard-setters must confront in developing new approaches to financial reporting for pensions. For Beechy, key issues relate to how to report the impact of changes in assumptions, how to recognize pension costs on the balance sheet and income statement, and how to reconcile the differences between accountants' and actuaries' approaches to pensions.

The paper considers the European pension accounting context and proposes some elements to improve current practices and rules. [START_REF] Napier | The logic of pension accounting[END_REF] clearly identifies one of the major strategic issues that pension accounting has been for standard-setters for over 30 years. "Standardsetters have made compromises to be able to develop standards that would be acceptable to preparers and users, but compromises have a tendency to return and haunt the standardsetting bodies" [START_REF] Napier | The logic of pension accounting[END_REF]. Moreover, the author reviews in detail the evolution of the various approaches and conceptual foundations that have marked the accounting for pension obligation. Lastly, we consider papers that are devoted to a precise issue or topic within pension accounting, such as the recognition of actuarial gains or losses and national or local application of the standard. Papers of [START_REF] Morais | Actuarial gains and losses: the choice of the accounting method Accounting in[END_REF] and [START_REF] Fasshauer | Adoption of IAS 19 by Europe's premier listed companies: Corridor approach versus full recognition: Summary of an ACCA research monograph[END_REF], based on a sample of European entities, and [START_REF] Demaria | Comptabilisation des écarts actuariels, mise en perspective des pratiques françaises[END_REF], based on a sample of French entities, show that a majority of firms adopt the corridor method to recognize actuarial gap. This is an interesting point knowing that the ED proposed the withdrawal of this method.

To sum up, it appears that there is no evidence suggesting that prior literature has sought to address in parallel the IASB's international due process and practitioners' viewpoint regarding the strategic issue that represents pension accounting. As such, this paper seeks to address this gap.

RESEARCH DESIGN

This section presents the research design; first we describe the empirical data and methods (2.1), then we discuss the content analysis (2.2).

EMPIRICAL DATA AND METHODS

Empirical data is based on comment letters received by the IASB during the due process.

These documents are available free of charge on the IASB website. All comment letters are published in English. The exposure draft generated 227 comment letters.

Most of the respondents are firms or members of the financial community (banks, accounting professionals, etc...) and are based in the USA or the UK, however nearly all industries and countries are represented (tables 1 and 2). We distinguish between respondents which are involved in the preparation of financial statement from those considered as users of the financial information. Such a contrast helps to enhance the understanding of the motives of respondents to the ED, since it is unlikely that these two groups have share the same expectations about financial statements. According to [START_REF] Mensah | Transparency in financial statements: a conceptual framework from a user perspective[END_REF] and [START_REF] Gray | Perceptions and misperceptions regarding the unqualified auditor's report by financial statement preparers, users, and auditors[END_REF] preparers of financial statement are firms' CFO and standard-setters, and users are bankers3 , analysts, and professional and non professional investors. Half of the preparers (47.6%) disagree with the Board's proposal whereas 21.4% of them agree. The approbation is slightly higher in the users group (26.3%) in contrast to 36.8% of the users who reject the proposal.

The next step in our analysis was aimed at uncovering common themes in the 227 comment letters. Furthermore, we perform a content analysis.

CONTENT ANALYSIS

We used an Optical Character Recognition (OCR) to obtain the textual primary data. We cut off each comment letter in text unit that corresponded to a question asked by the IASB.

We examined causal statements to better understand comment letters. This method was used in many previous research: Aerts (2005), [START_REF] Larson | An examination of comment letters to the IASC: special purpose entities Research in Accounting Regulation[END_REF], [START_REF] Hooghiemstra | Letters to the shaeholders: A content analysis comparison of letter written by CEOs in the United States and Japan[END_REF]. Our study can be viewed as a qualitative experiment based on a content analysis through which we focus on the meaning of the semantics used by respondents.

In a first stage, each comment letter was fully analyzed, namely we isolated the 17 questions in independent text units. The ED groups questions of different nature, such as recognition, presentation and disclosure. We have decided to focus only on the recognition theme which is the most important issue for preparers and users of financial statement. In particular, the recognition of defined benefit cost components and the newly introduced notion of net interest approach are the recurring themes throughout these questions, which are listed below:

Question 1: The exposure draft proposes that entities should recognize all changes in the present value of the defined benefit obligation and in the fair value of plan assets when they occur. Do you agree? Why or why not?

Question 2: Should entities recognize unvested past service cost when the related plan amendment occurs? Why or why not?

Question 3: Should entities disaggregate defined benefit cost into three components: service cost, finance cost and remeasurements? Why or why not?

Question 4: Should the service cost component exclude changes in the defined benefit obligation resulting from changes in demographic assumptions? Why or why not?

Question 5: The exposure draft proposes that the finance cost component should comprise net interest on the net defined benefit liability (asset) determined by applying the discount rate specified in paragraph 78 to the net defined benefit liability (asset). As a consequence, it eliminates from IAS 19 the requirement to present an expected return on plan assets in profit or loss. Should net interest on the net defined benefit liability (asset) be determined by applying the discount rate specified in paragraph 78 to the net defined benefit liability (asset)?

Why or why not? If not, how would you define the finance cost component and why?

Afterwards, we identified and coded responses (as yes, no, partial, none) and then we analyzed the rationale put forward by respondents. This segmentation is consistent with prior research [START_REF] Yen | A content analysis of the comprehensive income exposure draft comment letters[END_REF]. The next table summarizes our findings: Amongst the questions relating to recognition, question 5 has drawn our attention. It is the most controversial question: in contrast to other questions, most of the respondents who voice their opinion disagreed fully or partially with the IASB's proposal. The participation is also higher for question 5: respondents expressed their views in 193 comment letters (which is the highest frequency even when including the 17 questions). In addition, question 5 generated by far the smallest number of None's for a single question (15% in contrast to 22.9% to 32.6% for questions 1 through 4). In other words, those who chose to answer to question 5 had a firm opinion which they needed to stand for. Comments linked to question 5 were first analyzed with Nvivo 8. Content analysis requires breaking or rearranging the text into meaningful text units and coding these text units according to well-defined rules. As Hooghiemstra (2010) defines them: a causal statement is "one or more coherent sentences or phrases in which an outcome is connected to a cause or reason."

Based on this preliminary step, a coding grid was constructed as shown below: We implemented a systematic coding procedure. First, we independently did a read through each comment letters to identify common themes. Second, we established a common coding grid reflecting the various themes previously identified. Third, for each letter, two different researchers coded the comments using the pre-determined grid and results were cross-checked afterwards. Note that we assigned a series of categorical variables to each comment letter.

Table 5 displays a definition for each of the variables used in the study.

RESULTS

We use contingency tables to display our findings. The frequencies distributions are produced between the approbation to question 5 and each of the following variables: country of respondent, industry and rationales. Table 6 displays the relationship between the respondents' nationality and their views regarding the IASB's proposal to adopt the net interest approach and a single discount rate for defined benefit obligation and plan assets.

The Yes answers are mainly those of respondents from the UK (24% of the approvals), USA (12%), Canada (12%) and Germany (12%). Countries with the highest percentages of No's are USA (10.1% of the total number of comment letters), UK (7.5%), Australia (4.8%), and Japan (3.5%). Overall, it appears that respondents from the UK and USA massively expressed their views (roughly a third of the total number of common letters) but their views were fairly split between the Yes, No and None.

One striking element is that even though the FASB has collaborated with the IASB on this project, it appears that a majority of US respondents disagreed with the Board on question 5.

When referring back to table 6, we noticed that 23 US respondents out of 43 voted No. We could cautiously try to explain this phenomenon by advancing that there is more resistance on the US side to adopt the revised IAS 19 and especially the net interest approach (this could be as well interpreted as a persistent rift between US GAAP and IFRS despite the planned global convergence toward IFRS).

Table 7 (shown on the next page) highlights the following facts about respondents' views regarding the IASB's proposal and the industry they are affiliated to:

Within the Yes group, 40% of respondents are affiliated to the Accounting/Actuary/Audit sector, 12% from the public sector and 30% are firms or firm association

Those with most negative views are firms (15.4% of the No's), the Accounting/Actuary/Audit sector (20.2%) and the Bank/Insurance sector (12.8%).

The Accounting/Actuary/Audit sector accounts for the largest representation of the partial approvals with 46.2% of the mitigated answers. Interestingly enough, the accounting sector is fairly mixed, 39 respondents out of 66 have given their disapproval or only a partial approval. This could mean that the accounting profession

is not yet convinced by the IASB's proposal. If this is the case, this is not very reassuring for non-experts.

Half of the None approbations relates to the public sector.

Even the views of standard-setters are mixed. Out of the 14 standard-setters, 3 approve the board's proposal, 4 give a partial approbation, 4 disagree and 3 didn't voice their opinion. 8 compares approbation and the rationale(s) most frequently advanced by respondents to justify the reason for their approbation. For example, it appears that amongst those who approved question 5, 46% (or 23 letters out of the 50 Yes letters) mentioned consistency as the reason (or one of the reasons) for this choice. Columns do not add up to 100% because respondents may cite several criteria at once, for instance approbation could be decided because the revised standard brings more simplicity, consistency and comparability.

The discount rate is the most cited issue: more than half of the comment letters mentioned that point (54.6%). The inherent difference between DBO and plan assets (38.8%), the need of a fundamental review (25.1%), the investment strategy (20.3%), the simplicity (19.4%) and the consistency (16.3%) are also fairly recurrent. Comparability between entities (8.8%) and divergence from US GAAP (6.2%) are less frequent observations. There is a clear relation between the topical issues raised and approbation:

Respondents justify their approbation to question 5 by referring mainly to simplicity (42%), consistency (46%) and comparability (24%).

Respondents explain their opposition with the following rationale(s): Rate (91.3%), DBO (76%), and Strategy (36.5%) (recall that percentages do not add up to 100% since respondents may have use more than one reason to justify their approbation).

Only this group has mentioned the tax issue and there is no mention of Comparability, Useful info, or Change.

Respondents with None approbations tend to give no justification of their viewpoint.

Overall, we note that the IASB's proposal was supported because of its simplicity, consistency and comparability. Partial and negative approbation were mostly linked to Rate, DBO and Strategy. In most instances, respondents urged the Board to spearhead a fundamental review of the accounting for pension before adopting a revised IAS 19.

To sum up, when considering our findings from tables 6, 7 and 8, it appears that a majority of the respondents which have agreed with the Board on question 5 appraise the revised IAS 19 for its simplicity, consistency and comparability (this links with the Board's underlying goal of removing the subjectivity given to reporting companies in estimating the expected discount rate applied to plan assets). In contrast, the cons have explained their disagreement based on the fact that i) defined benefit obligations and plan assets are different and ii) a discount rate based on market yields of high quality corporate bonds cannot be applied to investment portfolios that contain various asset classes. Therefore, it appears that the two sides here advocate two contrasting themes: practical expediency for the pros and conceptual flaw for the cons.

DISCUSSION

In its June 2011 press release, the Board indicates that it had "received broad support for the overall objectives of improving transparency, comparability and understandability by eliminating the options for recognition and presentation of changes in defined benefit plans and improving disclosures about those plans" (IASB, 2011, p. 14). However, when discussing question 5 (which mainly addressed whether or not the standard-setter needed to adopt the net interest approach), the Board appears to be vague and to silence the amount of feedback and disagreement (or request for a "fundamental review") raised by question 5.

Table 3 has clearly identified question 5 (or more precisely the concept of the net interest approach) as an issue on which the financial community disagrees with the Board. More than half of the comment letters pointed the discount rate as the reason for disapproval (54.6%).

The inherent difference between DBO and plan assets represented 38.8%, the need of a fundamental review accounted for another 25.1%.

Nevertheless, the Board confirmed the ED proposal on the grounds that "the net interest approach better represents the economics of the net defined benefit asset or liability" (IASB, 2011, p. 16). The main technical implication is that the revision indeed addresses a peculiar issue with the former version: "under the previous approach, a deficit could result in net finance income if the expected return on plan assets exceeded the interest cost on the defined benefit obligation" (IASB, 2011, p. 10). Yet, in order to eliminate the amount of subjectivity involved in determining the expected rate of return on plan assets, the Board adopted a "practical expedient" (CL2, CL30, CL37, CL38, CL57 ....) and ignored the list of valid counter-arguments advanced by respondents. In particular, the cons explained that:

Applying a common discount rate to both the defined benefit obligation and plan assets the standard would in substance take away entities' ability to design a competitive and effective investment strategy. This view is echoed in the following citation: "even if the assets and obligations are presented on a net basis in the statement of financial position, they not do share the same characteristics nor are they measured on the same basis; entities do not invest in assets only to be rewarded by the time value of money."

(CL26)

By applying a discount rate based on market yields of high quality corporate bond rates, the standard eliminates the superior return expected from mixed investment portfolios that contain assets riskier than debt securities and thus ignores the fact that defined benefit obligations and plan assets are inherently different and therefore managed accordingly. In addition, respondents have on several instances indicated that such a discount rate would likely force asset managers to shift their investment strategy and favour lower-return assets (such as government bonds). Ultimately, it appears that the main beneficiaries of pension plan, employees, are the ones who will be worst off. For example, this view is shared by the Vice President in Finance of a large US mobile phone company: "requiring the use of a discount rate that is based on the current yield for high quality corporate bonds seems inconsistent with nature of the investment portfolios that we see in current benefit plan disclosures." (CL188)

Adopting the ED proposal without spearheading a fundamental review of IAS 19 would cause disruption and potentially produce misleading information for financial statement users. For instance, the Belgian Accounting Standards Board has formally called for such a review and further guidance regarding the determination of the discount rate: "given the fact that the current ED is an answer to short-term improvement needs of the Standard, we would have expected that the Board also included more guidance on the determination of the related discount rate." (CL1)

In contrast to what the Board advances, respondents' viewpoints regarding whether to adopt the net interest approach were more diverse than described by the Board in its feedback statement. This, however, does not mean that the Board has completely ignored these viewpoints in the due process. Question 5 was certainly the most controversial question since the financial implications relating to the discount rate are presumably the most significant, whether on earnings or financial position. A study seeking to quantify the financial impact of the revised IAS 19 on the earnings and/or financial position of European reporting entities (for example members of the Euro Stoxx 600 index over a two to three year study period) would bring more substance and depth to this debate.

In addition, on its corporate website, when describing the due process, the IASB employs an educative tone and explains that the development of an IFRS is carried out during IASB meetings, when the IASB considers the comments received on the exposure draft. After having resolved issues arising from the exposure draft, the IASB considers whether it should expose its revised proposals for public comment, for example by publishing a second exposure draft. Lastly, after an IFRS is issued, the staff and the IASB members hold regular meetings with interested parties, including other standard-setting bodies, to help understand unanticipated issues related to the practical implementation and potential impact of its proposals (IFRS.org, 2010).

Finally, when considering the various counter-arguments brought by respondents, we have the overall impression that the Board overlooked these valid viewpoints (sometimes made by experienced and long-established local or global practitioners) and rushed in adopting the net interest approach. In fact, it seems that the Board chose to deal with a recurring and painful issue (i.e. subjectivity in determining the discount rate) at the expense of a long-due conceptual debate. So we can conclude that arguments advanced during the due process have little influence on the final standard.

CONCLUSION

In conclusion, we have analyzed the 227 comment letters received for the IASB in relation to the Exposure Draft stage of the IAS 19 due process. We have sought to put in evidence the fact that respondents have mostly approved the Board's proposal relating to the recognition of defined benefit cost components. However, question 5, which deals with the net interest approach and the determination of the discount rate to be applied to both the defined benefit obligation and plan assets, is the exception. There is no consensus on that very controversial question.

To our knowledge, this paper is the first fully devoted to the study of the IAS 19 Exposure Draft stage. So it contributes to the prior research by analyzing all the comment letters on pension accounting. This paper also contributes to enrich the accounting perspective by articulating the viewpoint of practitioners on defined benefit obligations.

Finally, the validity of this paper (both internal and external) is constrained by the study's parameters that we have chosen to implement. We have considered a subset of the six-step IASB's due process. As such, the scope of our analysis remains limited indeed to the ED. It is conceivable that our findings would be amended in the case we had included in our study the comment letters received by the Board during the third stage (relating to the DP). Again, we have chosen to focus on the ED stage because i) it represents the "public consultative" part of the due process (and presumably the most visible and transparent part of the due process), and ii) it allows a richer debate about underlying conceptual issues. However, a study covering both the discussion paper and the exposure draft stages would provide a better longitudinal view of the IASB's international due process and could be an interesting element for further research.

Additionally, it appears that a study seeking to quantify the financial impacts of the revamped IAS 19 on a sample of public companies would allow the financial community to gauge the magnitude of the proposed changes. For instance, a simulation, in which variations in discount rates on the DBO and returns on plan assets are compared to changes in the finance cost (on the P&L) and in the net defined liability (asset) (on the B/S), could provide substance and depth to the pension accounting debate. As such, the work of [START_REF] Amen | Simulation-based comparison of existent IAS 19 accounting options[END_REF], targeting German entities, offer an interesting perspective for further research.

Table 1 : Analysis of ED respondents by country

 1

	COUNTRY	N	% COUNTRY	N %
	UK	45	19.8 PAKISTAN	2 0.9
	USA	43	18.9 ISRAEL	2 0.9
	INTERNATIONAL/EU	15	6.6 SOUTH AFRICA	2 0.9
	JAPAN	14	6.2 IRELAND	2 0.9
	AUSTRALIA	12	5.3 NEW ZEALAND	2 0.9
	GERMANY	12	5.3 NORWAY	2 0.9
	CANADA	11	4.8 BRAZIL	1 0.4
	SWITZERLAND	9	4.0 KENYA	1 0.4
	NETHERLANDS	9	4.0 MALAYSIA	1 0.4
	SWEDEN	7	3.1 RUSSIA	1 0.4
	INDIA	6	2.6 ZAMBIA	1 0.4
	FRANCE	6	2.6 TRINIDAD & TO	1 0.4
	CHINA/HK	6	2.6 FINLAND	1 0.4
	MEXICO	4	1.8 LUXEMBOURG	1 0.4
	BELGIUM	3	1.3 ITALY	1 0.4
	AUSTRIA	2	0.9 KOREA	1 0.4
			CHILI	1 0.4
			TOTAL	227 100
	Note: In the remainder of the paper, countries with less than 3 frequencies are gathered in a new category called
	OTHER COUNTRIES.

Table 2 : Analysis of ED respondents by industry

 2 (Note that the industry classification is based on Industry Classification Benchmark (ICB), which is used by Dow Jones and FTSE in various indexes. We retained the ICB's main industry categories but further dividing the Financials sector into Financials which include banks and insurers, Accounting which are accounting professionals, and we grouped together auditors and actuaries. We added the Standard-setter category which did not exist in the ICB classification) Note: In the remainder of the paper, the detailed sector is not used.

	Type of
	respondent	Sector	Detailed Sector	N	%
	PREPARERS TOTAL PREPARERS		189	83.3
		FIRM OR FIRM ASSOCIATION	SUB TOTAL	80	35.2
			INDUSTRIALS	14	6.2
			FIRM ASSOCIATION	13	5.7
			CONSUMER SERVICES		4.0
			OIL & GAS		4.0
			UTILITIES		3.5
			CONSUMER GOODS		3.1
			HEALTH CARE		2.6
			BASIC MATERIALS		2.2
			TELECOMMUNICATION		2.2
			CHEMICALS		0.4
			CUSTOMER SERVICES		0.4
			ENERGY		0.4
			TECHNOLOGY		0.4
		ACCOUNTING/ACTUARY/AUDIT SUB TOTAL	66	29.1
			ACCOUNTING	41	18.1
			ACTUARY	19	8.4
			AUDIT		2.6
		BANK/INSURANCE	SUB TOTAL	29	12.8
			BANK	25	11.0
			INSURANCE		1.8
		STANDARD-SETTER	n/a	14	6.2
	USERS	TOTAL USERS		38	16.7
		PUBLIC	SUB TOTAL	18	7.9
			PUBLIC FINANCE		4.0
			PUBLIC		2.6
			UNIVERSITY		0.9
			ACADEMIC		0.4
		ANALYST/CONSULTANT	SUB TOTAL	13	5.7
			CONSULTANT		3.1
			ANALYST		1.3
			PERSON		1.3
		PENSION	n/a		3.1
	TOTAL
	LETTERS			227	100.0

Table 3 : Approbation to questions relating to the recognition of defined benefit costs

 3

	Approbation	Question 1 N %	Question 2 N %	Question 3 N %	Question 4 N %	Question 5 N %
	1.Yes	117	51.5 110	48.5 108	47.6 131	57.7	50	22.0
	2.Partial	35	15.4	13	5.7	33	14.5	13	5.7	39	17.2
	3.No	23	10.1	30	13.2	20	8.8	12	5.3	104	45.8
	4.None	52	22.9	74	32.6	66	29.1	71	31.3	34	15.0
	With opinion 175		153		161		156		193
	Total 227

Table 4 : Abridged coding grid

 4

	Coding item		Verbatim examples
		Yes	CL10 (Q5): we support the BOARD's proposal
	Approbation to IASB's proposals	No Partial	CL5 (Q5): We do not agree with the proposed amendment CL26 (Q5): We are strongly opposed to this proposal CL51 (Q5): We do not support the IASB's view CL88 (Q5): We agree (…) But (..) CL105 (Q5): We thus have some concerns with the proposals, but for
			practicability reasons we would agree.
		None	CL11 (Q3): We have no particular views on this question. CL210 (Q2): No comment.
			CL11: The proposal would seem to be consistent with the overall
			structure of accounting for pension costs and would provide
			consistency across entities.
	Question 5 topics	Consistency	CL12: The application of the discount rate specified in paragraph 78 to the net defined benefit liability (asset) will promote consistency in the application of the standard.
			CL210: We are in favor of this proposal as it eliminates the
			inconsistency and subjectivity associated with arriving at the
			expected return on assets

Table 5 : Variable definitions

 5

	Variable name	Variable description	Variable categories
				australia/nz; canada; france;
				germany; india/pakistan;
	Country	Nationality of the author/company	international/europe; japan;
				netherlands; sweden/finland;
				switzerland; uk; usa; other
				accounting; actuary/audit; bas.
	Industry	Industry of the author/company	mat./ind.; consumer g/s; energy/oil/gas/; financials; public;
				standard setter; other
		Q1	Approbation to question 1	yes; no; partial; none
	Approbation	Q2	Approbation to question 2	yes; no; partial; none
	to IASB's	Q3	Approbation to question 3	yes; no; partial; none
	proposals	Q4	Approbation to question 4	yes; no; partial; none
		Q5	Approbation to question 5	yes; no; partial; none
		Consistency	Consistency	1 (mentioned); 0 (not mentioned)
		Review	Fundamental Review	1 (mentioned); 0 (not mentioned)
		Simplicity	Simplicity	1 (mentioned); 0 (not mentioned)
		DBO	DBO and Plan assets are inherently different	1 (mentioned); 0 (not mentioned)
			Discount rate based on market yields
		Rate	of high quality corporate bonds is not appropriate for investment portfolio	1 (mentioned); 0 (not mentioned)
			made of mixed assets (esp. equity)
	Question 5 topics	Comparability	Comparability	1 (mentioned); 0 (not mentioned)
		Useful_info	Meaningful / Useful information	1 (mentioned); 0 (not mentioned)
		Strategy	Take away ability to design/influence the corporate investment strategy	1 (mentioned); 0 (not mentioned)
		Tax	Ignore tax/fees issues relating to plan assets	1 (mentioned); 0 (not mentioned)
		Change	Firms may change their investment policy	1 (mentioned); 0 (not mentioned)
		GAAP	Method fails to consider convergence with GAAP practices	1 (mentioned); 0 (not mentioned)

Table 6 : Cross tabulations between question 5 approbation and country

 6

			1.Yes			2.Partial			3.No			4.None			ALL CL
		N	col %	row %	N	col %	row %	N	col %	row %	N	col %	row %	N	col %	row %
	BELGIUM	0	0	0	1	2.6	33.3	1	1.0	33.3	1	2.9	33.3	3	1.3	100.0
	INTERNATIONAL/EU	3	6.0	20.0	3	7.7	20.0	4	3.8	26.7	5	14.7	33.3	15	6.6	100.0
	MEXICO	0	0	0	0	0	0	2	1.9	50.0	2	5.9	50.0	4	1.8	100.0
	USA	6	12.0	14.0	5	12.8	11.6	23	22.1	53.5	9	26.5	20.9	43	18.9	100.0
	SWEDEN	0	0	0	0	0	0	5	4.8	71.4	2	5.9	28.6	7	3.1	100.0
	CHINA/HK	0	0	0	0	0	0	4	3.8	66.7	2	5.9	33.3	6	2.6	100.0
	NETHERLANDS	0	0	0	0	0	0	6	5.8	66.7	3	8.8	33.3	9	4.0	100.0
	FRANCE	0	0	0	2	5.1	33.3	4	3.8	66.7	0	0	0	6	2.6	100.0
	JAPAN	1	2.0	7.1	4	10.3	28.6	8	7.7	57.1	1	2.9	7.1	14	6.2	100.0
	AUSTRALIA	1	2.0	8.3	2	5.1	16.7	9	8.7	75.0	0	0	0	12	5.3	100.0
	INDIA	2	4.0	33.3	1	2.6	16.7	3	2.9	50.0	0	0	0	6	2.6	100.0
	UK	12	24.0	26.7	10	25.6	22.2	17	16.3	37.8	6	17.6	13.3	45	19.8	100.0
	SWITZERLAND	2	4.0	22.2	1	2.6	11.1	6	5.8	66.7	0	0	0	9	4.0	100.0
	GERMANY	6	12.0	50.0	2	5.1	16.7	3	2.9	25.0	1	2.9	8.3	12	5.3	100.0
	CANADA	6	12.0	54.5	0	0	0	5	4.8	45.5	0	0	0	11	4.8	100.0
	OTHER	11	22.0	44.0	8	20.5	32.0	4	3.8	16.0	2	5.9	8.0	25	11.0	100.0
	ALL LETTERS	50	100.0	22.0	39	100.0	17.2	104	100.0	45.8	34	100.0	15.0	227	100.0	100.0

Table 7 : Cross tabulations between question 5 approbation and industry

 7

			1.Yes			2.Partial			3.No			4.None			ALL CL
			col			col			col			col			col
		N	%	row % N	%	row %	N	%	row % N	%	row %	N	%	row %
	ACC./ACTUARY/AUDIT	20	40.0	30.3	18	46.2	27.3	21	20.2	31.8	7	20.6	10.6	66	29.1	100.0
	BANK/INSURANCE	2	4.0	6.9	8	20.5	27.6	15	14.4	51.7	4	11.8	13.8	29	12.8	100.0
	FIRM OR ASSOCIATION	15	30.0	18.8	5	12.8	6.3	50	48.1	62.5	10	29.4	12.5	80	35.2	100.0
	STANDARD-SETTER	3	6.0	21.4	4	10.3	28.6	4	3.8	28.6	3	8.8	21.4	14	6.2	100.0
	TOTAL PREPARERS	40	80.0	21.2	35	89.7	18.5	90	86.5	47.6	24	70.6	12.7	189	83.3	100.0
	ANALYST/CONSULTANT	3	6.0	23.1	2	5.1	15.4	8	7.7	61.5	0	0	0	13	5.7	100.0
	PENSION	1	2.0	14.3	1	2.6	14.3	4	3.8	57.1	1	2.9	14.3	7	3.1	100.0
	PUBLIC	6	12.0	33.3	1	2.6	5.6	2	1.9	11.1	9	26.5	50.0	18	7.9	100.0
	TOTAL USERS	10	20.0	26.3	4	10.3	10.5	14	13.5	36.8	10	29.4	26.3	38	16.7	100.0
	ALL RESPONDENTS	50	100.0	22.0	39	100.0	17.2	104	100.0	45.8	34	100.0	15.0	227	100.0	100.0

Table 8 : Cross tabulation between topics mentioned and approbation for question 5

 8

			1.Yes			2.Partial			3.No		4.None		ALL CL
		N	%*	row % N	%*	row %	N	%*	row %	N	N	%**	row %
	Tax	0	0.0	0.0	0	0.0	0.0	1	1.0	100.0	0	1	0.4	100.0
	Gaap	1	2.0	7.1	1	2.6	7.1	12	11.5	85.7	0		6.2	100.0
	Strategy	0	0.0	0.0	8	20.5	17.4	38	36.5	82.6	0		20.3	100.0
	DBO	0	0.0	0.0	9	23.1	10.2	79	76.0	89.8	0		38.8	100.0
	Rate	1	2.0	0.8	28	71.8	22.6	95	91.3	76.6	0	124	54.6	100.0
	Review	10	20.0	17.5	19	48.7	33.3	28	26.9	49.1	0		25.1	100.0
	Simplicity	21	42.0	47.7	20	51.3	45.5	3	2.9	6.8	0		19.4	100.0
	Consistency	23	46.0	62.2	13	33.3	35.1	1	1.0	2.7	0		16.3	100.0
	Comparability	12	24.0	60.0	8	20.5	40.0	0	0.0	0.0	0		8.8	100.0
	useful_info	3	6.0	75.0	1	2.6	25.0	0	0.0	0.0	0	4	1.8	100.0
	change	1	2.0	33.3	2	5.1	66.7	0	0.0	0.0	0	3	1.3	100.0
		(*% of comment letters within the approbation group, i.e. Yes, Partial, No, and None; **% of total number of comment letters)

Table

For the banking sector we distinguish banks that respond as firm preparers and banks that respond as users of the financial information.


Keywords: Test, Time-homogeneity, Maximum Entropy Bootstrap. JEL Classi…cation: C01, C12, C15

.

Introduction

Over the past two decades, unit roots have become the corner stone of modern time-series econometrics. Indeed, prior to estimation, testing for unit roots is required to avoid spurious results. In such an approach, unit roots are often seen as the main source of the moments heterogeneity of the considered series. Nevertheless, unit roots are only one kind of time-heterogeneity and then non-stationarity. Following [START_REF] Spanos | Probability Theory and Statistical Inference[END_REF], time-heterogeneity is a broader concept including for instance discrete breaks, smooth transition, time-varying moments, or other structural changes. Time-heterogeneity is therefore a more realistic concept, especially in macro-econometrics and in …nance. Moreover, as noticed by [START_REF] Perron | Dealing with Structural Breaks[END_REF]: "There is an intricate interplay between unit root and structural change". On the one hand, the presence of breaks is a source of global non-stationarity [START_REF] Granger | Nonstationarities in Stock Returns[END_REF] and [START_REF] Guégan | Non-Stationary Samples and Mete-Distribution[END_REF]), and on the other hand, breaks in trends are likely to bias toward rejection standard tests of trend-stationarity, as showed by [START_REF] Perron | The Great Crash, the Oil Price Shock and the Unit Root Hypothesis[END_REF]. Also, as pointed out by [START_REF] Diebold | Long Memory and Regime Switching[END_REF] and Char¤edine and Guégan (2011) among others, there is a close connection between structural breaks, especially in means, and long memory processes testing procedures. Indeed, structural breaks may ar-ti…cially generate long memory, thus incorrectly leading the econometrician to model series as long memory processes, whereas series are in fact generated by an other Data Generated Process, as the stop-break model for instance [START_REF] Engle | Stochastic Permanent Breaks[END_REF]). Hence, in addition to causing parameter instability, timeheterogeneity, or structural changes, may lead to erroneous statistical inference in unit root and long memory tests, and thus to incorrect modelling. [START_REF] Perron | Dealing with Structural Breaks[END_REF] reviews the huge literature dedicated to structural changes testing procedures. Clearly, two lessons at least, are to be understood: i) Testing for structural changes is a prior to modelling, or alternatively one can both model and take into account structural change using global minimizer, as in [START_REF] Bai | Computation and Analysis of Multiple Structural Change Models[END_REF]. ii) The alternative assumption is often very narrow, i.e. discrete shift or smooth transition, thus, the tests are generally speci…c to only one kind 1 of alternative. As a result, most will fail in detecting other kinds of ruptures as smooth ones, as showed by Heracleous, Koutris and Spanos (2008) (hereafter HKS), thus forcing the econometrician to implement di¤erent kinds of tests.

Hence, the need for an omnibus test having a broader alternative.

In a recent contribution, HKS have proposed such an omnibus test that detects time-heterogeneity arising from various sources as discrete and smooth transition or trended moments. Their test is based on rolling windows estimators of the …rst two moments of "de-memorized" series, i.e. residuals of ARMA models. On each rolling window, they use the Maximum Entropy BOOTstrap (MEBOOT) method developed by [START_REF] Vinod | Ranking Mutual Funds Using Unconventional Utility Theory and Stochastic Dominance[END_REF][START_REF] Vinod | Maximum Entropy Ensembles for Time Series Inference in Economics[END_REF] to compute more accurate estimates. On such built series, they estimate an auto-regressive process and add a Bernstein polynomial to possibly capture time-heterogeneity. With k, a su¢ ciently large polynomial degree, their procedure amounts to testing H 0 : time homogeneity, against H A : time heterogeneity, the decision rule being

H 0 : k = 0 against H A : k 1.
Using a standard F-test, and based on Monte-Carlo simulations, they show that their test behaves well.

In this paper, we propose an alternate test of time-homogeneity that deals with the main sources of structural changes, i.e. i) Discrete structural breaks, ii) Smooth transition, iii) time-varying moments, iv) probability-driven breaks, i.e. Markov switching models and v) GARCH and Stochastic Volatility Models. To test for the null of time-homogeneity, we use a signal plus noise model, and check that the signal, de…ned as an orthogonal Bernstein polynomial, is constant over time. Our test is therefore an extension of HKS, but it di¤ers in the following points. First, all tests are conducted on the overall series, and not locally, thus avoiding the di¢ cult choice of choosing a particular window, which may dramatically alter the results. Second, the test procedure does not use standard F-tests, but is rather based on bootstrap tailor-made statistics using the Minkowski distance of the forecasts of two auxiliary regressions (see for instance [START_REF] Davison | Bootstrap Methods and Their Application[END_REF]). The tailor-made-statistics are computed using the MEBOOT procedure. Third, in one of the two auxiliary regressions, the degree of the Bernstein polynomial is chosen using the AICu criterion, en-suring an optimal trade-o¤ between …tting and smoothing (McQuarrie and Tsai [1998]).

The paper is organized as follows. Section 2 discusses time-heterogeneity and introduces the test. Section 3 implements Monte-Carlo simulations to estimate the empirical size and power under various alternatives. Section 4 presents an empirical application, and Section 5 concludes.

A test for the null of time-homogeneity

Let fy t g T t=1 be an observed time series, and let f" t g T t=1 be the associated "dememorized"series, as in Andrews and Ploberger 1 (1994) or HKS. For instance, assume that f" t g T t=1 are the residuals of an ARMA model for fy t g T t=1 .

De…nition 1. The process fy t g T t=1 is said to be weakly stationary if the three conditions are ful…lled: i) E(y t ) = t = 8t 2 f1; :::

; T g, ii) V (y t ) = 2 t = 2 8t 2 [1; T ], cov (y t ; y t+h ) = g(h).
For instance in the simple Data Generating Process (DGP) de…ned by (1), De…nition 1 implies that to achieve stationarity, we must have: i) t = ; ii) 2 t = 2 and iii) 1 < t = < 1 8t 2 f1; T g: If additionally = 0, then data are said to be identically and independently distributed (iid).

y t = t + t y t 1 + " t ; " t N (0; 2 t ) (1)
In what follows, we focus only on the residuals f" t g T t=1 i.e. on the …ltered series. Our general DGP is given by (2):

" t = t + t t (2)
where: t is a zero-mean iid term with unit variance, t and t are possibly time varying parameters.

De…nition 2. There is time-homogeneity if t and t are constant over time.

What we want, is to track the process driving t and t over time, and analyze if such a process returns constant values, i.e. t = and t = 8t 2 [1; T ]: Therefore, the assumption we want to test is, for a given moment, for instance for the mean:

H 0 : t = ; 8t 2 [1; T ] against the broad alterna- tive: H A : 9 i 2 [1; T ] : i = i+1 .
Clearly, the alternative spans several processes, as i) Discrete shifts, ii) Smooth transition, iii) time-varying moments, iv) probability-driven breaks, i.e. Markov switching as well as complex and functions of time as v) GARCH and Stochastic Volatility Models.

To track the underlying process, the idea is to represent it as a signal plus noise model, and then test for the time-invariance of the signal.

Theorem 1 (Weierstrass). Let f be a continuous function on [a,b]. Then

for " > 0 there exists a polynomial p(t) with degree k such that for all t 2 [a; b] :

jf (t) p(t)j < ":
In what follows, based on Theorem 1, we chose extracting it from the "dememorized" series, by estimating the following model:

" t = B k (t) + t (3)
Where: B k (t) is a Bernstein polynomial2 of degree k de…ned as:

B k (t) = k P j=0 j k j t j (1 t) k j with 0 t 1; t is an iid noise.
For instance, Figure 1 plots a series with a rupture in mean in t = 50, together with a Bernstein polynomial of order k = 5 (AICu selected degree, see below).

Note that the polynomial perfectly captures the heterogeneity in mean, given the information set I T = f" 1 ; :::; " T g. To test for the null of time-homogeneity, focusing on the …rst moment, we proceed as follows:

1. Estimate (3) forcing k = 0; i.e. estimate:

" t = + t (4)
2. Estimate (3) with k de…ned according to the AICu criterion (5), McQuarrie and Tsai (1998):

AICu = log 0 T k + T + k T k 2 ; (5)
where = ( 1 ; 2 ; :::; T ).

Compute the Minkowski distance on the forecasts:

D p = T X i=1 b " 1 i b " 2 i p ! 1=p (6)
where:

b " 1 t = E[" t jI T ]: are the forecasts of model (4), Testing the signi…cance of the Minkowski distance is achieved by computing bootstrap (tailor-made) p-values using the MEBOOT procedure 4 . Interestingly, 3 See Appendix A form an empirical comparison of three di¤erent information criteria (AIC, AICc and AICu) in the Bernstein polynomial framework. 4 The MEBOOT procedure for a series f"tg T t=1 is as follows: the bootstrap procedure is designed to deal with both time-dependency and time-heterogeneity. For instance, Figure 3 plots a series with a discrete break in mean (in t = 50), as well as a 95 % con…dence interval using the bootstrap procedure. The procedure clearly captures the break. A similar pattern appears in Figure 4, showing a discrete break in the variance (in t = 50).

To build bootstrap p-values we sample, independently f"g T t=1 two times, and compute D p under the null as follows:

1. Sample f"g T t=1 using the maximum entropy bootstrap and estimate (4). Let fb " b1 g T t=1 be the forecast, 2. Sample f"g T t=1 using the maximum entropy bootstrap and estimate (4). Let fb " b2 g T t=1 be the forecast, 2 by Kernel method (10.000 replications) for a series (T = 50) presenting a single shift in mean (from 0 to 2) at the middle of the sample size.

In our simulation, the value of D 2 equals 6:97; with a p-value of 0, which is deeply coherent with our DGP.

We next turn to intensive Monte-Carlo simulations.

Monte-Carlo simulations

In this section, we implement intensive Monte-Carlo simulations to estimate the size and power of the procedure. We …rst introduce our di¤erent DGPs. The …rst one (case 0) is used to study the empirical size of the tests. The DGP is then altered to estimate the power under various alternatives. The basic DGP is as follows:

Case 0 [mean and variance]: iid process 1. Generate T zero-mean normally 6 distributed terms with unit variance We next alter the above DGP to study the power of the procedure.

f" t g T t=1 , 2
Case 1 [mean and variance]: Single discrete shift in mean or in variance Our DGP is the same except for steps 1 and 4 replaced by:

1. For the mean, de…ne f" t g T t=1 as " t = + 1 1 ft> g + t ; t N (0; 1), where 1(:) is the standard indicator function, 2 [T =3; 2T =3] is the braking date, and is randomly drawn with equiprobability within the interval at each replication, = 0 and 1 = 2.

1. For the variance, de…ne f" t g T t=1 as " t = ( + 1 1 ft> g ) t ; t N (0; 1), where 1(:) is the standard indicator function, 2 [T =3; 2T =3] is the brak-ing date, and is randomly drawn with equiprobability within the interval at each replication, = 1 and 1 = 2.

4. For both scenarii, report if it is a success, that is if k > 0 and D p is signi…cantly di¤erent from 0.

Case 2 [mean]. Smooth rupture in mean

We now allow the rupture in mean to be driven by a smooth process. Here a standard logistic function is used. Our DGP is the same as above, except that the Step 1 for the mean is replaced by: 1. De…ne f" t g T t=1 as " t = + 1+exp( =(T =10 ) + 1 + t ; t N (0; 1), = 0, 1 = 3, = 4; = 1 if t < and = (t ) otherwise; = 4,

[T =3;

2T =3] is the braking date, and is randomly drawn with equiprobability within the interval at each replication.

Thus, for t the process returns a constant mean, and for t > a timevarying mean reaching a bound.

A typical realization of such a process is given by Figure 5, with = 0:5 and T = 200:

" t = t + t (7) t = t 1 + 2 t 1 + 2 t 1 t 1 (8)
Such a model has been introduced by Engle and Smith (1999) and studied by [START_REF] Diebold | Long Memory and Regime Switching[END_REF] within the long-memory process framework. Our DGP is still the same, except that the above step 1 is replaced by the following:

1. De…ne f" t g T t=1 as " t = t + t , where the dynamics for t is given by ( 8), with = 0:05, t N (0; 1):

Case 4 [mean]: Markov-switching models Up to now, under the alternative, we have considered discrete, smooth and time-varying processes for the mean. Here, we consider a two-regime probability-driven switching model [START_REF] Hamilton | Analysis of Time Series Subject to Changes in Regime[END_REF]). The modi…ed DGP for f" t g T t=1 is a follows:

" t = St + t (9)
where: S t is a Markov chain, and the stochastic transition matrix is given by:

T = 2 4 p ii (1 p ii ) (1 p jj) p jj 3
5 ; with p ij = P (S t = jjS t 1 = i). The step 1 is as follows,

1. De…ne f" t g T t=1 as " t = St + t ; t N (0; 1), = (0; 2), p ii = 0:8 and p jj = 0:7.

Case 5 [variance]: GARCH errors Focusing now on the variance, We allow our process to have Generalized Autoregressive Conditional Heteroskedastic (GARCH) errors . Compared to case 3, the step 1 is as follows:

1. De…nef" t g T t=1 as " t = t t , where t N (0; 1) and the dynamics for t is given by ( 10)

2 t = 0 + q X i=1 i " 2 t i + p X i=1 i 2 t i (10)
Figure 6: Variance of the yearly US industrial production (USINDPRO) series, together with two Bernstein polynomials with degree k = 0 and k = 1, the latter being selected using the AICu criterion.

Table 1: Empirical size of tailor-made statistics at the 5% nominal size for the DGP introduced in case 0 where: q = p = 1, 0 = 0:01, 1 = 0:1 and 1 = 0:8:

H 0 : constant H 0 : 2 constant T p = 1 p = 2 p = 1 p = 1 p = 2 p =
Case 6 [variance]: Stochastic Volatility Models The above GARCH(1,1) returns a stationary conditional variance. We focus on a competing model, which is the Stochastic Volatility Model. Among others, stochastic volatility models have been considered by Jacquier, Polson and Rossi (1994) and Ghysels, Harvey and Renault (1996) within the state-space framework. To generate a variance following such a process, we alter our step 1 as:

1. De…nef" t g T t=1 as " t = exp( t =2) t , where t N (0; 1) and the dynamics for t is given by ( 11)

t = + t 1 + t (11)
where: = 0:05 and = 1:

We now discuss the results of the various simulations. The empirical size, at the 5% nominal size 7 of the procedure is reported in Table 1. For p = 1 (L1 norm) and p = 2 (L2 norm), the empirical sizes are all less than 5% or slightly above (for instance for T = 150 and for the variance). For p = 1, the empirical size is slightly higher but remains within an acceptable range.

Thus, the procedure perfectly recognizes time-homogeneity when there is timehomogeneity. Note the that the size does not decrease with the sample size. Tables 2 and3 present the power (and size) of the procedure. Table 2 is relative to models with structural changes in mean. Two results are to be

A real data example

We now implement the test on real data. We implement the procedure on three of the various series used in HKS, namely, the yearly US industrial production (USINDPRO), from 1921 to 2004, the quarterly US/Japan Exchange rate (US- Following [START_REF] Koutris | Testing for Structural Change: Evaluation of the Current Methodologies, a Misspeci…cation Testing Perspective and Applications[END_REF], we …rst …lter the series using an auto-regressive process (using the same order), and then implement our procedure. Our results are presented in Table 4. Focusing on D 2 the analysis leads to accept the null of mean-homogeneity for the the series, while rejecting variance-homogeneity for the same series (for USINDPRO at 10%) . Our results therefore slightly di¤er

Conclusion

In this paper we have proposed an omnibus test to detect global non-stationarity in time series, when the non-stationarity is not directly linked to unit-root, but to structural changes. Compared to the existing literature, the test is not speci…c to one kind of alternative, and is based on a broader alternative including i)

Discrete structural breaks, ii) Smooth transition, iii) time-varying moments, iv) probability-driven breaks, i.e. Markov switching models and v) GARCH and Stochastic Volatility Models. Note that the test is designed to capture heterogeneity, but returns no information about possible breaking dates in case of discrete shifts: This is let for further research with di¤erent technics. The test can also be used as a speci…cation test in a linear or non-linear model to check the iid assumption for the residuals, and has its place in the econometrician toolbox.

Figure 1 :

 1 Figure 1: Simulation of an iid sequence (T = 200), with a single rupture in mean: t = 0 for t 100 and t = 2 otherwise, together with a constant signal and a Bernstein polynomial (k = 5).

Figure 2 :

 2 Figure 2: Estimation of the Kernel density of (6) with p = 2, for an iid sequence (T = 100) with a single rupture in mean ( t = 0 for t 50 and t = 2 otherwise). Estimation is computed by bootstrapping under the null using ME-BOOT, 10.000 replications.

  a) Sort f"tg T t=1 by ascending order. Let f" [t] g T t=1 be the sorted series. De…ne findtg T t=1 as an index containing the ordering of the original series. b) Compute intermediate points zt = 1

Figure 3 :

 3 Figure 3: Sequence (T = 200) of iid terms, with a single rupture in mean ( t = 1 for t 100 and t = 2 otherwise), together with a 95% con…dence interval built by bootstrapping the series.

d)

  On each interval compute the desired means de…ned as m 1 = 0:75"[START_REF] Akaike | Stochastic Theory of Minimal Realization[END_REF] (1) + 0:25"[START_REF] Andrews | Tests for Parameter Instability and Structural Change With Unknown Change Point[END_REF] forI 1 , m T = 0:25" [T 1] + 0:75" [T ] for I T and m k = 0:25" [k 1] + 0:5" [k] + 0:25" [k+1] for intermediate values.e) Draw uniform realizations on [0,1] and compute the associated quantiles for f" [t] g T t=1 by linear interpolation. g) Adjust the quantiles using zt to preserve the means, and reorder the adjusted quantiles according to indt: This returns a bootstrap realization for f"tg T t=1 :h) Repeat steps a) to g) a large number of times.

Figure 4 :

 4 Figure 4: Sequence (T = 200) of iid terms, with a single rupture in variance ( t = 1 for t 100 and t = 4 otherwise), together with a 95% con…dence interval built by bootstrapping the series.

3 ., 4 .

 34 Compute a bootstrap value for D p ; say D b p = Repeat steps 1 to 3 a large number of times, and compute the empirical distribution of D b p , and then the tailor-made p-value. Reject the null if the p-value is less than a given threshold.

Figure 2

 2 Figure 2 illustrates the above four-step procedure 5 . It returns the estimated density of D b2 by Kernel method (10.000 replications) for a series (T = 50) presenting a single shift in mean (from 0 to 2) at the middle of the sample size.

3 . 4 . 5 .

 345 . Estimate (3) for various values of k 2 [0; 15], Choose the model minimizing the AICu criterion, If k = 0 then report a success, if k 6 = 0 then test for the signi…cance of D p using bootstrap p-values. Repeat steps 1 to 4, 1000 times.

Figure 5 :

 5 Figure 5: Sequence (T = 200) of iid terms, with a constant mean for t 100, and logistic driven otherwise.

Figure 7 :

 7 Figure 7: Variance of the quarterly US/Japan Exchange rate (USJEXR), together with two Bernstein polynomials with degree k = 0 and k = 1, the latter being selected using the AICu criterion.

Figure 8 :

 8 Figure 8: Variance of the quarterly US investment (USINVEST) series, together with two Bernstein polynomials with degree k = 0 and k = 2, the latter being selected using the AICu criterion.

  JEXR), from 1982Q2 to 2005Q2 and the quarterly US investment (USINVEST), from 1963Q2 to 1982Q4. HKS found out strong evidence of a structural change in the variance for USINDPRO and USJEXR, and a structural change in mean for USINVEST.

Table 2 :

 2 Empirical size and power at the 5% nominal size for models exhibiting structural changes in mean the modi…cations in mean. ii) Analyzing the results of the variance (size), since the second moment is empirically built using the …rst one, modi…cations of the mean deeply alter the size of the test, which is fact quite trivial. The size is maximal for the Stop-Break model. This imposes running the test sequentially, …rst test for the stationarity of the mean, and next, if not rejected, for the stationarity of the variance. Concerning Table3, i.e. constant mean but structural breaks in variance, the test appears to be also quite powerful for the three considered models: discrete shift, GARCH and

	Single discrete shift in mean, 2 [T =3; 2T =3] H 0 : constant H 0 : 2 constant
	T 80 1.000 1.000 p = 1 p = 2 p = 1 1.000	p = 1 p = 2 0.026 0.108	p = 1 0.300
	100 1.000 1.000	1.000	0.330 0.330	0.330
	150 1.000 1.000	1.000	0.442 0.442	0.442
	200 1.000 1.000	1.000	0.460 0.043	0.095
	Smooth transition in mean, 2 [T =3; 2T =3] H 0 : constant H 0 : 2 constant
	T 80 1.000 1.000 p = 1 p = 2 p = 1 1.000	p = 1 p = 2 0.118 0.118	p = 1 0.118
	100 1.000 1.000	1.000	0.156 0.156	0.156
	150 1.000 1.000	1.000	0.166 0.184	0.184
	200 1.000 1.000	1.000	0.220 0.244	0.272
		Stop-Break model
	H 0 : constant	H 0 : 2 constant
	T 80 0.998 1.000 p = 1 p = 2 p = 1 1.000	p = 1 p = 2 0.952 0.962	p = 1 0.972
	100 1.000 1.000	1.000	0.984 0.984	0.988
	150 1.000 1.000	1.000	1.000 1.000	1.000
	200 1.000 1.000	1.000	0.980 0.980	1.000
	Two-regime Markov switching model
	H 0 : constant	H 0 : 2 constant
	T 80 0.724 0.724 p = 1 p = 2 p = 1 0.724	p = 1 p = 2 0.856 0.856	p = 1 0.856
	100 0.710 0.710	0.710	0.842 0.842	0.842
	150 0.774 0.782	0.782	0.890 0.864	0.862
	200 0.758 0.780	0.788	0.910 0.884	0.854
	Note 1: Entries for 'H 0 : constant', represent the rejection frequencies
	when the null is not true, over 1000 replications.
	Note 2: Entries for 'H 0 : 2 constant', represent the rejection frequencies
	when the null is true, over 1000 replications.
	emphasized: i) For a single discrete shift, a smooth transition, or for the Stop-
	break model, the power of the procedure is unity. For a Markov-switching model,
	the power lies between 0.710 and 0.788, which is still acceptable. Hence, the

Stochastic Volatility Model. For a discrete shift in variance, the size of the test for the mean is not altered, as it is for the GARCH model and the Stochastic Volatility Model. Nevertheless, it remains within an acceptable range.

Table 3 :

 3 Empirical size and power at the 5% nominal size for models exhibiting structural changes in variance

	Single discrete shift in variance, 2 [T =3; 2T =3] H 0 : constant H 0 : 2 constant
	T 80 0.122 0.122 p = 1 p = 2 p = 1 0.122	p = 1 p = 2 0.908 0.908	p = 1 0.908
	100 0.128 0.128	0.128	0.962 0.962	0.962
	150 0.114 0.114	0.114	1.000 1.000	1.000
	200 0.102 0.110	0.110	1.000 1.000	1.000
		GARCH model
	H 0 : constant	H 0 : 2 constant
	T 80 0.286 0.286 p = 1 p = 2 p = 1 0.286	p = 1 p = 2 0.962 0.962	p = 1 0.962
	100 0.276 0.276	0.276	0.962 0.962	0.962
	150 0.254 0.254	0.254	0.950 0.950	0.950
	200 0.290 0.290	0.290	0.924 0.924	0.924
	Stochastic Volatility Model
	H 0 : constant	H 0 : 2 constant
	T 80 0.238 0.238 p = 1 p = 2 p = 1 0.238	p = 1 p = 2 0.860 0.860	p = 1 0.860
	100 0.170 0.170	0.170	0.882 0.882	0.882
	150 0.286 0.286	0.286	0.938 0.938	0.938
	200 0.152 0.262	0.318	0.958 0.981	0.986

Note 1: Entries for 'H 0 : 2 constant', represent the rejection frequencies when the null is not true, over 1000 replications. Note 2: Entries for 'H 0 : constant', represent the rejection frequencies when the null is true, over 1000 replications.

Table 4 :

 4 Values of (6) for the three (de-memorized) series, USINDPRO, US-JEXR and USINVEST

			H 0 : constant
	Series	k	D 1	D 2	D inf
	USINDPRO 0	0 (1)	0 (1)	0 (1)
	USJEXR	0	0 (1)	0 (1)	0 (1)
	USINVEST 0	0 (1)	0 (1)	0 (1)
			H 0 : constant
	Series	k	D 1	D 2	D inf
	USINDPRO 1	88.72 (0.111)	11.38 (0.072)	2.16 (0.003)
	USJEXR	1 2444.29 (0.038) 297.49 (0.015) 53.7140 (0.000)
	USINVEST 2	2.97 (0.010)	0.41 (0.001)	0.122 (0.000)

Note: P-values between parenthesis from HKS.

See also[START_REF] Andrews | Tests for Parameter Instability and Structural Change With Unknown Change Point[END_REF] and Andrews, Lee and Ploberger (1996).

Using polynomials to detect time-heterogeneity has been …rst suggested by MacNeill (1978) and extended by[START_REF] Perron | A Test for Changes in a Polynomial Trend Function for a Dynamic Time Series[END_REF] and[START_REF] Tang | The e¤ect of Serial Correlation on Tests for Parameter Change at Unknown Time[END_REF].

(" [t] + " [t+1] ); t = 1; :::; T 1: c) De…ne intervals I 1 ; :::; I T with equiprobability as well as bounds for the intervals (0; 1] and (T 1; T ]. For this compute the trimmed mean of j "tj and compute the lower bound by removing this mean to z 1 and the upper bound by adding this mean to z T 1 .

Alternatively, one can bootstrap Dp for the estimated k. Empirically, this returns very similar results.

In this section, we generate f"tg T t=1 as normally distributed terms. Nevertheless, since we don't use a residual-based bootstrap, any law with stable …rst two moments can be used.

For clarity of the exposé, we only report the empirical size and power at the 5% nominal size. Size and power at the 1%, 5%, 10% and 15% are available under request.

A Appendix

In this appendix, we analyse the relative performance of three di¤erent information criteria to select the correct degree k of the orthogonal Bernstein polynomial under the null. The three indicators are the classical AIC [START_REF] Akaike | Stochastic Theory of Minimal Realization[END_REF]) the AICc and the AICu (McQuarrie and Tsay [1998], Burnham and Anderson [2002]) respectivelly de…ned as:

where:

t are the residuals of the regression of " t on B k (t); T is the number of observations, k the degree of the polynomial.

To perform such a task, we run Monte-Carlo simulations. Our DGP is as follows:

1. Generate a series f" t g T t=1 where " t N (0; 1):

2. Estimate the model " t = B k (t) + t stepwise for k = 0; :::; 10:

3. For each model, compute AIC, AICc, AICu, and …nd the k corresponding to their minimal value. Note that k = 1 will return a linear trend, possibly with zero slope, thus being possibly equivalent to k = 0. Clearly, using AIC and to a less extent AICc results in overestimating the polynomial degree, whatever the sample size. For instance, basing the decison rule on AIC will return the correct information in only 65:8 % of the cases for T = 50, whereas for AICu the probability is 89:4 %. Also, the number of times the AIC returns k > 1 seems quite large, with for instance for T = 50, 24:8 % against 3:8 % for the AICu.

Since our DGP is based on H 0 , basing a stationarity test on the k minimizing the AICu, i:e: H 0 : k = 0 against H A : k > 0 will return a very simple and powerful test, even if not based on statistical inference.