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Quasi-Maximum Likelihood for Estimating Structural Models

  • Malek Ben-Abdellatif ORCID logo EMAIL logo , Hatem Ben-Ameur , Rim Chérif ORCID logo and Tarek Fakhfakh ORCID logo
Published/Copyright: March 19, 2025
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Studies in Nonlinear Dynamics & Econometrics
From the journal Studies in Nonlinear Dynamics & Econometrics Volume 29 Issue 4

Abstract

The estimation of the structural model poses a major challenge because its underlying asset (the firm asset value) is not directly observable. We consider an extended structural model that accommodates alternative underlying Markov processes, arbitrary debt payment schedules, several seniority classes, multiple intangible assets, and various intangible corporate securities. We derive the likelihood function given the observed time series of the firm equity values. Then, we use dynamic programming to solve the model and, simultaneously, extract the associated time series of the firm asset values (the pseudo-observations). Finally, the likelihood function is approximated and optimized, which results in the quasi-maximum likelihood (QML) estimates of the model’s unknown parameters. QML is highly flexible and effective. To assess our construction, we perform an empirical investigation, highlight the credit-spread puzzle, and discuss a partial remedy via jumps and bankruptcy costs.

Keywords: structural model; estimation; quasi-maximum likelihood; jump-diffusion processes; credit-spread puzzle
JEL Classification: C13; C51; C61; C63
Corresponding author: Malek Ben-Abdellatif, Department of Finance, School of Business, ESLSCA University, Giza 12511, Egypt, E-mail: 

Tarek Fakhfakh passed away in 2024. This work is published in his memory.

Funding source: Natural Sciences and Engineering Research Council of Canada

Award Identifier / Grant number: R55

Funding source: Canadian Statistical Sciences Institute (CANSSI)

Award Identifier / Grant number: 32-153-300-22-R2491

  1. Author contributions: All authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: This paper was supported by two research grants received by the second author from the Natural Sciences and Engineering Research Council of Canada (NSERC) and the Canadian Statistical Sciences Institute (CANSSI).

  3. Conflict of interest: The authors declare no conflicts of interest regarding this article.

  4. Data availability: The data that support the findings of this study are from CRSP and S&P Capital IQ databases. Restrictions apply to the availability of these data, which were used under license for this study.

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Supplementary Material

This article contains supplementary material (https://doi.org/10.1515/snde-2023-0052).

Received: 2023-07-17
Accepted: 2025-02-23
Published Online: 2025-03-19

© 2025 Walter de Gruyter GmbH, Berlin/Boston

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https://doi.org/10.1515/snde-2023-0052
Keywords for this article
structural model; estimation; quasi-maximum likelihood; jump-diffusion processes; credit-spread puzzle

Articles in the same Issue

  1. Frontmatter
  2. Interview
  3. From Model Misspecification to Multidimensional Welfare: A Conversation with Professor Esfandiar Maasoumi
  4. Research Articles
  5. A Test for Time-Varying Smooth Transition Conditional Covariance Models in Multivariate Time Series
  6. Quasi-Maximum Likelihood for Estimating Structural Models
  7. Monetary Policy Uncertainty in the United States and Investment Sentiment in Advanced Economies
  8. Inflation: Demand Pull or Cost Push? A Markov Switching Approach
  9. Divisia Monetary Aggregates for India
  10. Introducing sspaneltvp: A Code to Estimating State-Space Time-Varying Parameter Models in Panels. An Application to Okun’s Law
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