AMIS Seminar

Econometric Analysis of Accounting Choice

Summer 2022, Spring 2023

Instructor Information
Instructor: Professor D. Schroeder
Office: 424 Fisher Hall
Email: schroeder.9@osu.edu
Phone: 614-292-6427

Potential topics (we won’t find time for all but most have been addressed over the past five years):

Identification of causal effects:

Experimental design and inference:

Other topics of interest to participants

  • treatment effects and regression discontinuity designs
  • treatment effects and control or replacement functions
  • treatment effects and matching methods
  • dynamic treatment effects
  • synthetic controls
  • …

 

Archived material:

Focus:

Explore issues of (broad) interest raised in colloquium, papers, or formative ideas from a causal perspective.

  1. Describe the general problem.
  2. Identify a (causal) research question and the specific effects or quantities of interest.
  3. Explain your identification strategy for the effects of interest.
  4. Formulate an identification-consistent research design (possibly including a causal graph).
  5. Discuss interpretation of potential results.

Closely attend to the role of causal relations, probability assignment, and counterfactuals in devising an identification strategy and data analysis.

Background reading:

Pearl, Glymour, and Jewell, 2016, Causal inference in statistics: A primer, Wiley.

Angrist and Pischke, 2015, Mastering Metrics, Princeton University Press.

Angrist and Pischke, 2009, Mostly Harmless Econometrics, , Princeton University Press.

Wooldridge, 2002, Econometric analysis of cross section and panel data, The MIT Press.

Davidson and MacKinnon, 2004, Econometric theory and methods, Oxford University Press.

Cameron and Trivedi, 2005, Microeconometrics: Methods and applications, Cambridge University Press.

Strang, Introduction to linear algebra or Linear algebra and its applications.

Tentative outline for summer and spring:

session topic examples background reading
prediction (statistical)
1 summer inferring transactions Ralph’s structure; Ralph’s accounting information Arya, Felligham, Glover, Schroeder, and Strang, 2000, Contemporary Accounting Research, “inferring transactions from financial statements”; notes on updating from financial statements
2 summer accruals as statistics Ralph’s optimal accruals; Ralph’s GLS; Ralph’s Bayesian Accruals Arya, Fellingham, and Schroeder, 2002, European Accounting Review, “Depreciation in a model of probabilistic investment “; Demski, Fellingham, Lin, and Schroeder, 2007, “On the role of acccruals,” working paper
causality (structure and evidence)
3 spring Simpson’s paradox & causality – intervention & counterfactuals Ralph’s Technology Pearl, Glymour, and Jewell, 2016, Causal inference in statistics: A primer, Wiley
4 do-calculus Ralph’s back-door adjustment Pearl et al Primer; Pearl 1995, Biometrika, “Causal diagrams for empirical research”
5 do-calculus Ralph’s front door adjustment Pearl et al Primer; Pearl, Biometrika
6 linear models & instruments Ralph’s instrumental variables Pearl et al Primer

notes on SCM and fixed effects

SCM, random coefficients, fixed effects, and clustering

SCM and z-identification

SCM and proxy variables
7 cyclical models & instruments Ralph’s structural queries Pearl et al Primer
8 Berkson’s paradox; DAG testing Ralph’s “Kitchen Sink” Fallacy; Ralph’s covariate selection Pearl et al Primer
9 linear models & DAG testing Ralph’s Path Coefficients, Ralph’s DAG Pearl et al Primer
10 sampling selection bias Ralph’s Technology Selection notes on Sampling selection

parametric sample selection
11,12 external validity & missing data Ralph’s Transportability Pearl and Bareinboim, 2014, Statistical Science, “External validity: From do-calculus to transportability across populations”

SCM and meta-analysis

Mohan and Pearl, 2020, Journal of the American Statistical Association, “Graphical models for processing missing data.”

SCM graphs and missing data (examples 1, 2, and 10 from Mohan and Pearl [2020])
13,14 ETT, counterfactuals & partial identification examples in  SCM with diff-in-diff design notes on SCM with diff-in-diff design

notes on causes of effects

Tian and Pearl, 2000, “Probabilities of causation: bounds and identification.”

Mueller, Li, and Pearl, 2021, “Causes of effects: Learning individual responses from population data.”
15 treatment effects & counterfactuals examples in Inverse propensity score weighting & SCM notes on SCM and inverse propensity score weighting

notes on ignorable treatment and inverse propensity-score weighting
16 maxent; treatment effects & counterfactuals Ralph’s probability assignment; examples in entropy balanced causal effects ch 4 Maximum entropy distributions; notes on entropy balanced causal effects; Hainmueller, 2012, Political Analysis, Entropy balancing for causal effects.

 

Papers:

Greenland, Pearl, and Robins, 1999, Epidemiology, Causal diagrams for epidemiology research.

Haavelmo, 1943, Econometrica, The statistical implications of a system of simultaneous equations.

Pearl, 2012, Prevention Science, The causal mediation formula – A guide to the assessment of pathways and mechanisms.

notes on mediation

Demerjian et al, forthcoming, Contemporary Accounting Research, Income smoothing and the usefulness of earnings for monitoring in debt contracting.

Bonsall, Green, and Muller, 2018, The Accounting Review, Are credit ratings more rigorous for widely covered firms?

Genser, Teles, Baretto, and Fischer, 2015, Environmental Health, Within- and between-group regression for improving the robustness of causal claims in cross-sectional analysis.

Petersen, 2009, Review of Financial Studies, Estimating standard errors in finance panel data sets: Comparing approaches.

Gow, Ormazabal, and Taylor, 2010, The Accounting Review, Correcting for cross-sectional and time-series dependence in accounting research.

Thompson, 2011, Journal of Financial Economics, Simple formulas for standard errors that cluster by both firm and time.

Wooldridge, 2011, Labour Lectures EIEF, Cluster samples and clustering.

Abadie, Athey, Imbens, Wooldridge, 2017, NBER, When should you adjust standard errors for clustering?

Abadie, Athey, Imbens, Wooldridge, 2020, Econometrica, Sampling-based versus design-based uncertainty in regression analysis.

Arellano, 1987, Oxford Bulletin of Economics and Statistics, Computing robust standard errors for within-groups estimators.

Arellano, 2011, Cluster-robust standard errors.

Heckman, Ichimura, Todd, 1997, Review of Economic Studies, Matching as an econometric evaluation estimator:  Evidence from evaluating a job training programme.

Heckman, Ichimura, Smith, Todd, 1998, Econometrica, Characterizing selection bias using experimental data.

Bareinboim, Tian, and Pearl, 2014, AAAI Conference on Artificial Intelligence, Recovering from selection bias in causal and statistical inference.

notes on method of moments

notes on preference estimation via MSM

Duffie and Singleton 1993, Econometrica, Simulated moments estimation of Markov models of asset prices.

Kim, 2019, working paper, Spillover of financial reporting on public firm’s corporation’s investment.

Liang, 2019, working paper, How much value does accounting precision enhance?

Bareinboim and Pearl, 2016, Proceedings of the National Academy of Science, Causal inference and the data-fusion problem. (paper provides a nice summary of recent developments)

Knox, Lowe, and Mummolo, 2020, American Political Science Review, Administrative records mask racially biased policing.

Knox, Lowe, and Mummolo, 2020, on-line appendix, Administrative records mask racially biased policing.

Fryer, 2019, Journal of Political Economy, An empirical analysis of racial differences in policy use of force.

Potential project:

  1. Identify a topic of interest.
  2. Apply the above outline to the subject.
  3. Simulate data and apply your research design.
  4. If you have archival data, subject these data to your vetted design and interpret the results; otherwise, interpret the results for the simulated data.

“No successful mechanical algorithm for discovering causal or structural models has yet been produced, and it is unlikely that one will ever be found. At the same time, it is unlikely that the quest for a mechanical algorithm for determining causality from data will ever be abandoned. The tension between the use of tacit knowledge and formal algorithmic methods is likely to be a permanent feature of empirical research in economics. It arises because in most empirical studies there is always more knowledge about a problem being studied than appears in the sampling distributions of the measured variables being analyzed or in well-specified Bayesian priors. The best empirical work in economics uses economic theory as a framework for integrating all of the available evidence, tacit and algorithmic, to tell a convincing story.”

– James Heckman, Quarterly Journal of Economics 115, no. 1 Feb. 2000, p. 46.

Objectives:

The objectives are (i) to build a foundation for meaningful discussions, (ii) to complement econometrics (and statistics) courses (in my view, coursework provides an opportunity to survey what’s out there – this is an opportunity to develop a deeper understanding), and (iii) to explore implications for accounting.

  • Monograph: Accounting and causal effects: Econometric challenges (can be found below)
  • Work in progress: Accounting, managerial experimentation and causal effects (can be found below)
  • ASSETS (additional notes, some are repeated below, follow link on right side of page)
  • Bayesian Networks

Complementary Bayesian network exercises:

Pearl’s criteria for complete, consistent econometric treatment of structural causal modeling (SCM) 

A. Applicability of Econometric Models

  1. The author presents example problems that require causal reasoning.
  2. The author presents example problems that require prediction alone.

B. Interpreting Model Parameters

  1. The author states that each structural equation in the econometric model is meant to convey a causal relationship.
  2. The author defines beta to be causal and the equality, betaX = E [Y|X], is NOT generally valid.
  3. The author does NOT define the error term, in general, to be equal to the difference between E[Y|X] and Y.
  4. The author interprets the error term as omitted variables that (together with X) determine Y.
  5. The author states that each structural equation in the econometric model is meant to capture a ceteris paribus or “everything else held fixed” relationship.
  6. The author does NOT assume that exogeneity of X is inherent to the model.

C. Distinguishing E [Y | X] and E [Y | do (X)]

  1. The author makes clear the difference in the assumptions needed for answering causal as opposed to predictive problems?
  2. The author uses separate notation for E [Y | X ] and E [Y | do (X )].
  3. The author uses separate notation for the slope of the line associated with E [Y | X] and that associated with E [Y | do (X)].

Pearl’s fundamental structural causal modeling (SCM) questions

other papers and notes:

Outline:

Below is a list of potential topics for seminar. We surely will not cover them all (some will naturally get combined in the course of our discussions). It goes without saying, this is an ambitious, time and energy-taxing endeavor, but this seminar is purely optional (it’s an opportunity not an obligation). If you decide to participate, I would like you to choose a topic and tentative date for discussion. I believe you’ll get more out of seminar if you actively participate, therefore my plan for this summer is to give you some latitude in leading the discussion. Don’t think you have to exhaust the topic – that’s not possible, many of these topics warrant a course of their own. Do not expect closure.

There is some coverage of each of these issues in my monograph, Accounting and causal effects: Econometric challenges. But don’t think you have to limit yourself to these pages. The monograph is posted below along with some supplemental material developed (and still under development) subsequent to completion of the monograph along with some sample R programs.

As you know, linear algebra is an indispensable tool for these explorations. Amongst the supplemental materials is an appendix (not listed with the topics below) which includes a brief survey of some important concepts from linear algebra along with some examples.

Make use of the best tools at your disposal (spreadsheets, Mathematica, Matlab, etc.). I find R, the open source statistical software, to be invaluable especially for computationally intensive work like McMC simulation. Since it’s open source, it evolves rapidly and many of the contributors have fabulous programming skills that make R extraordinarily efficient. I plan to post a few sample programs to, hopefully, ease the learning curve but expect to discover your own tricks for gaining efficiency (sadly, not my forte).

Treatment effects

Treatment effects (a special case of causal effects) receive a substantial amount of attention in the topics below as well as in the monograph. Some key features (illustrated in the Tuebingen-style and supplementary pages examples) are

  • omitted, correlated variables (personally, I devote much of my efforts to this problem, in this case it leads to potential selection bias)
  • counterfactuals& inferring population-level parameters (this distinguishes the treatment effect problem from, say, a run of the mill endogenous regressor problem and is a source of controversy among scientists; see Dawid)
  • common support (how confident are you extrapolating outside the relevant range?)
  • there are numerous definitions of treatment effects (average treatment effect, average treatment effect on the treated, average treatment effect on the untreated, local average treatment effect, marginal treatment effect, policy-relevant treatment effect, ambiguity of treatment effects identified by linear IV, etc.) not all of them are accessible without full support and they are not all equally well suited to the problem at hand
  • choice of instruments is even more challenging than usual and greater care is required in interpreting the results
  • higher explanatory power (in either the selection or outcome equations) does not necessarily lead to a well-identified model

Topics:

  • Linear models (OLS, GLS, FWL, etc.)
    • Equilibrium earnings management (chapters 2 & 3)
  • Fixed effects & differences-in-differences and random effects & random coefficients
  • Linear instrumental variables (IV)
  • Discrete choice models
  • Nonlinear regression
  • Maximum likelihood estimation (James-Stein shrinkage estimators)
  • Nonparametric & semiparametric regression
  • Bootstrapping & posterior simulation
  • McMC (Markov chain Monte Carlo) simulation (chapters 7 & 12 and supplemental materials Bayesian notes)
  • Strategic choice models
  • Treatment effects (chapter 8 Tuebingen-style examples)
  • Ignorable treatment effects (chapter 9 Tuebingen-style examples)
    • Identification strategies: exogenous dummy variable regression, nonparametric regression, propensity score & propensity score matching, control functions, regression discontinuity design, etc. (mean conditional independence (ignorability) vis-a-vis conditional independence (strong ignorability))
    • Asset revaluation regulation (limitations of outcome measures for inferring welfare effects; chapters 2& 9)
  • Nonignorable (IV) treatment effects (chapter 10 Tuebingen-style examples)
    • Generalized Roy model interpretation
    • Identification strategies: endogenous dummy variable IV regression, propensity score IV, ordinate control function IV, inverse Mills control function IV, LATE and linear IV, etc.
    • IV control functions & projections examples (ANOVA, ANCOVA to control functions examples in supplemental materials projections notes)
    • Continuous treatment & (correlated) random coefficients
    • Regulated report precision (nonignorable versus ignorable identification strategy effectiveness; chapters 2 & 10)
  • Marginal treatment effects
    • Identification and LIV (local instrumental variables)
    • Regulated report precision (apparent nonnormality & marginal treatment effects; chapters 2 & 11)
  • Bayesian treatment effects
    • Identification via McMC data augmentation
    • Identification & McMC IV (restricted) data augmentation (supplemental materials Bayesian notes)
    • Regulated report precision (marginal & average treatment effects as well as policy-relevant treatment effects; chapters 2 & 12)
  • Bayesian networks
  • Informed priors & Bayesian data analysis (probability as logic)
    • Maximum entropy probability assignment & Jaynes’ widget problem
    • Conjugate families (supplemental materials Bayesian notes)
    • Inverting financial statements (to recover transactions)
    • Smooth accruals (valuation and performance evaluation implications)
    • Earnings management (stochastic& selective manipulation)
  • Strategic disclosure (some papers are listed at the bottom of the page)

Ross’ recovery theorem

  • Kelly’s long-run wealth maximizing investment strategy
  • Quantum production, synergy, and (product market) strategic disclosure
  • Other topics of interest to you

Monograph: Accounting and causal effects: Econometric challenges

table of contents for Accounting and causal effects: Econometric challenges

Supplemental materials: (most of this is work in progress – expect updates)

  1. Probability as logic
  2. Accounting, managerial experimentation and causal effects

R Statistical Computing Package

R samples programs

Tutorials:

source files for data augmented Gibbs sampler bivariate probit:

you will need to add bayesm library from Cran website if it’s not including in your base program

  • Gibbs probit.R
  • source files for Metropolis-Hastings bivariate logit (self-contained code and code utilizing MCMCpack library which you may need to add)
  • MH logit.R

source files for data augmented Gibbs sampler bivariate selection analysis of treatment effects:

you will need to add MASS library from Cran website if it’s not including in your base program

Another Bayesian McMC strategy for identifying treatment effects (perhaps, with panel data) can be found in Chib’s papers posted below:

Strategic disclosure papers include:

  • Shin, 1994, “News management and the value of firms,” RAND Journal of Economics, 25(1), 58-71.
  • Shin, 2003, “Disclosures and asset returns,” Econometrica, 71(1), 105-133.
  • Shin, 2006, “Disclosure risk and price drift,” Journal of Accounting Research, 44(2), 351-379.
  • Arya, Mittendorf. forthcoming, “The interaction between corporate tax structure and disclosure policy,” Annals of Finance.
  • Arya Mittendorf, 2010, “Input markets and the strategic organization of the firm,” Foundations and Trends in Accounting, 5(1), 1-97.