**Econometric analysis of
accounting choice**

**Spring 2014**

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 specific (causal) research question.

3. Formulate a research design.

4. Discuss interpretation of potential results.

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

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**

** **

**Work in progress: Accounting, managerial
experimentation and causal effects**

**AAA
August 2012 slides: Accounting and causal effects**

**Fellingham
monograph: Accounting as an information science**

**Imbens and WooldridgeÕs NBER
econometric minicourse**

**Notes on
maximum entropy probability assignment conditional on the Kelly criterion**

** **

**Ross, 2011, The Recovery Theorem.**

** **

** **

** **

** **

**Outline:**

** **

Below is a list of potential
topics for summer 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 **(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 99% 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)

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)

Quantum production, synergy,
and (product market) strategic disclosure

Other topics of interest to
you

Table of contents
for *Accounting and causal effects: Econometric challenges*

- including
OLS, GLS, FWL, and IV estimators

4. Loss functions
& estimation

- including MLE, James-Stein shrinkage estimators, and nonlinear regression

- employed
as propensity score in treatment effect analysis

6. Nonparametric
regression models

- employed
with Heckman's MTE

7. Repeated-sampling
inference

- including McMC Bayesian analysis

9. Treatment effects:
ignorability

11. Marginal
treatment effects

12. Bayesian
treatment effects

- including
widget example

- including
inferring transactions from financial statements

- including
convergence in probability, convergence in distribution, and rates of
convergence

Errata
(corrections for the 2010 Springer printed version)

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

1. Probability as logic (http://bayes.wustl.edu/etj/science.pdf.html)

2. *Accounting, managerial
experimentation** and causal effects*

stewardship and the search for a better Òmouse trapÓ

ANOVA,
ANCOVA, linear regression

double residual regression (FWL)

ch. 3 classical causal effects strategies

ignorable treatment

limited common support

regression discontinuity designs

synthetic controls

dynamic treatment effects

LATE
& 2SLS (linear) IV

control functions

continuous treatment effects

Causal effects and
difference-in-difference designs

Causal
effects and propensity-score matched regression

Causal
effects and saturated propensity-score matched regression

ch. 4 maximum entropy distributions

BayesÕ
theorem & consistent reasoning

maximum entropy probability assignment

posterior simulation & conjugate families

independent & conditional posterior simulation

Markov
chain Monte Carlo (McMC) simulation

irreducibility, time reversibility, & stationarity

Gibbs
sampler

Metropolis-Hastings
(MH) algorithm

data augmented sampler for Probit

random walk MH logit

uniform data augmented Gibbs sampler for logit

ANOVA,
ANCOVA, regression

ch. 9 Bayesian causal effects strategies

data augmented Gibbs sampler for treatment effects

data augmented IV restricted Gibbs sampler for treatment
effects

ch. 10 Bayesian treatment effects without joint
distribution of outcomes

ChibÕs
ATE and LATE

extensions (via bounding) to ATT and ATUT

ch. 11 Partial identification and missing data

Missing
outcomes

quantiles

expected values (point and partial identification)

inference

respecting stochastic dominance

refutability

missing covariates and outcomes

missing at random

missing by choice

stochastic dominance and treatment effects

Selection
problem

various instrumental variable strategies (missing at random,
statistical independence, means missing at random, mean independence)

monotone instrumental variable strategies (mean
monotonicity, exogenous treatment selection, monotone treatment selection,
monotone treatment response, MM-MTR, MTR-MTS)

quantile treatment effects (point
and partial identification)

Extrapolation
and the mixing problem

Appendix:
bounds on spreads

linear algebra basics

fundamental theorem of linear algebra

subspaces

exactly, under-, and over-identified

matrix decomposition

LU
factorization

Cholesky
decomposition

singular value decomposition (SVD) & pseudo inverse

spectral decomposition

Gram-Schmidt
orthogonalization

some determinant identities (& LU factorization)

iterated expectations

multivariate normal theory

generalized least squares (GLS)

two stage least squares IV (2SLS-IV)

seemingly unrelated regression (SUR)

maximum likelihood estimation of discrete choice models

quantum
information

common distributions

**R Statistical Computing
Package**

R is a freely available,
open-source version of S/S-plus.

Follow this link: R statistical computing
package

**R samples programs**

Tutorials:
R tutorial

http://en.wikibooks.org/wiki/R_Programming/

find your favorite on the web

source files for data augmented Gibbs sampler
bivariate probit:

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

source files for Metropolis-Hastings bivariate logit
(self-contained code and code utilizing MCMCpack library which you may need to
add)

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

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

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

Strategic disclosure
papers include:

Shin, 1993, "News management and the value
of firms," *RAND Journal of Economics*,
25(1), 58-71.

Shin, 1993, "Disclosures and asset returns,"
*Econometrica*, 71(1), 105-133.

Shin, 2006, ÒDisclosure risk and price drift,Ó *Journal of Accounting Research*, 44(2),
351-379.

Arya and Mittendorf, ÒThe interaction between
corporate tax structure and disclosure policy,Ó *Annals of Finance*, forthcoming.

Arya and Mittendorf, ÒInput markets and the
strategic organization of the firm,Ó *Foundations
and Trends in Accounting*, 5(1), 1-97.