# Issues in Empirical Finance Research

2020-10-27

## The challenge

• I will discuss some issues in using plain OLS models in Corporate Finance & Governance Research
• I will avoid the word “endogeneity” as much as I can
• I will also avoid the word “identification” because identification does not guarantee causality and vice-versa (Kahn and Whited 2017)

## The challenge

• Imagine that you want to investigate the effect of Governance on Q

• You may have more covariates explaining Q (omitted from slides)

$𝑸_{i} = α + 𝜷_{i} × Gov + Controls + error$

All the issues in the next slides will make it not possible to infer that changing Gov will CAUSE a change in Q

That is, cannot infer causality

## 1) Reverse causation

One source of bias is: reverse causation

• Perhaps it is Q that causes Gov

• OLS based methods do not tell the difference between these two betas:

$𝑄_{i} = α + 𝜷_{i} × Gov + Controls + error$

$Gov_{i} = α + 𝜷_{i} × Q + Controls + error$

• If one Beta is significant, the other will most likely be significant too

• You need a sound theory!

## 2) Omitted variable bias (OVB)

The second source of bias is: OVB

• Imagine that you do not include an important “true” predictor of Q

• Let’s say, long is: $𝑸_{i} = 𝜶_{long} + 𝜷_{long}* gov_{i} + δ * omitted + error$

• But you estimate short: $𝑸_{i} = 𝜶_{short} + 𝜷_{short}* gov_{i} + error$

• $𝜷_{short}$ will be:

• $𝜷_{short} = 𝜷_{long}$ + bias

• $𝜷_{short} = 𝜷_{long}$ + relationship between omitted (omitted) and included (Gov) * effect of omitted in long (δ)

• Where: relationship between omitted (omitted) and included (Gov) is: $Omitted = 𝜶 + ϕ *gov_{i} + u$
• Thus, OVB is: $𝜷_{short} – 𝜷_{long} = ϕ * δ$

• See an example in r here

## 3) Specification error

The third source of bias is: Specification error

• Even if we could perfectly measure gov and all relevant covariates, we would not know for sure the functional form through which each influences q

• Functional form: linear? Quadratic? Log-log? Semi-log?
• Misspecification of x’s is similar to OVB

## 4) Signaling

The fourth source of bias is: Signaling

• Perhaps, some individuals are signaling the existence of an X without truly having it:

• For instance: firms signaling they have good governance without having it
• This is similar to the OVB because you cannot observe the full story

## 5) Simultaneity

The fifth source of bias is: Simultaneity

• Perhaps gov and some other variable x are determined simultaneously

• Perhaps there is bidirectional causation, with q causing gov and gov also causing q

• In both cases, OLS regression will provide a biased estimate of the effect

• Also, the sign might be wrong

## 6) Heterogeneous effects

The sixth source of bias is: Heterogeneous effects

• Maybe the causal effect of gov on q depends on observed and unobserved firm characteristics:

• Let’s assume that firms seek to maximize q
• Different firms have different optimal gov
• Firms know their optimal gov
• If we observed all factors that affect q, each firm would be at its own optimum and OLS regression would give a non-significant coefficient
• In such case, we may find a positive or negative relationship.

• Neither is the true causal relationship

## 7) Construct validity

The seventh source of bias is: Construct validity

• Some constructs (e.g. Corporate governance) are complex, and sometimes have conflicting mechanisms

• We usually don’t know for sure what “good” governance is, for instance

• It is common that we use imperfect proxies

• They may poorly fit the underlying concept

## 8) Measurement error

The eighth source of bias is: Measurement error

• “Classical” random measurement error for the outcome will inflate standard errors but will not lead to biased coefficients.

• $y^{*} = y + \sigma_{1}$
• If you estimante $y^{*} = f(x)$, you have $y + \sigma_{1} = x + \epsilon$
• $y = x + u$
• where $u = \epsilon + \sigma_{1}$
• “Classical” random measurement error in x’s will bias coefficient estimates toward zero

• $x^{*} = x + \sigma_{2}$
• Imagine that $x^{*}$ is a bunch of noise
• It would not explain anything
• Thus, your results are biased toward zero

## 9) Observation bias

The ninth source of bias is: Observation bias

• This is analogous to the Hawthorne effect, in which observed subjects behave differently because they are observed

• Firms which change gov may behave differently because their managers or employees think the change in gov matters, when in fact it has no direct effect

## 10) Interdependent effects

The tenth source of bias is: Interdependent effects

• Imagine that a governance reform that will not affect share prices for a single firm might be effective if several firms adopt

• Conversely, a reform that improves efficiency for a single firm might not improve profitability if adopted widely because the gains will be competed away

• “One swallow doesn’t make a summer”

## 11) Selection bias

The eleventh source of bias is: Selection bias

• If you run a regression with two types of companies

• High gov (let’s say they are the treated group)
• Low gov (let’s say they are the control group)
• Without any matching method, these companies are likely not comparable

• Thus, the estimated beta will contain selection bias

• The bias can be either be positive or negative

• It is similar to OVB

## 12) Self-Selection

The twelfth source of bias is: Self-Selection

• Self-selection is a type of selection bias

• Usually, firms decide which level of governance they adopt

• There are reasons why firms adopt high governance

• If observable, you need to control for
• If unobservable, you have a problem
• It is like they “self-select” into the treatment

• Units decide whether they receive the treatment of not
• Your coefficients will be biased