Financial Econometrics

1. Formulate Research Question

2. Literature Review

3. Develop a theory

4. Formulate hypothesis

5. Design empirical tests for hypothesis testing

6. Interpret results

logically coherent set of ideas that can explain and predict empirical observations

1. are unambiguous

2. are simple

3. specifiy a specific relation between X and Y

4. are testable

1. archival

2. experimental

3. survey

4. qualitative

use of statistical methods to analyze economic data

1. Estimating relationships between economic variables

2. Testing economic theories and hypotheses

3. Forecasting (macro) economic variables

4. Evaluating and implementing government and firm policies/actions

1. Covariation -> variables of interest move together

2. Cause prior to effect -> causal event should occur before effect event

3. Absensce of plausible rival hypotheses -> no endogeneity concerns (omitted variables)

1. cross-sectional data -> many different variables at one point of time (observations are more or less independent)

2. time-series data -> observations of variable over time (serially correlated)

3. pooled cross sections -> combination of cross sectional data (drawn independently)

4. panel/longitudinal data -> same cross-sectional date followed over time

abstract idea which is not directly obserable or measureable

observable item which can assume different values and is used to measure a theoretical construct

degree to which variable captures the underlying theoretical construct it is supposed to measure

-> internal & external validity

degree of confidence that tested causal relationship is trustworthy and not influenced by other factors

extent to which studied results can be applied to ouhter situations, groups or events

degree to which a measurement provides consistent estimates

estimate of population parameter based on random sample from population

sample averages converge to the population mean as sample size increases & standard error decreases as sample size increases

even if population distribution is not nomral distributed -> sampling distribution of sample means will be approximately normal distributed (if sample size is large enough)

estimate of standard deviation of the sampling distribution of a statistic

-> z.B. sample standard error of means

1. draw a sample of n observations from the population

2. calculate sample statistic

3. calculate standard error os sample statistic

4. Calculate t-statistic

5. comparision t-statistic with critical values

rejecting null hypthesis that is actually true -> significance level alpha

accepting null hypothesis that is actually false

probability type 1 error

probabability of correctly rejecting null hypothesis when its indeed false

= 1 - beta

constant alpha

1. increasing sample size n

2. effect size is larger

Increasing alpha (5% -> 1%) -> higher risk type 2 error (lower power)

vs.

decreasing alpha (1% -> 5%) -> higher risk type 1 error but also higher power

1. Strong publication bias for significant results

2. P-Hacking -> play around with specifications until you get a result with significant p-values

3. HARKing -> hypotheses are formulated after reviewing data and sold as ‘a priori’

4. Outcome swichting -> check for various outcome variables and report only significant ones

variable that explains mechanism between independent und dependent variable

factors that strengthen or weaken the relation between dependent and independent variable

capture the effects of other factors (Z) that are related to X, Y or both but are not in direct interest when examining the effect of X on Y

indicates what would happend to the dependent variable if under identical circumstances the independent variable wouldn’t have changed

1. measure the change of Y before to after change in X

2. measure the change of Y if X had not changed (counterfactual)

3. test whether the difference is statistically significant of both measurements

1. presence of omitted correlated variables

2. reverse causality or simultaneity

3. measurement error in the independent variables

replace y and each variable x with a standardized version -> subtract mean and divide be standard deviation

-> coefficients reflects standard deviation change of y for on standard deviation change in x

causel inferences are difficult to make due to endogeneity concerns

1. Z is correlated with X and affects Y -> incl. otherweise endogeneity

2. Z is correlated with Y but not with X -> incl. to reduce overall error term (more of Y is explained)

3. Z is correlated with X but not with Y -> excl. because multicollinearity inflates standard error of regression coefficients

1. no estimations of the effect of certain variables that are constant within the level of fixed effects

2. reduction of variation in dataset and less precision -> equivalent to de-meaning all variables

whatever happened to control group over time would also have happened to treated group in absence of treatment -> parallel trends

1. treated & control group should have generally similar characteristic

2. treated & control grop had similar trajectories for the dependent variable before treatment