Econometrics

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In a simple random sample of size N from a given population:

- Each member of the population is equally likely to be in the sample - Every possible sample of size N from this population has an equal chance of being selected

discrete random vairable

- countable number of possible values, such as 0,1, 2

what does the standard error value show

- if an estimator has a large standard deviation, there is a higher probability that an estimate will be far from its mean - if an estimator has a small standard deviation, there is a higher probability that an estimate will be close to its mean

selection bias

- occurs when a sample selection systematically excludes or underrepresents certain groups - selection bias often happens when we use a convenience sample consisting of data that are readily available

survivor bias

-we necessarily exclude members of the past population who are no longer around - in a retrospective study (looks at past data for a contemporaneously selected sample)

what is difference between estimate and estimator?

Estimator- is a mathmatical technique applied to a sample of data to produce an estimate of the true population regression coefficient Estimate - is the computed value of a population regression coefficient by an estimator OLS is an estimator The Bs produced by OLS are estimates

what does a higher R^2 mean

The higher the R^2 is, the closer the estimated regression equation fits the sample

Econometrics

econometrics is the quantitative measurement and analysis of actual business and economic phenomena. Tries to quantify theoretical relationships

Intuition behind CLT

even if population doesn't have a normal distribution, the sampling distribution of the mean will approach a normal distribution as the sampling size increases

true or false: the goal is to maximize adjusted R^2

false

should the coefficient be 0 for a nonsensical variable?

in theory yes. but with any given sample there is some random correlation and provides a minor explanation. typical to get non 0 estimated coefficient even for nonsensical variable. only if new coefficient is exactly 0

adjusted R^2

is constructed to "correct" or penalize for more variables comparing 2 regressions with same dependent variable

Level of significance

level of significance indicates the probability of observing an estimated t-value greater than the critical value if the null hypothesis were correct Lower the significance level the better

residual

observation of dependent variable and value estimated from regression equation) The residual is an estimate of the error term (ε)

Self-selection bias-

occur when we examine data for a group of people who have chosen to be in that group

- sample:

part of the population that we actually observe

The exact distribution of t depends on

sample size -As sample size increases, we are increasingly confident of the accuracy of the estimated standard deviation -As the sample size increases N→ infinity, the sample standard deviation approaches the population standard deviation s→σ, and the distribution of t approaches the normal distribution, Z

population:

the entire group of items that interest us

Lower the degrees of freedom,

the less reliable the estimates are likely to be

Recall that efficiency is a measure of

the quality of an estimator. An inefficient estimator has a larger variance and results in a less precise estimate of the "true" parameter value. An inefficient estimator may then result in incorrect inference in a hypothesis test. An efficient estimator is also the minimum variance unbiased estimator (MVUE) and therefore "best".

nonresponse bias

the systematic refusal of some groups to participate in an experiment or to respond to a poll

Explained sum of squares (ESS)

variation that can be explained by the regression

Residual Sum of Squares (RSS):

variation that cannot be explained by the regression

If there is a nonsensical variable, how do we expect R^2 to be impacted

weakness of R^2 is ading a variable will decrease (Never increase) the summed square residual even if its a nonsensical variable. therefore, if you add nonsensical variable, usually increase R^2

if add a new independent variable, why does other coefficients change

when not including we are holding that variable constant, when we include it we are taking it into account

3 reasons for Econometrics

1) Describing Economic Reality - econometrics can quantify and measure marginal effects and estimate numbers for theoretical equations - ex: consumer demand - relationship between quantity demanded (Q) and Price 9P), price of subsittitue, and disposable income 2) Testing Hypothesies about economic theory and policy - much of economics involves building theoretical models and testing them against evidence 3) Forecasting Future Economic Activity - the most difficult use of econometrics is to forecast or predict the future using past data - Economists use econometrics to forecast a variety of variables (GDP, sales, inflation, etc) - accuracy of forecasts depends in large measure on the degree to which the past is a good guide to the future

7 classical assumptions

1) Linear in parameters 2) errors have 0 mean 3) errors uncorrelated with regressors 4) no perfect multicollinearity 5) no heteroskedasticity 6) no serial correlation 7) errors are normally distributed

4 sources of variation:

1) omitted or left-out variables 2) measurement error in the data 3) underlying theoretical equation that has a different functional form (or shape) than the one chosen for the regression 4) purely random and unpredictable behavior

define Central Limit Theorem

CLT- "if Z s a standardized sum of N indep identically distributed random variables with a finite, nonzero standard deviation, then the probability distribution of Z approaches the normal distribution as N increases" - even if population doesn't have a normal distribution, the sampling distribution of the mean will approach a normal distribution as the sampling size increases (Intuition behind CLT)

"Strictly speaking, what is the best interpretation of a 95% confidence interval for the mean?

If repeated samples were taken adn 95% interval was compued for each sample, 95% of the intervals would contain the population mean.

Z-score

Measures how many standard deviations X is above or below its mean -- Z score indicates the number of standard deviations a raw score lays above or below the mean. - Z score table shows % of values to the left of a given z-score on a standard normal distribution - to find score that is to the righ tof the mean - have to do 1- Z score found from table

what is mean and standard deviation of a standardized random variable

No matter what the initial units of X, the standardized random variable Z has a mean of 0 and standard deviation of 1

Omitted condition

Omitted condition- event not represented by a dummy variable - the omitted condition forms the baseline against which the included condition(s) are compared

how is it possible for adjusted R^2 decrease but R^2 increase

R^2 is adjusted for degrees of freedom vs adjusted R^2 is not

type I error

Type 1: reject a true null hypothesis Ex: H0: 0 HA: >0 assume true B is not positive but our estimate leads us to reject the null hypothesis

Type II error

Type 2: Do not reject a false null hypothesis Assume true B is positive but our estimate leads us to not (or fail to) reject the null hypothesis

^R2

^R2 will increase, decrease, or stay the same when a variable is added to an equation depending on whether the improvement in ft outweighs the loss of degrees of freedom ^R2 can be used to compare the fits of equations wththe same dependent variable ^R2 cannot be used to compare the fits of the equations with different dependent variables or dependent variables

stochiastic error term

added to a regression equatio to account for variation in Y that cannot be explained by the included X(s)

One issue w R^2 is adding another indep variable to an equation can never decrease R^2

adding a variable will not change TSS Adding another variable will, in most cases, decrease RSS and increase R^2


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