Econometrics Midterm & Final Exam Questions and answers

Econometrics Midterm & Final Exam Questions and answers Econometrics -Answer-The science of testing economic theories. Also it works as a set of tools used for forecasting future values of economic variables as well as being the process of fitting mathematical economic models to real world data. Econometrics uses historical data to make numerical, or quantitative, policy recommendations in government and business. Y-bar -Answer-The sampling average. It is an unbiased estimator for miuY, consistent, and is very efficient. More efficient than Y1. A smaller variance than the other one means it is more efficient. Y-bar is the Best Linear Unbiased Estimator (Blue). It is the least squares estimator of miuY. Multiple Regression Analysis -Answer-Used to isolate the effect of changes (in class size) from changes in other factors such as economic background. It provides a mathematical way to quantify how a change in one variable affects another variable, holding other things constant. Price Elasticity of Demand -Answer-The percentage change in the quantity demanded resulting from a percent increase in prices. Forecasting Inflation -Answer-The data we use to forecast inflation are the rates of inflation and unemployment in the United States. Phillips curve -Answer-A currently low value of the unemployment rate is associated with an increase in the rate of inflation over the next year. Causal Relationships (effect) -Answer-An action is said to cause an outcome if the outcome is the direct result or consequence, of that action. A specific action leads to a specific, measurable consequence. It is the effect on an outcome of a given action or treatment as measured in an ideal randomized controlled experiment. Randomized Controlled Experiment -Answer-a clinical trial in which the subjects are randomly distributed into groups which are either subjected to the experimental procedure (as use of a drug) or which serve as controls—called also randomized clinical trial. Control group & treatment group -Answer-Control receives no treatment and treatment receives the treatment. Experimental Data -Answer-Comes from experiments designed to evaluate a treatment or policy or to investigate a causal effect. Observational Data -Answer-Data obtained by observing actual behavior outside an experimental setting. They are collected using surveys, administrative records, etc. Cross sectional Data -Answer-Data on different entities - workers, consumers, firms, governmental units, and so forth - for a single time period. We can learn about relationships among variables by studying differences across people, firms, or other economic entities during a single time period. Example: Class sizes in schools. #1 Observation Number -Answer-An arbitrarily assigned number that organizes the data. Time Series Data -Answer-Are data for a single entity (person, firm, or country) collected at multiple time periods. Example: Data sets on the rates of inflation and unemployment in the United States is an example of a Time Series Data Set. The data set contains observations on two variables (inflation and unemployment) for a single entity (The United States) for 183 time periods. #2 Panel Data (Longitudinal Data) -Answer-Data for multiple entities in which each entity is observed at two or more time periods. Example: Our data on cigarette consumption and prices. Panel data can be used to learn about economic relationships from the experiences of the many different entities in the data set and from the evolution over time of the variables for each entity. Ch.1 Outcomes -Answer-The mutually exclusive potential results of a random process. (comp. crashing once, twice, or never, but only one of those outcomes will actually occur making them mutually exclusive. Ch.2 Probability -Answer-It is the proportion of the time that the outcome occurs in the long run. Sample Space -Answer-The set of all possible outcomes. Event -Answer-It is a subset of the sample space, that is, an event is a set of one or more outcomes. Random Variable -Answer-It is a numerical summary of a random outcome. Discrete And Continuous Random Variables -Answer-A discrete random variable take only a discrete set of values, like 0,1,2,..., whereas a continuous random variable takes on a continuum of possible values. Probability Distribution -Answer-The Probability distribution of a discrete random variable is the list of all possible values of the variable and the probability that each value will occur. They sum to 1 Cumulative Probability Distribution (Commutative distribution function, c.d.f. , or a cumulative distribution. -Answer-This is the probability that the random variable is less than or equal to a particular value. Bernoulli Random Variable -Answer-This is a binary random variable where the outcomes are 0 or 1. Its probability distribution is called the Bernoulli distribution. Probability Density Function (p.d.f. , Density Function, or simply Density) -Answer- Summarizes the probability of a continuous random variable. The area under the probability density function between any two points is the probability that the random variable falls between those two points. Expected Value -Answer-The expected value of a random variable Y, denoted E(Y), is the long run average value of the random variable over many repeated trials or occurrences. The expected value of a discrete random variable is computed as a weighted average of the possible outcomes of that random variable, where the weights are the probabilities of that outcome. Expectation Of Y Or The Mean -Answer-denoted as miuY. Variance -Answer-The variance of a random variable Y, denoted var(Y), is the expected value of the square of the deviation of Y from its mean: var(Y) = E[(Y - miuY)^2]. It measures spread. It is the probability-weighted average of the squared difference between M and its mean. Cannot be negative. A small variance indicates that the data points tend to be very close to the mean (expected value) and hence to each other, while a high variance indicates that the data points are very spread out around the mean and from each other. Standard Deviation -Answer-Measure of spread, which is the square root of the variance and is denoted with sigmaY. Skewness -Answer-Lack of symmetry of a distribution. It provides a mathematic way to describe how much a distribution deviates from symmetry. = (E[(Y - miuY)^3])/(sigmaY^3). Changing Y does not change its skewness. Long left tail means skewness is negative and positive for right tail. 1-3 moments of Y Kurtosis -Answer-Measures how thick, or "heavy", are the tails of a distribution. It measures how much mass is in its tails and, therefore, is a measure of home much of the variance of Y arises from extreme values. The greater Kurtosis of a distribution, the more likely there are outliers and large tails. Kurtosis cannot be negative. Normally distributed means you have a kurtosis of 3 and unit free. Changing Y does not affect kurtosis. 1-4 moments of Y. = (E[(Y - miuY)^4])/(sigmaY^4) Moments Of Distribution -Answer-The mean, variance, skewness, and kurtosis, are all based on what are called the moments of distribution. Outlier -Answer-An extreme value of Y is called an outlier. Leptokurtic -Answer-A distribution with kurtosis exceeding 3. This is heavily tailed. Rth Moment -Answer-The expected value of Y^r is called the rth moment of the random variable Y. The rth moment of Y is E(Y^r). Joint Probability Distribution -Answer-Joint Probability Distribution of two discrete random variables, say X and Y, is the probability that the random variables simultaneously take on certain values, say x and y. = Pr(X=x, Y=y). Marginal Probability Distribution -Answer-Marginal Probability Distribution of a random variable Y is just another name for its probability distribution. It is used to distinguish the distribution of Y alone (Marginal Distribution) from the joint distribution of Y and another random variable. Compute by adding up the probabilities of all possible outcomes for which Y takes on a specific value. Conditional Distribution -Answer-The distribution of a random variable Y conditional on another random variable X taking on a specific value is called the conditional distribution of Y given X. Conditional Expectation -Answer-The Conditional Expectation of Y given X, also called the Conditional Mean of Y given X, is the mean of the conditional distribution of Y given X. The conditional expectation id the expected value of Y, computed using the conditional distribution of Y given X. Law Of Iterated Expectations -Answer-E(Y) = E[E(Y given X)]. It is computed using the conditional distribution of Y given X and the outer expectation is computed using the marginal distribution of X. Conditional Variance -Answer-Var( Y given X=x ) = sigma [Yi - E( Y given X=x)]^2 Pr ( Y=yi given X=x ). Independence -Answer-X and Y are independent if knowing the value