Class Notes in Statistics and Econometrics Part 33 pptx
Class Notes in Statistics and Econometrics Part 33 pptx
... derivation of (65.4.3) again. The Σ Σ Σ −1 in numerator and denominator cancel out since they commute with Z. defining Ω Ω Ω = Σ Σ Σ ⊗ I, this “commuting” is the formula 66.3. INDIRECT LEAST SQUARES ... matrix of instruments is W = x 1 x 2 x 3 , i.e., x 1 and x 3 are instruments for themselves, and x 2 is an instrument for y 1 . Now remember the IV normal equation in this simplifi...
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Class Notes in Statistics and Econometrics Part 2 pptx
... intersection of a declining set sequence. And a converging sequence of nonnegative ε i which is not declining has a declining subsequence. A cumulative distribution function need not be continuous ... I.e., all the randomness is shunted off into the process of selecting an element of U . Instead of being an indeterminate function, it is defined as a determinate function of the random ω. It is...
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Class Notes in Statistics and Econometrics Part 9 pptx
... variables y t and y c , which, evaluated at individual ω, indicate the responses this individual would give in case he was subject to the treatment, and in case he was or not. Rubin defines y t − ... detail in order to ge t at the essence of things. Holland defines: x is not a Granger cause of y relative to the information in z (which in the timeseries context contains the past va...
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Class Notes in Statistics and Econometrics Part 16 pptx
... different linear combinations, and to ask: Which linear combination of the eleme nts of ˆ β is affected most if one drops the ith observation? Interestingly and, in hindsight, per- haps not surprisingly, ... become part of the standard procedures. Problem 373. 1 point Define multicollinearity. • a. 2 points What are the symptoms of multicollinearity? • b. 2 points How can one detect multi...
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Class Notes in Statistics and Econometrics Part 25 pptx
... : Apparel and Related Pro ducts ∗ 24 : Lumber and Pro ducts ∗ 25 : Furniture and Fixtures ∗ 26 : Paper and Allied Products 27 : Printing and Publishing Industries ∗∗ 28 : Chemicals and Allied ... noncorporate income + noncorporate inventory valuation adjustment + government subsidies + net interest. Denomina- tor: capital stock + inventories (the inventories come in part from...
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Class Notes in Statistics and Econometrics Part 1 pdf
... 1 Preface These are class notes from several different graduate econometrics and statistics classes. In the Spring 2000 they were used for Statistics 6869, syllabus on p. ??, and in the Fall 2000 for ... in B ∩ C, therefore it is also in the righthand side. If ω /∈ A and it is in the righthand side, then it must be both in B and in C, therefore i t is in the l...
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Class Notes in Statistics and Econometrics Part 3 pdf
... counter. They are hiding in the back, and whenever a customer steps up to the counter and rings the bell, they toss a coin. If the coin shows head, Herbert serves 152 5. SPECIFIC RANDOM VARIABLES will ... Pr[y=m and x=n]? Use a trick: express this intersection as the intersection of independent events. For this define z as the number of events in the interval (t, 1]. Then {y=m and...
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Class Notes in Statistics and Econometrics Part 4 pps
... argument inside. 220 8. VECTOR RANDOM VARIABLES 1), and if cov[x, y] = 0, then x and y are independent. (I.e., in this respect indicator variables have similar properties as jointly normal random ... independent. Problem 136. If the vector random variables x and y have the property that x i is independent of every y j for all i and j, does that make x and y independent random ve...
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Class Notes in Statistics and Econometrics Part 5 pps
... the inner integral becomes − 1 2π e −t ∞ 0 = 1 2π ; therefore the whole integral is 1. Therefore the product of the integrals of the marginal densities is 1, and since each such marginal integral ... First we will introduce the multivariate standard normal, which one obtains by applying only operations (1) and (2), i.e., it is a vector composed of independent univariate standard norma...
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Class Notes in Statistics and Econometrics Part 6 pot
... chapter 3] According to Friedman’s permanent income hypothesis, drawing at random families in a given country and asking them about their income y and consumption c can be modeled as the independent ... point Therefore z 3 is a linear combination of y 1 and y 3 only. Compute its coefficients. • d. 1 point How does the joint distribution of z 1 , z 2 , and z 3 differ from that of y 1 ,...
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