# Shared Flashcard Set

## Details

Econ Spring 2017
Econ Spring 2017
46
Economics
01/20/2017

Term
 μ,σ
Definition
 μ=1/n Σ[i=1,n] x_iσ=√(1/(n-1) Σ[i=1,n] (x_i-x_bar)^2)
Term
 Emperical Rule
Definition
 68%,95%,99.7%
Term
 DeMorgan's Law
Definition
 1) Complement(AnB) =C(A)uC(B)2) Complement(AuB)=C(A)nC(B)
Term
 Distributive Law
Definition
 3) An(BuC)=(AnB)u(AnC)4) Au(BnC)=(AuB)n(Auc)
Term
 3 Axioms of Probability
Definition
 1) P(A)≥02) P(S)=13) P(A1uA2u…uAn) = Σ[i=1,n] P(Ai)
Term
 Permutation
Definition
 # of ways of ordering n distinct objects taken r at a time: P[n,r]=n!/(n-r)!
Term
 Combination
Definition
 # of combos of n objects selected r at a time: C[n,r]=(n,r)=n!/(r!(n-r)!)
Term
 Extension of mn rule
Definition
 The # of ways of partitioning n distinct objects into k distinct groups containing n1,n2,…,nk objects, respectively, where each object appears in exactly one group and Σ[i=1,k] ni=n, is N= (n, n1 n2 … nk)=n!/(n1!n2!...nk!)
Term
 Conditional probability
Definition
 P(A|B)=P(AnB)/P(B)
Term
Definition
 P(AnB)=P(A)P(B|A) [if A,B are independent, =P(A)P(B)]P(AuB)=P(A)+P(B)-P(AnB) [if A,B are mutually exclusive, =P(A)+P(B)]
Term
 Law of total probability
Definition
 P(A)=Σ[i=1,k] P(A|Bi)P(Bi)
Term
 Bayes' Rule
Definition
 P(Bj|A) = P(A|Bj)P(Bj)/(Σ[i=1,k] P(A|Bi)P(Bi))
Term
 expected value, variance
Definition
 E(Y)=μ=Σ[y] yP(y)V(Y)=σ^2=E[(Y-μ)^2]=E[Y^2]-μ^2
Term
 Moment
Definition
 Moment: a set of numerical measures that describe or uniquely determine P(Y) under certain conditions The kth moment of the RV Y taken around the origin is E(Y^k) and is written as μ'_k
Term
 Skewness, kurtosis
Definition
 γ_1=(E(Y-μ)^3)/σ^3 (γ can be positive, negative or 0/symmetric)kurtosis replaces 3 with 4
Term
 Binomial experiment
Definition
 1) n identical, fixed trials2) each trial results in 1 of 2 possible outcomes3) probability of success is p, failure is 1-p (aka q)4) trials are independent5) R.V. Y is the # of successes
Term
 Binomial probability
Definition
 P(Y)=(n,y)(p^y)(q^(n-y)) E(Y)=npV(Y)=npq
Term
 Properties of CDF
Definition
 1) F(-∞)=02) F(∞)=13) F(*) is non-decreasing in y ST if y1
Term
 Rules of non-cooperative games
Definition
 1) Players ξ={1,2,…,I} where I≥22) Moves, feasible actions Ai=[0,∞)3) Order of moves: sequential or simultaneous4) Information: perfect (ie perfect recall) or imperfect5) Payoffs: preferences over outcomes
Term
 strategy
Definition
 A complete contigent play (decision rule) that specifies the player's action at every decision node s/he may encounter. Strategy profile: S={s1,s2,…,sI}
Term
 dominant strategy
Definition
 si€Si is a dominant strategy if u(si,s-i)>ui(si',s-I') A si'€Si, si'≠si and A s-i€S-i
Term
 strictly dominated
Definition
 si€Si is strictly dominated if E si'€Si ST ui(si',s-i)>ui(si,s-i) A s-i€S-i
Term
 Nash equilibrium
Definition
 There is an NE for the strategy profile S*={s1*,s2*,…,sI*} if for all i=1,…,I ui(si*,s-i*)≥ui(si',s-i*) A si€Si
Term
 Ball-Romer payoff function
Definition
 u_i = w(m/p,p_i/p)-zD_iFOC: W2(1,1)=0, SOC: W22(1,1)<0, W12>0 implies as income increases firms have an incentive to change prices
Term
 degree of real regidity
Definition
 d(Pi*/P)/d(M/P) = -W_12/W_22 = πsmall W12 can be the efficiency wage and large W22 is an extreme example of monopolistic competition
Term
 Ball-Romer private cost
Definition
 PC
Term
 Ball-Romer measure of nominal rigidity
Definition
 the band where price does NOT change is (1-x*,1+x*)SO Taylor Approximation is PC≈[-(W_12)^2 / 2W_22]x^2x*=√[(-2zW_22)/(W_12)^2] = √(2z/πW_12)
Term
 C-J SNE
Definition
 Symmetrical Nash Equilibria: S={s€[0,E]|V_1(e,e)=0} where: e_i is an agent's action, e is an action that at the SNE where ei*(e)=e, e-bar is everyone else's action, V(*) is the payoff function, E is the finite bound to an agent's action ei
Term
 C-J SCE
Definition
 Symmetric Cooperative Equilibria: S~ ={e€[0,E]|V1(e,e)+V2(e,e)=0;V11(e,e)+2V12(e,e)+V22(e,e)<0} where if i) V2(ei,e-bar)>0 the game exhibits positive spillovers, ii) if V2(ei,e-bar)<0 the game exhibits negative spillovers, iii) if V12(ei,e-bar)>0 the game exibits strtegic complementarity, iv) if V12(ei,e-bar)<0 the game exhibits strategic substitutability, and v) if dΣej*/dθi>dei*/dθi>δei*/δθi the game exhibits multiplier effects, where θi is a parameter of i's payoff function that we assume to be equal for all i
Term
 strictly dominated mixed strategy
Definition
 mi is S.D. if E mi'€m(si) ST ui(mi',m-i)>ui(mi,m-i) A m-i€M-i(to replace mixed strategies with a pure strategy, substitute m-I for s-i)
Term
 Existence of a Nash Equilibrium
Definition
 Proposition: A NE exists if i) si is non-empty, convex and compact in R^n, ii) ui(s1,…,sI) is continuous in (s1,…,sI) and quasi-concave in si
Term
 Fixed point theorem
Definition
 If f(x) is a function of x and f(x*)=x*, then x* is a fixed point
Term
 Brouwer's Fixed Point Theorem
Definition
 Let S C R^n be non-empty, convex and compact and f:S->S be continuous, the there exists x*€S ST f(x*)=x*
Term
 Integral ln(x)
Definition
 xln(x)-x+c
Term
 probability density function
Definition
 f(y)=dF(y)/dy=F'(y) p(a≤y≤b) = integral[a,b]f(y)dy=F(b)-F(a)
Term
 E(Y), E[g(y)] (area under a curve)
Definition
 integral [-∞,∞] yf(y)dy, integral [-∞,∞] g(y)f(y)dy
Term
 Uniform continuous distribution function, also mean & variance
Definition
 f(y) = { 1/(θ2-θ1) for θ1≤y≤θ2; 0 otherwise} E(Y)=(θ1+θ2)/2; V(Y)=σ^2=(θ2-θ1)^2/12
Term
 z
Definition
 z = (y-μ)/σ
Term
 P(y1|y2), f(y1|y2)
Definition
 P(y1|y2) = P(y1,y2)/P2(y2), provided p2(y2)>0f(y1|y2) = f(y1,y2)/f2(y2), provided f2(y2)>0
Term
 Indpendence for discrete and continuous random variables
Definition
 Discrete: P(y1,y2)=p1(y1)p2(y2)Continuous: f(y1,y2)=f1(y1)f2(y2)
Term
 COV(Y1,Y2), P(Cov. Coefficient)
Definition
 "COV(Y1,Y2)=E[(Y1-μ1)(Y2-μ2)]=E[Y1,Y2]-μ1μ2, where E[Y1,Y2]=Σ[for all y1]Σ[for all y2] y1y2p(y1,y2),P(Cov. Coefficient) = COV(Y1,Y2)/σ1σ2If Y1,Y2 are indpendent then COV(Y1,Y2)=0 (BUT converse is not true)"
Term
 Conditional expectation of g(Y1)|Y2=y2
Definition
 For jointly continuous Y1, Y2: E(g(Y1)|Y2=y2) = integral [-∞,∞] g(y1)f(y1|y2)dy1; For jointly discrete Y1, Y2: E(g(Y1|Y2=y2)=Σ[all y1] g(y1)p(y1|y2)
Term
 Statistic
Definition
 A function of the observable random variables in a sample and known constants
Term
 iid
Definition
 indentically and independently distributed
Term
 CLT
Definition
 Central Limit Theorem: Let y1,…,yn be random samples from any distribution with a pop. mean of μ, and variance σ^2, then E(y-bar)=μ, V(y-bar)=σ^2/n and y-bar will have approximately a normal distribution as long as the sample size is iid and sufficiently large, aka y-bar~N(μ,σ^2/n)
Term
 E(U1), V(U1), COV(U1,U2)
Definition
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