# Models and Their Specification

Suppose the focus of the analysis is to consider the behavior of the n x 1 vector of random variables wt = (w1t, w2t,…, wnt)’ observed over the period t = 1, 2,…, T. A model of wt, indexed by Щ-, is defined by the joint probability distribution function (pdf) of the observations

 + exp[(Zfe – ZitYy2 + Y 1(yis-1 – yi, t+1) + Y 1(yis+1 – yi, t-1)]1(t – s ^ 3)

(16.30)

 are unemployed in January and remain unemployed in December too;

 are unemployed in January and find a job before December.

 MC tests based on pivotal statistics: an exact randomized test procedure;

• MC tests in the presence of nuisance parameters:

(a) local MC p-value,

(b) bounds MC p-value,

(c) maximized MC p-value;

• MC tests versus the bootstrap:

(a) fundamental differences/similarities,

(b) the number of simulated samples: theory and guidelines;

 Let z = (X1,…, Xm, Y1,…, Yn) and s = m Xf 1X – n Щ=1 Y.

• Obtain all possible Q = (n + m)! permutations of z, z(1),…, z(Q), and calculate the associated "permuted analogs" of s

 From the observed data, compute:

(a) the test statistic S0, and

(b) a restricted consistent estimator P0n of 0.

 Compute 10 and 1, the restricted and unrestricted SURE (iterative) MLE.

• Compute 1 „ as the unconstrained (OLS) estimate of 1 in the "nesting" MLR model.

• Compute Л* = 110|/| 11 and LR* = n 1п(Л*).

• Draw 99 realizations from a multivariate (n, 3, I) normal distribution: U(1), U(2), …, U(p) and store.

• Consider the linear constraints



t-S

t=1