The law of excluded third

In logic, the law of the excluded third states that the formula
"P ∨ ¬P" ("P or not-P") can be deduced from the calculus under investigation.
It is one of the defining properties of classical systems of logic.



T = 16th February 2006 L = Oxford

Regret testing

1. Choose q ∈ Qd uniformly at random.
2. Play q for s periods in succession.
3. For each action a, compute the regret r(a) from not having played action a over these s periods.
4. If maxa r(a) > τ, go to step 1; otherwise retain the current q and go to step 2.
Given any two-person game G and any ε > 0, if both players use regret testing with sufficiently large s and d and sufficiently small τ, their behaviors constitute an ε-equilibrium of G in at least 1 – ε of all play periods (Foster and Young, 2006).








PMG

The use of the Pooled Mean Groups PMG technique in taking account of parameter heterogeneity, given the relatively small sizes of data sets used in empirical growth analyses, allowing full parameter heterogeneity implies estimating many parameters, with the associated imprecision. The pooled mean groups estimator provides a middle path, it allows different short run adjustment coefficients for each cross sectional unit but restricts the long run steady parameters to be constant across. Discussing the econometric methodology: specifically the rationale and mechanics of the pooled mean groups estimator, with unconstrained autoregressive distributed lag model, implies how to obtain common long run or steady relationships between the dependent and independent variables.

The pmg estimation procedure provides a sagacious middle path between assuming identical coefficients and allowing complete parameter heterogeneity.

The pmg estimator allow the intercepts, short run coefficients and error variances to differ freely across parameters.

Pmg estimation implies that the long run coefficient (Q) is a non-linear function of the short term adjustment parameters.

source: www.ox.ac.uk - working paper


A pooled mean group analysis on aid and growth

The paper uses the pooled mean group estimator and an extended annual dataset to examine the effectiveness of aid on growth. The results indicate a significant long-run impact of aid on growth, but conditioning aid on `good` policy reduces the long-run growth rate.

Keywords: Aid impact, Economic growth, Pooled mean group estimators

Date: November 2006 | Reference number: WPS/2006-14

www.economics.ox.ac.uk