### Table 6. Long-horizon Regression Estimates Null Hypothesis: No Prior Restrictions on Integration Status (1973q2-1994q4)

1997

"... In PAGE 13: ... Predictability of the Swiss Franc rate is robust to the sample, although the OUT/RW statistics indicate predictability at all horizons and the DM(A) at short horizons. In Table6 , we report the extended sample results with p-values tabulated under the null that or follow an unrestricted VAR. While the p-values are somewhat larger for both in-sample and out-of-sample statistics, they are qualitatively very similar to Table 5.... ..."

Cited by 2

### Table 4 Di use Prior Posterior Means and Standard Deviations for Coe cients of Equations (2) and (3) with Coe cients Restricted to be the Same Across Countries

"... In PAGE 10: ... The variables are then logged, rst- di erenced, and multiplied by 100 to convert to growth rates. Estimation results for the AR(3)LI model in equation (1) are presented in Table 3, and coe cient posterior means and standard deviations for the models in (2) and (3) with coe cients restricted to be equal across countries are presented in Table4 . On computing the roots of the AR(3) process for the countries apos; output growth rates from equation(2),6 we obtain one real root equal to .... ..."

### Table 6: Restricted Transition Model; All Failures

"... In PAGE 27: ...this is a special case of the transition model, and we have already seen that the effect of democracy on state failure changes dramatically depending on whether we are modeling entry into failure or exit from failure, we know the transition model is preferred to the restricted transition model for this data set and specification. But even so, it is interesting to compare the restricted transition results, shown in Table6 , with our prior results. Table 6: Restricted Transition Model; All Failures... ..."

### Table 2: Prior probabilities for additive and innovation outliers

1996

"... In PAGE 5: ... This restriction is achieved by setting the prior probability of all combination outliers to zero and greatly simpli es the computation. For example, Table2 shows the prior distribution for Kt used in the sludge example in Section 5. McCulloch and Tsay (1993, 1994) use a mixture of two components to model additive outliers, with one component having very large variance, but we have found that a multicomponent mixture does better at picking up outliers of di erent sizes.... In PAGE 14: ... Sampling scheme 1 in Section 3 is applied to a stationary autoregressive model with a maximal order p = 10 and no seasonal component. The prior distribution for Kt is given in Table2 , with additive and innovation outliers not allowed to occur simultaneously. Table 3 gives the prior probability that J1j = 1 for j = 1; : : :; 10.... ..."

Cited by 10

### Table 6. Restrictions on cointegrating space.

1995

"... In PAGE 11: ...able 7. Singular values of Australian model, JJ94 Table 3. J 0( 0) J 0(^ )r3; r10 I(^ )r3; r10 J 0(^ )R3; R10 I(^ )R3; R10 w1 3:242 5:923 1:783 107 134:6 2:044 107 w22 0:21929 0:11176 5:383 0:0015419 0:00029338 w23 0:022014 0:039729 1:052 2:227 10?5 0:00049829 w24 0:011014 0:00069562 8:623 10?5 1:158 10?6 7:451 10?8 w 9:7 10?12 1:6 10?11 4:9 10?5 5:3941 10?10 7:28327 10?5 Given the strong similarity of m3, p and the trend, there could be some concern about the ability to identify the cointegrating vectors. Estimation of the restriction on the cointegrating vectors presented in table 3 of JJ94 (see Table6 ) bears this out. Using Algorithm 1, PcFiml is able to warn prior to estim- ation that the vectors are exactly identified, so that no estimation is required for the test, just a rotation.... ..."

Cited by 4

### Table 2 Posterior Inclusion Probabilities Across Parameter Priors Model Prior = Uniform

2007

"... In PAGE 15: ... It thus seems possible that the BMA results would vary considerably between priors. Table2 reports the BMA posterior inclusion probabilities for all 12 prior distributions applied to the growth dataset. Jeffreys (1961) proposed rules of thumb, refined by Kass and Raftery (1995), suggesting that the evidence for a regressor having an effect is either weak, positive, strong, or decisive when the posterior inclusion probabilities range from 50-75%, 75- 95%, 95-99%, and gt; 99%, respectively.... In PAGE 16: ... Figure 2 shows scatterplots of posterior inclusion probabilities generated by the various priors against our baseline prior (Prior 1). Since Prior 1 was the most optimistic, with 22 candidate regressors showing an effect in Table2 , it is no surprise that most of the points in the scatterplots lie above the 45 degree line, indicating generally higher posterior inclusion probabilities for each regressor under Prior 1 as compared to other priors. More importantly, however, the scatterplots highlight not only that Prior 1 is more optimistic, but also how the differences between Prior 1 and alternative priors increase as the implied g-prior diverges.... In PAGE 16: ... Priors 1, 6, and 12 have relatively similar results, but most other priors show differing effects implied by the priors. Alternatively, one might be tempted to interpret Table2 as suggesting that 6 regressors (Confucius, Initial GDP, Life Expectancy, Rule of Law, Sub-Saharan Africa dummy, and Equipment Investment) are robustly related to growth, since there is clear evidence for an effect for each of these regressors across all priors. We view this interpretation as misguided because the selection criterion based on the lowest common denominator is inappropriately conservative.... In PAGE 19: ... This leads not only to fewer regressors that surpass the effect-threshold, but also to a different set of effective regressors. The restrictive model prior has the least impact on Prior 11; for this prior, the Rule of Law variable loses significance but otherwise the results are identical to Table2 . Thus forcing BMA to increase the weight on smaller models and penalize larger models affects priors differently: it can change the number of candidate regressors that pass the effect-threshold, and it can lead to different regressors with high inclusion probabilities.... ..."

### Table 1: A summary of the restrictions we impose to capture revision and update.

1999

"... In PAGE 29: .... Revision considers only total preorders, while update allows partial preorders. Our framework suggests a di#0Berent approach to categorizing the di#0Berences between revision and update #28and other approaches to belief change#29: focusing on the restrictions that have to be added to basic BCSs to obtain systems in C R and C U , respectively. In particular, we focus on three aspects of a system: #0F How does the environment state change? #0F How does the agent form her initial beliefs? What regularities appear in the agent apos;s beliefs at the initial state? #0F How does the agentchange her beliefs? Table1 summarizes the answers to these questions for revision and update; it highlights the di#0Berent restrictions imposed by each. Revision puts a severe restriction on changes of the environment #28more precisely,onhowwe describe the environment in the language#29 and a rather mild restriction on the agent apos;s prior beliefs #28they must form a total preorder#29.... In PAGE 31: ... #28See #28Fried- man amp; Halpern, 1998a#29 for a more detailed discussion of this point.#29 Table1 emphasizes that, despite the well-known di#0Berences between revision and update, they can be viewed as sharing one very important feature: they both use conditioning to do belief change. Thus, wehave a common mechanism both for understanding and extending them.... ..."

Cited by 27

### Table 2: Average percentage increase of sales revenues for clients with prior loans by sector and

in The Impact of Microfinance Loans on the Clients' Enterprises: Evidence from Caja Los Andes, Bolivia

"... In PAGE 19: ... In a #1Crst set of regressions we restricted the in#1Duence of prior loans to a proportional increase in sales revenues. Table2 lists the estimated coe#1Ecients for the three sets of estimates and for each sector. Taking into account the selection e#1Bects #28columns 1 and 2#29 we #1Cnd that commerce businesses with prior loans have approximately 4#25 higher sales revenues than businesses without prior loans, production businesses have 12#25 higher sales revenues, and service businesses have 16#25 higher sales revenues.... ..."

### Table 4: Algorithm comparisons on 2GM-2GM test data, with various prior assumptions for the SG algorithms.

"... In PAGE 30: ... The restricted \window sizes quot; for the SG3 and SG4 algorithms may be e ectively limiting the sample sizes and thus increasing the deviation of the sampled proportions from the expected proportions. This may explain the results, in Table4 , for the SG3 and SG4 algorithms with the equal prior assumption. 4.... ..."

### Table 4. Comparing prior structures for AIDS reporting delay example.

"... In PAGE 25: ...4. Hazard estimation Five models were estimated for the AIDS reporting delay data, using the prior structures indicated in Table4 and the discrete-time proportional-hazards likelihood from Section 2.2.... In PAGE 25: ...rs on and k as explained in Section 4.1. While the likelihood function involved estimates of the reporting delay distribution at 32 quarterly intervals, the series of models considered estimated the delay hazard at resolution of 1, 2, 4, 8 and 16 quarters, using the piecewise-constant hazard assumption to interpolate hazard values at intermediate times. As Table4 shows, Models 2 5 are restrictions of Model 1 which x \lower-level quot; subsets of the \split quot; parameters Rm;p at 0.5, e ectively estimating the hazard function at lower resolution.... In PAGE 30: ... The complete data included missing data imputed through binomial and negative binomial imputation models; the DIC was evaluated as explained above based on observed and imputed data for each draw from the posterior sample. Table4 displays our calculations for the DIC for Models 1 5 in the AIDS ex- ample. Interestingly, we can see that pD does not fall close to the \true quot; number of increments for Models 1-3, implying less than a \full quot; reduction in uncertainty due to the model t.... ..."