### Table 3 Industry Price Adjustment Under Polynomial Frictions a

1999

"... In PAGE 16: ... III.3 Empirical Estimates of Pricing Decision Rules under Polynomial Frictions Estimates of the industry pricing rules under the polynomial generalization of frictions are listed in Table3 . Because the conventional two-root decision rule, m = 1, is nested in the generalized frictions model, it is interesting to note that additional lags of the dependent variable are always price forecast model for each industry is a VAR containing the equilibrium price and the prices of production inputs.... In PAGE 17: ... Without exception, all of the problems noted for the estimated decision rules under geometric frictions in Table 2 are eliminated under polynomial frictions. The percentage of explained variation, R2, is considerably higher for most industries in Table3 ; mean lags are more plausible; the assumption of serially independent residuals is retained in all industries; and the rejection probabilities in the bottom row in Table 3 indicate that the rational expectations overidentifying restrictions are not rejected at confidence levels of 95% or higher. The latter is noteworthy because rejections of rational expectations overidentifying restrictions are often interpreted as evidence of non-rational forecasting by agents or of inadequate specifications of agent forecast models of forcing terms.... In PAGE 17: ... Without exception, all of the problems noted for the estimated decision rules under geometric frictions in Table 2 are eliminated under polynomial frictions. The percentage of explained variation, R2, is considerably higher for most industries in Table 3; mean lags are more plausible; the assumption of serially independent residuals is retained in all industries; and the rejection probabilities in the bottom row in Table3 indicate that the rational expectations overidentifying restrictions are not rejected at confidence levels of 95% or higher. The latter is noteworthy because rejections of rational expectations overidentifying restrictions are often interpreted as evidence of non-rational forecasting by agents or of inadequate specifications of agent forecast models of forcing terms.... In PAGE 17: ... The latter is noteworthy because rejections of rational expectations overidentifying restrictions are often interpreted as evidence of non-rational forecasting by agents or of inadequate specifications of agent forecast models of forcing terms. Because the only difference between industry model specifications used in the side-by-side comparisons of Table 2 and Table3 is the degree of the Euler equation polynomials, m, the culprit, at least in these examples and for the statistical properties considered, is rigid priors on the specification of dynamic frictions. More intuitive insights into the dynamic effects of the higher-order lag and lead polynomials are obtained by rearranging the Euler equation to define the current period response weights to lags and expected leads of the forcing term, Etfp t+ig, implied by the industry decision rules, Etfptg = EtfA(1)A(L)?1A(B)A(BF )?1p t g; = Etf 1 X i=?1 wip t+ig; (23) where negative subscripts, i lt; 0, denote responses to lagged events and positive subscripts, i gt; 0, responses to anticipated events.... In PAGE 19: ... Procyclical margins are indicated for primary metals (SIC 33) and countercyclical margins for motor vehicles (SIC371). All significant features of the rational error corrections in Table3 are retained in Table 4, including serially independent residuals and nonrejection of the RE overidentifying restrictions... ..."

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### Table 2. Speedup in Worst-Case Execution Time for Optimized Virtual Table Algorithm

"... In PAGE 5: ... However, for the OVTA, the optimiza- tion over VTA depends completely on the characteristics of the generator polynomial chosen. Table2 shows the improvement over the VTA for several different polyno- mials (refer to Section 4 for a description of CRC32sub8 and CRC32sub16) . Note that for the particular CRC24 and CRC32 polynomials we used for our experiments, the OVTA has no improvement at all over the VTA.... ..."

### Table 6 Interpreting the Walsh Coefficients

"... In PAGE 3: ... t j Sign of w(j) in reward values R(a(t)) 0 0 + 1 1 - + 2 2 3 - + + - - - + + 3 4 5 6 7 - + + - + - - + - + - + + - + - - - + + + + - - - - - - + + + + Table 5 Note that it parallels the procedure of the inverse Walsh transform. Rewards for the Walsh canonical form of the task shown in Table 2 are shown in Table6 . Note that a one-step greedy approach to this problem will yield a sub-optimal reward value of 13.... In PAGE 3: ... Its coefficient represents the joint reward gaining effect of actions at time steps 1 and 3. To see how order and can be used to interpret the complexity of a RL task, once again consider the task shown in Table 2, its Walsh coefficients in Table 4, and its Walsh canonical representation in Table6 . Orders and defining lengths for partitions in this problem are noted in Table 7.... ..."

### Table 6: Predicting Successful Adjustments - A Few Simple Specifications

"... In PAGE 18: ... The main variable of interest is Exchange Rate (t-1, t-2), the growth in the exchange rate in the two years preceding the adjustment.27 In Table6 we present results for the sub- sample of fiscal adjustments, whereas Tables 7 and 8 will present results for the whole sample, including year and country dummies. The control variables are: - Level of Public Debt (t-1), that is, Government Net Financial Liabilities as percent of GDP in the year preceding adjustment; - Change in Primary Deficit (t-2, t-1), the change in the primary deficit in the two years preceding adjustment; - GDP growth (t-1), the rate of growth in real GDP the year before the adjustment; - Change in Spending (t), the contemporaneous change in primary public spending, corrected for the business cycle.... In PAGE 20: ... Nevertheless, the small size of the coefficient in this and the other specifications confirms that money supply is not a key variable in determining success. In Table6 we follow the same procedure and specification to examine the impact of exchange rates on success, examining both nominal and real exchange rates, different lags of the exchange rate (one year and two year),29 different definitions of success (two and three years following the adjustment), with and without additional controls.30 For each variable we present the percentage point change in the density function of a 1 percent change in the right-hand side variable.... In PAGE 20: ... However, throughout the specifications, the coefficient on the exchange rate variable is negative and close to significance. 30 The coefficient and its significance for the control variables is not presented in Table6 for lack of space.... ..."

### Table 5: Predicting Successful Adjustments - A Few Simple Specifications

"... In PAGE 18: ... The change in public expenditure during adjustment captures the so-called composition effect, the empirical fact that successful fiscal adjustments tend to rely on spending cuts rather than tax increases. Table5 displays the results for the impact of lagged money supply growth on the sample of adjustments. We use one and two-year lags of M1 and M2 monetary aggregates, with and without the basic controls, and 2 and 3 year definitions of success.... In PAGE 18: ...28 As can be verified, money supply 26 Except in the case of developing countries and the rate of public debt accumulation. 27 In Table5 , where the effect of lagged money supply changes on the success of adjustment is examined, we use changes in the monetary aggregates M1 and M2 instead of the exchange rate. 28 Robust standard errors use the Huber/White/sandwich estimator of variance in place of the traditional estimators.... In PAGE 20: ... Tables 7 and 8 present results for the whole sample and for EMU countries, respectively. The results are robust and consistent with those in Table5 so that the coefficient on the exchange rate is negative throughout and significant or close to significant. Remarkably, these results hold also for the US$ and DM exchange rates, which are not reported here for reasons of parsimony.... ..."

### Table 7. Varying the Order of the Polynomial in GPA

2003

"... In PAGE 27: ....13 through 3.17. There is no clear spike in the log likelihood for those who were eligible for a Cal Grant B. Table7 explores the use of alternative specifications of the polynomial in GPA. We only report the results for those financially eligible for either type of Cal Grant and those financially eligible for a Cal Grant A in 1998.... ..."

### Table 7: Predicting Successful Adjustments All observations - Effective Exchange Rate

"... In PAGE 20: ... Remarkably, these results hold also for the US$ and DM exchange rates, which are not reported here for reasons of parsimony. In Table7 , the coefficient is significant at the 10% level for the sub-sample of adjustments but becomes highly 29 In all specifications, we used the second and third years of multi-year adjustments, appropriately defining success for those years. We find that the results are weakened when only single year adjustments are considered.... ..."

### Table 2: A comparison between polynomial and geometric basis functions for interpolation. Note that geometric

in Geometric-Shock-Capturing ENO Schemes for Subpixel Interpolation, Computation and Curve Evolution

1997

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