The figure depicts the impulse response responses to a neutral technology shock in the search and matching model and the sticky wage model. Also shown is a line, labeled “VAR Mean”, that shows the point estimates of the empirical impulse responses along with the 90% confidence interval. Inflation rates and the federal fund rate are annualized. There are 9 panels with 3 plots on each panel. All 9 panels have an x-axis with 2 tick marks that shows the number of periods, one at 5 and one at 10. The thick shaded area tracks the overall path of the VAR Mean line. In the top left panel, entitled “1. Output”, the y-axis has a range of -0.1 to 0.6. VAR Mean starts at 0.2 and decreases to 0.1 in period 1, then gradually increases to about 0.4 and levels off. The Stickywage line also starts at 0.2 in period 0, gradually increases to 0.35 by period 3, then slowly decreases downward to about 0.3 by period 10. The SearchM line starts at 0.15 in period 0, steadily increases to about 0.35 and then levels off to about 0.37 by period 10. The middle left panel, entitled “2. Unemployment Rate”, only shows the lines for VAR Mean and SearchM. The y-axis range is -0.15 to 0.15. Both lines have a y-intercept value (period 0) of 0.05. VAR mean increases slightly to about 0.06 in period 1, then slowly decreases to -0.08 by period 9, where it levels off for the remaining periods. SearchM decreases immediately to -0.07 by period 3, then to -0.9 by period 5. It levels off and remains constant at -0.1 for the remaining periods. The top right panel in the first row is entitled “3. Inflation” and has a y-axis with a minimum of -0.7 and a maximum of -0.1. VAR mean starts at -0.55 in period 0 and sharply increases to about -0.225 in period 1. Then, it decreases to -0.3 in period 3, then gradually increases for the remaining periods, eventually leveling off at -0.175. The SearchM and Stickywage lines start at about -0.43 and -0.40, respectively. They have very similar paths, both increasing steadily to -0.2 by period 4 and then leveling off with slightly positive slopes, with SearchM remaining at -0.18 and Stickywage remaining at -0.15. The first panel in the middle row, entitled “4. Federal Funds Rate”, has a y-axis with a minimum of -0.35 and a maximum of 0.1. VAR mean starts slightly below 0 in period 0, decreases quickly to -0.15 in period 3, then slowly increases to -0.1 in period 10, where it then begins to decrease very slowly for the remaining periods, finishing at about -0.12. SearchM and Stickywage again have similar paths, starting at -0.06 and decreasing to -0.13 and -0.15 by period 3, respectively. In period 5 Stickywage begins to increase steadily for the remaining periods, and ends up at about -0.12. Search M continues to decrease, although very slowly, for the remaining periods where it levels off at -0.15. The middle panel in the second row, entitled “5. Hours worked”, has a y-axis with a minimum of -0.1 and a maximum of 0.4. VAR Mean begins at 0.15 in period 0, decreases slightly to 0.1 in period 1, then increases rapidly to about 0.275 by period 8. Then, it begins a slow decrease to about 0.23 in the final period. SearchM starts at -0.15, increases quickly to 0.05 by period 4, then increases very slowly to about 0.08 in the final period. Stickywage begins at -0.1 in period 0, increases to 0.03 by period 4, then decreases steadily to zero in the remaining periods. The third and final panel in the middle row, entitled “6. Real Wage”, has a y-axis with a minimum of 0 and a maximum of 0.4 VAR Mean has a y-intercept of 0.6 and a very steady positive slope for the entire period, finishing at 0.275 in the final period. SearchM’s y-intercept is slightly less than zero, and its path begins with a sharp increase to 0.2 by period 2. The slope increases at a decreasing rate for the remaining periods, ending at about 0.275 as well. Stickywage begins at 0.1, increases quickly to about 0.27 by period 4, then levels off steadily to about 0.3 The paths are very similar between SearchM and Stickywage but they diverge slightly at the end. The first panel in the bottom row, entitled “7. Consumption”, has a y-axis range of 0.1 to 0.7. VAR mean has a y-intercept of 0.18 and a steady increasing slope until it reaches 0.5 in period 10. Then, it levels off with a very slight increase, finishing at about 0.52. SearchM also has a y-intercept of .18, although it increases sharply to 0.3 in period 3 where it smoothly levels off for the remaining periods. Stickywage begins at 0.24 in period 0, increases at a decreasing rate to 0.35, then begins a steady downward decline to 0.3, the same as the SearchM model. The middle panel of the bottom row, entitled “8. Job Finding Rate”, has a y-axis range of -1 to 1, and it does not show the Stickywage line. Both lines have a y-intercept of about -0.3. VAR mean increases slightly in period 1 to about -0.25, then decreases by the same amount in period 2, then begins a steady climb to about 0.4 by period 10, where it levels off for the remainder. SearchM has a different path, increases sharply in the beginning periods to about 0.375 in period 3, then slowly levels off to 0.375 as well. The last panel in the figure, the third panel in the third row, entitled “9. Vacancies”, has a y-axis minimum of -2 and a maximum of 2. It also does not show the Stickwage model. Both lines have a y-intercept of about -1. VAR mean decreases very slightly in the first period, then increases steadily to a peak of about 0.5 by period 7, where it then begins a slow decline to 0 by the final period. SearchM, on the other hand, has a rapid increase to 0.8 by period 2 and then levels off in a straight line for the remaining periods.
Figure 2, “Impulse response function matching under neutral technology shock with wage indexation in the sticky wage model”, looks exactly the same as Figure 1, with the same panel structure (3x3), the same labels, the same y and x-axis range, and the same lines in each panel. It depicts the impulse responses to a neutral technology shock in the search and matching model and the sticky wage model, each depicted by their own line. Another line, VAR Mean, shows the point estimates of the empirical impulse responses along with a 90% confidence interval, a shaded area. Inflation rates and the federal fund rate are annualized. In the first panel, entitled “1. Output”, VARmean has a y-intercept of .22; it decreases sharply in the first period then steadily increase to 0.4 by period 8, where it then begins a slow, gradual increase to .45 by the final period. Stickywage has a y-intercept of .19, increases steadily to 0.4 by period 5, then begins a steady decline to 0.36 by the final period. SearchM has a similar path, beginning at 0.15, increases to 0.35 by period 4, then increases at a very gradual pace as it levels off to 0.38 in the final period. In the second panel on the top row, “2. Unemployment Rate”, VAR Mean and SearchM both have a y-intercept of 0.04. VAR Mean increases to 0.06 in period one, then declines steadily at a decreasing rate to -0.08 by period 10, where it then begins a gradual increase to -0.065 in the final period. SearchM decreases sharply to -0.075 in period 3, then slowly and smoothly decreases to -0.1 where it remains for the rest of the periods. The third panel in the top row, “3. Inflation”, again shows all 3 lines. VAR Mean has a y-intercept of -0.55 and it very sharply increases to -0.25 in period 1, decreases to -0.3 in period 2, then increases steadily for the remaining periods, ending at about -0.18. SearchM and Stickywage have the same y-intercept of about -0.42. SearchM increases steadily to -0.2 by period 3, then levels off gradually with a very small, almost unnoticeable decrease in slope in the remaining periods where it ends up slightly above -0.2. Stickywage has a much simpler path, increasing steadily to about -0.15 by period 7, then levels off with a slightly increasing slope to about -0.12 in the final period. The first panel in the second row, “4. Federal Funds Rate”, shows VAR Mean with a y-intercept of slightly less than zero. It decreases immediately to -0.15 by period 2, then begins a gradual increase to about -0.12 by period 10, then slowly decreases to -0.13 for the remaining periods. SearchM begins in period 0 at -0.06, and decreases very smoothly to -0.15 by period 5, where it levels off for the remaining periods. The path for Stickywage is very similar, but the y-intercept is slightly higher at -0.15 and in the final periods it eclipses the SearchM model, finishing at about -0.13. The middle panel of the second row, entitled “5. Hours worked”, shows a strong divergence between the paths of VAR Mean and the other 2 models. VAR Mean starts at 0.14 in period 0, decreases slightly in period 1, then increases steadily to an apex of about 0.28 in period 7. Then, it begins a decline for the remaining periods, ending up at about 0.25. SearchM begins at the very bottom of the y-intercept range, at -0.15; it increases at sharply at first and then begins to round and level out around period 4 at about 0.08, where it remains for the rest of the periods. Stickywage has a slightly higher y-intercept but is still far from VAR Mean. The path of Stickywage is similar to that of SearchM but it’s apex of 0.1 in period 5 is higher, and the decline is more pronounced, finishing at slightly above zero in the final period. The third panel in the second row is labeled “6. Real Wage”. The line for VAR Mean has a y-intercept of about 0.5 and has a very steady path with a steady slope for most of the period. It increases to 0.2 in period 8 and finishes at about 0.26. SearchM’s y-intercept is slightly less than zero; it increases sharply to 0.2 in period 2, then increases at a decreasing rate to about 0.27 by period 5, then levels off and even decreases slightly by the final period to about 0.26. The Stickywage line starts slightly above 0.1 in period 0 and has a constant slope until about period 8 where it reached 0.25 and then begins to increase at a decreasing rate until it, too, converges on 0.26 with the other two lines. The first panel in the bottom row, labeled “7. Consumption”, shows all three lines with the same y-intercept, just slightly less than 0.2. VAR Mean increases steadily to about 0.45 in period 8, then its slope is increasing at a decreasing rate. Its final value in the last period is 0.5 SearchM increases steadily to 0.25 in period 2, then levels off at a very small increasing rate to 0.3 in the final periods. Stickywage increases quickly to 0.4 by period 5, then begins to decreases steadily to about 0.35 by the final period. The middle panel of the third row, “8. Job Finding Rate”, does not show the Stickywage model, similarly to Figure 1. VAR Mean has a y-intercept of -0.4. It increases slightly in period 1, decreases slightly in period 2 to about -0.42, then increases steadily to about 0.4 by period 10, where it levels off for the remaining periods. SearchM increases to 0.25 by period 2, then its slope increases at a decreasing rate until period 5 when it reaches 0.4. Then it levels off and converges with VAR Mean for the last several periods. The final chart, labeled “9. Vacancies”, also does not show the Stickywage model. VAR Mean has a y-intercept of slightly less than -1 and SearchM has a y-intercept of slightly more than -1. VAR Mean decreases barely in period 1, then increases steadily to about 0.2 in period 6. Then it begins a slow, gradual decline to 0 by the final period. SearchM increases immediately to 0.5 in period 1, climbs to 0.6 in period 2 and then remains at 0.6 for the rest of the periods.
Figure 3 is labeled “Figure 3: Targeting rules in the search and matching model: neutral technology shock”. The footnote says that this figure “plots the impulse responses in the search and matching model to a neutral technology shock when policy follows the optimal targeting rule from the search and matching model and the sticky wage model”. The figure features 12 panels, with 4 rows and 3 panels in each. The x-axis in every panel has a minimum of 0 and a maximum of 20 (periods). It’s important to note that there is room above and below the minimum and maximum labels on each plot. For example, if the minimum is zero but a line has a y-intercept “below the minimum”, this simply means that the label is not at the very bottom of the y-axis (and vice versa with the maximum-labeled axis value). Each panel contains two lines, a solid line labeled “NKMSearchM-Ramsey” and a line with circular markers labeled “NKMSearchM-exchangerule” (henceforth referred to as “SMRamsey” and “SMExchange”, respectively, for simplicity). The first panel in the first row, entitled “1. Individual Hour Worked”, has a y-axis with a minimum of -0.07 and a maximum of -0.01. SMRamsey’s y-intercept starts at zero (higher than the higher labeled tick mark of -0.01), and the line dips down to -0.011 in period 1 and remains there for the remaining 19 periods. SMExchange has a y-intercept of slightly below -0.07 and the line take an increasing concave down path, reaching -0.03 in period 5. Then the slope begins to taper off and it settles at -0.011 along with the SMRamsey line. The second panel in the top row, entitled “2. Output”, has a y-axis range of 0.25 to 0.4. The SMExchange line visually takes a similar path as the previous line, with a y-intercept of about 0.2 and a period 20 value of 0.4. SMRamsey has a y-intercept of 0.38, increases gradually in the first 3 periods until it hits the upper most value on the y-axis, 0.4, where it remains for the last 15 periods. The third panel in the top row, entitled “3. Consumption”, looks virtually identical to figure 2, except the y-intercept for SMRamsey and SMExchange are 0.32 and 0.20, respectively. Both lines converge at 0.32 in the same way that both previous lines converged at 0.4. The first panel in the second row, labeled “4. Price Inflation”, has a y-axis with a range of -0.25 to 0. SMRamsey starts in period 0 at zero, dips very, very slightly in period 1 (almost unnoticeably so) and quickly converges back to zero for the entire period. The SMExchange line again takes an increasing concave down path, with a y-intercept of zero. In period 5 it takes a value of about -0.1 and in period 10 it takes a value of about -0.04, as it gradually converges to zero with the other line. The middle panel in the second row, labeled “5. Wage Inflation”, has a y-axis minimum of zero and a maximum of 1.2 SMRamsey has a y-intercept value of 1.2 but it very rapidly shoots down to slightly less than zero in period 1, where after it increases to zero and remains there for the rest of the periods. SMExchange has a y-intercept of about 0.05, where it too drops to below zero in period 1, only to bounce back to zero where it converges with SMRamsey for the entire remaining periods. The third panel in the second row, entitled “6. Real Wage”, has a y-axis minimum of 0.1 and a maximum of 0.3. SMRamsey starts slightly above the maximum in period zero, drops to slightly below 0.3 for one period, then rises back to 0.3 and remains there for the last 19 periods. SMExchange again takes an increasing concave down path, starting at the minimum in period zero, rising to 0.25 in period 5, 0.28 in period 10, then converges with SMRamsey at 0.3 for the last 8 or so periods. The next three panels look almost identical to panel 6, with slight differences. In the first panel in row 3, labeled “7. Marginal Cost”, the y-axis minimum is -0.2 and the maximum is zero. SMRamsey starts slightly above zero in period 0, drops slightly below zero in period 1, then converges back to zero for the last 19 periods. The SMExchange line starts slightly below -0.2 on the y-axis, reached -0.07 in period 5, -0.02 in period 10, then converges with SMRamsey at zero for the last 10 periods. The second panel in row 3, labeled “8. Nominal SMExchange Rates”, has a y-axis minimum of -0.12 and a maximum of 0. SMRamsey starts slightly above zero in period 1 and quickly converges to zero for the remainder. SMExchange starts at -0.12 in period 0, rises to -0.03 in period 5, -0.01 in period 10, then converges on zero with the SMRamsey line for the remaining 10 periods. The third panel in row three, entitled “9. Job Finding Rate”, again looks very similar to the previous three panels. The minimum labeled y-axis value is 0.1 and the maximum-labeled y-axis value is 0.4 The line for SMRamsey starts slightly above 0.4, drops down to about 0.47 in periods 1 and 2, and remains there for the remaining periods. SMExchange has a y-intercept value close to zero, spikes up to 0.3 in period 5, 0.45 in period 10, then converges on 0.47 with the other line. The first panel in the fourth and final row, labeled “10. Unemployment Rate”, has a y-axis range of -0.1 to 0. SMExchange has a decreasing, concave up shape, starting in period zero at 0, decreasing sharply to -0.08 in period 5, then to -0.2 in period 10, then asymptotes near -0.1 for the remainder. SMRamsey, on the other hand, has a y-intercept value of -0.07, which drops to -0.3 in period 1, and then it, too, converges on -0.1 for the remainder of the periods. The middle panel in the bottom row, entitled “11. Employment”, has a y-axis range of zero to 0.1 SMExchange, with an increasing concave down shape, reaches 0.08 in period 5 and 0.1 in period 10, where after it increasing slightly above 0.1 for the remainder. SMRamsey has a y-intercept value of 0.08, shoots up to slightly above 0.1 in periods 2 and 3, then converges with SMExchange by period 15. Finally, the third and final panel in the fourth row, entitled “12. Total Vacancy”, has a y-axis with a range of zero to 1.6. SMRamsey has a y-intercept of 1.6. It decreases sharply to 1 in period 2, then settles at 1 for the remaining 18 or so periods. SMExchange has a y-intercept of 0, increases quickly to 0.8 by period 5, then settles on 1 along with the line for SMRamsey.
Figure 4, “Targeting rules in the search and matching model: price markup shock”, plots the impulse responses in the search and matching model to a price markup shock when policy follows the optimal targeting rule from the search and matching model and the sticky wage model. These are again labeled as “NKMSearchM-Ramsey” and “NKMSearchM-exchangerule” (henceforth referred to simply as “SMRamsey” and “SMExchange”). The figure is structured exactly like Figure 3, featuring 12 panels with 4 rows with 3 panels each. The x-axis in every panel depicts the number of periods from 0 to 20. The first panel in the first row, labeled “Individual Hour Worked”, has a y-axis with a minimum of -1.4 and a maximum of -0.2. SMRamsey has a y-intercept of -1.4. It drastically increases to -0.3 in period 2, then quickly to -0.15 by period 3. Period 4 and 5 see slight increases, and by period 6 it levels off at zero, where it remains for the rest of the periods. SMExchange has a y-intercept of -0.2 and it increases slowly to about -0.08 by period 5, then to -0.05 by period 7, then to zero by period 10, where it remains for the rest of the periods. The middle panel in the top row, labeled “2. Output”, has a y-axis minimum of -3 and a maximum of 0. SMRamsey has a y-intercept of -3. The increase in slope is immediate, and it has a value of -1 by period 2 and -0.3 by period 4. Then, the slope increase begins to slow down, as the line begins to asymptote at zero by period 6. SMExchange has a y-intercept of -0.5. The slope is steadily increasing until period 8, where it also hits zero and asymptotes for the remaining periods. The third panel in the first row, entitled “3. Consumption”, has a y-axis minimum of -2 and a maximum of zero. The line for SMRamsey again has a sharp increase to about -0.3 by period 3. Then the slope increase begins to slow down as it asymptotes at zero by period 5. SMExchange has a y-intercept value of -0.3 and the slope increases steadily to slightly below zero by period 5, where it stays for the remaining periods. The first panel on the second row, labeled “4. Price Inflation”, has a y-axis range of -1 to 3. SMRamsey has a y-intercept of 1.5 and it immediately decreases to 0 in period 1. Then it slowly climbs to -0.2 by period 3, -0.1 by period 4, and zero by period 5, where it remains for the last 15 periods. The line for SMExchange has a y-intercept value of 3 and it sharply shoots down to 0 in period 1. Then, with a constant slope, it increases slowly to zero by period 10 and remains at zero for the next 10 periods. The middle panel in the second row, entitled “5. Wage Inflation”, has a y-axis with a minimum of -15 and a maximum of 10. SMRamsey has a y-intercept of 10. There is a very sharp increase all the way to the maximum value of 10 in period 1, then a sharp decrease to 2 in period 2. Then it falls to 1 in period 3, where it begins to asymptote at zero. The SMExchange line has a y-intercept of zero and a slope of zero for the entire 20 periods. The third panel in the second row, labeled “6. Real Wage” has a y-axis minimum of -4 and a maximum of 0. SMRamsey has a y-intercept value of -4. It increases drastically to -0.5 by period 2 and then begins to taper off and asymptotes at 0 by period 5. SMExchange begins at -0.6 and slowly increases to -0.2 by period 5. Then it begins a very gradual increase to zero and reaches zero by period 8, where it remains for the last 12 periods. The first panel on the third row, labeled “7. Marginal Cost”, has a y-axis minimum value of -5 and a maximum of 0. SMRamsey starts with at -5 in period 0 and then very quickly increases to -1 by period 2. The slope increase then begins to slow down and it reaches -0.5 by period 3. Periods 4 and 5 see very slight increases and by period 6 SMRamsey reaches zero, where it remains for the last 14 periods. The line for SMExchange has a y-intercept value of -0.9. The slope is positive and steady for the first 6 periods as the line approaches zero. The middle panel in the second row, labeled “8. Nominal Interest Rate”, has a y-axis minimum of zero and a maximum of 4. SMRamsey begins in period 0 at 4, then drastically decreases to 1 by period 1. Then the slope begins to decrease at a decreasing rate. By period 4 SMRamsey is very close to zero and by period 6 it reaches zero and stays there for the remaining periods. SMExchange has a y-intercept value of slightly below zero and sees a steady increase in slope until period 6 when it reaches and asymptotes at zero as well. The third panel on the third row, labeled “9. Job Finding Rate”, has a y-axis minimum value of -10 and a maximum of 0. SMRamsey has a y-intercept value of -10 and shoots up dramatically to -2 in period 1 and -1 by period 3. Then, it begins to taper off and asymptote at zero by period 5. SMExchange has a y-intercept of slightly below -2. The increase in slope is steady for the first 6 periods until the line approaches zero and converges with SMRamsey. The first panel in the fourth and final row, labeled “10. Unemployment Rate”, has a y-axis range of zero to 1.4. SMRamsey has a y-intercept value of 1.4. The decrease in slope is sharp and steady, reaching a value of 0.2 by period 4 and 0.1 by period 5. In periods 5 to 7 the line slowly begins to asymptote toward zero, where it remains for the final 13 periods. SMExchange has a period 0 values of 0.2, then sees a very minimal increase in period 1 to 0.23, then begins a slow decrease until period 10 when it reaches zero and stays there for the last 10 periods. The middle panel in the final row, entitled “11. Employment”, has a y-axis range of -1.4 to zero. SMRamsey begins at -1.4 in period 0, then increases sharply and steadily to -0.2 by period 4, then to -0.05 by period 6, finally reaching zero by period 8. SMExchange has a y-intercept value of -0.2. In period 1 there is a slight, barely noticeable decrease followed by a steady increase in slope beginning in period 2. It reaches zero by period 10 and stays there for the remaining 10 periods. Finally, the third panel in the fourth row, entitled “12. Total Vacancy”, has a y-axis range of -30 to 0. SMRamsey has a y-intercept value of -30 and sees a very drastic increase to 0 in period 1. It briefly reaches above zero for 2 periods, only to gradually return to zero by period 5 where it stays for the remaining 15 periods.
Figure 5, “Targeting rules in the sticky wage model: neutral technology shock”, plots the impulse responses in the sticky wage model to a neutral technology shock when policy follows the optimal targeting rule from the sticky wage model and the search and matching model. The figure features 8 panels, with 4 rows of 2 panels each. Each panel has an x-axis from 0-20 with varying y-axis ranges. There are 2 lines in each panel, “NKMStickywage-Ramsey” and “NKMStickywage-exchangerule” (henceforth referred to as “SWRamsey” and “SWExchange”, respectively). In the first panel in the first row, labeled “1. Hour Worked”, the y-axis has a range from zero to 0.4. SWRamsey has a value slightly below zero for the first 5 periods, then sees a gradual increase until it reaches zero by period 10. SWExchange has a y-intercept of 0.3. It reaches 0.45 in period 2, then begins a slow and steady decline until it reaches 0.1 in period 10. From there, it keeps decreasing until it reaches zero by period 15. The second panel in the first row, labeled “2. Output”, looks almost exactly the same as the first panel, but it has a y-axis range of 0 to 0.75. SWRamsey begins at zero and reaches about 0.05 by period 5, then stays at 0.1 in period 10. SWExchange starts at 0.62, climbs to 0.75 by period 3, then begins a slow decline, reaching 0.45 by period 10 and 0.2 by period 15. Finally, it converges on zero by period 17. The first panel in the second row, labeled “3. Consumption”, is exactly the same as “Output”. The second panel in the second row, labeled “4. Nominal Interest Rate”, shows a y-axis range of -0.3 to 0.4. SWRamsey has a y-intercept value of -0.3. It increases to -0.1 by period 3, then to -0.05 by period 5. By period 6 and 7 it reaches zero where it remains for the remaining periods. SWExchange has a y-intercept value of 0.35. In period 1 it has a value of 0.1, in period 2 a value of -0.05, and period 5 a value of -0.2. In period 10 it has a value of -0.1, and by period 15 it reaches zero where it converges with the other line. The first panel in the third row, labeled “5. Price Inflation”, has a y-axis range of -0.3 to 0.1. SWRamsey has a y-intercept value of -0.3 and sees a steady positive increase in slope until period 5 when it reaches -0.1 Then, the slope begins to increase at a decreasing rate. By period 10, the value is -0.05 and by period 15 it approaches zero. SWExchange has a y-intercept of -0.15. It shows a steady increase in slope until period 5 as well, when it reaches 0.1. Then in period 10 it reaches slightly above zero and by period 15 it, too, reaches zero. The second panel in the third row, labeled “6. Wage Inflation”, has a y-axis range of zero to 0.25. SWRamsey has a y-intercept value of 0.02. It slowly decreases to 0.01 by period 5 and then converges on zero by period 10. SWExchange has a y-intercept value of 0.25. It shows a very steady decline in slope with a period 5 value of 0.15 and a period 10 value of 0.03. By period 12 it begins to converge on zero. The first panel on the fourth and final row, labeled “7. Real Wage”, has a y-axis range of 0.1 to 0.35. SWRamsey has a y-intercept value of 0.1 and increases steadily to 0.25 by period 5. Then, its slope begins to increase at a decreasing rate, reaching 0.3 by period 10 and 0.32 by period 15 through period 20. SWExchange also has a y-intercept of 0.1, and reaches 0.3 by period 5. By period 7 it reaches 0.35 and then begins to slowly decrease until it converges with SWRamsey by period 16. The second panel on the fourth row, labeled “8. Marginal Cost”, has a y-axis range of 0.25 to zero. SWRamsey has a y-intercept value of -0.25. Its slope is positive and steady, reaching a value of -0.05 in period 5. Then, the slope begins to decrease, reaching -0.03 by period 10 and asymptotes at zero by period 15. SWExchange has a y-intercept at -0.22 and also has a strong positive slope until period 5 when it reaches a value of 0.02. By period 7 it is slightly above zero, then begins to drift downward until it converges on zero by period 15.
Figure 6, “Targeting rules in the sticky wage model: price markup shock”, plots the impulse responses in the sticky wage model to a price markup shock when policy follows the optimal targeting rule from the sticky wage model and the search and matching model. This figure again features 8 panels with 2 lines in each, “NKMStickywage-Ramsey” and “NKMStickywage-exchangerule” (henceforth referred to as “SWRamsey” and “SWExchange”, respectively). The first panel, “1. Hour Worked”, has a y-axis range of -6 to 0. SWRamsey has a y-intercept of zero and a slope of zero for the entire 20 periods. SWExchange has a y-intercept of -6, a period 5 value of 0.1 and a period 10 value slightly above zero. After that, the line converges on zero. The second panel in the first row, labeled “2. Output”, is exactly the same as the first panel, with the same y-axis range and plots. The first panel on the second row, labeled “3. Consumption”, is also exactly the same as the first and second panel. The second panel in the second row, labeled “4. Nominal Interest Rate”, has a y-axis range of -1 to 8. SWRamsey has a y-intercept value of -1 and reaches zero in period 5, where it remains for the final 15 periods. SWExchange has a y-intercept value of 8, a period 1 value of 4.5, a period 2 value of 3, and a period 5 value of 1. From there, it gradually approaches and converges on zero in period 10. The first panel in the third row, labeled “5. Price Inflation”, has a y-axis range of -1 to 4. Both lines have almost the exact same path. The y-intercept value for both is 4. In period 1, SWRamsey drops to -1 and SWExchange drops to slightly below -1. The period 5 and 10 values are the same for both at -0.5 and 0, respectively. Both lines remain at zero for the final 10 periods. The second panel on the third row, labeled “6. Wage Inflation”, has a y-axis range of -0.9 to 1. SWExchange has a y-intercept value of -0.9 and shoots up to close to 1 in period 5 and then drops down to 0.5 in period 15, where after it slowly converges down to zero. The first panel in the fourth row, labeled “7. Real Wage”, has a y-axis range of -1.2 to zero. SWRamsey has a y-intercept value of -1. For the first 5 periods the slope is strong and positive, reaching values of -0.6 in period 3 and -0.3 in period 5. Then, the slope increases at decreasing rates, with values of -0.2 in period 7 and -0.1 in period 10. In the last 10 periods the line slowly converges on zero. SWExchange has a y-intercept value of -1.2 and also has a strong positive slop until period 5 when it reaches -0.4. in Period 10 the value is close to zero and in the final 10 periods it also converges on zero along with SWRamsey. The second graph on the fourth row, labeled “8. Marginal Cost”, is exactly the same as the previous panel.
Figure 7, “Targeting rules with simple loss function: price markup shock”, compares the performance of optimal targeting rules derived from the loss function (π2t + λxx2t) for both the search and matching model and the sticky wage model in response to a price markup shock. In the upper six panels, it is λx = λ* = 0.0429; in the lower size panels it is λx = 1. This figure features 4 rows of 3 panels each, each with two lines, “Ramsey” and “Misspecified Rule” (“MR”). The first row is labeled “Search and Matching Model: Simple Loss Function with λx = λ*”. The first panel in the first row, labeled “Price Inflation”, has a y-axis range of -1 to 3.5. MR drops sharply from its y-intercept value of 3.5 to -0.5 in period 1. Then, it steadily climbs back up to zero by period 15. Ramsey shows a very similar drop in period 1 from its y-intercept value of 2.5 to -1 in period 1. It climbs above zero more quickly than MR, reaching zero in period 5 and staying there for the last 15 periods. The second panel in the first row, “Wage Inflation”, has a y-axis range of -7 to 4.5. MR has a y-intercept of 3 and drops quickly below zero in period 1, then slowly converges on zero for the remaining periods. Ramsey has a value of -7 in period 0, quickly shoots up to 4.5 by period 1, then back down quickly to 1 in period 3. After that, it slowly converges on zero as well. The third panel on the first row, “Output”, has a y-axis range of -1.7 to 0. MR starts at zero in period 1, dips slightly below in period 2-5, and then begins to converge on zero again. Ramsey has a value of -1.7 in period 0, and rises quickly to -0.2 by period 5. Then it begins to converge on zero by period 10. The second row is labeled “Sticky Wage Model: Simple Loss Function with λx = λ*”. The first panel, “Price Inflation”, has a y-axis range of -1 to 4. MR drops quickly from 4 in period 0 to -1 in period 1. Then it begins a steady climb to zero by period 6. Ramsey has the exact same path and y-intercept. The second panel, “Wage inflation”, has a y-axis range of -0.5 to 0.1 MR starts at -0.5 in period 0, jumps quickly to 0.1 in period 5, then begins a slow and steady decline back to zero by period 20. Ramsey starts very slightly above zero in period 0 and converges back to zero by period 3. The third panel in the second row, entitled “Output”, has a y-axis range of -3 to 0.2. MR has a period 0 value of -3. It rises steadily to -0.5 in period 5, and then begins to slow down and eventually converges on zero by period 8. Ramsey starts very slightly below zero, dips down barely in periods 1 and 2, and then converges back on zero for the remaining periods. The third row is labeled “Search and Matching Model: Simple Loss Function with λx = 1”. The first panel, “Price Inflation”, has a y-axis of -0.5 to 4. Both lines have a value of 4 in period 0. Ramsey drops below zero in period 1, and slowly climbs to zero by period 10, while MR drops right to zero and stays there for the rest of the periods. The second panel, “Wage Inflation”, is exactly the same as the previous panel. The third panel, “Output”, has a y-axis range of -0.12 to 0. Ramsey starts at -0.12 and its slope increases at a decreasing rate until it hits zero by period 20. MR starts slightly above zero, drops slowly to zero in periods 1 and 2 and then stays there for the remaining periods. The fourth and final row is labeled “Search and Matching Model: Simple Loss Function with λx = 1”. The first panel in the fourth row, entitled “Price Inflation”, has a y-axis range of -1 to 4. Both lines have exactly the same y-intercept and path. The y-intercept is 4, they drop sharply to -1 in period 1, then slowly converge on zero by period 10. The second panel, “Wage Inflation”, has a y-axis range of zero to 0.1. Ramsey has a value of 0.1 in period 0. It decreases quickly to 0.02 by period 5, then the slope begins to decrease at a decreasing rate, converging on zero by period 15. MR has a value of 0.06 in period 0, drops to 0.01 by period 5, then slowly converges on zero by period 10. The third and final panel in the fourth row, labeled “Output”, has a y-axis range of -0.12 to zero. MR starts at -0.12, quickly rises to -0.04 by period 5, then to -0.02 by period 10, then converges on zero by period 20. Ramsey starts at zero, dips slightly in the first periods, then rises back to zero for the remaining periods.