Inflation Persistence, Backward-Looking Firms, and Monetary Policy in an Input-Output Economy

Figure 1: Impulse Responses to Shocks under Optimal Commitment

The figure plots the impulse responses of the nominal interest rate (annualized values) in the first row of panels, the real interest rate (percent deviation) in the second row, final goods inflation (annualized rate) in the third row, and intermediate goods inflation (annualized rate) in the fourth row to a positive one-standard-deviation productivity shock in the final goods sector (first column), productivity shock in the intermediate goods sector (second column), cost-push shock in the final goods sector (third column), and cost-push shock in the intermediate goods sector (fourth column). All together there are sixteen panels. The x-axis for each panel shows time in quarters, with quarter 0 containing the period with the shock. In each panel there are four curves: The purely forward-looking case is represented by a solid line with filled-in triangles. The case of high persistence in the final goods sector and forward-looking in the intermediate goods sector is represented by a dashed line. The case of high persistence in the final goods sector and low (but positive) persistence in the intermediate goods sector is represented by a solid line with vertical slashes. The case of high persistence in both sectors is represented by a solid line.

First Column (productivity shock in the final goods sector):

The top panel shows that in each case the nominal interest jumps below the steady state value and then returns gradually to the steady state value. The case with high persistence in both sectors decreases the most initially. The second panel shows that the real interest rate gap increases and then decreases back to the steady-state value for each case. However, the maximal response for the non-purely-forward-looking cases is delayed relative to the purely forward-looking case. Relative to the purely forward-looking case, the maximum response is higher when persistence is high in the final goods sector but zero or low in the intermediate goods sector, while the maximum response is lower when persistence is high in both sectors. The third panel shows that final goods inflation jumps down and then monotonically increases toward zero. When inflation is persistent in the final goods sector, final goods inflation displays a hump-shaped response, deceasing over a few quarters to its nadir, and then gradually returning to zero. The bottom panel shows that intermediate goods inflation jumps up and then decreases back toward zero for the three cases when inflation is not persistent in the intermediate goods sector. When inflation is persistent in the intermediate goods sector (and final goods sector), intermediate goods inflation jumps and continues to increase for a few quarters to its highpoint before gradually decreasing back to zero.

Second Column (productivity shock in the intermediate goods sector):

The top panel shows that in each case the nominal interest jumps below the steady state value, then moves down further, before inflecting and returning gradually to the steady state value. The case with high persistence in both sectors decreases the least initially. The second panel shows that the real interest rate gap decreases and then increases back to the steady-state value for each case. However, the maximal (in magnitude, the values are all negative) response for the non-purely-forward-looking cases is delayed relative to the purely forward-looking case. Relative to the purely forward-looking case, the maximum response is more negative when persistence is high in the final goods sector but zero or low in the intermediate goods sector, while the maximum response is less negative when persistence is high in both sectors. The third panel shows that final goods inflation jumps up and then monotonically decreases toward zero. When inflation is persistent in the final goods sector, final goods inflation displays a hump-shaped response, increasing over a few quarters to its highpoint, and then gradually returning to zero. The bottom panel shows that intermediate goods inflation jumps down and then increases back toward zero for the three cases when inflation is not persistent in the intermediate goods sector. When inflation is persistent in the intermediate goods sector (and final goods sector), intermediate goods inflation jumps down slightly and continues to decrease for a few quarters to its nadir before gradually decreasing back to zero.

Third Column (cost-push shock in the final goods sector):

The top panel shows that in each case the nominal interest jumps above the steady state value and then returns gradually to the steady state value. The forward-looking case experiences the largest jump. The other three cases behave similarly. The second panel shows that the real interest rate gap follows the same pattern as the nominal interest rate. The third panel shows that final goods inflation jumps up following the shock, then jumps down (below zero) and then gradually increases back to zero. In the other three cases (when inflation is persistent in the final goods sector), final goods inflation jumps (less than in the final goods case), and then slowly decreases back to zero. The bottom panel shows that intermediate goods inflation jumps down and then increases in the three cases that do not have high persistence in the intermediate goods sector. When inflation is highly persistent in both cases, intermediate goods inflation moves down slightly in the initial period, move down a little more, and then inflects, increasing and eventually returning to zero.

Fourth Column (cost-push shock in the intermediate goods sector):

The top panel shows that in each case the nominal interest jumps above the steady state value and then returns gradually to the steady state value. The three cases that have zero or low persistence in the intermediate goods sector behave similarly and experience the largest jump. The case of high persistence in both sector jumps less; however, like the other cases, it then decreases back to its steady-state value. The second panel shows that the real interest rate gap follows the same pattern as the nominal interest rate. The third panel shows that final goods inflation jumps down in each case, with the forward-looking case jumping down the most. In the forward-looking case, final goods inflation immediately increases following the initial jump down. In the other three cases, final goods inflation moves down slight after the initial downward jump, but then increases. All of the curves eventually return toward zero. The bottom panel shows, in the three cases of zero or low persistence in the intermediate goods sector, inflation in the intermediate goods sector experiences a positive jump, then jumps down (below zero), and the gradually increases back to zero. In the case of high persistence in both sectors, the initial jump in intermediate goods inflation is less; thereafter intermediate goods inflation slowly decreases toward zero.

Figure 2: Final Goods Price-Level Responses to Cost-Push Shocks

The figure plots the impulse responses of the price level of final goods due to positive one-standard-deviation cost-push shocks in each sector. The y-axis records percent deviation from the initial steady-state values, while the x-axis records quarters. In each panel there are four curves: The purely forward-looking case is represented by a solid line with filled-in triangles. The case of high persistence in the final goods sector and forward-looking in the intermediate goods sector is represented by a dashed line. The case of high persistence in the final goods sector and low (but positive) persistence in the intermediate goods sector is represented by a solid line with vertical slashes. The case of high persistence in both sectors is represented by a solid line. The left panel shows that, in response to a cost-push shock in the final goods sector, the price level of final goods jumps up. In the forward-looking case, the jump is followed by a monotonic decrease back to the pre-shock level. In the other three cases, which behave almost identically, the jump is lower than the forward-looking case. However, thereafter they continue to rising, reaching an apex, and then decreasing, but to a level above zero. The right panel shows that, in response to a cost-push shock in the intermediate goods sector, the price level of final goods drops initially in each case. The shapes of the four curves are similar: An initial drop followed by further declines, finally followed by increases until a new stable value is reached. The three cases of zero or low persistence in the intermediate goods sector behave similarly and converge to values close to zero (the pre-shock value). When persistence is high in both sectors, the drop is not as large, and the price level converges to a value above zero and above the other curves.

Figure 3: Intermediate Goods Price-Level Responses to Cost-Push Shocks

The figure plots the impulse responses of the price level of intermediate goods due to positive one-standard-deviation cost-push shocks in each sector. The y-axis records percent deviation from the initial steady-state values, while the x-axis records quarters. In each panel there are four curves: The purely forward-looking case is represented by a solid line with filled-in triangles. The case of high persistence in the final goods sector and forward-looking in the intermediate goods sector is represented by a dashed line. The case of high persistence in the final goods sector and low (but positive) persistence in the intermediate goods sector is represented by a solid line with vertical slashes. The case of high persistence in both sectors is represented by a solid line. The left panel shows that, in response to a cost-push shock in the final goods sector, the price level of intermediate goods jumps down. In the forward-looking case, the jump is followed by a second small decrease, and then a monotonic increase back to the pre-shock level. In the other three cases, which behave almost identically, the jump down is not as great as the forward-looking case. They display a similar pattern as the forward-looking case; however, they converge to a value above zero. The right panel shows that, in response to a cost-push shock in the intermediate goods sector, the price level of intermediate goods jumps up in each case. The three cases when inflation persistence in the intermediate goods sector is zero or low display almost identical behavior: their initial jump is followed by a monotonic decline toward zero. When inflation persistence is high in both sectors, the initial jump is lower than in the other three cases. However, it is followed by subsequent rises, reaching its apex after a few quarters, and then decreasing to a new stable value above zero.