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�𝑁0,𝑑𝑑𝑠𝑠𝑠𝑠 𝑁𝑁𝑠𝑠(𝑀𝑀𝑑𝑑,πœƒπœƒπ‘‘π‘‘) 𝐿𝐿𝐿𝐿(𝐿𝐿𝑑𝑑,𝑃𝑃0,𝑑𝑑𝑠𝑠𝑠𝑠) 𝐴𝐴𝑑𝑑𝐹𝐹(𝐾𝐾𝑑𝑑,𝑁𝑁𝑑𝑑) π‘Œπ‘Œπ‘‘π‘‘=π‘Œπ‘Œπ‘‘π‘‘ π‘Ÿπ‘Ÿπ‘‘π‘‘ 𝐴𝐴𝐴𝐴 𝑁𝑁0,π‘‘π‘‘π‘šπ‘šπ‘ π‘ =𝑁𝑁0,𝑑𝑑𝑓𝑓 π‘Œπ‘Œ0,π‘‘π‘‘π‘šπ‘šπ‘ π‘ =π‘Œπ‘Œ0,𝑑𝑑𝑓𝑓 𝑁𝑁𝑑𝑑(𝑀𝑀𝑑𝑑,𝐴𝐴𝑑𝑑,𝐾𝐾𝑑𝑑) 𝐴𝐴𝐴𝐴𝑓𝑓 𝑀𝑀0,π‘‘π‘‘π‘šπ‘šπ‘ π‘ =𝑀𝑀0,𝑑𝑑𝑓𝑓 Sticky price model Hypothetical flexible price model 0 subscript: equilibrium value f superscript: hypothetical flexible price equilibrium sr or mr superscript: short run or medium run 𝐿𝐿𝐿𝐿�𝐿𝐿𝑑𝑑,𝑃𝑃0,𝑑𝑑𝑓
𝑓�= 𝐿𝐿𝐿𝐿(𝐿𝐿𝑑𝑑,𝑃𝑃0,π‘‘π‘‘π‘šπ‘šπ‘ π‘ ) π‘Ÿπ‘Ÿ0,π‘‘π‘‘π‘šπ‘šπ‘ π‘ =π‘Ÿπ‘Ÿ0,𝑑𝑑𝑓𝑓 𝐴𝐴𝐴𝐴′ Sticky price model, post price adjustment 𝑀𝑀0,𝑑𝑑𝑠𝑠𝑠𝑠 𝑃𝑃0,𝑑𝑑𝑠𝑠𝑠𝑠=𝑃𝑃�𝑑𝑑𝑠𝑠𝑠𝑠 𝑃𝑃0,π‘‘π‘‘π‘šπ‘šπ‘ π‘ =π‘ƒπ‘ƒοΏ½π‘‘π‘‘π‘šπ‘šπ‘ π‘ =𝑃𝑃0,𝑑𝑑𝑓𝑓 in both the short run and the medium run. For these exercises, we use solid black lines to denote the curves corresponding to the original sticky price equilibrium, and solid orange lines to denote the supply-side curves corresponding with the original hypothetical flexible price equilibrium. Blue lines depict how the curves shift in response to a change in an exogenous variable in the sticky price model, while red lines depict how the supply-side curves in the hypothetical flexible price model would shift. The gray lines denote how the sticky price model reacts in the medium run after price adjustment has had a chance to take place. We use 0 subscripts to denote the original equilibrium and 1 subscripts to denote the equilibrium after the change in the relevant exogenous variable. sr superscripts denote the short run equilibrium (either before or after the shock), while mr superscripts denote the equilibrium after price adjustment has had a chance to take place. Figure 27.3 considers the case of an exogenous increase in the money supply. Holding the price level fixed, there is a rightward shift of the LM curve
, which results in a rightward shift of the AD curve (shown in blue). With a horizontal AS curve, this results in an increase 1,t and rsr in output and a lower real interest rate in the short run, which are labeled Y sr 1,t, respectively. To support the higher level of output, labor input must rise, to N sr 1,t. This is 1,t. Since a change in Mt has no effect on Y f supported by an increase in the real wage to wsr t, the short run equilibrium features a positive output gap. The firm is producing more than it would like. After a couple of years, the firm will adjust its price to Β―P mr. This adjustment will be such that the new AS curve (shown in gray) intersects the new AD curve at the original level of output. The increase in the price level causes the LM curve to shift back in to where it started. Labor input and the real wage are unaffected in the medium run relative to their = N mr pre-shock values, so wmr 0,t. 1,t 0,t and N mr 1,t = wsr t 594 Figure 27.3: Simple Sticky Price Model: Increase in Mt, Short Run to Medium Run What we see in Figure 27.3 is that an increase in the money supply temporarily results in an increase in output and a reduction in the real interest rate. Once the firm is able to adjust its price, the only effect of the increase in Mt is a higher price level (i.e. the same as in the neoclassical model). This is made clear in Figure 27.4. Here we plot responses of variables to a shock over period t, where we have split the period into three different time periods (years 595 𝑀𝑀𝑑𝑑 𝑃𝑃𝑑𝑑 π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ 𝑁𝑁𝑑𝑑 𝑁𝑁𝑑
𝑑 𝐴𝐴𝐴𝐴 𝐼𝐼𝐴𝐴 π‘Ÿπ‘Ÿ1,π‘‘π‘‘π‘šπ‘šπ‘šπ‘š=π‘Ÿπ‘Ÿ0,π‘‘π‘‘π‘ π‘ π‘šπ‘š π‘Œπ‘Œ0,π‘‘π‘‘π‘ π‘ π‘šπ‘š=π‘Œπ‘Œ1,π‘‘π‘‘π‘šπ‘šπ‘šπ‘š 𝑁𝑁0,π‘‘π‘‘π‘ π‘ π‘šπ‘š=𝑁𝑁1,π‘‘π‘‘π‘šπ‘šπ‘šπ‘š 𝑁𝑁𝑠𝑠(𝑀𝑀𝑑𝑑,πœƒπœƒπ‘‘π‘‘) 𝐿𝐿𝐿𝐿�𝐿𝐿0,𝑑𝑑,𝑃𝑃0,π‘‘π‘‘π‘ π‘ π‘šπ‘šοΏ½=𝐿𝐿𝐿𝐿�𝐿𝐿1,𝑑𝑑,𝑃𝑃1,π‘‘π‘‘π‘šπ‘šπ‘šπ‘šοΏ½ 𝐴𝐴𝑑𝑑𝐹𝐹(𝐾𝐾𝑑𝑑,𝑁𝑁𝑑𝑑) π‘Œπ‘Œπ‘‘π‘‘=π‘Œπ‘Œπ‘‘π‘‘ π‘Ÿπ‘Ÿπ‘‘π‘‘ 𝐴𝐴𝐴𝐴 𝑃𝑃1,π‘‘π‘‘π‘ π‘ π‘šπ‘š=𝑃𝑃0,π‘‘π‘‘π‘ π‘ π‘šπ‘š=𝑃𝑃�𝑑𝑑�
οΏ½π‘ π‘šπ‘š 𝑀𝑀1,π‘‘π‘‘π‘šπ‘šπ‘šπ‘š=𝑀𝑀0,π‘‘π‘‘π‘ π‘ π‘šπ‘š 𝐿𝐿𝐿𝐿(𝐿𝐿1,𝑑𝑑,𝑃𝑃0,π‘‘π‘‘π‘ π‘ π‘šπ‘š) π‘Œπ‘Œ1,π‘‘π‘‘π‘ π‘ π‘šπ‘š 𝑀𝑀1,π‘‘π‘‘π‘ π‘ π‘šπ‘š 𝑁𝑁1,π‘‘π‘‘π‘ π‘ π‘šπ‘š 𝐴𝐴𝐴𝐴′ π‘Ÿπ‘Ÿ1,π‘‘π‘‘π‘ π‘ π‘šπ‘š 0 subscript: original 1 subscript: post-shock sr or mr superscript: short run or medium run Original Post-shock, short run 𝐴𝐴𝐴𝐴𝑓𝑓 𝐴𝐴𝐴𝐴′ 𝑃𝑃1,π‘‘π‘‘π‘šπ‘šπ‘šπ‘š=π‘ƒπ‘ƒοΏ½π‘‘π‘‘π‘šπ‘šπ‘šπ‘š Post-shock, medium run Original, hypothetical flexible price Post-shock, flexible price 𝑁𝑁𝑑𝑑(𝑀𝑀𝑑𝑑,𝐴𝐴𝑑𝑑,𝐾𝐾𝑑𝑑) t 1, 2, and 3). For years 1 and 2, Β―P sr is fixed. In year 3, the exogenous component of the price t level adjusts to Β―P mr so as to restore the neoclassical equilibrium. The upper left panel simply plots what happens to Mt, which is exogenously given. In the upper right panel, we see that output jumps up when
Mt increases and remains high for two years before returning to its pre-shock value. The price level, plotted in the lower left portion, does not change in the short run in the simply sticky price model by construction. It only jumps up in year 3. The real interest rate response is the mirror image of the output response – it temporarily falls for years 1 and 2 before returning to its pre-shock value in year 3. Figure 27.4: Short Run and Medium Responses: Increase in Mt Next, consider the effects of a positive IS shock (either an increase in At+1 or Gt, or a decrease in Gt+1). This results in the IS curve shifting to the right, which results in a rightward shift of the AD curve. With a horizontal AS curve, this results in an increase in output. The real interest rate is higher. To support the higher level of output, labor input must increase, and so too must the real wage to be consistent with the labor supply curve. These effects are shown in Figure 27.5. 596 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝑀𝑀 π‘Œπ‘Œ 𝑃𝑃 π‘Ÿπ‘Ÿ 𝑑𝑑 𝑑𝑑 1 2 3 1 2 3 𝑃𝑃0,𝑑𝑑𝑠𝑠𝑠𝑠 π‘Ÿπ‘Ÿ1,π‘‘π‘‘π‘šπ‘šπ‘ π‘ =π‘Ÿπ‘Ÿ0,𝑑𝑑𝑠𝑠𝑠𝑠 π‘Œπ‘Œ1,π‘‘π‘‘π‘šπ‘šπ‘ π‘ =π‘Œπ‘Œ0,𝑑𝑑𝑠𝑠𝑠𝑠
𝑀𝑀0,𝑑𝑑 𝑀𝑀1,𝑑𝑑 π‘Œπ‘Œ1,𝑑𝑑𝑠𝑠𝑠𝑠 𝑃𝑃1,π‘‘π‘‘π‘šπ‘šπ‘ π‘  π‘Ÿπ‘Ÿ1,𝑑𝑑𝑠𝑠𝑠𝑠 Figure 27.5: Simple Sticky Price Model: Positive IS Shock, Short Run to Medium Run Since a positive IS shock does not impact the neoclassical level of output, in the short run the firm is producing more than it finds optimal. To reduce production, when given the opportunity to do so, the firm will increase its price to Β―P mr. This results in the AS curve shifting up so as to intersect the new AD curve at the original level of output. At this new medium run equilibrium labor market variables are back to their pre-shock values. The t 597 𝑀𝑀𝑑𝑑 𝑃𝑃𝑑𝑑 π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ 𝑁𝑁𝑑𝑑 𝑁𝑁𝑑𝑑 𝐴𝐴𝐴𝐴 𝐼𝐼𝐴𝐴 𝑁𝑁0,𝑑𝑑𝑠𝑠𝑠𝑠=𝑁𝑁1,π‘‘π‘‘π‘šπ‘šπ‘ π‘  𝑁𝑁𝑠𝑠(𝑀𝑀𝑑𝑑,πœƒπœƒπ‘‘π‘‘) 𝐿𝐿𝐿𝐿(𝐿𝐿𝑑𝑑,𝑃𝑃0,
𝑑𝑑𝑠𝑠𝑠𝑠) 𝐴𝐴𝑑𝑑𝐹𝐹(𝐾𝐾𝑑𝑑,𝑁𝑁𝑑𝑑) π‘Œπ‘Œπ‘‘π‘‘=π‘Œπ‘Œπ‘‘π‘‘ π‘Ÿπ‘Ÿπ‘‘π‘‘ 𝐴𝐴𝐴𝐴 𝐴𝐴𝐴𝐴′ 𝑁𝑁1,𝑑𝑑𝑠𝑠𝑠𝑠 𝐼𝐼𝐴𝐴′ 0 subscript: original 1 subscript: post-shock sr or mr superscript: short run or medium run Original Post-shock Post-shock, post price adjustment Original, hypothetical flexible price Post-shock, flexible price 𝑁𝑁𝑑𝑑(𝑀𝑀𝑑𝑑,𝐴𝐴𝑑𝑑,𝐾𝐾𝑑𝑑) 𝐴𝐴𝐴𝐴′ 𝐿𝐿𝐿𝐿(𝐿𝐿𝑑𝑑,𝑃𝑃1,π‘‘π‘‘π‘šπ‘šπ‘ π‘ ) π‘Ÿπ‘Ÿ1,π‘‘π‘‘π‘šπ‘šπ‘ π‘  𝐴𝐴𝐴𝐴𝑓𝑓 π‘Ÿπ‘Ÿ1,𝑑𝑑𝑠𝑠𝑠𝑠 π‘Ÿπ‘Ÿ0,𝑑𝑑𝑠𝑠𝑠𝑠 𝑀𝑀1,𝑑𝑑𝑠𝑠𝑠𝑠 𝑀𝑀1,π‘‘π‘‘π‘šπ‘šπ‘ π‘ =𝑀𝑀0,𝑑𝑑𝑠�
�𝑠𝑠 𝑃𝑃1,𝑑𝑑𝑠𝑠𝑠𝑠=𝑃𝑃0,𝑑𝑑𝑠𝑠𝑠𝑠=𝑃𝑃�𝑑𝑑𝑠𝑠𝑠𝑠 𝑃𝑃1,π‘‘π‘‘π‘šπ‘šπ‘ π‘ =π‘ƒπ‘ƒοΏ½π‘‘π‘‘π‘šπ‘šπ‘ π‘  π‘Œπ‘Œ0,𝑑𝑑𝑠𝑠𝑠𝑠=π‘Œπ‘Œ1,π‘‘π‘‘π‘šπ‘šπ‘ π‘  π‘Œπ‘Œ1,𝑑𝑑𝑠𝑠𝑠𝑠 > rsr higher price level results in the LM curve shifting in so as to intersect the new IS curve at the original, pre-shock level of output. The real interest rate is higher than in the short run, with rmr 1,t. Figure 27.6 plots the responses of output, the price level, and the real interest 1,t rate to a positive IS shock over the course of period t. For years 1-2, output and the real interest rate jump up and the price level is unchanged. Once year 3 rolls around, the firm can raise its price. This results in output falling back to its original pre-shock value and the real interest rate rising even further, so that rmr 1,t > rsr 0,t. > rsr 1,t Figure 27.6: Short Run and Medium Responses: Positive IS Shock Next, consider an increase in At. In the simple sticky price model, since the AS curve is horizontal and solely determined by Β―Pt, this results in no effect on the equilibrium values output or the real interest rate in the short run. If output is unchanged but productivity is higher, labor input must decline in the short run. To support lower labor input, the real wage must fall. The hypothetical flexible price vertical AS curve shifts to the right – i.e. the neoclassical level of output increases
to Y f 1,t. This means that equilibrium output in the short run, Y sr 1,t, is lower than it would be if the price level were flexible. Hence, there will be pressure on the firm to lower the price level. In Figure 27.7, we observe that this results in the AS curve shifting down (shown in gray) so as to intersect the AD curve at the new 598 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 π‘Œπ‘Œ 𝑃𝑃 π‘Ÿπ‘Ÿ 𝑑𝑑 𝑑𝑑 1 2 3 1 2 3 𝑃𝑃0,𝑑𝑑𝑠𝑠𝑠𝑠 π‘Ÿπ‘Ÿ0,𝑑𝑑𝑠𝑠𝑠𝑠 π‘Œπ‘Œ1,π‘‘π‘‘π‘šπ‘šπ‘ π‘ =π‘Œπ‘Œ0,𝑑𝑑𝑠𝑠𝑠𝑠 π‘Œπ‘Œ1,𝑑𝑑𝑠𝑠𝑠𝑠 𝑃𝑃1,π‘‘π‘‘π‘šπ‘šπ‘ π‘  π‘Ÿπ‘Ÿ1,𝑑𝑑𝑠𝑠𝑠𝑠 π‘Ÿπ‘Ÿ1,π‘‘π‘‘π‘šπ‘šπ‘ π‘  hypothetical vertical AS curve. The lower price level triggers an outward shift of the LM curve, resulting in a lower real interest rate. The higher level of output necessitates more labor input, so both labor input and the real wage rise, ending up at the point where labor demand intersects labor supply. Figure 27
.7: Sticky Price Model: Increase in At, Short Run to Medium Run Figure 27.8 plots the responses of variables over period t to an increase in At (plotted in 599 𝐴𝐴𝐴𝐴 𝑁𝑁𝑠𝑠(𝑀𝑀𝑑𝑑,πœƒπœƒπ‘‘π‘‘) 𝐴𝐴𝐴𝐴 𝑀𝑀0,𝑑𝑑𝑠𝑠𝑠𝑠 𝐴𝐴1,𝑑𝑑𝐹𝐹(𝐾𝐾𝑑𝑑,𝑁𝑁𝑑𝑑) 0 subscript: original 1 subscript: post-shock sr or mr superscript: short run or medium run Original Post-shock Post-shock, post price adjustment Original, hypothetical flexible price Post-shock, flexible price 𝐴𝐴𝐴𝐴′ 𝑀𝑀𝑑𝑑 𝑃𝑃𝑑𝑑 π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ 𝑁𝑁𝑑𝑑 𝑁𝑁𝑑𝑑 𝐿𝐿𝐿𝐿(𝐿𝐿𝑑𝑑,𝑃𝑃1,π‘‘π‘‘π‘šπ‘šπ‘ π‘ ) π‘Œπ‘Œ0,𝑑𝑑𝑠𝑠𝑠𝑠=π‘Œπ‘Œ1,𝑑𝑑𝑠𝑠𝑠𝑠 π‘Œπ‘Œ1,π‘‘π‘‘π‘šπ‘šπ‘ π‘  π‘Ÿπ‘Ÿ1,π‘‘π‘‘π‘šοΏ½
�𝑠𝑠 𝐴𝐴𝐴𝐴𝑓𝑓 𝐴𝐴𝐴𝐴𝑓𝑓′ 𝑁𝑁𝑑𝑑(𝑀𝑀𝑑𝑑,𝐴𝐴0,𝑑𝑑,𝐾𝐾𝑑𝑑) 𝐼𝐼𝐴𝐴 𝑁𝑁𝑑𝑑(𝑀𝑀𝑑𝑑,𝐴𝐴1,𝑑𝑑,𝐾𝐾𝑑𝑑) 𝑀𝑀1,𝑑𝑑𝑠𝑠𝑠𝑠 𝑀𝑀1,π‘‘π‘‘π‘šπ‘šπ‘ π‘  𝑁𝑁0,𝑑𝑑𝑠𝑠𝑠𝑠 𝐿𝐿𝐿𝐿(𝐿𝐿𝑑𝑑,𝑃𝑃0,𝑑𝑑𝑠𝑠𝑠𝑠) 𝐴𝐴0,𝑑𝑑𝐹𝐹(𝐾𝐾𝑑𝑑,𝑁𝑁𝑑𝑑) π‘Œπ‘Œπ‘‘π‘‘=π‘Œπ‘Œπ‘‘π‘‘ π‘Ÿπ‘Ÿπ‘‘π‘‘ π‘Ÿπ‘Ÿ1,𝑑𝑑𝑠𝑠𝑠𝑠=π‘Ÿπ‘Ÿ0,𝑑𝑑𝑠𝑠𝑠𝑠 𝑃𝑃1,π‘‘π‘‘π‘šπ‘šπ‘ π‘ =π‘ƒπ‘ƒοΏ½π‘‘π‘‘π‘šπ‘šπ‘ π‘  𝑃𝑃1,𝑑�
��𝑠𝑠𝑠𝑠=𝑃𝑃0,𝑑𝑑𝑠𝑠𝑠𝑠=𝑃𝑃�𝑑𝑑𝑠𝑠𝑠𝑠 𝑁𝑁1,𝑑𝑑𝑠𝑠𝑠𝑠 𝑁𝑁1,π‘‘π‘‘π‘šπ‘šπ‘ π‘  the upper left quadrant). In the short run (years 1-2), output, the price level, and the real interest rate are all unaffected. Once the firm has had a chance to adjust its price in year 3, output jumps up to the neoclassical level and the price level and the real interest rate fall. Figure 27.8: Short Run and Medium Responses: Increase in At We leave an analysis of the dynamic effects of an increase in ΞΈt as an exercise. Table 27.1 shows how endogenous variables qualitatively react to exogenous shocks during the transition from the short run to the medium run. A + sign indicates that a variable increases, whereas a βˆ’ sign indicates that a variable decreases. For example, in the column ↑ Mt, the entry for output is a βˆ’ sign. Output increases in the short run, but declines during the transition from short run to medium run. In the table, output and the price level always move in opposite directions during the transition period – if output is declining, the price level is increasing, and vice-versa. This is because it is the AS curve that is shifting during the transition from medium run to short run, so the price level and output must move opposite one another. 600 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝐴𝐴 π‘Œπ‘Œ 𝑃𝑃 οΏ½
οΏ½π‘Ÿ 𝑑𝑑 𝑑𝑑 1 2 3 1 2 3 𝑃𝑃0,𝑑𝑑𝑠𝑠𝑠𝑠 π‘Ÿπ‘Ÿ1,𝑑𝑑𝑠𝑠𝑠𝑠=π‘Ÿπ‘Ÿ0,𝑑𝑑𝑠𝑠𝑠𝑠 π‘Œπ‘Œ1,𝑑𝑑𝑠𝑠𝑠𝑠=π‘Œπ‘Œ0,𝑑𝑑𝑠𝑠𝑠𝑠 𝐴𝐴0,𝑑𝑑 𝐴𝐴1,𝑑𝑑 π‘Œπ‘Œ1,π‘‘π‘‘π‘šπ‘šπ‘ π‘  𝑃𝑃1,π‘‘π‘‘π‘šπ‘šπ‘ π‘  π‘Ÿπ‘Ÿ1,π‘‘π‘‘π‘šπ‘šπ‘ π‘  Table 27.1: Qualitative Effects of Exogenous Shocks on Endogenous Variables in the Sticky Price Model, Transition from Short Run to Medium Run Variable Yt Nt wt rt Pt Exogenous Shock ↑ IS curve - ↑ Mt - ↑ At + - - + + - - + + + + - - 27.2 Partial Sticky Price Model We next consider the partial sticky price model. The AS curve is given by Pt = Β―Pt + Ξ³(Yt βˆ’ Y f ). If Ξ³ = 0, then this reverts to the simple sticky price model. More generally, the AS t curve is upward-sloping but not horizontal. As in the simple sticky price model, if Yt β‰  Y f t, changes in Β―Pt are what will occur to shift the AS curve as the economy transitions from short run to medium run. 27.2.1 A Non-Optimal Short Run Equilibrium We first suppose that the initial short run equilibrium features equilibrium output below the neoclassical level of output; i.e. Y0,t < Y f 0,t. This is
depicted in Figure 27.9. 601 Figure 27.9: Partial Sticky Price Model: Y0,t < Y f 0,t If the AS and AD curves intersect at a lower level of output than would obtain if prices > P f were flexible and the AS curve were vertical, we know that it must be the case that P sr 0,t 0,t (i.e. the equilibrium price level if prices were flexible). We also know that the equilibrium 0,t, must be less than the exogenous component of the price level, Β―P sr price level, P sr 0,t. How t at Β―P sr do we know this? We know that the AS curve must pass through the point Yt = Y f. t 602 𝑀𝑀𝑑𝑑 𝑃𝑃𝑑𝑑 π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ 𝑁𝑁𝑑𝑑 𝑁𝑁𝑑𝑑 𝐴𝐴𝐴𝐴 𝐼𝐼𝐴𝐴 𝑁𝑁𝑠𝑠(𝑀𝑀𝑑𝑑,πœƒπœƒπ‘‘π‘‘) 𝐿𝐿𝐿𝐿(𝐿𝐿𝑑𝑑,𝑃𝑃0,𝑑𝑑𝑠𝑠𝑠𝑠) 𝐴𝐴𝑑𝑑𝐹𝐹(𝐾𝐾𝑑𝑑,𝑁𝑁𝑑𝑑) π‘Œπ‘Œπ‘‘π‘‘=π‘Œπ‘Œπ‘‘π‘‘ π‘Ÿπ‘Ÿπ‘‘π‘‘ 𝐴𝐴𝐴𝐴 𝑁𝑁0,𝑑
𝑑𝑓𝑓 π‘Œπ‘Œ0,𝑑𝑑𝑓𝑓 𝑁𝑁𝑑𝑑(𝑀𝑀𝑑𝑑,𝐴𝐴𝑑𝑑,𝐾𝐾𝑑𝑑) 𝐴𝐴𝐴𝐴𝑓𝑓 𝑀𝑀0,𝑑𝑑𝑓𝑓 Sticky price model Hypothetical flexible price model 𝑃𝑃0,𝑑𝑑𝑓𝑓 0 subscript: equilibrium value f superscript: hypothetical flexible price equilibrium sr or mr superscript: short run or medium run 𝐿𝐿𝐿𝐿(𝐿𝐿𝑑𝑑,𝑃𝑃0,𝑑𝑑𝑓𝑓) π‘Ÿπ‘Ÿ0,𝑑𝑑𝑓𝑓 𝑀𝑀0,𝑑𝑑𝑠𝑠𝑠𝑠 π‘Ÿπ‘Ÿ0,𝑑𝑑𝑠𝑠𝑠𝑠 𝑃𝑃0,𝑑𝑑𝑠𝑠𝑠𝑠 𝑁𝑁0,𝑑𝑑𝑠𝑠𝑠𝑠 π‘Œπ‘Œ0,𝑑𝑑𝑠𝑠𝑠𝑠 𝑃𝑃�𝑑𝑑𝑠𝑠𝑠𝑠 t < Y f t > P sr t initially, it must be the case that Β―P sr 0,t Since Y sr. What this means, in effect, is that the firm is stuck with a higher price than it would otherwise find optimal. It would like to lower its price to generate more demand. This means that, as the economy transitions from short run to medium run, Β―Pt will fall down to P f 0,t. This
will cause the AS curve to shift down so that it intersects the AD curve at Y f 0,t. This movement is conceptually similar to what is documented in 27.2, only with an upward-sloping rather than vertical AS curve. The dynamic effects are shown in Figure 27.10 below. 603 Figure 27.10: Partial Sticky Price Model: Y0,t < Y f 0,t, Short Run to Medium Run Price Adjustment 27.2.2 Dynamic Responses to Shocks As we did above, we now consider the dynamic responses to exogenous shocks. We suppose that initially the equilibrium of the partial sticky price model coincides with the 604 𝑀𝑀𝑑𝑑 𝑃𝑃𝑑𝑑 π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ 𝑁𝑁𝑑𝑑 𝑁𝑁𝑑𝑑 𝐴𝐴𝐴𝐴 𝐼𝐼𝐴𝐴 π‘Ÿπ‘Ÿ0,𝑑𝑑𝑠𝑠𝑠𝑠 π‘Œπ‘Œ0,𝑑𝑑𝑠𝑠𝑠𝑠 𝑁𝑁𝑠𝑠(𝑀𝑀𝑑𝑑,πœƒπœƒπ‘‘π‘‘) 𝐿𝐿𝐿𝐿(𝐿𝐿𝑑𝑑,𝑃𝑃0,𝑑𝑑𝑠𝑠𝑠𝑠) 𝐴𝐴𝑑𝑑𝐹𝐹(𝐾𝐾𝑑𝑑,𝑁𝑁𝑑𝑑) π‘Œπ‘Œπ‘‘π‘‘=π‘Œπ‘Œπ‘‘π‘‘ π‘Ÿ
π‘Ÿπ‘‘π‘‘ 𝐴𝐴𝐴𝐴 𝑃𝑃�𝑑𝑑𝑠𝑠𝑠𝑠 𝑀𝑀0,𝑑𝑑𝑠𝑠𝑠𝑠 π‘Œπ‘Œ0,π‘‘π‘‘π‘šπ‘šπ‘ π‘ =π‘Œπ‘Œ0,𝑑𝑑𝑓𝑓 𝑁𝑁𝑑𝑑(𝑀𝑀𝑑𝑑,𝐴𝐴𝑑𝑑,𝐾𝐾𝑑𝑑) 𝐴𝐴𝐴𝐴𝑓𝑓 𝑀𝑀0,π‘‘π‘‘π‘šπ‘šπ‘ π‘ =𝑀𝑀0,𝑑𝑑𝑓𝑓 Sticky price model Hypothetical flexible price model Sticky price model, post price adjustment 𝑃𝑃0,π‘‘π‘‘π‘šπ‘šπ‘ π‘ =π‘ƒπ‘ƒοΏ½π‘‘π‘‘π‘šπ‘šπ‘ π‘ =𝑃𝑃0,𝑑𝑑𝑓𝑓 0 subscript: equilibrium value f superscript: hypothetical flexible price equilibrium sr or mr superscript: short run or medium run 𝐿𝐿𝐿𝐿�𝐿𝐿𝑑𝑑,𝑃𝑃0,𝑑𝑑𝑓𝑓�=𝐿𝐿𝐿𝐿(𝐿𝐿𝑑𝑑,𝑃𝑃0,π‘‘π‘‘π‘šπ‘šπ‘ π‘ ) π‘Ÿπ‘Ÿ0,π‘‘π‘‘π‘šπ‘šπ‘ π‘ =π‘Ÿπ‘Ÿ0,𝑑𝑑𝑓𝑓
𝑃𝑃0,𝑑𝑑𝑠𝑠𝑠𝑠 𝐴𝐴𝐴𝐴′ 𝑁𝑁0,π‘‘π‘‘π‘šπ‘šπ‘ π‘ =𝑁𝑁0,𝑑𝑑𝑓𝑓 𝑁𝑁0,𝑑𝑑𝑠𝑠𝑠𝑠 equilibrium of a hypothetical flexible price economy. Then we consider an exogenous shock and look at how the values of endogenous variables change in the short run (denoted with a sr superscript). Then we ask how the AS curve must shift in response so as to restore the flexible price equilibrium in the medium run (once again denoted with a mr superscript). We begin with an exogenous increase in Mt. This is depicted in Figure 27.11. The immediate impact of an increase in Mt is a rightward shift of the LM curve, shown in blue. This shift is drawn holding the price level fixed. This results in the AD curve shifting out to the right. Since the AS curve is not horizontal, in equilibrium, both output and the price level increase. This means that output will rise by less than the magnitude of the horizontal shift of the AD curve. The higher price level causes the LM curve to shift back in partially (shown in green). The real interest is lower than it was before the increase in the money supply. To support higher output, labor input must increase and the real wage must rise in the short run. After the increase in the money supply, output is above potential and the equilibrium price level is higher than the exogenous component of the price level, i.e. P sr. The firm 1,t is producing more than it finds optimal and would like to raise Β―Pt when given the opportunity to do so. In particular, Β―P mr t will increase in such a way that the AS curve shifts up so as to intersect the new AD curve at the original level of output (i.e. Y mr 0,t ). At the new 1,t medium run equilibrium, we have P mr. The increase in the price level triggers an 1,t inward shift of the LM curve so that on net the
position of the LM curve is unaffected, leaving the real interest rate unchanged relative to its pre-shock value. Labor market variables are unchanged relative to their values from before the increase in the money supply. = Β―P mr t > Β―P sr t = Y sr 605 Figure 27.11: Partial Sticky Price: Increase in Mt, Short Run to Medium Run Figure 27.12 plots the dynamic paths of different variables throughout period t, which we again divide into three segments – years 1 and 2 are the short run, while by year 3 it is the medium run. 0 subscripts denote values prior to an exogenous shock, while 1 subscripts refer to values post-shock. Output increases in the short run from Y sr 0,t to Y sr 1,t, but in the medium run returns to its initial level, Y mr 0,t. The price level increases in the short run, from 1,t = Y sr 606 𝑀𝑀𝑑𝑑 𝑃𝑃𝑑𝑑 π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ 𝑁𝑁𝑑𝑑 𝑁𝑁𝑑𝑑 𝐴𝐴𝐴𝐴 𝐼𝐼𝐴𝐴 π‘Ÿπ‘Ÿ1,π‘‘π‘‘π‘šπ‘šπ‘šπ‘š=π‘Ÿπ‘Ÿ0,π‘‘π‘‘π‘ π‘ π‘šπ‘š 𝑁𝑁0,π‘‘π‘‘π‘ π‘ π‘šπ‘š=𝑁𝑁1,π‘‘π‘‘π‘šπ‘šπ‘šπ‘š 𝑁𝑁𝑠𝑠(𝑀𝑀𝑑𝑑,πœƒπœƒπ‘‘π‘‘) 𝐿𝐿𝐿𝐿��
�𝐿0,𝑑𝑑,𝑃𝑃0,π‘‘π‘‘π‘ π‘ π‘šπ‘šοΏ½=𝐿𝐿𝐿𝐿(𝐿𝐿1,𝑑𝑑,𝑃𝑃1,π‘‘π‘‘π‘šπ‘šπ‘šπ‘š) 𝐴𝐴𝑑𝑑𝐹𝐹(𝐾𝐾𝑑𝑑,𝑁𝑁𝑑𝑑) π‘Œπ‘Œπ‘‘π‘‘=π‘Œπ‘Œπ‘‘π‘‘ π‘Ÿπ‘Ÿπ‘‘π‘‘ 𝐴𝐴𝐴𝐴 𝑃𝑃0,π‘‘π‘‘π‘ π‘ π‘šπ‘š=π‘ƒπ‘ƒοΏ½π‘‘π‘‘π‘ π‘ π‘šπ‘š 𝑁𝑁𝑑𝑑(𝑀𝑀𝑑𝑑,𝐴𝐴𝑑𝑑,𝐾𝐾𝑑𝑑) 𝐴𝐴𝐴𝐴𝑓𝑓 𝐿𝐿𝐿𝐿(𝐿𝐿1,𝑑𝑑,𝑃𝑃0,π‘‘π‘‘π‘ π‘ π‘šπ‘š) 𝐴𝐴𝐴𝐴′ 𝑁𝑁1,π‘‘π‘‘π‘ π‘ π‘šπ‘š 𝑃𝑃1,π‘‘π‘‘π‘ π‘ π‘šπ‘š π‘Ÿπ‘Ÿ1,π‘‘π‘‘π‘ π‘ π‘šπ‘š 𝐿𝐿𝐿𝐿(𝐿𝐿1,𝑑𝑑,𝑃𝑃1,𝑑�
οΏ½οΏ½π‘ π‘ π‘šπ‘š) Original Post-Shock Post-shock, indirect effect of 𝑃𝑃𝑑𝑑 on LM curve 0 subscript: original 1 subscript: post-shock sr or mr superscript: short run or medium run Original, hypothetical flexible price Post-shock, flexible price 𝑃𝑃1,π‘‘π‘‘π‘šπ‘šπ‘šπ‘š=π‘ƒπ‘ƒοΏ½π‘‘π‘‘π‘šπ‘šπ‘šπ‘š Post-shock, post-price adjustment 𝐴𝐴𝐴𝐴′ 𝑀𝑀1,π‘‘π‘‘π‘ π‘ π‘šπ‘š 𝑀𝑀1,π‘‘π‘‘π‘šπ‘šπ‘šπ‘š=𝑀𝑀0,π‘‘π‘‘π‘ π‘ π‘šπ‘š π‘Œπ‘Œ1,π‘‘π‘‘π‘ π‘ π‘šπ‘š π‘Œπ‘Œ0,π‘‘π‘‘π‘ π‘ π‘šπ‘š=π‘Œπ‘Œ1,π‘‘π‘‘π‘šπ‘šπ‘šπ‘š > P sr 1,t, and increases by more moving from short run to medium run, with P mr 0,t to P sr P sr 1,t. 1,t The real interest rate declines in the short run before returning to its pre-shock value in the medium run. Figure 27.12: Short Run and Medium Responses: Increase in Mt To compare the behavior of the economy across the partial and simple sticky price models, in Figure 27.13 we plot the paths of variables in both the partial sticky price model (black) and the simple sticky price model (blue). This is essentially a combination of Figures 27.4 and 27.12. For the same change in the money supply, in the short run output reacts more in the simple sticky price model compared to the partial sticky price model. In contrast, the price level reacts more in the short run in the partial sticky price model. The real interest rate falls more in the simple sticky price model. The
value of Ξ³ (i.e. the slope of the AS curve in the partial sticky price model) determines where the partial sticky price responses lie compared to (i) the simple sticky price responses and (ii) the medium run responses. The smaller is Ξ³, the closer will be the partial sticky price model responses to the simple sticky price model in the short run, while the bigger is Ξ³, the closer these responses in the short run will be to the medium run values. Note that the medium run values of endogenous variables are the same for both the partial and simple sticky price models. 607 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝑀𝑀 π‘Œπ‘Œ 𝑃𝑃 π‘Ÿπ‘Ÿ 𝑑𝑑 𝑑𝑑 1 2 3 1 2 3 𝑃𝑃0,𝑑𝑑𝑠𝑠𝑠𝑠 π‘Ÿπ‘Ÿ1,π‘‘π‘‘π‘šπ‘šπ‘ π‘ =π‘Ÿπ‘Ÿ0,𝑑𝑑𝑠𝑠𝑠𝑠 π‘Œπ‘Œ1,π‘‘π‘‘π‘šπ‘šπ‘ π‘ =π‘Œπ‘Œ0,𝑑𝑑𝑠𝑠𝑠𝑠 𝑀𝑀0,𝑑𝑑 𝑀𝑀1,𝑑𝑑 𝑃𝑃1,π‘‘π‘‘π‘šπ‘šπ‘ π‘  π‘Ÿπ‘Ÿ1,𝑑𝑑𝑠𝑠𝑠𝑠 π‘Œπ‘Œ1,𝑑𝑑𝑠𝑠
𝑠𝑠 𝑃𝑃1,𝑑𝑑𝑠𝑠𝑠𝑠 Figure 27.13: Short Run and Medium Responses: Increase in Mt Comparing Simple Sticky Price to Partial Sticky Price Model We next consider some shock which shifts the IS curve to the right (i.e. increases in At+1 or Gt or a decrease Gt+1). This is depicted in Figure 27.14. The rightward shift of the IS curve triggers a rightward shift of the AD curve. In equilibrium, both output and the price level rise in the short run. The higher price level causes the LM curve to partially shift back in to the left (shown in green). The real interest rate is higher. To support higher output, labor input rises and the real wage rises. In the new short run equilibrium, output is above potential and the price level is greater than the exogenous component of the AS curve (i.e. P sr. The firm has an incentive to increase its price to reduce production. As the 1,t economy transitions from short run to medium run, the exogenous component of the price level will increase to Β―P mr. This is sufficient to shift the AS curve up (shown in gray) such that it intersects the new AD curve at the original, pre-shock value of output. At the new medium run equilibrium we have P mr. The higher price level causes the LM curve to 1,t shift in such that it intersects the new IS curve at the pre-shock level of output. This results in a further increase in the real interest rate, with rmr 1,t. Relative to prior to the shock, 1,t there are no changes in labor market variables. = Β―P mr t > Β―P sr t > rsr t 608 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝑀𝑀 π‘Œπ‘Œ οΏ½
�𝑃 π‘Ÿπ‘Ÿ 𝑑𝑑 𝑑𝑑 1 2 3 1 2 3 𝑃𝑃1,𝑑𝑑𝑠𝑠𝑠𝑠=𝑃𝑃0,𝑑𝑑𝑠𝑠𝑠𝑠 π‘Ÿπ‘Ÿ1,π‘‘π‘‘π‘šπ‘šπ‘ π‘ =π‘Ÿπ‘Ÿ1,π‘‘π‘‘π‘šπ‘šπ‘ π‘ =π‘Ÿπ‘Ÿ0,𝑑𝑑𝑠𝑠𝑠𝑠 π‘Œπ‘Œ1,π‘‘π‘‘π‘šπ‘šπ‘ π‘ =π‘Œπ‘Œ1,π‘‘π‘‘π‘šπ‘šπ‘ π‘ =π‘Œπ‘Œ0,𝑑𝑑𝑠𝑠𝑠𝑠 𝑀𝑀0,𝑑𝑑 𝑀𝑀1,𝑑𝑑 π‘Ÿπ‘Ÿ1,𝑑𝑑𝑠𝑠𝑠𝑠 π‘Œπ‘Œ1,𝑑𝑑𝑠𝑠𝑠𝑠 𝑃𝑃1,𝑑𝑑𝑠𝑠𝑠𝑠 π‘Œπ‘Œ1,𝑑𝑑𝑠𝑠𝑠𝑠 π‘Ÿπ‘Ÿ1,𝑑𝑑𝑠𝑠𝑠𝑠 𝑃𝑃1,π‘‘π‘‘π‘šπ‘šπ‘ π‘ =𝑃𝑃1,π‘‘π‘‘π‘šπ‘šπ‘ π‘  Partial sticky price Simple sticky price Figure 27.14: Partial Sticky Price: Positive IS Shock, Short Run to Medium Run Figure 27.15 plots the paths of variables in response to the IS shock over period t. Output
, the price level, and the real interest rate all rise in the short run. Although we do not show the comparison formally here, the short run increase in output is smaller than in the simple sticky price model and the short run increase in the real interest rate is larger. As the economy transitions to the medium run (i.e. in year 3), the price level and the real interest 609 𝑀𝑀𝑑𝑑 𝑃𝑃𝑑𝑑 π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ 𝑁𝑁𝑑𝑑 𝑁𝑁𝑑𝑑 𝐴𝐴𝐴𝐴 𝐼𝐼𝐴𝐴 π‘Ÿπ‘Ÿ0,𝑑𝑑𝑠𝑠𝑠𝑠 𝑁𝑁0,𝑑𝑑𝑠𝑠𝑠𝑠=𝑁𝑁1,π‘‘π‘‘π‘šπ‘šπ‘ π‘  𝑁𝑁𝑠𝑠(𝑀𝑀𝑑𝑑,πœƒπœƒπ‘‘π‘‘) 𝐿𝐿𝐿𝐿(𝐿𝐿𝑑𝑑,𝑃𝑃0,𝑑𝑑𝑠𝑠𝑠𝑠) 𝐴𝐴𝑑𝑑𝐹𝐹(𝐾𝐾𝑑𝑑,𝑁𝑁𝑑𝑑) π‘Œπ‘Œπ‘‘π‘‘=π‘Œπ‘Œπ‘‘π‘‘ π‘Ÿπ‘Ÿπ‘‘π‘‘ 𝐴𝐴𝐴𝐴 𝑃𝑃0,𝑑�
�𝑠𝑠𝑠𝑠=𝑃𝑃�𝑑𝑑𝑠𝑠𝑠𝑠 𝑀𝑀1,π‘‘π‘‘π‘šπ‘šπ‘ π‘ =𝑀𝑀0,𝑑𝑑𝑠𝑠𝑠𝑠 𝑁𝑁𝑑𝑑(𝑀𝑀𝑑𝑑,𝐴𝐴𝑑𝑑,𝐾𝐾𝑑𝑑) 𝐴𝐴𝐴𝐴𝑓𝑓 𝐴𝐴𝐴𝐴′ 𝐼𝐼𝐴𝐴′ 𝐿𝐿𝐿𝐿(𝐿𝐿𝑑𝑑,𝑃𝑃1,𝑑𝑑𝑠𝑠𝑠𝑠) 𝑀𝑀1,𝑑𝑑𝑠𝑠𝑠𝑠 𝑁𝑁1,𝑑𝑑𝑠𝑠𝑠𝑠 𝑃𝑃1,𝑑𝑑𝑠𝑠𝑠𝑠 Original Post-Shock Post-shock, indirect effect of 𝑃𝑃𝑑𝑑 on LM curve 0 subscript: original 1 subscript: post-shock sr or mr superscript: short run or medium run Original, hypothetical flexible price Post-shock, flexible price 𝐴𝐴𝐴𝐴′ Post-shock, post-price adjustment 𝐿𝐿𝐿𝐿(𝐿𝐿𝑑𝑑,𝑃𝑃1,π‘‘π‘‘π‘šπ‘šπ‘ π‘ ) π‘Ÿπ‘Ÿ1,π‘‘π‘‘π‘šπ‘šπ‘ π‘  π‘Ÿπ‘Ÿ1,𝑑𝑑𝑠�
�𝑠𝑠 𝑃𝑃1,π‘‘π‘‘π‘šπ‘šπ‘ π‘ =π‘ƒπ‘ƒοΏ½π‘‘π‘‘π‘šπ‘šπ‘ π‘  π‘Œπ‘Œ1,𝑑𝑑𝑠𝑠𝑠𝑠 π‘Œπ‘Œ0,𝑑𝑑𝑠𝑠𝑠𝑠=π‘Œπ‘Œ1,π‘‘π‘‘π‘šπ‘šπ‘ π‘  rate rise further, with output returning to its pre-shock value. Figure 27.15: Short Run and Medium Responses: Positive IS Shock Next consider an exogenous increase in At. As Figure 27.16 shows, this causes the AS curve to shift out horizontally to the right (shown in blue). The magnitude of the horizontal shift is identical to the magnitude of the horizontal shift of the hypothetical vertical neoclassical AS curve (which can be found be finding the level of Nt consistent with being on both labor demand and supply curves consistent with the production function). But because the AS curve is not vertical, in equilibrium output rises by less than the flexible price, neoclassical level of output does (i.e. the change in output is smaller than the horizontal shift of the AS curve). The price level falls. The lower price level triggers an outward shift of the LM curve and a resulting a decline in the real interest rate. It is ambiguous what happens to labor input and the real wage – if the AS curve is relatively flat, these will likely both fall, whereas if the AS curve is comparatively steep, they may both rise. The figure is drawn for the case where both fall in the short run. 610 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 π‘Œπ‘Œ οΏ½
��𝑃 π‘Ÿπ‘Ÿ 𝑑𝑑 𝑑𝑑 1 2 3 1 2 3 𝑃𝑃0,𝑑𝑑𝑠𝑠𝑠𝑠 π‘Ÿπ‘Ÿ0,𝑑𝑑𝑠𝑠𝑠𝑠 π‘Œπ‘Œ1,π‘‘π‘‘π‘šπ‘šπ‘ π‘ =π‘Œπ‘Œ0,𝑑𝑑𝑠𝑠𝑠𝑠 π‘Œπ‘Œ1,𝑑𝑑𝑠𝑠𝑠𝑠 𝑃𝑃1,π‘‘π‘‘π‘šπ‘šπ‘ π‘  π‘Ÿπ‘Ÿ1,𝑑𝑑𝑠𝑠𝑠𝑠 π‘Ÿπ‘Ÿ1,π‘‘π‘‘π‘šπ‘šπ‘ π‘  𝑃𝑃1,𝑑𝑑𝑠𝑠𝑠𝑠 Figure 27.16: Partial Sticky Price: Effect of Increase in At, Dynamics In the short run, output, Y sr 1,t, is less than the neoclassical level of output, Y f 1,t. The firm is producing less than it finds optimal. Once given the opportunity to do so, it will lower the exogenous component of the price level to Β―P mr so as to stimulate demand and increase production. This will result in the AS curve shifting down (shown in gray) such that it intersects the AD curve at the new neoclassical level of output. The price level declines t 611 𝑀𝑀𝑑𝑑 𝑃𝑃𝑑𝑑 π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ 𝑁�
��𝑑𝑑 𝑁𝑁𝑑𝑑 𝐴𝐴𝐴𝐴 𝐼𝐼𝐴𝐴 π‘Œπ‘Œ0,𝑑𝑑𝑠𝑠𝑠𝑠=π‘Œπ‘Œ0,𝑑𝑑𝑓𝑓 𝑁𝑁0,𝑑𝑑𝑠𝑠𝑠𝑠 𝑁𝑁𝑠𝑠(𝑀𝑀𝑑𝑑,πœƒπœƒπ‘‘π‘‘) 𝐿𝐿𝐿𝐿(𝐿𝐿𝑑𝑑,𝑃𝑃0,𝑑𝑑𝑠𝑠𝑠𝑠) 𝐴𝐴0,𝑑𝑑𝐹𝐹(𝐾𝐾𝑑𝑑,𝑁𝑁𝑑𝑑) π‘Œπ‘Œπ‘‘π‘‘=π‘Œπ‘Œπ‘‘π‘‘ π‘Ÿπ‘Ÿπ‘‘π‘‘ 𝐴𝐴𝐴𝐴 𝑃𝑃0,𝑑𝑑𝑠𝑠𝑠𝑠=𝑃𝑃�𝑑𝑑𝑠𝑠𝑠𝑠 𝑀𝑀0,𝑑𝑑𝑠𝑠𝑠𝑠 𝑁𝑁𝑑𝑑(𝑀𝑀𝑑𝑑,𝐴𝐴0,𝑑𝑑,𝐾𝐾𝑑𝑑) 𝐴𝐴𝐴𝐴𝑓𝑓 𝑁𝑁𝑑𝑑(𝑀𝑀𝑑𝑑,𝐴𝐴1,𝑑𝑑
,𝐾𝐾𝑑𝑑) 𝐴𝐴1,𝑑𝑑𝐹𝐹(𝐾𝐾𝑑𝑑,𝑁𝑁𝑑𝑑) 𝐴𝐴𝐴𝐴′ 𝐴𝐴𝐴𝐴𝑓𝑓′ 𝑀𝑀1,𝑑𝑑𝑠𝑠𝑠𝑠 π‘Œπ‘Œ1,π‘‘π‘‘π‘šπ‘šπ‘ π‘ =π‘Œπ‘Œ1,𝑑𝑑𝑓𝑓 π‘Œπ‘Œ1,𝑑𝑑𝑠𝑠𝑠𝑠 𝑃𝑃1,𝑑𝑑𝑠𝑠𝑠𝑠 𝐿𝐿𝐿𝐿(𝐿𝐿𝑑𝑑,𝑃𝑃1,𝑑𝑑𝑠𝑠𝑠𝑠) Original Post-Shock Post-shock, indirect effect of 𝑃𝑃𝑑𝑑 on LM curve Post-shock, post-price adjustment Original, hypothetical flexible price Post-shock, flexible price 0 subscript: original 1 subscript: post-shock f superscript: hypothetical flexible price sr or mr superscript: short run or medium run 𝐿𝐿𝐿𝐿(𝐿𝐿𝑑𝑑,𝑃𝑃1,π‘‘π‘‘π‘šπ‘šπ‘ π‘ ) 𝐴𝐴𝐴𝐴′′ 𝑀𝑀1,π‘‘π‘‘π‘šπ‘šπ‘ π‘  π‘Ÿπ‘Ÿ0,𝑑𝑑𝑠𝑠𝑠𝑠 π‘Ÿπ‘Ÿ1,𝑑𝑑𝑠𝑠𝑠𝑠 π‘Ÿπ‘Ÿ
1,π‘‘π‘‘π‘šπ‘šπ‘ π‘  𝑃𝑃1,π‘‘π‘‘π‘šπ‘šπ‘ π‘ =π‘ƒπ‘ƒοΏ½π‘‘π‘‘π‘šπ‘šπ‘ π‘  𝑁𝑁1,𝑑𝑑𝑠𝑠𝑠𝑠 𝑁𝑁1,π‘‘π‘‘π‘šπ‘šπ‘ π‘  further relative to its short run value, which results in a further outward shift of the LM curve and resulting further decline in the real interest rate. As output rises relative to the short run, labor input and the real wage also increase. Figure 27.17 plots the paths of variables across period t. Output rises, the price level falls, and the real interest rate falls in the short run. Relative to the medium run, these variables all β€œunder-shoot” in that they move by less than they would if the price level were flexible. As the transition to the medium run takes place, output rises further, the price level declines more, and the real interest rate declines further. Figure 27.17: Short Run and Medium Responses: Increase in At Table 27.2 qualitatively describes how different endogenous variables transition from short run to medium run in the partial sticky price model. These are qualitatively identical to what happens in the transition from short run to medium run in the simple sticky price model. Quantitatively, the transitions in the partial sticky price model are smaller than in the simple sticky price model. For example, after an increase in Mt, output declines less in the transition from short run to medium run in the partial sticky price model because it increases by less in the short run. 612 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 𝐴𝐴 π‘ŒοΏ½
οΏ½ 𝑃𝑃 π‘Ÿπ‘Ÿ 𝑑𝑑 𝑑𝑑 1 2 3 1 2 3 𝑃𝑃0,𝑑𝑑𝑠𝑠𝑠𝑠 π‘Ÿπ‘Ÿ0,𝑑𝑑𝑠𝑠𝑠𝑠 π‘Œπ‘Œ0,𝑑𝑑𝑠𝑠𝑠𝑠 𝐴𝐴0,𝑑𝑑 𝐴𝐴1,𝑑𝑑 π‘Œπ‘Œ1,π‘‘π‘‘π‘šπ‘šπ‘ π‘  𝑃𝑃1,π‘‘π‘‘π‘šπ‘šπ‘ π‘  π‘Ÿπ‘Ÿ1,π‘‘π‘‘π‘šπ‘šπ‘ π‘  𝑃𝑃1,𝑑𝑑𝑠𝑠𝑠𝑠 π‘Ÿπ‘Ÿ1,𝑑𝑑𝑠𝑠𝑠𝑠 π‘Œπ‘Œ1,𝑑𝑑𝑠𝑠𝑠𝑠 Table 27.2: Qualitative Effects of Exogenous Shocks on Endogenous Variables in the Partial Sticky Price Model, Transition from Short Run to Medium Run Variable Yt Nt wt rt it Pt Exogenous Shock ↑ IS curve - ↑ Mt - ↑ At + - - + + + - - + + + + + - - - 27.3 The Phillips Curve In macroeconomics, the so-called β€œPhillips Curve” is a name given to a relationship between some measure of real economic activity (e.g. the output gap, Yt βˆ’ Y f t ) and some measure of changes in nominal prices (e.g. the price inflation rate). Originally the Phillips Curve was simply an empirical observation noted in historical data. It was named after A.W.H. Phillips, who documented a clear negative relationship between wage inflation (the rate of growth of nominal wages) and the unemployment rate
in the United Kingdom (see Phillips (1958)). Most subsequent analyses of so-called Phillips Curve focus on general price inflation, rather than wage inflation. Also, many modern expositions use a measure of the output gap rather than unemployment as the β€œreal” variable in the model. We will also follow this approach, particularly since our model (as laid out) doesn’t feature unemployment as traditionally defined (we will return to this issue later in Chapter 17). Figure 27.18 shows a scatter plot (with a best-fitting regression line drawn in) between inflation on the vertical axis and the output gap on the horizontal axis for US data since 1960. To compute the output gap, we measure Y f t as the CBO’s measure of β€œpotential output.” This concept does not necessarily coincide with the concept of Y f t as being the hypothetical neoclassical level of output, but it is as close as we can easily get. In the figure, the output gap is measured in percentage deviations (so that 0.02 means that output is 2 percent above potential) and inflation is measured in annualized percentage units (so 4 means inflation, as measured by the GDP price deflator, is 4 percent in annualized terms). 613 Figure 27.18: Inflation and the Output Gap Each circle in the figure represents an inflation-output gap pair from a particular point in time. The empirical relationship between the output gap and inflation observed in the data is positive. Phillips’ original observation noted a negative relationship between wage inflation and the unemployment rate. This is consistent with the data in Figure 27.18 because one would expect the unemployment rate to be negatively correlated with the output gap. The Phillips Curve, as defined, is simply an empirical regularity. Does it have any basis in theory? It turns out that it does. The theoretical underpinnings of the Phillips Curve relationship can most easily be seen by focusing on the partial sticky price model. The assumed AS curve in that model is given by Pt = Β―Pt + Ξ³(Yt βˆ’ Y f ). This is written in terms of the price level. To think about changes in the price level (i.e. to think
about inflation rates), simply subtract Ptβˆ’1 from both sides to get: t Pt βˆ’ Ptβˆ’1 = Β―Pt βˆ’ Ptβˆ’1 + Ξ³(Yt βˆ’ Y f t ) (27.1) If we assume that the lagged price level is normalized to one, so that Ptβˆ’1 = 1, then the change in the price level also corresponds to the inflation rate (i.e. the percentage change in the price level). Then (27.1) can be written: 614 -202468101214-.08-.06-.04-.02.00.02.04.06Output GapInflationInflation - Output Gap Scatter Plot1960 - 2016 Ο€t = Ο€e t + Ξ³(Yt βˆ’ Y f t ) (27.2) t = Β―Pt βˆ’Ptβˆ’1. We can think of Ο€e In (27.2), we have defined Ο€t = Pt βˆ’Ptβˆ’1 and Ο€e t as measuring expected inflation – the exogenous component of the price level less the lagged price level. Since firms would presumably choose Β―Pt so that in expectation Yt = Y f t, we can think of Ο€e t as measuring the inflation rate that firms expect to obtain in period t. If inflation ends up higher than this, then output will be above potential, and vice-versa. Expression (27.2) is often referred to as an β€œexpectations augmented Phillips Curve” after Friedman (1968) and Phelps (1967). The empirical relationship documented in the scatter plot in Figure 27.18 is relatively weak. In fact, it masks strong sub-sample differences, as can be seen in Figure 27.19 below: Figure 27.19: Inflation and the Output Gap For the 1960-1984 period, the relationship between the output gap and inflation is weak, and the best-fitting line through all the circles is actually negatively sloped, which is inconsistent with the predictions of the New Keynesian model. For the 1984 to present period, in contrast, the relationship between the output gap and inflation is quite strong and positive – one can clearly see a positive relationship just by looking at all the circles in the οΏ½
οΏ½οΏ½gure. The full sample scatter plot (and best-fitting line) is roughly an average of the 615 02468101214-.08-.06-.04-.02.00.02.04.06Output GapInflationInflation - Output Gap Scatter Plot1960 - 1984-1012345-.08-.06-.04-.02.00.02.04Output GapInflationInflation - Output Gap Scatter Plot1984 - 2016 two sub-sample scatter plots. So there is one part of the sample where the theory-implied relationship between the output gap and inflation fits the data very well, one part of the sample where the empirical relationship is at odds with the data, and over the whole sample the relationship between inflation and the output gap is consistent with the theory but only weakly so. Our analysis in (27.1)-(27.2) gives us one way to potentially make sense of the empirical regularities documented in Figure 27.19. In particular, theory suggests that we should only expect to observe a positive relationship between the output gap and inflation to the extent t is stable (equivalently, Β―Pt is not shifting around significantly relative to Ptβˆ’1). to which Ο€e Has this always been the case? Figure 27.20 plots average current quarter expected inflation across time. These data are obtained from the Survey of Professional Forecasters (SPF), a survey of professional forecasters which is administered quarterly by the Federal Reserve Bank of Philadelphia. These data are available beginning in 1970. Figure 27.20: Average Inflation Expectations From Figure 27.20, we can draw two key observations. First, expected inflation was much higher in the 1970s and early 1980s than it has been since. This coincides with the behavior of actual price inflation, which was high in the 1970s and early 1980s and much lower since. Second, expected inflation was significantly more volatile in the early sample period in comparison to the later period. Since the early 1990s, expected inflation has been 616 12345678910606570758085909500051015Mean Expected Inflation quite stable. The fact that expected inflation was not stable during the early part of the
sample provides a potential rationale for the empirical regularities documented in Figure 27.19. In particular, if Ο€e t is fluctuating substantially (which in terms of our partial sticky price model would mean significant period-to-period changes in Β―Pt relative to Ptβˆ’1), we would not necessarily expect to see a positive relationship between Ο€t and Yt βˆ’ Y f t. Indeed, in the model an exogenous increase in Β―Pt would result in Yt βˆ’ Y f falling (since Yt would fall and Y f t would be unaffected) while Pt would rise, implying a negative relationship between the inflation rate and the output gap. This can help us understand why we observe a weak and slightly negative relationship between inflation and the output gap in the early part of the sample. In contrast, in the later part of the sample, expected inflation seems to be quite stable, and, consistent with the theory, we observe a robust positive relationship between the output gap and inflation. t The stabilization of inflation expectations in the last thirty or so years is widely considered to be both a significant and important achievement by the Federal Reserve. As we will discuss in Chapter 28, to the extent to which Β―Pt is stable (equivalently, Ο€e t is not moving around much), a central bank can simultaneously stabilize the output gap and inflation about target. 27.3.1 Implications of the Phillips Curve for Monetary Policy Due to nominal rigidity, a one time increase in Mt can temporarily raise output in the New Keynesian model. This effect eventually goes away as the economy transitions from short run to medium run, with the price level adjusting so that the only ultimate effect of an increase in Mt is a higher price level. A question worth pondering is the following: can a central bank persistently generate Yt > Y f t (i.e. high output) by continually increasing the money supply? For the partial sticky price version of the Phillips Curve above, (27.2), this would seem to be the case. A central bank could evidently achieve Yt > Y f if it were willing to tolerate higher inflation, provided t that expected inflation, Ο€e t, is unaff
ected by such a policy. This last provision is important. It is only possible for Yt > Y f t. In other words, monetary neutrality in the model in t a sense obtains by β€œfooling” people. If prices end up higher or lower than the firm expected, the existence of nominal rigidity triggers temporary deviations of output from its neoclassical level. if Ο€t > Ο€e While it seems possible that the firm could temporarily be fooled, it does not seem likely that it could be continually fooled. In other words, it should not be possible for a central bank to persistently push output above potential. If that is the central bank’s objective, the firm should catch on and adjust its expectations and behavior in such a way as to undo any 617 potential real effects of monetary expansion. To see this point clearly, suppose that the central bank increases Mt, but that this is completely anticipated by the firm in advance. Since the firm finds it optimal to produce the neoclassical level of output, a firm with this anticipation would increase Β―Pt in anticipation of the increase in Mt. The firm should not be caught surprised. It should preemptively raise its price by increasing Β―Pt in such a way that there would be no effect of the increase in Mt on Yt. In effect, an anticipated increase in Mt would cause the AD curve to shift right and but the AS curve to simultaneously shift up in such a way as to leave output unaffected. In terms of (27.2), a fully anticipated monetary expansion would be met with a coincident increase in Ο€t and Ο€e t, leaving output unaffected. This is documented for the partial sticky price model in Figure 27.21 below: 618 Figure 27.21: Sticky Price Model: Anticipated Increase in Mt, Reflected in Ο€e t Our analysis suggests that changes in the money supply can have real effects by, in a sense, fooling private agents. This is the point raised in the classic paper by Lucas (1972). If agents do not anticipate the change in the money supply and the price level is at least partially set in advance, then output expands when Mt increases. But if the change in
the money supply is fully anticipated, the price level can adjust in advance, with no change in 619 𝐴𝐴𝐴𝐴 𝐿𝐿𝐿𝐿�𝐿𝐿0,𝑑𝑑,𝑃𝑃0,𝑑𝑑𝑠𝑠𝑠𝑠�= 𝐿𝐿𝐿𝐿�𝐿𝐿1,𝑑𝑑,𝑃𝑃1,𝑑𝑑𝑠𝑠𝑠𝑠� 𝐴𝐴𝐴𝐴 𝑀𝑀1,𝑑𝑑𝑠𝑠𝑠𝑠=𝑀𝑀0,𝑑𝑑𝑠𝑠𝑠𝑠 𝐿𝐿𝐿𝐿(𝐿𝐿1,𝑑𝑑,𝑃𝑃0,𝑑𝑑𝑠𝑠𝑠𝑠) 𝐴𝐴𝐴𝐴′ 𝐴𝐴𝐴𝐴′ 0 subscript: initial equilibrium 1 subscript: post-shock equilibrium where 𝐿𝐿𝑑𝑑 increases but this is anticipated and reflected immediately in 𝑃𝑃�𝑑𝑑 𝑀𝑀𝑑𝑑 𝑃𝑃𝑑𝑑 Original π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ Post-shock, holding price fixed π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ Post-shock, including reaction of 𝑃𝑃�𝑑𝑑 𝑁𝑁𝑑𝑑 𝑁𝑁𝑑𝑑 𝐼𝐼𝐴𝐴 𝑁�
οΏ½οΏ½1,𝑑𝑑𝑠𝑠𝑠𝑠=𝑁𝑁0,𝑑𝑑𝑠𝑠𝑠𝑠 𝑁𝑁𝑠𝑠(𝑀𝑀𝑑𝑑,πœƒπœƒπ‘‘π‘‘) 𝐴𝐴𝑑𝑑𝐹𝐹(𝐾𝐾𝑑𝑑,𝑁𝑁𝑑𝑑) π‘Œπ‘Œπ‘‘π‘‘=π‘Œπ‘Œπ‘‘π‘‘ π‘Ÿπ‘Ÿπ‘‘π‘‘ 𝑃𝑃0,𝑑𝑑𝑠𝑠𝑠𝑠=𝑃𝑃�0,𝑑𝑑𝑠𝑠𝑠𝑠 𝑃𝑃1,𝑑𝑑𝑠𝑠𝑠𝑠=𝑃𝑃�1,𝑑𝑑𝑠𝑠𝑠𝑠 π‘Ÿπ‘Ÿ1,𝑑𝑑𝑠𝑠𝑠𝑠=π‘Ÿπ‘Ÿ0,𝑑𝑑𝑠𝑠𝑠𝑠 π‘Œπ‘Œ1,𝑑𝑑𝑠𝑠𝑠𝑠=π‘Œπ‘Œ0,𝑑𝑑𝑠𝑠𝑠𝑠 any real variable resulting from the increase in the money supply. In a sense, if the change in the money supply is fully anticipated, then there is no distinction between the short run and the medium run – it is as if the price level is perfectly flexible. If a central bank were to engage in a policy of trying to repeatedly push output above potential, it stands to reason that private sector agents would catch on to the scheme sooner or later, and the policy would not be effective at raising output, and would only generating persistently higher infl
ation. 27.3.2 The Possibility of Costless Disinflation Suppose that a central bank desires to reduce the price level in an economy (or inflation, if you prefer). How can it do this, and what are the costs associated with disinflation (by which we mean a policy designed to reduce the price level, or the rate of growth of the price level)? For the purposes of this section, we will focus on the partial sticky price model. Similar conclusions emerge in the simple sticky price model. Suppose that the central bank desires to reduce the price level. It can do this by reducing the money supply. If this reduction in the money supply is unanticipated by agents in the economy, output must decline in the short run. The effects of a reduction in the money supply are shown below in Figure 27.22. The reduction in the money supply causes the AD curve to shift in. This causes output to fall from Y sr 1,t in the short run. As the economy transitions to the medium run, the firm will adjust the price level to Β―P mr, the AS curve will shift down, and output will return to where it started with the desired fall in the price level eventually happens. Bringing the price level down evidently requires enduring a recession (a period of low output) in the short run. 0,t to Y sr t 620 Figure 27.22: Sticky Price Model: Unanticipated Disinflation Economists have adopted the term β€œsacrifice ratio” as the ratio of the percentage of lost output to the percentage change in inflation. So, if a central bank wants to reduce the inflation rate by 1 percent and output falls by 5 percent, the sacrifice ratio is 5. The experience of the US economy during the early 1980s suggests that the sacrifice ratio is large. As Fed chairman, Paul Volcker sought to bring the US inflation rate down from the high 621 𝐴𝐴𝐴𝐴 𝑁𝑁𝑠𝑠(𝑀𝑀𝑑𝑑,πœƒπœƒπ‘‘π‘‘) 𝐿𝐿𝐿𝐿�𝐿𝐿0,οΏ½
��𝑑,𝑃𝑃0,𝑑𝑑𝑠𝑠𝑠𝑠�=𝐿𝐿𝐿𝐿�𝐿𝐿1,𝑑𝑑,𝑃𝑃1,π‘‘π‘‘π‘šπ‘šπ‘ π‘ οΏ½ 𝐴𝐴𝐴𝐴 𝑃𝑃0,𝑑𝑑𝑠𝑠𝑠𝑠=𝑃𝑃�𝑑𝑑𝑠𝑠𝑠𝑠 𝑀𝑀1,π‘‘π‘‘π‘šπ‘šπ‘ π‘ =𝑀𝑀0,𝑑𝑑𝑠𝑠𝑠𝑠 𝐿𝐿𝐿𝐿(𝐿𝐿1,𝑑𝑑,𝑃𝑃0,𝑑𝑑𝑠𝑠𝑠𝑠) 𝐴𝐴𝐴𝐴′ 𝑀𝑀1,𝑑𝑑𝑠𝑠𝑠𝑠 𝑁𝑁1,𝑑𝑑𝑠𝑠𝑠𝑠 𝑁𝑁𝑑𝑑(𝑀𝑀𝑑𝑑,𝐴𝐴𝑑𝑑,𝐾𝐾𝑑𝑑) 𝑀𝑀𝑑𝑑 𝑃𝑃𝑑𝑑 π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ 𝑁𝑁𝑑𝑑 𝑁𝑁𝑑𝑑 𝐼𝐼�
��𝐴 𝑁𝑁1,π‘‘π‘‘π‘šπ‘šπ‘ π‘ =𝑁𝑁0,𝑑𝑑𝑠𝑠𝑠𝑠 0 subscript: original 1 subscript: post-shock sr or mr superscript: short run or medium run 𝐴𝐴𝑑𝑑𝐹𝐹(𝐾𝐾𝑑𝑑,𝑁𝑁𝑑𝑑) π‘Œπ‘Œπ‘‘π‘‘=π‘Œπ‘Œπ‘‘π‘‘ π‘Ÿπ‘Ÿπ‘‘π‘‘ Original Post-shock Post-shock, post price adjustment Original, hypothetical flexible price 𝐴𝐴𝐴𝐴′ 𝐴𝐴𝐴𝐴𝑓𝑓 𝑃𝑃1,𝑑𝑑𝑠𝑠𝑠𝑠 𝐿𝐿𝐿𝐿(𝐿𝐿1,𝑑𝑑,𝑃𝑃1,𝑑𝑑𝑠𝑠𝑠𝑠) π‘Ÿπ‘Ÿ1,π‘‘π‘‘π‘šπ‘šπ‘ π‘ =π‘Ÿπ‘Ÿ0,𝑑𝑑𝑠𝑠𝑠𝑠 π‘Ÿπ‘Ÿ1,𝑑𝑑𝑠𝑠𝑠𝑠 Post-shock, indirect of price on 𝑃𝑃1,π‘‘π‘‘π‘šπ‘šπ‘ π‘ =π‘ƒπ‘ƒοΏ½π‘‘π‘‘π‘šπ‘šπ‘ π‘  π‘Œπ‘Œ1,𝑑𝑑𝑠𝑠𝑠𝑠 π‘Œπ‘Œ1,π‘‘π‘‘π‘šπ‘šπ‘ π‘ =π‘Œπ‘Œ0,𝑑𝑑�
�𝑠𝑠𝑠 levels it had experienced during the 1970s. Inflation fell from about 9 percent in 1981 to about 4 percent in 1983. Relative to trend, real GDP fell by about 10 percent over the same period. This suggests the sacrifice ratio associated with the Volcker disinflation was about 2. Our analysis from the previous subsection suggests, in contrast to the experience of the US in the early 1980s, that disinflation need not be costly. In particular, suppose that a central bank effectively communicates its desire to lower the price level to the public in advance of reducing the money supply. If it does this, the firm will lower its price level in advance of the reduction in Mt. As a result, while the AD curve will shift in, the AS curve will shift down simultaneously, resulting in no change in real variables but a reduction in the price level. These effects are shown below in Figure 27.23. 622 Figure 27.23: Sticky Price Model: Anticipated Disinflation In a nutshell, if a central bank can effectively communicate its desire to lower the price level in advance, it may be able to do so without sacrificing any short run drop in output. It is sometimes said that there is the possibility of a β€œcostless disinflation.” In other words, if successfully communicated to the public, there may be no distinction between the short run and the medium run, with the effects of price stickiness neutralized. 623 𝐴𝐴𝐴𝐴 π‘Ÿπ‘Ÿ0,𝑑𝑑𝑠𝑠𝑠𝑠=π‘Ÿπ‘Ÿ1,𝑑𝑑𝑠𝑠𝑠𝑠 𝐿𝐿𝐿𝐿�𝐿𝐿0,𝑑𝑑,𝑃𝑃0,𝑑𝑑𝑠𝑠𝑠𝑠�=𝐿𝐿𝐿𝐿�𝐿𝐿1,𝑑𝑑,𝑃𝑃
1,𝑑𝑑𝑠𝑠𝑠𝑠� 𝐴𝐴𝐴𝐴 𝑀𝑀0,𝑑𝑑𝑠𝑠𝑠𝑠=𝑀𝑀1,𝑑𝑑𝑠𝑠𝑠𝑠 𝐿𝐿𝐿𝐿(𝐿𝐿1,𝑑𝑑,𝑃𝑃0,𝑑𝑑𝑠𝑠𝑠𝑠) 𝐴𝐴𝐴𝐴′ 𝑁𝑁𝑑𝑑(𝑀𝑀𝑑𝑑,𝐴𝐴𝑑𝑑,𝐾𝐾𝑑𝑑) 0 subscript: original 1 subscript: post-shock Original Post-shock, holding price fixed Original, hypothetical flexible price 𝐴𝐴𝐴𝐴′ 𝑀𝑀𝑑𝑑 𝑃𝑃𝑑𝑑 π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ 𝑁𝑁𝑑𝑑 𝑁𝑁𝑑𝑑 𝐴𝐴𝐴𝐴𝑓𝑓 𝐼𝐼𝐴𝐴 𝑁𝑁0,𝑑𝑑𝑠𝑠𝑠𝑠=𝑁𝑁1,𝑑𝑑𝑠𝑠𝑠𝑠 𝑁𝑁𝑠𝑠(𝑀𝑀𝑑𝑑,πœƒπœƒπ‘‘π‘‘) 𝐴𝐴𝑑𝑑𝐹𝐹(
𝐾𝐾𝑑𝑑,𝑁𝑁𝑑𝑑) π‘Œπ‘Œπ‘‘π‘‘=π‘Œπ‘Œπ‘‘π‘‘ π‘Ÿπ‘Ÿπ‘‘π‘‘ 𝑃𝑃0,𝑑𝑑𝑠𝑠𝑠𝑠=𝑃𝑃�0,𝑑𝑑𝑠𝑠𝑠𝑠 Post-shock, including reaction of 𝑃𝑃�𝑑𝑑 π‘Œπ‘Œ0,𝑑𝑑𝑠𝑠𝑠𝑠=π‘Œπ‘Œ1,𝑑𝑑𝑠𝑠𝑠𝑠 𝑃𝑃1,𝑑𝑑𝑠𝑠𝑠𝑠=𝑃𝑃�1,𝑑𝑑𝑠𝑠𝑠𝑠 The possibility of costless disinflation rests on the assumption that private sector agents have well-formed expectations (in addition to the assumption that the central bank can credibly communicate its desire to lower the general level of prices to them). The β€œrational expectations” hypothesis holds that agents in an economy use all available information to make optimal forecasts of variables relevant to their current decision-making. Rational expectations does not mean that forecasts are always correct, though it does imply that forecasts are not systematically wrong. For example, if agents always expected an inflation rate of 2 percent, even though the actual inflation rate always turned out to be 4 percent, their forecasts would be systematically wrong, a violation of rational expectations. In contrast, if agents always expected an inflation rate of 2 percent, but the actual inflation rate was sometimes 3 percent and sometimes 1 percent (without any predictable reason why the inflation rate is high or low), but on average was 2 percent, expectations are rational. The possibility of costless disinflation therefore rests on two assumptions: that expectations of inflation are fully rational and that the central bank can credibly communicate its desire to reduce the inοΏ½
οΏ½οΏ½ation rate to the public. This was evidently not the case during the Volcker disinflation of the early 1980s. 27.4 Summary β€’ There is no guarantee that the short run equilibrium of the New Keynesian model will coincide with the hypothetical equilibrium that would obtain if the price level were flexible. In other words, there is no guarantee that Yt = Y f t. We sometimes refer to Y f t as β€œpotential output” because this is the optimal level of output for the economy to produce (for a formal discussion of this point see Chapter 15). We refer to the term Yt βˆ’ Y f t as the β€œoutput gap.” β€’ In the sticky price model a suboptimal equilibrium is one in which the would like to change its price but is unable to. As prices become flexible over a longer time horizon, the firm will adjust its price bringing the equilibrium to the equilibrium of the neoclassical model. For instance, if output is lower than its flexible level, firms have an incentive to reduce prices which shifts the economy to the neoclassical equilibrium. The intuition runs in the reverse direction if output is greater than its flexible price level. β€’ The Phillips curve is a generic name that applies to the relationship between some measure of real activity (e.g. the output gap) and the change in prices. The relationship between the output gap and inflation in post war US data is weakly positive. However, after 1984 the relationship is strongly positive and, contrary to the theory, is actually 624 weakly negative prior to 1984. Exceptionally volatile inflation expectations helps explain the anomalous behavior prior to 1984. β€’ If firms completely anticipate a change in money supply, they can respond by changing prices. Consequently, only unanticipated changes in the money supply affect the real economy. β€’ If every individual and firm has rational expectations and the central bank can credibly commit to its actions, it is possible for the central bank to reduce inflation without reducing output. This is known as β€œcostless disinflation”. Key Terms β€’ Output gap β€’ Phillips Curve β€’ Costless disinflation Questions for Review 1. Suppose that you have a sticky price model in which Yt > Y f t. In this
situation, is the firm hiring more or less labor than it would like to? What pressure does this put on the price level and output as the economy transitions to the medium run? 2. Critically evaluate the following claim. β€œIn the New Keynesian model, a central bank can increase output by increasing the money supply. Therefore, the central bank should increase the money supply by ever larger amounts each period. This will generate sustain increases in output.” Exercises 1. Suppose the economy starts in the Neoclassical equilibrium and ΞΈt increases. (a) Draw the dynamics in the simple sticky price case. Verbally describe what is going on. (b) Draw the dynamics in the partial sticky price case. Verbally describe what is going on. 2. Consider the basic sticky price New Keynesian model as presented in the text. Suppose that the economy is driven into a recession caused by an exogenous reduction in At. 625 (a) Graphically show the effects of the reduction in At on the endogenous variables of the model. Include in your graph what happens to the flexible price, neoclassical values of the endogenous variables. (b) What pressure will there be on the position of the AS curve as the economy transitions from short run to medium run? (c) An observer looking at data generated from this model will observe a particular correlation between inflation and output conditional on a shock to At. Is that correlation consistent with the idea of the Phillips Curve as presented in the text? What is missing from looking at a simple correlation between inflation and output when comparing it to the predictions of the Phillips Curve? 3. Consider a sticky price New Keynesian model. Suppose that the equations of the demand side are given as follows: Ct = c1(Yt βˆ’ Gt) + c2(Yt+1 βˆ’ Gt+1) βˆ’ c3rt It = βˆ’b1(rt + ft) + b2At+1 βˆ’ b3Kt ) + m2Yt Mt = Pt βˆ’ m1(rt + Ο€e t+1 Here, c1, c2, and c3 are positive parameters, as are b1, b2, b3 and m1 and m2. Government spending, Gt, is exogenous. (a) Derive an algebraic expression for the AD curve. (b) Find an expression for how Yt will
react to an increase in ft when the price level is fixed at Β―Pt. (c) Solve for an expression for how much Β―Pt must adjust to keep Yt fixed after an increase in ft (as it would in the neoclassical model). Verify that the required increase in Β―Pt is positive. 626 Chapter 28 Monetary Policy in the New Keynesian Model We have thus far taken monetary policy to be exogenous with respect to the model. That is, Mt is an exogenous variable. This allowed us to think about how exogenous changes in Mt might impact the endogenous variables of the model, but is not realistic in the sense that most changes in monetary policy are not exogenous, but are rather reactions to changes in economic conditions. In this chapter, we study how monetary policy ought to be conducted in the New Keynesian model. We will focus on the partial sticky price model, which generalizes to the sticky price model when Ξ³ = 0. Appendix D also studies optimal monetary policy in the sticky wage New Keynesian model. In Chapter 22, it was argued that the neoclassical equilibrium is the efficient equilibrium allocation – a social planner could do no better than the private market left to its own devices. If the price level is sticky, in the short run, the equilibrium may not coincide with what it would be in the neoclassical model. In the medium run, pressures on the price level will naturally work to take the economy to the neoclassical, efficient, equilibrium. But how long does it take to go from the short run to the medium run? John Maynard Keynes famously said that β€œIn the long run, we are all dead.” By this he meant that short run frictions (like price rigidity) which impede the efficient allocation of resources might last for a very long time, and that it is important for the fiscal or monetary authority to step in to try to restore an efficient equilibrium. t, where Yt is the equilibrium level of output and Y f In a nutshell, optimal monetary policy in the New Keynesian model involves adjusting Mt (and hence interest rates) in response to other exogenous shocks so as to implement the hypothetical neoclassical equilibrium even when the price level is sticky. Mathematically, this means adjusting Mt such that Yt = Y f is what output would be if the price level were οΏ½
οΏ½exible. Effectively, what this entails is adjusting monetary policy in response to other shocks so as to not wait for the medium run dynamic adjustment of prices to take over. As we will see below, this involves using monetary policy to counteract demand shocks (i.e. a positive IS shock should be countered by a contraction in the money supply and increase in interest rates) but using policy to accommodate supply shocks (i.e. an increase in At should be met by an increase in the money supply and a reduction in interest rates). We will also argue that a policy of inflation targeting will be t 627 close to optimal provided fluctuations in Β―Pt are not very important. A natural question that might come to mind is the following. If the equilibrium of the New Keynesian model is inefficient, why not also consider fiscal policy (which in a model with Ricardian Equivalence just means adjustment of government spending, although more generally could also mean the adjustment of tax policy)? There are a couple of reasons for not using fiscal policy, except in unusual circumstances. Most importantly, changes in fiscal instruments, while not affecting the hypothetical neoclassical level of output under our maintained assumptions about labor supply (see Appendix C for a situation in which this is not the case), do affect the distribution of that output among consumption and investment and affect the real interest rate which would obtain in the neoclassical model. Put differently, one could use changes in Gt (or Gt+1) to implement Yt = Y f t, but the values of Ct and It would not be the same in the short run New Keynesian model as they would in the neoclassical model. We will return to this in more detail below in the section on the natural rate of interest. Another problem with fiscal policy is that it is associated with long legislative delays – by the time Congress can act, the underlying problem may have subsided. This is less of a problem with monetary policy, which can react to changes macroeconomic conditions rapidly. 28.1 Policy in the Partial Sticky Price Model In this Chapter we focus on the partial sticky price model. The full set of equations describing the equilibrium are shown below: Ct = C d(Yt βˆ’ Gt, Yt+1 βˆ’
Gt+1, rt) Nt = N s(wt, ΞΈt) Pt = Β―Pt + Ξ³(Yt βˆ’ Y f t ) It = I d(rt, At+1, Kt) Yt = AtF (Kt, Nt) Yt = Ct + It + Gt Mt = PtM d(rt + Ο€e t+1, Yt) rt = it βˆ’ Ο€e t+1 (28.1) (28.2) (28.3) (28.4) (28.5) (28.6) (28.7) (28.8) A graphical depiction of the equilibrium is presented in Figure 28.1 below. We assume that the economy initially sits in a short run equilibrium which coincides with the hypothetical flexible price equilibrium. 628 Figure 28.1: Equilibrium in the Partial Sticky Price Model Now let us consider how monetary policy ought to adjust to different exogenous shocks so as to implement the neoclassical equilibrium in the short run. Consider first a shock which makes the IS curve shift to the right. This could be because of an increase in At+1 or Gt, or a decrease in Gt+1. The initial equilibrium is depicted via black lines and labeled with a 0 subscript. The effects of the shock are shown in blue, and any indirect effect on the position 629 𝑀𝑀𝑑𝑑 𝑃𝑃𝑑𝑑 π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ 𝑁𝑁𝑑𝑑 𝑁𝑁𝑑𝑑 𝐴𝐴𝐴𝐴 𝐼𝐼𝐴𝐴 π‘Ÿπ‘Ÿ0,𝑑𝑑 π‘Œπ‘Œ0,𝑑𝑑=π‘Œπ‘Œ0,𝑑𝑑𝑓𝑓 οΏ½
�𝑁0,𝑑𝑑 𝑁𝑁𝑠𝑠(𝑀𝑀𝑑𝑑,πœƒπœƒπ‘‘π‘‘) 𝐿𝐿𝐿𝐿(𝐿𝐿𝑑𝑑,𝑃𝑃0,𝑑𝑑) 𝐴𝐴𝑑𝑑𝐹𝐹(𝐾𝐾𝑑𝑑,𝑁𝑁𝑑𝑑) π‘Œπ‘Œπ‘‘π‘‘=π‘Œπ‘Œπ‘‘π‘‘ π‘Ÿπ‘Ÿπ‘‘π‘‘ 𝐴𝐴𝐴𝐴 𝑃𝑃0,𝑑𝑑=𝑃𝑃�0,𝑑𝑑 𝑀𝑀0,𝑑𝑑 𝑁𝑁𝑑𝑑(𝑀𝑀𝑑𝑑,𝐴𝐴𝑑𝑑,𝐾𝐾𝑑𝑑) 𝐴𝐴𝐴𝐴𝑓𝑓 of the LM curve owing to a change in the price level is shown in green. 1 subscripts denote what the equilibrium would be in the short run with no policy response (i.e. with keeping the money supply fixed). Figure 28.2: Optimal Monetary Response to Positive IS Shock Absent any policy change, a positive IS shock would result in output rising, the price level rising, the real interest rate rising, and the real wage and labor input both rising. Since there 630 𝑀𝑀𝑑𝑑 𝑃𝑃𝑑𝑑 π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ 𝑁𝑁�
��𝑑 𝑁𝑁𝑑𝑑 𝐴𝐴𝐴𝐴 𝐼𝐼𝐴𝐴 π‘Ÿπ‘Ÿ0,𝑑𝑑 π‘Œπ‘Œ0,𝑑𝑑=π‘Œπ‘Œ2,𝑑𝑑=π‘Œπ‘Œ0,𝑑𝑑𝑓𝑓 𝑁𝑁0,𝑑𝑑=𝑁𝑁2,𝑑𝑑 𝑁𝑁𝑠𝑠(𝑀𝑀𝑑𝑑,πœƒπœƒπ‘‘π‘‘) 𝐿𝐿𝐿𝐿(𝐿𝐿0,𝑑𝑑,𝑃𝑃0,𝑑𝑑) 𝐴𝐴𝑑𝑑𝐹𝐹(𝐾𝐾𝑑𝑑,𝑁𝑁𝑑𝑑) π‘Œπ‘Œπ‘‘π‘‘=π‘Œπ‘Œπ‘‘π‘‘ π‘Ÿπ‘Ÿπ‘‘π‘‘ 𝐴𝐴𝐴𝐴=𝐴𝐴𝐴𝐴′′ 𝑃𝑃0,𝑑𝑑=𝑃𝑃2,𝑑𝑑=𝑃𝑃�0,𝑑𝑑 𝑀𝑀0,𝑑𝑑=𝑀𝑀2,𝑑𝑑 𝑁𝑁𝑑𝑑(𝑀𝑀𝑑𝑑,𝐴𝐴𝑑𝑑,𝐾𝐾𝑑𝑑) 𝐴𝐴𝐴𝐴𝑓𝑓 Original Post-Shock, no policy response Post-shock, indirect effect of 𝑃𝑃𝑑�
οΏ½οΏ½ on LM curve, no policy response Optimal policy response 0 subscript: original 1 subscript: post-shock, no policy response 2 subscript: post-shock, optimal policy 𝐴𝐴𝐴𝐴′ 𝐼𝐼𝐴𝐴′ 𝐿𝐿𝐿𝐿(𝐿𝐿0,𝑑𝑑,𝑃𝑃1,𝑑𝑑) π‘Ÿπ‘Ÿ1,𝑑𝑑 𝑀𝑀1,𝑑𝑑 𝑁𝑁1,𝑑𝑑 π‘Œπ‘Œ1,𝑑𝑑 𝑃𝑃1,𝑑𝑑 Original, flexible price Post-shock, flexible price π‘Ÿπ‘Ÿ2,𝑑𝑑 𝐿𝐿𝐿𝐿(𝐿𝐿2,𝑑𝑑,𝑃𝑃0,𝑑𝑑) is no effect on Y f t, the output gap would be positive – the short run equilibrium features more output than is optimal. If monetary policy wanted to counteract this, it should change the money supply in such a way as to reduce output. This necessitates reducing the money supply, the effect of which would be to shift the LM curve in and the AD curve back in to where it started (shown in purple in the figure). If the change in Mt is sufficient to result in no net change in output (the 2 subscripts denote the short run equilibrium values with the optimal policy adjustment), then there will be no change in the price level, no change in labor input, and no change in the real wage. Relative to what would happen absent any policy t, there would be no pressure for Β―Pt change, the real interest rate would rise. Since Y2,t = Y f to adjust and hence no dynamics from the short run to the medium run. We can therefore see that the optimal policy is to counteract the expansionary IS shock – the money supply should move opposite how output would move absent a policy change, and the real interest rate (and also the nominal rate, since we are treating
expected inflation as an exogenous constant) would move in the same direction as output would move absent a policy change. Consider next an exogenous increase in productivity, manifested in an increase in At. This is shown in Figure 28.3. The blue lines and 1 subscripts show what would happen in the short run absent any policy change. The AS curve would shift right, by a horizontal amount equal to the shift of the hypothetical vertical neoclassical AS curve, ASf (the shift of which is shown in red). Output would rise, but by less than the neoclassical level of output. The price level and the real interest rate would fall. It is not possible to definitively sign the effects of an increase in At on labor market variables, though the figure is drawn where these both decrease. Relatively to the neoclassical equilibrium, the short run equilibrium of the New Keynesian model features output under-reacting to the productivity improvement. Optimal policy would want to implement the neoclassical equilibrium, and therefore expansionary monetary policy is needed. The monetary authority should increase the money supply by an amount sufficient to shift the AD curve (shown in purple) such that it intersects the new AS curve (blue) at the new neoclassical AS curve (red). If this happens, there will be no resulting change in the price level. The real wage and labor input will both rise. The real interest rate will fall by more than it would if policy did not react to the shock. 631 Figure 28.3: Optimal Monetary Response to Increase in At Next, let us consider an exogenous increase in the exogenous component of the price level, Β―Pt. One could think of this as an β€œexpected inflation” shock, or perhaps as a shock to the price of materials input (e.g. the price of oil). This is shown in Figure 28.4 There is no effect of this shock in the neoclassical model. It causes the upward-sloping AS curve to shift up, crossing the hypothetical neoclassical AS curve at the unchanged neoclassical level 632 𝑀𝑀𝑑𝑑 𝑃𝑃𝑑𝑑 π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘
𝑑 π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ 𝑁𝑁𝑑𝑑 𝑁𝑁𝑑𝑑 𝐴𝐴𝐴𝐴 𝐼𝐼𝐴𝐴 π‘Ÿπ‘Ÿ0,𝑑𝑑 π‘Œπ‘Œ0,𝑑𝑑=π‘Œπ‘Œ0,𝑑𝑑𝑓𝑓 𝑁𝑁0,𝑑𝑑 𝑁𝑁𝑠𝑠(𝑀𝑀𝑑𝑑,πœƒπœƒπ‘‘π‘‘) 𝐿𝐿𝐿𝐿(𝐿𝐿0,𝑑𝑑,𝑃𝑃0,𝑑𝑑) 𝐴𝐴0,𝑑𝑑𝐹𝐹(𝐾𝐾𝑑𝑑,𝑁𝑁𝑑𝑑) π‘Œπ‘Œπ‘‘π‘‘=π‘Œπ‘Œπ‘‘π‘‘ π‘Ÿπ‘Ÿπ‘‘π‘‘ 𝐴𝐴𝐴𝐴 𝑃𝑃0,𝑑𝑑=𝑃𝑃2,𝑑𝑑=𝑃𝑃�0,𝑑𝑑 𝑀𝑀0,𝑑𝑑 𝑁𝑁𝑑𝑑(𝑀𝑀𝑑𝑑,𝐴𝐴0,𝑑𝑑,𝐾𝐾𝑑𝑑) 𝐴𝐴𝐴𝐴𝑓𝑓 𝑁𝑁𝑑𝑑(𝑀𝑀𝑑𝑑,𝐴�
οΏ½1,𝑑𝑑,𝐾𝐾𝑑𝑑) 𝐴𝐴1,𝑑𝑑𝐹𝐹(𝐾𝐾𝑑𝑑,𝑁𝑁𝑑𝑑) 𝐴𝐴𝐴𝐴′ 𝐴𝐴𝐴𝐴𝑓𝑓′ 𝑀𝑀1,𝑑𝑑 𝑁𝑁1,𝑑𝑑 π‘Œπ‘Œ2,𝑑𝑑=π‘Œπ‘Œ1,𝑑𝑑𝑓𝑓 π‘Œπ‘Œ1,𝑑𝑑 𝑃𝑃1,𝑑𝑑 π‘Ÿπ‘Ÿ1,𝑑𝑑 𝐿𝐿𝐿𝐿(𝐿𝐿0,𝑑𝑑,𝑃𝑃1,𝑑𝑑) Original Post-Shock, no policy response Post-shock, indirect effect of 𝑃𝑃𝑑𝑑 on LM curve, no policy response Optimal policy response 0 subscript: original 1 subscript: post-shock, no policy response 2 subscript: post-shock, optimal policy Original, flexible price Post-shock, flexible price 𝐴𝐴𝐴𝐴′ 𝐿𝐿𝐿𝐿(𝐿𝐿2,𝑑𝑑,𝑃𝑃0,𝑑𝑑) π‘Ÿπ‘Ÿ2,𝑑𝑑 𝑁𝑁2,𝑑𝑑 𝑀𝑀2,𝑑𝑑 of output. If there is no policy change, output will decline and the price level will rise. To accommodate falling output, the real interest rate must rise, which is graphically achieved through an inward shift of the LM curve (shown in green) owing to the increase in the price level. The real wage and labor input must both fall. If the monetary authority wishes to implement
the neoclassical equilibrium level of output, it must engage in expansionary policy. It must increase the money supply so as to shift the AD curve out (purple), so that the new AD curve intersects the new AS curve at the unchanged neoclassical equilibrium level of output. In the new optimal policy equilibrium, the price level will be higher. The higher price level exactly offsets the higher money supply, so that the position of the LM curve is unaffected. Hence, there is no change in the real interest rate, nor any change in labor market variables. 633 Figure 28.4: Optimal Monetary Response to Increase in Β―Pt We leave a detailed analysis of the optimal policy response to an exogenous change in ΞΈt as an exercise. Table 28.1 shows the qualitative direction in which the money supply (and the real and nominal interest rates) ought to move in response to different exogenous shocks in the partial sticky price model. These directions are expressed relative to what would happen after a shock absent any policy change. This table would be the same for the simple sticky 634 𝑀𝑀𝑑𝑑 𝑃𝑃𝑑𝑑 π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ 𝑁𝑁𝑑𝑑 𝑁𝑁𝑑𝑑 𝐴𝐴𝐴𝐴 𝐼𝐼𝐴𝐴 π‘Ÿπ‘Ÿ0,𝑑𝑑=π‘Ÿπ‘Ÿ2,𝑑𝑑 π‘Œπ‘Œ0,𝑑𝑑=π‘Œπ‘Œ2,𝑑𝑑=π‘Œπ‘Œ0,𝑑𝑑𝑓𝑓 𝑁𝑁0,𝑑𝑑=𝑁𝑁2,𝑑𝑑 𝑁𝑁𝑠𝑠(𝑀𝑀�
�𝑑,πœƒπœƒπ‘‘π‘‘) 𝐿𝐿𝐿𝐿�𝐿𝐿0,𝑑𝑑,𝑃𝑃0,𝑑𝑑�=𝐿𝐿𝐿𝐿(𝐿𝐿2,𝑑𝑑,𝑃𝑃2,𝑑𝑑) 𝐴𝐴𝑑𝑑𝐹𝐹(𝐾𝐾𝑑𝑑,𝑁𝑁𝑑𝑑) π‘Œπ‘Œπ‘‘π‘‘=π‘Œπ‘Œπ‘‘π‘‘ π‘Ÿπ‘Ÿπ‘‘π‘‘ 𝐴𝐴𝐴𝐴 𝑃𝑃0,𝑑𝑑=𝑃𝑃�0,𝑑𝑑 𝑀𝑀0,𝑑𝑑=𝑀𝑀2,𝑑𝑑 𝑁𝑁𝑑𝑑(𝑀𝑀𝑑𝑑,𝐴𝐴𝑑𝑑,𝐾𝐾𝑑𝑑) 𝐴𝐴𝐴𝐴𝑓𝑓 𝑃𝑃2,𝑑𝑑=𝑃𝑃�1,𝑑𝑑 𝑃𝑃1,𝑑𝑑 𝐴𝐴𝐴𝐴′ 𝐿𝐿𝐿𝐿(𝐿𝐿0.𝑑𝑑,𝑃𝑃1,𝑑𝑑) π‘Ÿπ‘Ÿ1,𝑑𝑑 π‘Œπ‘Œ1,𝑑𝑑 𝑀𝑀1,𝑑𝑑 𝑁𝑁1,𝑑𝑑 Original Post-Shock, no policy response Post-
shock, indirect effect of 𝑃𝑃𝑑𝑑 on LM curve, no policy response Optimal policy response 0 subscript: original 1 subscript: post-shock, no policy response 2 subscript: post-shock, optimal policy Original, flexible price Post-shock, flexible price 𝐴𝐴𝐴𝐴′ price model as well. Table 28.1: Optimal Monetary Policy Reaction to Different Shocks Exogenous Shock Variable Mt rt it ↑ IS curve + + ↑ At + - ↑ Β―Pt + - Focusing on the first two inner columns of the table (the entries labeled β€œβ†‘ IS curve” and β€œβ†‘ At”), we see that optimal monetary policy seeks to counteract IS shocks but to accommodate productivity shocks (the same would be true for exogenous changes in ΞΈt). By β€œcounteract” we mean that policy should move the money supply opposite how output would react absent a policy change, and by β€œaccommodate” we mean that the money supply should move in the same direction as how output would move absent a policy change. It is sometimes said that policy should counteract demand shocks (IS shocks) and accommodate supply shocks (changes in At or ΞΈt). This statement does not hold for the case of shocks to Β―Pt, where optimal policy would counteract these shocks. We discuss this in more detail in the section immediately below. 28.2 The Case for Price Stability Many central banks around the world (including the Federal Reserve in the US) have as one of their stated goals (if not their only goal) β€œprice stability.” In the US and other developed economies, price stability is typically interpreted as an inflation rate around 2 percent per year. It is common to refer to central banks with a price stability goal as following an inflation target. From the perspective of the New Keynesian model, does price stability as a normative goal make sense? It turns out that the answer is yes, at least so long as fluctuations are not primarily driven by changes in Β―Pt. We can see this in the section above, where we analyzed the optimal monetary policy responses to positive IS shocks (Figure 28.2) and positive productivity shocks (Figure 28.3). In both cases, we see that in the new short run equilibrium with optimal monetary policy, the price level is un
affected by the IS or productivity shock. In other words, implementing optimal policy, which we have defined as adjusting the money supply in response to shocks so as to implement the hypothetical neoclassical equilibrium level of output, implies price stability. In other words, price stability is not the goal per se, but is an outcome of the implementation of optimal policy. 635 We can formally think about a central bank with a motivation for price stability as adjusting the money supply so that the price level is constant in equilibrium. This results in what we will call the effective AD curve, or ADe, being horizontal. If the ADe curve is horizontal at Β―Pt, then equilibrium output will equal the hypothetical, efficient neoclassical level. When thinking about the effective AD curve, we need not consider explicitly the LM curve. rt is determined from the IS curve at the level of output where the AS and ADe curves intersect. In the background, the central bank adjusts the money supply to make this happen. This is shown below in Figure 28.5: Figure 28.5: A Strict Inflation (Price Level) Target and the Effective AD Curve We can use these curves to think about how the economy will react to different exogenous shocks. Consider first a positive IS shock. This results in the IS curve shifting to the right. But if the ADe curve is horizontal and its position solely determined by the central bank, 636 π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ 𝑃𝑃𝑑𝑑 π‘Ÿπ‘Ÿπ‘‘π‘‘ 𝐼𝐼𝐼𝐼 𝐴𝐴𝐼𝐼 𝐴𝐴𝐴𝐴𝑒𝑒 π‘Ÿπ‘Ÿ0,𝑑𝑑 π‘Œπ‘Œ0,𝑑𝑑=π‘Œπ‘Œ0,𝑑𝑑𝑓𝑓 𝑃𝑃0,𝑑𝑑=𝑃𝑃�0,𝑑𝑑 there is no shift in it and no
change in equilibrium output or the price level. The real interest rate must rise given the new position of the IS curve for output to remain unchanged. This is shown in Figure 28.6 below: Figure 28.6: A Strict Inflation (Price Level) Target: Response to Positive IS Shock Consider next an increase in Y f t. This could be driven either by an increase in At or a reduction in ΞΈt. This is shown in Figure 28.7. The AS curve shifts to the right. With the ADe curve being horizontal, output rises by the full amount of the change in Y f t and the price level is unaffected. The real interest rate must fall to support the higher level of output. 637 π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ 𝑃𝑃𝑑𝑑 π‘Ÿπ‘Ÿπ‘‘π‘‘ 𝐼𝐼𝐼𝐼 𝐴𝐴𝐼𝐼 𝐴𝐴𝐴𝐴𝑒𝑒 π‘Ÿπ‘Ÿ0,𝑑𝑑 π‘Œπ‘Œ0,𝑑𝑑=π‘Œπ‘Œ1,𝑑𝑑=π‘Œπ‘Œ0,𝑑𝑑𝑓𝑓 𝑃𝑃0,𝑑𝑑=𝑃𝑃1,𝑑𝑑=𝑃𝑃�0,𝑑𝑑 𝐼𝐼𝐼𝐼′ π‘Ÿπ‘Ÿ1,𝑑𝑑 Figure 28.7: A Strict Inflation (Price Level) Target: Response to ↑ At or ↓ ΞΈt The analysis above reveals a critical point. If a central bank wants to implement the efficient equilibrium, it need only commit to price stability (and, in effect, cause the AD curve to become horizontal). Why is this a critical point? In reality, central banks may have difficulty in observing the exogenous shocks buffeting the economy in real time, and determining Y
f is no easy task in practice. Our analysis reveals that the central bank may t not need to know what Y f is, or what the actual exogenous shocks in the economy are, in t order to achieve the efficient equilibrium. All it needs to do is to commit to price stability. This is a rather remarkable result. It is so remarkable that Blanchard and GalΒ΄Δ± (2007) have called it the β€œDivine Coincidence.” The basic idea of the Divine Coincidence is that a central bank faces no tradeoff in achieving price stability and β€œfull employment” (which in our model means Yt = Y f t ). Achieving one may automatically imply the other. Since Y f t is hard to determine, especially in real time, the Divine Coincidence implies that monetary 638 π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ 𝑃𝑃𝑑𝑑 π‘Ÿπ‘Ÿπ‘‘π‘‘ 𝐼𝐼𝐼𝐼 𝐴𝐴𝐼𝐼 𝐴𝐴𝐴𝐴𝑒𝑒 π‘Ÿπ‘Ÿ0,𝑑𝑑 π‘Œπ‘Œ0,𝑑𝑑=π‘Œπ‘Œ0,𝑑𝑑𝑓𝑓 𝑃𝑃0,𝑑𝑑=𝑃𝑃1,𝑑𝑑=𝑃𝑃�0,𝑑𝑑 𝐴𝐴𝐼𝐼′ π‘Œπ‘Œ1,𝑑𝑑=π‘Œπ‘Œ1,𝑑𝑑𝑓𝑓 π‘Ÿπ‘Ÿ1,𝑑𝑑 policy is relatively easy since fluctuations in the price level (or inflation rates) are much easier to observe at high frequencies and in real time. Does the Divine Coincidence always hold in the New Keynesian model? Unfortunately, the answer turns out to be no. Conditional on IS shocks (demand) and shocks to At or
ΞΈt (potential output shocks), the divine coincidence holds. Committing to stabilizing the price level automatically results in the efficient equilibrium outcome. But the Divine Coincidence does not hold conditional on shocks to Β―Pt. We have thought of changes in Β―Pt as primarily reflecting changes in expected rates of inflation, but more generally fluctuations in Β―Pt could reflect changes in the prices of important material inputs like oil. We can see this in Figure 28.8, which considers an exogenous increase in Β―Pt. If the central bank is committed to price stability, then the increase in Β―Pt necessitates a decline in output below potential, i.e. Yt < Y f t. Figure 28.8: A Strict Inflation (Price Level) Target: Response to ↑ Β―Pt 639 π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ 𝑃𝑃𝑑𝑑 π‘Ÿπ‘Ÿπ‘‘π‘‘ 𝐼𝐼𝐼𝐼 𝐴𝐴𝐼𝐼 𝐴𝐴𝐴𝐴𝑒𝑒 π‘Ÿπ‘Ÿ0,𝑑𝑑 π‘Œπ‘Œ0,𝑑𝑑=π‘Œπ‘Œ0,𝑑𝑑𝑓𝑓 𝑃𝑃0,𝑑𝑑=𝑃𝑃1,𝑑𝑑=𝑃𝑃�0,𝑑𝑑 𝐴𝐴𝐼𝐼′ π‘Ÿπ‘Ÿ1,𝑑𝑑 π‘Œπ‘Œ1,𝑑𝑑 𝑃𝑃�1,𝑑𝑑 If in contrast, if the central bank tries to prevent output from declining in the face of an increase in Β―Pt, it must accept some inflation. The central bank cannot have its cake and eat it too conditional on Β―Pt shocks – it cannot simultaneously stabilize both prices and output. Somewhat
ironically, this analysis actually potentially strengthens the case for price stability. In particular, to the extent to which one thinks of Β―Pt as reflecting exogenous changes in expected inflation, then a central bank with a track record of achieving price stability is likely to face fewer and smaller fluctuations in Β―Pt. Hence, while a commitment to price stability may involve significant output costs when Β―Pt changes, a credible commitment to price stability likely means that those costs rarely have to be borne. 28.3 The Natural Rate of Interest and Monetary Policy t, where Y f In the sections above, we have thought about monetary policy as in essence targeting Yt = Y f is the hypothetical neoclassical equilibrium level of output. For a fixed money supply, Yt reacts differently to exogenous shocks than Y f t, and an optimizing central bank ought to adjust the money supply (and hence interest rates) to bring the two into alignment. t An alternative way to think about monetary policy is in terms of targeting interest rates rather than output. In particular, let rf t denote the β€œnatural rate of interest,” or the real interest rate which would be the equilibrium real interest rate in the neoclassical model. The concept of the natural rate of interest was first developed by Wicksell (1898) and more recently popularized by Woodford (2003). In popular writings, the natural rate of interest is also sometimes called the β€œneutral” rate of interest or even sometimes (quite erroneously) the β€œequilibrium” rate of interest. The basic idea of optimal monetary policy can be cast in terms of adjusting rt (through an adjustment of the money supply) so that rt = rf t. The natural rate of interest can be graphically determined by combining the vertical, t ) with the IS curve. This can be seen hypothetical neoclassical AS curve (which gives Y f graphically below: 640 Figure 28.9: The Natural Rate of Interest Mathematically, rf t is determined as the solution to the following expression: βˆ’ Gt, Yt+1 βˆ’ Gt+1, rf (28.9) is one equation in one unknown, rf = C(Y f t Y f t t t, one t as the solution to this equation. This is exactly what is shown graphically in t.
Given exogenous variables and Y f ) + I d(rf t, At+1, Kt) + Gt (28.9) determines rf Figure 28.9. The natural rate of interest is affected by IS shocks and shocks to Y f t. In Figure 28.10, we show how a positive IS shock (e.g. an increase in At+1 or Gt, or a reduction in Gt+1) impacts the natural rate of interest. The IS curve shifts right. But with no change in Y f t, the natural rate of interest rises by the amount of the vertical shift of the IS curve. The natural rate of interest would fall in response to a negative IS shock. 641 π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ 𝑃𝑃𝑑𝑑 π‘Ÿπ‘Ÿπ‘‘π‘‘ 𝐼𝐼𝐼𝐼 𝐴𝐴𝐼𝐼𝑓𝑓 π‘Œπ‘Œπ‘‘π‘‘π‘“π‘“ π‘Ÿπ‘Ÿπ‘‘π‘‘π‘“π‘“ Figure 28.10: IS Shocks and the Natural Rate of Interest Consider next a positive shock to Y f reduction in ΞΈt. There is no shift of the IS curve. But with Y f shown below in Figure 28.11. t, which could occur because of an increase in At or a t must fall. This is t higher, rf 642 π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ 𝑃𝑃𝑑𝑑 π‘Ÿπ‘Ÿπ‘‘π‘‘ 𝐼𝐼𝐼𝐼 𝐴𝐴𝐼𝐼𝑓𝑓 π‘Œπ‘Œπ‘‘π‘‘π‘“π‘“ π‘Ÿπ‘Ÿ0,𝑑𝑑𝑓𝑓 𝐼𝐼𝐼𝐼′ π‘Ÿπ‘Ÿ1,𝑑𝑑𝑓𝑓 Figure 28
.11: Y f t Shocks and the Natural Rate of Interest As we have seen, implementation of optimal policy requires targeting Yt = Y f t, which implies targeting rt = rf t. Though we have heretofore thought of policy in terms of adjustments in Mt, it is just as easy to think about the central bank as adjusting the interest rate (technically, central banks can only impact nominal rates, but to the extent to which expected inflation is constant, movements in the nominal and real rates are the same). In particular, we can think of optimal policy as targeting rt = rf t. To see how the money supply must adjust to hit this target, consider the mathematical expression for the LM curve: Mt Pt = M d(rf t + Ο€e t+1, Y f t ) (28.10) Taking rf t and Y f t as given, we can think of optimal policy as choosing Mt to make (28.10) hold. In particular, suppose that there is a positive IS shock. This raises rf t but has no effect on Y f t. This makes the demand for money (the right hand side of the equation) fall. To accommodate this demand for money, the central bank ought to reduce the money supply in such a way that Mt falls to meet the fall in the right hand side without Pt changing. Similarly, Pt suppose that there is a positive shock to, say, At. This causes Y f t to t decline, the combined effect of which is to increase the demand for money. The central bank to increase and rf 643 π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ 𝑃𝑃𝑑𝑑 π‘Ÿπ‘Ÿπ‘‘π‘‘ 𝐼𝐼𝐼𝐼 𝐴𝐴𝐼𝐼𝑓𝑓 π‘Œπ‘Œ0,𝑑𝑑𝑓𝑓 π‘Ÿπ‘Ÿ0,𝑑𝑑𝑓𝑓 π‘Œπ‘Œ1,𝑑𝑑𝑓𝑓 𝐴𝐴𝐼𝐼𝑓𝑓′ οΏ½
οΏ½π‘Ÿ1,𝑑𝑑𝑓𝑓 ought to increase the money supply so as to accommodate this increase in the demand for money without the price level changing. t nor Y f The above analysis helps us to understand why most economists do not favor using fiscal policy as a stabilization tool, except perhaps in unusual circumstances to be discussed later. One reason that economists favor monetary over fiscal policy is outside of the confines of our model: with fiscal policy, there are long legislative lags and it takes a while to get things done. In contrast, monetary policy can react quickly to shocks. Furthermore, monetary policy makers are experts in the economy, whereas the same is not necessarily true of members of legislatures. The other reason, related to our discussion above, is that changes in fiscal variables (e.g. Gt) impact rf t. Changes in the money supply, in contrast, do not. It is therefore a well-defined thought experiment to adjust Mt to make (28.10) hold, since changes in Mt affect neither rf t. The same is not true in general for fiscal policy. As a trivial example, as can be seen in Figure 28.10, an increase in Gt raises rf t, even if it has no effect on Y f t. This means that, in the context of the New Keynesian model, fiscal variables (like Gt) should not be used to combat shocks. As an example, suppose that the economy is hit with a positive IS shock (say people are more optimistic about the future, and At+1 increases). Gt can be deployed to ensure that Yt does not rise above Y f t, but this requires leaving the real interest rate unchanged. This can be seen in Figure 28.12 below. There we consider the effects of a positive IS shock in the partial sticky price model, and engage in the thought experiment of counteracting this with a change in Gt so as to keep Yt = Y f t. The positive IS shock raises rf t. Using fiscal policy to make Yt = Y f t would necessitate reducing Gt, which would shift the IS and AD curves back in to their original positions. But this would entail no change in the equilibrium real
interest rate, which would mean that, even though Yt = Y f t, rt would be less than what it would be in the neoclassical model with no policy response (which in the graph is labeled rf 1,t). This means that using fiscal policy to combat the IS shock would result in the output gap being zero, but would affect the composition of output (between consumption, investment, and government spending) relative to the efficient, neoclassical equilibrium. t even though there is no effect on Y f 644 Figure 28.12: Using Fiscal Policy to Combat an IS Shock 28.4 The Taylor Rule We have thought about monetary policy as being conducted in terms of setting the money supply, Mt. We initially thought about Mt being exogenous, and in this chapter we have discussed how Mt ought to adjust in response to different exogenous shocks so as to implement 645 𝑀𝑀𝑑𝑑 𝑃𝑃𝑑𝑑 π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ 𝑁𝑁𝑑𝑑 𝑁𝑁𝑑𝑑 𝐴𝐴𝐴𝐴 𝐼𝐼𝐴𝐴=𝐼𝐼𝐴𝐴′′ π‘Ÿπ‘Ÿ0,𝑑𝑑=π‘Ÿπ‘Ÿ0,𝑑𝑑𝑓𝑓=π‘Ÿπ‘Ÿ2,𝑑𝑑 π‘Œπ‘Œ0,𝑑𝑑=π‘Œπ‘Œ0,𝑑𝑑𝑓𝑓=π‘Œπ‘Œ2,𝑑𝑑 𝑁𝑁0,𝑑𝑑=𝑁𝑁2,𝑑𝑑 𝑁𝑁𝑠𝑠(𝑀𝑀
𝑑𝑑,πœƒπœƒπ‘‘π‘‘) 𝐿𝐿𝐿𝐿(𝐿𝐿𝑑𝑑,𝑃𝑃0,𝑑𝑑) 𝐴𝐴𝑑𝑑𝐹𝐹(𝐾𝐾𝑑𝑑,𝑁𝑁𝑑𝑑) π‘Œπ‘Œπ‘‘π‘‘=π‘Œπ‘Œπ‘‘π‘‘ π‘Ÿπ‘Ÿπ‘‘π‘‘ 𝐴𝐴𝐴𝐴=𝐴𝐴𝐴𝐴′′ 𝑃𝑃0,𝑑𝑑=𝑃𝑃�0,𝑑𝑑=𝑃𝑃2,𝑑𝑑 𝑀𝑀0,𝑑𝑑=𝑀𝑀2,𝑑𝑑 𝑁𝑁𝑑𝑑(𝑀𝑀𝑑𝑑,𝐴𝐴𝑑𝑑,𝐾𝐾𝑑𝑑) 𝐴𝐴𝐴𝐴𝑓𝑓 Original Post-Shock, no policy response Post-shock, indirect effect of 𝑃𝑃𝑑𝑑 on LM curve Fiscal policy response to stabilize output gap 0 subscript: original 1 subscript: post-shock, no policy response 2 subscript: post policy response 𝐴𝐴𝐴𝐴′ 𝐼𝐼𝐴𝐴′ 𝐿𝐿𝐿𝐿(𝐿𝐿𝑑𝑑,𝑃𝑃1,𝑑𝑑) π‘Ÿπ‘Ÿ1,𝑑𝑑𝑓𝑓 𝑀𝑀1,𝑑𝑑 𝑁𝑁1,𝑑𝑑 π‘Œπ‘Œ1,
𝑑𝑑 𝑃𝑃1,𝑑𝑑 π‘Ÿπ‘Ÿ1,𝑑𝑑 the neoclassical equilibrium. There are a couple of potential drawbacks of this approach. First, modern monetary policy is typically conducted via targeting a short term nominal interest rate (like the Fed Funds Rate in the US), not the money supply. This is perhaps not such a big problem, because changes in Mt are what bring about changes in the target nominal interest rate and hence real interest rates, as we have seen. Second, while one can think about optimal monetary policy in terms of adjusting Mt in response to different shocks, it is not very transparent how this is done and a central bank behaving in this way has a lot of discretion. For these reasons, many economists now think about monetary policy in the form of explicit rules relating target values of economic variables to a central bank’s policy interest rate. The most famous monetary policy rule is attributed to John Taylor, Taylor (1993), and is often simply called the β€œTaylor Rule.” Taylor posited that the Federal Reserve’s target nominal interest rate equals the long run real interest rate, rβˆ—, plus a long run inflation target, Ο€βˆ—, and responds positively to deviations of the actual inflation rate from target and to the output gap. The response coefficients φπ and Ο†y are both assumed to be positive. Formally, we can express this type of monetary policy rule as: it = rβˆ— + Ο€βˆ— + φπ(Ο€t βˆ’ Ο€βˆ—) + Ο†y(Yt βˆ’ Y f t ) (28.11) Suppose that the long run target real interest rate is rβˆ— = 2.5 and the long run inflation target is Ο€βˆ— = 2. Taylor proposed coefficient values of φπ = 1.5 and Ο†y = 0.5. Figure 28.13 below plots the actual Fed Funds Rate (black line) and the rate implied by (28.11) with these coefficients for the period 1984q1 through 2008q3. We omit the period prior to 1984 because of a large switch in the conduct of monetary policy occurring in the mid-1980s, and omit the period after 2008 because the
actual Federal Funds rate has been at or near zero ever since. 646 Figure 28.13: Actual and Monetary Policy Rule Implied Fed Funds Rate One can observe that, at least qualitatively, (28.11) provides a fairly good description of actual Fed policy. The correlation between the actual Funds rate and the rate implied by (28.11) is about 0.6. The two series can be made to look much more similar if one incorporates an interest-smoothing motive into the policy rule by including a lagged nominal interest rate term on the right hand side (i.e. something like ρitβˆ’1, where 0 < ρ < 1). It turns out that a monetary policy rule like the Taylor rule implies similar policy actions to what we have argued are optimal in the text. In particular, in the Taylor rule the Fed reacts to positive demand shocks by raising interest rates (which implies reducing the money supply) and to positive supply shocks by cutting interest rates (which involves increasing the supply of money). One can formally incorporate a policy rule like (28.11) into our model. This effectively involves replacing the LM curve (which treats the money supply as exogenous) with something like (28.11). The model can be graphically analyzed and has very similar implications to what we have studied in the text. This version of the model, which we call the IS-MP-AD-AS model, is presented and studied in Appendix E. 647 -4-202468101284868890929496980002040608Federal Funds RateMonetary Policy Rule Chapter 29 The Zero Lower Bound In Chapter 28, we discussed how a central bank can optimally adjust the money supply (and hence interest rates) in response to changing economic conditions. The basic idea of optimal policy is that a central bank wants to use its control of the money supply to impact the position of the AD curve in such a way that the short run equilibrium of the New Keynesian model coincides with the hypothetical equilibrium which would emerge in the medium run neoclassical model. Provided fluctuations in Β―Pt are not a major source of fluctuations, one way to think about this is that the central bank desires for the effective AD curve to become horizontal, which coincides with a policy of price stability. A practical problem with this approach to policy that is particularly relevant of late is that nominal interest rates cannot go below zero (or cannot go
very far below zero). Why is this? The nominal interest rate is the return on holding money across time. If you save one unit of money, you get back 1 + it units of money in the next period. Since money is storable across time (one of the functions which defines money is that it is a store of value), one should never accept a negative nominal return. Why? Suppose that the nominal interest rate is βˆ’5 percent. Putting one unit of money in the bank would yield 0.95 units of money in the next period. The outside option is simply to hold the money on your own, which would yield one unit of money in the future. Only if the nominal interest rate is positive is there a disincentive to hold money and put it in interest bearing bonds or bank accounts. Note that the real interest rate, in contrast, can be negative. Because of the non-storability of goods, one might accept a negative rate of return – i.e. you may give up a unit of goods today in exchange for 0.95 goods in the future if your outside option is to have zero units of the good in the future. But because money is storable, one ought to not be willing to accept a negative nominal return. We can see the effects of the zero lower bound by referencing back to the first order condition for the holding of money we derived in Chapter 14. It is: vβ€² (Mt Pt ) = it 1 + it uC(Ct, 1 βˆ’ Nt) (29.1) In (29.1), if it = 0, then the only way for this expression to hold is if Mt Pt β†’ ∞, which in 648 turn drives the marginal utility of holding money to zero. In other words, if the nominal interest rate goes to zero, there is an infinite demand for real money balances. For this reason, the nominal interest rate going to zero is sometimes called a β€œliquidity trap” – when the nominal interest rate is zero, there is an infinite demand for money (i.e. liquidity) relative to less liquid, interest-bearing assets. We can see from (29.1) that this first order condition cannot hold if it < 0 – this would require that the marginal utility of real balances or of consumption must be negative, which is inconsistent with the assumptions we have made on
those functions. In other words, it < 0 is inconsistent with this equation holding. it = 0 is therefore a lower bound on the nominal interest rate. We refer to this as the β€œzero lower bound” and abbreviate it ZLB. Until very recently, conventional wisdom among economists was consistent with what has been laid out here – nominal interest rates cannot go negative. Recently, several central banks around the world – including several central banks in Europe and Japan – have experimented with negative interest rates, and there have been calls from some for the US Federal Reserve to follow suit. Contrary to the predictions of our simple theory, embodied in the money demand specification (29.1), the demand for liquidity has not gone to infinity in those areas with negative nominal interest rates. Why not? Our modeling assumptions abstract from the fact that it is probably costly to hold liquidity. To use a literal example, suppose that holding money means stuffing it under one’s mattress. Surely there is some inconvenience associated with this (as well as a heightened probability of theft), and individuals may be willing to tolerate slightly negative nominal interest rates in exchange for not having to store all of their wealth under their mattress. There is likely some lower bound on nominal interest rates below which individuals would have an infinite demand for liquidity. It just may not be exactly zero. Since central banks experimenting with negative nominal interest rates have not lowered interest rates that far below zero, we don’t really know what that lower bound might be. Some economists prefer the term effective lower bound (ELB) rather the ZLB. In what follows, we will assume that zero is in fact the lower bound on nominal interest rates. For the analysis which we do, it is actually not crucial that the lower bound is zero, just that there is some lower bound. What matters for our analysis is not so much that the nominal interest rate gets stuck at some particular point, but rather that the nominal interest rate becomes fixed at that point. Whether that invariant nominal interest rate is zero or slightly negative is not that important. As we show in the subsections below, the ZLB introduces a flat portion to the LM curve. Most of the time, this flat portion of the LM curve is irrelevant, and the analysis of the New Keynesian model conducted in previous chapters is unaffected. But if the economy ventures
into the flat portion of the LM curve, the AD curve becomes vertical. This means that output 649 becomes completely demand determined, which is a 180 degree change from the neoclassical model where output is completely supply determined. Furthermore, the real interest rate becomes constant when the ZLB binds. This will mean that shocks to the IS curve will have particularly large impacts on aggregate demand and total output. Furthermore, a binding ZLB could result in a deflationary spiral wherein the economy gets β€œtrapped” at a suboptimally low level of output, where the economy’s supply-driven self-correcting mechanism does not work. A binding ZLB has important implications for policy. First, it opens the door for the potential desirability of fiscal stimulus. This is because fiscal stimulus does not impact the real interest rate if the ZLB binds, which means that it does not crowd out private expenditure. Second, normal monetary policy will not work at the ZLB – the central bank cannot adjust interest rates in response to shocks since the interest rate becomes fixed. Exiting the ZLB can be difficult to engineer, and central banks will in general try to avoid ever hitting the ZLB in the first place. We conclude the chapter with a discussion of the tradeoffs involved in trying to design policies to avoid the ZLB. 29.1 The IS-LM-AD Curves with the ZLB Given an exogenous amount of expected inflation, we can think about the ZLB as imposing t+1, it β‰₯ 0 t+1. Since expected inflation can be positive, the lower bound on the real a lower bound on the real interest rate. From the Fisher relationship, since rt = it βˆ’ Ο€e means that rt β‰₯ βˆ’Ο€e interest rate can be negative. In the upper panel of Figure 29.1, we plot the conventional LM curve, which is upwardsloping in a graph with rt on the vertical axis and Yt on the horizontal axis. Along with this, we plot a dashed line corresponding to the implied lower bound on the real interest rate of βˆ’Ο€e t+1 (where again we take expected inflation to be exogenous.) 650 Figure 29.1: The LM Curve and the ZLB The effective LM curve is the upper bound
of the conventional LM curve and the dashed line corresponding to the ZLB. In other words, the ZLB introduces a kink into the LM curve. For rt > βˆ’Ο€e t+1, the effective LM curve is a horizontal line at rt = βˆ’Ο€e t+1, the LM curve looks normal. For rt < βˆ’Ο€e t+1. This is shown in the lower panel of Figure 29.1. How does one go from the effective LM curve (with the kink at rt = βˆ’Ο€e t+1) to the AD curve? We will first consider three different cases, one in which the ZLB is β€œnon-binding,” one in which it always β€œbinds,” and one in which it sometimes binds and sometimes does not. The first is for a β€œnon-binding” ZLB. By this we mean that the IS curve is sufficiently far to the right that we need not worry about the ZLB binding. This case is considered in Figure 29.2 below. We proceed in the normal way. An increase in the price level causes the LM curve to shift in, which results in a higher real interest rate and hence lower output along the IS curve. Hence, the AD curve slopes down, just as it did before. 651 π‘Ÿπ‘Ÿπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ βˆ’πœ‹πœ‹π‘‘π‘‘+1𝑒𝑒 𝐿𝐿𝐿𝐿(𝐿𝐿𝑑𝑑,𝑃𝑃𝑑𝑑) 𝑍𝑍𝐿𝐿𝑍𝑍 βˆ’πœ‹πœ‹π‘‘π‘‘+1𝑒𝑒 𝐿𝐿𝐿𝐿(𝐿𝐿𝑑𝑑,𝑃𝑃𝑑𝑑) π‘Œπ‘Œπ‘‘π‘‘ π‘Ÿπ‘Ÿπ‘‘π‘‘ Figure 29.2: AD Derivation with a Non-Binding ZLB Next, we consider
the case of a binding ZLB. This case is considered graphically in Figure 29.3. By binding ZLB we mean that the position of the IS curve is such that it intersects the effective LM curve in the flat region at rt = βˆ’Ο€e t+1. An increase in the price level causes the upward-sloping portion of the LM curve to shift in, but does not affect the flat portion of the effective LM curve. As long as the change in the price level is not so large as to shift upward-sloping portion of the LM curve in to the point where the IS curve would intersect it above rt = βˆ’Ο€e t+1 (which we rule out for the purposes of these exercises), the change in the price level has no impact on the real interest rate (it is effectively fixed), and hence no effect on Yt. Put slightly differently, the IS curve is one equation in two unknowns – Yt and rt. But at the ZLB, rt effectively becomes exogenous. This means that output is determined solely from the IS curve, and Pt does not affect the IS curve. This means that the AD curve becomes vertical. 652 π‘Ÿπ‘Ÿπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ βˆ’πœ‹πœ‹π‘‘π‘‘+1𝑒𝑒 𝐿𝐿𝐿𝐿(𝐿𝐿𝑑𝑑,𝑃𝑃0,𝑑𝑑) π‘Œπ‘Œπ‘‘π‘‘ 𝐿𝐿𝐿𝐿(𝐿𝐿𝑑𝑑,𝑃𝑃1,𝑑𝑑) 𝐿𝐿𝐿𝐿(𝐿𝐿𝑑𝑑,𝑃𝑃2,𝑑𝑑) 𝑃𝑃𝑑𝑑 𝑃𝑃0,𝑑𝑑 𝑃𝑃1
,𝑑𝑑 𝑃𝑃2,𝑑𝑑 𝐴𝐴𝐴𝐴 Figure 29.3: AD Derivation with a Binding ZLB Finally, we consider the case where sometimes the ZLB binds and sometimes it does not. This is shown in Figure 29.4. With the price level sufficiently high, the upward-sloping portion of the LM curve is sufficiently far to the left that it intersects the IS curve above the lower bound on the real interest rate. In this region, the AD curve is downward-sloping as it ordinarily is. When the price level is sufficiently low, in contrast, the LM curve is sufficiently far to the right that the IS curve intersects the lower bound on the real interest rate before hitting the upward-sloping portion of the LM curve. In this region, the AD curve is vertical. Hence, we can think of the ZLB as introducing a kink into the AD curve – below some cutoff price level, the AD curve is vertical. Note that the ZLB is most likely to bind when the price level is low. 653 π‘Ÿπ‘Ÿπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ βˆ’πœ‹πœ‹π‘‘π‘‘+1𝑒𝑒 𝐿𝐿𝐿𝐿(𝐿𝐿𝑑𝑑,𝑃𝑃0,𝑑𝑑) π‘Œπ‘Œπ‘‘π‘‘ 𝐿𝐿𝐿𝐿(𝐿𝐿𝑑𝑑,𝑃𝑃1,𝑑𝑑) 𝐿𝐿𝐿𝐿(𝐿𝐿𝑑𝑑,𝑃𝑃2,𝑑𝑑) 𝑃𝑃𝑑𝑑 𝑃𝑃0,𝑑𝑑 𝑃𝑃1,𝑑𝑑 𝑃𝑃2,𝑑𝑑 𝐴
𝐴𝐴𝐴 𝐼𝐼𝐼𝐼 Figure 29.4: AD Derivation with Both a Binding and Non-Binding ZLB For the rest of this chapter, we will not worry about whether the ZLB is binding or non-binding, and will focus our attention on the case in which it does bind. In this case the LM curve is effectively horizontal and the AD curve becomes vertical. In a sense, we can think about the ZLB as representing the polar opposite of the neoclassical model. In the neoclassical model, the AS curve is vertical and hence output is completely supply determined. In the New Keynesian model with a binding ZLB, output is completely demand determined. Note that we cannot entertain the neoclassical model with a binding ZLB – this would result in either no equilibrium or an indeterminate equilibrium, since both the AS and AD curves would be vertical. There would either be no equilibrium (the AS and AD curves do not lie on top of one another), or an indeterminate price level (the AD and AS curves lie on top of one another, which would determine Yt but not Pt). When the ZLB binds, the level of the money supply does not impact the position of the 654 π‘Ÿπ‘Ÿπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ βˆ’πœ‹πœ‹π‘‘π‘‘+1𝑒𝑒 π‘Œπ‘Œπ‘‘π‘‘ 𝑃𝑃𝑑𝑑 𝑃𝑃0,𝑑𝑑 𝑃𝑃1,𝑑𝑑 𝑃𝑃2,𝑑𝑑 𝐴𝐴𝐴𝐴 𝐼𝐼𝐼𝐼 𝐿𝐿𝐿𝐿(𝐿𝐿𝑑𝑑,𝑃𝑃1,𝑑𝑑) 𝐿𝐿𝐿𝐿(𝐿𝐿𝑑𝑑,𝑃𝑃0,𝑑𝑑) 𝐿𝐿𝐿�
οΏ½οΏ½(𝐿𝐿𝑑𝑑,𝑃𝑃2,𝑑𝑑) AD curve. This is shown graphically in Figure 29.5. Since changes in the money supply only impact the position of the upward-sloping portion of the effective LM curve, and not the flat portion, they do not impact the real interest rate and hence do not impact the level of output or the position of the AD curve when the ZLB binds. Note that we do not consider a sufficiently large decline in the money supply, which would shift the upward-sloping portion of the LM curve in so much that the ZLB would cease to bind. Figure 29.5: Changes in the Money Supply and a Binding ZLB That the money supply does not impact the position of the AD curve when the ZLB binds has important implications. In particular, it means that the central bank ceases to have any control over the real interest rate and output. As we will see, this means that conventional monetary policy is no longer an option at the ZLB. 655 π‘Ÿπ‘Ÿπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ βˆ’πœ‹πœ‹π‘‘π‘‘+1𝑒𝑒 𝐿𝐿𝐿𝐿(𝐿𝐿0,𝑑𝑑,𝑃𝑃0,𝑑𝑑) π‘Œπ‘Œπ‘‘π‘‘ 𝐿𝐿𝐿𝐿(𝐿𝐿2,𝑑𝑑,𝑃𝑃0,𝑑𝑑) 𝐿𝐿𝐿𝐿(𝐿𝐿1,𝑑𝑑,𝑃𝑃0,𝑑𝑑) 𝑃𝑃𝑑𝑑 𝐴𝐴𝐴𝐴 𝐼𝐼𝐼𝐼 𝑃𝑃0,𝑑𝑑 𝐿𝐿1,𝑑𝑑>𝐿𝐿0,𝑑
𝑑>𝐿𝐿2,𝑑𝑑 29.2 Equilibrium Effects of Shocks with a Binding ZLB In this section, we consider the equilibrium effects of changes in exogenous variables when the ZLB binds. We focus on the partial sticky price model. In the analysis which follows, we assume that the ZLB binds before a shock hits and continues to bind after that shock hits. Put differently, we do not consider the case in which a shock causes the equilibrium to switch to the downward-sloping portion of the AD curve. As such, we will draw pictures where the LM curve is simply a horizontal line – i.e. we do not consider the upward-sloping portion of the LM curve in the ensuing analysis. Consider first a negative shock to the IS curve. This could be caused by a reduction At+1 or Gt, or an increase in Gt+1. We plot out the effects of this negative IS shock in Figure 29.6. We abstract from looking at the behavior of labor market variables. To understand how the and why the ZLB matters, we also draw in hypothetical curves corresponding to a situation in which the ZLB does not bind. The original LM and AD curves when the ZLB binds are shown in black, while the hypothetical original positions of these curves with a non-binding ZLB are shown in orange. After the IS shock, the new curves with the binding ZLB are shown in blue, while they appear in red for the hypothetical case in which the ZLB does not bind. 656 Figure 29.6: Sticky Price Model: Negative IS Shock with Binding ZLB When the ZLB binds, the real interest rate is fixed at βˆ’Ο€e t+1. The inward-shift of the IS curve causes the vertical AD curve to shift in. The inward shift of the vertical AD curve is the same as the horizontal shift of the IS curve. Output falls from Y0,t to Y1,t. Now consider the case where the ZLB does not bind (but the original equilibrium value of output is the same). The inward shift of the IS curve is the same in either case. But because the LM curve is upward-sloping, the level of Yt where the IS and LM curves intersect does not fall by as much as it does when the LM curve
is horizontal. Consequently, the downward-sloping AD curve shifts in, but not as much as the vertical AD curve shifts in when the ZLB binds. In addition, the decline in the price level causes the LM curve to shift out some, further reducing the real interest rate and further mitigating the fall in output. On net, when the ZLB does not bind, output falls, but not by as much as it does when the ZLB binds. The price level declines by more in response to the shock when the ZLB binds in comparison to when it does 657 π‘Ÿπ‘Ÿ0,𝑑𝑑=π‘Ÿπ‘Ÿ1,𝑑𝑑=βˆ’πœ‹πœ‹π‘‘π‘‘+1𝑒𝑒 𝐿𝐿𝐿𝐿 𝐴𝐴𝐴𝐴 𝐼𝐼𝐼𝐼 𝐴𝐴𝐼𝐼 𝐼𝐼𝐼𝐼′ 𝐴𝐴𝐴𝐴′ π‘Œπ‘Œ1,𝑑𝑑 π‘Œπ‘Œ0,𝑑𝑑 𝐿𝐿𝐿𝐿𝑛𝑛𝑛𝑛 𝐴𝐴𝐴𝐴𝑛𝑛𝑛𝑛 𝐴𝐴𝐴𝐴𝑛𝑛𝑛𝑛′ π‘Œπ‘Œ1,𝑑𝑑𝑛𝑛𝑛𝑛 𝑃𝑃0,𝑑𝑑 π‘Ÿπ‘Ÿ1,𝑑𝑑𝑛𝑛𝑛𝑛 π‘Ÿπ‘Ÿπ‘‘π‘‘ 𝑃𝑃1,𝑑𝑑𝑛𝑛𝑛𝑛 π‘Œπ‘Œ π‘Œπ‘Œπ‘‘π‘‘ Original Original, hypothetical no ZLB 𝑃𝑃𝑑𝑑 Post-shock Post-shock, hypothetical
no ZLB 0 subscript: original equilibrium 1 subscript: post-shock equilibrium nb superscript: hypothetical no ZLB Post-shock, hypothetical no ZLB, indirect effect on LM 𝐿𝐿𝐿𝐿𝑛𝑛𝑛𝑛′ 𝑃𝑃1,𝑑𝑑 not. The reason why output falls by less after the negative IS shock when the ZLB does not bind is because the real interest rate falls. This fall in the real interest rate works to increase desired spending, partially offsetting the decline in desired expenditure resulting from the negative IS shock. When the ZLB binds, the real interest rate cannot fall. This means that output falls by more after the negative IS shock than it would if the ZLB did not bind. Consider next a positive supply shock. Think of this as resulting from an increase in At or a reduction in ΞΈt. The effects of the supply shock with and without the ZLB binding are shown in Figure 29.7. If the AD curve is vertical, the rightward shift of the AS curve results in no change in output and a large decline in the price level. Intuitively, the reason that output cannot rise is that the real interest rate cannot fall, so there is no incentive for the household or firm to spend more. In contrast, when the ZLB does not bind, the decline in the price level triggers a rightward shift of the LM curve, which allows the real interest rate to fall and output to expand. 658 Figure 29.7: Sticky Price Model: Positive Supply Shock with Binding ZLB The exercises demonstrated graphically in Figures 29.6 and 29.7 reveal an important point. The ZLB accentuates the differences between the New Keynesian and neoclassical models. Output responds even more to IS shocks, and even less to supply shocks (in fact, not at all) compared to the neoclassical model. 29.3 Why is the ZLB Costly? Central bankers and academics often speak of the ZLB as if it is something of which to be afraid. Why is this? Why is the ZLB considered to be costly? Firstly, the ZLB is costly because normal monetary policy ceases to work when the nominal interest rate gets stuck at zero. This was touched on in reference to Figure 29.5 above. When changes in the money
supply do not affect the real interest rate, conventional 659 π‘Ÿπ‘Ÿ0,𝑑𝑑=π‘Ÿπ‘Ÿ1,𝑑𝑑=βˆ’πœ‹πœ‹π‘‘π‘‘+1𝑒𝑒 𝐿𝐿𝐿𝐿 𝐴𝐴𝐴𝐴 𝐼𝐼𝐼𝐼 𝐴𝐴𝐼𝐼 π‘Œπ‘Œ0,𝑑𝑑 𝐿𝐿𝐿𝐿𝑛𝑛𝑛𝑛 𝐴𝐴𝐴𝐴𝑛𝑛𝑛𝑛 𝑃𝑃0,𝑑𝑑 π‘Ÿπ‘Ÿ1,𝑑𝑑𝑛𝑛𝑛𝑛 π‘Ÿπ‘Ÿπ‘‘π‘‘ π‘Œπ‘Œ π‘Œπ‘Œπ‘‘π‘‘ Original Original, hypothetical no ZLB 𝑃𝑃𝑑𝑑 Post-shock Post-shock, hypothetical no ZLB 0 subscript: original equilibrium 1 subscript: post-shock equilibrium nb superscript: hypothetical no ZLB Post-shock, hypothetical no ZLB, indirect effect on LM 𝐿𝐿𝐿𝐿𝑛𝑛𝑛𝑛′ 𝐴𝐴𝐼𝐼′ 𝑃𝑃1,𝑑𝑑𝑛𝑛𝑛𝑛 𝑃𝑃1,𝑑𝑑 π‘Œπ‘Œ1,𝑑𝑑𝑛𝑛𝑛𝑛 monetary policy will not work. This means that central banks cannot engage in the type of endogenous monetary policy actions discussed in Chapter 28 in response to exogenous shocks. Not being able to conduct policy in this way will therefore accentuate the costs associated with not being at the neoclassical equilibrium. The ZLB is mostly likely to bind after a sequence of negative IS shocks (which shift the
IS curve to the left, making it more likely that it intersects the effective LM curve in the flat portion). In response to negative IS shocks, a central bank would like to increase the money supply (and hence lower interest rates) to combat this. But if the interest rate is at the ZLB, it is not possible to lower interest rates further. The second reason that the ZLB is costly is that the economy’s self-correcting mechanism will not restore the short run equilibrium to the medium run neoclassical equilibrium when the ZLB binds. Suppose that an economy finds itself in a situation where the ZLB binds and Y0,t < Y f t – i.e. the output gap is negative. This outcome could happen after a sequence of negative IS shocks, which drive output down and cause the ZLB to bind. A situation with a binding ZLB and a negative output gap is depicted in Figure 29.8. 660 Figure 29.8: Medium Run Supply-Side Dynamics at the ZLB, Sticky Price Model Let us now reference back to our discussion in Chapter 27 about how the AS curve out to adjust starting from a situation with Yt < Y f t. In the sticky price model, this means that the equilibrium price level, P0,t, is lower than the predetermined component of the price level, Β―P0,t. Given the chance to adjust, the firm will lower the predetermined component of the price level to something like Β―P1,t. If the AD curve were its usual downward-sloping shape, 661 π‘Ÿπ‘Ÿ0,𝑑𝑑=π‘Ÿπ‘Ÿ1,𝑑𝑑=βˆ’πœ‹πœ‹0,𝑑𝑑+1𝑒𝑒 𝐴𝐴𝐴𝐴 𝐼𝐼𝐴𝐴 π‘Œπ‘Œ0,𝑑𝑑=π‘Œπ‘Œ1,𝑑𝑑 π‘Œπ‘Œ0,𝑑𝑑𝑓𝑓 𝐴𝐴𝐴𝐴 𝐴𝐴𝐴𝐴𝑓𝑓 𝑃𝑃�0,𝑑
𝑑 𝑃𝑃�1,𝑑𝑑 𝐴𝐴𝐴𝐴′ π‘Ÿπ‘Ÿπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ 𝐿𝐿𝐿𝐿 Original ZLB equilibrium Hypothetical flexible price AS π‘Œπ‘Œπ‘‘π‘‘ 𝑃𝑃𝑑𝑑 Sticky Price AS dynamics 0 subscript: original equilibrium 1 subscript: post-price adjustment equilibrium f superscript: hypothetical flexible price output 𝑃𝑃0,𝑑𝑑 𝑃𝑃1,𝑑𝑑 this would cause the output gap to disappear as the economy transitions from short run to medium run. But since the AD curve is vertical when the ZLB binds, the downward shift of the AS curve only results in falling prices and no change in output. In other words, the output gap does not disappear. Furthermore, because P1,t < Β―P1,t after the transition of the AS curve, there will be further pressure on the AS curve to shift downward in the future. This will just result in more price level declines but no change in output. Not only might the economy get stuck with a suboptimally low level of output at the ZLB, things may actual get worse depending on how expectations are formed. As shown in Figure 29.8, the natural dynamics of the price level when the output gap is negative are for prices to fall. In other words, it is natural for a negative output gap to exert deflationary pressures in the economy. If household and firm inflation expectations are exogenous, the economy may get stuck with a suboptimally low level of output, like that shown in Figure 29.8. But what would happen if both the household and the firm start to expect falling prices? Suppose that the economy finds itself in a situation like that depicted in Figure 29.8. The AS curve has shifted down, but because the AD curve is vertical, this results in no change in output. Now suppose that agents start to expect further future declines in the price level. That is, suppose that expected inflation decreases, from Ο€e 0,t+1. A decrease in expected in
flation effectively raises the lower bound on the real interest rate. This causes the flat portion of the effective LM curve to shift up. The resulting higher real interest rate results in a decline in desired expenditure, and results in the AD curve shifting to the left. This scenario is depicted in Figure 29.9. 2,t+1, where Ο€e 0,t+1 to Ο€e < Ο€e 2,t+1 662 Figure 29.9: Medium Run Supply-Side Dynamics at the ZLB, Deflationary Expectations, Sticky Price Model Hence, not only might the economy get stuck with a suboptimally low level of output, as in Figure 29.8, if agents start to expect falling prices, things could actually get worse, as depicted in Figure 29.9. Furthermore, the worsening of conditions depicted above can become self-reinforcing – output will fall further and further below potential, which will put more and more deflationary pressure on the economy. This might fuel further declines in expected inflation, resulting in even higher real interest rates and even lower output. We call such a scenario a β€œdeflationary spiral.” A negative output gap puts downward pressure on prices, but given that the nominal interest rate is fixed at zero, expected deflation pushes the real interest rate up, which only worsens the output gap. 663 π‘Ÿπ‘Ÿ0,𝑑𝑑=π‘Ÿπ‘Ÿ1,𝑑𝑑=βˆ’πœ‹πœ‹0,𝑑𝑑+1𝑒𝑒 𝐴𝐴𝐴𝐴 𝐼𝐼𝐴𝐴 π‘Œπ‘Œ0,𝑑𝑑=π‘Œπ‘Œ1,𝑑𝑑 π‘Œπ‘Œ0,𝑑𝑑𝑓𝑓 𝐴𝐴𝐴𝐴 𝐴𝐴𝐴𝐴𝑓𝑓 𝑃𝑃�0,𝑑𝑑 𝑃𝑃�1,𝑑�
οΏ½ 𝐴𝐴𝐴𝐴′ π‘Ÿπ‘Ÿπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ 𝐿𝐿𝐿𝐿 Original ZLB equilibrium Hypothetical flexible price AS π‘Œπ‘Œπ‘‘π‘‘ 𝑃𝑃𝑑𝑑 Sticky Price AS dynamics 𝑃𝑃0,𝑑𝑑 𝑃𝑃1,𝑑𝑑 𝐿𝐿𝐿𝐿′ π‘Ÿπ‘Ÿ2,𝑑𝑑=βˆ’πœ‹πœ‹2,𝑑𝑑+1𝑒𝑒 𝐴𝐴𝐴𝐴′ 𝑃𝑃2,𝑑𝑑 π‘Œπ‘Œ2,𝑑𝑑 0 subscript: original equilibrium 1 subscript: post-price adjustment equilibrium 2 subscript: post-inflation expectation adjustment equilibrium f superscript: hypothetical flexible price otpt 29.4 Fiscal Policy at the ZLB In Chapter 28, we mentioned how fiscal policy is an undesirable stabilization tool under normal circumstances. The reason for this is that changes in government spending (or taxes, to the extent to which Ricardian Equivalence does not hold) alter the hypothetical neoclassical real interest rate, rf t, and therefore impact the split of output between consumption, investment, and government spending. Put somewhat differently, away from the ZLB an increase in government spending may raise output (and hence move output closer to potential), but it results in consumption and investment falling (because of β€œcrowd-out” associated with a higher real interest rate). Fiscal policy may be substantially more desirable when the ZLB binds. The essential gist of why is that, because the real interest is fixed at the ZLB, there is no crowd out. This is shown graphically in Figure 29.10 when the ZLB ninds. An increase in Gt shifts the IS curve out to the right. With a fixed real interest rate, this results in the vertical AD curve shifting out to the right, and no change in the real interest rate. 664
Figure 29.10: Sticky Price Model: Fiscal Expansion with Binding ZLB Because there is no change in the real interest rate when the ZLB finds, investment will not fall after the increase in Gt. Assuming Ricardian Equivalence holds, Yt will increase by the increase in Gt. This, coupled with no change in rt, means that consumption will not fall either. Output will simply increase one-for-one with government spending. While this may not stimulate consumption and investment, it will stimulate labor input and the real wage. If the ZLB did not bind, in contrast, the rightward shift of the AD would be much smaller, the real interest rate would rise, and the resulting increase in Yt would be significantly smaller. If Ricaridan Equivalence does not hold for some reason, then output could increase by more than government spending, and consumption could rise. In a sense, the reason why fiscal expansion might be more desirable at the ZLB is just a corollary to the fact that IS shocks have bigger effects on output at the ZLB. 665 π‘Ÿπ‘Ÿπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ π‘Ÿπ‘Ÿ0,𝑑𝑑=π‘Ÿπ‘Ÿ1,𝑑𝑑=βˆ’πœ‹πœ‹π‘‘π‘‘+1𝑒𝑒 𝐿𝐿𝐿𝐿 π‘Œπ‘Œπ‘‘π‘‘ 𝑃𝑃𝑑𝑑 𝐴𝐴𝐴𝐴 𝐼𝐼𝐼𝐼′ 𝐴𝐴𝐼𝐼 𝐼𝐼𝐼𝐼 𝐴𝐴𝐴𝐴′ π‘Œπ‘Œ1,𝑑𝑑 π‘Œπ‘Œ0,𝑑𝑑 𝑃𝑃0,𝑑𝑑 𝐿𝐿𝐿𝐿𝑛𝑛𝑛𝑛 𝐴𝐴𝐴𝐴
𝑛𝑛𝑛𝑛 𝐴𝐴𝐴𝐴𝑛𝑛𝑛𝑛′ π‘Œπ‘Œ1,𝑑𝑑𝑛𝑛𝑛𝑛 Original Original, hypothetical no ZLB Post-shock Post-shock, hypothetical no ZLB 0 subscript: original equilibrium 1 subscript: post-shock equilibrium nb superscript: hypothetical no ZLB π‘Ÿπ‘Ÿ1,𝑑𝑑𝑛𝑛𝑛𝑛 𝑃𝑃1,𝑑𝑑𝑛𝑛𝑛𝑛 𝐿𝐿𝐿𝐿𝑛𝑛𝑛𝑛’ Post-shock, hypothetical no ZLB, indirect effect on LM 𝑃𝑃1,𝑑𝑑 29.5 How to Escape the ZLB The ZLB is costly. Once there, conventional monetary policy is unavailable. Furthermore, the economy will not tend to close an output gap through the usual supply-side adjustments. Furthermore, if expectations are sufficiently forward-looking, anticipation of these supply-side adjustments could trigger changes in expected inflation that only make things worse. That the ZLB is costly naturally leads to the following question. If an economy finds itself at the ZLB, how can policy be conducted so as to escape it? In a nutshell, there are two options. The first is to use fiscal policy to influence the position of the IS curve. This is similar to the exercise considered in Figure 29.10. If the fiscal expansion is sufficiently large, the IS curve may shift out to the right sufficiently much so that the ZLB no longer binds. This is depicted in Figure 29.11. Figure 29.11: Fiscal Expansion to Exit the ZLB The other option available for escaping the ZLB relies on the manipulation of expected inflation. In particular, the lower bound on the real interest rate is the negative of the rate of expected inflation. If policymakers can engineer an increase in expected inflation, this eases the
lower bound on the real interest rate, allows the real interest rate to decline and output to expand, and may result in the ZLB no longer binding. Figure 29.12 considers the case where the ZLB is initially binding with expected inflation of Ο€e 0,t+1. Then it considers an increase in expected inflation to Ο€e 0,t+1. This increase in expected inflation is sufficiently large > Ο€e 1,t+1 666 π‘Ÿπ‘Ÿ0,𝑑𝑑=βˆ’πœ‹πœ‹π‘‘π‘‘+1𝑒𝑒 π‘Ÿπ‘Ÿπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ 𝐿𝐿𝐿𝐿 𝐼𝐼𝐼𝐼 𝐼𝐼𝐼𝐼′ π‘Œπ‘Œ0,𝑑𝑑 π‘Œπ‘Œ1,𝑑𝑑 π‘Ÿπ‘Ÿ1,𝑑𝑑 Original equilibrium, binding ZLB Sufficiently large fiscal expansion such that ZLB no longer binds so that the IS curve now crosses the effective LM curve in the upward-sloping region – i.e. the ZLB no longer binds. Relative to the original equilibrium, the real interest rate falls and output rises. Figure 29.12: Engineering Higher Expected Inflation to Exit the ZLB Using policy to engineer higher expected inflation may sound simple in theory, but is likely not easy to do in practice. This is especially true given that the natural dynamics with a binding ZLB are for prices to fall over time, not rise. How might the central bank do this? Effectively, what the central bank would need to do is to communicate to the public that it plans to engage in highly expansionary future monetary policy (by future we mean after the ZLB no longer binds). In other words, the central bank needs to commit to creating sufficiently high future inflation. In order to be able to do this, the central bank needs to have a lot of credibility with the public – for this to work, the public must believe that
the central bank will do what it says it plans to do. Committing to higher future inflation is one way to think about the recent β€œForward Guidance” policy in which the Federal Reserve has been engaging – it has promised to keep interest rates low for a long time, in the hopes that this will stimulate current inflation expectations. We will return more to a discussion of this policy in Chapters 34 and 37. 667 π‘Ÿπ‘Ÿ0,𝑑𝑑=βˆ’πœ‹πœ‹0,𝑑𝑑+1𝑒𝑒 π‘Ÿπ‘Ÿπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ 𝐿𝐿𝐿𝐿 𝐼𝐼𝐼𝐼 𝐼𝐼𝐼𝐼′ π‘Œπ‘Œ0,𝑑𝑑 π‘Œπ‘Œ1,𝑑𝑑 π‘Ÿπ‘Ÿ1,𝑑𝑑 Original equilibrium, binding ZLB Sufficiently large increase in expected inflation such that ZLB no longer binds βˆ’πœ‹πœ‹1,𝑑𝑑+1𝑒𝑒 29.6 How to Avoid the ZLB The ZLB is costly and may be difficult to escape. As such, central banks would like to design policy so as to minimize the occurrence of hitting the ZLB in the first place. How might policy makers do this? As we discussed in Chapter 21, over long periods of time the primary determinant of the level of the nominal interest rate is the inflation rate. The inflation rate is in turn determined by the growth rate of the money supply relative to output. A central bank can lower the incidence of hitting the zero lower bound by raising the average level of the nominal interest rate. It can do this by raising its long run inflation target, which can be accomplished by increasing the average growth rate of money relative to output. In light of the analysis pursued in this chapter, the logic is quite simple. The lower bound on the real interest rate is rt = βˆ’Ο€e t+1. To the extent to which expected inflation coincides with realized
inflation over long periods of time, a higher level of average inflation will correspond to a higher level of expected inflation, which lowers the lower bound on the real interest rate. The smaller lower bound on the real interest rate naturally means that it is less likely that the IS curve will shift sufficiently far to the left to intersect the effective LM curve in the flat region. In short, the higher is the average inflation rate, the less likely it is to hit the zero lower bound. Another way to think about the effects of the inflation rate on the incidence of hitting the ZLB is to appeal to the discussion of the natural rate of interest from Chapter 28. An optimizing central bank would like to implement rt = rf is the real interest rate which would emerge in the absence of price rigidity. From the Fisher relationship, rt = it βˆ’ Ο€e t+1. Equating these two, we can think about optimal monetary policy as adjusting the money supply so as to set it = rf t+1. To the extent to which expected inflation is stable, the t central bank wants to adjust the nominal interest rate to move along with the natural rate of interest. The higher is Ο€e t+1, the more β€œwiggle room” the central bank has to lower it when rf t falls sufficiently. Hence, by raising its inflation target (and hence expected inflation), the central bank can make it less likely that it would want to lower it to less than zero. t, where rf + Ο€e t Based on the logic expounded upon in the paragraphs above, why wouldn’t central banks want to raise inflation targets to a point where the economy would never bump into the ZLB? The reason, as discussed in Chapter 22, is that high inflation rates (and hence high nominal interest rates) are costly. This can be seen from (29.1) above. In the medium run, real quantities are independent of nominal variables. Hence, the marginal utility of consumption, uC(Ct, 1 βˆ’ Nt), is not influenced by nominal variables. The larger is it, the larger is it. 1+it This means that vβ€² (
Mt must be Pt smaller. Hence, the larger is the nominal interest rate, the smaller will be real money balances ) must be larger for (29.1) to hold, which means that Mt Pt 668 in the medium run. Since the household receives utility from holding real balances, lower real balances translate into lower utility. As we discussed in Chapter 15, the Friedman rule characterizes optimal monetary policy in the neoclassical model, and entails setting it = 0, which maximizes utility from real money balances. Hence, when thinking about avoiding the ZLB in the short run, a central bank must balance its desire to have low inflation and low nominal interest rates in the medium run (i.e. its desire to be at or near the Friedman rule), with its desire to have the nominal interest rate sufficiently far from zero to avoid hitting the ZLB in the short run. There are other potential costs associated with higher nominal interest rates (and hence higher inflation rates) which are not captured in our model. These include so-called β€œshoeleather costs” referencing the fact that, in a high inflation environment, people will try to avoid holding money to the extent possible, which entails trips to and from the bank to get cash (hence wearing out the leather on one’s shoes). In addition, in a more sophisticated model with firm heterogeneity, higher rates of average inflation can introduce non-optimal distortions into the relative price of goods when some firms can adjust their prices and others cannot. Coibion, Gorodnichenko, and Wieland (2012) study the optimal inflation rate in a sticky price New Keynesian model similar to the one developed in this book. Their analysis balances the costs of higher inflation (and hence higher nominal interest rates) with the benefit of a reduced incidence of hitting the ZLB. They find that the optimal inflation rate is about 2 percent per year, which is close to what it has been in the US since the early 1980s. 29.7 Summary β€’ Since the nominal interest rate is the return on investing money, it cannot go much below 0. The reason is that instead of investing money in a bank for a negative return, one could put money in their mattress and receive no return. In actuality, there are transaction
costs to holding large amounts of money which opens the door to slightly negative nominal interest rates. Near zero nominal interest rates is described as the zero lower bound (ZLB). β€’ In the region where the ZLB is binding the LM curve is flat and the AD curve is vertical. An implication of this is that output is completely demand determined which is completely opposite of the Neoclassical model in which output is supply determined. β€’ At the ZLB, changes in the money supply do not affect the AD curve. However, the effects of any other demand shock exacerbates the output response at the ZLB relative to normal times whereas the effects of supply shocks are smaller. 669 β€’ The ZLB is bad from a policy perspective because it prevents monetary policy makers from lowering nominal interest rates and because it prevents the dynamics transitioning from the short to medium run. β€’ Increases in government spending are particularly effective at the ZLB becuase such spending does not raise the real interest rate so there is no crowding out. β€’ Policy makers can attempt to exit the ZLB by increasing government spending or by increasing inflation expectations. β€’ Economies can avoid hitting the ZLB in the first place by maintaining a sufficiently high inflation rate. The higher the inflation rate the farther the economy is away from the Friedman rule. Hence, there is a tension of wanting the interest rate high enough in the short run to avoid the ZLB and low enough in the medium term to come close to the Friedman rule. Questions for Review 1. Explain what is meant by a β€œdeflationary spiral” and why the normal mechanism which restores the efficient neoclassical equilibrium may not work at the ZLB. 2. Explain the tradeoffs at play when considering raising the long run inflation target as a means by which to avoid hitting the ZLB. 3. Intuitively, explain why changes in government spending have a bigger effect on output at the ZLB than away from it. 4. In the text, we have thought about the kind of shock which might make the ZLB bind as a negative shock to the IS curve (e.g. a reduction in ft). Could a shock to At make the ZLB bind? What sign would this shock have to be
to make it bind? In the data, most episodes where the ZLB binds (the US in the wake of the Great Recession, Japan during the 1990s, and the US during the Great Depression) output is low. Given this, would a supply shock as the reason for a binding ZLB make empirical sense? Exercises 1. Suppose that you have a sticky price New Keynesian model in which the ZLB is binding. Consider an exogenous reduction in At+1. Show how this affects the equilibrium values of the endogenous variables of the model, including 670 labor market variables. Comment on how these effects compare relative to the case in which the ZLB does not bind. 671 Chapter 30 Open Economy Version of the New Keynesian Model In this chapter we consider an open economy version of the New Keynesian model with which we have been working. For this chapter, we will focus on the partial sticky price New Keynesian model, which generalizes the simple sticky price model and the neoclassical model. As in the open economy version of the neoclassical model explored in Chapter 23, the openness of the economy affects only the demand side. In particular, there is a new term in desired expenditure, net exports. Net exports depend on the real exchange rate and a variable which we take to be exogenous to the model, Qt. The real exchange rate in turn depends on the real interest rate differential between the home and foreign economy. The equations characterizing the equilibrium of the open economy version of the sticky price model are similar to Chapter 23, with the exception that we replace the labor demand curve with the partial sticky price AS curve. Ct = C d(Yt βˆ’ Gt, Yt+1 βˆ’ Gt+1, rt) It = I d(rt, At+1, Kt) N Xt = N X d(rt βˆ’ rF t, Qt) Yt = Ct + It + Gt + N Xt Nt = N s(wt, ΞΈt) Pt = Β―Pt + Ξ³(Yt βˆ’ Y f t ) Yt = AtF (Kt, Nt) Mt = PtM d(rt + Ο€e t+1, Yt) rt = it βˆ’ Ο€e t+1 t = h(rt βˆ’ rF t ) et = t Pt P F t 672 (30.1
) (30.2) (30.3) (30.4) (30.5) (30.6) (30.7) (30.8) (30.9) (30.10) (30.11) t, where rF t (30.1) is the standard consumption function, and (30.2) is the conventional investment demand function. (30.3) is the net export demand function. Net exports depend negatively on the real interest rate differential, rt βˆ’ rF is the exogenous foreign real interest rate. (30.4) is the open economy resource constraint. (30.5) is the labor supply curve, where labor is increasing in the real wage and decreasing in the exogenous variable ΞΈt. The sticky price AS curve is reflected in (30.6). The aggregate production function is (30.7). Money demand is given by (30.8), with the money supply exogenously set by a central bank. The Fisher relationship is (30.9). The real exchange rate, t, is a function of the real interest rate differential. This is given in (30.10). The real exchange rate is a decreasing function of the real interest rate gap. If the domestic real interest rate is higher than the foreign real interest rate, then there will be excess demand for domestic goods, which will cause the domestic currency to appreciate (which means t declines). The relationship between the real and nominal exchange rates is given by (30.11), where et is the nominal exchange rate. These are exactly the same expressions as in the open economy version of the neoclassical model, except that we replace the labor demand curve with an exogenously fixed price level. Note that the supply side of the model is unaffected by the openness of the economy; hence Y f in t the open economy is the same as it would be in a closed economy. In the sections below, we will provide a graphical depiction of these equilibrium conditions. We will then use the graphical setup to analyze the effects of changes in exogenous variables on endogenous variables. We will discuss how monetary policy interacts with the exchange rate regime (floating or fixed) and what this means for domestic policy. On the basis of this, we will include a discussion about the costs and benefits of monetary
unions (such as the Euro), which can be thought of as many countries grouping together with a fixed exchange rate. 30.1 Deriving the AD Curve in the Open Economy The sticky price assumption affects only the supple side of the economy, which is identical in both the open and closed variants of the model. As with the closed economy variant of the model, we will again use the IS-LM-AD curves to summarize the demand side of the economy. As we discussed in Chapter 23, the open economy IS curve is flatter than the closed economy IS curve. Intuitively, this is simply because aggregate expenditure is more sensitive to the real interest rate when there is an additional expenditure component which depends negatively on the real interest rate (net exports). How does the flatter IS curve impact the shape of the AD curve? 673 We can graphically derive the AD curve in the usual way. For point of comparison, in Figure 30.1, we derive the AD curve both for a closed economy (red, relatively steep IS curve) and an open economy (black, comparatively flatter IS curve). An increase in the price level causes the LM curve to shift in. Along a downward-sloping IS curve, an inward shift of the LM curve results in a higher real interest rate and consequently a lower level of Yt. For a given inward (or outward) shift of the LM curve, the decline in Yt is larger the flatter is the IS curve. Tracing out the (Pt, Yt) combinations where the economy sits on both the IS and LM curves, one can see that the AD curve will be flatter in the open economy compared to the closed economy. Figure 30.1: The AD Curve: Open vs. Closed Economy The AD curve will shift in response to changes in exogenous variables which affect the positions of the IS or LM curves. This includes the usual set of variables from the closed economy version of the model – At+1, Gt, and Gt+1 affect the IS curve, and Mt affects the LM curve. In the open economy version of the model, rF t and Qt will also affect the position of the AD curve through an effect on desired expenditure through net exports. An increase in 674 𝐼𝐼𝐼�
��𝑐𝑐𝑐𝑐 πΌπΌπΌπΌπ‘œπ‘œπ‘œπ‘œ 𝐿𝐿𝐿𝐿(𝐿𝐿𝑑𝑑,𝑃𝑃0,𝑑𝑑) 𝐿𝐿𝐿𝐿(𝐿𝐿𝑑𝑑,𝑃𝑃1,𝑑𝑑) π‘Ÿπ‘Ÿπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ 𝑃𝑃𝑑𝑑 𝑃𝑃0,𝑑𝑑 𝑃𝑃1,𝑑𝑑 π΄π΄π΄π΄π‘œπ‘œπ‘œπ‘œ 𝐴𝐴𝐴𝐴𝑐𝑐𝑐𝑐 Open economy Closed economy lowers rt βˆ’ rF t rF for a given rt; this results in a currency depreciation and an increase in net t exports, which causes the IS curve to shift to the right. Hence, an increase in rF t will cause the AD curve to shift out to the right. An increase in Qt represents an exogenous increase in desired net exports. This will also result in outward shift of the IS curve and therefore a rightward shift of the AD curve. 30.2 Equilibrium in the Open Economy Model t The supply side of the open economy version of the sticky price New Keynesian model is identical to the supply side in the closed economy model. The AS curve is given by Pt = Β―Pt + Ξ³(Yt βˆ’ Y f ). Β―Pt is an exogenous variable and represents the predetermined component of the price level. The intersection of the AD and AS curves determines Yt. Given Yt, Nt is determined from the production function to be consistent with this level of output. The real wage is then determined from the labor supply curve at this level of labor input. Y f is t the level of output which would be consistent with being on both labor demand and supply curves. Figure 30.2 graph
ically characterizes the equilibrium of the sticky price open economy model. Qualitatively, this picture looks exactly the same as in the closed economy model. The effects of changes in exogenous variables will therefore by qualitatively similar to the closed economy version of the model, but some care needs to be taken, because the IS curve (and hence the AD curve) are flatter in the open economy version of the model. The labor demand curve is drawn in orange because this allows us to determine Y f t. We assume that the economy initially begins with Yt = Y f t, which means that Pt = P f t. 675 Figure 30.2: Equilibrium in the Open Economy Sticky Price Model 30.3 Comparing the Open and Closed Economy Variants of the Model In this section, we want to examine how the endogenous variables of the model change in response to shocks in the open economy model in comparison to the closed economy variant 676 𝐴𝐴𝐴𝐴 𝑁𝑁𝑠𝑠(𝑀𝑀𝑑𝑑,πœƒπœƒπ‘‘π‘‘) 𝑀𝑀𝑑𝑑 𝑃𝑃𝑑𝑑 π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ π‘Œπ‘Œπ‘‘π‘‘ 𝑁𝑁𝑑𝑑 𝑁𝑁𝑑𝑑 𝐼𝐼𝐴𝐴 π‘Ÿπ‘Ÿ0,𝑑𝑑 π‘Œπ‘Œ0,𝑑𝑑=π‘Œπ‘Œ0,𝑑𝑑𝑓𝑓 𝑁𝑁0,𝑑𝑑 𝐿𝐿𝐿𝐿(𝐿𝐿𝑑𝑑,𝑃𝑃0,𝑑𝑑) 𝐴𝐴𝑑𝑑𝐹𝐹(οΏ½