Is Price Level Targeting Really a Free Lunch: Essay Example

price-level targeting directly focuses on achieving price stability by targeting the general price level rather than an inflation rate (City, 2002). The central bank achieves this by announcing a constant or gradually increasing target for the price level. If there is a positive shock to the price level within a period, it must be countered by lowering it in the next period (Gender, 2006). However, implementing price-level targeting is believed to result in frequent inflation and output variability. Sweden stands out as the only country that has implemented this approach. Some argue against conventional wisdom and suggest that price-level targeting offers a better trade-off between output and inflation variability, particularly when considering a Lucas-type Phillips curve that accounts for output persistence. Despite different preferences in target selection, price-level targeting seems to persist. Nevertheless, due to its limited use, most research and evidence on this topic remains theoretical or simulation-based.The debate between price-level targeting and inflation targeting has gained intensity since the publication of Seventeen's paper. If price-level targeting proves to be more effective in achieving a balance between output and inflation variability during persistent output situations, it would mark a significant change in monetary policy. This challenge to conventional wisdom could have implications for international decision-making and long-term nominal contracts. Price-level targeting also reduces the long-term variability of prices, which is advantageous with credible central banks. The topic has been extensively covered in literature, with multiple authors testing and refining models of price-level targeting.Killed (1998) argues against the use of a Neoclassical Phillips Curve by Sevenths (1999). The question arises as to whether Sevenths would have found similar results in favor of price-level targeting if

a New Keynesian Phillips Curve was used instead (Dimmitt, Gavin, & Jutland, 1999). Dimmitt and Gavin (2000) prove this claim false and show that a New Keynesian Phillips Curve provides stronger evidence for price-level targeting compared to a Neoclassical Phillips Curve. They also find that price-level targeting yields a more favorable trade-off between output and inflation, even when the current level of output is not reliant on the previous period's output. Vesting (2000) finds that price-level targeting produces superior results compared to inflation targeting in a standard New Keynesian model with forward-looking expectations, especially in an environment characterized by discretion. Seventh (1999) obtains a similar result when the central bank acts with discretion using a Lucas-type Phillips Curve and requiring some persistence in the output gap. On the other hand, Manikins (2000) supports inflation targeting and argues it should remain the preferred regime for achieving price stability. Manikins questions the results of those advocating for price-level targeting as they rely on assumptions about the price-setting process and its forward or backward-looking nature.Additionally, the authors suggest that implementing price-level targeting could result in more frequent periods of deflation, leading to lower average interest rates and overall financial instability (Mclean and Prior, 2000). In their simulation study, they found that expectations played a crucial role in determining the impact of price-level targeting when using a Taylor rule-based reaction function. If agents have a high degree of backward-looking behavior, there is a trade-off between slightly decreased output and increased interest rate variability. However, if expectations are highly model-consistent, introducing a price level target may reduce both inflation and output variability without significantly affecting nominal interest rate variability.

The model

presented by Sevenths (1999) compares price-level and inflation targeting under moderate output persistence. Section one focuses on an inflation-targeting central bank with the introduction of the short-run Phillips Curve from Lucas (1973). This curve reflects incomplete information about the general price level (p.Yet= pity-l+ Exit-TTT-1+ Et.). Section two introduces a price-level targeting central bank while section three discusses a commitment mechanism for the central bank. Lastly, section four evaluates the scenario where society prefers inflation targeting but has a price-level targeting central bank.The equation (1) represents the relationship between the log of the output gap in period t (Yet), a constant (p), and the log of the gross inflation rate difference between periods t and t-1 (TTt= opt - opt-l). The equation also includes variables such as the log price level (opt), expected inflation rate in period t-1 for period t (TTT-1), and a temporary supply shock with mean zero and variance 02 (Et).

The private sector, which has rational expectations, can be represented by equation (2): TTT-1=Et-TTT. In this equation, Et-l represents expectations based on information available in period t-1, including all variables up to that point and constant parameters.

Equations (1) and (2) represent the constraints faced by the central bank. Seventeen's model of inflation targeting involves stabilizing not only inflation around a long-run target IT*, but also stabilizing the output gap around an output gap target y*. This concept is illustrated by an international loss function given by equation (3): 2+Ext-y*2. The relative weight on output-gap stabilization is represented by period loss function equation (4), assuming a nonnegative output-gap target y*.

In Sevenths' model, the central bank assumes perfect control over the inflation rate lit

and sets it after observing the current supply shock Et.The effectiveness of monetary policy in this model relies on the assumptions of the Phillips curve, which states that some prices or wages are predetermined by previous expectations. The central bank's decision problem can be expressed as Wit-1 =mint 12th-TO* 2+ŸV(Yet), where the minimization is done for given inflation expectations TTT-1, subject to the Phillips curve assumption. The central bank acknowledges that changes in the current output gap will influence future inflation expectations, but it doesn't consider the impact of its decisions on inflation expectations. The decision rule and the output gap can be written as Yet=pity-1+ (1 -ABA)?¬t, where the output gap has a negative coefficient. Alternatively, it can be expressed as a function of the lagged output gap and the current supply shock. According to Sevenths (1999), under discretion, the output gap follows an AR (1) process and an average inflation bias occurs. If the output-gap is positive, then there will be a positive average inflation bias.However, if the target for the output-gap is zero, y*=y=O ,then there is no average inflation bias.Additionally,Sprinkles(1999) finds thatthe unconditional variance oftheoutput-gapisproportional totheunconditionalvarianceofinflation(row5),andthatthevarianceofthepricelevelisinfinite( row7)duetothe factthattheprice-levelisan'(1)process(row6).Section Two of the text discusses price-level targeting, where Sevenths (1999) presents a revised form of his Phillips Curve. The equation is given as opt-opt-1=TTt-TTT-1, with opt-l representing expectations in period t-1 of the log price level in period t. It is assumed that the private sector has rational expectations and that the central bank has a loss function called opt-1=Et-opt.

The assumption of rational expectations also implies that the central bank has complete control over inflation and the price level. The central bank observes

the supply shock Et and then determines the price level for each period. Under discretion, this decision problem is represented by Wit-1=Et-1 input opt-. Equation (13) takes into account both given price-level expectations opt-l and changes in the current output-gap affecting future price-level expectations opt+let. This minimization process follows equation (1).

For price-level targeting, the decision problem remains unchanged from inflation targeting, except for a change in variables from Tit to opt. Consequently, there is no change in the indirect loss function or in regards to the average bias towards the price level instead of inflation.The text demonstrates that the price-level will have a stationary state with a finite unconditional variance. Inflation is represented by Tit = opt-opt-l - ABA(Yet-Yet-l) and is a linear function of the output gap when using inflation targeting. However, under price-level targeting, inflation becomes a linear function of the first-difference of the output gap. Consequently, the level of unconditional variance for inflation in both targeting approaches relies on the level and first-difference of the output-gap's unconditional variances.

Researchers have discovered that if there is enough persistence in the output-gap, then its first-difference has lower variability compared to its level. The author illustrates this relationship between unconditional variances for both output-gap and inflation in equations (16) and (17). When p>12, it is evident that the unconditional variance of the first-difference of the output-gap is lower than that of the output-gap itself. This implies that when there is moderate persistence, employing price-level targeting leads to lower unconditional variance in inflation.

In Section Three, assuming a commitment mechanism for central bank adherence to optimal rules, equations (18) and (19) define this rule under inflation targeting. With

commitment, inflation no longer depends on lagged output-gaps but solely on new information. As a result, there is no bias towards inflation under commitment.The private sector's reliance on previous information only affects expected inflation and does not impact the output-gap or the loss function. Both inflation and price-level targeting have the same optimal rule under commitment, with some variable substitutions. Equation (20) can be used to calculate the price level, while equation (19) is used for determining the output-gap. These results are presented in a table.

When comparing price-level targeting to inflation targeting, it is observed that inflation is higher and more variable under price-level targeting. This increased variability occurs because there is no resistance to inflation and the price-level when the central bank acts under commitment. However, if society prefers price-level targeting, then it is better for the central bank to use this approach.

The question arises regarding what happens if society prefers inflation targeting instead. According to Sevenths (1999), if moderate output-gap persistence exists, it would be beneficial for the central bank to use price-level targeting again as it causes less inflation variability while resulting in similar output-gap behavior. Additionally, when there is a positive output-gap, using price-level targeting eliminates any average inflation bias.

For an inflation-targeting central bank under discretion, the optimal decision rule can be expressed as TTt=a-be-x byte (22 where b>b*.The decision rule for a central bank implementing price-level targeting under discretion suggests that the first-difference of the output-gap (Yet-Yet-l) is a better approximation of the unanticipated change in the output-gap (Yet-pity-l) than the output-gap itself (Yet), when there is enough persistence in the output-gap. Additionally, if the output-gap is positive, price-level targeting

also eliminates average inflation bias. This evidence supports the argument that price-level targeting is a preferable regime for a central bank, even if society prefers inflation targeting.

Evaluating Seventeen's theoretical model, it must be taken with caution since price-level targeting has only been used once in history. Therefore, it would be unwise to solely rely on Seventeen's research to conclude that price-level targeting should be the preferred regime for central banks. Furthermore, Seventeen's findings heavily depend on certain assumptions, particularly moderate output persistence being crucial for the success of price-level targeting over inflation targeting.

However, it raises questions about whether moderate output persistence assumption holds true and if many countries actually experience it. Sevenths argues that persistence in output movements is indeed more realistic.The author supports his claim about output persistence by providing two examples: sticky prices in the P-Dare model and imperfections in the labor market. However, I believe that these two instances alone are not enough to support his claim, and he should provide more explanation as to why persistence in output is more realistic.
Additionally, it may not be necessary to make the assumption presented by Seventeen. Research conducted by Cover and Peignoir (2005), using the same model as Seventeen but assuming that the output-gap is not persistent and that the central bank's policy choice must be made before knowing the current value of the supply shock, has yielded similar results (Watcher, 2011). Criticism has been raised against using a Neoclassical Phillips Curve due to its inability to derive the social loss function as an approximation to expected utility loss for representative households (Watcher, 2011).
Therefore, welfare analyses based on the Neoclassical Phillips curve lack micro-foundations

according to Watcher (2011). The curve has also faced criticism for suggesting that only unanticipated inflation affects output, contradicting evidence from structure VARY literature (Watcher, 2011). Instead of utilizing this curve, Sevenths could have used the New Keynesian Phillips curve which has demonstrated better outcomes and allows for micro-founded welfare analysis (Watcher, 2011).The New Keynesian Phillips curve was used by Vesting (2000) to compare price-level and inflation targeting. The study found similar results to Sevenths regarding the robustness of Seventeen's free lunch outcome when altering the Phillips Curve (Watcher, 2001). This supports the validity of price-level targeting under different specifications. In Seventeen's model, backward-looking expectations were utilized, but it is questioned whether forward-looking expectations should have been used instead. Many econometric model simulations that relied on backward-looking expectations showed that price-level targeting increases short-run variability in both inflation and output growth (Dimmitt & Gavin, 2000). On the other hand, models with forward-looking expectations are more effective in reducing inflation and output variability, while fixed adaptive expectations result in forward-looking expectations being the least effective (Dimmitt & Gavin, 2000). Therefore, careful consideration must be given to expectation assumptions in the model as they greatly impact results. Including section four comparing price-level and inflation targeting reflects current preferences and was a wise decision made by Sevenths. Thus, finding that price-level targeting outperforms inflation targeting is highly important. However, understanding Seventeen's model results is challenging due to equations presented without much explanation.Readers must spend a significant amount of time deciphering the implications of the text and forming their own opinions. Some argue that Tanat tons is good tong, but in my view, Sevenths should have spent more time

explaining the equations used and providing a clearer interpretation of the equations in the results tables. Sevenths did not anticipate that periods of deflation resulting from price-level targeting could lead to negative interest rates, which is a concern according to economic experts as it may render monetary policy ineffective. Thus, if price-level targeting leads to negative interest rates, it would be considered a worse regime compared to inflation targeting, contradicting Seventeen's findings. The lack of real-world data is the main obstacle in implementing price-level targeting since existing studies heavily rely on assumptions and lack evidence from econometric simulations. As a result, the conventional wisdom surrounding price-level targeting remains unchanged and no central bank has been willing to take the risk. Currently, most research on this topic follows a New Keynesian approach, suggesting that Sevenths' Neoclassical approach is outdated or inferior. Despite being published over ten years ago, no central bank has been willing to implement price-level targeting.The implication is that despite the research conducted by Seventeen and others, there is insufficient compelling evidence to change the preference towards price-level targeting. However, if price-level targeting were proven effective, its advantages would surpass those obtained solely through improved output/inflation trade-offs.