Wicksellian Model of Inflation

The paper begins by criticizing the traditional Quantity Theory of Money, arguing that it provides an inadequate explanation for inflation. A prevailing consensus among economic practitioners has shifted away from this theory, favoring short-term interest rates as the primary instrument for monetary policy and inflation control. The relationship captured by the LM curve, representing the equality of money demand and supply, is deemed largely irrelevant in contemporary macroeconomic thinking. This critique highlights the limitations of using money supply as the sole determinant of the price level, especially in modern economies where central banks actively manage interest rates and money supply is not strictly exogenous.

The paper proposes a Wicksellian model as a more suitable framework for understanding inflation. This approach emphasizes the role of central bank policy on nominal interest rates in determining price levels. The Wicksellian model departs significantly from the Quantity Theory by asserting that the price level is shaped by the interaction of the nominal rate of return on capital and a rule governing the interest rate at which the central bank supplies money. The equality of money supply and demand is deemed irrelevant in this context. The model is motivated by the observation that modern central banks readily lend whatever amount of money is demanded at a specific interest rate, thereby rendering the traditional equilibrium between money supply and demand obsolete. This fundamental shift in perspective highlights the central bank's active role in shaping the price level through its interest rate policies, a key departure from the Quantity Theory's focus on the money supply itself.

The Wicksellian model, while differing significantly from the Quantity Theory, retains several assumptions from classical approaches, such as full employment and the separation of the real and monetary sectors. However, unlike the Quantity Theory, which centers on money supply as an exogenous factor determining price levels, the Wicksellian model positions central bank lending policies, specifically the interest rate, as the core determinant. The central bank's willingness to lend at a given interest rate, rather than fixing the money supply, is a critical distinction. A central element in the Wicksellian model is the 'interest rate reaction function' (IRRF), which indicates how the central bank's lending rate adjusts based on the relationship between the actual and reference price levels. This function directly ties the central bank's actions to the price level, thus moving away from the Quantity Theory's emphasis on money supply as the primary driver of price changes.

The Wicksellian model, while offering a stark contrast to the Quantity Theory of Money, retains several core assumptions from classical economic thought. Crucially, it maintains the assumption of full employment and accepts a clear separation of the economy into real and monetary sectors. This signifies a focus on the interaction of real and nominal variables within the model. However, the model diverges sharply in its treatment of the money supply. Unlike the Quantity Theory, which views the money supply as exogenous and directly influencing price levels, the Wicksellian model considers the central bank’s willingness to lend as the crucial factor. The money supply is considered endogenous and adjusts to the demand, thus playing no direct causal role in price level determination. This represents a significant shift in perspective on the mechanisms of inflation.

A central component of the Wicksellian model is the Interest Rate Reaction Function (IRRF). This function describes how the central bank sets its lending rate based on the relationship between the actual price level (P) and a 'reference price level' (PR). The IRRF posits that as the actual price level deviates from the reference price level, the central bank adjusts its lending rate accordingly. A higher excess of P over PR results in a higher interest rate imposed by the central bank. This relationship is assumed to be continuous and positively monotonic, meaning a higher P always leads to a higher interest rate (although a logarithmic relationship is used for convenience). The IRRF parameter φ signifies the sensitivity of monetary policy. A smaller φ value indicates a less responsive interest rate adjustment to price level deviations. The IRRF replaces the concept of a fixed money supply in determining price levels, placing emphasis on central bank actions.

The Wicksellian model incorporates the Fisher equation, which links the nominal interest rate (i), the real rate of return (ρ), and inflation (π). While both the Quantity Theory and the Wicksellian models utilize this equation, they differ in interpreting the direction of causality. The Quantity Theory posits that inflation causes changes in the interest rate, while the Wicksellian model suggests that the causality can also run the other way. In the Wicksellian model, the interest rate is endogenous, determined by the central bank’s policy and the relationship between the actual and reference price levels. This is contrasted with the credit market's price determination, focusing on both the supply price of credit (the minimum interest rate lenders will accept) and the demand price of credit (maximum rate borrowers will accept), the latter driven by equimarginal conditions for capital and bonds. The Wicksellian theory, therefore, fundamentally recasts the roles of interest rates and price levels, compared to the Quantity Theory. The model replaces the money supply’s direct impact with the central bank's willingness to lend, as expressed through the IRRF, fundamentally reshaping the understanding of inflation mechanisms.

The Wicksellian model's equilibrium is defined by a simultaneous interaction between the interest rate and the price level. Unlike the Quantity Theory where causality flows primarily from inflation to the interest rate, the Wicksellian model allows for a bidirectional causal relationship. A higher interest rate (i) can lead to a lower price level (P), and conversely, a higher real rate of return on capital (ρ) can lead to a higher P. This simultaneous causation arises because the interest rate is endogenous in this model, a function of the price level itself, as defined by the Interest Rate Reaction Function (IRRF). The equilibrium is a point where the nominal interest rate equals the nominal rate of return on capital; any deviations from this equality trigger adjustments in both interest rates and prices that eventually restore equilibrium. This dynamic interaction highlights the intricate interplay between central bank policy and market forces in price level determination.

The paper explores comparative statics to analyze the effects of changes in key variables on the equilibrium price level. An increase in the reference price level (PR) leads to an increase in the actual price level (P), but the increase is not proportional; P is inelastic to PR. This suggests that central bank actions, as reflected in PR, exert a significant but not perfectly proportionate impact on the overall price level. Similarly, changes in the real rate of return (ρ) and the benchmark interest rate (i) affect the price level, highlighting the interdependencies between real and nominal variables. Importantly, the model demonstrates that shocks to money demand or the money supply itself have no direct effect on the price level (P). The central bank’s willingness to adjust its lending to meet demand nullifies the influence of the money supply as a primary determinant of prices, solidifying the model's departure from traditional monetary theory.

The concept of a reference price level (PR) is crucial to the Wicksellian model. This represents the price level the central bank aims for, which influences the benchmark interest rate (i). The IRRF illustrates the central bank’s response to deviations of the actual price level (P) from this reference. The model demonstrates how changes in PR directly affect the actual price level. For example, an increase in PR initially lowers the interest rate (as P is temporarily fixed), leading to increased borrowing and a subsequent rise in prices. This rise, in turn, triggers a central bank response to raise the interest rate via the IRRF, ultimately restoring equilibrium between interest rates and the rate of return on capital. The magnitude of the central bank's reaction (parameter φ) determines the speed of adjustment and the relative importance of present versus future shocks in price level determination. This mechanism shows how central bank policy, through the IRRF, critically shapes the price level, highlighting the interplay of monetary policy and market dynamics in reaching equilibrium.

The paper examines the conditions for price stability within the Wicksellian framework. Wicksell's original contention that price stability requires the nominal interest rate to equal the rate of profit is revisited. However, because the interest rate is endogenous (determined within the model) rather than exogenous (set by policy), Wicksell's prescription cannot be directly applied. This emphasizes a key difference from traditional monetary policy prescriptions, where the interest rate serves as an exogenous policy instrument. In the Wicksellian model, the central bank's actions still play a crucial role in achieving price stability, but it does not involve setting the interest rate to a specific target that is independent of price levels.

Achieving price stability in the Wicksellian model relies on the central bank's consistent response to any deviation of the price level from the target, as reflected in the Interest Rate Reaction Function (IRRF). It does not rely on a specific level of the interest rate, or any particular reaction coefficient (φ). The model suggests that price stability is ensured not by the size of the interest rate adjustments but by the central bank's sustained willingness to adjust the interest rate whenever inflation is present. This consistent responsiveness, rather than any specific magnitude of adjustment, is essential for price stability. Even small and gradual interest rate increases in response to persistent inflation can effectively maintain price stability. This highlights a more nuanced approach to monetary policy, emphasizing the continuous responsiveness of the central bank, rather than aiming for a specific interest rate or level of inflation.

The impact of permanent versus temporary changes on both the interest rate (i) and the price level (P) is explored. The model suggests that permanent changes in the real rate of return (ρ) or the reference price level (PR) affect the level of both i and P, but they have no lasting impact on the inflation rate itself. The sensitivity of the price level to shocks is described in terms of the IRRF parameter (φ). The model reveals that as φ approaches zero (a flat IRRF, or interest rate peg), future shocks become equally significant to current shocks. Conversely, larger φ values mean that price determination becomes heavily biased towards present shocks, with future impacts becoming less relevant. This analysis emphasizes the central bank’s ability to influence price stability through its continuous adjustments to the interest rate via the IRRF, and the complexities of monetary policy responses over time, especially with regards to maintaining price stability through interest rate targeting.

The paper assesses the Wicksellian model's ability to explain historical inflation and deflation, contrasting it with the Quantity Theory. The evaluation focuses on distinguishing between trend and cyclical components of inflation. The model emphasizes profit rates and benchmark interest rates as primary drivers of cyclical inflation, contrasting with other short-run factors often cited, such as scarce inventories, commodity price booms, exchange rate fluctuations, oil shortages, bottlenecks, and labor market pressures. However, the relevance of several of these factors to inflation is arguably consistent with the Wicksellian focus on the profit rate, as these factors all can impact the rate of return on capital. The difficulty of directly observing the 'reference price level' (PR), a key parameter of the model, is acknowledged. The paper proposes using 'soft data,' such as central bank inflation predictions or announced inflation targets, as potential proxies for PR.

The paper applies the Wicksellian model to the Great Inflation of the 1970s. A key hypothesis is that the reference price level (PR) increased more rapidly during this period compared to previous decades. This suggests that higher actual price levels could arise without prompting the central bank to increase interest rates as significantly. The end of the Great Inflation is explained by a subsequent decline in the rate of increase in PR. In this context, the unexpectedly high interest rates implemented under Paul Volcker's chairmanship of the Federal Reserve are interpreted as a signal of this shift towards a lower tolerance for price increases. This illustrates a situation where central bank behaviour, captured by the model's parameters, has a significant influence on inflation trends.

The paper outlines methods to investigate the Wicksellian hypothesis concerning the Great Inflation. One approach involves examining whether central bank behavior, specifically its interest rate response to price level changes, underwent a structural shift during the 1970s. This could be analyzed by estimating an interest rate reaction function for earlier periods and then examining its predictive accuracy for the 1970s. A significant overprediction of interest rates during the 1970s would suggest a 'loosening' of interest rate policy – a higher tolerance for price increases – supporting the Wicksellian explanation. Alternatively, researchers could construct a 'trend-adjusted price level' to proxy for the reference price level (PR) and then investigate the interest rate reaction function using this proxy. This approach would help determine if the rate of increase of PR varied during the 1970s, providing further support for the model's explanation of the Great Inflation. This methodological discussion illustrates how the model can be tested and validated using empirical data.