Price Rigidity & Endogenous Growth

The core of the model is a Schumpeterian growth framework incorporating quality-improving innovations and nominal price rigidity. This setting allows for an examination of the long-run interaction between inflation, employment, and output growth, a relationship largely unexplored in traditional models that often assume the long-run neutrality of money. The model posits a unique steady-state equilibrium where both employment and output growth are not linearly related to money growth, but instead exhibit a hump-shaped function. This means that increases in money growth initially lead to higher levels of employment and output growth, but beyond a certain point, further increases in money growth lead to declines. This non-linear relationship is crucial, departing from the often assumed vertical long-run Phillips curve.

The hump-shaped relationship between money growth and economic outcomes stems from four distinct effects operating under the assumption of price rigidity. First, inflation erodes the relative price of money, impacting firm profits. Second, firms set an initial optimal markup anticipating future inflation. Third, dispersion in relative prices, a direct consequence of price rigidity, introduces inefficiencies into production. Finally, changes in the average markup across the economy significantly affect aggregate demand. The interaction of these four effects is what creates the non-linear response of employment and growth to changes in money growth and subsequently, inflation. The model highlights the crucial role of price stickiness in determining the dynamic interplay between monetary variables and real economic activity.

The model's findings challenge the long-held assumption of a vertical long-run Phillips curve and the long-standing view that money is neutral in the long run. For decades, the prevailing belief, supported by seminal works like those of Friedman (1968) and Phelps (1967), focused on a vertical long-run Phillips curve. While the New Neoclassical Synthesis of the 1990s renewed interest in the relationship between money and the real economy, analysis largely focused on short-run effects around a zero-inflation steady state. The long-run implications of positive steady-state inflation were largely overlooked. Only recently has this model begun to address these long-run implications in the context of a Dynamic General Equilibrium (DGE) framework, leading to the significant insights discussed within this model.

The model emphasizes the significant impact of price rigidity on long-run growth and employment. Inflation, in the presence of price rigidity, distorts relative prices, directly affecting resource allocation and the efficiency with which resources are used. These distortions impact the real wage, which in turn determines labor supply and employment. Because long-run growth is essentially a series of repeated short-run growth cycles driven by the incentive to innovate within the R&D sector, the distortions introduced by price rigidity affect long-run growth rates both directly and indirectly via their influence on employment. This creates a complex, non-trivial relationship between the money growth rate, employment, and output growth. Importantly, the model suggests that even in the long run, monetary policy possesses a degree of power to influence economic outcomes, which is unexpected given traditional perspectives on monetary neutrality.

The paper begins by noting the historical underemphasis on long-run relationships between monetary variables (money growth, inflation) and real economic outcomes (employment, output growth). For many years, the dominant view, solidified by the work of Friedman (1968) and Phelps (1967), held that the long-run Phillips curve was vertical, implying no long-run trade-off between inflation and unemployment. The rise of the New Neoclassical Synthesis in the 1990s brought renewed focus on the connection between money and the real economy, yet this interest primarily centered on short-run effects. These analyses typically linearized the economy around a zero-inflation steady state, simplifying the model by assuming inflation's long-run irrelevance. The consequences of positive, steady-state inflation in a Dynamic General Equilibrium (DGE) framework were thus largely ignored until recently.

The review then turns to recent empirical studies investigating the superneutrality of money – the idea that money has no long-run effects on real variables. Research exploring this question concerning employment, output levels, and growth rates has yielded mixed results. Some studies failed to reject the hypothesis of a vertical long-run Phillips curve, suggesting the absence of a long-run trade-off between inflation and unemployment. However, other studies found evidence hinting at a favorable long-run trade-off. This inconsistency in empirical findings underscores the complexity of the relationship and highlights the need for a more nuanced theoretical model capable of explaining these diverse results. The methodological difficulties in disentangling long-term relationships from short-term fluctuations are also acknowledged.

The literature review further examines the empirical relationship between inflation and economic growth, noting a developing consensus that high inflation rates are detrimental to growth. Several studies, primarily using panel regression models, support this negative relationship. The robustness of this relationship appears stronger when using data averaged over longer periods (10-15 years), suggesting it reflects medium-to-long-term effects. Conversely, some evidence suggests a positive, though weak, relationship between inflation and unemployment in certain contexts and time periods. The studies cited include works by Barro (1996), Judson and Orphanides (1999), Gylfason and Herbertsson (2001), Gillman, Harris, and Mátyás (2004), as well as others that highlight methodological challenges and the potential for non-linear effects. Specific examples of quantitative effects from various studies are also cited, such as Setterfield and Leblond (2003) and Beyer and Farmer (2002) and Russell and Banerjee (2006).

The paper introduces price rigidity not as a temporary shock but as a persistent characteristic of the economy. While individual prices may be fixed only for short periods, the overall rigidity remains a constant factor. Under non-zero inflation, this persistent price rigidity consistently distorts relative prices in the short run. Since relative prices are key determinants of resource allocation, price rigidity permanently affects the economy's resource allocation efficiency. The paper argues that long-run growth, seen as repeated short-run growth, is also influenced by these short-run rigidities because agents' optimal choices between consumption and investment are affected by both relative prices and short-run economic conditions. Therefore, short-run price rigidity is not merely a short-term phenomenon but directly influences long-run economic growth and the levels of other macroeconomic variables.

The model's innovation lies in its integration of price rigidity, typically a focus of short-run business cycle models, into an analysis of long-run economic performance. This approach is justified by the argument that while individual prices are adjusted infrequently, price rigidity is a permanent feature. The continuous distortion of relative prices under inflation significantly impacts resource allocation and the efficiency of resource use. Long-run growth, which is essentially a repetition of short-run growth, is inherently influenced by these short-run relative price distortions and levels of other key variables, resulting in a direct link between short-term frictions and long-term economic outcomes. This integration fills a gap in the existing literature by investigating the sustained impact of short-term frictions on long-run relationships within a growth model framework.

The model incorporates several key features to analyze the interaction between monetary policy and long-run economic outcomes. It utilizes a Dynamic General Equilibrium (DGE) framework with differentiated labor as a production input and staggered wage setting (à la Taylor, 1980). Households derive utility from both consumption and real money balances (following Sidrauski, 1967), introducing a role for money in the model. Crucially, nominal price rigidity is introduced using Calvo (1983) pricing in the intermediate goods market. This price rigidity is a key element influencing the relationship between inflation and the real economy. The model explores how changes in relative prices due to inflation, under the condition of price rigidity, impact the demand for intermediate goods, their productivity, labor productivity, and ultimately, the profits of innovators, shaping economic growth.

A central mechanism in the model is the average markup charged by intermediate goods producers. This average markup is influenced by money growth through two channels. First, increased money growth and inflation raise marginal costs while prices remain fixed due to rigidity, lowering effective markups. Second, anticipating this erosion, firms initially set higher markups, tending to increase the average markup. This dynamic interaction creates a complex relationship. The model's results show how the average markup influences the total amount of intermediate goods used in final good production, which in turn determines aggregate demand and interacts with the production efficiency. This mechanism is crucial for understanding the impact of monetary policy on long-run employment and growth.

The model's main result is the demonstration of a hump-shaped relationship between money growth and both employment and output growth. This means that increasing money growth initially boosts employment and growth but, after a certain point, further increases lead to declines. This non-linearity is a direct consequence of the interplay of the mechanisms described above. The optimal money growth rate, from the perspective of a monetary authority aiming to maximize growth, is associated with a positive (moderate) inflation rate, suggesting that a policy of price stability might not be ideal for long-run economic performance. This counter-intuitive result stems from the interaction of the various effects of money growth under price rigidity, leading to an optimal point where the positive effects dominate the negative ones.

The model's implications for monetary policy are significant. It suggests that the influence of short-term price rigidities extends far beyond the short run, affecting long-run levels of employment and output as well as output growth. Inflation's impact on these long-run outcomes is shown to be consistent with a non-linear long-run Phillips curve. The findings challenge traditional views of monetary neutrality and suggest a non-trivial role for monetary policy in shaping long-run economic performance, even under price rigidity. The results demonstrate that moderate inflation can improve employment and economic growth by lowering the average markup, overcoming inefficiencies due to monopolistic competition. Therefore, a carefully calibrated monetary policy focusing on moderate inflation rather than strict price stability could be beneficial.

The model's findings have significant implications for monetary policy. The research demonstrates that monetary authorities can influence long-run employment and output growth, even in the presence of price rigidities. Contrary to traditional views advocating for price stability, the model suggests that a policy of moderate inflation might be more effective at maximizing both employment and growth. This stems from the model's mechanism where moderate inflation, in the context of price rigidity, helps lower average markups, thus stimulating aggregate demand and increasing economic activity. The model offers a counter-intuitive result: price rigidity, despite its distortions, provides the monetary authority with a tool to manipulate the average markup and stimulate long-run growth beyond what is possible in a frictionless economy. This is because a moderate level of inflation can counteract some of the negative impacts of price rigidity on resource allocation and productivity.

A key takeaway is the close relationship between short-run and long-run economic development, particularly regarding the effects of inflation on growth and employment. Short-run frictions, such as price rigidity, have significant long-run consequences. The model reveals that the effects of inflation are not merely short-term phenomena but deeply impact long-run economic outcomes. This interaction challenges traditional economic models that frequently treat short-run and long-run dynamics separately. The model's findings strongly support further exploration of this interplay through both empirical investigation and advanced theoretical modeling. The interconnectedness between short-term frictions and long-term economic behavior should be recognized when designing and implementing economic policy.

The model's mechanisms, which highlight a non-linear relationship between monetary variables and real economic outcomes, are particularly relevant in the context of a non-vertical long-run Phillips curve. The conclusion emphasizes the need for further investigation, both empirical and theoretical, to fully understand the dynamic interactions between short-run frictions and long-run behavior. The model provides a framework for future research to test its predictions and explore the implications of its findings in a variety of economic settings and policy contexts. The inherent interconnectedness of short-run frictions and long-run behavior underscores the importance of considering these factors when constructing and evaluating economic policies that aim to increase employment and economic growth.