
Inflation, Human Capital & Tobin's q
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Summary
I.The Negative Correlation Between Inflation and Tobin s q in the US Economy
This research paper investigates the empirically observed negative correlation between inflation and the normalized market price of capital (Tobin's q) in the US economy. A dynamic stochastic general equilibrium (DSGE) model of endogenous growth is developed to explain this relationship. The model highlights the role of human capital as a primary driver of growth, suggesting that inflation acts as a tax on human capital, diverting resources away from productive activities towards leisure. This leads to lower human capital utilization, negatively impacting growth and subsequently reducing Tobin's q.
1. Empirical Evidence and Research Objective
The paper begins by establishing a well-documented negative correlation between inflation and Tobin's q in the US economy. This inverse relationship also extends to inflation and economic growth. The core research objective is to develop a theoretical model that can adequately explain this empirically observed phenomenon. The abstract highlights the intention to utilize a dynamic stochastic general equilibrium (DSGE) model of endogenous growth, emphasizing human capital's role as the primary driver of sustained economic expansion. A key aspect of the model is to explore how inflation diverts scarce time resources toward leisure activities, reducing human capital utilization, negatively affecting growth, and ultimately decreasing Tobin's q. The short-run dynamics are also considered, acknowledging the potential for a Tobin effect of inflation on growth to moderate the negative association between inflation and Tobin's q. This introduction lays the groundwork for the model's development and the subsequent analysis of long-run and short-run relationships.
2. Data Sources and Existing Literature
The analysis relies heavily on data concerning Tobin's q and inflation. Figure 1, sourced from Smithers & Co., illustrates the negative correlation, particularly pronounced after 1965Q1 (correlation coefficient of -0.55 from 1960:1 to 2008:2). The paper notes the use of alternative Tobin's q series from Hall (2001) (up to 1999) to validate the findings. The authors reference prior research, acknowledging the established negative association between stock prices and inflation in general equilibrium models, citing Danthine and Donaldson (1986) as an example. However, the paper argues that a complete explanation within a calibrated DSGE monetary economy is still lacking, setting the stage for their contribution. The authors contrast their monetary approach with the findings of McGrattan and Prescott (2005), who attribute the rise in the stock price to GDP ratio (until 2000) to lower taxes on capital. The study aims to provide a monetary counterpart to this earlier work. This section emphasizes the data foundation and situates the current research within the context of existing literature.
3. Model Overview and Theoretical Framework
The paper introduces an endogenous growth model to explain the observed relationship between inflation, Tobin's q, and economic growth. The model builds upon earlier work exploring the impact of inflation taxes on endogenous growth (Gomme, 1993; Gillman and Kejak, 2005). Inflation, within a cash-only economy, prompts agents to shift from consumption toward leisure, thus reducing the returns on human capital and overall growth. The model incorporates adjustment costs for physical capital (Lucas and Prescott, 1971; Basu, 1987; Hercowitz and Sampson, 1991), and importantly, includes implicit human capital adjustment costs (Becker, 1975; Lucas, 1988), reflecting the opportunity cost of diverting productive time to human capital development. The combination of these adjustment costs allows the negative impact of inflation taxes on growth (through reduced human capital utilization) to directly translate into lower Tobin's q. The theoretical foundation is supported by the existing empirical evidence for endogenous growth models (Kocherlakota and Yi, 1996). This section provides a detailed explanation of the model's structure and its key components.
II.The Model Inflation Human Capital and Tobin s q
The paper develops a DSGE model where inflation impacts Tobin's q through a human capital channel. The model incorporates both physical and implicit human capital adjustment costs. In the long run, higher inflation reduces human capital utilization, lowers growth, and decreases Tobin's q. Short-run dynamics are influenced by real and monetary shocks, with the overall correlation between inflation, growth, and Tobin's q depending on the relative strengths of these shocks. Smithers & Co. data on Tobin's q is utilized for analysis. The model also considers the impact of factors like capital taxes (as discussed by McGrattan and Prescott, 2005), offering a monetary perspective on their findings.
1. The Model s Mechanism Inflation Human Capital and Tobin s q
The core of the model lies in its explanation of how inflation affects Tobin's q through a human capital channel. The model is embedded within a real business cycle framework, but uniquely integrates both standard physical capital adjustment costs (à la Lucas and Prescott, 1971) and implicit human capital adjustment costs (drawing upon Becker, 1975 and Lucas, 1988). The latter cost represents the opportunity cost of diverting productive human capital towards further human capital creation. The model posits that inflation acts as a tax on human capital, reducing its utilization rate by decreasing the amount of time productively employed. This reduction in human capital utilization, caused by increased leisure due to the inflation tax, directly contributes to a fall in the firm's value, mirroring the impact of capital income taxes on physical capital as noted by McGrattan and Prescott (2005). The dual adjustment cost mechanism is crucial, translating the negative effects of the inflation tax on growth (via reduced human capital utilization) into a lower magnitude of Tobin's q. This approach aligns with the empirical support for endogenous growth models dating back to Kocherlakota and Yi (1996).
2. Short Run and Long Run Dynamics
The model incorporates both long-run balanced growth and short-run transitional dynamics in response to economic shocks. Long-run relationships are established to form a baseline for the short-run analysis and calibration. The long-run comparative statics analysis emphasizes that the negative effects of inflation on Tobin's q operate through reduced human capital utilization. In the short run, however, the relationship between inflation, Tobin's q, and growth becomes more nuanced and dependent on the types of shocks affecting the economy. The model includes both real shocks (productivity shocks in goods and human capital investment sectors) and monetary shocks (purely money supply shocks). Real shocks tend to reinforce the negative correlations between inflation and both Tobin's q and growth. Conversely, monetary shocks, through a Tobin (1965) effect, can increase physical capital accumulation, weakening the negative correlations between inflation and both growth and Tobin's q. The overall observed correlations are therefore determined by the relative strengths of these real and monetary shocks.
3. Market Sequencing and Model Structure
The model details the sequencing of markets: households first trade goods using cash in advance (Mt), followed by trading in asset markets (stocks Vt and nominal bonds Ptb). Nominal bonds pay one unit of currency with certainty in subsequent periods. Cash is exclusively used for goods transactions and is augmented by the central bank through lump-sum transfers. A firm in the model produces goods using a production function incorporating physical capital (kt) and effective labor (lGtht), with At representing total factor productivity (TFP). The firm accumulates physical capital and employs workers, distributing dividends to households. Investment goods and labor are treated as credit goods, meaning the firm faces no exchange constraints. The firm is subject to investment adjustment cost technology, increasing with the investment rate. The firm's optimization problem involves maximizing discounted dividends, using the household's perceived intertemporal marginal rates of substitution as a stochastic discount factor. This intricate structure allows the model to capture the complex interactions between inflation, investment, and human capital accumulation.
III.Model Calibration and Results Long Run and Short Run Analysis
The model is calibrated using US annual data (1960-1999) and quarterly data (1960Q1-2008Q2). Long-run comparative statics analysis confirms the negative relationship between inflation and Tobin's q. Short-run analysis, based on impulse responses to various shocks, shows that the correlation between Tobin's q and inflation depends on the nature of the shocks (productivity vs. monetary). Data from sources such as Hall (2001) and the Bureau of Labor Statistics (BLS) are employed in the calibration process. The model generally performs well in matching long-run data, but the volatility of Tobin's q is under-predicted in the short run, a common limitation in such models.
1. Calibration Methodology and Data Sources
The model's calibration involved several key considerations: data frequency, sample period, and specific data series used. Annual data (1960-1999) was initially employed to target key variables: GDP growth rate, inflation rate, Tobin's q, investment rate, and leisure usage rate. The annual average Tobin's q, exceeding unity, was calibrated using Hall's (2001) series. For the short-run calibration, more recent estimates from Smithers & Co. (2008) were used, noting the similarity in short-run second moment properties between the Hall and Smithers series. Leisure was estimated at 0.55 based on annual average weekly hours of work from the Bureau of Labor Statistics (BLS) data, starting in 1964. The baseline sample period (1960-1999) was extended to 1960-2008 to incorporate the post-1999 period, which saw Tobin's q fall below unity after a stock market crash. This calibration strategy aimed to capture both long-run and short-run characteristics of the US economy. The choice of data sources and the calibration strategy are essential for the validity and reliability of the model's results.
2. Long Run Analysis Comparative Statics
The long-run analysis utilizes comparative statics based on the baseline calibration (1960-1999 annual data). A key result is the demonstration of the model's ability to replicate the long-run relationship between inflation, Tobin's q, and growth. Comparative statics analysis, specifically examining changes in money growth rates, shows that an inflationary monetary policy leads to a shift towards leisure, a decline in human capital investment and utilization, lower growth, and a decrease in Tobin's q. The rise in leisure induces higher real wages, lower real interest rates, and a higher physical-to-human capital ratio. The analysis reveals that the impact of inflation on Tobin's q depends on the underlying drivers of inflation, including monetary policy, human capital total factor productivity (TFP), and adjustment costs. Sensitivity analysis with respect to the adjustment cost parameter shows that higher adjustment costs lower growth, raise inflation, and exert an upward pressure on Tobin's q, ultimately dominating the negative growth effect. This comprehensive long-run analysis helps to establish the fundamental relationships predicted by the model.
3. Short Run Analysis Impulse Responses and Model Fit
The short-run analysis focuses on impulse responses to orthogonalized shocks (goods sector TFP, human capital TFP, and monetary shocks) derived from the log-linearized version of the model. These responses show that the correlation between Tobin's q and inflation is heavily influenced by the relative strengths of productivity and monetary shocks. Productivity shocks (either goods sector or human capital sector TFP shocks) tend to generate a negative association between Tobin's q and inflation, alongside a negative correlation between Tobin's q and growth. Monetary shocks, however, induce a Tobin effect, increasing physical capital accumulation, thereby weakening these negative correlations. The model's ability to replicate short-run properties of financial data is assessed. Calibration of the forcing processes aims to match the correlations between Tobin's q, inflation, and growth observed in the data. Second moment properties (volatilities and correlations) are compared for two sample periods: 1960Q1-1999Q4 and 1960Q1-2008Q2. While the model captures the correlations reasonably well, especially the 1960Q1-2008Q2 correlation between output growth and Tobin's q, the volatility of Tobin's q is consistently under-predicted. The analysis highlights that this under-prediction may be related to the role of leisure shocks, criticized by Chari et al. (2008), which are necessary to match the observed correlations.
IV.Conclusion Inflation Human Capital and the Market Price of Capital
The study provides a novel explanation for the negative correlation between Tobin's q and inflation, emphasizing the role of human capital utilization. The DSGE model demonstrates how inflation's distortionary effects on human capital investment can simultaneously explain the negative relationships between inflation and both Tobin's q and economic growth. The findings contribute to the understanding of monetary policy's impact on stock markets, particularly through the lens of human capital-driven endogenous growth.
1. Summary of Findings and Model Performance
The conclusion summarizes the paper's main contribution: a novel explanation for the negative correlation between the market price of capital (Tobin's q) and inflation, within an endogenous growth framework. The model successfully identifies plausible fundamental factors driving the relationship between Tobin's q, inflation, and growth. A key finding is the importance of human capital utilization as a transmission mechanism. The model's long-run comparative statics and short-run impulse response analyses help to elucidate how real and monetary shocks are transmitted through a human capital channel, a novel contribution to the literature. The model effectively explains two stylized facts: the negative correlation between Tobin's q and inflation and the negative correlation between output growth and inflation. Inflation's distortionary effects on human capital utilization, leading to a diversion of time toward leisure, are central to this explanation. This reduces growth and increases adjustment costs, lowering Tobin's q. While the model performs well in matching long-run target variables, the short-run volatility of Tobin's q is under-predicted, a common limitation of consumption-based CAPM models. The conclusion highlights the model's success in capturing the essential correlations between the key economic variables.
2. Significance and Novel Contributions
The study's significance lies in its explanation of the negative correlation between Tobin's q and inflation, offering a framework that explicitly considers human capital's role as a major driver of growth. This contrasts with existing literature that primarily focuses on the effects of monetary policy on stock market boom-bust cycles through channels like sticky wages and inflation targeting (Christiano et al., 2007). The research adds to our understanding of how monetary policy influences stock markets through the lens of human capital-driven growth. The development of a closed-form solution for Tobin's q, incorporating physical adjustment costs, allows for a clearer understanding of the long-run relationship between inflation, Tobin's q, and human capital utilization. The transmission mechanism of real and monetary shocks via the 'human capital channel' represents a novel aspect of the study's contribution. The paper's findings provide a unified explanation for the negative correlations between both (i) the market price of capital and inflation, and (ii) output growth rate and inflation, showing that inflation affects the stock market through its distortionary impact on human capital utilization and subsequently on the cost of physical capital accumulation.
3. Limitations and Future Research
The conclusion implicitly acknowledges limitations, particularly regarding the model's under-prediction of Tobin's q volatility in the short run. This limitation is a common feature of consumption-based CAPM models and suggests potential areas for future research. The need to utilize implausibly large standard errors for the leisure shock to accurately match the q-growth and q-inflation correlations suggests that further refinements to the model's structure or shock specifications might be needed. The paper also opens avenues for future research by highlighting the relatively unexplored area of monetary policy effects on stock markets through the lens of human capital-driven growth, encouraging further investigation into this 'human capital channel' of transmission. The conclusion subtly points toward the need for addressing this limitation and suggests opportunities for expanding upon the model's insights in future research efforts.