Hysteresis and the learning-By-doing mechanism in the monetary policy context: a bayesian vector autoregression appoach

Standard macroeconomic theory typically assumes that output in the long-run is independent of the short-run business cycle. The hysteresis hypothesis assumes the contrary and supposes that short-run economic shocks can have a permanent effect on the level of output. This paper empirically tests the existence of hysteresis within the monetary policy context using both linear and non-linear (time-varying) Bayesian vector autoregressions. We focus on a particular channel in which hysteresis can operate: the learning-by-doing mechanism. Within the context of monetary policy, this paper finds little evidence to suggest semi-permanent hysteresis effects via this channel when considering the response of output and total factor productivity (a long-run driver of output growth) to monetary policy and employment shocks. While this paper finds some persistent shocks within the linear models, these shocks appear to largely decay over time, and may be explained as a long-term adjustment period toward equilibrium within a standard New Keynesian macroeconomic model.

HYSTERESIS AND THE LEARNING-BY-DOING MECHANISM IN THE MONETARY POLICY CONTEXT: A BAYESIAN VECTOR AUTOREGRESSION APPROACH by Matthew Gordon A Senior Honors Thesis Submitted to the Faculty of The University of Utah In Partial Fulfillment of the Requirements for the Honors Degree in Bachelor of Science In The Department of Economics Approved: __________ Ivan Mendieta-Muñoz, PhD Thesis Faculty Supervisor _ ____ Norman Waitzman, PhD Chair, Department of Economics Gabriel Lozada, PhD Honors Faculty Advisor _____________________________ Sylvia D. Torti, PhD Dean, Honors College May 2022 Copyright © 2022 All Rights Reserved ABSTRACT Standard macroeconomic theory typically assumes that output in the long-run is independent of the short-run business cycle. The hysteresis hypothesis assumes the contrary and supposes that short-run economic shocks can have a permanent effect on the level of output. This paper empirically tests the existence of hysteresis within the monetary policy context using both linear and non-linear (time-varying) Bayesian vector autoregressions. We focus on a particular channel in which hysteresis can operate: the learning-by-doing mechanism. Within the context of monetary policy, this paper finds little evidence to suggest semi-permanent hysteresis effects via this channel when considering the response of output and total factor productivity (a long-run driver of output growth) to monetary policy and employment shocks. While this paper finds some persistent shocks within the linear models, these shocks appear to largely decay over time, and may be explained as a long-term adjustment period toward equilibrium within a standard New Keynesian macroeconomic model. ii TABLE OF CONTENTS ABSTRACT ii INTRODUCTION 1 LITERATURE REVIEW 2 METHODOLOGY 5 Learning-by-doing Mechanism 5 Data 7 Linear BVAR 8 BVAR-SV-TVP 10 RESULTS 11 BVAR Model 11 BVAR-SV-TVP Model 20 CONCLUSION 30 REFERENCES 32 iii 1 INTRODUCTION Do short-run economic shocks influence long-term output? Standard real business cycle and New Keynesian theories suggest that the answer is no. According to these theories, most shocks are transitory and, thus, have little effect on long-term output. As a result, fluctuations in the business cycle and fluctuations in long-term output are independent. However, there is growing support for what is known as the hysteresis hypothesis. This hypothesis states that short-run economic shocks can have a semi-permanent effect on the level of output as these shocks alter drivers of long-run economic growth. In the case of recessions, the hypothesis assumes that drivers of long-run economic growth are negatively affected, and that recessions can semi-permanently scar the economy. The presence of hysteresis is of particular interest to policymakers. If recessions can both negatively and permanently affect the economy, then policymakers may wish to be more proactive in instituting stabilization policies that address fluctuations in the business cycle. On the other hand, if standard macroeconomic models hold, then stabilization policies can be implemented without worrying about the possible long-term detrimental effects. The presence (or lack of) of hysteresis during the 2008 recession or the COVID-19 pandemic might suggest that policymakers should have taken rapidly different stabilization measures. As a result, the identification and empirical validity of hysteresis are of particular importance. This paper aims at determining whether there is empirical support for hysteresis effects within the monetary policy context, focusing on a particular channel in which hysteresis may operate: the learning-by-doing mechanism. To do so, this paper looks to determine through structural analysis of linear and non-linear Bayesian vector 2 autoregressions (BVARs) whether there is evidence to suggest hysteresis effects in either the output gap or the total factor productivity (TFP) gap (that is, a long-run economic driver of output). LITERATURE REVIEW Standard macroeconomic theories of long-run output implicitly assume that short-run economic shocks have little to no effect on the steady-state level of output. Kydland and Prescott (1982) provide the foundation for one of these theories: the real business cycle view of macroeconomics. In this work, they build upon the exogenous long-run growth model of Solow (1956) and create models in which fluctuations in the business cycle may be attributed entirely to technological shocks. In the construction of these models, shortrun shocks such as demand shocks are seen as having little to no effect on the steady-state of the economy. Seminal empirical studies such as Blanchard and Quah (1989) support this construction by assumption and find that demand shocks are transitory and have little effect on long-term output. New Keynesian theory also largely ignores the effect that short-run shocks can have upon long-term output. For example, Fischer (1977) outlines a model that incorporates nominal rigidities, such as in the labor market, and concludes that monetary policy has no effects on long-run output. Textbook New Keynesian models, such as the one presented by Galí (2015, Chapter 3), show a basic model in which monetary and preference shocks have little effect on changing the natural (long-run) level of output, and 3 that short-run exogenous shocks generally have a limited effect on changing long-run output. However, other strands of literature suggest alternative frameworks in which short-run shocks may affect long-run output. Cerra, Fatás, and Saxena (2020) provide an overview of how endogenous growth models provide a theoretical basis for this. In general, underneath the conditions of endogenous growth, short-run shocks may semipermanently alter drivers of long-run growth such as productivity, capital accumulation, or research and development. Citing the work of King, Plosser, and Rebelo (1988) and King and Rebelo (1988), Cerra, Fatás, and Saxena (2020) note how these works found that “temporary technology shocks can become permanent in the presence of endogenous growth. The otherwise temporary shocks would produce permanent effects on GDP because they temporarily altered the long-term growth engine.” In general, the hypothesis that short-run economic shocks may have a permanent effect on the level of output is known as the hysteresis hypothesis. As a result, recessions may have a permanently detrimental effect on output underneath this hypothesis. While the hypothesis has some theoretical framework underneath endogenous growth theory, it runs contrary to some of the theoretical findings of the real business cycle and New Keynesian theories. Tervala (2021) notes that the presence of hysteresis would also challenge the conclusions of Lucas (1987, 2003), who argued that the welfare costs from recessions are minimal and stabilization policy is unnecessary. Tervala (2021) finds that empirical estimates of hysteresis suggest an increase in welfare costs during a recession by a factor of 121, where costs are sustained decreases in consumption due to recessions. 4 If the hysteresis hypothesis were true, then the sustained detrimental effects on output and the associated welfare costs of recessions suggest that policymakers would need to focus on more aggressive counter-cyclical stabilization policies. Engler and Tervala (2018) study the effect that the hypothesis has on policy using a hysteresisextended New Keynesian DSGE model. They suggest that more accommodative fiscal policy should be employed to minimize the harms of recessions underneath hysteresis. Tervala (2021) finds that “stabilization policy should respond forcefully to recessions.” Furthermore, Cerra, Fátas, and Saxena (2020) give an additional overview of recent works focusing on the policy implications of hysteresis. Overall, these works suggest that, in the presence of hysteresis, central banks and fiscal authorities should focus on even more aggressive and responsive fiscal and monetary policies during recessions. Empirical confirmation of the hysteresis hypothesis would not only challenge the real business cycle and New Keynesian theories but would also suggest the necessity of a more forcible policy response against recessions. However, empirical identification of hysteresis has produced mixed results. Cerra and Saxena (2008) find that there appears to be persistent global output loss caused by financial and political crises, which is consistent with the theory of hysteresis. Furthermore, Furlanetto et al. (2020) incorporate the structural VAR framework of Blanchard and Quah (1989) along with sign-restrictions and find that both supply and demand shocks generate hysteresis effects. However, Benati and Lubik (2021) find no evidence of hysteresis in the USA when analyzing cointegrated structural VARs in a Classical and Bayesian context. As a result, the presence of hysteresis is not well established, and further empirical work is required. 5 METHODOLOGY The empirical approach of this paper is to consider a version of the learning-by-doing mechanism that is employed by Engler and Tervala (2018) in their hysteresis-extension of the standard New Keynesian dynamic stochastic general equilibrium (DSGE) model. This mechanism is incorporated into the context of monetary policy and provides a potential channel through which hysteresis may affect output. The empirical viability of this channel may then be tested in the face of monetary policy shocks. Following this idea, a five-variable monetary policy Bayesian vector autoregression (BVAR) model that incorporates the learning-by-doing mechanism is estimated. Both a linear BVAR and a non-linear BVAR incorporating stochastic volatility and time-varying parameters are used. This paper considers models that incorporate both 1-lag and 4-lags. The impulse response functions of these models are then used in structural analysis to both determine the empirical feasibility of the learning-by-doing mechanism as a channel for hysteresis and to identify the presence of hysteresis. The rest of this section is structured as follows. First, the learning-by-doing mechanism is discussed. Second, the data employed and the transformations used are discussed. Finally, the estimation details of the BVAR models and the process of the structural analysis used is discussed. The Learning-by-doing Mechanism The learning-by-doing mechanism considered in this paper follows the mechanism employed by Engler and Tervala (2018). This mechanism supposes that the skill level of a worker and, thus, productivity increases as they gain experience within the 6 workforce. The mechanism is not novel, and Lucas (1988) uses the mechanism in a model for human capital accumulation. Similarly, Arrow (1962) employs the mechanism to propose a system of endogenous economic growth where technical change is ascribed to workers’ experience. This paper assumes a learning-by-doing mechanism in which the level of total factor productivity (TFP) accumulates over time according to past employment. Following Engler and Tervala (2018), equation (1) is the log-linear form used to describe the exact single-lag case considered by Engler and Tervala (2018) while equation (2) is the case for arbitrary p-lags. Note that in equations (1) and (2), ϕ and μ are parameters, and hatted variables denote the percentage change from the steady-state where 𝑎𝑎𝑡𝑡 (𝑧𝑧) represents the level of TFP and 𝑙𝑙𝑡𝑡 (𝑧𝑧) represents the level of labor used. Similarly, note for equation (1) that ϕ = 1 means that labor shocks have a permanent effect on TFP while for ϕ < 1 labor shocks have persistent but non-permanent effects on TFP. Although these equations provide the theory for the learning-by-doing mechanism, the empirical implementation of this paper modifies the above equation to be consistent with a VAR(p) of N variables with intercept terms. It is expected that increases in labor employed above the steady-state result in increases in productivity above the steady-state, and that similarly decreases in labor employed below the steady-state result in decreases in productivity below the steady- 7 state. Thus, this learning-by-doing mechanism allows for hysteresis effects to be realized depending on how persistently a labor shock will impact productivity. If hysteresis is realized through this type of learning-by-doing mechanism, as Engler and Tervala (2018) suppose, then it is expected that labor shocks will have a persistent effect on productivity, one of the drivers of long-run growth, and will, in turn, affect long-run output. As a result, the potential identification of the learning-by-doing mechanism as an empirically viable mechanism for the realization of hysteresis is of interest. If it can be shown that labor shocks have a persistent effect on productivity empirically then there would be evidence to support this mechanism. Additionally, identification of this mechanism would provide an empirically supported channel for the realization of hysteresis even if direct empirical identification of hysteresis is inconclusive. In this paper, structural analysis of impulse-response functions from BVAR models will be used to determine if labor shocks have a persistent effect on productivity and thus support the learning-by-doing mechanism. Data The raw data for total factor productivity used within this paper comes from quarterly U.S. estimates provided by the Federal Reserve Branch of San Francisco and John Fernald following Fernald (2012). The data ranges from 1947:Q2 to 2021:Q2 and focuses on the U.S. business sector. While alternative measures of total factor productivity exist, such as the yearly multi-factor productivity estimates from the Bureau of Labor Statistics or estimates from the Penn World Table, the quarterly estimates are preferred due to the increased number of observations over the annual estimates.. These 8 additional observations are necessary to estimate the additional parameters associated with stochastic volatility and time-variation in the non-linear models. For the five-variable monetary policy case, this paper considers real output, employment, inflation, TFP, and the interest rate in that order, and uses the following data stand-ins: real GDP (GDPC1), hours worked for all employed persons in the business sector (HOABS), CPI inflation (CPIAUCSL), the TFP estimates of Fernald (2012), and the federal fund rate (FEDFUNDS). Following Hamilton (2018), a Hamilton Filter with a 2-year look-ahead period and 4 lags was employed to produce the trend of each data variable. The log-difference between the observed data and estimated trend was used to obtain an approximation for the percent deviation from the steady state. The final data set includes the output gap, employment gap, inflation gap, and TFP gap computed using this Hamilton Filter; while the interest rate is left at levels. The resulting data set spans from 1954:Q3-2021:Q2. Linear BVAR For estimation of the linear BVAR models, this paper uses the ‘BVAR’ R package implementation following Kuschnig and Vashold (2021). Here, a model takes the form of: for a VAR(p) model of p lags and N variables, where subscript 𝑡𝑡 represents the time period, 𝑦𝑦𝑡𝑡 is an 𝑁𝑁 × 1 vector of endogenous model variables, 𝑏𝑏0 is an 𝑁𝑁 × 1 vector of intercept terms, 𝐵𝐵𝑖𝑖 is an 𝑁𝑁 × 𝑁𝑁 matrix of model coefficients for 𝑖𝑖 = 1, … , 𝑝𝑝 , and the 9 𝑁𝑁 × 1 vector of model shocks are distributed such that εt ∼ 𝒩𝒩 (0, Σ) where shocks are Gaussians with mean zero and variance-covariance matrix of Σ. To estimate the BVAR model shown in equation (3), this paper employs a Metropolis-Hasting algorithm of 50,000 draws and a burn-in sample of 5,000, using the Minnesota prior of Litterman (1980) and following the hierarchical selection of Giannone et al. (2015). For structural analysis of the linear BVARs, impulse response functions with 95% and 68% equal credible sets and median estimates are employed. The structure of the system is imposed through a Cholesky decomposition of the estimated variancecovariance matrices, and variables are ordered as mentioned in the data subsection. Furthermore, additional structure is also imposed so that total factor productivity has no contemporaneous effect on the interest rate. This restriction is imposed as there is no theoretical basis for productivity to affect the interest rate contemporaneously when considering monetary policy. The analysis of the impulse response functions will assess whether shocks in monetary policy model can have a persistent effect on the output gap. If these shocks are found to be permanent or semi-permanent, then there would be evidence suggesting that traditionally considered “transient” shocks have a more persistent effect on long-term output, and thus be empirically supportive of the hysteresis hypothesis. Similarly, even if the empirical evidence is inconclusive regarding the hysteresis hypothesis, structural analysis of the learning-by-doing mechanism can be employed to determine if there is an empirically supported channel for the realization of hysteresis in the U.S. economy. 10 BVAR-SV-TVP For the implementation of the Bayesian VAR models with stochastic volatility and time-varying parameters (BVAR-SV-TVP), this paper uses the ‘bvarsv’ package from Krüger (2015). This package is an R implementation of Primiceri (2005), which lays the framework for BVAR-SV-TVP models. Following the notation of Primiceri (2005) and Krüger (2015): where 𝑦𝑦𝑡𝑡 is a 𝑁𝑁 × 1 vector of model variable, 𝑋𝑋 ′ = 𝐼𝐼𝑛𝑛 ⊗ 1, 𝑦𝑦𝑡𝑡−1 , … , 𝑦𝑦𝑡𝑡−𝑝𝑝 , 𝐵𝐵𝑡𝑡 is a collection of intercepts and model coefficients, 𝐴𝐴𝑡𝑡 is a lower triangular matrix where free elements are stacked in the vector α𝑡𝑡 , and Σ𝑡𝑡 is a diagonal matrix where σ = 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑(Σ𝑡𝑡 ). ε𝑡𝑡 ∼ 𝒩𝒩 (0,1), and {ν𝑡𝑡 , ζ𝑡𝑡 , η𝑡𝑡 } are mutually independent Gaussians with mean zero and are homoscedastic. Models of this form are estimated using the corrected MCMC algorithm of Del Negro and Primiceri (2015) with 50,000 draws, a burn-in sample of 5,000, and a thinning factor of 10 due to memory constraints. Priors are set to that of Primiceri (2005), with adjustments for the number of variables considered. However, for lags p=4 the degrees of freedom of the prior Q are set to 120. This is necessary to reduce time-variation and prevent numerical errors due to an increase in both lag-order and variables over what was considered in Primiceri (2005). 11 Similar to the linear case, structural analysis of the BVAR-SV-TVP models uses impulse response functions with 95% and 68% credible sets and median estimates. Structure is imposed through a Cholesky decomposition where variables are ordered as noted in the data subsection. For the monetary policy context, additional structure is imposed so that total factor productivity has no contemporaneous effect on the interest rate. To detect non-linearities such as time-variation within the structural relationship of the model variables, these impulse-response functions are considered using parameters for the periods of 1965:Q1, 1990:Q1, 2019:Q1, and 2021:Q2. These dates are selected as they correspond to a period before stagflation, a period during the Great Moderation, a period before the COVID-19 pandemic, and the latest data period considered within this paper. Once again, these impulse response functions can be employed to identify whether shocks in the monetary policy model have a near-permanent effect on the output gap and thus would be suggestive of the hysteresis hypothesis, or whether the learning-by-doing mechanism is empirically viable as a channel for the realization of hysteresis. RESULTS Linear BVAR Results of the Monetary Policy Model Using the methods described in the methodology section of this paper, a linear BVAR is estimated and the impulse response functions of the model are analyzed to determine whether there is evidence to support the hysteresis hypothesis via the learningby-doing mechanism. This paper considers two versions of the linear BVAR model, one 12 in which only the first lag (p=1) of the data is used in the estimation of the model, as described by equation (3), and a second in which four lags (p=4) are considered. As mentioned in the methodology section, this paper considers a monetary policy model using the variables of real output, employment, inflation, TFP, and the interest rate. For structural analysis, this paper considers the Cholesky ordering in which data is ordered as presented, with the additional restriction such that total factor productivity has no contemporaneous effect on the interest rate. This restriction is imposed as there is no theoretical basis for productivity to affect the interest rate contemporaneously in the monetary policy model. Figure 1 shows the impulse response functions for the linear BVAR with 1-lag as previously described. A one standard deviation positive employment shock will have an initial positive effect and then a negative impact on real output1 that will persist until around 20 periods (5 years) after the shock using the 95% credible set, for around 22 periods (5.5 years) using the 68% credible set, and around 26 periods (6.5 years) using the median of the responses. This rather non-intuitive result suggests that positive employment shocks have a relatively persistent negative impact on real output. It is possible that an increase in labor overcrowds the work environment and results in the less effective use of capital. This would then result in reduced productivity and output, consistent with what was observed in these results. It is also possible that the model is misspecified, either by lacking important economic variables or by an insufficient number of lags, and thus produces inaccurate results. However, if the model Note the choice of a steady-state gap over levels does not substantially affect the results. When output is considered in levels, the results for this paper are essentially the same for both p=1 and p=4 and show a decaying trend over time. These findings also hold for when TFP is considered in levels. 1 13 is correctly specified, then the persistence of this labor shock provides evidence in support of hysteresis effects in output. Second, it appears that productivity shocks have around 11 periods (2.75 years) of positive effect using the 95% credibility set, around 13 periods (3.25 years) using the 68% credible set, and around 16 periods (4 years) using the median of responses. This result is more theoretically reasonable and is supported by some of the literature following Solow’s growth model and some New Keynesian models that emphasize the role of technological/productivity shocks in explaining output fluctuations. Given the multi-year persistent nature of productivity shocks on output, it would be reasonable to conclude that productivity shocks will likely translate to effects on output, and as a result, would support hysteresis effects upon output. However, identification of economic variables that may affect productivity would then remain, and many economic models assume productivity shocks to be generally exogenous. Figure 1 shows that productivity is credibly affected by shocks in output, employment, and the interest rate. Output shocks upon employment are relatively transient, persisting for less than 10 periods. However, employment shocks persist for around 16 periods (4 years) and interest rate shocks persist for around 24 periods (6 years) using the 95% credible set. Both shocks are relatively persistent, and in the case of employment, shocks are consistent with the results found for output responses. A negative response in productivity to a positive shock in employment runs contrary to the learning-by-doing mechanism assumed by Engler and Tervala (2018)2. However, the The fact that a labor shock elicits a negative response in total factor productivity is not unique to this model specification. A two-variable single-lag BVAR, following the exact specifications as used by Engler and Tervala (2018), will produce similar IRFs. A three-variable single-lag and 4-lag BVAR of output, employment, and TFP will also produce similar IRFs. 2 14 results are consistent with what was found when output was a response and suggest a potential mechanism in which employment shocks affect productivity which then, in turn, affects real output. Furthermore, the persistent negative effects of an increase in the interest rate upon real output are of interest. This suggests that monetary policy influences real output and not just nominal output, as is commonly suggested. Additionally, this suggests that monetary policy has medium-run effects on real output and that there is a delay in which interest rate shocks have a credible effect on output. While not necessarily the focus of this paper, this suggests a dilemma for central banks in which they must respond very early with active monetary policy for it to be noticeably effective during a recession. However, central banks must also take heed to not unnecessarily damage real output by responding too early and thus unnecessarily. Overall, the results of this model provide mixed evidence for the hysteresis hypothesis. While it is certainly true that some shocks have a persistent effect on real output, often lasting for more than 4 years, the impulse response functions do not provide evidence to suggest that these shocks are permanent. Thus, it may be possible that frictions, such as in a New Keynesian view of the macroeconomy, simply result in a long adjustment period in reaching equilibrium when shocks occur. Therefore, persistence may be attributed to long adjustment rather than hysteresis effects. Additionally, the learning-by-doing mechanism does not appear to be empirically consistent with the theory in the methodology section. Instead, it appears that labor shocks negatively impact productivity. While these shocks have a persistent credible effect on productivity, there is no empirical evidence to suggest that the mechanism 15 employed in Engler and Tervala (2018) and Tervala (2021) has empirical backing. Thus, while the persistence of these shocks is suggestive of hysteresis, the empirical evidence does not support the theoretical channel for hysteresis. Furthermore, there is no conclusive evidence to distinguish this persistence as originating from a long equilibrium adjustment period or semi-permanent hysteresis effects. As a result of the concern of misspecification of the model due to failing to incorporate sufficient lags, this paper now considers the use of a linear BVAR with 4-lags (p=4). Figure 2 shows the result of the impulse response functions from this model. In general, the results of this model are consistent with the parsimonious 1-lag (p=1) model. However, there are some interesting things to note. First, inflation shocks have a transient effect on real output and an interest rate shock has an even more transient effect. Second, the credible length of a productivity shock on output has been reduced such that productivity positively affects output for around 6, 8, and 10 periods (1.5, 2, and 2.5 years, respectively) using the 95% and 68% credible sets and the median response. Additionally, the 4-lag model suggests that employment, inflation, and interest rate shocks all have a credible effect on productivity, with 95% credible sets suggesting an effect for around 13 periods (3.25 years), 6 periods (1.5 years), and 5 periods (1.25 years) respectively. This suggests that the 4-lag model shows significantly fewer persistent shocks on productivity than the 1-lag model. This lack of persistence may be due to increased uncertainty due to additional parameter estimations, or perhaps due to the increase in lags capturing time dynamics that were obscured in the parsimonious model. Based on the results of the 4-lag model, empirical evidence in support of hysteresis via the learning-by-doing mechanism is weaker. First, credible shocks upon the 16 output gap are less persistent than in the parsimonious model. This is not supportive of the hysteresis hypothesis, in which shocks that affect output should have a semipermanent effect. Furthermore, shocks in employment have no credible effect on the output gap while shocks in monetary policy have limited to no credible effects on output. This suggests that employment or monetary policy shocks do not induce hysteresis effects in real output. Furthermore, while productivity still has a less persistent but credibly positive effect on labor, shocks that affect productivity such as inflation shocks and interest rate shocks are relatively transient. This is not supportive of a theoretical mechanism in which shocks on the productivity gap, a potential long-run driver of output, then affect the output gap semi-permanently. Additionally, while employment still seems to affect productivity for a medium-run level of persistence, this persistence does not translate over to employment shocks to outputs. Thus, there is little to no evidence for semi-permanent hysteresis effects in this 4-lag model. As previous mentioned, there is a question of whether the difference in persistence between shocks in the 1-lag or the 4-lag models is due to uncertainty caused by extra parameter estimation or caused by the 4-lag model capturing time dynamics that were missed in the 1-lag model. While it is true the number of coefficients estimated increases from 30 in the 1-lag model to 105 in the 4-lag model, the advantage of the Bayesian context of statistical analysis is the ability to apply prior information, such as shrinkage priors, to coefficient estimates. As a result, the use of the hierarchical Minnesota prior acts as a shrinkage prior and helps to reduce the uncertainty in the model estimates. Furthermore, not only did the increase in lags decrease the persistence, but it also captured new credible effects that were not present in the 1-lag model. Had the 4-lag 17 model only reduced the credible persistence of shocks by increasing the width of the credible sets, then it would be reasonable to suggest that the loss in persistence was due to increased uncertainty. However, the introduction of extra lags also changed some of the dynamics of the model, and as a result, suggests that additional time dynamics were captured in the more complex model. This suggests that some of the loss in persistence could have possibly been caused by these additional dynamics. Additionally, median estimates for both models are consistent and suggest that all shocks upon output and productivity will eventually fade to zero, regardless of uncertainty in the credible sets. This is not supportive of the semi-permanent hysteresis effects, and as a result, it can further be concluded that there is little empirical evidence for the hysteresis hypothesis working via the learning-by-doing mechanism in the monetary policy context. 18 Figure 1: IRFs of the linear BVAR model (lags p=1) 19 Figure 2: IRFs of the linear BVAR model (lags p=4) 20 BVAR-SV-TVP Results of the Monetary Policy Model There is reasonable evidence to suggest that the dynamics of the U.S. economy have changed and evolved (Primiceri, 2005). Policies and expectations have changed, and, thus, the relationships between economic variables have likely changed. As a result, it is of interest to model time-variation during the search for hysteresis effects. It is possible that hysteresis effects have either weakened or strengthened over time, and as a result, a linear model may have obscured the identification of hysteresis effects. Therefore, this paper also employs a Bayesian vector autoregression with stochastic volatility and time-varying parameters (BVAR-SV-TVP) to capture any timevariation that may have obscured the identification of hysteresis. Impulse-response functions using parameters for the periods of 1965:Q1, 1990:Q1, 2019:Q1, and 2021:Q2 are considered within this paper to track the effect of time-variation on the structural relationship of variables. These dates are selected as they correspond to a period before stagflation, a period during the Great Moderation, a period before the COVID-19 pandemic, and the latest data period considered within this paper. Therefore, the selection of these periods should increase the likelihood of detecting time-variation due to the wide berth of periods considered. This paper considers two non-linear BVAR-SV-TVP models, one in which only the first lag (p=1) is considered, and the second in which the last four periods are considered (p=4). We also consider the same monetary policy model using the variables of real output, employment, inflation, TFP, and the interest rate. Cholesky decomposition of that ordering is employed, and the additional restriction of total factor productivity having no contemporaneous effect upon the interest rate is employed for structural 21 analysis of impulse response functions. As four periods are considered and there are 25 combinations of impulses to responses, for the sake of brevity, only the impulse response functions for shocks upon output and shocks upon TFP are considered. Figure 3 shows the impulse response functions for each variable upon the output gap for each mentioned period when p=1. As can be seen, there exists substantial uncertainty regarding the response of the output gap to model shocks 3. Except for output shocks, it appears that there is no credible effect at either the 95% credible set or the 68% credible set for any possible shock considered within this model. Output shocks persist upon output for around 5-6 periods (1.25 to 1.5 years) before no longer being credible. Additionally, it appears that over time the relationship of the variables has substantially weakened. Shocks to output have a much weaker to no effect as time progresses. For the latest period considered, it appears as if the short-run effects of a shock upon the output gap are credibly zero. Figure 4 shows the impulse response functions for each variable upon the TFP gap for each mentioned period when p=1. Unlike output, the response of the TFP gap to shocks appears to be a more interesting, with credible positive effects of output gap shocks for 3-4 periods (.75 to 1 year), negative effects of the employment gap for around 2-3 periods (.5 to .75 years), and positive effects of TFP upon TFP for around 1-2 periods (.25 to .5 years) using the 95% credible set. However, it appears that shocks upon the TFP gap are rather transient given the short lengths of these credible effects. Similarly, the relationship of shocks on the TFP gap seems to weaken with time. Finally, consistent Like before, the choice of using either the steady-state gaps or levels for output and TFP do not substantially affect the results. Responses of output and TFP exhibit the same behavior regardless of the choice of units employed. This holds true for both p=1 and p=4. 3 22 with what was found in the linear BVAR case, the employment gap seems to have a negative effect on the TFP gap, not a positive effect as is assumed by the learning-bydoing mechanism. Thus, there is no evidence of the learning-by-doing mechanism as employed by Engler and Tervala (2018) within this model. Overall, there appears to be no evidence to support hysteresis effects when using the BVAR-SV-TVP model with p=1. Shocks upon GDP are not credible, and shocks upon TFP are transient at best. As a result, there is no evidence to suggest persistent or semi-permanent effects of shocks on real output. Now, it is important to note that Primiceri (2005), the foundational paper for the BVAR-SV-TVP model, only considers a three-variable model with p=2. Therefore, the five-variable model considered within this paper introduces a significant extra number of coefficients to estimate than was considered in Primiceri (2005). Since an inverseWishart prior is employed for the BVAR-SV-TVP models, not a Minnesota prior, then uncertainty is not minimized through shrinkage techniques. As a result, it is possible that the credible sets are wider than is ideal and that the width of these sets hide hysteresis effects. However, even if the 68% credible set or even median responses are considered, the impulse response functions give no evidence of semi-permanent effects. Some shocks, such as those upon TFP, become more persistent. However, these shocks will eventually decay to zero, and thus there is no evidence to suggest semi-permanent hysteresis effects in the model. 23 Figure 3: IRFs of the BVAR-SV-TVP model (lags p=1). Output response 24 Figure 4: IRFs of the linear BVAR-SV-TVP model (lags p=1). TFP response 25 It is possible that the parsimonious 1-lag (p=1) model fails to capture significant time dynamics that occur more than 1-lag away from an observed period. To account for this possibility, this paper extends the BVAR-SV-TVP model to include four lags (p=4), and thus incorporates data from the past year of a given observation. The data used, priors, mechanisms, and structural analysis all remain the same as in the 1-lag case. Figure 5 shows the response of the output gap to the various variable shocks considered within this model. Like the 1-lag case, except for an output shock upon output, it does not appear that any of the variable shocks have a credible effect upon output using the 95% credible set. There is significant uncertainty regarding the relative effect that a non-output shock has upon output. However, as previously noted, this model is significantly more complex and estimates more parameters than the Primiceri (2005) model. As a result, these additional parameter estimates likely contribute to additional uncertainty in the model. However, even restricting the analysis to just the 68% credible set or the median, it does not appear as if any shock is semi-permanent or even persistent. Output shocks upon output persist for less than 2 years, and no other shock has a credible effect. As a result, there is no evidence of semi-permanent hysteresis effects upon output when considering this model. However, it is of interest to note that, unlike the 1-lag BVAR-SV-TVP case, impulse response functions of more current periods do not appear to have shrinking credible sets that suggest that shocks have zero effect on output response. Rather, impulse response functions continue to exhibit similar general behavior with slightly narrower credible sets. This suggests that the inclusion of additional lags within the model has helped to capture time dynamics that were missed in the parsimonious case. In 26 conjunction with the results from Figure 3 and Figure 4, this suggests that the history of economic variables has become more important as time has progressed. While looking at only 1-lag of history was satisfactory up until 1990:Q1 to capture time dynamics within the model, for 2019:Q1 and 2021:Q2 4-lags of history are necessary to capture these same time dynamics. Thus, history appears has become increasingly more important in determining the structural relationship of the model variables as time has progressed. Figure 6 shows the response of the TFP gap in response to model variable shocks. The responses are largely like those considered in the 1-lag BVAR-SV-TVP case. That is, there is much uncertainty regarding how the TFP gap responds to shock, and credible effects such as an output or TFP shock will only have a credible response by TFP for less than 2 years (using the 95% credible set). As a result, there is no evidence of semipermanent hysteresis effects in TFP, nor evidence of persistence, and thus the theoretical mechanism of the learning-by-doing mechanism in realizing hysteresis is not supported by this model. Additionally, it is also found that history has become increasingly more important as time progresses. Overall, the BVAR-SV-TVP models show no evidence to support semi-permanent hysteresis effects within the monetary policy context, but there is significant uncertainty regarding the relative effects of output and TFP responses to model shocks. As a result, hysteresis effects may exist and are obscured by this uncertainty. This is possible given the number of estimated parameters in the BVAR-SV-TVP model. The inclusion of the linear BVAR models provides a much more parsimonious interpretation of the monetary policy context and attempts to minimize uncertainty. As a result, even if the BVAR-SVTVP models show no evidence due to significant uncertainty, the linear BVAR models 27 have shown, at best, very weak evidence for hysteresis in the form of persistent shocks. However, even these persistence shocks are not indicative of semi-permanent effects and may be easily attributed to long adjustment periods in equilibrium. Even if the significant uncertainty in the BVAR-SV-TVP models is unsatisfactory, the parsimonious linear BVAR models also do not provide significant evidence to suggest hysteresis effects. To sum up, both the linear BVAR and BVAR-SV-TVP provide little evidence to support the hysteresis hypothesis in the monetary policy context. 28 Figure 5: IRFs of the BVAR-SV-TVP model (lags p=4). Output response 29 Figure 6: IRFs of BVAR-SV-TVP (lags p=4). TFP response 30 CONCLUSION This paper has sought to find whether there is empirical evidence to suggest hysteresis effects working via the learning-by-doing mechanism in the response of output and total factor productivity within the monetary policy context in the U.S. This paper has employed two different sets of Bayesian vector autoregression (BVAR) models, with both sets incorporating 1-lag and 4-lags. The first set, which considers relatively parsimonious linear BVAR models, found evidence of persistent medium-run shocks but found no evidence to suggest semi-permanent hysteresis effects. The second set, which considers BVAR models that incorporate stochastic volatility and time-varying parameters, found no evidence to suggest persistent or semi-permanent hysteresis effects when considering four different periods of U.S. economic history. The second model found much uncertainty regarding the relative effects that shocks have upon the response of output and total factor productivity. As a result, hysteresis effects may have been hidden within this uncertainty. However, the parsimonious linear BVAR model with shrinkage priors attempts to reduce this uncertainty and only very weakly supports hysteresis working through the learning-bydoing mechanism. Thus, this paper provides a wide variety of models, from 1-lag to 4lags and from linear to non-linear, which suggests a relatively robust result: there seems to be little evidence of this type of hysteresis when considering the monetary policy context. Hence, the results of this paper suggest that, in terms of monetary policy, policymakers should be aware of the risks and dangers of hysteresis, but should not necessarily worry about adversely affecting long-run output or productivity, 31 The findings of this paper are consistent with the recent findings of Lubik and Benati (2021), who also find no evidence of hysteresis effects on the U.S. economy; while our findings challenge the results of Furlanetto et al. (2020), who find that both supply and demand shocks generate hysteresis effects. However, it is worth mentioning that this paper has only considered a specific type of hysteresis, that is, the learning-bydoing mechanism, if it operates in the monetary policy context, and as a result, it does not consider both the supply and demand shocks identified by Furlanetto et al. (2020). The inclusion of both the monetary policy context and the shocks considered by Furlanetto et al. (2020) would face significant applied challenges, given the number of parameters that would need to be estimated (i.e., the curse of dimensionality). Nevertheless, one of the advantages of the Bayesian context of statistics is the ability to shrink models and to limit the effect of dimensionality constraints. As a result, further work into the development of shrinkage and dimensionality-reduction models may allow for the synthesis of the models considered within this paper and that of Furlanetto et al. (2020), thus providing a more comprehensive model for the U.S. economy. 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