Optimal monetary policy during the pre-Volcker period in the United States

(1)

U

NIVERSITY OF

A

MSTERDAM

M

ASTER

T

HESIS

Optimal Monetary Policy During the

Pre-Volcker Period in the United States

Author:

Tanvi N

AUTIYAL

(11087528)

Supervisor:

Dr. Christian A.

S

TOLTENBERG

August 15, 2016

(2)

Kriwoluzky and Stoltenberg (2015) found that passive interest rate policy ensured de-terminacy in the Pre-Volcker period. I further study the relation between monetary policy, price stability and interest rate policy by computing the optimal monetary policy for the U.S. during the pre-Volcker era by means of a Ramsey policy and an Optimal Simple Rule. I compare this to the estimated interest rate policy. I find that passive interest rate policy was optimal because of the transaction role of money, but the estimated interest rate policy was far from optimal, resulting in a notable welfare loss.

Keywords: Optimal Monetary Policy, Ramsey Policy, Optimal Simple Rules, Pre-Volcker era

(3)

Contents

1 Introduction

Monetary policy shares a complex relationship with price stability and interest rate policy. While the creation of theory, linking these aspects is easy, and many relationships are possible; an optimal monetary policy cannot be designed without taking into account the prevalent envi-ronment, as also human behaviour. This implies that what shows success here and now, may not work at a different place, as also at a different time. The relationship is so complex, that the same environment and human sample, may behave differently in the same period of time; resulting in varying levels of success of such policies. Notwithstanding this fact, clear patterns can be discerned, and if adequate leeway is catered for, models can be created to formulate policies, which will portend a high degree of success. Let us now analyse a specific period in American Economic History and look at these facts.

Volcker was the Chairman of the Fed Reserve between Feb 1979 and Aug 1987. He is widely credited with ending the high levels of inflation seen in the United States during 1970s and early 1980s. It is believed that a combination of sound monetary and fiscal integrity helped sustain the goal of price stability, as ensured by Volcker, thereby improving the relevance of the Fed itself. However, the conventional view that persists is that monetary policy before Volcker was badly managed. Is this assumption based on hard facts? Have we analysed this period enough, or are there important lessons therein which may have been missed out? Or was the prevalent policy implemented then, relevant to the times? While analysing this aspect, I plan to derive the optimal monetary policy for the pre-Volcker period and compare this to the estimated pre-Volcker policy.

Clarida et al. (2000) and Lubik and Schorfheide (2004) found out that interest rate policy was passive before the Volcker era and active after the disinflation years. Kriwoluzky and Stoltenberg (2015) point out that the passive interest rate policy before Volcker is difficult to interpret through the lens of standard cashless New Keynesian model, because it will lead to indeterminacy (Woodford, 2003). This would also induce possibility of sunspot fluctuations as a source of macroeconomic instability. They further connect the changing role of money to the conduct of monetary policy. Based on the interest rates policy implemented by the Fed-eral Reserve, they provide an alternative explanation towards the switch in interest rates by analyzing the decreasing role of money in transactions and its implications on the stability of the economy. They are able to prove that interest rate policy before Volcker was passive, but still ensured determinacy because money played an important role in facilitating transactions. They also prove that consistent with Clarida et al. (2000) and Lubik and Schorfheide (2004), an active interest rate policy ensured determinacy in the United States after 1982, when money no longer played an important role. This evokes a question as to what was the optimal monetary policy that would have been relevant to the pre-Volcker period in the USA? Contrary to the

(5)

1 Introduction

popular view that the policy was badly managed, Kriwoluzky and Stoltenberg (2015) provide an alternative explanation which indicates that the prevalent monetary policy before Volcker did not necessarily play a negative role. However, in this paper, the authors do not conduct a welfare analysis.

As part of my thesis, I plan to conduct this analysis using Optimal Simple Rule and Ramsey policy in Dynare. I will attempt to study, correlate, and find the relationship between the mon-etary policy, price stability, interest rate policy and the transactional role of money. During the Literature Review, based on the findings of various studies listed above, my research ques-tion will focus on ‘Computing the Optimal Monetary Policy for the pre-Volcker United States’. To achieve this, I will be using the model and the parameter estimates from Kriwoluzky and Stoltenberg (2015). In more specific terms, the method that I will adopt to compute the optimal monetary policy will be to compute the Ramsey policy and Optimal Simple Rule with Dynare and compare it to the estimated model proposed in Kriwoluzky and Stoltenberg (2015). I will thus compare the results of the estimated policy to an Optimal Simple Rule, which I in turn ex-amine against the Ramsey Policy. I will also look at the optimized values of the loss functions obtained from both the methods and analyze the results to draw relevant inferences, which is how I contribute to the existing knowledge of monetary policy as applicable to the pre-Volcker period.

I find that in the pre-Volcker period it was optimal for a central bank to pursue a passive interest rate policy while examining the impulse response graphs for government expenditures, produc-tivity, cost push shock and transaction frictions. Additionally, the period was characterized by a suboptimal policy indicated by the calculated welfare loss, which is higher for the estimated model. I also find that both Ramsey and optimal simple rule give highly comparable results and Ramsey policy leads to a lower loss than the optimal simple rule.

The paper is structured into five sections. After the Introduction (Section I), Section II will cover the literature review. Thereafter, in Section III, I will describe the model I am using and define all the variable and parameters for it. Furthermore I will elaborate on the proce-dure to compute optimal policies, in specific, Ramsey policy and the Optimal Simple Rule and compare them. I will also state the loss function I have taken for this analysis. Thereafter in Section IV, I will analyze the impulse response and state and discuss my main results. I will finally conclude my thesis in Section V with an analysis of the monetary policy applicable to the pre-Volcker period.

(6)

2 Literature Review

Economists agree that conduct of monetary policy in the US changed considerably with the appointment of Paul Volcker as the Chairman of the Fed Reserve in 1979 (i.e. Clarida et al. (2000), Dennis (2001), Favero (2005), Boivin (2006)). Thus, the existing US economic envi-ronment can be divided into two distinct phases: the pre-Volcker period, and the Volcker along with the post-Volcker years. In this section, based on an in-depth analysis of the available literature, I will try and dichotomize the Fed’s policy in the pre-Volcker era and the Volcker-Greenspan era, where my main focus will be on the optimal monetary policy that would have been applicable to the pre-Volcker era. My analysis will focus on the main players in this era, their policies, and changes that were instituted in this period, which are relevant to my study.

The existing literature on the pre-Volcker period shows this period was characterized by high and volatile inflation, often dubbed as ‘The Great Inflation’. This period occurred in mid-1960s and 1970s and was followed by stagnation throughout the 1970s. The Great Inflation was a re-sult of the policy makers’ overconfidence in their ability to stabilize deviations of output from the economy’s potential supply. The activist monetary policy during the Great Inflation placed too much emphasis on short-run stabilization of economic activity at the expense of the Fed Reserve’s long-term price stability objective. Despite the best intentions of the policymakers, monetary policy itself became the engine of inflation and a source of instability during the Great Inflation (Orphanides, 2004).

Clarida et al. (2000) argue that during the Great Inflation the Fed Reserve pursued a policy that accommodated inflation and induced instability in the economy by lowering real interest rates when expected inflation increased and vice versa. To better understand the prevalent economic environment in the pre-Volcker period, and the changing relevant constituents that created and affected this environment, I will first compare this period with the ‘Volcker-Greenspan era’.

Lubik and Schorfheide (2004) emphasize that interest rate policy was passive in the pre-Volcker years, whereas it became and remained active thereafter. The passive interest rate policy in this period indicates that the pre-Volcker era may have been characterized by indeterminacy. How-ever, the theory is ambiguous when extending the role of money to this analysis (Stoltenberg (2012), Benhabib et al. (2001)).

Ireland (2004) corroborates the fact that one of the most important changes that affected mon-etary policy highly is the importance of cash to facilitate transactions. This plays a pivotal role in the analysis, as to which monetary policy rules lead to determinacy, where a determinate equilibrium is one that is unique. Clarida et al. (2000) states that from a welfare perspective, determinacy is superior to indeterminacy, i.e. the possibility of multiple equilibria. Woodford (2003) state that an active interest rate policy is necessary to ensure determinacy, whereas a

(7)

2 Literature Review

passive interest rate policy can lead to non-fundamental sunspot shock equilibria. A passive interest policy here means that an increase in inflation above target will be followed by a less than one-to-one increase in the nominal interest rate, causing the real interest rate to decrease. Conversely, an active interest rate policy implies that an increase in inflation above target will be countered by a more than one-to-one increase in the nominal interest rate, leading to a rise in the real interest rate.

Lubik and Schorfheide (2004) find how the interest rate policy before Volcker resulted in an in-determinate equilibrium in a cashless economy by Bayesian estimation techniques. The notion that the pre-Volcker policy led to indeterminacy is put forward as an explanation of the high inflation period during the 1970s. Self-fulfilling expectations may have arisen as it can occur that these are not suppressed by a passive interest rate policy.

Favero (2005) points out that the transition from the pre-Volcker era to the Volcker-Greenspan era in late 1979 marked the onset of the Taylor principle for monetary policy, which required that the monetary authority adjust the nominal interest rate actively to changes in inflation. Clarida et al. (2000) proves that the pre–Volcker period exhibited higher volatility and vari-ances of monetary policy shocks while the volatility of monetary policy shocks was very low and substantially constant in the post-Volcker period.

On the other hand, Coibion and Gorodnichenko (2011) find that the Fed likely satisfied the Taylor principle in the pre-Volcker era, but the US economy was still subject to self-fulfilling fluctuations. The switch from indeterminacy to determinacy in the US economy was due to the changes in the Fed’s response to macroeconomic variables i.e. monetary policy changes. The paper also states that a change in the policy rule and a decline in the inflation target of the Fed Reserve during the Volcker disinflation, both together, lead to the shift from indeterminacy to determinacy. The change in response to output growth could not by itself lead to determinacy around the time of the Volcker disinflation. They further state that if the Fed had responded as strongly to the output gap as they did before Volcker, then the US economy would still be in the indeterminacy region, particularly at higher rates of inflation.

Clarida et al. (2000) reiterate that active interest rate policy ensured determinacy in the US after 1982 when role of money vanished. Between end 1960s and beginning 1980s, US went through a prolonged episode of high inflation, accompanied by high volatility.

However, various other factors come into play when analyzing both periods. Kriwoluzky and Stoltenberg (2015) deduce that the transaction role of money plays an important role in the analysis of both the periods. Their paper concludes that a passive interest rate policy led to determinacy in the pre-Volcker era due to the fact that money still played an important role in facilitating consumption purchases. When this role vanished, an active interest rate policy became necessary for achieving a determinate equilibrium.

(8)

The change in use of money in transactions is furthermore documented by Schreft and Smith (2000). If the demand for cash to facilitate transactions went down due to advances in technol-ogy and communication systems, the demand for reserves also went down, whereas the demand for bonds increased. Whenever there was a positive interest rate, agents would not want to hold excess cash balances.

Humphrey (2004) gives an explanation as to why the transaction role of money changed over the years. Cheques replaced cash in the 70s, cheques were replaced by credit cards in the 80s and eventually debit cards replaced both cash and cheques in the 90s. Daniels and Murphy (1994) rely on two mechanisms regarding the costs involved in obtaining currency. First of all, the availability of ATMs affects choices by agents, regarding which means of payment to use. This pins down the level of currency demanded. Secondly, taken this level as given, technology such as ATMs affects the transaction costs of actually obtaining this currency.

Castelnuovo (2012) ties in with this finding, as it shows, how the importance of money for explaining business cycle fluctuations has declined. This paper finds that money is important when aiming to replicate the output volatility observed during the period of high inflation in the 1970s in the United States. This indicates that money was indeed an important variable that should be incorporated in pre-Volcker DSGE models.

The novelty of the new era is also documented among others by Ireland (2009) who shows how the data points from the post-1980 period trace out a stable money demand relationship. Subsequently, Ludvigson et al. (2002) show that the wealth channel of monetary transmission to consumption was stronger in the pre-Volcker period than during the succeeding period. The sharpest decline in wealth resulting from a federal funds rate shock was in the pre-Volcker period. Since approximately 1990, federal funds rate shocks are shown to have a negligible effect on wealth. Evidence by Sims (1999) and Sims and Zha (2004) show that most observed changes between the pre-Volcker and post-Volcker periods can be attributed to changes in the variance of the shocks that affect inflation.

Bilbiie and Straub (2013) explain why pre-Volcker period had a passive interest rate policy. They analyze a conventional sticky price model with the unconventional feature that if asset market participation is sufficiently low, interest rate increases become expansionary and a pas-sive monetary policy ensures equilibrium determinacy and maximizes welfare. This implies that the Fed Reserve in fact executed an optimal policy during the pre-Volcker era, contrary to what most standard models describe. In the period preceding the start of the Volcker era, the share of agents participating in asset markets changed substantially. This gives a rationale for the observed change from a passive to an active interest rate policy executed by the Fed Reserve.

(9)

2 Literature Review

passive interest rate policy destabilizes the economy as it gives rise to the potential of fluctu-ations driven by expectfluctu-ations and sunspot equilibria. This indicates indeterminacy. They also look at the role money plays in various preferences and technologies to examine when a pas-sive or an active interest rate policy leads to local stability and uniqueness. One result is that if preferences can be separated, in consumption and money, and at the same time money is productive, then an active monetary policy leads to indeterminacy. The same holds if money is not productive, but consumption and money are substitutes. On the other hand, if money is not productive but consumption and money are complimentary, an active interest rate policy gives rise to determinacy. So, all in all, the paper indicates that there is high sensitivity determinacy for monetary policy rules on preferences and technology.

So all in all, several factors appear to have altered the US monetary environment sufficiently to ensure a high degree of indeterminacy among economists as to what policies should have been implemented. Common consensus is limited to the notion that the transaction role of money has diminished over the years and that the pre-Volcker interest rate policy was passive while the monetary policy became active in the Volcker-Greenspan era.

Hetzel (1998) analyzes Arthur Burns period as Chairman of the Fed Reserve from 1970 to 1977. He was opposed to inflation, but could not control it effectively and monetary policy was expansionary. He maintained the ideology that the government should control the economy through activist monetary and fiscal policy, with an eye on the unemployment rate. He was accredited to have a credit view regarding monetary policy, whilst having a non-monetary view of inflation. In other words, he was of the opinion that inflation could arise from sources differ-ent than merely money supply. He claimed that corporations and labor unions exercising their monopoly power caused the high inflation of the early 1970s, reflecting in both higher wages and higher mark-ups. On top of that, he was of the opinion that monetary policy affected the business cycle mostly through psychological channels. Changing the interest rate was supposed to have an effect on the psychology of businessmen. As a result, Burns focused on the velocity of money rather than the growth rate, as he deemed velocity to be a proxy for confidence. Con-sequently, he was unwilling to increase interest rates substantially during periods of economic recovery, going against the notion of the Taylor Rule.

Burns conducted monetary policy on the assumption that the price level is a non-monetary phe-nomenon. The Congress and the administration, public opinion, and most of the economics profession supported that policy. It has been argued that this is a cause of the Great Inflation. Eventually this led to the realization that inflation should indeed be the main responsibility of central banks.

As can be derived from the above-mentioned section, various descriptions have been put for-ward to explain and try to rationalize the pre-Volcker period of high and volatile inflation, where

(10)

the main explanations are indeterminacy and sub-optimally conducted monetary policies, po-tentially caused by the notion that Arthur Burns had an alternative explanation for inflation, now commonly refuted. The results of the pre-Volcker period’s policies not being optimal, are put into question by Kriwoluzky and Stoltenberg (2015), who argue that the passive monetary policy executed during the pre-Volcker era may in fact have been optimal due to the transaction role of money.

The existing literature presented in this section simultaneously sheds light on the general ideas regarding the disparity between the actual monetary policy conducted during the pre-Volcker era and what would have been optimal from a welfare perspective. However, as can easily be observed from the large spectrum of often opposing views, the study of this period requires further analysis to draw out inferences. The most compelling framework is proposed by Kri-woluzky and Stoltenberg (2015), which is why I take their model as the starting point of my analysis. I will contribute to the aforementioned discussion by computing and analyzing the optimal monetary policy during the pre-Volcker era using different solution concepts. Subse-quently I will compare my findings to the estimated monetary policy rule in Kriwoluzky and Stoltenberg (2015) to analyze the extent to which the conducted policies during the pre-Volcker era were in fact optimal.

3 Economic Environment

In this section I will elaborate on the basics of the model I use. I use the model proposed by Kriwoluzky and Stoltenberg (2015), a relatively standard New Keynesian macroeconomic DSGE model with the main contribution being a transaction friction. In this model, agents face a transaction cost when making consumption purchases, and holding money mitigates this friction. On the downside, holding money means forgoing interest. This is the opportunity cost of holding money, and agents will balance out the effects of the two above mentioned mecha-nisms.

In the considered economy, every household lives infinitely long and has identical initial asset endowments and preferences. Households are indexed by j ∈ [0, 1]. They are assumed to sup-ply labor services lj ∈ [0, 1] and are monopolistic in nature.

The budget of household j, at the beginning of the period t, comprises of a random payment Xjt, generated from a portfolio of state-contingent claims on other households and one-period

nominally non-state-contingent government bonds Bjt−1 carried over from the previous

pe-riod. The random payment is priced by Et(qt,t+1Xjt+1), ct denotes a Dixit–Stiglitz aggregate

of consumption with elasticity of substitution ς, and Mjt end-of-period nominal balances.

(11)

3 Economic Environment

τta lump-sum tax, Rtthe gross nominal interest rate on government bonds and Djitdividends

from monopolistically competitive firms indexed by i.

The following expression shows the households’ financial wealth

Mjt+ Bjt+ E(qt,t+1Xjt+1) + Ptcjt+ Ptφ(cjt, ztMjt−1/Pt)

≤ Mjt−1+ Rt−1Bjt−1+ Xjt+ Ptwjtljt+

Z 1

0

Djitdi − Ptτt (1)

Kriwoluzky and Stoltenberg (2015) assume that real resource costs of transactions are captured by φ(cjt, hjt) ≥ 0 with hjt = ztMjt−1/Pt as the effective real money balances. Additionally,

they assume that purchasing consumption goods is costly and that transaction costs increase in consumption, decrease strictly in real money balances, marginal resource gains of holding money are strictly decreasing, marginal transaction costs of consumption are non-increasing in real money balances and non-decreasing in consumption.

The objective of household j is given by:

Et0

∞

X

t=t0

βt[u(cjt, νt) − υ(ljt)] (2)

where β ∈ (0, 1) represents the subjective discount factor. The utility function is strictly in-creasing in consumption, strictly dein-creasing in labor time, strictly concave, twice differentiable. The taste shock νt has a mean of 1. At the deterministic steady state, uc is set equal to ucν.

Households are subject to a borrowing constraint that prevents them from engaging in Ponzi schemes and they are wage setters. They supply differentiated types of labour ljt, which is

transfigures into aggregate labour lt.

The final consumption good ytis an aggregate of differentiated goods produced by

monopolisti-cally competitive firms indexed i ∈ [0, 1]. Kriwoluzky and Stoltenberg (2015) denote the price of good i set by firm i as Pit. The productivity shock a has a mean of 1. Additionally, the labour

demand satisfies the condition ψit = wt/atwhere ψit = ψtrepresents the real marginal costs

independent of the quantity that is produced by the firm. Kriwoluzky and Stoltenberg (2015) follow Calvo (1983) and allow for a nominal rigidity in the form of a staggered price setting. A fraction α ∈ [0, 1) of firms is assumed to adjust prices according to the rule Pit = ¯πPit−1

where ¯π denotes the average inflation rate. Furthermore, in each period, firms may reset their prices with probability 1 − α independent of time.

(12)

feedback rule contingent on inflation

ˆ

Rt= ρππˆt+ t; (3)

Furthermore, Mt−1+ Rt−1Bt−1+ Ptgt= Mt+ Bt+ Ptτtis the government budget constraint.

The exogenous government expenditures gtare restricted to be a constant steady state output,

¯

g = ¯y(1 − sC), where ¯g is the mean of gt and sC ∈ (0, 1] denotes the average output share

of private consumption. Kriwoluzky and Stoltenberg (2015) also assume that tax policy τt

guarantees government solvency.

Subsequently, the model specifies the aggregate resource constraint as

yt=

atlt

∆t

(4)

where ∆t gives the price dispersion in the model. Lastly, it is necessary for goods market

clearing that

ct+ gt+ φ(ct, ht) = yt (5)

For a competitive equilibrium, it is firstly required that households maximize their utility sub-ject to their budget constraint. Secondly, firms are assumed to maximize profits taken input prices as given. It then needs to be the case that the aggregate resource constraint and the goods market clearing equation are satisfied, and lastly the transversality condition has to hold.

3.1 Log-Linearized Equations

For the purpose of analyzing the model, I follow the log-linear approximations to the non-linear equations and analyze the equilibrium properties in the neighborhood of a deterministic steady state as postulated in Kriwoluzky and Stoltenberg (2015).

Maximizing (2) with respect to (1) leads to the conditions that describe the households op-timal behavior and the households’ opop-timal choices for consumption, labour and real money balances.

Combining the private sector behavior with the aggregate resource constraint and goods mar-ket clearing we get a set of equilibrium sequences for consumption, output, inflation, interest, wages and real money balances. They must satisfy the following equations:

˜

σEtˆct+1− Etνˆt+1− ηch( ˆmt− Etπˆt+1+ Eˆzt+1) = ˜σˆct− ˆνt− ηch( ˆmt−1− ˆπt+ ˆzt) + ˆRt− Etπˆt+1

(6)

(13)

3 Economic Environment ˆ πt = βEtπˆt+1+ κ( ˆwt− ˆat) (8) ˆ mt= −ηRRˆt+ ηch σhE tˆct+1+ Etπˆt+1+ 1 − σh σh E tzˆt+1 (9) ˆ yt= 1 −g y − φ y + ηc ˆ ct+ ˆgt− ηh( ˆmt−1− ˆπt+ ˆzt) (10)

where σc = −uccc/uc, ω = νlll/νl, κ = (1 − α)(1 − αβ)/α, ηch = −φchh/(1 + φc), ηhc ≡

φhcc/φh, ηR = R/σh(R − 1), σh = −φhhh/φh, ηcc = φccc/(1 + φc) and ˜σ = σc+ ηcc.

The model of Kriwoluzky and Stoltenberg (2015) is closed by a simple Taylor rule:

ˆ

Rt= ρππˆt+ mt (11)

with ρπ ≡ fπ(π, 1)π/R. In this paper, I compare this estimated rule to an optimal rule, in

which case this equation will be replaced.

The definitions of the variables follow Kriwoluzky and Stoltenberg (2015). Any ’hat’ indicates that the variable in question is defined as the deviation from its steady state value. First of all, rt

is the real interest rate, defined as the nominal interest rate minus inflation. Secondly, ctgives

the household consumption and mtis defined as money holdings by the household. wt is the

wage rate agents receive from providing labor services, and Rt is the nominal interest rate set

by the central bank. Equation (6) is the money demand equation where real money balances react negatively to changes in the nominal interest rate and positively to changes in expected consumption and inflation.

Additionally, real marginal transaction costs φcinfluences both the intra-temporal and the

inter-temporal optimal consumption choices and mt= Mt/Pt. The cross derivative ηchcaptures the

transaction frictions and importance of money.

3.2 Optimal Monetary Policy

Before continuing to my main analysis, I will first shed light on the different solution methods that I use in my examination of optimal monetary policy during the pre-Volcker era. In this section I first elaborate on the Taylor rule, after which I give a description of the two solution mechanisms I use to compute optimal policies in the subsequent part of my paper, namely the Ramsey Policy and the Optimal Simple Rule (OSR).

(14)

the nominal interest rate in response to changes in inflation and output. In particular, the Taylor principle states that for every one-percent increase in inflation, the central bank should raise the nominal interest rate by more than one percentage point.

The optimal policy framework is flexible because the implied interest rate rule contains a larger set of variables than the simple instrument rule (Taylor rule) but it also comes at a cost of introducing new restrictions.

Optimal monetary policy can be computed in two ways through Dynare. One being the Ramsey policy i.e. optimal rule under commitment, the second one being the optimal simple rule (OSR). The policy maker tries to define the best policy rule to maximize their objective function.

3.2.1 Ramsey Policy

Ramsey policy assumes that monetary policy is conducted optimally, i.e. the central bank chooses the interest rate that minimizes the inter-temporal loss function. This allows the cen-tral bank to make efficient use of all information. It is a convenient benchmark for welfare analysis of economic models. Ramsey policy is the optimal policy under commitment. It is a time inconsistent policy and is only valid if the policy maker can commit to never re–optimizing in the future.

In Dynare, the Ramsey model computes the first order conditions for maximizing the policy-maker’s objective function subject to the constraints provided by the equilibrium path of the economy. The planner objective command performs perfect foresight simulation but does not perform any computations. The command computes the first order approximation of the policy that maximizes the policymaker’s objective function with respect to the constraints provided by the equilibrium path of the economy.

For the Ramsey process you specify the one-period objective. The discount factor is given by the planner discount option of ramsey policy. The planner’s objective represents the welfare of the economy. The objective function contains the current endogenous variables. Ramsey policy lets you give any arbitrary nonlinear expression. The loss function that I employ in this paper is not derived but taken from Paustian and Stoltenberg (2008). It is reasonable to employ this for the model under consideration because it is shown in Woodford (2003) that similar loss functions apply to a broad range of models that incorporate transaction frictions. The loss function is given by the following equation:

Ut0 = −ΩEt0 ∞ X t=t0 βt−t0_[λ xyˆ2+ ˆπ2t + λRRˆ2t] + t.i.s.p + O(k·k 3₎ ₍₁₂₎

(15)

3 Economic Environment

where t.i.s.p indicate terms independent of stabilization policy, O(k·k3) terms of order higher than 2, κ = (1 − α)(1 − αβ)(ω + σ)/α and Ω = ucyθ(ω + σ)/(2κ). From equation (12) it can

be seen that the weights given to output gap, inflation and the nominal interest rate are given by λx, 1 and λR, where λx and λRare defined as follows:

λx = κ θ (13) λR = ηRλx v(ω + σ) (14)

where v = y/m > 0 and ηRis the interest elasticity of money demand at the steady state. The

numerical values are given by λx ≈ 0.2273 and λR ≈ 0.1671.

3.2.2 Optimal Simple Rules

Optimal simple rule (OSR) is a simple policy rule specified as part of the model and numer-ical optimization in Dynare is done to determine the optimal value of its coefficients. In this approach, the policy feedback rule is specified as part of the model. The problem is to find the optimal value of the parameters of the policy rules for a given objective function. Dynare implements the objective function taking the form of a loss function that is a weighted sum of unconditional variance of some endogenous variables (see equation 12). The optimal values of the parameters of the policy rule are found by a numerical optimizer. In this paper, I use the following simple rule:

ˆ

Rt = ρππˆt (15)

where ρπ is the parameter to be optimized. When the OSR command is run, the simple rule is

set to its optimal value so that subsequent runs of stoch simul will be conducted at these values.

3.2.3 Comparison Between Optimal Simple Rule and Ramsey Policy

Theoretically, the most interesting part of comparing Optimal Simple Rule and Ramsey is the resulting welfare under both policies. However, there are technical difficulties that do not allow a simple procedure to do so. The problem boils down to the following. When Dynare runs the Ramsey policy, the resulting ’planner objective value’ is the discounted sum of the future squared deviations from the mean, whereas the resulting ’objective function’ after having run the OSR program is the expectancy of the squared deviations. These two are not identical, and there exists no simple procedure to exactly convert one into the other.

To be able to compare the policies to some degree I employ a trick that boils down to the fol-lowing. The OSR program tries to minimize the weighted variance of the specified endogenous variables. Given that Dynare stores the variances in ’oo .var’, this allows for manually

(16)

comput-ing the optimal value for the objective function, which I verify first. Given that these variances are also stated when running the Ramsey policy in Dynare, we can construct the corresponding value through this procedure.

Ramsey optimal policy provides a convenient way to perform a welfare analysis in economic models. However, it may be the case that the instruments used to implement the policy are not available to the policy maker. Therefore, I primarily focus on simple and implementable rules that come close to the welfare outcomes implied by Ramsey Policy. I will evaluate the validity of this approach this later on.

In terms of maximizing agents’ welfare, Ramsey optimal policy is preferable over simple rules because a Ramsey policy is constructed in such a manner that it react to all endogenous vari-ables, whereas simple rules only react to several observable variables. One reason I will focus on the OSR regime nevertheless is that it is usually hard to find closed solutions for Ramsey, which makes the practical applicability rather limited.

(17)

4 Quantitative Results

3.3 Calibration

Name Notation Value

Discount factor β 0.99

Average output share of private consumption sc 0.8

Coefficient of relative risk aversion σ˜ 1

Frisch elasticity ω 3.5

Steady state nominal interest rate Rss 1.0146

Transaction friction proxy ηch 0.3

Output elasticity of real money balances σh 3.5

Cross derivative of real money balances and consumption ηhc 2.8

Calvo pricing coefficient α 0.3304 Coefficient of relative risk aversion σc 0.8

AR1 coefficient productivity ρa 0.5

AR1 coefficient inflation ρπ 0.85

AR1 coefficient government spending ρg 0.5

AR1 coefficient wage mark-up ρµ 0.5

AR1 coefficient taste shock ρv 0.5

AR1 coefficient transaction cost shock ρz 0.5

Demand elasticity of real money balances ηh 0.0284

Demand elasticity of consumption ηc 0.2649

Standard deviation productivity shocks σa 1

Standard deviation government spending shocks σg 1

Standard deviation wage mark-up shocks σµ 1

Standard deviation taste shocks σv 1

Standard deviation transaction cost shocks σz 1

Standard deviation monetary policy shocks σm 1

Real resource cost of transactions φ 0.5

Income velocity v 6

Theta θ 6

Table 1: Variables and corresponding values

4 Quantitative Results

In this section I will illuminate the workings of the model by analyzing impulse response graphs after one standard deviation innovations in various variables. In Kriwoluzky and Stoltenberg (2015) the central bank uses a Taylor-like rule for its conduct of monetary policy where the

(18)

parameters are estimated using U.S. data. These results will be compared with the computa-tionally optimized simple monetary policy rule as postulated in equation (15).

As described before, I utilize Dynare to compute the optimal parameter ρπ. This section will

show impulse response graphs with the estimated model from Kriwoluzky and Stoltenberg (2015), and the optimal responses where the central bank uses an optimized simple monetary policy rule. Subsequently, I will compare the two aforementioned methods, i.e. Ramsey policy and OSR, to compute an optimal policy in the setting of the proposed model to extend the anal-ysis further and to unveil the discrepancy between an optimal simple rule and a central bank facing the freedom to set monetary policy in an optimal manner without following a prescribed function, which is the case for the Ramsey policy.

So the first step is to compare the estimated monetary policy of the pre-Volcker era to the optimal one as a response to a variety of shocks. Here, optimal monetary policy should be interpreted with a hint of caution, as it only deals with an optimal simple rule, rather than a full-fledged optimal path followed by the Fed. However, intuitively it seems more reasonable that a central bank follows a relatively simple rule that it tries to optimize, which is why the specification in this section provides insightful results. After having run both programs, the main difference boils down to the parameter ρπ, i.e. the sensitivity of the nominal interest rate

to changes in inflation. Kriwoluzky and Stoltenberg (2015) use a value of 0.85. The coefficients and the resulting losses can be found in table 2.

Policy Coefficient Loss Estimated pre-Volcker 0.85 5.838

Optimal Simple Rule 0.401 1.202 Ramsey Policy 0.838

Table 2: Coefficients and losses resulting from policies

4.1 Innovation in Government Expenditures

I will start the analysis with a one standard deviation innovation in government expenditures, ˆ

gt, for which the results can be found in figure 1. On impact, private consumption is crowded

out by the increase in government expenditures, and it can readily be seen that the initial de-cline is nearly identical for both policies. When consumption decreases, the marginal utility of consumption goes up, inducing agents to work more. Hence, the labor supply will increase. This in turn reflects in a higher output, which already faced a positive impulse due to the in-crease in government expenditures. It is evident that consumption growth needs to be positive for it to return to its steady state value. The prescribed boost in consumption is only possible if the real interest rate increases, following equation (11). This effect can indeed be seen from

(19)

Figure 1: Impulse responses to a one st. dev. innovation in government expenditures with the estimated pre-Volcker policy (black) and the optimal simple rule (red-dashed)

the impulse response graph. From the impulse responses, it can also be observed that a passive interest rate is the optimal policy for the central bank in this setting. This results from the fact that the increase in the real interest rate is caused by the nominal interest rate being lowered less than the fall in inflation, which is the defining characteristic of a passive monetary policy. This corroborates the finding in Kriwoluzky and Stoltenberg (2015) that a passive interest rule was optimal during the pre-Volcker era.

The main difference between the estimated response compared to the optimal response appears in the nominal interest rate graph. In the estimated version, the nominal interest rate is lowered substantially more than if the central bank had followed an optimal simple rule. This in turn leads to a slower convergence of both output and inflation to their steady state values and furthermore corresponds to the notion that the Fed did not respond sufficiently strongly to macroeconomic changes during the pre-Volcker era.

4.2 Productivity Shock

The second shock I will analyze here is a shock in productivity, ˆat. The impulse response

(20)

Figure 2: Impulse responses to a one st. dev. innovation in productivity with the estimtaed pre-Volcker policy (black) and the optimal simple rule (red-dashed)

to be substantially different compared to an innovation in government expenditures. First of all, it can be seen that there is an increase in consumption on impact. This can be explained by the notion that the shock in productivity leads to an increased marginal product of labor and thus a higher wage, making more resources available for consumption. To steer consumption back to the steady state, a negative real interest rate is required following the Euler equation of consumption. The higher output also serves as a push on inflation, which is countered by the central bank by increasing the nominal interest rate. Again, the passive interest policy can be seen in the notion that this increase is less than one-to-one. The higher interest rate increases the opportunity cost of holding money, which reflects in a lower money demand. This is some what surprising as consumption purchases increase substantially, exacerbating the transaction friction, but it appears that the effect of increased opportunity costs trumps the consumption effect.

Comparable to the innovation in government spending, the productivity shock also triggers a too strong reaction from the central bank under the estimated pre-Volcker policy. In response to the higher productivity, the nominal interest rate is raised by more than twice as much as what should have been done if the central bank had followed an optimal strategy. This results in a smaller initial decrease in the real interest rate, but a slower convergence back to the steady state level. This also explains the persistent inflation, still far from its long run equilibrium after

(21)

40 quarters.

4.3 Transaction Cost Technology Shock

Thirdly I will look at the dynamics of a shock in the transaction cost technology ˆzt. Here a

care-ful analysis of the model is required to interpret the impulse response graphs. The transaction cost technology zteffectively boils down to a shock to real money balances, defined as

hjt = ztMjt−1/Pt

Furthermore it is given that the transaction friction φ(cjt, hjt) decrease strictly in effective real

money balances hjt. Hence, a positive shock to ztleads to higher effective real money balances

and lower transaction cost, culminating in the impulse response graphs exhibited in figure 3.

Figure 3: Impulse responses to a one st. dev. innovation in the transaction cost technology with the estimated pre-Volcker policy (black) and the optimal simple rule (red-dashed)

After the one standard deviation shock to the transaction cost technology occurs, consumption increases. This can be explained by the notion that more resources will be available due to the lower transaction costs. This in turn pushes output in the same direction. The policy response of the central bank is to lower the nominal interest rate as inflation is below the steady state

(22)

value, caused by the decrease in production costs. As before, the monetary policy conducted by the Fed is too accomodative in the sense that it does not fight the dip in inflation sufficiently strongly, leading to a relatively persistent off-steady-state path of inflation. This is also reflected in the comparatively minor increase in the real interest rate when measured against the optimal simple rule response. In spite of the fact that transaction costs have decreased, the demand for money still increases. This is due to the higher consumption spending by households. Similar as with the previous two analyses of shocks, a positive impulse response of consumption requires the real interest rate to be above steady state value to ensure that consumption moves back to its steady state value, and symmetrical to the prior analyses, the passive interest rate policy leading up to this can be observed from the graphs, as the nominal interest rate declines less than inflation.

4.4 Cost-Push Shock

As a last illustration of the differences between the estimated policy and the optimal policy, I will analyze the responses to a cost-push shock, expressed as a shock in the wage markup ˆµt.

Figure 4: Impulse responses to a one st. dev. cost push shock with the estimated pre-Volcker policy (black) and the optimal simple rule (red-dashed)

(23)

but certain patterns can be unveiled nevertheless. Oddly enough, inflation falls after the cost push shock. This may be due to the fall in output and consumption at impact. When a wage mark-up shock hits, the real wage declines, which in turn reduces consumption and output, as workers are less inclined to supply labor. If the resulting effect on inflation is stronger than that of the initial shock, inflation can indeed fall after a cost-push shock, which appears to be the case under both policy regimes. The initial dip in consumption is reversed through an increased real interest rate. The central bank achieves this through lowering the nominal interest rate by less than the inflation rate, as required by a passive monetary policy regime. So again it can be seen that the policy conducted during the pre-Volcker era was not optimal, but the fact that it was passive does correspond to what the optimal simple rule prescribes. Similar as before, the central bank’s reaction was too strong and the result is a slow convergence of the inflation rate back to its steady state value compared to what would have been optimal.

To conclude the comparison between the estimated pre-Volcker policy and the policy given by the optimal simple rule (15), a few notable results can be derived. Firstly and most im-portantly, there appears to be a substantial discrepancy between the two regimes, indicating that the central bank did not pursue an optimal policy, corroborating the results of i.e. Lubik and Schorfheide (2004); Clarida et al. (2000); Orphanides (2004). However, it turns out that the optimal policy is passive when money plays an important role in facilitating transactions, which is also found by Kriwoluzky and Stoltenberg (2015). In general, it can be said that the Fed was too accommodating of inflation, which serves as a likely cause of the Great Inflation. Following such a policy, the economy, output and inflation in particular, take a long time to go back to their steady state values, and often even after 40 quarters the differences are still substantial. This contrasts sharply by what the optimal simple rule dictates.

To have a more quantitative comparison, the trick used in section 3.2.3 to convert the loss of the Ramsey policy to the loss of the OSR can also be applied here. In other words, the variances of the variables that feature in the loss function can be retrieved from the program running the estimated policy, after which the analogous loss can be computed. There could be one poten-tial problem being, that both the policies were computed under different loss functions. This procedure is flawed in the sense that the central bank did not try to minimize the same function in the estimated model, so the results have to be interpreted with a hint of caution, but it is still insightful to examine them. As it turns out, the calculated loss is substantially higher for the estimated model as can be seen in table 2. The value the objective takes after conversion is 5.8378, whereas it is 1.2023 for OSR. So, all in all, it turns out that the pre-Volcker policy was certainly suboptimal, also when looking at a more objective measure.

(24)

4.5 Ramsey Policy Versus Optimal Simple Rule

To shed more light on the applicability and optimality of the Optimal Simple Rule, I will now compare the Optimal Simple Rule to the optimal policy under commitment, which gives the central bank more freedom to execute the exact policy that is optimal, rather than having to follow a pre-specified function for which the parameters are optimized. Following the method for comparing the values of the objective function under both regimes as described in section 3.2.3, the notion that a Ramsey policy leads to a lower loss than the optimal simple rule can be verified. Indeed, it turns out that the the objective function following OSR, with a value of 1.2023, is higher than the Ramsey policy objective, which takes a value of 0.8382 when con-verted (see table 2). The following impulse reponse graphs after an innovation in government expenditures pinpoint the differences between both regimes.

Figure 5: Impulse responses to a one st. dev. innovation in government expenditures with the Ramsey policy (black) and the optimal simple rule (red-dashed)

The economic interpretation of the impulse responses after a shock in government expenditures is given in section 4.1, so here I will solely focus on the differences between the Ramsey policy and Optimal Simple Rule. As can be seen from figure 5, the two regimes give highly similar results, both qualitatively and quantitatively. The most important distinction can be found in the nominal interest rate response. The Optimal Simple Rule regime imposes a stronger de-cline in the nominal interest rate, which leads to slightly higher inflation and output, combined

(25)

5 Conclusion

with slower convergence to the steady state. Money holdings is the variable that exhibits the strongest reaction, and the difference is caused by differences the interest rate response. The lower interest rate under Optimal Simple Rule lowers the opportunity cost of holding money, which evidently causes households to increase their money holdings. This effect is less stark for the Ramsey policy. However, all in all it is most relevant to see that both policies give highly comparable results, further justifying the use of an optimal simple rule to model the behavior of the central bank.

5 Conclusion

In their paper, Kriwoluzky and Stoltenberg (2015) prove that interest rate policy before Volcker was passive, but still ensured determinacy because money played an important role in facili-tating transactions. They also prove that consistent with Clarida et al. (2000) and Lubik and Schorfheide (2004), an active interest rate policy ensured determinacy in the United States after 1982, when money no longer played an important role. I compared the estimated pre-Volcker policy from Kriwoluzky and Stoltenberg (2015) to an optimal simple rule computed through Dynare. Subsequently I conducted a welfare analysis comparing the estimated policy, the OSR and the Ramsey policy.

I compare the results of an Optimal Simple Rule with a Ramsey policy and look at the op-timized values of the loss functions obtained from both the methods and analyze the results. Further, I examine the relationship between monetary policy, price stability, interest rate pol-icy and the transactional role of money by using the model and the parameter estimates from Kriwoluzky and Stoltenberg (2015). I find that passive interest rate policy was optimal because of the transaction role of money, but the estimated interest rate policy was far from optimal, resulting in a notable welfare loss.

It can be seen from the analysis of the impulse response graphs after one standard deviation in-terventions in government expenditures, productivity, cost push shock and transaction frictions that it is optimal for the central bank to execute a passive monetary policy for the analyzed pe-riod. This can be seen from the fact that the nominal interest rate changes less than one-to-one for changes in inflation. I find that the pre-Volcker policy was suboptimal and the central bank did not pursue an optimal policy since the calculated loss is higher for the estimated model.

I also look at the objective functions and verify that Ramsey policy leads to a lower loss than the optimal simple rule. There are some distinctions between the policies such as the response to nominal interest rate but, all in all, both policies give highly comparable results, which further justifies the use of an optimal simple rule to model the behavior of the central bank.

(26)

References

Benhabib, J., Schmitt-Grohe, S. and Uribe, M. (2001), ‘Monetary policy and multiple equilib-ria’, American Economic Review 91(1), 167–185.

Bilbiie, F. O. and Straub, R. (2013), ‘Asset market participation, monetary policy rules, and the great inflation’, Review of Economics and Statistics 95(2), 377–393.

Boivin, J. (2006), ‘Has u.s. monetary policy changed? evidence from drifiting coefficients and real-time data’, Journal of Money, Credit and Banking 38(5), 1149–1174.

Calvo, G. A. (1983), ‘Staggered price setting in a utility-maximizing framework’, Journal of Monetary Economics12(3), 383–398.

Castelnuovo, E. (2012), ‘Estimating the evolution of money’s role in the u.s. monetary business cycle.’, Journal of Money, Credit and Banking 44(1), 23–52.

Clarida, R., Gali, J. and Gertler, M. (2000), ‘Monetary policy rules and macroeconomic stabil-ity: Evidence and some theory’, Quarterly Journal of Economics 115(1), 147–180.

Coibion, O. and Gorodnichenko, Y. (2011), ‘Monetary policy, trend inflation and the great moderation: An alternative explanation’, American Economic Review 101(1), 341–370.

Daniels, K. N. and Murphy, N. B. (1994), ‘The impact of technological change on the currency behavior of households: An empirical cross-section study’, Journal of Money, Credit and Banking26(4), 867–874.

Dennis, R. (2001), ‘The policy preferences of the u.s. federal reserve’. Federal Reserve Bank of San Fransisco, Working Paper No. 2001-08.

Favero, C. A. Monacelli, T. (2005), ‘Fiscal policy rules and regime (in)stability: evidence from the u.s. manuscript’. IGIER Working Paper No. 282.

Hetzel, R. L. (1998), ‘Arthur burns and inflation’, FRB Richmond Economic Quarterly 84(1), 21–44.

Humphrey, D. B. (2004), ‘Replacement of cash by cards in u.s. consumer payents’, Journal of Economics and Business56(3), 221–225.

Ireland, P. N. (2004), ‘Money’s role in the monetary business cycle’, Journal of Money, Credit and Banking36, 969–983.

Ireland, P. N. (2009), ‘On the welfare cost of inflation and the recent behavior of money de-mand’, American Economic Review 56(3), 211–225.

Kriwoluzky, A. and Stoltenberg, C. A. (2015), ‘Monetary policy and the transaction role of money in the u.s.’, The Economic Journal 125, 1452–1473.

(27)

References

Lubik, T. A. and Schorfheide, F. (2004), ‘Testing for indeterminacy: An application to u.s. monetary policy’, American Economic Review 94(1), 190–217.

Ludvigson, S., Steindel, C. and Lettau, M. (2002), ‘Monetary policy transmissions through the consumption-wealth channel’, Federal Reserve Bank New York Economic Policy Review 8(1), 117–133.

Orphanides, A. (2004), ‘Monetary policy rules, macroeconomic stability and inflation: A view from the trenches’, Journal of Money, Credit and Banking 36(2), 151–175.

Paustian, M. and Stoltenberg, C. A. (2008), ‘Optimal interest rate stabilization in a basic sticky-price model’, Journal of Economic Dynamics and Control 32, 3166–3191.

Schreft, S. L. and Smith, B. D. (2000), ‘The evolution of cash transactions: Some implications for monetary policy’, Journal of Monetary Economics 46(1), 97–120.

Sims, C. (1999), Drifts and breaks in monetary policy, Unpublished manuscript. Department of Economics, Princeton University.

Sims, C. and Zha, T. (2004), Were there regime switches in U.S. monetary policy?, Unpublished manuscript. Department of Economics, Princeton University/Research Department, Federal Reserve Bank of Atlanta.

Stoltenberg, C. A. (2012), ‘Real balance effects, timing and equilibrium determination’, Jour-nal of Money, Credit and Banking44(5), 981–994.

Woodford, M. (2003), Interest and prices: Foundations of a theory of monetary policy, Prince-ton University Press.

(28)

A

Appendix

A.1 Estimated Interest Policy

clc;

%************************************************************************** % MODEL

% DEFINITION OF ALL THE VARIABLES % l labour services

% h real money balances % c consumption

% m real money balances

% y output/final consumption good % pi inflation

% w real wage rate

% z transaction cost technology % a productivity shock

% g government expenditures

% R gross nominal interest rate on government bonds % phi(func) captures real resource costs of transaction % beta discount factor

% sigma_tilda coefficient of relative risk aversion % rho_pi interest rate policy

%************************************************************************** % Endogenous variables:

var r_m r_hat c_hat v_hat m_hat y_hat pi_hat w_hat z_hat a_hat mu_hat g_hat R_hat;

% Exogenous variables:

varexo epsilon e_a e_g e_mu e_v e_z e_rm ;

% Parameters:

parameters eta_R R_ss eta_h eta_c s_c kappa phi sigma_r_m sigma_m sigma_a sigma_g sigma_mu sigma_v sigma_z rho_a rho_g rho_mu rho_v rho_z beta omega sigma_tilda rho_pi eta_ch sigma_c sigma_h eta_hc alpha;

%************************************************************************** %INITIALISATION

(29)

A Appendix beta = 0.99; s_c=0.8; sigma_tilda = 1; omega = 3.5; R_ss = 1.0146; eta_ch = 0.3; sigma_h = 3.5; eta_hc = 2.8; alpha = 0.3304; sigma_c = 0.8; rho_pi = 0.85; rho_a = 0.5; rho_g = 0.5; rho_mu = 0.5; rho_v = 0.5; rho_z = 0.5; eta_h = 0.0284; eta_c = 0.2649; sigma_a = 1; sigma_g = 1; sigma_mu = 1; sigma_v = 1; sigma_z = 1; sigma_m = 1; sigma_r_m = 1; phi = 0.5; kappa=((1-alpha)*(1-alpha*beta))/alpha; eta_R=R_ss/(sigma_h*(R_ss-1)); %************************************************************************** %************************************************************************** % The Model: model(linear);

a_hat = rho_a*a_hat(-1) + e_a; g_hat = rho_g*g_hat(-1) + e_g; mu_hat = rho_mu*mu_hat(-1) + e_mu; v_hat = rho_v*v_hat(-1) + e_v; z_hat = rho_z*z_hat(-1) + e_z; log(r_m) = e_rm;

(30)

c_hat(+1) = (v_hat(+1)+(eta_ch*(m_hat-pi_hat(+1)+z_hat(+1)))+ sigma_tilda*c_hat-v_hat-eta_ch*(m_hat(-1)-pi_hat+z_hat)+R_hat -pi_hat(+1))*sigma_tilda; w_hat = omega*(y_hat-a_hat)-v_hat+sigma_tilda*c_hat-eta_ch*(m_hat(-1) -pi_hat+z_hat)+mu_hat; pi_hat = beta*pi_hat(+1)+kappa*(w_hat-a_hat); y_hat = s_c*c_hat + g_hat;

m_hat = -eta_R*R_hat+(eta_hc/sigma_h)*c_hat(+1)+pi_hat(+1)+((1-sigma_h) /sigma_h)*z_hat(+1); R_hat = rho_pi*pi_hat+epsilon; %(ˆm) end; %************************************************************************** shocks;

var e_a = sigma_aˆ2; var e_g = sigma_gˆ2; var e_mu = sigma_muˆ2; var e_v = sigma_vˆ2; var e_z = sigma_zˆ2; var e_rm = sigma_r_mˆ2;

%var epsilon = sigma_mˆ2;

end; %************************************************************************** initval; a_hat = 0.5; g_hat = 0.5; mu_hat = 0.5; v_hat = 0.5; z_hat = 0.5; %r_m = 0.5; end; %**************************************************************************

stoch_simul c_hat y_hat pi_hat m_hat R_hat r_hat; check;

(31)

A Appendix

A.2 Ramsey Policy

clc;

%************************************************************************** % MODEL

% h real money balances % v taste shock

% c consumption

% w real wage rate

% z transaction cost technology % a productivity shock

% g government expenditures

% n_ch transaction frictions

var r_hat c_hat v_hat m_hat y_hat pi_hat w_hat z_hat a_hat mu_hat g_hat R_hat;

% Parameters:

parameters eta_R R_ss eta_h eta_c s_c kappa phi sigma_m sigma_a

sigma_g sigma_mu sigma_v sigma_z rho_a rho_g rho_mu rho_v rho_z beta omega sigma_tilda rho_pi eta_ch sigma_c sigma_h eta_hc alpha lambda_x lambda_R v_p theta;

%************************************************************************** %INITIALISATION

(32)

theta = 6; v_p = 6; beta = 0.99; s_c = 0.8; sigma_tilda = 1; omega = 3.5; R_ss = 1.0146; eta_ch = 0.3; sigma_h = 3.5; eta_hc = 2.8; alpha = 0.3304; sigma_c = 0.8; rho_pi = 0.85; rho_a = 0.5; rho_g = 0.5; rho_mu = 0.5; rho_v = 0.5; rho_z = 0.5; eta_h = 0.0284; eta_c = 0.2649; sigma_a = 1; sigma_g = 1; sigma_mu = 1; sigma_v = 1; sigma_z = 1; sigma_m = 1; phi = 0.5; kappa = ((1-alpha)*(1-alpha*beta))/alpha; eta_R = R_ss/(sigma_h*(R_ss-1)); lambda_x = kappa/theta; lambda_R = (eta_R*lambda_x/(sigma_tilda+omega))*(1/v_p); %************************************************************************** %************************************************************************** % The Model: model(linear);

a_hat = rho_a*a_hat(-1) + e_a; g_hat = rho_g*g_hat(-1) + e_g; mu_hat = rho_mu*mu_hat(-1) + e_mu; v_hat = rho_v*v_hat(-1) + e_v; z_hat = rho_z*z_hat(-1) + e_z;

(33)

A Appendix r_hat = R_hat-pi_hat(+1); c_hat(+1) = (v_hat(+1)+(eta_ch*(m_hat-pi_hat(+1)+z_hat(+1)))+ sigma_tilda*c_hat-v_hat-eta_ch*(m_hat(-1)-pi_hat+z_hat)+ R_hat-pi_hat(+1))*sigma_tilda; w_hat = omega*(y_hat-a_hat)-v_hat+sigma_tilda*c_hat-eta_ch*(m_hat(-1)-pi_hat+z_hat)+mu_hat; pi_hat = beta*pi_hat(+1)+kappa*(w_hat-a_hat); y_hat = (0.8+eta_c)*c_hat+g_hat-eta_h*(m_hat(-1)-pi_hat+z_hat); %1-(g/y)-(phi/y)=0.8 m_hat = -eta_R*R_hat+(eta_hc/sigma_h)*c_hat(+1)+pi_hat(+1)+ ((1-sigma_h)/sigma_h)*z_hat(+1); %R_hat = rho_pi*pi_hat+epsilon; %(ˆm) end; %************************************************************************** shocks;

var e_a = sigma_aˆ2; var e_g = sigma_gˆ2; var e_mu = sigma_muˆ2; var e_v = sigma_vˆ2; var e_z = sigma_zˆ2;

end; %************************************************************************** initval; a_hat = 0.5; g_hat = 0.5; mu_hat = 0.5; v_hat = 0.5; z_hat = 0.5; end; %**************************************************************************

(34)

ramsey_policy(planner_discount=0.99);

stoch_simul c_hat y_hat pi_hat m_hat R_hat r_hat; check;

(35)

A Appendix

A.3 Optimal Simple Rule (OSR)

clc;

%************************************************************************** % MODEL

% h real money balances % v taste shock

% c consumption

% w real wage rate

% z transaction cost technology % a productivity

% g government expenditures % mu wage markup

var r_hat c_hat v_hat m_hat y_hat pi_hat w_hat z_hat a_hat mu_hat g_hat R_hat;

% Parameters:

parameters eta_R R_ss eta_h eta_c s_c kappa phi sigma_m sigma_a

sigma_g sigma_mu sigma_v sigma_z rho_a rho_g rho_mu rho_v rho_z beta omega sigma_tilda rho_pi eta_ch sigma_c sigma_h eta_hc alpha lambda_x lambda_R v_p sigma theta;

%************************************************************************** %INITIALISATION

(36)

theta = 6; v_p = 6; beta = 0.99; s_c = 0.8; sigma_tilda = 1; omega = 3.5; R_ss = 1.0146; eta_ch = 0.3; sigma_h = 3.5; eta_hc = 2.8; alpha = 0.3304; sigma_c = 0.8; rho_pi = 0.85; rho_a = 0.5; rho_g = 0.5; rho_mu = 0.5; rho_v = 0.5; rho_z = 0.5; eta_h = 0.0284; eta_c = 0.2649; sigma_a = 1; sigma_g = 1; sigma_mu = 1; sigma_v = 1; sigma_z = 1; sigma_m = 1; phi = 0.5; kappa = ((1-alpha)*(1-alpha*beta))/alpha; eta_R = R_ss/(sigma_h*(R_ss-1)); lambda_x = kappa/theta; lambda_R = (eta_R*lambda_x/(sigma_tilda+omega))*(1/v_p); %************************************************************************** %************************************************************************** % The Model: model(linear);

a_hat = rho_a*a_hat(-1) + e_a; g_hat = rho_g*g_hat(-1) + e_g; mu_hat = rho_mu*mu_hat(-1) + e_mu; v_hat = rho_v*v_hat(-1) + e_v;

(37)

A Appendix

z_hat = rho_z*z_hat(-1) + e_z;

R_hat = rho_pi*pi_hat; r_hat = R_hat-pi_hat(+1); c_hat(+1) = (v_hat(+1)+(eta_ch*(m_hat-pi_hat(+1)+z_hat(+1)))+ sigma_tilda*c_hat-v_hat-eta_ch*(m_hat(-1)-pi_hat+z_hat)+ R_hat-pi_hat(+1))*sigma_tilda; w_hat = omega*(y_hat-a_hat)-v_hat+sigma_tilda*c_hat-eta_ch*(m_hat(-1)-pi_hat+z_hat)+mu_hat; pi_hat = beta*pi_hat(+1)+kappa*(w_hat-a_hat); y_hat = (0.8+eta_c)*c_hat+g_hat-eta_h*(m_hat(-1)-pi_hat+z_hat); %1-(g/y)-(phi/y)=0.8 m_hat = -eta_R*R_hat+(eta_hc/sigma_h)*c_hat(+1)+pi_hat(+1)+ ((1-sigma_h)/sigma_h)*z_hat(+1); %R_hat = rho_pi*pi_hat+epsilon; %(ˆm) end; %************************************************************************** shocks;

var e_a = sigma_aˆ2; var e_g = sigma_gˆ2; var e_mu = sigma_muˆ2; var e_v = sigma_vˆ2; var e_z = sigma_zˆ2;

end; %************************************************************************** initval; a_hat = 0.5; g_hat = 0.5; mu_hat = 0.5; v_hat = 0.5; z_hat = 0.5; end;

(38)

%************************************************************************** optim_weights; pi_hat 1; y_hat lambda_x; R_hat lambda_R; end; osr_params rho_pi; osr; %**************************************************************************