7. RBC Flashcards
What are vector autoregressions?
Ways of summarising the dynamics of macro data where we are interested in obtaining the impulse response functions
What are impulse responses?
They trace out the response of current and future values of each variable to a one unit increase (or a one standard deviation increase, when scale matters) in the current value of one of the VAR errors
What does DSGE stand for?
Dynamic Stochastic General Equilibrium model
What is the simplest DSGE?
RBC
What is the New Keynesian model?
It combines DSGE structure of RBC models with assumptions that depart from classical monetary models. Features include monopolistic competition and nominal rigidities
What is the consequence of nominal rigidities on changes in short term interest rates?
They aren’t matched by one to one changes in expected inflation
How do financial frictions impact shocks?
They amplify them
What are business cycles?
Expansions and contractions that appear at the same time in different economic sectors.
They are periodical but with variable duration.
What should business cycle models be able to answer?
The source of cyclical fluctuations and the shock transmission mechanism
What second moments are we interested in?
Variance - volatility
Covariance, cross correlation - co-movements
Autocorrelation - degree of persistence
What are the two extreme cases of persistence?
-A random walk Px=1, the series never returns to average, a transitory shock produced permanent effects
-White noise Px=0, a transitory shock doesn’t generate any persistence, it isn’t possible to identify cyclical fluctuations due to the shock
How persistent are most macro variables?
Highly persistent
What must be added to the Ramsey model to understand aggregate fluctuations?
-There must be a source of disturbances.
-They are added in the form of fluctuation shocks- technology shocks. -This is known as an RBC model
What is good about the RBC?
It provides a coherent framework that integrates growth and business cycles
Why is the RBC controversial?
Because the only fluctuations are technology shocks?
What is the HP filter?
It is a model free approach to decomposing a time series into its trend and cyclical components
How is the parameter lambda used in the HP filter?
If lambda is zero we only care about fitting and if lambda is infinity the trend value will never change from one period to the next
How do we adjust lambda when the frequency of our data increases?
We increase lambda
How do empirical VARs suggest that price level and output react to an increase in interest rate?
The aggregate price level doesn’t respond much initially (inflection inertia) but then goes down. Output falls initially with a j shaped response and zero LR effect
What are the advantages of micro founded models?
-they are elegant
-they can be used to evaluate welfare effects of alternative policy
-we can do counterfactual experiments with them since their deep parameters are generally robust to Lucas’ critique
Conceptually what does the RBC highlight?
The efficiency of business cycles
The importance of technology shocks as a source of economic fluctuations
The limited role of monetary factors
Roles of money in the economy
- Medium of exchange
- Store of value
- Unit of account
What do we call the RBC model with money introduced?
The MIU model (money in utility)
What is the result of the MIU model?
It is able to generate non trivial effects to monetary shocks
What assumption is required for the MIU model?
We assume nonseperability between money and consumption (strong assumption)
Keynesian features
It combines the DSGE structure characteristic of RBC models with assumptions that depart from those found in classical monetary models
-Monopolistic competition
-Nominal rigidities
What are the three components of the NK model?
-demand side represented by a linear approximation to the representative Euler condition for optimal consumption
-inflation adjustment is derived under the assumption of monopolistic comp yielding the New Keynesian Phillips curve
-monetary policy is represented by a rule for setting the nominal rate of interest
What does the credit view stress?
Stresses the distinct role played by financial assets and liabilities. It also stresses that some borrowers may be more vulnerable to changes in credit conditions than others
What is the key mechanism involved in the financial accelerator?
It involves the link between external finance premium and the net worth of potential borrowers.
With credit market frictions present and asymmetric info, the external finance premium depends inversely on borrowers’ net worth.
How can collateral constraints create financial accelerator effects?
-adjustment of asset prices following contractionary monetary policy
-borrowers are limited in the amount they can borrow by the value of their assets that can serve as collateral
Simplifying assumptions of RBC
-Capital doesn’t depreciate
-Labour is supplied inelastically
-Utility is logarithmic in consumption
-Technology shocks effect society’s ability to produce goods
In the RBC what do we get when we combine the first two FOCs?
The Euler equation for consumption
What does the Euler equation say in words?
At the margin consumers are indifferent between consuming one unit today and saving it for the future
What is the intuition of the transversality condition?
Consumers don’t accumulate capital up to infinity
What is the zero lower bound and how does it relate to the NK model?
The zero lower bound is the idea that policy rates can only go as lower as zero. This is ignored in the basic NK model. This has ramifications for the effects of other shocks, including fiscal policy shocks
What is the forward guidance puzzle?
It is the idea that effects of a temporary 1% increase in the policy rate 100 years from now is predicted in the basic NK model to be the same as if the increase took place today
What is the HANK model?
Heterogeneous Agent New Keynesian model. It assumes there are idiosyncratic shocks to households labour productivity and hence wages. This causes households to have different marginal propensities to consume
How do low interest rates affect the asset price channel?
Low interest rates increase asset prices. High asset prices increase wealth for consumers and they condone more this shifts AD and inflation and output increase
When do firms use networth as collateral for loans?
When there is asymmetric info
How can the credit channel lead to output shifts?
Expansionary monetary policy increases with firms networth. The problem of moral hazard and adverse selection gets reduced, lending increases, investment increases further as a shift in the investment demand curve, output increases
Following the financial crisis how did the worsening of financial frictions manifest itself?
Widening credit spreads, causing higher costs of credit for households and businesses and tighter lending standards. The resulting decline in lending meant that both consumption expenditure and investment fell, causing the economy to contract
How did the crisis expose micro prudential supervision?
The crisis proved micro prudential supervision isn’t enough to prevent financial crises because the problems of one financial institution can harm others that are otherwise healthy
What is micro prudential supervision?
Focusing on safety and soundness of individual financial institutions
What is macroprudential supervision?
Focusing on the safety and soundness of the financial system as a whole
Which aspects of the crisis in particular does the NK model not display?
The amplification effect attributed to the role of credit supply in the monetary transmission, since it is based on the assumption that the Modigliani- Miller theorem holds and there are no credit market imperfections
Who are the agents in the NK model?
-Households
-Final good firms
-Intermediate good firms
-Government
What do households do in the NK model?
-make consumption and labour supply decisions
-demand money and bonds
What do final good firms do in the NK model?
-produce homogeneous final goods Yt
-use intermediate goods Yjt to produce the final good
What do intermediate good firms do in the NK model?
-use labour to produce intermediate goods Yjt
-over each of these goods they have monopoly power
-demand labour
-can set price of good Yj
What does the government do in the NK model?
Runs monetary policy
In the households maximisation problem what variables do they choose in order to maximise the equation? NK model
Consumption Ct, labour Lt, money Mt, nominal bonds Bt
What does Eo denote in the household maximisation problem? NK model
Denotes the expectation operator conditional on time 0 info
In the NK model what does Ft denote?
Lump sum dividends received from ownership of intermediate good firms
What are total goods given by in the NK model?
The CES aggregator of the different quantities of intermediate goods produced
How are the returns of the production function distributed in the NK model?
Production function has constant returns to scale
Characteristics of intermediate goods firms in NK model
Monopolistically competitive firms
Each firm faces downward sloping demand for its product
It uses labour to produce output according to the following technology Yjt= AtLjt
Calvo pricing
Each producer chooses her own price Pjt
He can reset his price only when given the chance to do so, which occurs with prob 1- theta in each period
What are the constraints of the intermediate goods firms in the NK model?
Production constraint
Demand curve
Prices can only be adjusted with prob 1- theta
How do intermediate goods firms pick the optimal price when given an option to change price in the NK model?
The optimal price is a weighted average of current and expected future nominal marginal costs. Weights depend on expected demand in the future, and how quickly the form discounts profits
What are fluctuations in the markup due to in the NK model?
Due to firms being unable to adjust prices
What is the AD equation in the equilibrium of the NK model?
AD equation combines goods market clearing with the Euler equation for bonds
How do we get the labour market equilibrium equation in the NK model?
Take labour demand and labour supply and impose market clearing. Then equate labour demand and labour supply so as to eliminate the real wage w from that expression
What is the Taylor rule?
It is a monetary policy rule founded by Taylor. It assumes that the central bank chooses money supply so as to set the nominal interest rate to be s function of previous interest rate, current inflation, and current real marginal costs (as a fraction of the steady state value)
What is the new Keynesian Phillips curve?
It is an expectations augmented Phillips curve which states that inflation rises when the real marginal costs rise. It is an aggregate supply curve for the whole economy
Describe what happens in the NK model with sticky prices following a rise in technology
MC falls, since not all prices can fall immediately, markups will rise, a fraction 1- theta of flexible price firms will lower their prices and hire more factors of production, the rest of the firms will hire less factors of production so production rises less than with flexible prices
Describe what happens in the NK model with sticky prices following a monetary contraction
Drop in output, rise in nominal interest rate, fall in inflation, and rise in the output gap. These predictions which are quantitatively in line with the VAR evidence, are hard to obtain in the flexible price model
How does the DNK model perform poorly and what techniques can alter this?
In its ability to match slow responses of macro variables to given shocks. Habit formation and inflation indexation
If the central bank isn’t able to observe the output gap with certainty then how will a strong monetary response affect the economy?
Will result in higher inflation and output variability
How are asset prices and interest rates related?
Inversely related
How do nominal prices, real housing prices, and GDP respond to an increase in interest rates?
They all fall
How do real housing prices and output respond to a positive inflation disturbance?
A significant fall in real housing prices and a small fall in output
Who are the four groups in the Iacovello 2005 model
There are 4 groups
Savers
Borrowers
Firms (intermediate/ final)
Monetary authority
What does having savers and borrowers instead of a representative consumer allow us to do?
Keep track of credit
How are borrowers constrained?
They face a limit on the debt they can acquire. The max amount they can borrow is proportional to the value of their collateral, in this case the stock of housing
How does the collateral constraint effect the Euler equation of borrowers?
It makes them have a sub optimal Euler equation so they don’t act optimally as a result
Explain how an increase in interest rate contracts the economy in terms of borrowers and savers
Savers postpone current consumption. Value of collateral for borrowers decreases since asset prices fall. This means they can borrow less and therefore consume less. Drop in consumption is larger for borrowers than savers. Output falls further than in standard model due to the financial accelerator
How useful are DSGE models in explaining structural vs cyclical nature of fluctuations in the labour market
Bloody useless
Why aren’t DSGE models designed to analyse longer term shifts in demographics, productivity, preferences, or other structural shifts?
Because DSGE models assume that all shocks are transitory and that the economy eventually returns to a fixed steady state
Why might central banks like the New Keynesian model?
Because in this framework, the economy’s response to shocks is generally inefficient. Room for potentially welfare enhancing interventions by the monetary authority in order to minimise existing distortions.
What has become an important tool for forecasting, simulation and monetary policy design?
The NK-DSGE models
How do we remove a trend from Ā macroeconomic series?
Let us define xt as the original series and xt^T as its trend component. Then, x(hat)t= ln(xt)- ln(xt)^T is the relative deviation of the series wrt it’s trend
What are methods to estimate the trend of a macro series?
-adjust by OLS some kind of deterministic temporal function
-use a smoothness method like the Hodrick-Prescott filter
Procyclical
Cross correlation is positive. Óx,y>0
Two series move together at the cycle frequency
Countercyclical
Cross correlation is negative . Óx,y<0
Two series move separately at the cycle frequency
Acyclical
Cross correlation is zero. Óx,y=0
One series moves and the other remains constant
What measures persistence?
Autocorrelation coefficient px. The higher the value the more persistent a series is
Facts about volatility
-C, K and G less volatile than Y
-I and durable C more volatile than Y
-Labour hours volatility, relative to output, has increased over time
-Real wages volatility is less than output volatility, but ratio has increased
-employment is as volatile as Y
-labour productivity less volatile than Y
Facts about comovements
-most macro series are procyclical
-wages, gov spending and K are acyclical or slightly procyclical
-output gap and inflation correlation can be +ve or -ve
-the +ve correlation between labour productivity and output has decreased over time
What effect did the Great Depression have on business cycle research?
-economists began to believe that micro theory was an inadequate basis for understanding business cycles
-real factors came to be less stressed, greater weight given to monetary conditions and psychology of households and firms
-gov management seen as essential
What did Kydland and Prescott rely on?
The micro empirical studies and the long run properties of the economy to choose parameter values whilst exploring the workings of stochastic dynamic models
What percentage of business cycles does the RBC explain?
77%
Breakdown what DSGE models are
-D: they describe the comovement of economic variables over time.
-S: they rely on random fluctuations in tech, preferences and other exogenous sources as the primary impulse for the movement of economic variables
-GE: they are normally based on micro foundations and are based on the hypothesis that markets first through adjustment of prices and quantities
Simplistically what does the HP filter do?
It tries to find values for trend GDP which are as close as possible to GDP but don’t change much over time
What is a typical value for lambda in the HP filter?
1600 for quarterly data
However, greater frequency of data requires higher lambda
What does Taylor (1999) find on nominal rigidities?
He concludes there is ample evidence of price rigidities, with the average frequency of price adjustment being about one year
What is needed to get nominal rigidities in the traditional, dynamic general model?
We need some firm of pricing power, for instance coming from monopolistic competition, and therefore some heterogeneity among goods.
Firms face some price stickiness
Limitations of plain NK model
-majority of NK models are based on the assumption that markets are complete so there are no financial market frictions.
-after the financial crisis hit, it become apparent that these models were missing something crucial about the behaviour of the economy
Modigliani-Miller 1958 theorem
Financial structure is both indeterminate and irrelevant to real economic outcomes.
In reality this likely doesn’t hold
What are the main missing elements in the NK model?
-financial intermediation
-Insolvency and default
-Liquidity
-Regulation of intermediaries and markets
-Booms and busts in asset markets
When might a raise in interest rates have a stronger contractionary impact on the economy?
If balance sheets are already weak
When might a raise in interest rates have a stronger contractionary impact on the economy?
If balance sheets are already weak
How do credit market frictions affect the response of real variables to a shock?
They lead to a stronger response of real variables. In particular, with the financial accelerator, the initial response of output to a given monetary impulse is about 50% greater and the effect on investment is nearly twice as great
Equation for VAR of lag length p VAR(p)
Zt= B1/A x zt-1 + B2/A x zt-2 + … + Bp/A x zt-p + ut/A
What is a recursive VAR
A recursive VAR tries to identify the structure of the model by constructing the error term in each regression to be uncorrelated with the error term in the preceding equations
Why might the openness and transparency of DSGE models make them easy to criticise?
-suspicious assumptions can be highlighted
-inconsistencies with evidence can easily be spotted
-forces that are missing from the model can be identified
Which policy related questions is the RBC mute on?
-what are the consequences of different monetary policy rules for aggregate economic activity
-what are the effects of the alternative exchange rate?
-what regulations should we impose on the financial sector?
What is calibration?
Researchers choosing parameter values to match unconditional model and data moments or referencing findings in the empirical micro literature
Apart from calibration what is another way to estimate DSGE models?
Bayesian estimation
What does Iacoviello (2005) do?
Develops and estimates a DSGE model with nominal loans and collateral constraints tied to housing values
In the RBC what does the representative consumer solve?
Max Et sum of beta^(s-t) x logCs
St
Kt-Kt-1= At^(1-alpha) x Kt-1^alpha -Ct
This is essentially Yt=Ct+It
In the RBC what do we assume about the process of technology?
We assume technology follows an AR(1) process in logs, that is
Log(At)= rho x log(At-1) + log(Ut)
Where rho is the autocorrelation of the shock and we assume that the innovation to technology logUt has mean zero and finite variance
In the RBC, what are the three equations we have to simultaneously solve?
The Euler equation
The technological progress equation
The constraint (Yt=Ct+It)
What is the compact notation that can be used for the system of equations in RBC?
Et(fø(xt+1, xt, xt-1, Ęt))=0
x is the vector collecting all endogenous variables
Ęt is the vector collecting the exogenous stochastic shocks
ø is the vector collecting the structural parameters of the model
In RBC what is the steady state?
In steady state all variables are constant
In practice we drop the subindex t from all the variables in the equilibrium equations
What can the solution to the RBC model be used to calculate?
-impulse responses
-dynamic simulations
-theoretical moments
-simulated moments
-variance decompositions
3 significant changes from RBC to NK
- Introduces nominal variables rather than all variables being real. Explicitly prices, wages, and a nominal interest rate
- NK departs from the assumption of perfect competition in the goods market, allowing for positive price markups
- NK introduces nominal rigidities, generally using the formalism proposed by Calvo
What are the three relationships that the NK model is composed of?
AD
AS
Monetary rule
Give the equation for AD in the NK model
yt=Etyt+1- 1/rho (rt-Et x pit+1)
Current output is equal to the difference between the expected output one period in the future and an amount that is proportional to the real interest rate
Give the equation for AS in NK model
AS is represented by the NK Phillips curve
pit= beta x Et x pit+1 + kyt
Through what channel does the monetary policy transmission mechanism in the NK model operate?
Through the traditional interest- rate channel. It misses important channels like the asset price channel or the credit channel
What is an alternative to calibration?
Estimating parameters with econometric techniques.
Standard values in the literature
-discount factor beta=0.99 which corresponds to 4% annual interest rate
-Ęl elasticity of substitution between labour types =1
-Ęh elasticity of substitution between services from home ownership and rent =2
Problems with MLE in DSGE models
May not have unique maximum or be nearly flat along the dimension of a given parameter of interest
Which model has become a benchmark for analysing monetary and fiscal policy in eirk lean central banks?
Smets-Wouters
Budget constraint of households in NK model
Ct+ Bt/Pt= Rt-1 x Bt-1/Pt + WtLt/Pt + Ft- (Mt-Mt-1)/Pt + Tt
How is the gross rate of inflation denoted in the NK model?
Capital Pit= Pt/Pt-1
When solving the first order conditions in the NK model what equations do we get?
Euler, labour supply, money demand
Euler equation for NK
1/Ct^rho= beta x Et x Rt/(Pit+1 x Ct+1^rho)
Euler equation for NK
1/Ct^rho= beta x Et x Rt/(Pit+1 x Ct+1^rho)
Labour supply equation for NK model
wt/Ct^rho= Lt^(n-1)
What is the equation for money demand in the NK model?
1/Ct^rho= Et(beta/Pit+1 x Ct+1^rho)+ X/mt
Where mt are real balances Mt/Pt
Equation in NK model of producing final hood
Yt= (integral of Yjt^((ę-1)/ę) dj)^(ę/(ę-1))
Where ę>1 represents the elasticity of substitution between intermediate goods
What is the langrangian of the firm in the NK model?
L= integral of PjtYjt dj + PtYt -(integral of Yjt^((ę-1)/ę) dj)^(ė/(ę-1))
What does Pt represent?
-The minimum cost of producing one unit of the final goods bundle Yt.
-for this reason we interpret Pt (the Lagrange multiplier) as the aggregate price index
-Pt tells us at the optimum what is the value for the form of relaxing the constraint on production
What is the downward sloping demand curve that firms face for their product in the NK model?
Yjt= (Pjt/Pt)^-ę x Yt
Equation for how intermediate firms produce output
Yjt=AtLjt
What is the minimisation problem producers face? In the NK model?
Min WtLjt/Pt + Zt(Yjt-AtLjt)
Where Zt is the Lagrange multiplier
How does the FOC for the producer in the NK model suggest we can write the cost?
COSTjt= WtLjt/Pt = ZtYjt
What are Zt and Xt in the NK model?
Zt is the Marginal cost
Xt=1/Zt is the markup
What is the finding of the NK model without sticky prices?
Money and nominal rigidities don’t have any effect in the dynamics of the model. It acts like the RBC with MIU
What is the optimal price in the NK model with sticky prices in words?
A weighted average of current and expected future nominal marginal costs
With habit formation how do we rewrite the momentary utility function (aside for money balances and labour supply)?
u= (Ct-hCt-1)^(1-rho) /(1-rho)
What is inflation indexation?
If prices aren’t reoptimised, they are indexed to lagged inflation according to
Log(pjt)= log(pjt-1)+ gamma x pit-1
What were the reasons why the NK model didn’t predict the financial crisis?
Lack of financial block.
Assumptions of rational expectations, perfect info, and infinitely lived representative household
Monetary policy transmission mechanism
This is the process through which monetary policy decisions affect the economy in general and the price level in particular
How does a change in interest rates work through the asset price channel?
-Lower interest rates increase the value of alternatives assets such as stocks and houses.
-Higher asset prices increase wealth for consumers and they can consume more out of their wealth
-Shifts AD out- increase in inflation
How does a change in interest rates have an affect through the credit channel?
-Firms use net worth for collateral for loans when there is asymmetric info.
-expansionary monetary policy increases firms net worth so the problem of moral hazard and adverse selection is reduced
-lending increases, investment increases further as a shift in the investment curve (financial accelerator)
-AD shifts out
What is Ht and qt in Iacoviello model?
Ht is the stock of housing
qt is the price of housing
