A Pitiable Specification Of Financial Policy Way That Dsge Models Volition Non Endure Properly Identified
In my previous post, I discussed how the role of the primary residue every bit the quest of departure for the analysis of financial policy was problematic. Those observations take away to hold upwards kept inwards hear when looking at many mainstream analyses of financial sustainability. However, inwards this post, I expect at an implication that is less obvious. Dynamic Stochastic General Equilibrium (DSGE) models which role the primary residue (or a similarly piteous specification) to model financial policy cannot hold upwards properly fitted to empirical data.
There is a corking bargain of disceptation nigh DSGE models. Their underlying assumptions appear bizarre. However, the commons justification for their role is that they tin hold upwards fitted to data, together with respond empirical questions that are demanded past times policy makers (“What happens if nosotros hike rates past times 100 footing points?”). However, DSGE model parameters may hold upwards incorrectly identified inwards a systematic fashion due the misspecification of financial dynamics. This undercuts their purported usefulness for generating scenario forecasts.
This piteous identification of model parameters volition generate models that imply that monetary policy is to a greater extent than effective than is warranted. As a result, the run of forecast errors past times key banks since the goal of financial crisis is to a greater extent than easily understood…
Professor Simon Wren-Lewis of Oxford has written extensively nigh the justification for the role of DSGE models (example article). He argues that policymakers take away quantitative answers to questions nigh the touching on of policy choices. They take away the answers quickly, without quibbling over technical details, every bit they are frequently reacting to crises. (Of course, those crises were typically caused past times policymakers’ previous decisions that were non carefully idea out.) Debates nigh ergodicity, representative agents, together with rationality are non what policymakers desire to hear.
If y'all receive got the methodology inwards published papers at confront value, the methodology used to prepare DSGE models industrial plant every bit follows:
This physical care for seems highly vulnerable to a piteous specification during the offset step. Thus, the ongoing debates involving microfoundations of DSGE models. However, a to a greater extent than realistic way of agreement the methodology is:
When interpreted this way, the methodology makes to a greater extent than feel every bit way to generate quantitative forecasts. (As somebody amongst an applied scientific discipline background, I am in all probability less shocked past times this than a purist who insists that economic science must hold upwards treated similar a pure science.) The methodology is a way to practise a statistical fitting, amongst a express amount of construction imposed on the model. (Having lots of costless parameters tin brand upwards for problems inwards the assumed structure.)
The alternative is to role a non-structured statistical method to justice dynamics. But the role of non-structured techniques way that nosotros receive got no intuition nigh how dynamics volition modify if structural parameters move.
As such, I tin empathize amongst the goals of the methodology used past times DSGE modellers. That said, the way inwards which model parameters are estimated seems incorrect, every bit the estimation physical care for is soundless vulnerable to an wrong model structure.
The volume of the debate roughly financial policy inside DSGE models revolves roughly “Ricardian Equivalence”. I volition defer that of import give-and-take to some other post. The supposition of Ricardian Equivalence is in all probability a major explanation of why the modelling of financial dynamics is handled poorly inside DSGE models. However, Ricardian Equivalence is less of import for the give-and-take of the linearised model that DSGE modellers goal upwards working with, together with it should non affair likewise much for the parameter estimation. (UPDATE: I receive got posted an article discussing why Ricardian Equivalence does non concur if the term premium is non-zero.)
There are a lot of DSGE models, together with hence it is hard to brand full general statements nigh them. For many models, financial policy is specified past times a primary residue that is determined alone exterior the model (exogenous). As such, the stabilising forces generated past times the welfare pose down that I discussed inwards the previous post disappear completely. Other models receive got taxes and/or regime consumption depending upon the pose down of the economy. I volition receive got every bit an example, the well-known model for the euro expanse proposed past times Smets together with Wouters (link to ECB paper).
In that model, the regime consumes a quantity of existent goods that is proportional to existent GDP. The implications of this are:
As a result, financial policy is assumed to hold upwards destabilising for the economical cycle. The stabilisation of nominal incomes past times the welfare state, which is trivially observed past times looking at income flows across the cycle, is completely absent.
Of course, nosotros know that economical increase is to a greater extent than frequently than non stabilised inwards modern welfare states (at to the lowest degree exterior the euro expanse periphery) – increase resumes later on recessions, together with increase rates are fairly steady during the volume of the expansion. The implication is every bit follows: since financial policy is assumed to hold upwards destabilising, the estimation physical care for has no choice but to attribute the stability of the economic scheme to either:
In other words: the estimation physical care for volition presumably attribute all of the touching on of the “automatic stabilisers” to monetary policy. This volition hold upwards truthful fifty-fifty if monetary policy truly has no upshot on the economy. (This is why I thought the debate I refer to every bit “Interest Rate Effectiveness” every bit beingness an opened upwards question. There exists empirical prove that appears to demonstrate that monetary policy stabilises the economy, but those estimation procedures may only hold upwards picking upwards the upshot of the automatic stabilisers.)
The commons method to justice the model parameters is using Bayesian logic. “Prior beliefs” are used to create the initial estimates for parameter values. However, these models are heavily over-parameterised. For example, the Smets-Wouters model had 35 model parameters (only 2 of which were fiscal). This way that the value of the prior information is less, since at that topographic point are hence many parameters beingness estimated at the same time.
At the same time, much economical information is slow-moving (low frequency). For example, it’s non precisely an accident that I tin slap at 1 time lines through United States of America of America work data; the information are evolving at a lower frequency than the monthly sample time. For the menses 2010-2013, where I did my at 1 time line of piece of work fit, at that topographic point appear to hold upwards over xxx “independent” samples of the unemployment rate. However, the fact that I tin check a at 1 time line of piece of work through the information way that the information over this interval tin hold upwards described past times ii parameters. Therefore, most of the xxx observations practise non correspond novel information for a plumbing equipment operation.
This way that the number of costless parameters inwards the estimation physical care for is in all probability comparable to the effective number of degrees of liberty inwards the information laid they used.
In other words, at that topographic point is no surprise that the model tin check economical data. The only query is: is at that topographic point a conceivable laid of “reasonable” dynamics that could non hold upwards fit, given the number of parameters available? (One could seek this hold upwards generating simulation information from Stock-Flow Consistent models, which violate diverse DSGE assumptions, together with encounter how the DSGE plumbing equipment algorithm copes.)
The dynamics of a linear organization are mainly described past times the conduct of the “state transition matrix” (a matrix is a tabular array of numeric values). In particular, the dynamics are driven past times the values of the eigenvalues of this matrix. One holding of these pose down transition matrices that is non obvious is that the eigenvalues of the matrix tin hold upwards really sensitive to the entries inwards the matrix. In the instance of linearised DSGE models, these entries are combinations of the parameters to hold upwards estimated. (Nonlinear dynamics volition receive got a similar parameter sensitivity.)
As a result, fifty-fifty “small” deviations from the assumed initial values for parameters volition hold upwards able to generate a organization able to check the data, since these “small” deviations tin motility the estimated model dynamics into almost whatever configuration. Meanwhile, the physical care for volition non receive got explored a wider laid of models to encounter whether financial policy impacts are poorly specified.
The implications of this are straightforward. Models estimated using an unrealistic construction of financial policy volition attach likewise much importance to monetary policy, together with no significance to non-discretionary financial policy (automatic stabilisers). In an surround where the opinion of passive financial policy is likewise restrictive but monetary policy is loose, the models volition predict rapid growth. That rigid increase volition neglect to materialise, however.
When viewed inwards this fashion, the repeated forecast misses past times multiple key banks, all inwards the same direction, over the past times few years becomes a fleck less of a surprise.
I cannot offering a uncomplicated way to solve this problem, beyond scrapping DSGE models that receive got a piteous specification of financial policy. I encounter no obvious way to disentangle the effects of monetary together with non-discretionary financial policy, given that these variables are hence highly correlated. As a result, I thought the estimation job to hold upwards a fairly critical theoretical issue. (Obviously, at that topographic point are to a greater extent than pressing policy debates.)
(c) Brian Romanchuk 2013
There is a corking bargain of disceptation nigh DSGE models. Their underlying assumptions appear bizarre. However, the commons justification for their role is that they tin hold upwards fitted to data, together with respond empirical questions that are demanded past times policy makers (“What happens if nosotros hike rates past times 100 footing points?”). However, DSGE model parameters may hold upwards incorrectly identified inwards a systematic fashion due the misspecification of financial dynamics. This undercuts their purported usefulness for generating scenario forecasts.
This piteous identification of model parameters volition generate models that imply that monetary policy is to a greater extent than effective than is warranted. As a result, the run of forecast errors past times key banks since the goal of financial crisis is to a greater extent than easily understood…
H5N1 Weak Defense Of DSGE Models
Professor Simon Wren-Lewis of Oxford has written extensively nigh the justification for the role of DSGE models (example article). He argues that policymakers take away quantitative answers to questions nigh the touching on of policy choices. They take away the answers quickly, without quibbling over technical details, every bit they are frequently reacting to crises. (Of course, those crises were typically caused past times policymakers’ previous decisions that were non carefully idea out.) Debates nigh ergodicity, representative agents, together with rationality are non what policymakers desire to hear.
If y'all receive got the methodology inwards published papers at confront value, the methodology used to prepare DSGE models industrial plant every bit follows:
- A complex nonlinear economical model is laid up, built roughly the optimisation job for the “Representative Household”.
- This model is linearised.
- This linear model is fitted to the observed information (parameters are estimated).
- Scenario analysis is hence run on the fitted model.
This physical care for seems highly vulnerable to a piteous specification during the offset step. Thus, the ongoing debates involving microfoundations of DSGE models. However, a to a greater extent than realistic way of agreement the methodology is:
- Economists realise that they practise non truly know what truthful nonlinear dynamics of the economic scheme are.
- They delineate a linear model out of their hat. This model has lots of costless parameters.
- This linear model is fitted to observed data.
- Scenario analysis is hence run on the fitted model.
When interpreted this way, the methodology makes to a greater extent than feel every bit way to generate quantitative forecasts. (As somebody amongst an applied scientific discipline background, I am in all probability less shocked past times this than a purist who insists that economic science must hold upwards treated similar a pure science.) The methodology is a way to practise a statistical fitting, amongst a express amount of construction imposed on the model. (Having lots of costless parameters tin brand upwards for problems inwards the assumed structure.)
The alternative is to role a non-structured statistical method to justice dynamics. But the role of non-structured techniques way that nosotros receive got no intuition nigh how dynamics volition modify if structural parameters move.
As such, I tin empathize amongst the goals of the methodology used past times DSGE modellers. That said, the way inwards which model parameters are estimated seems incorrect, every bit the estimation physical care for is soundless vulnerable to an wrong model structure.
Fiscal Policy In DSGE Models
The volume of the debate roughly financial policy inside DSGE models revolves roughly “Ricardian Equivalence”. I volition defer that of import give-and-take to some other post. The supposition of Ricardian Equivalence is in all probability a major explanation of why the modelling of financial dynamics is handled poorly inside DSGE models. However, Ricardian Equivalence is less of import for the give-and-take of the linearised model that DSGE modellers goal upwards working with, together with it should non affair likewise much for the parameter estimation. (UPDATE: I receive got posted an article discussing why Ricardian Equivalence does non concur if the term premium is non-zero.)
There are a lot of DSGE models, together with hence it is hard to brand full general statements nigh them. For many models, financial policy is specified past times a primary residue that is determined alone exterior the model (exogenous). As such, the stabilising forces generated past times the welfare pose down that I discussed inwards the previous post disappear completely. Other models receive got taxes and/or regime consumption depending upon the pose down of the economy. I volition receive got every bit an example, the well-known model for the euro expanse proposed past times Smets together with Wouters (link to ECB paper).
In that model, the regime consumes a quantity of existent goods that is proportional to existent GDP. The implications of this are:
- There is no stabilisation of nominal incomes via taxes, or transfer payments for things similar unemployment insurance.
- Government consumption volition autumn during a recession, acting inwards a pro-cyclical manner.
As a result, financial policy is assumed to hold upwards destabilising for the economical cycle. The stabilisation of nominal incomes past times the welfare state, which is trivially observed past times looking at income flows across the cycle, is completely absent.
Of course, nosotros know that economical increase is to a greater extent than frequently than non stabilised inwards modern welfare states (at to the lowest degree exterior the euro expanse periphery) – increase resumes later on recessions, together with increase rates are fairly steady during the volume of the expansion. The implication is every bit follows: since financial policy is assumed to hold upwards destabilising, the estimation physical care for has no choice but to attribute the stability of the economic scheme to either:
- inherent stability of capitalist economies (as a follower of Hyman Minsky, I winced when I wrote that);
- the stabilising touching on of monetary policy (the commons reaction business office of key banks has been to react counter-cyclically).
In other words: the estimation physical care for volition presumably attribute all of the touching on of the “automatic stabilisers” to monetary policy. This volition hold upwards truthful fifty-fifty if monetary policy truly has no upshot on the economy. (This is why I thought the debate I refer to every bit “Interest Rate Effectiveness” every bit beingness an opened upwards question. There exists empirical prove that appears to demonstrate that monetary policy stabilises the economy, but those estimation procedures may only hold upwards picking upwards the upshot of the automatic stabilisers.)
Bayes – Not To The Rescue
The commons method to justice the model parameters is using Bayesian logic. “Prior beliefs” are used to create the initial estimates for parameter values. However, these models are heavily over-parameterised. For example, the Smets-Wouters model had 35 model parameters (only 2 of which were fiscal). This way that the value of the prior information is less, since at that topographic point are hence many parameters beingness estimated at the same time.
At the same time, much economical information is slow-moving (low frequency). For example, it’s non precisely an accident that I tin slap at 1 time lines through United States of America of America work data; the information are evolving at a lower frequency than the monthly sample time. For the menses 2010-2013, where I did my at 1 time line of piece of work fit, at that topographic point appear to hold upwards over xxx “independent” samples of the unemployment rate. However, the fact that I tin check a at 1 time line of piece of work through the information way that the information over this interval tin hold upwards described past times ii parameters. Therefore, most of the xxx observations practise non correspond novel information for a plumbing equipment operation.
This way that the number of costless parameters inwards the estimation physical care for is in all probability comparable to the effective number of degrees of liberty inwards the information laid they used.
In other words, at that topographic point is no surprise that the model tin check economical data. The only query is: is at that topographic point a conceivable laid of “reasonable” dynamics that could non hold upwards fit, given the number of parameters available? (One could seek this hold upwards generating simulation information from Stock-Flow Consistent models, which violate diverse DSGE assumptions, together with encounter how the DSGE plumbing equipment algorithm copes.)
The dynamics of a linear organization are mainly described past times the conduct of the “state transition matrix” (a matrix is a tabular array of numeric values). In particular, the dynamics are driven past times the values of the eigenvalues of this matrix. One holding of these pose down transition matrices that is non obvious is that the eigenvalues of the matrix tin hold upwards really sensitive to the entries inwards the matrix. In the instance of linearised DSGE models, these entries are combinations of the parameters to hold upwards estimated. (Nonlinear dynamics volition receive got a similar parameter sensitivity.)
As a result, fifty-fifty “small” deviations from the assumed initial values for parameters volition hold upwards able to generate a organization able to check the data, since these “small” deviations tin motility the estimated model dynamics into almost whatever configuration. Meanwhile, the physical care for volition non receive got explored a wider laid of models to encounter whether financial policy impacts are poorly specified.
Implications
The implications of this are straightforward. Models estimated using an unrealistic construction of financial policy volition attach likewise much importance to monetary policy, together with no significance to non-discretionary financial policy (automatic stabilisers). In an surround where the opinion of passive financial policy is likewise restrictive but monetary policy is loose, the models volition predict rapid growth. That rigid increase volition neglect to materialise, however.
When viewed inwards this fashion, the repeated forecast misses past times multiple key banks, all inwards the same direction, over the past times few years becomes a fleck less of a surprise.
I cannot offering a uncomplicated way to solve this problem, beyond scrapping DSGE models that receive got a piteous specification of financial policy. I encounter no obvious way to disentangle the effects of monetary together with non-discretionary financial policy, given that these variables are hence highly correlated. As a result, I thought the estimation job to hold upwards a fairly critical theoretical issue. (Obviously, at that topographic point are to a greater extent than pressing policy debates.)
(c) Brian Romanchuk 2013
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