### Introduction

DSGE models have become the standard macro modelling technique for mainstream economists, particularly at central banks. These models are fairly controversial, particularly after the financial crisis after 2008-2009.

Unfortunately for the point of view of writing about DSGE models, this is actually a very wide class of mathematical models, which are not just used in macroeconomics. There are uses in overlapping generations models (which model consumer behaviour, but abstract out the rest of the economy), and pricing of financial instruments. I am not really interested in those uses of DSGE models, and nothing I write applies to those forms of DSGE mathematical models; I am only referring to the DSGE models applied to macro analysis.

Within the macroeconomic usages, there are two broad classes: Real Business Cycle (RBC) models, and an offshoot, New Keynesian models. The RBC models came first, and assumed completely flexible prices. The New Keynesian models added price stickiness, which changes the cyclical behaviour of the models considerably. Thousands of these models have been churned out by academics and central banks, and they often add various "frictions" to adjust the behaviour of the models.

### Endowment Economy Example

In a series of posts, I discuss a simple "endowment" economy (an economy where output happens without a labour/consumption trade-off). I explain what the solution looks like, and I discuss the problems with the government budget constraint. These problems cast doubt on the model solutions that are discussed in the literature.- The Fiscal Theory of the Price Level and Chartalism. How "fiscal backing" drives the value of the currency in a DSGE model, and how this relates to Chartalism.
- Understanding the Fiscal Theory of the Price Level with Flexible Prices.
- Monetary Frictions in DSGE Models. On how to add constraints to pin down the initial price level in DSGE models.
- If r<g, DSGE Model Assumptions Break Down
*Non-transversality*- [to be published]

### Complaints About DSGE Assumptions

There are many who object to the assumptions based on microeconomic theory embedded in these models. The use of a representative household, which is assumed to live forever and rationally plan out a consumption path for all time, is a particular point of scorn.

### Justification Of DSGE Models

The justifications given for the use of DSGE models include:

- Sensible reaction of embedded expectations to policy changes ("Lucas Critique").
- A unified, flexible framework for analysis.
- The use of math, instead of literary exposition, (hopefully) gives an objective measure of whether academic articles represent new knowledge or not. (As an example of the problems with non-mathematical economic theory, Austrian economics has largely devolved into parsing texts written by dead economists.)
- Mathematical models can be fitted (calibrated) to real world data, leading to quantitative predictions for scenario analysis.

These models have a large number of free parameters. Since an infinite number of nonlinear models can have the same linear approximation ("linearisation"), the calibration techniques could conceivably identify the correct linearisation, even if the nonlinear model they use is incorrect. This means that scenario analysis output would be correct, even if they have the wrong nonlinear model.

###
**External References:**

(This is under construction.)- Sebastien Dullien - The New Consensus from a Traditional Keynesian and Post-Keynesian Perspective. This article discusses a variety of problems with DSGE models. (Some were problems that I had noted in my own blog articles before I was aware of this reference.)

### Complaint: DSGE Models Are Mathematically Or Economically Incoherent

DSGE models, as currently described in the literature, appear to have problems with the mathematics and/or macroeconomic dynamics.

**Posts:**

- The use of the Representative Household means that solutions cannot deviate from the "full employment" equilibrium, if the optimisation is solved correctly. This assumption also makes the models unable to model government debt dynamics.
- Formal mathematical proof of the previous point (draft article).
- The inter-temporal government budget constraint does not apply to real-world economies. There is an embedded assumption that the term premium is zero (which I have not seen noted in the literature). I give a counter-example that shows the pricing error may be arbitrarily large.
- Linearisation breaks the stock-flow consistency of the model (noted here).
- The assumption that the Net Present Value of government debt is zero at infinity appears problematic. One problem is that the macro accounting does not allow the representative household to determine the level of government debt.
- Most of these models have essentially a single consumer good (or an uncountably infinite number of goods that are integrated out into a single good). Models with only a single consumer good have inherent problems modelling cyclical dynamics.

### Complaint: DSGE Models Cannot Be Properly Fitted To Data

If DSGE models cannot be fitted correctly to the data ("calibrated" in economist-speak; "identified" to control systems engineers), the empirical arguments in their defense disappear.

- A poor specification of fiscal policy within many DSGE models means that their fit to data will be systematically incorrect. The stabilising effect of the welfare state's "automatic stabilisers" (passive fiscal policy) will be attributed to other factors. It may be possible to modify the model to handle this, but the modified version will run into "Ricardian Equivalence" (which I argued above is incoherent).
- It is not clear to me that the linearisation could be correctly fitted from observed economic data, even if the nonlinear model was correct. (
*Post to be written.*)

### Other Complaints

- If DSGE models are state-of-the-art, how come nobody in the private sector uses them? (My comments on a point raised by others.)

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