Workshop on Building and Estimating a Small Open Economy
Model for Uganda

By Lawrence J.
Christiano

**Overview**

The
purpose of this workshop is to develop a small open economy model and begin
estimating it with Ugandan data. The model can be used to think about inflation
targeting, foreign exchange management and fiscal tax rules. We will take as
given the basic concepts of Bayesian estimation with Dynare and the structure
of the simple closed New Keynesian (NK) model with Calvo-sticky prices. Still,
to fix notation and ideas, part 1 of the outline below provides a review of Bayesian
estimation and the NK model. However, we will not systematically go through
this material in the workshop.

The
workshop will begin with part 2 below: a discussion of a simple New Keynesian
open economy model without capital. Then, we introduce capital, but without any
financial frictions (the approach is similar to the
way investment is financed in a real business cycle model). After that, we
introduce financial frictions. For this, we start with a discussion of a simple
micro model of the relationship between a borrower (‘entrepreneur’) and lender
(‘bank’). This allows us to fix notation and ideas about a particularly
important model of financial frictions: the costly state verification model
popularized in a classic paper by Bernanke, Gertler and Gilchrist. With the
basic concepts and notation in hand, we introduce financial frictions into the
small open economy model with capital. The last step in model construction
considers the policy issues that can be addressed in the model: government
fiscal policy, monetary policy in the form of an interest rate rule (‘open
economy Taylor rule’) and foreign exchange intervention. Finally, we will begin
the process of estimating the model on Ugandan data. We will also talk about
how to use the model to construct forecasts.

An overarching theme of our analysis is that
the fully developed open-economy macro, in effect, ‘turnes
on its head’ the prefious open-economy consensus
referred to as the Mundell-Fleming model (the latter will be captured by the
‘simple’ model in part 2). Notably, the International Monetary Fund has played
a central role in forging both the previous and the new consensus. At the core
of the change in thinking is the empirical evidence that the classic
expenditure switching channel is often not the prime channel by which an exchange
rate depreciation affects the economy (the ‘taper tantrum’ of 2013 is an
illustration). We will capture these observations through (i)
the introduction of capital investment, (ii) capital losses are suffered by
dollar borrowers when the exchange rate depreciates, perhaps forcing them to
cut back on investment and cut back on employment, (iii) the apparent fact that exports are
sticky in dollars and (iv) the observation that exports often require imports
as inputs and (v) fact that central banks often intervene in foreign exchange
markets.

Note:
the attached slides will be adjusted as needed, both before and during the
workshop.

**Outline**

1)
Background,
not expected to be covered in the workshop:

a)
Estimation, with
application to open economy model.

i)
Simple
exercise to understand:

(1)
The
likelihood principle (which motivates maximum likelihood as an estimator) using
the probability theory at the start of the handout.

(2)
The Monte Carlo strategy for computing integrals discussed in the
slides.

ii)
Intuitive
illustration of mapping from priors to Bayesian posteriors (US monetary base, US base growth and
inflation).

iii)
Questions 2-10 in Assignment9.pdf provide simple exercises that
review (a) the use of impulse responses to study the properties of a simple New
Keynesian model, (b) demonstrate how the MCMC algorithm works to uncover the
details of a (posterior) distribution and (c) estimation of an NK model (using
artificial data generated from the correct NK model) using Dynare. All
necessary code is provided.

b)
Simple Closed Economy Model.

i)
Basic model construction, including sticky prices.

ii)
Linearizing and solving a model. More detailed notes on the Phillips curve.

2)
A simple version of the open economy model.

a) Basic structure of the model.

b) Some properties of the model
(‘Mundell-Fleming’).

3)
Introducing Capital into the Model without ‘Financial
Frictions’.

a) Introducing new equations into the model.

b) Properties: model deviates substantially
from Mundell-Fleming.

4)
Financial
Frictions:

a) Costly State Verification model
(Bernanke-Gertler-Gilchrist).

ii)
Closed
economy macro implications. (References: (CMR, JMCB 2003, AER 2014))

b) Introduce the frictions into the small open economy
model with capital.

c) Balance sheet effects can have a major
impact on model properties.

5)
Sterilized Interventions and Dominant
Currency Pricing

a) Introducing Dominant Currency Pricing into
the model (reference).

b) Sterilized Intervention.

Readings:

1) The complete
technical discussion of the model appears in this manuscript, which is
joint work with Santiago Camara and Hüsnü Dalgic.
This should at best only be used for reference in case of interest. The
handouts are designed to convey the basic model.

2)
For
some informal background, see this interview and this.

**Closed
Economy DSGE Modeling:**

3)
Christiano, Lawrence J., Martin Eichenbaum,
and Mathias Trabandt, 2018,
“On DSGE Models,” *Journal of Economic Perspectives*, Vol.
32, No. 2, (Summer), pp. 113–40.

4) Christiano,
Lawrence J., Roberto Motto, and Massimo Rostagno, 2014, “Risk Shocks,” *American Economic Revie**w**, *Vol. 104, No. 1, pp. 27–65.

5) Christiano,
Lawrence J., Mathias Trabandt, and Karl Walentin,
2011, “DSGE Models for
Monetary Policy Analysis,” in *Handbook of Monetary Economics, *Vol. 3A, ed. by Benjamin Friedman
and Michael Woodford (Amsterdam: Elsevier Science B.V.).

**Open Economy
DSGE Modeling: **

6) Christiano,
Lawrence, Mathias Trabandt and Karl Walentin,
“Introducing financial frictions and unemployment into a small open economy model,”
Journal of Economic
Dynamics and Control, 35 (2011) 1999-2041.

7) Adolfson, Malin, Stefan Laseen, Lawrence Christiano, Mathias Trabandt and Karl Walentin, 2013, ‘Ramses II –
Model description,’ Sveriges Riskbank Occasional Paper Series 12, 2013.

8)
Adolfson,
Malin, Stefan Laseen,
Jesper Linde, and Mattias Villani, 2008, “Evaluating an Estimated New Keynesian
Small Open Economy Model”, *Journal
of Economic Dynamics and Control*, August.

**Open Economy DSGE Modeling with Sterilized Interventions:**

9)
Jaromir
Benes, Andrew Berg, Rafael A. Portillo and David Vavra,
“Modeling Sterilized Interventions and Balance Sheet Effects of Monetary Policy
in a New-Keynesian Framework,” *Open Econ Rev* (2015)

10) Ruy Lama and Juan Pablo
Medina, “Mundell meets Poole: Managing capital flows with multiple instruments
in emerging economies, *Journal of Money and
Finance*,
2020.

11) Gabriel Rodriguez, Paul Castillo, and Harumi Hasegawa, “Does
the Central Bank of Peru Respond to Exchange Rate Movements? A Bayesian
Estimation of a New Keynesian DSGE Model with FX Interventions,” PUCP working paper.

**Empirical Analysis Related to Sterilized
Interventions:**** **

12)
Adler and Tovar (2011); Hnatkovska, et. al. (2016); Fratzscher, et. al. (2019); Gómez, et. al. (2020); Lu, et. al. (2022); Brandao-Marques, et. al.
(2020); Mohanty and Berger
(2014); Naef and Weber (2021); Scalia (2008).

13) Failure of UIP: Chinn and Meredith
(2005) and Chinn and Quayyum (2012).