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).

i)      Microeconomics

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 Review, 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).