A DSGE Model for an Emerging Open Economy Oil-Producer: Foreign Exchange Interventions as a Policy Instrument

Transcription

1 A DSGE Model for an Emerging Open Economy Oil-Producer: Foreign Exchange Interventions as a Policy Instrument Fred Iklaga University of Surrey June 2, 206 Preliminary and not to be Quoted Abstract This paper develops an open-economy DSGE model of an emerging oilproducing economy and incorporates a number of features important for emerging economies in general and the Nigerian economy in particular: creditconstrained consumers, incomplete exchange rate pass-through, oil revenue and foreign exchange FX) interventions a second monetary instrument. FX interventions has been extensively used as a policy instrument to manage the impact of capital flows on the exchange rate in emerging economies with questions raised regarding its effectiveness. Simulations are undertaken to assess the effects of FX interventions on macroeconomic management in this study. JEL Classification: E52, E37, E58 Keywords: Nigerian economy, open economy, DSGE model, simulations, foreign exchange interventions, monetary interest rate rules, oil exporter. To be presented at the st Eurasian Conference Baku, Azerbaijan, August 28-3, 206.

2 Contents Introduction 2 Open Economy Model 2 2. The Central Bank An Oil Sector and Oil Price Changes Calibration of Parameters and Results 5 3. Parameter Calibrations Conclusions 6 A Summary of the Full Open Economy Model 7 A. Dynamic Model A.2 Zero-Growth Steady State B A Balanced-Non-Zero-Growth Steady State 5

3 Introduction Developments in commodity markets have stimulated renewed interest in the study of the impact of large external shocks on oil exporters. The Nigerian economy is heavily dependent on revenues from oil exports and is therefore considerably vulnerable to oil price fluctuations. Over the past four decades, oil and gas revenues have accounted for about 80.0 per cent of total government financing and represents around 90.0 per cent of its total exports. With proven crude oil reserves estimated at 37 billion barrels and a production output of approximately only 2.5 million barrels of crude daily OPEC Annual Statistical Bulletin 205), Nigeria remains a pricetaker subject to the interplay of market forces which are determined by the dictates of dominant producers and the global demand for oil and gas. Consequently, the mono-product nature of exports and fiscal revenue in the economy makes macroeconomic outcomes susceptible to the vagaries of oil prices. Against this perspective and inherent uncertainties, it is evident that the determination of crude oil prices exhibit a volatile process which poses considerable challenges to macroeconomic stability and management particularly in heavily dependent oil exporting economies. Indeed, this scenario shows a fundamental feature of oil exporting economies which is significant exposure to fluctuations in foreign markets and business cycle dynamics Bergholt, 204). As highlighted by the conclusions in the literature on SSA economies, the effects of terms of trade shocks on oil producers could be substantial and is of special interest particularly where the shock is strongly positively correlated with domestic output and capital inflows. Capital flows may witness a sharp reversal or even a dramatic sudden stop during a negative oil price shock as emphasized by Calvo 998) and evident for some oil exporters as a result of the second round effects of the 2008 crises, output developments, on the other hand may vary depending on the structure of the sectoral contributions to overall output. This implies that the debilitating effects of such reversals on the financial system may sometimes be more amplified than the somewhat transient impact of oil price shocks on output. Therefore, macroeconomic management requires intervention markets including the FX markets while maintaining the broad objectives of price stability and output growth. This paper develops an open-economy DSGE model of an emerging oil-producing economy and incorporates a number of features important for emerging economies in general and the Nigerian economy in particular: a large proportion of creditconstrained consumers, incomplete exchange rate pass-through, oil revenue and foreign exchange FX) interventions a second monetary instrument. FX interventions has been extensively used as a policy instrument to manage the impact of capital flows

4 on the exchange rate in emerging economies. First we will introduce Foreign reserves intervention as a second monetary instrument in this paper. Widely acknowledged as a monetary policy instrument, the use of foreign exchange FX) interventions by central banks to dampen currency appreciation or depreciation has become common place in not just emerging economies but also in some developed economies post the financial crisis of 2008/09. Formalising such interventions as an additional monetary policy instrument in macroeconomic models should further epitomize the actions of central banks when faced with the two-pronged effects of volatile developments in international financial markets and oil price shocks. In particular, monetary authorities may undertake regular interventions in FX market to moderate supply or demand pressures by sterilizing the surplus proceeds from oil exports to control liquidity in the system or conversely intervene by providing FX from its international reserves in order to maintain exchange rate stability when there is a deficit of inflows to the market as it is the case for oil producers. I follow research by Benes et al. 205) to introduce sterilized interventions in the DSGE model for Nigeria. This involves a study of various hybrid monetary policy rules and managed exchange rate regimes to analyse their implications for inflation, output and the exchange rate in the presence of various domestic and external shocks. I present details of the model in this paper. The DSGE model for an oil exporting economy in this paper follow the prototypical new-keynesian framework of the open economy Gali, 2008). The rest of the paper is organized as follows. Section 2 presents the oil exporting emerging economy model. Section 3 concludes. 2 Open Economy Model A standard New Keynesian NK) DSGE model with features associated with emerging economy oil exporters is developed in this section. The model description is summarised, while the details of the central bank actions are presented. Households A single-period utility for the representative agent in terms of consumption, C t, external habit χc t and leisure, L t, as U C,t = ϱ)c t χc t ) ϱ) σ) L ϱ σ) t ) U L,t = ϱc t χc t ) ϱ) σ) L ϱ σ) t 2) 2

5 In this utility function σ is a risk-aversion parameter which is also the inverse of the intertemporal rate of substitution. The parameter ϱ 0, ) defines the relative weight households place on consumption. The value function at time t of the representative household is given by [ ] Ω t = E t β s UC t+s, L t+s ) 3) s=0 where β is the discount factor. In a stochastic environment, the household s problem at time t is to choose state-contingent plans for consumption {C t }, leisure, {L t } and holdings of financial savings to maximize Ω t given its budget constraint in period t B t+ = B t R t + W t h t C t + Γ t T L t + T CB t 4) where B t is the net stock of real financial riskless assets at the beginning of period t, W t is the real wage rate, Γ t are dividends from ownership of firms, T L t are lumpsum taxes, T CB t central bank transfer to households and R t is the real interest rate paid on assets held at the end of period t. Hours worked are h t = L t 0, ) and the total amount of time available for work or leisure is normalized at unity. Government spending is financed by lump-sum non-distortionary taxes throughout. The first-order conditions for this optimization problem are U C,t = R t βe t [U C,t+ ] 5) U L,t U C,t = W t 6) An equivalent representation of the Euler consumption equation 5) is = R t E t [Λ t,t+ ] 7) where Λ t,t+ β U C,t+ U C,t is the real stochastic discount factor over the interval [t, t + ]. Equation 5) or 7)) is the Euler consumption function. Firms For production I assume that output Y t is produced using hours, h t and beginningof-period capital K t with a Cobb-Douglas production function Y t = F A t, h t, K t ) = A t h t ) α K α t 8) 3

6 where A t is a technology parameter and Y t, h t and end-of-period capital, K t, are all in per-capita household) units. Assume first that capital can adjust instantly without investment costs. Then equating the marginal product of labour with the real wage and the marginal product of capital with the cost of capital given by the real interest rate plus the depreciation rate, R t + δ), we have F h,t = α Y t h t = W t 9) F K,t = α) Y t K t = R t + δ 0) Let investment in period t be I t. Then capital accumulates according to K t+ = δ)k t + I t ) In setting up the NK features of the model a differentiated goods market and nominal rigidities that constraint firms price adjustment frequency are introduced. For investment adjustment costs in the functional form SX) = φ X X t X)) 2 2) 2. The Central Bank The gross nominal and ex post real interest rates are related by R t = R n,t Π t 3) where the nominal interest rate is a policy variable, typically given in the literature by a standard Taylor-type rule: log Rn,t R n ) = ρ log Rn,t R n ) + θ π log ) Πt + θ y log Π 2.2 An Oil Sector and Oil Price Changes Yt ) + ɛ MP S,t 4) Y We introduce an oil sector treating output as an exogenous endowment Y O. Revenues is then driven only by the price of oil PO,t denominated in foreign currency which is a exogenous process as for the other shock processes in the model. The only change to the model is in the trade balance which now becomes T B t = S t P O,tY O + Y t C t P I,t I t G t 5) 4

7 The details of the model is in the Appendix. 3 Calibration of Parameters and Results 3. Parameter Calibrations We simulate the model based on the theoretical underpinnings of the model and findings from previous studies on oil exporters and open economies. The parameters are calibrated as follows: Calibrated parameter Symbol Value for Nigeria Discount factor β 0.99 Depreciation rate δ Risk premium - scaling k B.00 FA risk premium θ.00 Labour share α.00 Risk premium elasticity χ B 0.50 Implied steady state relationship hours worked/time available h 0.35 Preference parameter ϱ calibrated to hit proportion of hours worked Imported investment share is import 0.5 Imported consumption share cs import 0.0 Exported investment share is export 0.02 Exported consumption share cs export 0.23 oil revenues/gdp oil 0.20 Table : Calibrated Parameters 5

8 4 Conclusions Developments in New-Keynesian DSGE models have improved how optimising agents are modelled with the ultimate goal to provide a better informed framework for policy decision making. Incorporating the peculiar features of oil exporting economies further supports this conclusion. FX intervention can be incorporated as an additional policy instrument into an emerging oil exporting economy DSGE model with an inflation objective. The model confirms some recent conclusions in the literature on the benefits of FX interventions by central banks that respond to significant external shocks which may drive sudden and huge capital flows. Foreign exchange interventions can be useful depending on agents perception on overall policy objectives. Therefore, FX interventions may be used to support the achievement of inflation stability and output goals of a central bank. References Benes, J., Berg, A., Portillo, R., and Vavra, D. 205). Modeling sterilized interventions and balance sheet effects of monetary policy in a new-keynesian framework. Open Economies Review, 26), Bergholt, D. 204). Monetary policy in oil exporting economies. Working paper, CAMP Working Paper Series No 5. Calvo, G. A. 998). Capital Flows and Capital-Markets Crises. Journal of Applied Econometrics, ),

9 A Summary of the Full Open Economy Model We now bring together all the features in the context of an open economy - creditconstrained consumers, international financial frictions, incomplete exchange rate pass-through and oil revenue. A. Dynamic Model C,t = W t h,t A.) [ ) UC2,t+ = βe t A.2) R n,t U C2,tΠ t+ C t = λc,t + λ)c 2,t A.3) U L,t U C,t = U L 2,t U C2,t = W t A.4) h t = λh,t + λ)h 2,t A.5) U C,t = ϱ)c ϱ) σ) t h t ) ϱ σ) ; for C t = C,t, C 2,t ; h t = h,t, h 2,t A.6) U L,t = ϱc ϱ) σ) t h t ) ϱ σ) ; for C t = C,t, C 2,t ; h t = h,t, h 2,t A.7) = = [ w C PH,t ) µc + w C ) [w C + w C )T µ C PF,t ) µc ] µ C A.8) A.9) µ t ] C where T t P F,t ) µc PH,t C H,t = w C C t A.0) C F,t = w C ) C H,t = ω C) PF,t ) µc C t A.) RER C,t θ + θ) S )) µ tph,t l C C t A.2) 7

10 PCP Price Setters in Home Currency H t ξ H βe t [Π ζ H,t+ H t+] = Y t U C,t A.3) J t ξ H βe t [Π ζ H,t+ J t+] = MS t Y t U C,t MC t ζ A.4) MC t = P W H,t = P W H,t / / = W t h t αy t A.5) LCP Price Setters in Foreign Currency ) ζ = ξ H Π ζ H,t + ξ Jt H) A.6) H t Ht l ξ H βe t [Π H,t+) l Ht+] l = Yt S t U C,t J l t ξ H βe t [Π l H,t+) ζ J l t+] = ζ MC l t = MC t S tp l H,t MS t Y t S t U C,t MC l t A.7) A.8) A.9) Define the LoP gap for LCPers as = ξ H Π l H,t) ζ + ξ H ) J l t H l t ) ζ A.20) Then Ψ t S tp l H,t Ψ t Ψ t = S t Π l H,t S t Π H,t Aggregate export inflation in foreign currency is then A.2) A.22) Π H,t = θ Π H,t S t + θ)π l H,t A.23) but this is not an input into the rest of the model. 8

11 Yt W = A t h t ) α Kt α Y t = W c)yt t A.24) A.25) t = ξπ ζ t t + ξ) Jt H t ) ζ A.26) P W H,t = MC t A.27) E t [Λ t,t+ R t+ ] = R t = R n,t E t Λ t,t+ [ P W H,t+ P t+ Π t α) Y W t+ K t + δ)q t+ ] Q t K t = δ)k t + SX t ))I t A.28) A.29) S, S 0 ; S + g) = S + g) = 0 A.30) X t = I t I t A.3) SX t ) = φ I 2 X t + g)) 2 A.32) [ ] P I,t = Q t SX t ) X t S X t )) + E t Λ t,t+ Q t+ S X t+ ) I2 t+ I 2 t A.33) 9

12 ) µi PH,t / I H,t = w I I t A.34) P I,t / ) µi PF,t / I F,t = w I ) I t A.35) P I,t / IH,t = ωi) / θ + θ) S )) ρ tp l I H,t It A.36) P I,t / RER I,t [ ) µi ) ] µi µ P I I,t PH,t PF,t = w I + w I ) A.37) Y t = C H,t + I H,t + CH,t + IH,t + G t A.38) S t RER C,t Π t = S t RER C,t Π t A.39) T t = Π F,t T t Π H,t A.40) RER C,t = [ ] wc + w C T µ C µ C t A.4) RER I,t = [ wi + w I T µ I t ] µ I A.42) Π t = [w C Π H,t ) µ C + w C )Π F,t ) µ C µ ] C A.43) log R n,t /R n = ρ r log R n,t /R n + ρ r )θ π E t [log Π t+ ]/Π + θ s log S t /S) + ɛ r,t+ A.44) RER r t = U C,t U C,t R t = R n,t Π t A.45) A.46) R n,tφ StB F,t Y t ) S tbf,t = S t BF,t + T B t A.47) φ S tbf,t φb S t B ) F,t ) = exp ; φ B < 0 A.48) Y t Y t T B t = S t PO,tY O + Y t C t P I,t I t G t A.49) 0

13 Then the real exchange rate is given by RER C,t = RERt d RERt r A.50) 0 = E t U C,t+ RERt+ r U C,t RERt r Π t+ φ StB F,t Y t ) expɛ UIP,t+ ) RER d t+ RER d t A.5) An alternative to A.5) which uses an exogenous process for R n,t rather than U C,t which drives RER r t ) is StB ) F,t φ Y t expɛ UIP,t )Rn,t Shocks There are 7 domestic shocks: log A t+ A [ ] UC,t+ S t+ = E t U C,t Π t+ S t = ρ a log A t A + ɛ a,t+ log G t+ G = ρ g log G t G + ɛ g,t+ log MS t+ MS log MP S t+ MP S = ρ ms log MS t MS + ɛ ms,t+ = ρ mps log MP S t MP S + ɛ mps,t+ A.52) A.53) A.54) A.55) A.56) log UIP t+ UIP = ρ UIP log UIP t UIP + ɛ uip,t+ A.57) ɛ r,t+ = ρ e ɛ r,t + ν r,t+ A.58) log Ψ C,t+ Ψ C = ρ ψc log Ψ C,t Ψ C + ɛ ψc,t+ A.59) log Ψ I,t+ Ψ I = ρ ψi log Ψ I,t Ψ I + ɛ ψi,t+ A.60) If the ROW is not modelled explicitly we close the model with 4 exogenous AR shocks log R n,t/r n = ρ r logr n,t /R n + ɛ r,t+ A.6) log Π t+ Π = ρ π log Π t Π + ɛ π,t+ log C t+ C = ρ c log C t C + ɛ c,t+ log I t+ I = ρ i log I t I + ɛ i,t+ A.62) A.63) A.64)

14 and UC,t = ϱ )Ct χ Ct ) ϱ ) σ ) h t ) ϱ σ ) A.65) h t = h A.66) Y = C + I A.67) A.2 Zero-Growth Steady State First assume zero growth in the steady state: g = g = 0 and non-negative inflation Π = Π = Π H = Π F > 0. Then we have R n = ) SB Rnφ P C = W h R n = β C = λc + λ)c 2 U L = U L 2 U C U C2 = W h = λh + λ)h 2 U C = ϱ)c ϱ) σ) h) ϱ σ) ; for C = C, C 2 ; h = h, h 2 U L = ϱc ϱ) σ) h) ϱ σ) ; for C = C, C 2 ; h = h, h 2 2

15 = P H P C = [ w C PH P C C H = w C PH P C ) µc ) ] µc µ C PF + w C ) P C [w C + w C )T µ C ] µ C ) µc C PF C F = w C ) C H MC = P W = J H = P P C ) µc C ) µ = ωc) P C H C P C RER C = ξ) ζ ξπ ζ ) ζ ζ ξπ ζ ξ ζ ξπ ζ ) ζ H ξ H βπ ζ ) = Y U C J ξ H βπ ζ ) = Y U C MC ζ H l = H J l = J MC l = MC Ψ = ) J βξπ ζ ) H βξπ ζ ) 3

16 Y = P W H P C = MC P H P C K = α)mc P H PC Y R + δ)q A.68) A.69) A.70) Y W = AH) α K α A.7) W c)y A.72) R = R n A.73) Π I = g + δ)k A.74) X = A.75) SX) = S X) = 0 A.76) Q = P I P C A.77) ) µi PH /P C I H = w I I A.78) P I /P C ) µi PF /P C I F = w I ) I A.79) P I /P C ) µ IH = ωi) PH I I A.80) P RER [ ) µi ) ] µi µ P I I PH PF = w I + w I ) A.8) P C P C P C A.85) A.86) Y = C H + I H + EX C + EX I + G t A.82) ) µ EX C = CH,t = ωc,t) P C H C A.83) P C RER C ) µ EX I = IH,t = ωi,t) PH I I A.84) P I RER I RER C = [ w C + w C T µ C µ ] C RER I = [ w I + w I T µ I µ ] I = βrn A.87) R = R n Π A.88) 4

17 The problem now there are 3 variables but only 30 SS equations! The model is only complete if we pin down the steady state of the foreign assets or equivalently the trade balance. In other words there is a unique model associated with any choice of the long-run assets of our SOE.. Our missing equation is therefore the trade balance T B = POSY O +P H Y P C C P I I P H G = P H EX C P C C P H C H ) + P }{{} H EX I P I I P H I H ) }{{} Net Exports of C-goods Net Exports of I-goods A.89) using Y = C H + I H + EX C + EX I + G t, for some choice of T B, say zero. B A Balanced-Non-Zero-Growth Steady State We can easily set up the model with a balanced-exogenous-growth steady state. Now the process for A t is replaced with A t = ĀtA c t Ā t = + g)āt expɛ A,t ) log Āt = µ + log Āt + ɛ trend,t log A c t log A c = ρ A log A c t log A c ) + ɛ A,t where µ = log+g) g and A t is a labour-augmenting technical progress parameter which we decompose into a cyclical component, A c t, modelled as a temporary AR process, a stochastic trend, a random walk with drift, Ā t. Thus the balanced growth deterministic steady state path bgp) is driven by labour-augmenting technical change growing at a net rate g. If we put g = ɛ trend,t = 0 and Āt =, we arrive at our previous formulation with A c t = A t. The same point applies to government debt when we introduce fiscal policy 5

18 Now stationarize variables by defining cyclical and stationary components: Y c t Y t Ā t = K c t K t Ā t C c t C t Ā t I c t I t Ā t W c t W t Ā t ) α a t H t ) α Kt Ā t = t ) a t H t ) α K c α t +g t) for all non-stationary variables. Then dynamic equation in cyclical components involving a lead or lag needs modifying as follows: Ut c = Cc t χct / c + g t )) ϱ) h t ) ϱ ) σc σ c U C,t = ϱ)c Ā ϱ) σc) t c χct / c + g t )) ϱ) σc) h t ) ϱ σc) t U c C,t Λ t,t+ = β U C,t+ U C,t = β + g t+ ) ϱ) σc) U c C,t+ U c C,t K c t = δ) Kc t + g t + SX c t ))I c t Xt c = + g t ) Ic t I c t SXt c ) = φ X Xt c g) 2 S X c t ) = 2φ X X c t g) where the growth-adjusted discount rate is defined as t β g,t+ U c C,t+ U c C,t the Euler equation is still and β g,t β + g t ) ϱ) σc), E t [Λ t,t+ R t+ ] B.) B.2) H c t ξe t [ Π ζ t+ H c t+β g,t+ + g t+ )] = Y c t U c C,t J c t ξe t [ Π ζ t+j c t+β g,t+ + g t+ )] = Y c t U c C,tMC t MS t 6

19 where is the stochastic steady state growth rate. g t Āt Āt ) Ā t = + g) expɛ A,t ) The steady state for the rest of the system is the same as the zero-growth one except for the following relationships: R = + g)+σc ) ϱ) = Rc n β β g Π R n = ΠR B.3) Λ = R I c = δ + g)kc + g X c = + g J c H c = MC = ξπ ζ ξ ζ ) ζ ) J βg + g)ξπ ζ ) H β g + g)ξπ ζ ) B.4) where R and R n are the real and nominal steady state interest rates and Π is inflation. 7