Dynamic stochastic general equilibrium (DSGE) models to evaluate monetary policy rules anchored in rich micro-foundations have become a popular tool for macroeconomic analysis in recent years (Tovar, 2008). In this vein, we estimate a small open economy DSGE model for Jordan. These models—often refered to as New Keynesian—demonstrate the non-trivial effects of monetary policy on real variables in the presence of nominal and real rigidities. In particular, the existence (or absence) of certain rigidities have implications for the trade-off between output and inflation stabilization that central banks face. For instance, standard new Keynesian models with nominal price rigidities and flexible wages generate a strong policy prescription: the role of monetary policy is to fully stabilize inflation. In this setup, inflation depends only on expected inflation and the gap between current output and its natural level (that is, the level that would prevail in the absence of nominal stickiness). Standard reduced-form models, with no explicit microeconomic foundations, are unable to identify, in practice, the source of nominal and real frictions.
Erceg, Henderson, and Levin (2000) find two important results when both wage and price decisions are staggered (i.e., removing the assumption that wages are flexible). First, the policymaker’s welfare function depends on the variance of output, price inflation, and wage inflation; second, it becomes impossible to set more than one variance to zero in the face of exogenous shocks. They thus demonstrate that, in contrast to the standard new Keynesian model with only price rigidities, there is a trade-off between stabilizing the output gap, price inflation, and wage inflation.
The staggered wage setting imposes a welfare cost because households dislike variations in their labor supply, given that they have an increasing marginal disutility of labor. The policymaker’s welfare function thus depends not only on the variance of output and inflation (as in the standard new Keynesian model with only price rigidities), but also on the variance of wage inflation, which is directly correlated with the variance of employment. The variances of output, price inflation, and wage inflation have a negative weight in the policymaker’s objective function. Staggered wages also imply that marginal costs depend not only on the output gap, but also on the difference between the observed real wage and the equilibrium real wage (Blanchard and Galí, 2005). As a consequence, the New Keynesian Phillips curve is a function of both the output and real wage gap. In this context, any shock that moves the equilibrium real wage generates a movement in price inflation (because the observed real wage cannot fully adjust toward its equilibrium level). This movement can only be offset by altering the output gap. Therefore, when both wage and price stickiness are introduced, there is a trade-off between stabilizing price inflation and output. In contrast to the ad-hoc supply shocks that are usually introduced to generate a trade-off between price inflation and output gap stabilization (see Clarida, Galí, and Gerler, 1999), in the Erceg, Henderson, and Levin (2000) case this trade-off arises endogenously.
A monetary policy rule that seeks to fully stabilize inflation is clearly suboptimal in the presence of wage rigidities. In particular, it can exacerbate the volatility of both output and wage inflation. An alternative policy rule that seeks to minimize the volatility of a weighted average of wage and price inflation may perform better (Erceg, Henderson, and Levin, 2000; and Blanchard and Galí, 2005). In other words, optimal policy prescriptions depend on the set of frictions that the economy faces and, in particular, the importance of nominal and real rigidities in the wage setting process.
In this paper, following Smets and Wouters (2003), Christiano et al. (2005), Galí and Monacelli (2005), Adolfson et al. (2007), Medina and Soto (2007), we lay down a structural model containing both nominal and real frictions and estimate it for Jordan. Our model features habit formation in the consumer’s utility function, wage and price rigidities, and imperfect competition. Oil imports are explicity modeled in the consumption basket and domestic production.2 Following Lubik and Schorfheide (2007), in addition to the standard specification of the Taylor rule, we explore a specification for the monetary policy reaction function that gauges whether the central bank reacts to real exchange rate volatility and aims for interest rate smoothing, Finally, we analyze the impulse response functions to shocks pertinent to the Jordanian economy, including oil price shocks.
We use Bayesian methods to estimate the model. To apply this methodology we combine priors and the likelihood function to obtain the posterior distribution of structural parameters. The likelihood function of the parameters is evaluated using the Kalman filter of a log-linear approximation of the model. We use the Metropolis-Hastings algorithm to approximate the posterior distribution.
We adopt a Bayesian approach for various reasons detailed in Fernández-Villaverde and Rubio-Ramírez (2004) and Lubik and Schorfheide (2005). First, the Bayesian approach is system-based and fits the DSGE model to a vector of time series. Second, the estimation is based on the likelihood function generated by the DSGE model, rather than, for instance, the discrepancy between DSGE model responses and vector autoregression (VAR) impulse responses. Third, prior distributions can be used to incorporate additional information into the parameter estimation. Fourth, this approach can cope with potential model misspecification and possible lack of identification of the parameters of interest. In a misspecified model, if the likelihood function peaks at a value that is at odds with the prior information on any given parameter, the posterior probability will be low. The prior density thus allows us to weigh information about different parameters according to its reliability. Lack of identification, in turn, may result in a likelihood function that is flat for some coefficient values. Hence, based on the likelihood function alone, it would not be possible to identify the value of the parameters of interest. The Bayesian approach copes with this problem by introducing prior distributions. In fact, a proper prior can introduce curvature into the objective function, the posterior distribution, making it possible to identify the value of different parameters. Finally, as pointed out by Fernández-Villaverde and Rubio-Ramírez (2004) and Rabanal and Rubio-Ramírez (2005), Bayesian estimation delivers a tool for comparing models through the marginal likelihood. This makes it possible to determine the extent to which additional ingredients of the model help explain the Jordanian data.
The main results from the Bayesian estimation are as follows. Similar to other oil-importer DSGE studies (relative to advanced economies), this paper finds: (i) a low degree of substitution and share of oil in the consumption basket and production function; (ii) a smaller elasticity of labor supply; (iii) a smaller habit formation coefficient in consumption; (iv) a higher elasticity of substitution between home and foreign goods in consumption; (v) smaller estimated Calvo probabilities of optimally resetting prices and wages—implying that prices are reset optimally every 3.5 quarters whereas wages are re-optimized every 4 quarters; (vi) relatively low wage indexation; (vii) a significant degree of interest rate smoothing; (viii) the response of the interest rate to inflation’s deviation from target is similar to output growth’s deviation from potential; (ix) the response of the interest rate to real exchange rate volatility is quite large; and finally, (x) the pegged exchange rate regime affords a lower risk premium (relative to a hypothetical floating exchange rate regime).
The main results from the impulse response analysis under the current peg are as follows. First, foreign demand shocks raise income and consumption, cause real exchange rate appreciation, and deteriorate the current account/NFA position. Second, foreign interest rate shocks contract consumption and output, depreciate the real exchange rate and improve the current account. Third, monetary-policy shocks (with a high domestic interest rate) induces households to choose a consumption profile characterized by an increasing growth rate of consumption given its inertial behavior, with a rise in foreign debt and an associated deterioration in current account position. Fourth, international and domestic oil price shocks result in a large negative income effect, depreciating the real exchange rate, and improving the current account position.3
The rest of the paper is organized as follows. Section II describes the structure of a dynamic general equilibrium model for the Jordanian economy. Section III then explains the econometric strategy used to estimate the parameters and compare models. In this section, we also describe the data used and our choice of priors and calibrated parameters to construct the posterior distribution. In section IV, we present the results of the Bayesian estimation. Finally, section V concludes.
II. A Small Open Economy Model
In this section, we describe a dynamic stochastic general equilibrium (DSGE) model with nominal and real rigidities, which is designed to account for the main features of the Jordanian economy. This microfounded model is closely related to the new open economy literature of Christiano et al (2005), Altig et al (2003, 2004), Smets and Wouters (2003, 2007), Galí and Monacelli (2005), Medina and Soto (2007), and the monetary policy rule is based on Lubik and Schorfheide (2007).4 To make the paper self-contained we describe the structure of the model and the decision problems facing agents.
The domestic economy is open and it is small vis-a-vis the rest of the world (see Chart 1). The latter assumption implies that international prices, the foreign interest rate and foreign demand are not affected by domestic agents’ decisions. Prices and wages are sticky. They are adjusted infrequently, and they are partially indexed to past inflation. The introduction of wage rigidities together with price rigidities is very important in our model not only because it increases the realism of the model but also because it implies a stronger trade-off between inflation and output fluctuations (see Erceg et al., 2000, and Blanchard and Galí, 2005).
Chart 1:Flow Chart of the Economy
Domestic households consume domestically-produced goods (home goods), imported differentiated goods (foreign goods), and fuel (oil). All three goods are imperfect substitutes in the consumption basket. We assume that consumption exhibits habit formation. Home goods are partly sold domestically and partly exported abroad. There is also a commodity good (whose endowment is exogenously determined) that is exported and not consumed domestically. The exogenous endowment of this good is subjected to stochastic shocks. Households supply a differentiated labor service and receive the corresponding wage compensations. Each household has monopolistic power over the type of labor service it provides. Furthermore, households are the owners of firms producing home goods, and therefore, they receive the income corresponding to the monopolistic rents generated by these firms.
Domestic firms produce differentiated varieties of home goods. For simplicity, we assume that labor and oil are the only variable inputs used for production. These firms have monopolistic power over the variety of goods they produce. There is a third single firm that produces a commodity good which is completely exported abroad. This firm has no market power. It takes the international price of the commodity good as given, and produces utilizing only natural resources. The stock of natural resources is determined exogenously and it is owned by the government and by foreign investors. This commodity-exporting sector is meant to characterize the potash and phosphate sector in Jordan, which accounts for about 4 percent of GDP and 12 percent of total exports.
Monetary policy is conducted through the interest rate. Despite the pegged exchange rate regime, the central bank has some room to conduct an independent monetary policy given imperfect asset substitution. Thus monetary policy is modeled as a Taylor-type rule that incorporates interest rate inertia, reflecting an interest rate premium of borrowing from abroad. In particular, the interest rate reacts to inflation, GDP growth, and its own lagged value. The rule is augmented to include a response to real exchange movements. For simplicity there is no fiscal sector.
The model exhibits a balanced growth path. We assume that in steady-state labor productivity grows at rate gy. However, we assume that productivity is subject to both transitory and permanent shocks. A permanent productivity shock introduces a unit root in major aggregates.
The domestic economy is inhabited by a continuum of infinitely-lived households indexed by j ∊ [0, 1]. The expected present value of the utility of household j is given by:
Where Et denotes the mathematical expectation conditional on information available in period t, β ∊ (0,1) is the subjective discount factor, lt (j) is labor effort, Ct (j) is total consumption, and ℳt(j) corresponds to the total nominal balances held at the beginning of period t. The inverse elasticity of labor supply with respect to real wages is represented by σL, while ζL is a AR(1) preference shock that shifts the labor supply which can be interpreted as a technology change in the home production technology. The parameter a determines the weight of nominal balances in the household’s utility function while μ defines the semi-elasticity of money demand to the nominal interest rate. Preferences display habit formation, whose strength is measured by the parameter h. The consumption bundle is a composite of core (non-fuel) consumption goods and imported fuel:
where Co,t represents fuel (oil) consumption, and Cz,t is a bundle of non-fuel consumption (core consumption). The parameter η is the elasticity of substitution between oil and core consumption, and δ defines their corresponding shares. The composition of this core consumption bundle is given by the following constant elasticity of substitution (CES) aggregator of home and foreign goods:
where CH,t presents a bundle of domestically produced (home) goods and CF,t corresponds to a bundle of imported goods (foreign goods). The parameter 1 − γ represents home bias in consumtpion. Finally, the parameter θ is the intratemporal elasticity of substitution between home and foreign goods. For any level of consumption, each household purchases a composite of home and foreign goods in period t to minimize the total cost of its consumption basket. The aggregate consumption price level is given by:
where Po,t are Pz,t the price of oil and core consumption, respectively. Therefore, the demand for oil and core consumption goods are given by:
Analogously, each household determines the optimal composition of core consumption by minimizing the cost of the core consumption basket, PH,tCH,t(j) + PF,tCF,t (j), subject to equation (3). The demand functions for home foreign goods are given by:
We assume that all households are Ricardian and therefore can smooth consumption intertemporally,5 having access to three different assets: money, ℳt(j); one-period noncontingent nominal foreign bonds,
where the variable Qt,t+1 is the price of domestic contingent bonds in period t, normalized by the probability of the occurrence of the state;
Our assumption that the premium depends on the aggregate net foreign asset position of the economy implies that households take Θ (·) as given when deciding their optimal portfolios. In other words, households do not internalize the effect of changes in their own foreign asset position on the premium. In the steady state, the Θ (·) function is parameterized as:
Here B* corresponds to the steady-state net foreign asset position (or current account evolution), while is PXX is the steady-state value of nominal exports. When the country as a whole is a net debtor, ϱ is the elasticity of the upward slopping supply of international funds.7
Consumption and saving decisions
Ricardian households choose a consumption path and the composition of their portfolios by maximizing equation (1) subject to equation (3). Since we are assuming the existence of a complete set of contingent claims, consumption is equalized across Ricardian households. Therefore, in what follows we omit index j from consumption. Aggregating the first-order conditions on different contingent claims over all possible states we obtain the following Euler equation:
where in equilibrium it must be true that 1 + it =1/Et[Qt,t+1] with it being the domestic risk-free interest rate.
The first order condition with respect to foreign bond holdings is:
The return on international bonds in the international market,
Labor supply decisions and wage setting
Further, following Erceg, Henderson and Levin (2000), each household j is a monopoly supplier of a differentiated labor service which implies that they can set their own wage. After having set their wage, households supply the firms’ demand for labor at the going wage rate. Firms, which hire labor from each household, combine it into an aggregate labor service unit, lt, that is then used by the intermediate goods producer. The labor service unit is defined as the following Dixit-Stiglitz function:
where ∊L is the elasticity of substitution of different types of labor. The optimal composition of this labor service unit is obtained by minimizing its cost, given the different wages set by different households. Thus, the demand for the labor service provided by household j is:
where Wt(j) is the wage rate set by household j and Wt is an aggregate wage index defined as:
Following Calvo (1983), we assume that wage setting is subject to a nominal rigidity. In each period, each household faces a constant probability (1 − ϕL) of being able to re-optimize its nominal wage. In this set-up, parameter ϕL is a measure of the degree of nominal wage rigidity The larger is this parameter the less frequently wages are adjusted (i.e. the more sticky they are). A particular household j that is able to re-optimize its wages at time t solves the following problem:
subject to the labor demand. The variable Λt,t+i is the relevant discount factor between periods t and t+i; it is given by:
In contrast, we assume that there is a passive updating rule of thumb for all households that cannot re-optimize their wages. In particular, if a household cannot optimize during i periods between t and t+i, then its wage at time t+i is given by:
This “passive” adjustment rule implies that workers who do not optimally reset their wages update them by considering a geometric weighted average of past CPI inflation and the implict inflation target set by the authority,
Once a household has decided on a wage (whether through optimal or passive adjustment), it must supply any quantity of labor service that is demanded at that wage.
B. Domestic Production
Domestic firms use a CES technology to assemble home goods using domestic intermediate varieties. Intermediate varieties are produced by firms that have monopoly power. These firms maximize profits by choosing the prices of their differentiated good subject to the corresponding demands, and the available technology. Let YH,t (ZH)be the total quantity produced of a particular variety ZH The available technology is given by:
where YH,t (ZH) represents the total quantity of a particular variety ZH; AH,t represents a stationary productivity shock to the home goods sector that is common to all firms; LH,t is labor used; and OH,t, is imported oil used both in the production of the variety ZH The parameter;α defines the weight of oil in production; and ω determines the degree of substitution between oil and the other factor of production, with its value being key to determine the effects of oil-price shocks on output, marginal cost and inflation.
Demand for inputs and marginal cost
Let YH,t (ZH) be quantity of home goods sold domestically, and
where PH,t (ZH) is the price of the variety ZH when used to assemble home goods sold in the domestic market; and
Firms face a nominal rigidity that prevents them from adjusting prices optimally in every period and determine the optimal mix of inputs by minimizing the total cost of production, subject to the constraint imposed by the technology. From the first-order condition we obtain the following cost-minimization relationship:
where the oil price in domestic currency is given by
whereby the marginal cost is common across firms which share the same technology and is independent to the scale of production. Analogous to the introduction of wage rigidities in the household optimization problem, we introduce price rigidities following Calvo (1983). The assumption is that firms adjust their prices infrequently. The adjustment occurs when they receive a signal. In every period, the probability of receiving such a signal (and thus adjusting prices) is 1 –ϕH for all firms, and is independent of their history. Thus, if a firm receives a signal in period t, then it will optimally adjust the price of its variety, PH,t (ZH)so as to maximize the following expression:
subject to the restrictions imposed by the technology and considering the demand the firm faces for its variety ZH given by:
In contrast, if the firm does not receive a signal, then it follows a simple passive updating
rule of thumb defined by the function.
where πt = (PH,t/PH,t−1)
Relative price changes may have a feedback impact through this adjustment rule. Firms that do not optimally adjust take into consideration the implict inflation target, which is set in terms of consumption goods inflation. The parameter ξH captures the degree of price indexation in the domestic economy. The larger this parameter, the larger is the weight of past inflation in defining new prices. Given the price charged by a firm producing variety ZH, its profits are given by:
C. Foreign Sector
For simplicity we assume that the economy exports two types of goods: home goods and an exportable commodity (in Jordan’s case, phosphate/potash). Foreign demand for home goods is given by the following expression:
where γ*corresponds to the share of domestic intermediate goods in the consumption basket of foreign agents; and η* is the price elasticity of foreign demand. We assume that domestic firms cannot price discriminate across markets. Therefore, the law of one price holds for home goods sold abroad:
The real exchange rate is defined as the relative price of the foreign consumption basket,
whereby the assumption is that the price of foreign goods is the relevant international price to be used when constructing the real exchange rate. In other words, the consumption bundle for the rest of the world implicitly does not include oil and the share of home goods in this bundle, γ*, is negligible.
The domestic real price of oil is given by the following expression:
Commodity production is assumed to be completely elastic with respect to its international price,
Where YS,t is domestic production of the exportable commodity;
D. Monetary Policy
Where: Yt is aggregate production; and the nominal interest rate, it, which is the monetary policy instrument. In this specification, ϖY, ϖπ and, ϖΔe are, respectively, the long run responses of the central bank to deviations of GDP growth and inflation from their steady- state levels, and smoothing real effective exchange volatility. As ϖY → ∞ the central bank would be strictly targeting the output gap; or ϖπ → ∞ it would be a strict inflation targeter; or ϖΔe →∞ it would be exchange rate targeter. If ϖπ is finite and, ϖΔe > 0 a managed float is being implemented. Finally, ρi controls for the degree of (nominal) interest rate smoothing, which is an important variable for the conduct of monetary policy in Jordan due to imperfect asset substitution, where 0< ρi< 1 The parameter
This Taylor-type rule has been estimated for Korea11 (Elekdag et al., 2005); Australia, New Zealand, Canada, and the United Kingdom (Lubik and Schorfheide, 2007); Chile12 (Medina and Soto, 2007); and Latvia13 (Ajevskis and Vitola, 2009) and the emprical evidence generally supports the existence of a policy reaction function that responds to inflation deviations from target, to output movements from potential, and to real exchange rate misalignments.
For simplicity we assume that there is no public spending.14 Therefore, the government budget constraint is simply given by:
Aggregate equilibrium conditions in each market are as follows:
The labor market:
The home goods market:
Letting PY,t denote the implicit output deflator, then total GDP at current prices satisfies:
where total exports are:
total imports are:
total oil imports are:
net foreign asset position is:
F. Stochastic Processes
The economy is subject to nine orthogonal AR(1) stochastic shocks representing log-linear deviation from the steady-state, denoted by lowercase variables with a symbol ^ (see Appendix I): a domestic productivity shock (âH,t); a foreign interest rate shock
|Households and labour|
|β||0.99||Subjective discount rate (quarterly)|
|σL||1.00||Inverse of the elasticity of labor supply|
|h||0.50||Coefficient of habit formation|
|gy||3.50||Annual productivity growth rate|
|Private consumption basket|
|δ||0.10||Share of imported oil in consumption|
|η||0.20||Elasticity of substitution in consumption between core consumption and imported oil|
|1-γ||0.60||Home bias in core consumption|
|θ||1.00||Intratemporal elasticity of substitution between domestic and foreign goods|
|ϕL||0.75||Probability of adjusting wages|
|ξL||0.50||Wage indexation/weight of past inflation|
|ϕH||0.75||Probability of adjusting PH,t|
|ξH||0.50||Domestic goods indexation at home|
|Domestic production technology|
|α||0.40||Share of imported oil in domestic production|
|ω||0.30||Elasticity of substitution between oil and other factors of production|
|εL||9.00||Elasticity of substitution of different labour varieties|
|NX/Y||0.27||Net exports to GDP ratio|
|γ*||1.00||Price elasticity of foreign demand for domestic goods|
|ϱ||0.001||Elasticity of FX borrowing (supply)|
|YS/Y||0.12||Share of potash/phosphate in total exports|
|ρi||0.75||Interest rate smoothing|
|0.75||Reaction to inflation|
|0.70||Reaction to output gap|
|0.70||Reaction to real exchange rate misalignment|
|h||Habit formation of preferences||Normal||0.5000||0.2500||0.4871|
|θ||Intratemporal elasticity of substitution between home and foreign goods||Inverse gamma||1.0000||0.3000||0.9730|
|η||Elasticity of substitution between oil and core consumption||Inverse gamma||0.1500||0.0500||0.1322|
|η*||Elasticity of foreign demand||Normal||0.1000||0.0100||0.1607|
|ϱ||Share of oil in consumption||Gamma||0.1000||0.0100||0.0771|
|σL||Inverse elasticity of labor supply with respect to real wages||Normal||1.0000||0.3000||0.9529|
|Risk premium on FX borrowing||Inverse gamma||0.7500||0.2000||0.7350|
|ω||Degree of substitution between oil and the other factor of production||Inverse gamma||0.1000||0.5000||0.0865|
|α||Weight of oil in domestic production||Gamma||0.3000||0.1000||0.2893|
|фH||Calvo probability of re-optimizing domestic goods prices||Gamma||0.7500||0.0500||0.7027|
|фL||Calvo probability of re-optimizing domestic wage contracts||Gamma||0.7500||0.0500||0.7436|
|ξH||Measure of the domestic price rigidity/indexation||Gamma||0.1000||0.0100||0.1108|
|ξL||Measure of nominal wage rigidity/indexation||Gamma||0.1000||0.0100||0.0496|
|ρ||Domestic interest smoothing||Gamma||0.7500||0.2000||0.6832|
|ωπ||MPC reaction to inflation deviations from its steady-state value||Normal||0.7500||0.1500||0.7514|
|ωУ||MPC reaction to output deviations from its steady-state value||Normal||0.7500||0.1500||0.7201|
|ωΔe||MPC reaction to real exchange misalignment from its steady-state value||Inverse gamma||0.5000||0.1500||0.4893|
|ρah||Perisitence of domestic productivity shock||Gamma||0.7000||0.2500||0.7029|
|ρs||Persistence of potash/phosphate shock||Gamma||0.7000||0.2500||0.6941|
|ρc*||Persistence of foreign demand shock||Gamma||0.7000||0.2500||0.7070|
|ρi*||Persistence of foreign interest rate shock||Gamma||0.7000||0.2500||0.7196|
|ρπ*||Persistence of foreign inflation shock||Gamma||0.7000||0.2500||0.6692|
|ρζ||Persistence of preference shock||Gamma||0.7000||0.2500||0.6928|
|ρψ||Persistence of domestic oil price shock||Gamma||0.7000||0.2500||0.6768|
III. Econometric Methodology
Having set up a theoretical model with nominal and real rigidities, we estimate the structural coefficients that characterize the economy. We follow Rabanal and Rubio-Ramírez (2005), Lubik and Schorfheide (2006) and Adolfson et al. (2005b) in using Bayesian estimation techniques for both the model estimation and our evaluation.
Appendix I presents the log-linearized version of the model developed in the previous section. Equations (A1) through (A32) form a linear rational expectation system that can be written in canonical form as:
is a vector containing the model’s variables expressed as log-deviations from their steady-state values, and
is a vector of containing white noise innovations to the structural shocks of the model, and ξt is a vector containing rational expectation forecast errors. Matrices Ωi are non-linear functions of the structural parameters contained in vectorϑ. The solution to this system can be expressed as follows:
where Ωz and Ωε are functions of the structural parameters.
The Bayesian approach is a system-based methodology that fits the DSGE model to a vector of time series. The estimation is based on the likelihood function generated by the solution of the log-linear version of the model. Prior distributions are used to incorporate additional information into the parameters’ estimation. Simply stated, the Bayesian approach works as follows:
Let yt be a vector of observable variables. This vector is related to the variables in the model through a measurement equation:
where H is the matrix that selects elements from Zt. In our case we assume that the vector of observable variables is given by
Equations (33) and (34) correspond to the state-space form representation of yt. If we assume that the white noise innovations are normally distributed, we can compute the conditional likelihood function for the structural parameters using the Kalman filter since the Bayesian approach first places a prior distribution with density p(ϑ) on the structural parameters, ϑ The data, YT, are then used to update the prior distribution through the likelihood function, L((ϑ/YT), to obtain the posterior distribution of ϑ. According to Bayes’ theorem, this latter distribution, p(ϑ/)YT, takes the form:
Draws from this posterior distribution can be generated through Bayesian simulation techniques (Metropolis-Hastings algorithm). Based on these draws, we can compute the summary statistics (namely, posterior means and standard deviations) that characterize the structural coefficients.
The parameter vector to be estimated is
Parameters ρ0 and (persistence—which introduces inertia through its effect on core consumption and marginal costs—and variance of the oil price shock, respectively) are estimated outside the model using international World Economic Outlook data on oil prices. Parameter ρv (persistence of the monetary shock) is assumed to be zero. We kept a number of parameters fixed throughout the estimation procedure. Most of these of parameters can be related to the steady-state values of the observed variables in the model, and they are therefore calibrated so as to match long-run statistics in Jordanian data (Table 1). In particular, we assume an annual long-run labor productivity growth of 3.5 percent. This is consistent with 6 percent long-run GDP growth and 2 percent labor force growth. The long-run annual inflation rate is 6 percent. The subjective discount factor, β, is set close to 0.99 (quarterly basis) to yield an annual nominal interest rate of 7.5 percent in the steady state. The share of imported goods in the consumption basket, γ, is set at 40 percent, while the share of home goods production in total GDP,
To compute the steady-state share of oil in the production of home goods OH/YH we utilize the figures for the total oil imports ratio to GDP, (OC + OH)/Y, which is around 0.15, and then subtract the share of fuel consumption by households. Finally, the estimation of the autoregressive process for the real international price of oil implies that ρO = 0.92 and = σO 12.4 percent.
To estimate the model, we use quarterly Jordanian data for the period 1992:1 to 2009:4. We choose the following seven observables variables: real GDP, the short-term real interest rate, consumer price inflation (CPI), the real exchange rate, nominal exchange rate devaluation, real wages, and labor input. Labor input is constructed as the fraction of total employment over the working-age population. Real GDP, consumer prices, real wages, and labor input are seasonally adjusted. We also utilize the series on oil imports and the real price of oil (international price of WTI oil deflated by an index of relevant external prices for the Jordanian economy). We use headline inflation as a measure of consumer price inflation. Headline inflation is also used to deflate nominal wages and construct the real exchange rate. We demean all variables. In the case of real wages and GDP, we detrend and demean the series using a linear trend in order to work with stationary series. The short-term real interest rate corresponds to the monetary policy rate and the real interest rate is constructed as the difference between the nominal monetary policy rate and the expected inflation rate implicit in the CBJ’s forecast.
B. Prior Distribution
Priors’ density functions reflect our beliefs about parameter values. Setting a relatively high standard deviation for a density function implies that our prior for the corresponding parameter is more diffuse. In general, we choose priors based on evidence from previous studies on emerging and developing markets with relatively similar economic structures and macroeconomic policy rules—Chile (Medina and Soto, 2007; and Batini et al., 2009); Hungary (Jakab and Világi, 2007); Latvia (Ajevskis and Vītola, 2009); and Mozambique (Peiris and Saxegaard, 2010); and hereafter referred to as “other oil-importer DSGE studies”. When the evidence is weak or nonexistent, we impose more diffuse priors.
Broadly in line with the estimated policy-rule coefficients of other oil-importer DSGE studies, Table 2 depicts the prior distribution for each parameter contained in ϑ its mean and its standard deviation. For the inverse elasticity of labor supply, σL, we assume a truncated normal distribution with mean 1.0 and standard deviation 0.3. The habit formation, coefficient, h, has a truncated normal distribution with mean 0.5 and standard deviation 0.25. The probabilities that prices and wages are not reset optimally every quarter, ϕH and ϕL, respectively, are assumed to follow a gamma distribution with mean 0.75 and standard deviation 0.05. These are similar priors to the ones considered by Adolfson et al. (2007) for the euro area and by Rabanal and Rubio-Ramírez (2005) for the U.S., and other oil-importer DSGE studies. The elasticity of substitution between foreign and domestic goods, θ, follows an inverse gamma distribution with mean 1.0 and standard deviation 0.3. The prior assumed for η* follows a truncated normal distribution with mean 0.1 and standard deviation 0.01. The elasticity of the international supply of funds, ϑ, is assumed to follow an inverse gamma distribution with mean 0.75 and standard deviation 0.2.
As in these other oil-importer DSGE studies, we do not impose non-negativity restrictions on the policy rule coefficients.17 In particular, we assume truncated normal distributions for, ϖπ, ϖy, and an inverse gamma distribution for ϖΔe (the long-run responses of the central bank to deviations of GDP and inflation from their steady-state levels, respectively, and real effective exchange rate volatility). For ϖπ and ϖy we set a mean of 0.75 with a standard and deviation of 0.15. For ϖΔe, and we set a mean of 0.5 and a standard deviation of 0.15. Finally, for the interest rate smoothing coefficient, ρi we assume a gamma distribution with mean 0.75 and a standard deviation of 0.2.
Following these other oil-importer DSGE studies, we assume a low degree of substitution of oil in the consumption basket and also in the production function. In particular, our priors are such that η and ω have inverse gamma distributions with mean 0.15 and 0.10, respectively, and the same standard deviation 0.5. The autoregressive parameters (persistence) of the stochastic shocks, ρζ, ρi*, ρπ*, ρS, ρC* ρψ, ρα have gamma distributions. We do not impose tight priors on these distributions, so shocks can be either persistent or non-persistent. In particular, for all parameters we set the prior mean at 0.7 and the standard deviation at 0.25. The shape of this distribution implies a rather diffuse prior (i.e., we do not have strong prior information on those coefficients).
IV. Bayesian Estimation Results
Once the priors have been specified, we estimate the model by first computing the posterior mode, and then constructing the posterior distribution with the Metropolis-Hastings algorithm. In Table 2 (last column) we present the posterior mean of each parameter under the fixed exchange rate regime specifications.18
The elasticity of labor supply,
This is lower than the estimates for the inertial behavior of consumption found for Europe (Adolfson et al., 2007); close to the Hungarian estimate (Jakab and Világi, 2007); but significantly larger than that found for Chile (Medina and Soto, 2007). This could be explained by the explicit inclusion of imported oil in the consumption basket. Since we estimate an elasticity of substitution between oil and core consumption of less than one, the persistence of oil shocks by itself will also generate more persistence in aggregate consumption, without having to rely on habit formation.
The estimated elasticity of substitution between home and foreign goods in the consumption basket of domestic households, θ, is 0.97 (larger than the Chilean estimate—Medina and Soto, 2007). In turn, the estimated value for demand elasticity of home goods abroad, η*, is 0.16 (smaller than the unitary Chilean estimate) implying limited price elasticity of foreign demand. Both estimates are smaller to the corresponding estimates for the U.S. (Rabanal and Rubio-Ramírez, 2005) and the euro area (Adolfson et al., 2007). Finally, in line with other fixed exchange rate regimes, the estimated risk premium facing Jordan on its foreign borrowing is 0.74.19
The estimated value of the elasticity of substitution between oil and core consumption, η, is comparable to the one between labor and oil in production, ω. In particular, η is estimated to be around 0.13, whereas ω is 0.09. These elasticities are much lower than those estimated for Chile (Medina and Soto, 2007), reflecting perhaps limited alternative energy sources and technological constraints. Moreover, the weight of oil in production, α, is estimated to be considerably larger than in consumption, δ, 0.29 and 0.08, respectively. This should imply larger persistence (and volatility of macro variables) in response to oil price shocks.
The posterior mean of the Calvo probability is 0.70 for home goods prices, ϕH and 0.74 for domestic wages, ϕL. These results imply that domestic wages are set optimally more goods prices. In particular, wages are are reset optimally every 3.5 quarters whereas home goods prices are re-optimized, on average, every 4 quarters. This is in line with Batini et al. (2009) and less rigid than Hungary (Jakab and Világi, 2007) and advanced economies’ results.2021
The coefficient ξL is estimated to be 0.05, implying relatively low wage indexation—and indication of an ability to absorb real terms of trade shocks.222324 We also do not find significant evidence of large price indexation, ξH = 0.11 These results are consistent with Hungary (Jakab and Világi, 2007), but considerably lower than Chile (Medina and Soto, 2007) and the euro area. The reduced-form coefficient on lagged inflation in the home goods Phillips curve, ξH/(1+β ξH), is close to 0.1(relative to 0.2 for Chile (Medina and Soto, 2007)). Our estimated values for ξL and ξH are thus consistent with the lower values of rigidities estimated for some small net-oil importer economies, relative to advanced economies.
The results for the policy rule coefficients, ρi, ϖπ,ϖy and ϖΔe tend to confirm the findings of other oil-importer DSGE studies. First there is a significant degree of interest rate smoothing (ρi =0.68).25 Second, the response of the interest rate to inflation’s deviation from its implicit target or expectation is similar to output growth’s deviation from its potential. In particular, ϖπ is estimated to be 0.75, whereas ϖyis estimated to be 0.72.26 Third, the response of the interest rate to the volatility in the real exchange rate is quite large. In particular, ϖΔe is estimated to be 0.49.2728
V. Effects of Shocks
A. Baseline Results
In order to gauge the importance of the individual shocks, we estimate impulse response functions. The results for simulations with posterior mean parameters under the current fixed exchange rate cases are reported in Figures 2–8.29 Bayesian estimates of impulse responses to shocks are also reported in Table 2. The posterior distributions of the impulse responses are constructed by pulling parameters, together with the variances of the shocks, from the corresponding posterior distributions and for each set of draws generating an impulse response. Repeating this process many times generates posterior distributions of impulse responses.
Figure 1.Priors Figure 2.Impulse Response to a Foreign Demand Shock— Figure 3.Impulse Response to a Foreign Interest Rate Shock— Figure 4.Impulse Response to a Monetary Shock— Figure 5.Impulse Response to an International Oil Price Shock— Figure 6.Impulse Response to a Domestic Oil Price Shock— Figure 7.Impulse Response to a Foreign Demand Shock to Potash— Figure 8.Impulse Response to a Labor Preference Shock—
Figures 2–8 show 90 percent confidence intervals of impulse response distributions to seven shocks: a foreign demand shock shock
Impulse responses of our model to different structural shocks are calculated and displayed (Figures 2–8) as reactions of endogenous variables for a 1 standard deviation increase of innovation in the initial period. Price and wage inflation, nominal and real interest rates are defined as annualized growth rates.
A positive foreign demand shock raises domestic production of home goods and induces an even larger positive income effect/expansion in total output on impact (Figure 2). The large income effect results in higher total consumption, with this being tilted more towards foreign consumption goods, rather than domestic goods. Consumption of imported oil increases, more towards consumption than production. As a result, imports rise faster than exports and the current account/NFA position deteriorates—measured by an increase in foreign debt. With productivity held constant, this expansion leads firms to demand more labor/employment and given relatively low indexation of wages, real wages rise. With higher marginal costs of production, domestic prices—core and headline inflation, as well as real home goods prices rise inducing the central bank to tighten the monetary stance by raising the nominal interest rate inducing real exchange rate appreciation31 which also contributes in turn to dampening export growth.
An increase in foreign interest rates—a foreign interest rate shock—sharply contracts consumption and output on impact (Figure 3). The contraction in aggregate demand in turn induces firms to hire less and employment/labor falls, exerting downward pressure on real wages and core and headline inflation. With lower aggregate demand, imported oil and goods fall. Lower marginal costs and sluggish domestic demand induce the central bank gradually lower its policy rate. Jordanian firms benefit from lower interest rates and marginal costs, shifting their production to exportation. This results in real exchange rate depreciation; a fall in the stock of foreign debt; and thus an improvement in the current account/NFA position.
A monetary-policy shock in traditional Keynesian models with no frictions result in intertemporal consumption smoothing—(i.e., households shift consumption from today to tomorrow). However, New Keynesian models with frictions suggest that a high interest rate induces households to choose a consumption profile characterized by an increasing growth rate of consumption (Christiano et al., 2005).32 In the case of Jordan (h= 0.49), with a one off increase to the interest rate, the intertemporal budget balance generates a hump-shaped consumption profile given its inertial behavior and not fully flexible prices and wages, reflecting an inability to shift quickly from consumption to savings in response to the one off nominal interest rate shock (Figure 4).33 As a result import growth and foreign debt rise. It appears that in Jordan the intertemporal positive effect of a contractionary monetary policy shock does not dominate its negative intratemporal effect.
Given that Jordan is an oil importer and that a fraction of households’ expenditure and firm costs are devoted to oil, an unanticipated international or domestic oil price shock implies a negative income effect that contracts total consumption and output on impact (Figure 5). As a consequence, the demand for all types of goods in the consumption basket falls, particularly foreign goods—and to a lesser extent imported oil and home goods, given low substitution elasticities. Given that firms face increasing marginal costs due to the higher real oil price and have a low elasticity of substitution between oil and labor in production, they shed labor given lower output due to weaker domestic demand and contracting income. As a result real wages and prices fall fast, while core and headline inflation rise initially due to the higher oil price but then adjust downward, on the back of falling real wages and real home good prices. Monetary policy responds to the contraction in output and initial uptick in inflation by lowering its nominal interest rate. Firms still manage to shift production towards exports and this is helped by lower prices and a depreciating real exchange rate. As a result, of the large fall in imports and some pickup in exports, the current account improves and the stock of foreign debt falls. There is no difference between the international and domestic oil price shock (Figure 5 versus Figure 6) other than that the magnitude of the former is much larger.
A positive production shock to the exportable commodity (potash/phosphate) increases production of the commodity good and directly implies an increase in output and consumption (Figure 7). The expansion is inflationary, with higher real domestic prices and wages, prompting the central bank to tighten monetary policy. As with any expansion biased towards tradable goods, a boom in this sector would induce real appreciation of the exchange rate. While exports of potash rise, net exports growth does not rise since the appreciation harms non-commodity exports. The extent of real appreciation would depend on the structural parameters governing the degree of intratemporal and intertemporal substitution in aggregate demand and production.
Two approaches to robustness are employed in the DSGE literature. The first approach is to estimate in parallel a VAR (or a BVAR). If a particular DSGE prior is overruled by the data when estimating the VAR this questions the theoretical restrictions included in the DSGE model and indicates misspecification. The second approach is comparing priors and posteriors within the DSGE model to assess overlap; concentration, symmetry, mean and pile up, and overall reasonableness. We adopt this second approach.
First, we modify the distributional assumption on parameters and set all distributions to a truncated Normal. This is in line with other computational packages, such as the IMF’s GPM+ and IRIS, in which truncated Normal distribution is the only choice available to the researcher. The estimation results (Table 3) do not reveal any substantial differences from the baseline model. Posterior estimates for some parameters are slightly higher (e.g., the elasticity of foreign demand parameter goes up from 0.16 to 0.20), while estimates for other parameters are slightly lower (e.g., the domestic interest rate smoothing parameter goes down from 0.68 to 0.60). However, these differences are insubstantial and go in both directions, supporting the robustness of our findings to the set of distributional assumptions.
|h||Habit formation of preferences||Normal||0.5000||0.2500||0.4738|
|θ||Intratemporal elasticity of substitution between home and foreign goods||Normal||1.0000||0.3000||0.9353|
|η||Elasticity of substitution between oil and core consumption||Normal||0.1500||0.0500||0.1327|
|η*||Elasticity of foreign demand||Normal||0.1000||0.0100||0.2036|
|ϱ||Share of oil in consumption||Normal||0.1000||0.0100||0.0387|
|σL||Inverse elasticity of labor supply with respect to real wages||Normal||1.0000||0.3000||0.9163|
|Risk premium on FX borrowing||Normal||0.7500||0.2000||0.6871|
|ω||Degree of substitution between oil and the other factor of production||Inverse gamma||0.1000||0.5000||0.0899|
|α||Weight of oil in domestic production||Normal||0.3000||0.1000||0.2880|
|фH||Calvo probability of re-optimizing domestic goods prices||Normal||0.7500||0.0500||0.6456|
|фL||Calvo probability of re-optimizing domestic wage contracts||Normal||0.7500||0.0500||0.7569|
|ξH||Measure of the domestic price rigidity/indexation||Normal||0.1000||0.0100||0.0773|
|ξL||Measure of nominal wage rigidity/indexation||Normal||0.1000||0.0100||0.0373|
|ρ||Domestic interest smoothing||Normal||0.7500||0.2000||0.6001|
|ωπ||MPC reaction to inflation deviations from its steady-state value||Normal||0.7500||0.1500||0.7410|
|ωУ||MPC reaction to output deviations from its steady-state value||Normal||0.7500||0.1500||0.7406|
|ωΔe||MPC reaction to real exchange misalignment from its steady-state value||Inverse gamma||0.5000||0.1500||0.4776|
|ρah||Perisitence of domestic productivity shock||Normal||0.7000||0.2500||0.7138|
|ρs||Persistence of potash/phosphate shock||Normal||0.7000||0.2500||0.7127|
|ρc*||Persistence of foreign demand shock||Normal||0.7000||0.2500||0.6741|
|ρi*||Persistence of foreign interest rate shock||Normal||0.7000||0.2500||0.7041|
|ρπ*||Persistence of foreign inflation shock||Normal||0.7000||0.2500||0.6405|
|ρζ||Persistence of preference shock||Normal||0.7000||0.2500||0.6559|
|ρψ||Persistence of domestic oil price shock||Normal||0.7000||0.2500||0.6305|
Next, we expand the standard deviation of the prior distribution by 0.05 in order to allow the posterior estimate to move around the mean more freely. Estimation results (Table 4) provide further evidence of the robustness of Bayesian estimation. Similar to the previous robustness check, the posterior estimates do not differ much from the baseline model and the differences go in both directions. This implies that prior distributions are not too tight and do not restrict the posterior estimates to deviate largely from their priors.
|h||Habit formation of preferences||Normal||0.5000||0.3000||0.4776|
|θ||Intratemporal elasticity of substitution between home and foreign goods||Normal||1.0000||0.3500||0.9553|
|η||Elasticity of substitution between oil and core consumption||Normal||0.1500||0.1000||0.1224|
|η*||Elasticity of foreign demand||Normal||0.1000||0.0600||0.1550|
|ϱ||Share of oil in consumption||Normal||0.1000||0.0600||0.0569|
|σL||Inverse elasticity of labor supply with respect to real wages||Normal||1.0000||0.3500||0.9217|
|Risk premium on FX borrowing||Normal||0.7500||0.2500||0.7256|
|ω||Degree of substitution between oil and the other factor of production||Inverse gamma||0.1000||0.5500||0.0767|
|α||Weight of oil in domestic production||Normal||0.3000||0.1500||0.2880|
|фH||Calvo probability of re-optimizing domestic goods prices||Normal||0.7500||0.1000||0.6838|
|фL||Calvo probability of re-optimizing domestic wage contracts||Normal||0.7500||0.1000||0.7302|
|ξH||Measure of the domestic price rigidity/indexation||Normal||0.1000||0.0600||0.1027|
|ξL||Measure of nominal wage rigidity/indexation||Normal||0.1000||0.0600||0.0250|
|ρ||Domestic interest smoothing||Normal||0.7500||0.2500||0.6414|
|ωπ||MPC reaction to inflation deviations from its steady-state value||Normal||0.7500||0.2000||0.7352|
|ωУ||MPC reaction to output deviations from its steady-state value||Normal||0.7500||0.2000||0.6980|
|ωΔe||MPC reaction to real exchange misalignment from its steady-state value||Inverse gamma||0.5000||0.2000||0.4747|
|ρah||Perisitence of domestic productivity shock||Normal||0.7000||0.3000||0.7013|
|ρs||Persistence of potash/phosphate shock||Normal||0.7000||0.3000||0.6852|
|ρc*||Persistence of foreign demand shock||Normal||0.7000||0.3000||0.7076|
|ρi*||Persistence of foreign interest rate shock||Normal||0.7000||0.3000||0.7168|
|ρπ*||Persistence of foreign inflation shock||Normal||0.7000||0.3000||0.6529|
|ρζ||Persistence of preference shock||Normal||0.7000||0.3000||0.6816|
|ρψ||Persistence of domestic oil price shock||Normal||0.7000||0.3000||0.6576|
Finally, we increase prior means by 5 percent from their benchmark value to check robustness of the results to a shift in the mean. The estimation results (Table 5) show that while most posterior estimates indeed shifted upward in response to the increase in the prior means, some parameters (e.g., the elasticity of foreign demand) have actually shifted downwards. This finding provides further evidence of robustness, since it shows that not all values of posterior parameters are driven by the assumption on prior means.
|h||Habit formation of preferences||Normal||0.5250||0.2500||0.5225|
|θ||Intratemporal elasticity of substitution between home and foreign goods||Normal||1.0500||0.3000||1.1007|
|η||Elasticity of substitution between oil and core consumption||Normal||0.1575||0.0500||0.1593|
|η*||Elasticity of foreign demand||Normal||0.1050||0.0100||0.1101|
|ϱ||Share of oil in consumption||Normal||0.1050||0.0100||0.1078|
|σL||Inverse elasticity of labor supply with respect to real wages||Normal||1.0500||0.3000||1.0543|
|Risk premium on FX borrowing||Normal||0.7875||0.2000||0.7881|
|ω||Degree of substitution between oil and the other factor of production||Inverse gamma||0.1050||0.5000||0.1090|
|α||Weight of oil in domestic production||Normal||0.3150||0.1000||0.2880|
|фH||Calvo probability of re-optimizing domestic goods prices||Normal||0.7875||0.0500||0.7817|
|фL||Calvo probability of re-optimizing domestic wage contracts||Normal||0.7875||0.0500||0.7893|
|ξH||Measure of the domestic price rigidity/indexation||Normal||0.1050||0.0100||0.0912|
|ξL||Measure of nominal wage rigidity/indexation||Normal||0.1050||0.0100||0.1073|
|ρ||Domestic interest smoothing||Normal||0.7875||0.2000||0.7826|
|ωπ||MPC reaction to inflation deviations from its steady-state value||Normal||0.7875||0.1500||0.7986|
|ωУ||MPC reaction to output deviations from its steady-state value||Normal||0.7875||0.1500||0.7957|
|ωΔe||MPC reaction to real exchange misalignment from its steady-state value||Inverse gamma||0.5250||0.1500||0.5198|
|ρah||Perisitence of domestic productivity shock||Normal||0.7350||0.2500||0.7334|
|ρs||Persistence of potash/phosphate shock||Normal||0.7350||0.2500||0.7302|
|ρc*||Persistence of foreign demand shock||Normal||0.7350||0.2500||0.7272|
|ρi*||Persistence of foreign interest rate shock||Normal||0.7350||0.2500||0.7429|
|ρπ*||Persistence of foreign inflation shock||Normal||0.7350||0.2500||0.7341|
|ρζ||Persistence of preference shock||Normal||0.7350||0.2500||0.7365|
|ρψ||Persistence of domestic oil price shock||Normal||0.7350||0.2500||0.7340|
Overall, the above discussion suggests that the model parameters are stable and robust to the distributional assumptions on priors.
In this paper we present an estimated dynamic stochastic general equilibrium (DSGE) model for the Jordanian economy. The model is framed in the New Keynesian tradition, where firms are assumed to adjust prices infrequently and wages are set in a staggered fashion. Oil is used as an input to production, and it is also part of the consumption basket of households. We allow for a flexible elasticity of substitution between oil and other types of consumption goods in the consumption bundle, and also in the technology utilized by domestic firms. Key structural parameters of the model are jointly estimated following a Bayesian approach. The estimates of the structural parameters fall within plausible ranges. To evaluate different exchange rate policies for Jordan, we simulate the model using different policy parameters and compare the results under various policy rules.
Our main results are as follows. First, foreign demand shocks raise income and consumption, cause real exchange rate appreciation, and deteriorate the current account/NFA position. Second, foreign interest rate shocks contract consumption and output, depreciate the real exchange rate and improve the current account. Third, monetary-policy shocks (of a high domestic interest rate) induce households to choose a consumption profile characterized by an increasing growth rate of consumption, while foreign debt rises deteriorating the current account. Fourth, international and domestic oil price shocks result in a large negative income effect, depreciating the real exchange rate, and improving the current account. Fifth, models with both price and wage rigidities best account for the Jordanian data.
Notably, the degree of wage rigidities is lower than that of domestic prices. Our results show that nominal wages are adjusted optimally every four quarters, on average, whereas prices are re-optimized every three and a half quarters, on average. On the other hand, low wage indexation generates a less persistent response of inflation to shocks, and it is not therefore one of the main determinants of the policy trade-off. Finally, real rigidities such as habit formation also provide a better account of the aggregate data, and the estimated values are quantitatively larger than for other net-oil importer models.
AjevskisV. and K.Vītola.2009. “Advantages of Fixed Exchange Rate Regimes from a General Equilibrium Perspective.” Latvijas Banka Working Paper4.2009
AdolfsonM.S.LaseénJ.Lindé and M.Villani. 2008. “Evaluating an Estimated New Keynesian Small Open Economy Model.” Journal of Economic Dynamics and Control32(8) 2690-2721.
AdolfsonM.S.LaseénJ.Lindé and M.Villani. 2007. “Bayesian Estimation of an Open Economy DSGE Model with Incomplete Pass-Through.” Journal of International Economics72481-511.
AgénorP-R and P.Montiel. 2007. “Credit Market imperfections and the Monetary Transmission Mechanism” Unpublished manuscript.
AltigD.L.ChristianoM.Eichenbaum and J.Lindé. 2004. “Firm-Specific Capital, Nominal Rigidities and the Business Cycle.” Working Paper No. 176Sveriges Riksbank.
BatiniN.P.Levine and J.Pearlman. 2009. “Monetary and Fiscal Rules in an Emerging Small open Economy” IMF Working Paper 09/22. Washington, D.C.: International Monetary Fund.
Beidas-StromS. and M.Kandil. 2005. “Setting the Stage for a National Currency in the West Bank and Gaza: The Choice of Exchange Rate Regime.” IMF Working Paper 05/70. Washington, D.C.: International Monetary Fund.
Beidas-StromS.forthcoming. “Do Net-Oil Exporters Respond Uniformly to External Shocks? A Calibrated DSGE Approach” IMF Working Paper.
BenignoP. and M.Woodford. 2004. “Optimal Stabilization Policy When Wages and Prices are Sticky: The Case of a Distorted Steady State”. NBER Working Paper 10839. Cambridge, MA.
BlanchardO. and J.Galí. 2005. “Real Wage Rigidities and the New Keynesian Model.” Working paper 05-28. Massachusetts Institute of Technology, Department of Economics.
CaballeroR. and A.Krishnamurthy. 2001. “International and Domestic Collateral Constraints in a Model of Emerging Market Crises.” Journal of Monetary Economics48(3): 513–48.
CalvoG.1983. “Staggered Prices in a Utility-Maximizing Framework.” Journal of Monetary Economics12(3): 383–98.
CaputoR. F. Liendo And J. P.Medina. 2007. “New Keynesian Models for Chile in the inflation Targeting Period: A Structural Investigation” in F.Mishkin and K.Schmidt-Hebbeleds.Monetary Policy under Inflation Targeting.
CespedesL.R.Chang and A.Velasco. 2004. “Balance Sheet and Exchange Rate Policy” American Economic ReviewVol. 94No. 4 pp. 1183-93.
ChristianoL.R.Motto and M.Rostagno. 2009. “Financial Factors in Economic Fluctuations.” Mimeo. Northwestern University and ECB.
ChristianoL.M.Eichenbaum and C.Evans. 2005. “Nominal Rigidities and the Dynamic Effects of a Shock to Monetary Policy.” Journal of Political Economy113(1): 1–45.
ClaridaR.J.Galí and M.Gertler. 1999. “The Science of Monetary Policy: A New Keynesian Perspective.” Journal of Economic Literature37(4): 1661–1707.
ElekdagS. and I.Tchakarov. 2004. “Balance Sheets, Exchange Rate Policy and Welfare” IMF Working Paper 04/63. Washington, D.C.: International Monetary Fund.
ElekdagS.A.Justiniano and I.Tchakarov. 2005. “An Estimated Small Open Economy Model of the Financial Accelerator” IMF Working Paper 05/44. Washington, D.C.: International Monetary Fund.
ErcegC.D W.Henderson and A. T.Levin. 2000. “Optimal Monetary Policy with Staggered Wage and Price Contracts.” Journal of Monetary Economics46(2): 281–313.
Fernández-VillaverdeJ. and L.Ohanian. 2009. “The Spanish Crisis from a Global Perspective.” MimeoUniversity of Pennsylvania.
Fernández-VillaverdeJ. and J.Rubio-Ramírez. 2004. “Comparing Dynamic Equilibrium Economies to Data: A Bayesian Approach.” Journal of Econometrics123(1): 153–87.
FuhrerJ.C.2000. “Habit Formation in Consumption and Its Implications for Monetary Policy Models.” American Economic Review90(3): 367–90.
GalíJ. and T.Monacelli. 2005. “Monetary Policy and Exchange Rate Volatility in a Small Open Economy.” Review of Economic Studies72(3): 707–34.
GertlerM. and N.Kiyotaki. 2010. “Financial Intermediation and Credit Policy in Business Cycle Analysis.” Handbook of Monetary Economics. Feb. 2010.
GoodfriendM. and R.King. 1997. “The New Neoclassical Synthesis and the Role of Monetary Policy.” In NBER Macroeconomics Annual 1997edited by B.S.Bernanke and J.Rotemberg231–83. MIT Press.
JakabZ. M and B.Világi. 2007. “An Estimated DSGE Model of the hungarian Economy” Central Bank of Hungarymimeo.
LaxtonD. and P.Pesenti. 2003. “Monetary Rules for Small, Open, Emerging Economies” NBER Working Paper 9568. Cambridge, Mass.
LeighD.2008. “Achieving a Soft Landing: The Role of Fiscal Policy” IMF Working Paper 08/69. Washington, D.C.: International Monetary Fund.
LubikT. and F.Schorfheide. 2005. “A Bayesian Look at New Open Economy Macroeconomics” NBER Macroeconomics Annual20313-366.
LubikT. and F.Schorfheide. 2007. “Do Central Banks Respond to Exchange Rate Movements? A Structural Investigation.” Journal of Monetary Economics.
MedinaJ. P. and C.Soto. 2005. “Oil Shocks and Monetary Policy in an Estimated DSGE Model for a Small Open Economy” Central Bank of Chile. No. 353.
MedinaJ. P. and C.Soto. 2007. “The Chilean Business Cycles Through the Lens of a Stochastic General Equilibrium Model” Central Bank of Chile. No. 457.
PeirisS. J. and M.Saxegaard. 2010. “An Estimated Dynamic Stochastic General Equilibrium Model for Monetary Policy Analyisis in Mozambique” IMF Staff PapersVol. 57No. 1.
RabanalP. and J.Rubio-Ramírez. 2005. “Comparing New Keynesian Models of the Business Cycle: A Bayesian Approach.” Journal of Monetary Economics52(6): 1151–66.
RotembergJ. and M.Woodford. 1997. “An Optimization-Based Econometric Framework for the Evaluation of Monetary Policy.” In NBER Macroeconomics Annual 1997edited by B. S.Bernanke and J.Rotemberg231–83297–46. MIT Press.
Schmitt-GrohéS. and M.Uribe. 2003. “Closing Small Open Economy Models” Journal of International Economics61(1): 163–85.
Schmitt-GrohéS. and M.Uribe. 2004. “Optimal Fiscal and Monetary Policy Under Sticky Prices” Journal of Economic Theory114(2): 198–230.
Schmitt-GrohéS. and M.Uribe. 2005. “Optimal Fiscal and Monetary Policy in a Medium-Scale Macroeconomic Model: Expanded Version” NBER Working Paper 11417. Cambridge, Mass.
SmetsF. and R.Wouters. 2003a. “An Estimated Stochastic Dynamic General Equlibrium Model of the Euro Area” Journal of the European Economic Association1(5): 1123–75.
SmetsF. and R.Wouters. 2003b. “Shocks and Frictions in U.S. Business Cycles: A Bayesian DSGE Approach” Frankfurt: European Central Bank.
TovarC.E.2008. “DSGE Models and Central Banks” BIS Working Papers No 258.
UhligH.1997. “A Toolkit for Analyzing Nonlinear Dynamic Stochastic Models Easily” University of Tilburg.
The model is log-linearized using Taylor expansions around the steady state. In order to simplify the model we normalize the steady state level of productivity to
Let a variable in lowercase with a hat (^) represent the log deviation with respect to the steady state. In what follows a “real” price, denoted by
A.1 Aggregate Demand
The optimal conditions can be combined to obtain the log-linear expressions for the Euler equation and the uncovered interest parity condition
A.2 Aggregate Supply and Inflation
From the optimal price setting and the passive resetting price equation (19) we obtain the following expression for the inflation of home goods:
The first-order condition for cost minimization problem of firms producing home goods determines the following relation between the quantity demanded of both inputs, labor and oil, and their relative prices:
From the production function we obtain the following log-linearized version output in the home goods sector:
where the technology in the home goods sectors evolves according to:
Combining the optimal choice of wages with the updating rule and the definition of the aggregate real wage, we obtain the following log-linear expression for real wages, wr:
and where υL = βϕL. Variable
with Et–1(εζ,t)= 0 and
The marginal rate of substitution between labor and consumption,
A.3 Relative Prices
The real price of home goods and the domestic currency real price of oil evolve according to the following equations:
The real price of oil abroad—the relative price of oil abroad with respect to the foreign price index—evolves according to the following expression:
with Et–1(εζ,t) = 0 and
We assume that the variable that captures the deviation of the law of one price for oil,
Foreign inflation evolves according to the following exogenous stochastic process:
Finally, from the definition of the CPI and the core consumption price level we have the following relation among the real price of oil, the real price of home goods and the real exchange rate:
A.4 Aggregate Equilibrium
The detrended and log-linearized expression for exports is:
The evolution of commodity exports,
The real price index of exports is—exports deflator relative to the CPI—is given by
The detrended and log-linearized expression for imports and its real price are given by:
where total oil imports are given by:
The real price index of imports—i.e. the imports deflator relative to the CPI—is given by
The net foreign asset position of the domestic economy evolves according to the following expression:
where X = 1/[(1 + π*) (1+gy) ].
A.5 Policy Rule
The linearized version of the baseline policy rule can be expressed as:
In this specification, ϖπ and ϖy are, respectively, the long run responses of the monetary authority to deviations of inflation and GDP growth from their steady-state levels. We also include a reaction to real devaluation, ϖΔe and ρi controls for the degree of interest rate smoothing. Finally, the monetary shock is given by
We would like to thank Nicoletta Batini, Fabio Canova, Mohd Zaher, and Paul Cashin for valuable comments on an earlier draft; Kholoud Saqqaf, Adel Sharkas and seminar participants at the joint Central Bank of Jordan-IMF Research Workshop (July and December 2010) and MCD Exchange Rate Analytical Group for comments delivered during the presentations, including Peter Montiel for suggestions on robustness; and Heesun Kiem for Matlab and Dynare support. Remaining errors are our own.
However, the fiscal sector, investment (inertia) and capital are not modeled. This would entail a larger model (see Beidas-Strom, forthcoming, for such a model calibrated for a group of net-oil exporters).
The responses of macro variables are broadly similar under a hypothetical flexible exchange rate regime, but with much less magnitude. This implies that a hypothetical flexible exchange rate regime could serve to lower consumption and output volatility in Jordan against external shocks. These results are available upon request.
The main innovation to DSGEs since this group of papers has been the introduction of financial frictions and leverage effects (e.g. Christiano et al., 2009; Fernández-Villaverde and Ohanian, 2009; and Kiyotaki and Gertler, 2010).
See Beidas-Strom (forthcoming) for a relaxation of this assumption.
Another way of achieving a stationary solution would be to introduce intermediation costs as per Cespedes et al. (2004).
The premium could be endogenous and non-linear as it approaches a certain debt threshold, as in Leigh (2008). See Adolfson et al. (2007) for a novel specification of the risk premium which hinges on the expected change in the exchange rate.
See Coady et al. (2006) and references to emerging markets (such as Jordan and Indonesia) therein.
In Jordan commodities represent an important share of total exports, despite the country being a net commodity importer (mainly oil and gas). These commodities (potash and phosphate) are produced independently of domestic economic conditions (the interest rate, real wages, and so forth) and therefore are considered to be exogenous in the short run.
While Korea maintains a floating exchange rate regime, Elekdag et al. (2005) find evidence of a heavily managed exchange rate (due to balance sheet and external debt vulnerabilities).
Prior to 2001 (when inflation targeting began), Chile targeted the exchange rate through a crawling band.
Latvia maintains a pegged exchange rate regime.
Natural commodity resources, S, account for the remaining 10 percent.
Christiano, Eichenbaum, and Evans (2005) use ∊L = 21 and ∊H = 6 for a closed economy model calibrated for the United States. Adolfson et al. (2005b) use the same values for an open economy model calibrated for the euro area. Brubakk and others (2005) use ∊L = 5.5 and ∊H = 6 for a calibrated model of the Norwegian economy. Jacquinot et al. (2005) calibrate ∊L = 2.65 and ∊H = 11. Medina and Soto (2007) calibrate each at 11 for Chile. Batini et al. (2009) calibrate (as per Smets and Wouters (2003)) ∊L at 3 implying a markup of 50 percent, and ∊H at 7.7, corresponding to a markup of 15 percent. Peiris and Saxegaard (2010) estimate the mark up factor for intermediate goods to be 9.
Batini et al. (2009) is an exception, which imposes a non-zero lower bound constraint on the nominal interest rate.
As mentioned, we also experimented with an alternative hypothetical specification which considers a floating exchange regime where nominal exchange rate deviations take place. These hypothetical results are available upon request.
The estimated premium increases by 13 percent under a hypothetical float. Sweden’s estimated risk premium under its pegged regime (pre-1992) was 0.61. This falls sharply (0.01–0.05) for the post-1992 period when inflation targeting was adopted (Adolfson et al., 2007).
Adolfson et al. (2007) estimations for the euro area find values for ϕH and ϕL of 0.895 and 0.710, respectively. These values imply average duration between re-optimization of prices and wages of 9.5 and 3.5 quarters, respectively. On the other hand, Rabanal and Rubio-Ramírez (2005) find that for the US, the average duration between re-optimization of prices and wages is 6.2 and 2.4 quarters. In sharp contrast to others, Medina and Soto (2007) find these values to be 0.17 and 0.82, with prices reset optimally every 1.2 quarters while wages being more rigid being optimized every 5 to 6 quarters. Batini et al. calibrate both at 0.75, implying adjustment every 4 quarters.
Interestingly, and contrary to the Jordanian result, ϕL, falls to 0.52 for a specification under the pegged Swedish regime of pre-1992, implying more flexible re-optimization of wage contracts (every 2 quarters). One could conclude therefore that if wages in Jordan were to be more flexible (i.e., adjust more frequently than the current 3.5 quarters), the response of macro variables to shocks could be less.
While for Chile (Medina and Soto, 2007) this was estimated to be 0.91.
However, given missing data for real wages and employment for Jordan, these results should be taken with caution, as the missing points were randomly generated.
Economic theory tends to suggest that floating the exchange rate is an option when real wages are flexible and money demand is stable (Beidas-Strom and Kandil, 2005).
Medina and Soto (2007) find these to be 0.85 and 0.12, respectively, implying relatively more importance to inflation than output, as can be expected given inflation targeting. Ajevskis and Vitola (2009) find these to be 0.016 and 0.51, respectively for Latvia.
This is close to that of Latvia, which is to be expected given the pegged exchange rate regime.
The estimates under an alternative specification, a hypothetical floating exchange rate regime—available upon request—are broadly similar with a few differences; namely: the coefficients for the share of oil in consumption doubles; the risk premium increases by about 30 percent; the elasticity of labor supply with respect to real wages increases; the probabilities of re-optimizing wages and prices increase; the weight of oil in domestic production falls; price indexation increases; monetary policy rule differ in that reaction of the interest rate to deviations from inflation and output in the steady state increase while the weigh assigned to real exchange rate volatility falls.
We also ran these for a hypothetical flexible exchange rate regime and found smaller responses of macro variables, although the risk premium rose. This implies that a flexible exchange rate regime could serve to lower volatility of macro variables in response to shocks. These results are available upon request.
We do not report the impact of a productivity shock or foreign inflation shock. The former is available upon request while the latter is immaterial given the pegged exchange rate.
Note that the hump shape of the impulse response function for the real exchange rate (with a peak after about one year) is similar to vector autoregressive (VAR) model evidence and unlike standard uncovered interest parity (UIP) evidence from estimated DSGEs (implying a peak effect within the quarter followed by a relatively quick mean reversion). This is due to our model’s inclusion of the risk premium, similar to Adolfson et al.(2008).
This is particularly obvious when investment/capital formation is present in the model.
When Christiano et al (2005) eliminated habit formation, h=0, they found that while the monetary shock led to a large rise in output the rise in inflation was even larger, as consumption responded quickly without nominal frictions.
Note that the interest rate will respond sharply to nominal exchange rate movements so as to keep it constant, with this formulation the interest rate will, for instance, respond almost one to one to foreign interest rate movements (see Adolfson et al. 2007). For the hypothetical flexible exchange rate regime, we removed the restriction on the nominal exchange rate movement, Δêt >0.