A Small New Keynesian Model to Analyze Business Cycle Dynamics in Poland and Romania

In this paper, we derive a small textbook New Keynesian DSGE model to evaluate Polish and Romanian business cycles during the 2003-2014 period. Given the similarities between the two economies, we use an identical calibration procedure for certain coefficients and marginal prior distributions for the others, rendering the resulting cross-country differences as primarily data-driven. The estimated structural coefficients for the two countries have comparable values, implying similar qualitative macroeconomic transmission mechanisms. However, the Romanian shocks display much more variability, and the impulse response functions have similar shapes but deeper trajectories. The model-simulated theoretical moments for the output growth, the inflation rate and the nominal interest rate (means, standard deviations and cross-correlations) are close to their actual data counterparts, demonstrating the models’ ability to match and replicate statistical properties of the observed variables. Shock decompositions of the output and the inflation rate revealed the driving forces of the business cycles; demand shocks explain much of the GDP growth dynamics (persistent positive contributions before the crisis and negative thereafter), whereas prices were also driven by supply and monetary policy shocks, the latter being more important for Poland.


Introduction
In recent years, New Keynesian Dynamic Stochastic General Equilibrium (DSGE) models have become standard workhorses in analyzing business cycle fluctuations in both academic and institutional (particularly central bank) environments. These models' theoretical advantages originate from microeconom-ic optimizations and the immunity to the Lucas critique (because of the assumed rational expectations behavior of the agents) and have been augmented by practical advances in Bayesian estimation and computer power.
The origins of the DSGE models are usually associated with the Real Business Cycle (RBC) literature, and more precisely, with the seminal contribution of Kydland and Prescott (1982). Given the assumption that the agents are characterized by rational expectations, agents re-optimize their decisions following any shock, rendering the model invulnerable to the Lucas (1976) critique. Calibrating most parameters and estimating those remaining, the Kydland and Prescott (1982) model-implied theoretical moments and crosscorrelations were remarkably compatible with actual United States data.
A harsh hypothesis adopted by the RBC school was the impossibility of economic policymakers to affect real variables. The New Keynesian paradigm restored monetary non-neutrality by acknowledging the shortterm capability of a central bank or a fiscal authority to influence the output, given the existence of temporary price rigidity. Mankiw and Romer (1991) provide an ample overview of the New Keynesian literature, covering both general and specific features of this economic theory stream.
Literature regarding modern DSGE models is composed of theoretical derivations and empirical estimations for different scale models. Ireland (2004) and An and Schorfheide (2007) derive and estimate small New Keynesian models with sticky prices using three observable variables (similar to the model employed in this paper). The next generation of DSGE models includes Smets and Wouters (2003) and Christiano, Eichenbaum and Evans (2005), whose models encompass additional nominal and real rigidities, such as consumption habit, capital depreciation, investment adjustment costs, price indexation, and sticky wages. The estimated models of the early 2000s associated the DSGE environment as a powerful modelling device, and stimulated the adoption of these tools by actual policymakers for real-life/realtime economic policy design and forecast. EAGLE of the European Central Bank (Gomes, Jacquinot, & Pisani, 2010) and Ramses of the Sveriges Riksbank (Adolfson et al., 2013) are a few examples.
The labor market block was enriched similar to Erceg, Henderson and Levin (2010) monopolistic labor supplying households and sticky wages, and Mortensen and Pissarides' (1994) search and matching framework. The financial frictions gained a reputation after the late 2000s crisis, given it was driven and propagated within domestic and international financial flows. However, the financial accelerator mechanism was introduced and formalized much earlier, in Bernanke, Gertler and Gilchrist (1999 Two distinct methods are usually applied when evaluating a DSGE model. Calibration has been used at least since Kydland and Prescott (1982). Calibration implies fixing certain parameters to certain values, which are derived outside the model, but have meaningful interpretations (such as matching certain moments in the data or ensuring particular steady state values). Combined with the accelerated development of computer power in recent decades, estimation became the preferred approach to link data to the model equations. Among the estimation approaches, the maximum likelihood and Bayesian methods (which allow the inclusion of non-sample information via prior distributions for the parameters of interest) remain dominant, with the latter recently gaining increased popularity; refer to DeJong and Dave (2007) for extended reviews and technical details. However, the datasets of observable variables usually do not allow for proper identification of all the parameters; therefore, calibrating certain coefficients and estimating the others represents a common procedure to follow.
Despite the general consensus achieved in the literature regarding the usefulness of the DSGE models, certain limitations exist. The oversimplifying assumptions when modelling the real economy structure were partially resolved because of recent developments, which insert financial and labor markets into the A small New Keynesian model to analyze business cycle dynamics in Poland and Romania model (as noted above), but at the cost of increased complexity. Additionally, when compared to reducedform models, such as Vector Autoregressions (VAR), DSGE models often lose in terms of data fit and forecasting accuracy. Pagan (2003) argues VAR models display an increased degree of empirical coherence (and match actual data well), whereas DSGE models inherit a higher degree of theoretical coherence (given rich parameter restriction structures), but are not very compatible with the data.
In this paper, we derive a small-scale New Keynesian DSGE model. The reduced dimension offers increased flexibility and tractability, in contrast to larger models with many structural shocks. Additionally, a simple model environment and stochastic structure facilitates estimation for short samples. As opposed to Ireland (2004) and An and Schorfheide (2007), we explicitly include the consumption habit in the households utility function. Additionally, we consider Calvo's (1983) mechanism for staggered price setting in a monopolistic environment instead of the ad-hoc price adjustment costs function as in Rotemberg (1992). The resulting hybrid aggregate demand and Phillips curves, completed by an interest rate smoothing reaction function as in Taylor (1993) for the central bank, determines a satisfactory degree of persistence. The stylized economy is perturbed by three structural innovations: a demand/consumption preferences shock, a supply/technology shock, and a monetary policy shock. We estimate the model using Polish and Romanian data, with the following observed variables for

The model
The model we employ has a standard textbook small New Keynesian structure, similar to Clarida, Gali andGertler (1999), Ireland (2004) or An and Schorfheide (2007). In spite of its simple architecture and reduced dimensions, the model embeds certain features and rigidities present in medium-and large-scale seminal DSGE models, such as Smets and Wouters (2003), Christiano et al. (2005), Adolfson et al. (2007) or Christiano et al. (2011).
The stylized economy is populated by a large number of identical households. The homogeneity of these is guaranteed by the assumption of certain perfect consumption insurance that can be traded between the households, making the application of the representative agent framework possible. The issue each household encounters is represented by the following utility maximization problem: is the utility function of current and past consumption good t C purchased from a final good producer, t h measures the labor induced disutility, and t a is a consumption preference shock that affects the intertemporal consumption allocation. We assume the following functional forms for with b representing the consumption habit coefficient and C σ the relative risk aversion or (inverse) elasticity of intertemporal substitution. The consumption preference shock follows an AR(1) process with autoregressive parameter a ρ and normally distributed The household maximizes (1) subject to the budget constraint (4): purchasing a quantity of bonds that will earn a noncontingent revenue t B in the next period. The first order conditions with respect to t C , t B and t h are: where t λ is the Lagrange multiplier associated to the budget constraint, which also represents the welfare's marginal value to the household. Note that a combination of (5) and (6) results in a common aggregate demand or investment-savings curve, according to which current consumption depends on past and future consumptions and the real interest rate ( ) is the expected gross inflation rate.
The production of final good t Y is performed by a representative retail firm that operates in a perfectly competitive environment and uses the following Dixit-Stiglitz aggregator production function: where θ measures the elasticity of substitution between the intermediate goods . Cost minimization implies the demand schedule for intermediate goods (9) and the aggregate price index (10): Next, we focus on the description of the production process in the intermediate goods sector. These firms are characterized by monopolistic competition, and we as-A small New Keynesian model to analyze business cycle dynamics in Poland and Romania sume a linear constant return to scale production function using labor services ) (i h t supplied by the households and a common stationary technology t z as inputs: As previously noted, because the households own these firms, any profits obtained ( t D ) are channeled to the former and appear in the budget constraint (4). Solving the cost minimization problem subject to the production function (11) it has the power to independently set the price for his good, ) (i P t . In accordance with Calvo (1983), we assume that each period a random share γ − 1 of the firms can optimally set their prices, whereas the remaining γ firms simply index their prices with past inflation, corrected with an indexation coefficient P γ .
The indexation is found to be important in Copaciu, Neagu and Braun-Erdei (2010), because Romanian firms use both forward-and backward-looking information when reviewing prices. Those who can reset the prices choose their optimal price * t P (which is equal for all the firms) by maximizing discounted future profits flows: Solving the above problem by using demand function (9), the solution * t P satisfies Applying the law of large numbers to (10), the aggregate price index (gross) inflation rate can be expressed as: (16) (15). Because we assume no other goods than the con- Additionally, the bonds market clearing implies , whereas the profits are cancelled with the government transfers: To close the model, we assume the central bank uses a standard Taylor rule for the nominal interest rate dynamics: where SS superscript indicates steady state values, and i t ε is a monetary policy shock with Summarizing the description of the model, the full list of endogenous variables includes , for which an equal number of equations is considered: (3), (5)- (7), (12)

Estimation methodology and data
For the Bayesian estimation of the model, we use three observable variables: the seasonally adjusted real GDP quarterly growth rates ( Additionally, a proper assessment of forecasting accuracy is difficult to perform in a short sample environment.
The measurement equations link the variables from the data to the model endogenous variables: where µ is the steady state gross quarterly growth rate of real GDP. Similar to Smets and Wouters (2005), we use a deterministic trend for real variables, given by µ . However, because the samples are short, we prefer calibrating µ at the historical mean quarterly growth rate of the real GDP series instead of treating it as an unknown parameter.   Table 2. Formally, the risk aversion parameter's prior mean is set to 1.5 (to facilitate estimation, we specify the C σ coefficient in (2) as implementing a Gamma prior without bounds on C * σ ), whereas the standard deviation is reasonably large. This value is in accordance with the posterior mean of 1.39 obtained in Smets and Wouters (2003) and with the prior mean of 2 in Benchimol (2014)

Results
The results are discussed with respect to three dimensions: the estimated parameters and implied macroeconomic transmission mechanisms (i), the consistency of the variables simulated within the model with actual data (ii), and the decomposition of GDP growths and inflation rates dynamics into corresponding structural shocks (iii).

Model's consistency with actual data
Within the Bayesian estimation of the model, we utilize the Kalman filter to recursively specify and maximize the likelihood function. A one-sided (i.e., using the information set before the current moment) Kalman filter estimates for the observed data are plotted in Figure 1  Because we calibrate the steady states of output growth, the inflation rates and the interest rates to their sample averages, the model perfectly matches the means of these variables, as presented in Table 3.
However, the corresponding 90% confidence bands       We also perform a historical decomposition procedure in which we decompose (demeaned) observed