El tema fundamental que se estudia en este articulo es la formacion de expectativas sobre las fluctuaciones futuras en la produccion como un factor clave para explicar el ciclo economico en Costa Rica. La principal contribucion de esta investigacion es la propuesta de un modelo econometrico para estimar el efecto que un incremento en el nivel esperado del PIB real para el siguiente trimestre ejerce sobre el PIB real del trimestre actual. Para este fin, un modelo Dinamico Estocastico de Equilibrio General se utiliza como base teorica para explicar la naturaleza de la relacion de causalidad entre la variabilidad esperada en la produccion y las fluctuaciones economicas. Ademas, un modelo de expectativas racionales en representacion de espacio de estados se desarrolla para efectos de construir un mecanismo de actualizacion de expectativas que caracterice totalmente la dinamica de la variabilidad esperada en la produccion. Esta investigacion concluye que un incremento del 1% en el PIB esperado para el siguiente trimestre genera, en promedio, un aumento del 0.67% en el PIB trimestral actual (en terminos reales). Desde esta perspectiva en que se modela el tema en cuestion, el analisis econometrico concluye que este efecto es estadisticamente significativo y tambien identifica otros factores relevantes para explicar el ciclo economico costarricense, tales como los pronosticos de variables economicas que determinan las fluctuaciones en la produccion a lo largo del tiempo.
PALABRAS CLAVE: EXPECTATIVAS, MODELO DINAMICO ESTOCASTICO DE EQUILIBRIO GENERAL, EXPECTATIVAS RACIONALES, PRONOSTICO, REPRESENTACION EN ESPACIO DE ESTADOS
Expectations formation of future output fluctuations as a factor for explaining Costa Rican business cycle is the main subject addressed in this paper. The main contribution of this research is the proposition of an econometric model for estimating the effect that an increase in the next quarter expected real GDP has on current quarterly real GDP level. To this end, a dynamic stochastic general equilibrium model is used as the theoretical base for explaining the nature of the causality relationship between expected output variability and economic fluctuations. Furthermore, a state-space representation of a Rational Expectations (R.E.) model is developed for constructing an expectations updating mechanism which fully characterizes the dynamics of the expected output variability. This investigation concludes that a 1% increase in the next quarter's expected GDP is predicted to generate, on average, an approximate 0.67% growth on current quarterly GDP (in real terms). From this modeling perspective, the econometric analysis concludes this effect is statistically significant and also identifies other relevant factors for explaining Costa Rican business cycle, such as the forecasts of economics variables that determine output fluctuations throughout time.
KEYWORDS: EXPECTATIONS, DYNAMIC STOCHASTIC GENERAL EQUILIBRIUM MODEL, RATIONAL EXPECTATIONS MODEL, FORECAST, STATE-SPACE REPRESENTATION.
This paper investigates the effect that variations in future output expectations have on current output level, specifically for the case of Costa Rica (2). The subject in question is relevant for practical purposes because of the possibility to achieve real effects through economic policy by appealing to convenient forms of announcing monetary or fiscal rules in order to modify agents' forecasts of economic variables. For instance, if expectations that economic agents (consumers, producers and government) have on future output (and in this way of their expected real income) adjust to perceived modifications of their environment, then these adjustments finally induce individuals to alter their production and saving decisions, which have real effects on the economy. Unfortunately, although research in this matter is useful and necessary in Costa Rica, it is also scarce. Therefore, the paper at hand is intended to narrow the gap between current investigation on the topic and real needs.
Regarding the structure of this paper, a short revision of literature is done in section II. Furthermore, an economic model which presents a causality relationship between the expected future output and the current observed level (i.e. the "output equation") will be derived in the first part of section III. This result is used in the second part of section III for developing a state-space representation of a rational expectations model for fully describing the dynamic behaviour of output's expectation. The main purpose of the paper will be achieved in this section, which is to propose an econometric model in order to empirically estimate the effect that variability on future output expectations has on the current output level. The corresponding estimation results are presented in section IV. Finally, concluding remarks shall be presented in section V.
A BRIEF LITERATURE SURVEY
Although the focus of this paper is not to make a revision of literature about the topic in question, some survey could be adequate for contextualizing the problem. There are three papers in particular which must be highlighted. Regarding the first one, Campbell and Mankiw (1986) estimated standard ARIMA processes for the real GNP (in logs) of the American economy using post-war quarterly time series (3). Their objective was to test how persistent were output shocks in order to support their skepticism about all output fluctuations being "transitory". The investigation is relevant because it considered a model which implicitly suggested a relationship between realized output growth rates and expected output growth rates. Namely, their main conclusion was that unexpected changes of one percent in real GNP would change one's forecast of output growth by nearly one percent over very long periods. This conclusion (according to the authors) suggested doubts about the transience of output shocks, because if output deviations from its natural level were temporary, then unexpected changes in current output should not affect one's forecast in long time periods. Furthermore, Beaudry and Koop (1993) (4) used an ARMA representation for modeling output growth in a similar fashion like Campbell and Mankiw (1986), but including also the possibility of asymmetric persistence in GNP. Their primary concern was to determine if positive and negative output shocks were equally persistent in the American economy. Their investigation proposed another methodology for analyzing the relationship between realized output growth rates and expected output growth rates. Specifically, the authors concluded that recessions affected output forecasts just eight to twelve quarters. Finally, it must be outlined the investigation conducted by Cerra and Saxena (2008)5. The authors develop various AR representations of output in order to link output expectations with the occurrence of currency and financial crises, and currency and financial crises with output volatility. Therefore, their model describes an explicit causality relationship between output expectations and output volatility. Using panel data of a specific set of countries (Indonesia, Korea, Malaysia, Thailand, Argentina, Brazil, Chile, Mexico, Burundi, El Salvador, Nicaragua, Sierra Leone, and others) their research concluded that output expectations were significant for determining banking crises and in this way output fluctuations in countries included in the sample set.
All previous research underline different empirical methodologies for studying the relationship between expected output growth and realized output growth. However, the model used for addressing the topic in this paper avoids any ARIMA, ARMA or AR representation for accomplishing this end. The reason is because a less "atheoretical" and a more micro-based approach is desired in order not just to quantitatively determine the relationship in question, but also to provide a full theoretic characterization of the expectations mechanism that rules it. This is one of the contributions the present paper is expected to offer. Another relevant aspect to consider is that research in Costa Rica has fallen short in the study of these relationships, meanwhile the previous cited literature shows that it has been an important investigation topic in the macroeconomics research mainstream. Investigation like the one conducted by Castrillo and Torres (2010), Castrillo, Mora y Torres (2008) and Munoz (2006) provide some insights of earlier research related to the specific topic of this paper, although none addressed this paper's main subject specifically. This implicates that another contribution of the present article is to narrow the gap between current investigation on the topic and real needs. Namely, the paper will draw conclusions on implications of the model's estimation results for monetary policy.
The economic model
The theoretical derivation of the output equation presented in the subsequent analysis is based on the Sidrauski-Brock model developed by McCallum and Nelson (1997) (6). Consider an infinitely-lived consumer which maximizes the discounted utility function [[SIGMA].sup.+[infinito]].sub.i=0] [[beta].sup.i]U([c.sub.t+i],[c.sup.f.sub.t+i], [m.sub.t+i]). The variable ct designates its consumption of the compound good produced by the local economy, [c.sup.f.sub.t] is the consumption of the compound good produced abroad, [m.sub.t] denotes the real money stock the individual holds at the beginning of period t and 0
Thus, the output equation will be obtained from the solution of the individual's dynamic problem:
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and so, the associated Bellman equation is:
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Then, the Lagrangian function to maximize shall be:
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After determining explicit expressions for the derivatives of the...