Adaptive learning and survey databy Agnieszka Markiewicz, Andreas Pick

Journal of Economic Behavior & Organization


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ARTICLE IN PRESSG ModelJEBO-3344; No. of Pages 23

Journal of Economic Behavior & Organization xxx (2014) xxx–xxx

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Journal of Economic Behavior & Organization j ourna l h om epa ge: w ww.elsev ier .com/ locate / jebo

Adaptive learning and survey data

Agnieszka Markiewicza,∗, Andreas Picka,b a Erasmus University Rotterdam, Netherlands b De Nederlandsche Bank, Netherlands a r t i c l

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E-mail add http://dx.doi.o 0167-2681/© this article in press as: Markiewicz, A., Pick, A., Adaptive learning and survey data. J. Econ. Behav. Organ. (2014), e i n f o rch 2013 vised form 29 March 2014 ril 2014 e xxx n: essional forecasters ing nality a b s t r a c t

This paper investigates the ability of the adaptive learning approach to replicate the expectations of professional forecasters. For a range of macroeconomic and financial variables, we compare constant and decreasing gain learning models to simple, yet powerful benchmark models. We find that constant gain models provide a better fit for the expectations of professional forecasters. For macroeconomic series they usually perform significantly better than a naïve random walk forecast. In contrast, we find it difficult to beat the no-change benchmark using the adaptive learning models to forecast financial variables. © 2014 Elsevier B.V. All rights reserved. ction ions are a key ingredient of many economic and financial models. They reflect behavior of agents and influence utcomes. The macroeconomic and finance literature usually endows agents with rational expectations. Although reality, they present some advantages over bounded rationality. Under rational expectations, agents’ subjective distribution coincides with the true distribution of the model economy. This model consistency makes rational s unique to the model. In contrast, there is an infinite number of non-rational ways to form expectations. ely cited alternative to rational expectations has been suggested by Bray (1982), Bray and Savin (1986), Marcet t (1989) and Sargent (1993). This approach assumes that agents, modeled by economists, have at most the same as these economists themselves and hence they behave as econometricians. This approach, called adaptive like to thank participants at the CDMA Conference on “Expectations in Dynamic Macroeconomic Models” and two anonymous referees for ents. ding author at: Erasmus School of Economics, Erasmus University Rotterdam, Burgemeester Oudlaan 50, 3000 DR Rotterdam, Netherlands. 81429. ress: (A. Markiewicz). rg/10.1016/j.jebo.2014.04.005 2014 Elsevier B.V. All rights reserved.

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ARTICLE IN PRESSG ModelJEBO-3344; No. of Pages 23 2 A. Markiewicz, A. Pick / Journal of Economic Behavior & Organization xxx (2014) xxx–xxx learning, has the advantage of imposing modeling discipline. Similar to rational expectations, adaptive learning generates forecasts which are optimal given agents’ information at the time.1,2

In this paper, we systematically test for the empirical validity of this approach. Specifically, we investigate in how far agents’ expectations can be approximated by adaptive learning. For this purpose, we use a set of financial and macroeconomic survey data and fit adaptive learning laws of motions. The formal test of this approach is conducted by assessing the out-ofsample forecasting performance of such estimated models.

We assume that economic agents use simple time series models to make forecasts and they update their parameters using recursive least squares.3 We consider simple time-series models, where the parameters are updated by recursive least squares with constant and decreasing gains, adaptive expectations and the random walk model.4 Additionally, for each variable we use macroeconomic and financial regressors.

We first estimate parameters in an initial training sample and assess their forecasting accuracy out-of-sample. We also conduct forecast accuracy tests against the simple, yet powerful benchmark of the random walk. Additionally, we evaluate constant gain specifications against decreasing gain models and against constant parameter models.

We find that most models have very low estimated gain parameters, which suggests that agents use a relatively long history of observations to make their forecasts. Out-of-sample Diebold–Mariano tests show that for all macroeconomic series at least one only on the macroecon for Yen-U.S decreasing

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The aver anism, whi econometri adaptive le posed by Br agents knew constant ga 1 By optima 2 There is an example, Adam (2011) and Pre 3 Numerous time series mo based models et al. (2005) d 4 A recent tr of the current 5 An import this article in press as: Markiewicz, A., Pick, A., Adaptive learning and survey data. J. Econ. Behav. Organ. (2014), model performs significantly better than a naïve, random walk forecast. This suggests that, instead of relying last available observation, agents use more complex models to form their expectations about the behavior of omic variables. In contrast, among the financial variables’ forecasts only the first order autoregressive specification . Dollar exchange rate significantly beats the no-change benchmark. The comparison between constant gain and gain specifications suggests that the former approximates survey expectations better. ody of literature in macroeconomics and finance employed survey data to examine expectation formation by gents. This literature can be broadly divided in two strands: studies testing rational expectations hypothesis and posing alternative modeling approaches to match survey expectations. The first branch consists of a group of ing to verify the hypothesis of rationality for inflation survey expectations, including Bonham and Dacy (1991), d Cohen (2001), Croushore (1997), and Evans and Gulamani (1984). This body of research largely documents the e rational expectations hypothesis for inflation expectations.5 results have been found using survey expectations of foreign exchange market traders by Frankel and Froot 0a) and Ito (1990). Froot (1989), Friedman (1980), and Jeong and Maddala (1996), who also reject the hypothesis y for interest rate forecasts. More recently, Bacchetta et al. (2009) investigate the link between the predictability turns and expectational errors in a set of financial markets using survey data. They find predictability of excess expectational errors in foreign exchange, stock and bond markets. y data reject the rational expectations hypothesis for a large number of markets, new ways of modeling agents’ e been proposed. Allen and Taylor (1990), Ito (1990), and Frankel and Froot (1987a, 1990a,b) argue that the f survey expectations of foreign exchange traders display behavioral rather than rational features. Specifically, forecast heterogeneity across individuals and over time. Ito (1990) argues that, in line with behavioral bias of nking’, exporters tend to anticipate a currency depreciation while importers anticipate an appreciation. Frankel 987a, 1990a,b) and Taylor and Allen (1992) show that, at short horizons, traders tend to use extrapolative chartist t at longer horizons they tend to use mean reverting rules based on fundamentals. -varying heterogeneity of expectations have been modeled by Brock and Hommes (1997) within the framework ively rational equilibrium dynamics (ARED). Branch (2004) uses ARED to test whether inflation survey data ationally heterogeneous expectations. Similarly, Jongen et al. (2012) explained dispersion in survey data on ovements using the ARED framework. age dynamics displayed by economic agents’ beliefs have often been modeled by the adaptive learning mechch presumes that agents behave as econometricians in the sense that they estimate model parameters using c techniques (for example, Evans and Honkapohja, 2001). Numerous applications and extensions of standard arning have been suggested in the recent literature. Initially, recursive least squares parameter learning, as proay (1982) and Marcet and Sargent (1989), suggested small departures from rationality by assuming that economic the model of the economy and updated only its parameters. Additional extensions of this approach include in learning that occasionally leads to escape dynamics (Cho et al., 2002). l we mean here that the forecasts are orthogonal to forecast errors. extensive literature that uses adaptive learning to understand numerous unexplained, stylized facts in finance and macroeconomics. For et al. (2009) and Evans and Branch (2010) who show that adaptive learning helps in replicating a variety of asset pricing puzzles. Milani ston and Eusepi (2011) argue that learning dynamics can explain business cycle fluctuations. empirical studies have demonstrated that fundamentals-based models can frequently underperform forecasts derived from simple univariate dels. For instance, Orphanides and van Norden (2005) show that autoregressive models generate better forecasts than the Phillips curvewhile Stock and Watson (2007) demonstrate that an IMA model provides better forecasts for inflation. Meese and Rogoff (1983) and Cheung emonstrate forecasting superiority of random walk over fundamentals-based models for exchange rates. end in the literature on forecasting is the use of model combinations as surveyed by Timmermann (2006). This is, however, beyond the scope work. ant exception is the work by Keane and Runkle (1990), which fails to reject the rational expectations hypothesis.